Volume 08 - Mechanical Testing and Evaluation Part 15 potx

• Preparation of the surface for strain gage adherence may induce residual stresses that introduce substantial error to the subsequent measurement Ref 71.. For more than six decades, en

• The area in which stresses are to be measured must be accessible to a rather bulky drilling or coring alignment device

• Preparation of the surface for strain gage adherence may induce residual stresses that introduce substantial error to the subsequent measurement (Ref 71)

In conclusion, the drilling and ring coring methods are nearly nondestructive variations of the destructive mechanical stress relief techniques and require only rather simple equipment and instrumentation The state-of-the-art is relatively well developed compared to many nondestructive methods, some of which require considerable research and development work before they will ever be suitable to general application in terms of alloys and stress field conditions Technological advancements in hole drilling and ring coring have largely been due to advancements in the more general areas of mechanical stress relief methods and research in new metal removal techniques for metal fabrication

Indentation Methods For more than six decades, engineers and scientists have proposed the use of indentors, such as those used to perform hardness measurements, as a means to measure or detect surface residual stresses Kokubo in 1932 reported that stresses applied under bending load changed the apparent Vickers hardness values in carbon steel rolled sheets, both as rolled and annealed He showed that tensile stresses tended to decrease the apparent hardness, and compressive stresses tended to increase the hardness The stresses applied

in tension and compression were sufficient to cause 0.3% strain

Two decades later Sines and Carlson (Ref 72) proposed a method that required various amounts of external loads to be applied to the component in which residual stresses were to be measured while hardness measurements were made The loads were made to cause both tensile and compressive applied stresses The quality—that is, whether the residual stress was compressive or tensile—was then revealed by comparing the effect of the applied stress and whether the applied stress was tensile or compressive on the hardness measurement At about the same time, Pomey et al (Ref 73) proposed that residual stresses could be measured

by pressing a ball-shaped penetrator into the component in which residual stresses were to be measured and establishing the relationship between the pressing load while it was progressively increased and the electrical resistance at the interface between the penetration and the component He maintained that a smaller decrease in electrical resistance indicated that portions of material under the ball were plastically yielding and that the corresponding load on the ball could be related to the existing residual stress

Later, Chiang et al (Ref 74) provided a critique of several existing indentation analyses and proposed an interpretation of indentations exhibiting hemispherical plasticity Nevertheless, the applications illustrated in this article were focused on brittle materials and not metals

There have been numerous papers published proposing various approaches to interpreting the indentation loads and shapes so as to estimate the residual stress field on the surface and near-surface regions of materials However, indentation methods have not earned the degree of confidence of XRD or hole drilling methods for general applications and, thus, are rarely applied

Spot Annealing Another semidestructive method that has been proposed to measure residual stresses in metal surfaces is to reduce the residual stresses in a small volume by annealing the metal in the volume It has been proposed that this annealing be performed by intense laser light (Ref 52) This technique was envisioned to be similar to relief of residual stresses by removal of the material as accomplished in the hole drilling techniques However, as Cullity discussed (Ref 53), such localized heating would induce high surface residual tensile stresses in the heat-affected region, and this would be detrimental to the component being tested

References cited in this section

9 A.J Bush and F.J Kromer, “Residual Stresses in a Shaft after Weld Repair and Subsequent Stress Relief,” Paper No A-16 presented at Society for Experimental Stress Analysis (SESA) Spring Meeting,

1979 (Westport, CT), 1979

52 C.S Vikram, M.J Pedensky, C Feng, and D Englehaupt, Residual Stress Analysis by Local Laser

Heating and Speckle-Correlation Interferometry, Exp Tech., Nov/Dec 1996, p 27–30

53 B.D Cullity, Elements of X-Ray Diffraction, 2nd ed., Addison-Wesley Publishing Co., Inc., 1978, p

469–472

59 J Mathar, Determination of Initial Stresses by Measuring Deformation Around Drilled Holes, Arch Eisenhuttenwes., Vol 6, p 277–281 and Trans ASME, Vol 56 (No 4), 1934, p 249–254

60 “Determining Residual Stresses by the Hole Drilling Strain-Gage Method,” E 837, ASTM, 1983

61 H Wolf and D.C Sauer, “New Experimental Technique to Determine Residual Stresses in Large Turbine-Generator Components,” presented at the American Power Conf., (Chicago, IL), 1 May 1974

62 H Wolf and W Bohn, Origin, Measurement and Assessment of Residual Stresses in Large Forging for

Turbines and Generators, Arch Eisenhüttenwes., Vol 42 (No 7) 1971, p 509–511 (in German)

63 H Wolf, E Stucker, and H Nowack, “Investigations of Residual Stresses in the Turbine and Generator

Industry,” Arch Eisenhuttenwes., Vol 48 (No 3), March 1977, p 173–178

64 J Lu and J.F Flavenot, “Applications of the Incremental Hole-Drilling Method for Measurement of Residual Stress Distributions—Experimental Techniques, paper presented at the Society for Experimental Mechanics (SEM) Spring Conference,” 5–10 June 1988 (Portland, OR), SEM

65 M.T Flaman and B.H Manning, Determination of Residual Stress Variation with Depth by the

Hole-Drilling Method, Exp Mech., Vol 25, 1985, p 205–207

66 R.A Kelsey, Measuring Nonuniform Residual Stresses by the Hole Drilling Method, Proc Society for Experimental Stress Analysis, Vol 14 (No 1), 1956, p 181–184

67 A.J Bush and F.J Kromer, Simplification of the Hole-Drilling Method of Residual Stress

Measurement, ISA Transactions, Vol 12 (No 3), 1973, p 249–259

68 N.J Rendler and I Vigness, Hole-Drilling Strain-Gage Method of Measuring Residual Stress, Exp Mech., Vol 6 (No 12), Dec 1966, p 577–586

69 J.W Dini, G.A Beneditti, and H.R Johnson, Residual Stresses in Thick Electro-deposits of a

Nickel-Cobalt Alloy, Exp.l Mech., February 1976, p 56–60

70 F Witt, F Lee, and W Rider, A Comparison of Residual Stress Measurements Using Blind-Hole,

Abrasive-Jet and Treppaning Methods, Exp Tech., Vol 7, Feb 1983, p 41–45

71 P.S Prevey, “Residual Stress Distribution Produced by Strain Gage Surface Preparations,” 1986 SEM Conference on Experimental Mechanics, 1986

72 G Sines and R Carlson, “Hardness Measurements for the Determination of Residual Stresses,” ASTM Bulletin 180, Feb 1952, p 35–37

73 J Pomey, F Goratel, and L Abel, “Determination des Cartraintes Residuelles dans les Pieces Einentees,” Publication Scientifiques et Techniques du Ministere de l'air, 1950, p 263

74 S.S Chiang, D.B Marshall, and A.G Evans, The Response of Solids to Elastic/Plastic Indentations I:

Stresses and Residual Stresses, J Appl Phys., Vol 53 (No 1), 1982, p 298–311

Residual Stress Measurements

Clayton O Ruud, The Pennsylvania State University

Nondestructive Procedures

The methods for strain measurement described previously all measure the change in some dimension (strain) of the component produced by the removal of a finite volume of stressed metal from that component Thus, these methods measure the strain induced by removing material so as to perturb the residual stress field On the other hand, the nondestructive procedures measure a dimension in the crystal lattice of the metal or some physical parameter affected by the crystal lattice dimension Whenever a mechanical force resulting in stress that is less than the yield strength is placed on a solid metal component, that component distorts (strains) elastically That elastic strain results in a change in the atomic lattice dimension, and this dimension, or change, is measured by

a nondestructive stress measurement procedure For example, the diffraction methods, x-ray and neutron, measure an actual crystal dimension, and this dimension can be related to the magnitude and direction of the stress that the metal is subject to, whether that stress is residual or applied Subsequently in this section, the following methods of nondestructive stress measurement are described: XRD, neutron diffraction, ultrasonic velocity, and magnetic Barkhausen noise

X-ray diffraction techniques exploit the fact that when a metal is under stress (applied or residual), the resulting elastic strains cause the atomic planes in the metallic crystal structure to change their spacings X-ray diffraction can directly measure this interplanar atomic spacing; from this quantity, the total stress on the metal can then be obtained

Because metals are composed of atoms arranged in a regular three-dimensional array to form a crystal, most metal components of practical concern consist of many tiny crystallites (grains), randomly oriented with respect

to their crystalline arrangement and fused together to make a bulk solid When such a polycrystalline metal is placed under stress, elastic strains are produced in the crystal lattice of the individual crystallites In other words, an externally applied stress or one residual within the material, when below the yield strength of the material, is taken up by interatomic strain X-ray diffraction techniques can actually measure the interatomic spacings, which are indicative of the elastic strain in the specimen Stress values are obtained from these elastic strains in the crystals by knowing the elastic constants of the material and assuming that stress is proportional to

strain, a reasonable assumption for most metals and alloys of practical concern An article published in Journal

of Metals describes the XRD method and instrumentation in some detail References 8 and 75 are excellent

sources of practical, more detailed information on XRD stress measurement

There are three basic techniques for measuring stresses, based on the XRD method They are the double exposure (or two-angle) technique (DET), the single exposure (or one-angle) technique (SET), and the sin-square-psi (or multiangle) technique The angle of exposure referred to is that between the incident x-ray beam and the specimen surface normal It should be noted that in any XRD stress measurement technique, x-ray peaks in the far back-reflection range, that is, peaks with Bragg (θ) angles of near 90°, are much preferred because they show the greatest effect with a given amount of applied or residual stress This is illustrated in the following equation:

(Eq 34)

In Eq 34, θ1 is the Bragg angle of the planes diffracting at ψ1; θ2 is the Bragg angle of the planes diffracting at

ψ2 In Fig 13, it can be seen that as θ1 increases, its cotangent decreases; therefore, a larger difference (2θ1 - 2θψ) would result from a given σφ to maintain an equality

Fig 13 One-angle arrangement or the single exposure technique (SET) Ns is the specimen normal, and β

is the angle that the incident beam makes with Ns Np1 and Np2 are the normals to the diffracting planes 1 and 2 respectively, and ψ 1 and ψ 2 are the angles between Ns, Np1, and Np2 respectively η is the angle

between the incident beam and the diffracting plane normals Ro is the camera radius, and O is the point

of incidence of the x-ray beam of the specimen 1 and 2 represent the diffracting planes at various

attitudes to the specimen surface S1 and S2 are the measured parameters representing the distance from

a reference point of known distance from the incident beam and the diffracted x-ray beam position S1

and S2 are directly related to the Bragg angles, θ 1 and θ 2 The stress being measured is parallel to the specimen surface and in the plane containing the x-ray source vector and the specimen surface normal,

Ns

For a residual stress measurement, the diffracting angle, θ, of interatomic planes of at least two different psi (ψ) angles with respect to the surface normal must be measured (Fig 13) These planes are crystallographically equivalent (same Miller indices, hkl) and in the unstressed state of the metal would have the same interatomic,

d, spacing for the planes labeled 1 and 2 in Fig 13 (Ref 53, 76, 77) In a stressed material, however, the two or

more orientations of diffracting planes are selected so that they are at different angles to the surface; thus their normals are at different (ψ) angles to the surface normal Then, depending on the angle of these planes to the stress vector, their interplanar atomic spacing is increased or decreased by varying amounts

The most common sources of errors and misapplications in stress measurements by x-rays are related to stress constant selection, focusing geometry, diffracted peak location, and cold-working, crystallographic texture, grain size, microstructure, and surface condition The source, significance, and correction techniques for these errors are not elaborated on here; details may be found in an article by Ruud and Farmer (Ref 78) and (Ref 8)

A point of interest in the error sources listed above concerns cold working and microstresses Microstresses are usually considered to be those manifested by strain variation across single metallic grain This strain variation is detected in the XRD method as broadening of the x-ray peak—a distinctly different phenomenon from the peak shift caused by residual stresses However, microstrain variation can be measured simultaneously with stress This microstrain phenomenon has been proposed as a means of judging cold work, dislocation density, and fatigue damage (Ref 79)

Despite the facts that x-rays provide stress readings only to a depth of less than 0.025 mm (0.001 in.) and that the error sources listed above must be considered, the noncontact XRD method is presently the only time-proven, generally applicable, truly nondestructive method for measuring residual stresses Its reliability has been proved and documented by thousands of engineers and scientists over the past four decades beginning with the classic work of Bolstad et al at Boeing using x-ray film cameras (Ref 80) This documentation includes measurement of stresses in the Brooklyn Bridge (Ref 20) and tempering evaluation of carburized steels The Society of Automotive Engineers (SAE) considers the method of sufficient practical importance to have printed three handbook supplements on the subject (Ref 8), and another supplement is under revision

Even so, this nondestructive technology has been largely restricted to the laboratory because of the general lack

of knowledge regarding the state-of-the-art instruments and the limitations of the more widely known and available conventional scanning XRD equipment Instrumentation for bringing this technology into the field and manufacturing area has advanced rapidly in the last two decades, especially toward increased portability, compactness, and speed of operation

As shown in Fig 14, instrumentation has been developed and is commercially available for stress measurement

in situ on the inside diameter of 10 mm (4 in.) diameter pipe (Ref 39) Position sensitive x-ray detectors have been largely responsible for these improvements to both laboratory-based and field deployable residual stress measuring instruments (Ref 10, 21, 22, 39, 81, 82, and 83) Also, with the speed of data collection being less than 0.1 s with conventional x-ray tube sources in some applications, XRD stress measurement can be performed on moving components (Ref 12) Nevertheless, many engineers have been frustrated in applying XRD to residual stress measurement This has been largely due to crystallographers inexperienced in residual stress measurement, attempting to apply conventional scanning x-ray diffractometers and techniques to residual stress measurement For example, in conventional XRD analysis and crystallography, sharp resolution of the diffracted spectra is very beneficial However, in XRD stress measurement, the need to measure (ψ) angles that are not zero defocuses the beam, and attempts to refocus lead to significant error in the stresses read (Ref 84)

In XRD stress measurement, what is more important than sharp resolution is the repeatable ability to measure the position of a defocused diffracted x-ray peak (Ref 85) Thus, it is recommended in most cases that XRD residual stress measurement be performed by trained technologists using x-ray instrumentation specifically designed and built for stress measurement, not conventional scanning diffractometers Software packages specifically for residual stress measurement used with conventional scanning diffractometers do not in most cases eliminate the mechanical and focusing problems of applying these instruments to residual stress measurement It is necessary to mount the component (or specimen) in which stresses are to be measured on the conventional scanning diffractometer, which usually requires sectioning of the component and which complicates and adds error to the measurement procedure

Fig 14 Photograph of a miniature x-ray diffractometer for the one angle technique arrangement of XRD stress measurement This device incorporates a Ruud-Barrett position sensitive scintillation detector and

is capable of being inserted in a 101.60 mm (4 in.) inside diameter for measuring residual stress (Ref 39)

Neutron diffraction (ND) allows measuring the elastic strains induced by residual stresses throughout the volume of relatively thick steel components with a spatial resolution as small as 1 mm3 Such capability provides for the measurement of residual stress inside of components without the necessity of sectioning or layer removal Principal ND methods, like the XRD methods, measure the spacing between crystallographic planes in a component, and this spacing is affected by residual and applied stress The spacing between a selected set of crystallographic planes (φ) is related to the angle of incidence and diffraction of the neutron radiation, θ, which are equal, and the wavelength of the monochromatic radiation (λ) by Bragg's law:

principal stress directions E and ν are the Young's modulus and Poisson's ratio, respectively If the principal

stress directions are not known, strains in at least six directions must be measured to determine the residual stresses acting on the volume of material in which strains are being measured

For residual stress measurement in most alloys, the unstressed spacing (do) between crystallographic planes at

the exact point of strain measurement is not known and not easily measured This means that do or θ0 in Eq 36 cannot be precisely established, and this leads to various degrees of error in the accuracy and precision of ND residual stress measurements This condition is aggravated by the fact that the elemental composition, and thus

do, vary considerably within a component and markedly within the phase (e.g., martensite, austenite, and ferrite for steel) of the alloy at various locations Additional limitations are that the component must be brought to a nuclear reactor, each strain measurement requires over an hour, a single stress determination in one small volume of the component requires at least three strain measurements, and the measurements are very costly Nevertheless, the ND methods have been applied to residual stress measurements in weldments (Ref 86), cylindrical forgings (Ref 87), plastically deformed plate (Ref 88), rocket case forgings (Ref 86), and many other types of components

Ultrasonic Velocity The principle underlying the measurement of stress and thus elastic strain by ultrasonic (acoustic) techniques is the phenomenon of an approximately linear change in ultrasound velocity with applied stress It has been shown that under certain restricted conditions, residual stress can be measured by exploiting this phenomenon Stress is measured by inducing a sound wave in the frequency of several megahertz in the metal specimen and measuring the time of flight or some other velocity-related parameter Because many other characteristics of metals besides stress-induced elastic strain affect velocity, their effect must be sorted out, but neither the technology nor the fundamental knowledge for such sorting is usually available The great interest in ultrasonic techniques for residual stress measurement stems from their promise for three-dimensional nondestructive measurements within the material

Principle A number of velocity-related phenomena have been used in various methods to measure stress effects

by ultrasound All utilize the deviation of the reaction of the metal from the linearity of Hooke's law of

elasticity, σ = Mε, where σ = stress, ε = strain, and M = elastic modulus This has been referred to as the anharmonic property of the solid and may be represented by a power series σ = Mε + Cε2 + Dε3 + …, where C

= third order anharmonic constant, D = fourth, and so on Most research done for stress measurement has used expressions in which terms past the third order constant, C, are dropped Of the several anharmonic property

effects that may be used to measure stress, the following are probably the most exploited: velocity dependence

on the elastic modulus; dispersion of frequency amplitudes in surface waves; birefringence of orthogonally polarized shear waves; and harmonic generation in surface waves

A very simplified form of the anharmonic stress strain law has been written as σ = Mε + Cε2 and rewritten as σ

= ε(M + Cε) The term in parentheses is approximately related to the velocity of sound as ρV2 M + Cε, where

ρ is the density of the medium and V is the velocity of sound This may be approximately rewritten in terms of

velocity dependence on strain as:

(Eq 38)

Then, to solve for strain, ε = 2(V ρ − 2M)/C (Ref 89)

A simple view of the dependency of ultrasonic velocity on the elastic modulus and density may be shown by

rewriting the equation πV2 = M + Cε in terms of V, differentiating and dividing by V to yield an expression for ΔV/V The result will readily show that a fractional change in elastic modulus or density would affect the

velocity The density of metal, for which the Poisson ratio is near 0.3, obviously changes as a compressive or tensile stress is placed on the specimen, and it is reasonable that the speed of sound would then change

Limitations and Applications Ultrasonic technology offers a number of types of wave modes in which to probe metals; these include bulk waves, such as longitudinal and shear, and surface waves, usually confined to Rayleigh type Each mode offers many unique parameters for extracting information As has been discussed, the primary effect of stress—induced strain on ultrasonic propagation in metals—is on velocity This may be detected in a number of ways, including measurements of wave velocity, shear wave birefringence, and dispersion However, there are other characteristics of metals that affect the ultrasonic velocity to the same degree as stress These include crystallographic texture, microstresses, multiple phases, coherent precipitates, composition gradients, and dislocation density and distribution

Crecraft (Ref 90) discussed velocity effects, manifested as texture, induced birefringence, and the marked change seen with ultrasonic frequency He also reported birefringence due to cold work in nickel-steel specimens but did not attempt to separate the cold-work effects in terms of texture, dislocation density, and so

on In the early 1950s, Bradfield and Pursey (Ref 91) and Pursey and Cox (Ref 92) reported showing the influence of small degrees of texture on ultrasonically measured elasticity in polycrystalline bars They showed how the true isotropic elastic constants can be determined by using measurements of both longitudinal and shear wave speeds along several directions They presented stereographic charts that illustrated the relationship between elastic behavior of cubic crystals and results of x-ray texture determinations

McGonagle and Yun (Ref 93) noted the cold-work effects in an article comparing x-ray diffraction results with Rayleigh wave velocity measurements Boland et al (Ref 94) also recognized that other material properties can affect ultrasonic velocity and recommended that methods be developed to distinguish stress-induced velocity changes from those from other sources

James and Buck (Ref 95) pointed out that since the third order elastic constants for most structural materials are not readily available from the literature, ultrasonic stress measurement must be calibrated relative to the particular material being investigated In the same paper they discounted the possible effect of mobile dislocations on the sound velocity in structural engineering metals with high yield strengths due to the short dislocation loop lengths prevalent However, they did mention that crystallographic preferred orientation (texture) during deformation or fatigue is capable of severely modifying the elastic constants on which the sound velocity depends

Papadakis (Ref 96) noted marked velocity changes for ultrasonic waves in various steel microstructures, and Moro et al (Ref 97) measured the effect of microstructural changes caused by tempering on the ultrasonic velocity in low-alloy steel

Tittman and Thompson (Ref 98) evaluated the near-surface hardness of case-hardened steel with Rayleigh waves; because hardness in this case is a combination of composition, microstress, and macrostress, the velocity change was due to a combined effect

The temperature sensitivity of ultrasonic stress measurements has also been cited as an important source of error Salma et al (Ref 99, 100) proposed that this dependence be used as a means to measure stress but also noted the marked effect of dislocations and did not address a methodology of separating the stress from the dislocation effect

Much of the work cited above is concerned with attempts to measure the effects of a variety of material properties on the changes in ultrasonic velocity However, there apparently is no comprehensive study that demonstrates the capability of quantitatively separating stress effects on ultrasonic propagation from other variables found in structural metals, such as dislocation density or crystallographic texture Furthermore, most

of the studies cited observed velocity changes in bulk waves Velocity measurements on these waves must be measured through the thickness of a component and, as most metallurgists recognize, obtaining uniform properties through thicknesses greater than a few millimeters, especially in steels, is difficult The subtle property variations to which ultrasound velocity is sensitive, the inherent lack of homogeneity in engineering metals, and the high residual stress gradients often found in manufactured components present additional serious problems for through-thickness stress measurements

In spite of the microstructural variations in manufactured steel products, success in the application of ultrasonic methods to residual stress measurement has been achieved in specific cases One is in the measurement of hoop

stresses in railroad wheels (Ref 101) Here changes or variations of the residual stress in the hoop direction is of concern, while that in the radial or axial direction can often be assumed to be constant or negligible Some techniques, then, for the measurement of the residual hoop stresses have relied on normalizing the hoop velocity against the axial velocity (Ref 102) Also, European railroads have monitored ultrasonic velocity along the wheel rims during use and attributed changes to residual stress changes (Ref 103) Schramm in his article mentioned a number of approaches for the application of ultrasound to the measurement of residual stresses in railroad wheels, and these examples may find application in the measurement of residual stress in other axially symmetric shapes (Ref 101) Ultrasonic residual stress measurements have also been applied to rails as reported

by Egle and Bray (Ref 104) and Bray and Leon-Salamanca (Ref 105)

Magnetic Barkhausen Noise The Barkhausen noise analysis technique (BNA) is concerned with measuring the number and magnitude of abrupt magnetic reorientations made by expansion and contraction of the magnetic domains in a ferromagnetic metal These reorientations are observed as pulses somewhat random in amplitude, duration, and temporal separation, and therefore roughly described as noise

Applications A few applications of BNA to ferromagnetic metallic components have been made Gardner (Ref 106) mentions a number of applications, which include helicopter rotor blade spans, autofrettaged gun tubes, gas turbine engine components, and rolling element antifriction bearing components In these examples the change in residual stresses caused by known service histories was measured

Chait (Ref 107) qualitatively measured the residual stress condition of a high-hardness laminar composite steel weldment and compared some of the BNA data with XRD stress readings Sundstrom and Torronen (Ref 108) applied their BNA method to a number of microstructural measurements, including evaluation of grain size measurement for low-carbon ferritic and ferritic-pearlitic steels, evaluation of anisotropy in deep drawing and textured steels for electrical applications, measurement of the degree of aging in rimmed carbon steels, and pearlite morphology in steel wires These researchers have also measured iron loss in magnetic material used for transformers and have proposed using BNA for residual stress measurements, pointing out that quantitative results can be obtained if the material and its fabrication history are known and calibration is possible

Most studies and applications of BNA to stress measurement have focused on the uniaxial stress state However, Sundstrom and Torronen (Ref 108) implied that the instrumentation they used could simultaneously measure stress in two directions to give biaxial stress conditions for magnetic inspection of roller bearing components, including BNA for monitoring residual stress change

The BNA method certainly has been demonstrated to be sensitive to the stress condition in ferromagnetic materials (Ref 109) Nevertheless, its possibilities for application are limited by the condition that the material must be ferromagnetic, the narrow total range of stress sensitivity (i.e., ±40 ksi, or 275 MPa), and the shallow depth of measurement The latter condition might be relieved by using magnetomechanical-acoustic emission (MAE) (Ref 110), an ultrasound analog to BNA However, the sensitivity of either of these techniques to other characteristics of metallic components and the consequent need for calibration with a nearly identical specimen severely restricts the general applicability of BNA and MAE Many misapplications have been made that have severely damaged the reputation of the BNA methods (Ref 107, 111) Such restrictions can be removed only if the basic phenomena responsible for the effect of microstructural properties on BNA and MAE are understood and quantified in terms of the signal

BNA is not recommended where variations in elemental composition, phase composition, grain size, strain hardening, crystallographic texture, grain shape, grain orientation, carbide size and distribution, and other microstructural characteristics accompany variations in residual stress A recent evaluation of BNA by Allison and Hendricks (Ref 112) confirms the uncertainty of BNA residual stress measurements

References cited in this section

8 Residual Stress Measurement by X-Ray Diffraction-SAE J784a, Society of Automotive Engineers Handbook Supplement, Warrendale, PA, 1971

10 M.E Brauss and J.A Pineault, Residual Strain Measurement of Steel Structures, NDE for the Energy Industry, NDE Vol 13 (Book No H00930-1995), D.E Bray, Ed., American Society of Mechanical

Engineers, 1995

12 C.O Ruud and M.E Jacobs, Residual Stresses Induced by Slitting Copper Alloy Strip, NDC of Materials VI, Plenum Press, 1994, p 413–424

20 M Brauss, J Pineault, S Teodoropol, M Belassel, R Mayrbaurl, and C Sheridan, Deadload Stress Measurement on Brooklyn Bridge Wrought Iron Eye Bars and Truss Sections Using X-ray Diffraction

Techniques, Proc of 14th Annual International Bridge Conf and Exhibition, Engineering Society of

Western Pennsylvania, Pittsburgh, ICB-97-51, 1997, p 457–464

21 M.G Carfaguo, F.S Noorai, M.E Brauss, and J.A Pineault, “X-Ray Diffraction Measurement of Stresses in Post-Tensioning Tendons,” International Association for Bridge and Structural Engineering (IABSE) Symposium, 1995 (San Francisco), “Extending the Life Span of Structures,” IABSE, ETH Honggerberg, Zurich, Switzerland, Vol 71/1, 1995, p 201–206

22 J.A Pineault and M.E Brauss, In Situ Measurement of Residual and Applied Stresses in Pressure Vessels and Pipeline Using X-ray Diffraction Techniques, Determining Material Characterization:

Residual Stress and Integrity with NDE, PUP-Vol 276, NDE-Vol 12, American Society of Mechanical

Engineers, New York, 1994

39 C.O Ruud, P.S DiMascio, and D.J Snoha, A Miniature Instrument for Residual Stress Measurement,

Adv X-Ray Anal., Vol 27, Plenum Press, 1984, p 273–283

53 B.D Cullity, Elements of X-Ray Diffraction, 2nd ed., Addison-Wesley Publishing Co., Inc., 1978, p

77 C.S Barrett and T.B Massalski, Structure of Metals, 3rd ed., McGraw-Hill, 1966, p 474–476

78 C.O Ruud and G.D Farmer, Residual Stress Measurement by X-rays: Errors, Limitations, and

Applications, Nondestructive Evaluation of Materials, J.J Burke and V Weiss, Ed., Plenum Press,

1979, p 101–116

79 R.N Pangborn, S Weissman, and I.R Kramer, Dislocation Distribution and Prediction of Fatigue

Damage, Metall Trans A, Vol 12 (No 1) 1981, p 109–120

80 D.A Bolstad, R.A Davis, W.E Quist, and E.C Roberts, Measuring Stress in Steel Parts by X-Ray

Diffraction, Metals Progress, 1963, p 88–92

81 D.S Kurtz, P.R Moran, K.J Kozaczek, and M Brauss, Apparatus for Rapid Psi Squared Stress

Measurement and Its Applications to Titanium Alloy Jet Engine Fan Blades, The Fifth International Conference on Residual Stresses, Vol 2, Institute of Technology, Linkopings University, Sweden, 1997,

p 744–749

82 B.B He and K.L Smith, Strain and Stress Measurements with Two-Dimensional Detector, Adv X-Ray Anal., Vol 41, 1977

83 M.R James and J.B Cohen, The Application of a Position-Sensitive X-Ray Detector to the

Measurements of Residual Stresses, Adv X-Ray Anal., Vol 19, Gould, Barnett, Newkirk, and Ruud, Ed.,

1976, p 695–708

84 H Zantopulou and C.F Jatczak, Systematic Errors in Residual Stress Measurement Due to Specimen

Geometry, Adv in X-Ray Anal., New York, Plenum Press, Vol 14, 1970

85 C.O Ruud, D.J Snoha, and D.P Ivkovich, Experimental Methods for Determination of Precision and

Estimation of Accuracy in XRD Residual Stress Measurement, Adv X-Ray Anal., Vol 30, 1987, p 511–

522

86 J.H Root, R.R Hosbaus, and T.M Holden, Neutron Diffraction Measurements of Residual Stresses

Near a Pin Hole in a Solid-Fuel Booster Rocket Casing, Practical Applications of Residual Stress Technology, C.O Ruud, Ed., ASM International, 1991, p 83–93

87 R.C Donmarco, K.J Kozaczek, P.C Bastias, G.T Hahn, and C.A Rubin, Residual Stress and Retained Austenite Distribution and Evaluation in SAE 52100 Steel under Rolling Contact Loading, PVP-Vol

322, NDE-Vol 15, NDE Engineering Codes and Standards and Materials Characterization, J.S Cook,

Sr., C.D Cowfer, and C.C Monahan, Ed., American Society of Mechanical Engineers, 1996, p 63–70

88 M Hayaski, S Ohkido, N Minakawa, and Y Murii, Residual Stress Distribution Measurement in

Plastically Bent Carbon Steel by Neutron Diffraction, The Fifth International Conf on Residual Stresses, Vol 2, Institute of Technology, Linkopings University, Sweden, 1997, p 762–769

89 G.A Alers, Ultrasonic Methods—Overview, Proc of a Workshop on Nondestructive Evaluation of Residual Stress, NTIAC-76-2, 1975, p 155–161

90 D.I Crecraft, Ultrasonic Measurement of Stresses, Ultrasonics, 1968, p 117–121

91 G Bradfield and H Pursey, Philos Mag., Vol 44 (No 295), 1953

92 H Pursey and H.L Cox, Philos Mag., Vol 45, 1954, p 295

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Proc of the 5th International Conf on Nondestructive Testing, 1967, p 159–164

94 A.J Boland et al., “Development of Ultrasonic Tonography for Residual Stress Mapping,” Final Report, EPRI RP 504-2, Electric Power Research Institute, 1980

95 M.R James and O Buck, Quantitative Nondestructive Measurement of Residual Stresses, Crit Rev Solid State Mater Sci., August 1980, p 61–105

96 E.P Papadakis, Ultrasonic Attenuation and Velocity in Three Transformation Products of Steel, J Appl Phys., Vol 35 (No 5), 1964, p 1474–1482

97 A Moro, C Farina, and F Rossi, Measurement of Ultrasonic Wave Velocity of Steel for Various

Structures and Degrees of Cold-Working, Nondestruct Test Int., Aug 1980, p 169–175

98 B.R Tittman and R.B Thompson, Measurement of Physical Property Gradients with Elastic Surface

Wave Dispersion, Proc Ninth Symposium on NDE, 1980, p 20–28

99 K Salama and C.K Ling, The Effect of Stress on The Temperature Dependence of Ultrasound

Velocity, J Appl Phys., Vol 51 (No 3) March 1980, 1505–1509

100 K Salama and G.A Alers, Third-Order Elastic Constants of Copper at Low Temperature, Phys Rev., Vol 161 (No 3), Sept 1967, p 673–680

101 R.E Schramm, J Szelazek, and A Van Clark, Jr., Ultrasonic Measurement of Residual Stress in

the Rims of Inductively Heated Railroad Wheels, Mater Eval., August 1996, p 929–933

102 H Fukuaka, H Tada, K Hirakawa, H Sakawoto, and Y Toyo, Acoustoelastic Measurements of

Residual Stresses in the Rim of Railroad Wheels, Wave Propagation in Inhomogenous Media and Ultrasonic Nondestructive Evaluation, Vol 6, G.C Johnson, Ed., American Society of Mechanical

Engineers, 1984, p 185–193

103 E.R Schneider, R Harzer, D Bruche, and H Frotscher, Reliability Assurance of Railroad

Wheels by Ultrasonic Stress Analysis, Proc of Third European Conf on Residual Stress Analysis, 4–6

Nov 1992, DGM Informationsgesellschaft mbH

104 D.M Egle and D.E Bray, Ultrasonic Measurement of Longitudinal Rail Stresses, Mater Eval.,

Vol 378 (No 4), March 1979, p 41–46

105 D.E Bray and T Leon-Salamanca, Zero-Force Travel-Time Parameters of Ultrasonic

Head-Waves in Railroad Rail, Mater Eval., Vol 43 (No 7), June 1985, p 854–858

106 C.G Gardner, Barkhausen Noise Analysis, Proc of a Workshop on Nondestructive Evaluation of Residual Stress, NTIAC-76-2, 1975, p 211–217

107 R Chait, “Residual Stress Pattern in a High Hardness Laminar Composite Steel Weldment,”

Proc of a Workshop on Nondestructive Eval of Residual Stress, NTIAC-76-2, 1975, p 237–245

108 O Sundstrom and K Torronen, The Use of Barkhausen Noise Analysis in Nondestructive

Testing, Mater Eval., Feb 1979, p 51–56

109 J.R Barton, F.N Kusenberger, R.E Beissner, and G.A Matskanin, Advanced Quantitative

Magnetic Nondestructive Evaluation Methods, Theory and Experiment, Nondestructive Evaluation of Materials, J.J Burke and V Weiss, Ed., Plenum Press, 1979, p 461–463

110 K Ono, M Shibata, and M.M Kwan, “Determination of Residual Stress by Magnetomechanical Acoustic Emission,” ONR Technical Report 80-01, April 1980

111 R.R King and V.D Smith, “Residual Stress Measurements in Structural Steels,” Final Report SWRI Project 15-4600, Contract DOT-FH-11-9133, January 1978

112 H.D Allison and R.W Hendricks, Correlation of Barkhausen Noise Signal and X-Ray Residual

Stress Determinations in Grinding-Burned 52100 Steel,” The Fifth International Conference on Residual Stresses, Vol 2, Institute of Technology, Linkopings University, Sweden, 1997, p 640–645

Residual Stress Measurements

Clayton O Ruud, The Pennsylvania State University

residual stresses are due to surface stresses and can be measured by surface measuring methods including XRD and, for some cases, hole drilling In these cases good spatial resolution and identification of the magnitude and location of the highest stresses is of primary importance On the other hand, when distortion of metallic components presents a problem, the distribution and magnitude of residual stresses through the bulk of the component are of most interest, and high resolution and identification of areas of high stress magnitude are not

of primary concern In either case, stress measurement precision on the order of 5 ksi (35 MPa) is usually sufficient Measurement of residual stresses can be very expensive and time consuming, and it is often worthwhile to consult experts in the field before deciding on a measurement method Before an engineer or scientist not experienced in residual stress measurement selects a method and attempts to measure stresses, consultation with an expert experienced in residual stress measurement and analysis should be sought

Residual Stress Measurements

Clayton O Ruud, The Pennsylvania State University

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86 J.H Root, R.R Hosbaus, and T.M Holden, Neutron Diffraction Measurements of Residual Stresses

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87 R.C Donmarco, K.J Kozaczek, P.C Bastias, G.T Hahn, and C.A Rubin, Residual Stress and Retained Austenite Distribution and Evaluation in SAE 52100 Steel under Rolling Contact Loading, PVP-Vol

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91 G Bradfield and H Pursey, Philos Mag., Vol 44 (No 295), 1953

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94 A.J Boland et al., “Development of Ultrasonic Tonography for Residual Stress Mapping,” Final Report, EPRI RP 504-2, Electric Power Research Institute, 1980

95 M.R James and O Buck, Quantitative Nondestructive Measurement of Residual Stresses, Crit Rev Solid State Mater Sci., August 1980, p 61–105

96 E.P Papadakis, Ultrasonic Attenuation and Velocity in Three Transformation Products of Steel, J Appl Phys., Vol 35 (No 5), 1964, p 1474–1482

97 A Moro, C Farina, and F Rossi, Measurement of Ultrasonic Wave Velocity of Steel for Various

Structures and Degrees of Cold-Working, Nondestruct Test Int., Aug 1980, p 169–175

98 B.R Tittman and R.B Thompson, Measurement of Physical Property Gradients with Elastic Surface

Wave Dispersion, Proc Ninth Symposium on NDE, 1980, p 20–28

99 K Salama and C.K Ling, The Effect of Stress on The Temperature Dependence of Ultrasound

Velocity, J Appl Phys., Vol 51 (No 3) March 1980, 1505–1509

100 K Salama and G.A Alers, Third-Order Elastic Constants of Copper at Low Temperature, Phys Rev., Vol 161 (No 3), Sept 1967, p 673–680

101 R.E Schramm, J Szelazek, and A Van Clark, Jr., Ultrasonic Measurement of Residual Stress in

the Rims of Inductively Heated Railroad Wheels, Mater Eval., August 1996, p 929–933

102 H Fukuaka, H Tada, K Hirakawa, H Sakawoto, and Y Toyo, Acoustoelastic Measurements of

Residual Stresses in the Rim of Railroad Wheels, Wave Propagation in Inhomogenous Media and Ultrasonic Nondestructive Evaluation, Vol 6, G.C Johnson, Ed., American Society of Mechanical

Engineers, 1984, p 185–193

103 E.R Schneider, R Harzer, D Bruche, and H Frotscher, Reliability Assurance of Railroad

Wheels by Ultrasonic Stress Analysis, Proc of Third European Conf on Residual Stress Analysis, 4–6

Nov 1992, DGM Informationsgesellschaft mbH

104 D.M Egle and D.E Bray, Ultrasonic Measurement of Longitudinal Rail Stresses, Mater Eval.,

Vol 378 (No 4), March 1979, p 41–46

105 D.E Bray and T Leon-Salamanca, Zero-Force Travel-Time Parameters of Ultrasonic

Head-Waves in Railroad Rail, Mater Eval., Vol 43 (No 7), June 1985, p 854–858

106 C.G Gardner, Barkhausen Noise Analysis, Proc of a Workshop on Nondestructive Evaluation of Residual Stress, NTIAC-76-2, 1975, p 211–217

107 R Chait, “Residual Stress Pattern in a High Hardness Laminar Composite Steel Weldment,”

Proc of a Workshop on Nondestructive Eval of Residual Stress, NTIAC-76-2, 1975, p 237–245

108 O Sundstrom and K Torronen, The Use of Barkhausen Noise Analysis in Nondestructive

Testing, Mater Eval., Feb 1979, p 51–56

109 J.R Barton, F.N Kusenberger, R.E Beissner, and G.A Matskanin, Advanced Quantitative

Magnetic Nondestructive Evaluation Methods, Theory and Experiment, Nondestructive Evaluation of Materials, J.J Burke and V Weiss, Ed., Plenum Press, 1979, p 461–463

110 K Ono, M Shibata, and M.M Kwan, “Determination of Residual Stress by Magnetomechanical Acoustic Emission,” ONR Technical Report 80-01, April 1980

111 R.R King and V.D Smith, “Residual Stress Measurements in Structural Steels,” Final Report SWRI Project 15-4600, Contract DOT-FH-11-9133, January 1978

112 H.D Allison and R.W Hendricks, Correlation of Barkhausen Noise Signal and X-Ray Residual

Stress Determinations in Grinding-Burned 52100 Steel,” The Fifth International Conference on Residual Stresses, Vol 2, Institute of Technology, Linkopings University, Sweden, 1997, p 640–645

Dale Wilson, The Johns Hopkins University, Leif A Carlsson, Florida Atlantic University

Introduction

THE CHARACTERIZATION of engineering properties is a complex issue for fiber-reinforced composites (FRC) due to their inherent anisotropy and inhomogeneity In terms of mechanical properties, advanced composite materials are evaluated by a number of specially designed test methods These test methods are mechanically simple in concept but extremely sensitive to specimen preparation and test-execution procedures, often requiring complex data reduction analysis The rigor of specimen fabrication and testing practices employed determine the quality and cost of the resulting mechanical property data It is important to define the purpose of mechanical characterization prior to conducting tests The purpose determines the type of testing program, specimen fabrication, testing rigor, and, ultimately, the cost of characterization Costs are controlled and time is saved by matching quality and accuracy requirements to the intended materials usage

Footnote

* The section “Interlaminar Shear Properties of Fiber-Reinforced Composites at High Strain Rates” was written

by John Harding and Stephen Hallett, Oxford University The section “Fatigue Testing and Behavior of Reinforced Composites” was written by W Steven Johnson and Ramesh Talreja, Georgia Institute of Technology

Fiber-Mechanical Testing of Fiber-Reinforced Composites

Dale Wilson, The Johns Hopkins University, Leif A Carlsson, Florida Atlantic University

General Concepts

Before describing the principal tests used for mechanical characterization of composites, the authors offer a review of the purposes of such tests and general considerations related to the mechanical properties of anisotropic systems, specimen fabrication, equipment and fixturing, environmental conditioning, and analysis

of test results

Purposes of Mechanical Characterization

The three most common purposes of mechanical property characterization are research and development, quality control (QC), and design data generation Various levels of rigor are practiced within each category, but,

in general, design data generation is the most rigorous Rigor, as applied here, refers to the process of strictly following processing, fabrication, testing, and data reduction standards and specifications on statistically significant sample sets made from commercially standard materials

Testing in support of research and development serves a variety of purposes and, by definition, must be flexible Research and development testing is used to develop and assess the validity of the test methods, to aid

in exploring materials science and mechanics concepts, and to support scientific discovery in materials development and applications research In the materials industry, research and development testing supports the study of materials performance in comparison to program objectives, competitive materials, or other developmental materials Once a material is developed, the tests can also be used to produce the first generation

of property data used to market the new material The goal of most industrial research and development testing

is to control costs, keep turnaround times short, and develop data with accuracy and repeatability sufficient for comparisons Often this is achieved by using small sample sizes, less rigor in specimen preparation, and minimal levels of test instrumentation Testing is defined by internal procedures for specimen fabrication, test execution, and data reduction Flexibility exists to modify specimen preparation and test procedures or to create new test methods, as required to meet research and development objectives

Quality control characterization is defined primarily by customer acceptance of test methods and/or product specifications The specimen sampling, specimen preparation, and test procedures must rigorously follow documented specifications Sample sizes are statistically specified, but reduced levels are often allowed to control costs once production history is demonstrated to be consistent Quality control tests usually characterize

a couple of the most critical characteristics that define a product and strive for comparison against historical values rather than absolute properties Many QC tests do not measure absolute mechanical properties For example, flexural strength and modulus do not in general coincide with the strength and modulus of a material tested in uniaxial tension

Design data generation strives to produce absolute property data The data must represent the actual mechanical performance of the material under loading conditions like those that will be encountered in service The tests used must be capable of measuring the material property desired, and specimen preparation must rigorously conform to the standards specified in the test methods Sample sizes must meet the statistical requirements for A-basis or B-basis design allowables The number of test-specimen replicates is usually greater than in either of the two previous types of testing Also, specimen inspection, test instrument calibration, and test method execution are very rigorous

In summary, different testing approaches are appropriate to meet the range of objectives that one may encounter

in materials characterization The cost of the testing and the time required to generate the results increase with increasing rigor of the characterization process In order to strike the proper balance in addressing testing needs, the test engineer must fully understand the cause-effect relationships of all aspects of the specimen preparation and testing procedures on the quality and the cost of the results To that end, this article provides a condensed yet concise presentation of the key concepts of mechanical characterization of composite materials

Mechanical Properties of Anisotropic Systems

In order to focus on testing, the authors assume that the reader has an understanding of the various types of composite material systems and their special characteristics If background in laminate mechanics is required, the reader is referred to (Ref 1, 2, 3) Methods for measuring properties of fiber and matrix constituents are not covered, although it is important that the reader understand the relationship that constituent properties, volume

fraction, and void content have to engineering property development in composite systems This article focuses, thus, exclusively on measuring the engineering and structural performance of laminates and composite structures

Mechanical properties of a composite material refer to the elastic and strength properties of the material under tensile, shear, or compression loading Other properties, such as fracture toughness and flexural strength and stiffness, are also useful in characterizing the performance of a composite material Finally, thermomechanical and hydromechanical properties are of importance under changing temperature and moisture environments The homogeneity assumption that microstructural features of the material are small enough to be inconsequential to the average behavior of the material on a macroscale may not apply to composites, especially when strength and fracture are considered Fabrics and laminates are very inhomogeneous in character The scale of homogeneity of a composite system must be taken into account for fixture design, instrumentation decisions, and in data analysis

The fundamental description of the engineering properties for a lamina under tension, compression, and shear loading is given in terms of the lamina coordinate system shown in Fig 1 The strength and stiffness properties are defined in Table 1 If the material is transversely isotropic, then the indicated properties need not be determined The fracture toughness is sometimes measured as part of durability assessment of a material

system These properties are the mode I and II critical strain energy release rates (GIc and GIIc, respectively) Flexural properties are also determined routinely and result from bending the material to produce tension, compression, and shear stresses The result is more a structural property than an intrinsic material property, but

it is very useful in materials screening and quality control

Table 1 Listing of mechanical properties typically determined for composite materials

Symbol Property

Tensile modulus in the fiber direction

Tensile modulus transverse to the fiber

Tensile modulus transverse through the thickness (a)

Compression modulus in the fiber direction

Compression modulus transverse to the fiber

Compression modulus transverse through the thickness (a)

G12 Shear modulus in the 1–2 plane

G13 Shear modulus in the 1–3 plane (a)

G23 Shear modulus in the 2–3 plane

Tensile strength in the fiber direction

Tensile strength transverse to the fiber

Tensile strength through the thickness (a)

Compression strength in the fiber direction

Compression strength transverse to the fiber

Compression strength through the thickness (a)

S12 Shear strength in the 1–2 plane

S13 Shear strength in the 1–3 plane (a)

S23 Shear strength in the 2–3 plane

ν12 Poisson's ratio in the 1–2 plane

ν13 Poisson's ratio in the 1–3 plane

ν23 Poisson's ratio in the 2–3 plane

Ultimate tensile strain in fiber direction

Ultimate tensile strain transverse to the fiber

Ultimate tensile strain through the thickness (a)

Ultimate compression strain in the fiber direction

Ultimate compression strain transverse to the fiber

Ultimate compression strain through the thickness (a)

(a) This property does not need to be determined if the 2–3 plane is transversely isotropic

Fig 1 Lamina and plate coordinate designation system for composites Plate coordinates are labeled x, y, and z Lamina coordinates are labeled 1, parallel to the fiber axis; 2, perpendicular to the fiber axis; and

3, normal to the fiber plane

Properties of laminated composites are defined similarly to those for the lamina, except a laminate coordinate

system (x, y, z) is employed The subscripts 1, 2, 3 on the properties defined in Table 1 are respectively changed

to x, y, and z, and the properties become the effective laminate properties The word “effective” is very

important because it signifies that the measured response is an average response through the material thickness

In reality, the stresses in a composite are nonuniform It should also be noted that composites may behave differently in compression and tension; the elastic and strength properties must be characterized in both tension and compression to fully characterize the material

Role of Specimen Fabrication

The test results from any characterization are critically dependent on material and specimen integrity Material processing and specimen machining strongly influence the quality and reproducibility of test results The recently issued ASTM D 5687, “Guide for Preparation of Flat Composite Panels with Processing Guidelines for Specimen Preparation,” provides descriptions of current practices for autoclave processed composites Machining of test specimens influences the cost of characterization, and trade-offs must often be weighed between machining tolerance (program costs) and the requirements on the end use of that data

Specific specimen geometry and laminate configuration requirements are defined for each test type and are associated with the discussion of the test methods Materials for the test specimens are either cast, molded to shape, pultruded, filament wound, or machined from plaques or plates fabricated using autoclave or other processing methods For laminates, a reference edge must be established, and each ply must be oriented accurately with respect to the reference edge Before cure, the laminate reference edge is accurately scribed with a reference line that is used to maintain alignment when the cured plate is trimmed The fiber volume fraction, void content, and the uniformity of fiber wetout in the part are controlled by the processing of the test panel or specimen All of these factors strongly influence the mechanical properties of the material Relationships between processing conditions and material microstructure must be understood and controlled to produce valid test specimens that are representative of the actual material being characterized (i.e., specimens that have the same microstructure and properties that the material will have in a structure) The specimen must

be fabricated or machined so that the material axes align properly with the test axes

Specimen Machining When fabricated from panels, specimens are normally machined using a diamond wafing saw A cut is first made along the reference edge, and then all subsequent cuts are made relative to the reference edge to preserve the accuracy of the fiber orientation in the panel When machining specimens to final geometry, make allowances for scrap, and machine specimens from the heart of the material away from edges

A diamond saw blade produces a very smooth surface along the cut edges, and no further finishing is required usually In specimens requiring holes, a diamond core bit provides satisfactory hole quality Other methods

include ultrasonic drilling, or drilling with special drill bits in conjunction with templates to guard against punch-through delamination

If a specimen is designed to have tabs, the tabs are bonded into place before the specimen is machined to its final shape The tab material is typically 3.2 mm (0.13 in.) thick [0/90°] glass/epoxy or a woven fabric glass/epoxy material, although steel or aluminum can be used When required, bevels are machined onto the tab, and then the tab is bonded onto the test panel using special jigs to ensure alignment of the tabs with the specimen reference edge Individual specimens are cut from the tabbed panel, again taking care to maintain alignment with the reference edge (test axis)

Good quality composite specimens should be of uniform dimensions, have a precise fiber alignment, and possess high-quality finish on machined edges There should be no evidence of delamination along machined edges The laminate should contain no dry fiber regions, voids, or other obvious flaws If available, ultrasonic C-scan should be employed to nondestructively evaluate composite panels for flaws prior to specimen fabrication and testing Flawed panels or flawed regions within panels should be discarded

Test Equipment and Fixturing Considerations

The availability of suitable, well-maintained, and accurately calibrated testing equipment is essential for reliable characterization of composite materials Standard test instrumentation is used for load introduction and strain measurement of composite materials, but test fixturing must be specially designed to meet the specific requirements of the composite tests The drawings and specifications for standard composite test fixtures are available for most test standards, and many fixtures are now available commercially Testing is usually performed in a screw-driven or a servo-hydraulic universal test machine

The test machine must have sufficient stiffness and load capacity to insure accurate load application and deformation measurement A universal test machine with a load capacity greater than or equal to 110 kN (25 ×

103 lbf) is recommended to test composite materials Longitudinal tension and compression properties of some composite specimens require this capacity Fiber tests, transverse tension, and flex properties require much lower load capacity Universal test machines allow interchangeability of load cells to accommodate different testing requirements, and, when needed, small capacity load cells can be used in a 110 kN frame The load cell must be properly matched to the loading requirements of the specimen in order to ensure required levels of accuracy and sensitivity

Fixturing Issues Proper fixturing is critically important to composite testing The special fixtures for each test are designed to perform two important functions: (a) to transfer loads or displacements from the test machine to the test specimen, and (b) to achieve load introduction such that the desired stress state and deformation are produced in the specimen test section The quality of test results is governed by proper fixture design, accurate machining to design specifications, and meticulous maintenance of the fixture

No fixture functions perfectly in generating required states of uniform stress in test specimens; good tests closely approximate desired stress states and minimize stress concentrations in the test section Mechanically, fixtures must provide reproducible alignment of the specimen in the test machine, and specimens should be easy to insert and remove after testing The fixture must be strong and stiff enough not to change the characteristics of the state of stress in the specimen during the test It must also be constructed of hardened materials that will not wear excessively with repeated use Mating surfaces designed to slip relative to each other must be polished to stringent flatness-finish requirements to minimize friction binding during testing Fixture functionality must conform to specifications in all required test environments

All fixtures should be inspected routinely before testing to ensure that they are not worn or damaged in any way that will affect the test results With use, all fixtures wear and eventually decrease the reliability of test results Electronic Transducers for Strain Measurement Strain and deformation measurements are performed on composites using methods and instruments similar to those used for metals (Ref 4, 5, 6) A few issues must be addressed when using standard, bondable-foil strain gages on composites

Gage heating is a problem that must be addressed when using bondable-foil strain gages on polymeric matrix composites because the polymer does not conduct heat very well This allows heat to build up in the gage, and the resulting temperature change causes a resistance change, which is falsely recorded as an apparent strain The use of 350 Ω (or greater) strain gages is recommended for composite testing, and the excitation voltage should be between 2 and 5 V Measurement sensitivity is related to the excitation voltage, and 2 V is the lowest voltage that will ensure sufficient sensitivity

Composites, especially woven fabrics and braided structures, have very coarse microstructure The size of the strain-gage grid area must be large enough to average deformation over a representative area of the specimen If the material is heterogeneous, such as a woven fabric, the grid must be large enough to cover at least one unit cell of the structure A comprehensive discussion of this issue is covered by Masters and Ifju (Ref 6), based on their extensive survey of experimental results using strain gages of varying size on different types of fabric and braided composite structures

The third problem that can occur when using bondable-foil strain gages for testing composites is that transverse strain sensitivity can influence strain measurements This is especially prevalent for certain types of angle-ply lay-ups, such as the [±45°] laminate Correction factors must be applied to achieve accurate longitudinal readings measured under such conditions

Environmental Conditioning

Environmental conditioning is perhaps one of the most controversial aspects of composites testing It is not just the temperature at which the material is to be tested that is important The entire temperature and moisture histories of the specimen influence the properties Specimens should be preconditioned before testing by exposure to the specified temperature and humidity conditions Specimens to be tested under standard laboratory conditions (21 ± 1.0°C, 50% ± 20% relative humidity) can be conditioned in the laboratory for a period of 24 h prior to testing Specimens designed to evaluate effects of environmental exposure must be conditioned by using conventional environmental chambers or temperature-controlled baths using the procedures outlined below

Moisture conditioning is covered under a relatively new method (ASTM D 5229) and is usually specified in one of three ways:

• Exposure at a specific temperature and relative humidity or in a water bath to attain a target percentage weight gain

• Exposure for a specified time duration

• Exposure to attain equilibrium weight gain

Diffusion constants for composites are often very small, and sometimes accelerated conditioning practices are employed A specimen can be soaked in water for short durations and attain a certain moisture content instead

of being conditioned for months at 95% relative humidity to attain the same moisture content Increase of temperature greatly increases the diffusion rate

Accelerated conditioning is usually not equivalent to normal conditioning The aging of the material is a rate process that depends on path; thus, specimens may not yield the same properties when conditioned using accelerated processes Accelerated conditioning is considered a conservative approach, because accelerated conditioning typically yields larger degradation of properties than tests that are more representative of actual service conditions

Prior to conditioning, polymeric matrix composites should ideally be fully characterized using infrared spectroscopy, thermomechanical analysis, and differential scanning calorimetry to determine the state of cure,

moisture content, and glass transition temperature (Tg) of the matrix material This information defines the preconditioned state of the material The material can then be subjected to the specified environmental conditioning regimen Once conditioned, specimens should again be characterized by analytical equipment This is best done on travelers, which are dummy specimens conditioned along with the test specimens for this purpose The test specimen cannot be used, since the analytical tests will influence the conditioning of the specimen and render it useless for testing

Metal matrix and ceramic matrix composites also have requirements for environmental conditioning The key difference is that these types of composites have less sensitivity to moisture uptake, because metallic or ceramic materials do not exhibit moisture-induced “aging” phenomena

Analysis of Test Results

Statistical principles should be employed in test program design and analysis of test results (Ref 7) Variability

is normal in all testing, and proper statistical treatment of data ensures that variability is handled properly in

deducing conclusions about the meaning and trends of the measured data To start, typical variability of a given test should be used to determine the sample sizes needed to meet statistical significance requirements Sample means, medians, and standard deviations are useful but may not be sufficient if the population is not normally distributed or if variance is large Analysis of variance techniques may need to be employed to determine significance in comparisons of results

Many investigators conduct parametric experiments changing one variable at a time to determine relationships among experimental variables This approach results in huge, costly test matrices and often produces poor results Design of experiments is a rigorous, statistically based method for testing the relationship of experimental variables The design minimizes the number of tests necessary to determine the relationships between the test variables to a desired level of statistical significance Consultation with an expert is advised, since this can save money and produce more reliable results Several software packages are available to support statistical analysis and design of experiments

In any experimental test program, failure modes must be carefully noted Specimen failures should be the proper mode for the test being conducted and be consistent Improper failures are an indication that the test is poorly designed, the specimen is flawed, or the test fixture or setup is improper Failed specimens should always be saved, and typical failures should be photographed and documented

Footnote

* The section “Interlaminar Shear Properties of Fiber-Reinforced Composites at High Strain Rates” was written

by John Harding and Stephen Hallett, Oxford University The section “Fatigue Testing and Behavior of Reinforced Composites” was written by W Steven Johnson and Ramesh Talreja, Georgia Institute of Technology

Fiber-References cited in this section

1 R.M Jones, Mechanics of Composite Materials, 2nd ed., Taylor and Francis, Philadelphia, 1999

2 S.W Tsai, and H.T Hahn, Introduction to Composite Materials, Technomic, Lancaster, 1980

3 J.R Vinson, and T.W Chou, Composite Materials and Their Use in Structures, Halstead Press, Applied

Science Publishers, Barking, 1975

4 J.M Whitney, I.M Daniel, and R.B Pipes, Experimental Mechanics of Fiber Reinforced Composite Materials, revised ed., Society for Experimental Mechanics; Prentice-Hall, Englewood Cliffs, 1984

5 R.B Pipes, Test Methods, Delaware Composites Design Encyclopedia, Vol 6, (L.A Carlsson and J.W

Gillespie, Jr., Ed.), Technomic, Lancaster, 1990, p 3

6 J.E Masters and P.G Ifju, Strain Gage Selection Criteria for Textile Composite Materials, J Compos Technol Res., Vol 19 (No 3), 1997, p 152

7 H.M Wadsworth, Handbook of Statistical Methods for Engineers and Scientists, McGraw-Hill, New

York, 1990

Mechanical Testing of Fiber-Reinforced Composites

Dale Wilson, The Johns Hopkins University, Leif A Carlsson, Florida Atlantic University

Characterization of Mechanical Properties

The basic building block of laminated composites is the unidirectional lamina (Fig 1) Specific test methods are available to measure lamina mechanical properties The unidirectional lamina is highly anisotropic, which complicates mechanical testing Alignment of the test specimen in the test frame is an important requirement for obtaining adequate test results, and undesirable transverse failures are a common occurrence in such materials For these reasons, a number of investigators propose to back out unidirectional properties from laminate tests, but no acceptable standards have yet emerged, except for the [±45°] laminate coupon subjected

to uniaxial tension for the generation of lamina shear stress-strain response (ASTM D 3518) There exists a host

of test fixtures, specimen geometries, and test procedures for the generation of mechanical property data for composite materials Reviews and further information on the subject are provided in Ref 4, 5, and 8–10 Space limitations prohibit discussion of each test method Only test methods accepted by the community as ASTM standards or as candidates for ASTM standardization are considered in this article In cases where more than one method is discussed, the differences are clearly brought out, and guidelines are given about the use of each method

Tension Testing

The most basic mechanical test is the tension test For most structural materials, the tensile properties are essential elements of the material design allowables The tension test is used to measure Young's modulus, Poisson's ratio, tensile strength, and ultimate strain to failure for composites The properties reduced from tension tests on composite materials are effective (averaged) properties The test method applies to unidirectional composites but can also be performed on laminates, woven fabrics, or discontinuous fiber composites For asymmetric and/or unbalanced laminates, extension/bending coupling and extension/shear coupling effects produce nonuniform stress states in the test section Under these conditions, effective properties cannot be accurately determined from the test results using the standard data reduction methods The adequate gripping of the test specimen is the major issue in tension tests Any tension test specimens (Fig 2) require gripping regions where loads are introduced through the specimen surfaces, a transition region, and a gage section region that may be of reduced cross-sectional area to promote failures away from the grips Sufficient volume should be involved in the gage section to achieve adequate sampling of the material being tested

Fig 2 Generic tension test specimen

The widthwise tapering popular with metals (Fig 2) usually leads to splitting failures of highly anisotropic composites in the gripping region prior to ultimate failure of the material in the gage section This problem is avoided by using uniform width (rectangular) test specimens (Ref 10) The grips of the tension test frame introduce large clamping forces that can cause splitting failures or surface damage in the gripped region These forces, coupled with normal stress concentrations induced by load introduction, can lead to anomalous failures Tabs with tapered (beveled) ends, therefore, are bonded on each side of the specimen The load is transferred into the specimen test section through shear (see Fig 3) When tabs are used, the properties of the adhesive

must be carefully chosen to meet the strength and elongation requirements of the composite under the temperature and moisture conditions imposed by the test Figure 4 shows the geometry of the ASTM D 3039 tension test specimen Stress analysis of tabbed specimens (Ref 11, 12) indicates that intense out-of-plane peel and shear stress exist at the tip of the bevel and that the axial tensile stress in the specimen is increased Consequently, tabbed specimens may fail at the tab ends or inside the tabs, but low bevel angles will reduce the stress concentration (Ref 11) Typically, bevel angles in the range of 15 to 30° are used because tabs with small taper angles occupy too much of the gage section

Fig 3 Load transfer in gripping region of tension test specimen through end tabs

Fig 4 Specimen for tension testing of composites as defined in ASTM D 3039, Lg = gage length; LT = tab

length; θ = tab bevel angle; w = width

To characterize the tensile response of the unidirectional lamina, 0° and 90° specimens are employed to determine longitudinal and transverse properties The [±45°] laminate tension test measures shear properties of the lamina and is discussed under shear testing When characterizing multidirectional laminates, the tabs are sometimes replaced by emery paper inserted between the grips and specimen surface to avoid slippage and minimize surface damage, but in composite laminates with 0° surface plies, fiber damage is likely to occur in the gripping region if tabs are not used

Specimen Machining and Instrumentation For unidirectional composites of 0° fiber orientation, a specimen width of 12.7 mm (0.5 in.) and a thickness of 6 plies are common Unidirectional 90° specimens are typically

25 mm (1 in.) wide and 8 to 16 plies thick Laminates and sheet molding compound use the same geometry as the 90° specimen and have the specimen thickness defined by laminate configuration or fundamental sheet thickness Loading eccentricity may arise due to variations in tab and specimen thickness As proposed in ASTM standard D 3039, tolerances for tab and specimen thicknesses are ±1 and 4%, respectively (Ref 10) Tabs should be made from [±45°] or [0/90°] glass/epoxy or woven fabric composites Printed circuit board (NVF Co., Kennett Square, PA) is often used because of its tight thickness tolerances Laminates and sheet molding compound can be tested with or without tabs, although tabs are recommended for thin specimens

Gage length (Lg), (Fig 4) is commonly 125 to 150 mm (5 to 6 in.)

It is common to bond continuous end tabs on the panels prior to machining the specimens After careful surface preparation of the bonding surfaces of the specimens and end tabs (Ref 8), the end tabs are attached with an adhesive, typically Hysol 9309, 934 or 929 (Hysol Division, The Dexter Corporation, Pittsburg, CA) or similar

epoxy adhesive appropriate to the test conditions specified The tab length, LT in Fig 4, should be at least 38

mm (1.5 in.), and the tab material should be 1.6 to 3.2 mm (0.06 to 0.13 in.) thick As pointed out in Ref 10 and

13, strips of beveled tab material of similar or slightly larger length than the width of the uncut composite panel should be bonded on both ends of the composite panel prior to machining the specimens It is desirable to use a special tab-fixturing jig to symmetrically secure the position of the four strips of tabs on the composite panel to maintain positive alignment between the tabs and composite panel Such fixtures are available commercially, (e.g., Ref 14)

Resin matrix composites are typically machined using a slitting saw or a water-cooled diamond saw (Ref 8) Polishing of the edges has been found to increase the strength, but the finish produced by diamond sawing meets the requirements of ASTM methods and is the commonly accepted industry practice Alignment of the specimen axis with respect to the fiber direction is an important issue in machining of composites (Ref 8, 15) Hart-Smith (Ref 15) found that specimens cut with 1° of misalignment may cause as much as a 30% decrease in strength due to reduced effective width of the specimen The variations of the specimen width should not exceed 1% (ASTM D 3039) If Poisson's ratio is desired, a 0/90° strain gage rosette should be bonded in the center-gage-section region of the specimen If only Young's modulus and strength are desired, a longitudinal strain gage or an extensometer attached to the specimen can be used When load eccentricity is of concern, back-to-back strain gages may be used to detect bending of the specimen When using strain gages on woven fabric materials, one must select the strain gage size to average deformation over a representative portion of the fabric structure Failure to use a sufficiently large strain gage will result in large variability in the measured strain

The specimen geometry and dimensions discussed so far are strictly valid for polymeric resin matrix composites but also apply to other types of composites, after some modifications Johnson et al (Ref 16) for example, who studied metal matrix composites containing unidirectional silicon-carbide fibers, found that laminates containing 0° fibers required reduction of the gage-section cross-sectional area (as shown in Fig 5)

so that the specimen would fail in the gage section without slipping or failing in the grips

Fig 5 Dog-bone specimen used for tension strength testing of fiber-dominated metal matrix composites All dimensions are in millimeters Source: Ref 16

Test Procedure Use of standard wedge-action grips with hardened steel serrated jaws is the common practice With such grips, the clamping pressure increases in proportion to the axial load acting on the specimen Hydraulic grips provide means to adjust the clamping pressure to avoid crushing of the specimen ends at high loads Alignment of the test specimen is especially important for unidirectional composites The specimen is tested monotonically to failure while recording load, crosshead displacement, and strain Normally, the test is run at a crosshead speed of 2 mm/min (0.08 in./min) Failure mode and location should be noted for each test along with ultimate failure load A failure located outside the test section justifies rejection of the result Figure

6 shows acceptable and common failure modes for 0 and 90° carbon fiber composites Some 0° specimens literally explode Safety glasses and a protective shield are recommended during tension testing

Fig 6 Commonly observed, acceptable failure modes of (a) 0°, and (b) 90° carbon/epoxy unidirectional composites

Figure 7 shows a representative example of stress-strain curves for a 0° glass/polyphenylene sulfide (PPS) composite, that is, stress σ1 versus longitudinal and transverse strains, strains ε1 and ε2 The stress σ1 is defined

as load divided by cross-sectional area in the test section Based on the data collected from the test, the modulus

E1 was reduced using a least squares linear fit to the linear initial portion of the curve σ1 versus ε1 Poisson's ratio, ν12, was determined from the ratio of the initial slopes of σ1 versus ε1 and σ1 versus -ε2, with ν12 = -ε2/ε1 The ultimate strength in tension = is the maximum value of σ1 Values of E1, ν12 and are given in Fig 7

Fig 7 Stress-strain response for a unidirectional [0] 8 glass/polyphenylene sulfide (PPS) specimen

Compression Testing

Compression testing is performed by subjecting a test specimen to an increasing compressive load until the specimen fails in a failure mode that is representative of that in an actual structure As discussed in Ref 10, however, compressive failure is triggered by phenomena on the microlevel that are very difficult to observe, and detailed study is required to reach a clear definition of valid failure modes It is clear, however, that strength degradation due to stress concentrations in the specimen arising from load introduction or slight eccentricities in load-specimen alignment should be minimized and that failure caused by global specimen buckling must be suppressed Buckling and kinking of the fibers within the composite are features regarded as representative for the material and should not be inhibited

To avoid buckling instability, relatively short gage lengths are necessary, but short gage lengths generally tend

to amplify sensitivities due to clamping Thus, for very short gage lengths, the apparent compressive strength tends to decrease (Ref 17, 18, 19) It is likely that nonuniformities in specimen thickness or in the bond or tab thicknesses result in nonuniform loading in the short gage section, leading to premature failure Figure 8 shows

some typical failure modes The failure modes shown in Fig 8(a–c) are acceptable, but the column buckling failure (Fig 8d) is clearly unacceptable, although difficult to visually observe Because of the stress concentration at the tab ends, it is common to observe failure at the tabbed region (Ref 20) Such failures are not acceptable in tensile testing but are usually accepted in compression testing, because they rarely can be avoided (Ref 10)

Fig 8 Typical failure modes for composite compression specimens

Several compression test methods have emerged during the past twenty years, and much confusion exists on their relative virtues The methods may be grouped into three categories based on load introduction and specimen design: shear loading, end-loading, and sandwich beam specimen testing (Fig 9) The sandwich beam specimen (Fig 9c), may be tested in flexure or axial compression Chatterjee et al (Ref 10) presented a thorough review of currently available compression test methods and rated the methods according to problems associated with load introduction, uniformity of stress field, sensitivity to imperfections, simplicity, acceptability of failure modes, adequacy of data reduction, specimen preparation and fixture requirements, and consistency of results Table 2 summarizes the various test methods and their ratings (1, 2, and 3) The test methods included in Table 2 are essentially based on polymer matrix composites but should be applicable to metal matrix and ceramic matrix composites as well According to Ref 10, the Illinois Institute of Technology Research Institute (IITRI) test method (ASTM standard D 3410) is the most reliable and versatile Because of space limitations, only the methods with the highest rating (1) are described here with the exception of the Boeing-modified ASTM D 695 method, which has been adopted as a recommended method (SRM 1-88) by the (Suppliers of Advanced Composite Materials Association) (SACMA) It should be emphasized that while all the methods provide adequate measures of modulus, the “true” composite strength may not be determined

Table 2 Compression test methods for fiber-reinforced composites

Shear-loaded specimen test methods

Celanese (ASTM D 3410) Long-established ASTM standard Results are very sensitive

to accuracy of fixture and test procedure

2

Wyoming-modified Celanese Cone grips replaced by tapered cylindrical grips Post and

bearing alignment replaces sleeve Reduced fixture cost

Wider specimen

1

IITRI (Illinois Institute of

Technology Research Institute)

Wyoming-modified IITRI Smaller, more simply fabricated version of standard IITRI

fixture

2

End-loaded specimen test methods

ASTM D 695 Designed for unreinforced plastics Not very suitable for

composites

3

Modified ASTM D 695 Currently a Boeing and SACMA recommended method

Deviates extensively from the ASTM standard Short (4.8 mm) gage length

Block compression Limited by end crushing to low-strength composites unless

end reinforcement is used

3

Sandwich beam specimen test methods

ASTM D 3410 Method C-flexure Large specimen Expensive to fabricate Simple fixture

Reliable results if specimen is properly designed to prevent core failure

3

Sandwich column, axial loading Must fabricate sandwich laminate End crushing a problem 3

Mini-sandwich column, axial

short-fiber composites, 25 mm (1 in.) wide specimens are recommended (Ref 9) Variations in specimen width and thickness should be within ±0.03 mm (±0.001 in.) Untapered tabs are specified (Ref 20) Thickness, materials, and bonding procedures for the end tabs are the same as for the tension test Extreme care should be taken to achieve tab surfaces parallel within 0.08 mm (0.003 in.)

Fig 10 Compression test fixture developed at the Illinois Institute of Technology Research Institute (IITRI) Source: Ref 10

Fig 11 Dimensions for unidirectional specimens for the IITRI compression test

As with any compression test, concern about specimen buckling exists, and back-to-back strain gages should be attached to the specimen surfaces in the gage region (Fig 11) By monitoring the stress-strain response for each gage, loading eccentricity and buckling instability can be detected For a well-aligned, precisely machined specimen, the strains from both surfaces will be in close agreement (Fig 12) Bending caused by loading eccentricity will cause the strains to diverge with increasing load until instability causes strain reversal (Fig 12) When buckling instability occurs, the gage on the convex side will be relieved of some of its compressive stress and the corresponding magnitude of strain will decrease The gage on the concave side (A in Fig 12) will correspondingly experience an increased compressive strain As a result of buckling, the apparent strength is decreased, and the compression test is invalidated

Fig 12 Schematic of stress-strain responses for well aligned (good test) and eccentrically loaded (bad test) compression test specimens

Since the compressive load is introduced in the specimen through shear (Fig 9a) via tabs, there are stress concentrations in the regions at the ends of the end tabs at the beginning of the gage section Consequently, failures are commonly observed close to the ends of the end tabs, but, as mentioned previously, such failures are difficult to avoid and are commonly accepted

Test Procedure Measure the width and thickness of the specimen to within 0.03 mm (0.001 in.) at several locations, and calculate the cross-sectional area Attach strain gages on both sides of the specimen Mount the specimen in the grips and place the grips in the fixture, which should be placed between the crosshead and the base on the centerline of the test machine Set the crosshead speed at 0.59 to 1.2 mm/min (0.02 to 0.05 in./min) The strain readings may be recorded continuously or at discrete load intervals If discrete data are taken, the strain readings should be captured at small load intervals in order to get at least 25 points in the linear response region A total of 40 to 50 points is desirable to establish the total stress-strain response Monitor all specimens

to failure Plot the data for reduction and inspect the stress-strain curves for signs of global bending of the specimen To obtain the ultimate strain, the response curve may need to be extrapolated, assuming linear elastic behavior or curve fitting to the available stress-strain data The modulus should be established by a least squares fit of the initial slope and, once established, the procedure should be consistently employed for modulus calculation

Wyoming Modified Celanese Compression Test Method The Wyoming-modified Celanese fixture is shown in Fig 13 This fixture was developed at the University of Wyoming and avoids several shortcomings of the original Celanese fixture (ASTM standard D 3410) The fixture has wedge grips with a constant radius and does not require the troublesome alignment sleeve of the Celanese fixture (see Ref 10, 22) The fixture is much smaller than the IITRI fixture and weighs only about 4.5 kg, (10 lb), compared to about 40 kg (88 lb) for the IITRI The low weight provides for easier handling and requires less time for reaching thermal equilibrium in nonambient temperature testing The grips can, like the IITRI fixture (Fig 10), be pretightened onto the test specimen and allow alignment of each pair of wedges with respect to each other

Fig 13 Wyoming-modified Celanese compression test fixture Source: Ref 10

The test specimen is 114 mm (4.5 in.) long and 12.7 mm (0.5 in.) wide The gage length is 12.7 mm (0.5 in.) The fixture can accommodate specimens that are between 3.8 and 6.4 mm (0.15 and 0.25 in.) thick in the tab region Specimen fabrication, bonding of end tabs, tolerances, and testing and failure modes are equivalent to those outlined for the IITRI test

Boeing Modified ASTM D 695 Test The ASTM D 695 method as modified by Boeing (Ref 23) is illustrated in Fig 14 The test method was adopted by SACMA as a recommended test method (SRM 1-88, April 1989) and

is also under consideration for adoption by ASTM As shown in Fig 14, the specimen is end-loaded and supported with a 0° orientation; the test is predominantly used to measure longitudinal properties To obtain both modulus and strength data, two tests are required For strength measurement, tabs are bonded onto the specimen, increasing the bearing area in the end-loaded regions For modulus determination, the specimen is not tested to failure, and the tabs are omitted

face-Material t, mm D, mm

0° Uni tape 1.00 3.00

90° Uni tape 2.50 7.50

Fabric 2.50 7.50

Fig 14 Boeing-modified ASTM D 695 compression test fixture Source: Ref 10

The standard specimen is 80.8 mm (3.2 in.) long and 12.7 mm (0.5 in.) wide Specimen thickness recommendations are given in the table in Fig 14 A thin, tabbed specimen subjected to compression is face-supported along its length, except for the 4.8 mm (0.19 in.) long gage section, and buckling is commonly not a problem For compressive strength determination, two continuous lateral supports without the strain gage recess are used Typically, untapered [0/90°] or plain-weave fabric tabs made from the same type of material as that being tested are used To determine the modulus, a strain gage is bonded at the center of an untabbed specimen, and a lateral support with a central cutout to provide clearance for the strain gage and its connections is used

As an alternative, continuous supports may be used with an extensometer attached to the specimen edge The specimen should be deformed at least to 0.3% (Ref 10)

The end-load introduction can cause axial splitting or bearing failures on the loaded ends This must be prevented and has prompted the use of tabs and end caps Another problem is alignment Alignment depends on the machining precision of the specimen ends; that is, on the parallelism between opposing ends and the perpendicularity of these ends to the specimen loading axis Not only must the specimen be precise, but the test machine platens must also be precisely parallel and aligned with the axis of the test machine Tolerances for

specimen thickness and thickness of the tabbed region (t and D in Fig 14) are ±0.1 mm (±0.004 in.) Tabs must

be flat, parallel, and of equal thickness to within 0.05 mm (0.002 in.) Ends must be surface ground flat to within 0.03 mm (0.001 in.) and perpendicular to the reference axis The third source of alignment error is specimen insertion Much of the fixture-design complexity revolves around the preservation of specimen alignment in the test machine

Because of the end loading, severe stress concentrations exist at the loaded ends For the untabbed specimens used to measure modulus, this is not considered a problem because the central region is far away from the loaded edges For the tabbed strength specimen, the use of tabs prevents failure at the loaded ends For valid strength tests, failure modes and strength values similar to those seen with other compression test methods have been observed (Ref 10) Specimen fabrication, bonding of end tabs, and testing are equivalent to those specified for the IITRI test

A number of studies have been conducted exploring the use of [0/90°] laminate configurations to obtain better strength results (Ref 24, 25) Results have shown that the highest strengths and lowest variability are measured using [90/02/90°]s laminates Work by Welsh and Adams (Ref 26) confirmed the benefit of using [90/0°] laminate subgroupings to achieve higher strengths for either IITRI or modified ASTM D 695 test configurations This is one area where serious consideration is being given to develop a standard based on laminate tests for determination of lamina properties

Extending this concept, Adams and Welsh (Ref 27) have developed a new test method that uses combined loading to measure compression strength The method uses both shear and end loading to test the [90/0°] laminate specimen and has been shown to produce results that are consistent with properly conducted tests using existing ASTM methods An advantage of the method is the ease of testing and very consistent (low scatter) results The method is currently under review for ASTM standardization

Flexure Testing

Flexure, or bending, tests have emerged because of the simplicity of specimen preparation and testing Figure

15 shows stresses developed in the three-point flexure test It is readily observed that gripping, buckling, and end-tabbing are not issues for this test and that testing is very simple Analysis of the test reveals that the bending moment is balanced by a distribution of normal stress, σx The top side is under compression while the bottom surface is under tension Theoretically, the neutral axis is identically at the midplane where the shear stress, τxy, is maximum (see, e.g., Ref 28) In practice, differences in the tension and compression moduli exhibited by many composites invalidate this assumption, moving the neutral axis off the midplane of the beam and, unless corrected, making standard data reduction calculations erroneous Depending on the span-to-

thickness ratio (L/h) and the strengths in tension, compression, and shear, the beam may fail in tension,

compression, or shear It can be shown that shear failure occurs at very short spans, and that failure in tension and compression occurs for longer spans The three-point bend test for interlaminar shear strength determination is discussed in the section “Shear Testing” in this article In this section it is assumed that the beam span is long enough to promote failure in tension or compression Flexure tests are not recommended for determination of design data because deformation and failure of the material occurs under a combined stress state, and stress concentrations at load introduction points and supports may trigger failure (Ref 29) Consequently, the flexural modulus and strength are combinations of the corresponding tensile and compressive properties of the material The flexure tests, however, may be used as a reference to previously obtained tensile and compressive data

Fig 15 Illustration of bending and shear stresses in the three-point flexure test

The flexure test is generally limited to unidirectional materials with the fibers aligned parallel or perpendicular

to the beam axis For laminates, interpretation of the results requires laminated beam theory (Ref 30)

Flexure Test Methods Flexure testing utilizes the three-point or four-point methods (Fig 16) The four-point flexure test is commonly performed with load noses located at the quarter-span points (Fig 16b) but is

sometimes configured with the loading at the third span (L/3) locations Flexure tests are most commonly used

to generate flexural modulus and strength for the purpose of quality control Proper testing and data reduction

may render the test data of more value than just a quality check The span-to-thickness ratio, L/h, should be

large for materials with a large ratio between the tensile and interlaminar shear strengths For glass/epoxy tested

along the fiber direction and graphite/epoxy tested perpendicular to the fiber direction, L/h = 16 is appropriate For high tensile strength composites such as graphite/epoxy tested along the fiber direction, L/h = 32 is

recommended (Ref 4) The diameter of the load noses and support pins should, according to ASTM standard D

790, be at least 6.4 mm (0.25 in.) The maximum diameter is three times the specimen thickness

Fig 16 Schematic of flexure tests (a) Three-point loading (b) Four-point loading

Specimen Preparation and Flexure Testing The specimen is nominally 130 mm (5.1 in.) long, although longer span lengths would require longer specimens (see ASTM standard D 790) Although the ASTM standard D 790 does not indicate tolerances for the width, the ASTM D 3039 standard for tension testing specifies variations within ±1%, which would amount to ±0.13 mm (±0.005 in.) for the flexure specimen The accuracy of the total

length is less critical Typically, 0° specimens use 12 to 16 plies, and 90° specimens use 16 to 30 plies (0.127

mm or 0.005 in., ply thickness)

Measure the cross-sectional dimensions of the test specimens to obtain an average of six measurements and check for parallelism of the edges If a strain gage is to be used, bond one longitudinal strain gage at the geometrical center on the intended tension side of the specimen The flexure fixture should be mounted in a properly aligned and calibrated test fixture Determine the support span according to the beam thickness and material specifications as discussed previously, and set the support and load spans within 1% of their desired

values The crosshead rate, , should be selected so that the maximum strain rate (for a surface fiber) is =

0.01/min For both the three-point and four-point methods (at quarter points), this leads to (Ref 4):

Commonly, a crosshead rate in the range 1 to 5 mm/min (0.05 to 0.2 in./min) is selected For three-point loading, place the specimen in the fixture with the strain gage on the tension side centered directly under the central loading pin For four-point loading, the strain gage may be on either the top (compression) or bottom (tension) surface If the vertical beam deflection, δ, is measured, place a calibrated linear voltage differential transformer (LVDT) or extensometer at the beam midspan The vertical displacement may be approximated as the crosshead travel if the additional displacement due to the machine compliance is subtracted The strain or displacement readings may be recorded continuously or at discrete load intervals If discrete data are recorded, take the load and strain/displacement readings at small load intervals with at least 25 points in the linear response region A total of at least 40 points is desirable for description of the response up to failure

Data Reduction for Three-Point Loading The flexural stress at the specimen surface at beam midspan is calculated from:

σ = 3PL/2bh2

(Eq 2)

where P is the applied load, L is the span, b is the specimen width, and h is the specimen thickness

If specimens with greater than a 16 to 1 span-to-thickness ratio are used, a correction factor must be used to compensate for the geometric nonlinearity caused by the large deflections that occur By calculating the stress from the load data and plotting it versus the strain gage readings, a stress-strain plot for flexure can be

constructed, and flexural modulus, Ef, is evaluated from the initial slope of the curve, and flexural strength, Xf

from the maximum stress For the case that the specimen is not strain gaged, the flexural modulus is determined from the deflection δ according to (Ref 30):

(Eq 3)

where G xz is the interlaminar shear modulus in the x-z plane The last term in Eq 3 is a shear correction factor

that may be significant for high axial modulus specimens with a low interlaminar shear modulus, that is, beams with the fibers along the beam axis

For beams with the fibers perpendicular to the beam axis, shear deformation is generally not significant in bending, and the flexural modulus is given by the first term only:

Fig 17 Illustration of graphical method to determine flexural modulus free of influence of shear deformation

Data Reduction for Four-Point Loading (Quarter Point) The flexural stress at the specimen surface in the region between the inner load noses is given by:

σ = 3PL/4bh2

(Eq 5)

If a strain gage is used, calculation of the stress from the load data and plotting stress versus strain allow determination of flexural modulus and strength exactly as previously outlined for three-point loading If load and midspan deflection are measured, the flexural modulus is evaluated from:

(Eq 6)

where the symbols have the meaning as in Eq 3

If the beam deflection is measured at the quarter points, which would be equal to the crosshead travel compensated for test machine compliance, the flexural modulus is (Ref 30):

A shear test is performed to determine shear modulus and shear strength of a composite material The response

of a material subjected to shear is commonly nonlinear, and full characterization requires the entire stress-strain curve The tests may be grouped as in-plane tests that relate to the structural response of plates and shells, and interlaminar tests that relate to the behavior of local details such as joints Figure 18 defines in-plane shear stress, τxy, and out-of-plane (interlaminar) shear stresses τxz and τyz The corresponding shear moduli are denoted

by Gxy, Gxz and Gyz and the corresponding shear strengths, S6, S5 and S4, according to contracted stress notation

Fig 18 Definition of shear stress components τxy is the in-plane shear stress, and τxz and τyz are plane shear stresses

out-of-The ideal shear test method should provide a region of pure, uniform shear stress It is also required that the shear stress and strain can be straightforwardly evaluated from the applied load and deformation measurements The major difficulty in designing shear tests for composite materials is attaining a uniform state of pure shear stress in the test section Many shear test methods exist as documented by Chatterjee et al (Ref 10) Chatterjee

et al (Ref 10) ranked the various shear test methods using the same criteria as for the previously discussed compression test methods Table 3 presents the various shear tests and their rankings In this section, only the methods with the highest ranking (1) are discussed except for the [±45°]ns tension test because of its popularity

in industry

Table 3 Shear test methods for fiber-reinforced composites

2

Iosipescu, ASTM D 5379 Acceptable Correction factor and measurement of all strains with

rosettes and back-to-back gages may be required

1

Rail shear rectangular or

parallelogram, ASTM

Guide D 4255

Controlled 0° test required 90° tests appear to yield good data

Measurement of all strains may be required for [0/90°] lay-ups

1

Torsion-circular bar Acceptable, but ultimate strains appear to be lower than Iosipescu and

rail shear Data reduction procedure is simple but needs approval from composites community Machining required Damage progression needs study

2

Torsion-rectangular bar Acceptable, but ultimate strains appear to be lower than Iosipescu and

rail shear Data reduction procedure is complicated Damage progression needs study

1

Off-axis tension Acceptable only for modulus; correction factors based on aspect ratio

required

… Picture frame or cross May be acceptable but more studies required Tests are highly …

Iosipescu, ASTM D 5379 Thick specimens with bonded layers required Appears to be the best

choice for unidirectional and fabric composites Laminates may suffer from free-edge effects because of small width

span-to-is all 0° lay-up, and the beam span-to-is usually 6.35 mm (0.25 in.) wide and between 2 and 3.5 mm (0.08 and 0.14 in.)

thick The specimen length should be approximately 4h + 16 mm (4h + 0.6 in.), where h is the thickness The

apparent shear strength is calculated as:

Fig 19 ASTM D 3518 [±45°] ns tension test specimen for evaluation of in-plane shear stress-strain response of unidirectional composites

Determination of the lamina shear properties from the tension test requires stress analysis of the [±45°]nsspecimen Using laminated plate theory, Rosen (Ref 31) showed that the shear stress τ12 (see Fig 19), is simply given by:

where σx is the axial stress (P/A), and the shear strain is given by: