Volume 08 - Mechanical Testing and Evaluation Part 13 pdf

Cyclic loading, though not required to induce growth in glasses and many ceramics, tends to accelerate fatigue crack growth.. “Standard Test Method for Determination of Slow Crack Growth

Fatigue Testing of Brittle Solids

J.A Salem, Glenn Research Center at Lewis Field; M.G Jenkins, University of Washington

Summary

Fatigue testing of ceramics and glasses is performed by either indirect or direct methods Indirect or strength methods employ smooth tensile or flexure specimens and infer the fatigue parameters from strength measurements without crack length measurements Direct methods employ either long cracks or short cracks, and the crack length is measured by observation of the crack or by inference from devices such as strain gages and electrical resistance grids Long crack test specimens include fracture mechanics specimens such as the DT, DCB, CT, and SEPB Short crack methods employ surface cracks formed by indentation, or surface cracks that develop naturally on the surface of a smooth test specimen Structural ceramic and glass components that are designed to have long lives will fail from small cracks developed over long periods of time The cracks will develop from either inherent processing flaws or from damage generated in component machining and handling (e.g., machining cracks) Cyclic loading, though not required to induce growth in glasses and many ceramics, tends to accelerate fatigue crack growth Thus the measurement of fatigue parameters should be done with tests employing realistic crack sizes, environments, and the applicable load histories As a result, the development of standardized static and cyclic fatigue test methods has revolved around the use of small, inherent flaws

Fatigue Testing of Brittle Solids

J.A Salem, Glenn Research Center at Lewis Field; M.G Jenkins, University of Washington

4 R.E Mould and R.D Southwick, Strength and Static Fatigue of Abraded Glass under Controlled

Ambient Conditions, Part II: Effect of Various Abrasions and the Universal Fatigue Curve, J Am Ceram Soc., Vol 42, 1959, p 582–592

5 S.M Weiderhorn, Influence of Water Vapor on Crack Propagation in Soda-Lime Glass, J Am Ceram Soc., Vol 50, 1967, p 407–414

6 A.G Evans and F.F Lange, Crack Propagation and Fracture in Silicon Carbide, J Mater Sci., Vol 10

(No 10), 1975, p 1659–1664

7 J.E Ritter and J.N Humenik, Static and Dynamic Fatigue of Polycrystalline Alumina, J Mater Sci.,

Vol 14 (No 3), 1979, P 626–632

8 S.M Weiderhorn and L.H Boltz, Stress Corrosion and Static Fatigue of Glass, J Am Ceram Soc., Vol

11 T Fett, K Germerdonk, A Grossmuller, K Keller, and D Munz, Subcritical Crack Growth and

Threshold in Borosilicate Glass, J Mater Sci., Vol 26, 1991, p 253–257

12 S.M Wiederhorn, Moisture Assisted Crack Growth in Ceramics, Int J Fract Mech., Vol 4 (No 2),

1968, p 171–177

13 S.M Wiederhorn, B.J Hockey, and D.E Roberts, Effect of Temperature on the Fracture of Sapphire,

Philos Mag., Vol 28 (No 4), 1973, p 783–796

14 T.A Michalske, B.C Bunker, and S.W Freiman, Stress Corrosion of Ionic and Mixed Ionic/Covalent

Solids, J Am Ceram Soc., Vol 69 (No 10), 1986, p 721–724

15 DD ENV 843-3 Advanced Technical Ceramics—Monolithic Ceramics—Mechanical Properties at Room Temperature, Part 3: Determination of Subcritical Crack Growth Parameters from Constant Stressing Rate Flexural Strength Tests, British Standards Institution, London, 1997

16 “Testing Method for Bending Fatigue of Fine Ceramics,” JIS R 1621, Japanese Standards Association, Tokyo, Japan, 1996

17 “Standard Test Method for Determination of Slow Crack Growth Parameters of Advanced Ceramics by

Constant Stress-Rate Flexural Testing at Ambient Temperature,” C 1368, Annual Book of ASTM Standards, ASTM, Vol 15.01, 1999, p 706–714

18 “Test Methods for Static Bending Fatigue of Fine Ceramics,” JIS R 1632, Japanese Standards Association, Tokyo, Japan, Dec 1998

19 Standard Practice for Constant-Amplitude, Axial Tension-Tension Cyclic Fatigue of Advanced

Ceramics at Ambient Temperatures,” C1361, Annual Book of ASTM Standards, ASTM

20 J.A Salem, N.N Nemeth, L.M Powers, and S.R Choi, Reliability Analysis of Uniaxially Ground

Brittle Materials, J Eng Gas Turbines Power (Trans ASME), Vol 118, 1996, p 863–871

21 D.H Roach and A.R Cooper, “Etching of Soda Lime Glass-Another Look,” in the third proceedings of

a symposium sponsored by the Etel Institute for Silicate Research/The University of Toledo and the Northwestern Ohio Section of the Am Ceram Soc., W Kneller, Ed., March 1983, p 1–7

22 F Gigu, Cyclic Fatigue of Polycrystalline Alumina in Direct Push-Pull, J Mater Sci Lett., Vol 13 (No

6), 1978, p 1357–1361

23 M.V Swain, Lifetime Prediction of Ceramic Materials, Mater Forum, Vol 9 (No 1–2), 1st and 2nd

Quarter 1986, p 34–44

24 H Kawakubo and K Komeya, Static and Cyclic Fatigue Behavior of a Sintered Silicon Nitride at Room

Temperature, J Am Ceram Soc., Vol 70 (No 6), 1987, p 400–405

25 R.H Dauskardt, W Yu, and R.O Ritchie, Fatigue Crack Propagation in Transformation Toughened

Zirconia, J Am Ceram Soc., Vol 70 (No 10), 1987, p C-248–C-252

26 G Grathwohl, Fatigue of Ceramics under Cyclic Loading, Mater Sci Technol., Vol 19 (No 4), April

1988, p 113–124 (in German)

27 M.J Reece, F Guiu, and M.F.R Sammur, Cyclic Fatigue Crack Propagation in Alumina under Direct

Tension-compression Loading, J Am Ceram Soc., Vol 72 (No 2), 1989, p 348–352

28 Y Mutoh, M Takahashi, T Oikawa, and H Okamoto, Fatigue Crack Growth of Long and Short Cracks

in Silicon Nitride, Fatigue of Advanced Materials, R.O Ritchie, R.H Dauskardt, and B.N Cox, Ed.,

Material and Component Engineering Publications, Ltd., Edgbaston, U.K., 1991, p 211–225

29 S Horibe and H Hirahara, Cyclic Fatigue of Ceramics Materials: Influence of Crack Path and Fatigue

Mechanisms, Acta Metall Mater., Vol 39 (No 6), 1991, p 1309–1317

30 M Okazaki, A.J McEvily, and T Tanaka, On the Mechanism of Fatigue Crack Growth in Silicon

Nitride, Metall Trans A, Vol 22A, 1991, p 1425–1434

31 T Tanaka, N Okabe, H Nakayama, and Y Ishimaru, Fatigue Crack Growth of Silicon Nitride with

Crack Wedging by Fine Fragments, Fatigue Fract Eng Mater Struct., Vol 17 (No 7), 1992, p 643–

653

32 R.O Ritchie, C.J Gilbert, and J.M McNaney, Mechanics and Mechanisms of Fatigue Damage and

Crack Growth in Advanced Materials, Int J Solids Struct., Vol 37, 2000, p 311–329

33 R Dauskardt, Cyclic Fatigue-Crack Growth in Grain Bridging Ceramics, J Eng Mater Technol (Trans ASME), Vol 115, 1993, p 115–251

34 T.A Michalske and B.C Bunker, Slow Fracture Based on Strained Silicate Structures, J Appl Phys.,

Vol 56 (No 10), 1984, p 2686–2694

35 T Yishio and K Oda, Aqueous Corrosion and Pit Formation of Si3N4 under Hydrothermal Conditions,

Ceram Trans., Vol 10, 1990, p 367–386

36 M.K Ferber, H.T Lin, and J Keiser, Oxidation Behavior of Non-Oxide Ceramics in a High-Pressure,

High-Temperature Steam Environment, Mechanical, Thermal and Environmental Testing and Performance of Ceramic Composites and Components, STP 1392, M.G Jenkins, E Lara-Curzio, and S

Gonczy, Ed., ASTM, 2000

37 G Vekinis, M.F Ashby, and P.W Beaumont, R-Curve Behaviour of AP2O3 Ceramics, Acta Metall Mater., Vol 38 (No 6), 1990, p 1151–1162

38 D.A Krohn and D.P.H Hasselman, Static and Cyclic Fatigue Behavior of a Polycrystalline Alumina, J

Am Ceram Soc., Vol 55 (No 4), 1972, p 208–211

39 M Masuda, T Soma, M Matsui, and I Oda, Fatigue of Ceramics, Part 1: Fatigue Behavior of Sintered

Silicon Nitride under Tension-Compression Cyclic Stress, J Ceram Soc Jpn Int Ed., Vol 96, 1988, p

275–280

40 A Steffen, R.H Dauskardt, and R.O Ritchie, Cyclic Fatigue Life and Crack Growth Behavior of

Microstructural Small Cracks in Magnesia-Partially-Stabilized Zirconia Ceramics, J Am Ceram Soc.,

Vol 74 (No 6), 1991, p 1259–1268

41 S.M Wiederhorn and J.E Ritter, Application of Fracture Mechanics Concepts to Structural Ceramics,

Fracture Mechanics Applied to Brittle Materials, STP 678, S.W Frieman, Ed., ASTM, 1979, p 202–

214

42 K Jakus, J.E Ritter, and J.M Sullivan, Dependency of Fatigue Predictions on the Form of the Crack

Velocity Equation, J Am Ceram Soc., Vol 64 (No 6), 1981, p 372–374

43 S.M Weiderhorn, Prevention of Failure in Glass by Proof-Testing, J Am Ceram Soc., Vol 56 (No 4),

1973, p 227–228

44 G Evans and S.M Weiderhorn, Proof Testing of Ceramic Materials-An Analytical Basis for Failure

Prediction, In J Fract., Vol 10 (No 3), 1974, p 379–392

45 A.G Evans and E.R Fuller, Crack Propagation in Ceramic Materials under Cyclic Loading Conditions,

Metall Trans A, Vol 5 (No 1), 1974, p 27–33

46 B.J.S Wilkins and L.A Simpson, Errors in Estimating the Minimum Time-to-Failure in Glass, J Am Ceram Soc.—Discussion and Notes, Dec 1974, p 505

47 W.P Minnear and R.C Bradt, (K-V) Diagrams for Ceramic Materials, J Am Ceram Soc.—Discussion and Notes, Vol 58 (No 7–8), 1975, p 345–346

48 G Sines, Rationalized Crack Growth and Time-to-Fracture of Brittle Materials, Am Ceram Soc.— Discussion and Notes, Vol 59 (No 7–8), 1976, p 370–371

49 S Hillig and R.J Charles, Surfaces, Stress-Dependent Surface Reactions and Strength, High Strength Materials, V.F Zackay, Ed., John Wiley & Sons, 1965, p 682–705

50 B.R Lawn, An Atmospheric Model of Kinetic Crack Growth in Brittle Solids, J Mater Sci., Vol 10,

1975, p 469–480

51 E.M Lenoe and D.M Neil, “Assessment of Strength Probability-Time Relationships in Ceramics,” AMMRC Tech Report 75-13, ARPA Order No 2181, Army Mater and Mech Res Center, Watertown, MA, 1975

52 “Standard Test Method for Plane Strain Fracture Toughness of Metallic Materials,” E 399, Annual Book

of ASTM Standards, Vol 03.01, ASTM, 1998

53 W.G Clark, Jr., Fracture Mechanics and Nondestructive Testing of Brittle Materials, J Eng Ind (Trans ASME), Feb 1972, p 291–298

54 J.N Masters, “Cyclic and Sustained Load Flow Growth Characteristics in 6Al-4V Titanium,” CR-92231, NASA, 1968

NASA-55 J.E Ritter, Jr., K Jakus, and D.S Cooke, Predicting Failure of Optical Glass Fibers, Environmental

Degradation of Engineering in Aggressive Environments, Proceedings of the 2 nd International Conference on Environmental Degradation of Engineering Materials, Va Polytech Inst and State

Univ., NASA Lewis Res Center, NACE, and Va Polytech Inst., Lab for the Study of Environ Degrad

of Eng Mater., 1981, p 565–575

56 “Test Method for Flexural Strength (Modulus of Rupture) of Fine Ceramics,” JIS R 1601, Japanese Standards Association, Tokyo, Japan, 1995

57 J.E Ritter, Jr., Assessment of Reliability of Ceramic Materials, Fracture Mechanics of Ceramics, Vol 6,

R.C Bradt et al., Ed., Plenum Press, 1983, p 227–251

58 J.E Ritter, Jr., Engineering Design and Fatigue Failure of Brittle Materials, Fracture Mechanics of Ceramics, Vol 4, R.C Bradt et al., Ed., Plenum Press, 1978, p 667–685

59 E.B Haugen, Probabilistic Mechanical Design, John Wiley & Sons, 1980

60 N.N Nemeth, L.M Powers, L.A Janosik, and J.P Gyekenyesi, “Durability Evaluation of Ceramic Components Using CARES/LIFE,” ASME Paper 94-GT-362 and NASA-TM 106475, ASME/IGTI Gas Turbine Conference, June 1994

61 A.D Peralta, D.C Wu, P.J Brehm, J.C Cuccio, and M.N Menon, Strength Prediction of Ceramic

Components under Complex Stress States, Proceedings of the International Gas Turbine and Aeroengine Congress and Exposition, 5–8 June 1995 (Houston, TX), American Society of Mechanical

Engineers, 1995; Allied Signal Document 31-12637, 1995

62 “Fatigue Crack Growth Program NASA/Flagro 2.0,” JSC 22267A, NASA Johnson Space Flight Center, May 1994

63 J.E Ritter, N Bandyopadhyay, and K Jakus, Am Ceram Soc Bull., Vol 60, 1981, p 798

64 “Standard Test method for Flexural Strength of Advanced Ceramics at Ambient Temperature,” C 1161,

Annual Book of ASTM Standards, ASTM, Vol 15.01, 1999, p 309–315

65 H.A Linders and B Caspers, Method for Determining Life Diagrams of Mechanoceramic Materials

DKG/DKM-Joint Experiment, Ceramics in Science and Practice, Mechanical Properties of Ceramic Construction Materials, G Grathwohl, Ed., DGM Information Association, Verlag, Germany, 1993, p

191–195 (in German)

66 S Freiman, “Pre-Standardization and Standardization Activities in the USA in Mechanical Property Testing of Advanced Structural Ceramics,” presentation at the 7th CIMTEC World Ceramics Congress, Montecatini Terme, Italy, 23 June 1990

67 S.W Freiman and E.R Fuller, Versailles Project on Advanced Materials and Standards, VAMAS TWA

3 Bulletin 8, July 1988

68 W.P Byrn and R Morrell, “Results of the UK Interlaboratory Strength Test Exercise,” NPL Report DMM (D) 72, National Physical Laboratory, Teddington, Middelsex, U.K., Crown Copyright, Dec 1990

69 “Standard Test Method for Tensile Strength of Monolithic Advanced Ceramics at Ambient

Temperatures,” C 1273, Annual Book of ASTM Standards, Vol 15.01, ASTM, 1999, p 671–678

70 Cyclic Fatigue Testing of Silicon Nitride, Ceramics (newsletter), Ceramics Division of IIT Research Institute, Chicago, IL, 42, March 1978; Ceram Eng and Sci Proc of the 18th Annual Conference on Composites and Advanced Ceram Mater.-A, Part 1 of 2, 9–14 Jan 1994, Vol 15 (No 4), July–Aug 1994

(Cocoa Beach, FL), Am Ceram Soc., Westerville, OH, 1994, p 32–39

71 H.N Ko, Cyclic Fatigue Behavior of Ceramics under Rotary Bending, Materials Research Society International Meeting on Advanced Materials, Materials Research Society, Vol 5, 1989, p 43–48

72 H.N Ko, Cyclic Fatigue Behavior of Sintered Al2O3 under Rotary Bending, J Mater Sci Lett., Vol 6,

1987, p 801–805

73 R Kossowsky, “Cyclic Fatigue of Hot Pressed Silicon Nitride,” J Am Ceram Soc., Vol 56, 1973, p 10,

76 K Ohya, K Ogura, and M Takatsu, Cyclic Fatigue Testing Device for Fine Ceramics by Using

Piezo-Electric Bimorph Actuator, J Soc Mater Sci., Jpn., Vol 38 (No 424), 1989, p 44–48

77 J.A Salem, L.J Ghosn, and M.G Jenkins, A Strain Gage Technique to Measure Stable Crack Extension

in Ceramics, Post Conference Proceedings of the 1997 SEM Spring Conference on Experimental Mechanics, Society for Experimental Mechanics, Bethel, CT, 1997, p 1–8

78 J.A Salem, L.J Ghosn, and M.G Jenkins, Back-Face Strain as a Method for Monitoring Stable Crack

Extension in Ceramics, Ceram Eng Sci Proc., Vol 19 (No 3), 1998, p 587–594

79 J.O Outwater and D.J Gerry, “On the Fracture Energy of Glass,” NRL Interim Contract Report, Contract NONR 3219(01)(x), AD 640848, University of Vermont, Burlington, VT, Aug 1966

80 J.O Outwater and D.J Gerry, “On the Fracture Energy, Rehealing Velocity and Fracture Energy of Cast Epoxy Resin,” Paper 13-D, presented at the 22nd Society of Plastic Industry Conference, 1967; also, J Adhes., Vol 1, 1969, p 290–298

81 G.W Weidmann and D.G Holloway, Slow Crack Propagation in Glass, Phys Chem Glasses, Vol 15

(No 5), Oct 1974, p 116–122

82 C.D Beacham, J.A Kies, and B.F Brown, A Constant K Specimen for Stress Corrosion Cracking

Testing, Mater Res Standards, Vol 11, 1970, p 30

83 A.G Evans, Method For Evaluating the Time-Dependent Failure Characteristics of Brittle Material and

Its Application to Polycrystalline Alumina, J Mater Sci., Vol 7 (No 10), 1972, p 1137–1146

84 A.G Evans and S.M Wiederhorn, Crack Propagation and Failure Prediction in Silicon Nitride at

Elevated Temperatures, J Mater Sci., Vol 9, 1974, p 270–278

85 A.G Evans, L.R Russel, and D.W Richerson, Slow Crack Growth in Ceramic Materials at Elevated

Temperatures, Metall Trans A, Vol 6A (No 14), 1975, p 707–716

86 K.R McKinney and H.L Smith, Method of Studying Subcritical Cracking of Opaque Materials, J Am Ceram Soc., Vol 56 (No 1), 1973, p 30–32

87 P.N Thornby, Experimental Errors in Estimating Times to Failures, J Am Ceram Soc., Vol 59 (No

11–12), 1976, p 514–517

88 E.R Fuller, Jr., an Evaluation of Double Torsion Testing: Analysis, Fracture Mechanics Applied to Brittle Materials, STP 678, S.W Frieman, Ed., ASTM, 1979, p 3–18

89 B.J Pletka, E.R Fuller, Jr., and B.G Koepke, An Evaluation of Double Torsion Testing: Experimental,

Fracture Mechanics Applied to Brittle Materials, STP 678, S.W Frieman, Ed., ASTM, 1979, p 19–37

90 C.G Annis and J.S Cargill, Modified Double Torsion Method for Measuring Crack Velocity in NC-132

Si3N4, Fracture Mechanics of Ceramics, Vol 4, R.C Bradt et al., Ed., Plenum Press, 1978, p 737–744

91 D.P Williams and A.G Evans, A Simple Method for Studying Slow Crack Growth, J Test Eval., Vol

1 (No 4), 1973, p 264–270

92 K.R Linger and D.G Holloway, Fracture Energy of Glass, Philos Mag., Vol 18 (No 156), 1968, p

1269–1280

93 J.A Salem, M.G Jenkins, M.K Ferber, and J.L Shannon, Jr., Effects of Pre-Cracking Method on

Fracture Properties of Alumina, Proceedings of Society of Experimental Mechanics Conference on Experimental Mechanics, 10–13 June 1991 (Milwaukee, WI), Society for Experimental Mechanics,

Bethel, CT, 1991, p 762–769

94 S.W Freiman, D.R Mulville, and P.W Mast, J Mater Sci., Vol 8 (No 11), 1973, p 1527–1533

95 S Mostovoy, P.B Crosley, and E.J Ripling, Use of Crack-Line-Loaded Specimens for Measuring

Plane-Strain Fracture Toughness, J Mat., Vol 2 (No 3), Sept 1967, p 661–681

96 A.G Evans and H Johnson, The Fracture Stress and Its Dependence on Slow Crack Growth, J Mater Sci., Vol 10, 1975, p 214–222

97 T Sadahiro, Transverses Rupture Strength and Fracture Toughness of WC-Co Alloys, J Jpn Inst Met.,

Vol 45, 1981, p 291–295

98 D.J Martin, K.W Davido, and W.D Scott, Slow Crack Growth Measurement Using an Electric Grid,

Am Ceram Soc Bull., Vol 65 (No 7), 1986, p 1052–1156

99 P.K Liaw, H.R Hartmann, and W.A Lodgson, A New Transducer to Monitor Fatigue Crack

Propagation, J Test Eval., Vol 11 (No 3), 1983, p 202–207

100 R.H Dauskardt, R.O Ritchie, J.K Takemoto, and A.M Brendzel, Cyclic Fatigue in Pyrolytic Carbon-Coated Graphite Mechanical Heart-Valve Prostheses: Role of Small Cracks in Life Prediction,

J Biomed Mater Res., Vole 28, 1994, p 791–804

101 R.H Dauskardt, M.R James, J.R Porter, and R.O Ritchie, Cyclic Fatigue-Crack Growth in a

SiC-Whisker-Reinforced Alumina Ceramic Composite: Long- and Small-Crack Behavior, J Am Ceram Soc., Vol 75 (No 4), 1992, p 759–771

102 “Standard Test Methods for Fracture Toughness of Advanced Ceramics,” C 1421, Annual Book

of ASTM Standards, ASTM, Vol 15.01, 2000, p 631–662

103 L Ewart and S Suresh, Dynamic Fatigue Crack Growth in Polycrystalline Alumina under

Cyclic Compressive Loads, J Mater Sci., Vol 5, 1986, p 774–778

104 L Ewart and S Suresh, Crack Propagation in Ceramics under Cyclic Loads, J Mater Sci., Vol

22, 1987, p 1173–1192

105 F Sudreau, C Olagnon, and G Fantozzi, Lifetime Prediction of Ceramics: Importance of Test

Method, Ceram Int., Vol 10, 1994, p 125–135

106 E.M Rockar and B.J Pletka, Fracture Mechanics of Alumina in a Simulated Biological

Environment, Fracture Mechanics of Ceramics, Vol 4, R.C Bradt et al., Ed., Plenum Press, 1978, p

725–735

107 Pletka and Wiederhorn, Subcritical Crack Growth in Glass-Ceramics, Fracture Mechanics of Ceramics, Vol 4, R.C Bradt et al., Ed., Plenum Press, 1978, p 745–759

Multiaxial Fatigue Testing

Yukitaka Murakami, Kyushu University, Japan

The influence of loading history and phases is also a topic of recent studies Cylindrical specimens or tubular specimens are mostly used for these studies Perhaps the most important recent topic in multiaxial fatigue studies is the behavior of cracks The threshold condition of macrocracks and crack propagation paths in large structures have been investigated by many researchers

Although cracks mostly propagate by mode I (the opening tension mode), even under mixed mode loading, the propagation behavior is affected by mixed mode loadings due to various factors such as the size of the yield zone at the crack tip, crack closure, and friction between crack surfaces

On the other hand, a crack seldom grows by pure mode II (sliding or shear mode) or mode III (tearing mode) in real structures Some examples of mode II fatigue are contact fatigue damage in rolls of steelmaking mills, contact fatigue of rails and bearings, and fretting fatigue In these cases, the criteria for the threshold condition for mode II cracks and the resistance to mode II crack growth are needed Crack growth by mode III is the form studied in the torsional fatigue test of circumferentially notched specimens Thus, the fatigue testing method, specimen geometries, and stress intensity factors are all important factors in the study of multiaxial fatigue Many factors of multiaxiality make the testing method more complicated than mode I fatigue testing, and, accordingly, many researchers, working independently, have developed their own original methods This article first explains stress states of combined stress and stress fields near crack tips and then describes various multiaxial fatigue testing methods

Multiaxial Fatigue Testing

Yukitaka Murakami, Kyushu University, Japan

Stress States

Most engineering designs and/or failure analyses involve three-dimensional combinations of stress and strain (multiaxiality) in the vicinity of surfaces and notches, which can be limiting in fatigue applications This section provides a brief review of these stress states Additional information is provided in the article “Multiaxial

Fatigue Strength” in Fatigue and Fracture, Volume 19 of Asm Handbook

Two dimensional stress states without cracking are defined in Fig 1, where the basic relations are:

(Eq 1)

where σ1, σ2 are the principal stresses σx = σ0 and σy = -σ0 in Fig 1(d), and this is equivalent to the case shown

in Fig 1(b) if τxy = σ0

Fig 1 Two-dimensional stress states without cracking

The yield criterion or yield stress, σY, is:

Stress states at the tip of a crack in combined mode I and mode II are defined by stress-intensity factors KI is the mode I stress intensity factor, and KII is the mode II stress intensity factor Radial stress (σr), normal stress

(σθ, and shear stress (τrθ ) in polar coordinate (r, θ) in the vicinity of the crack tip are given as follows (Fig 2):

(Eq 4)

(Eq 5)

(Eq 6)

Fig 2 Stress state near a crack in a polar coordinate

The direction (θ0) where σθ has the maximum value is given by:

(Eq 8)

This equation gives θ0 = ± 70.5° for pure mode II (KI = 0)

The stress intensity factor that prescribes σθ is defined by:

(Eq 9)

The maximum value (Kθmax) of Kθ for pure mode II is derived, substituting θ0 = ±70.5° into Eq 9 Thus:

Stress State at the Tip of a Crack in Mode III If there is a semielliptical surface crack and the crack is subjected

to pure shear (Fig 3), the condition at the deepest point of crack front, A, is pure mode III, and the condition at surface corner points, B and C, is pure mode II, which means the branching angle at B and C by mode I crack

growth is 70.5° under reversed torsion (Ref 1) (There have been some discussions among researchers about the irregular singularity close to the corner point where a crack meets the free surface It is known that a mode I

stress component in tension has a singularity different from - If KIII ≠ 0 at the surface point, it means that there exists a shear stressb τyz on the free surface Therefore, KIII must be zero at points B and C.)

Fig 3 A semielliptical surface crack under shear A, pure mode III; B, C, pure mode II

Reference cited in this section

1 Y Murakami and K Takahashi, Torsional Fatigue of a Medium Carbon Steel Containing an Initial Small Surface Crack Introduced by Tension-Compression Fatigue: Crack Branching, Non-Propagation

and Fatigue Limit, Fatigue Fract Eng Mater Struct., Vol 21, 1998, p 1473–1484

Multiaxial Fatigue Testing

Yukitaka Murakami, Kyushu University, Japan

Testing of Cylindrical Specimens

Torsion-Rotating Bending Fatigue In a classical type of torsion-rotating bending fatigue test, cylindrical specimens similar to those for rotating bending fatigue are used (Ref 2) A static twisting moment is applied through the axis of the specimen In this type of machine, the normal stress in the rotating test piece is continuously varied between positive and negative stress of equal magnitudes Furthermore, the steady shearing stress is simultaneously induced in the specimen by connecting the testing machine with an electric absorption dynamometer, which consists of a small direct-current dynamo placed on an iron frame suspended by ball bearing The specimen geometry for this type of fatigue testing is essentially similar to those for rotating bending except for the special grip shape This type of testing machine has still been used in recent studies (Ref 3) In another classical test, bending moment is coupled with twisting moment, which is loaded by the reversed motion of a fly wheel The specimen geometry for this test is shown in Fig 4

Fig 4 Specimen for conventional reversed torsion test Dimensions are in mm Source: Ref 4

Torsion Coupled with Tension Compression Biaxial fatigue testing machines of the closed-loop type in which torsion can be coupled with tension-compression are now commonly used In the closed-loop type of testing machine, torsion and tension-compression can be loaded independently in phase or out of phase Figure 5 shows a biaxial fatigue testing machine of this type Figure 6 shows the extensometer used to measure axial and angular displacement A cylindrical specimen (Fig 7) is the standard geometry for this type of testing machine

Fig 5 Biaxial fatigue testing machine Courtesy of Instron Corporation

Fig 6 Biaxial extensometer for simultaneous measurement of axial and torsional strain (a) Adjustment screws and clamps (b) Extensometer mounted on specimen Courtesy Instron Corporation

Fig 7 Specimen for biaxial fatigue test Dimensions are in mm Source: Ref 1

Triaxial Fatigue Testing In addition to torsion and tension-compression stresses, internal or external pressures can be applied to the tubular specimen (Fig 8) Fatigue behavior in a complex three-dimensional stress condition then can be studied However, the operating system of this type of testing machines is very complicated and expensive Very few testing machines of this type are available in the world (Ref 5)

Fig 8 Tubular specimen for triaxial fatigue test; dimensions are in mm D, diameter; ID, inside diameter; R, radius Source: Ref 5

References cited in this section

1 Y Murakami and K Takahashi, Torsional Fatigue of a Medium Carbon Steel Containing an Initial Small Surface Crack Introduced by Tension-Compression Fatigue: Crack Branching, Non-Propagation

and Fatigue Limit, Fatigue Fract Eng Mater Struct., Vol 21, 1998, p 1473–1484

2 A Ono, “Fatigue of Steel under Combined Bending and Torsion,” Mem Coll Eng., Kyushu Imp Univ., Vol 2, 1921, p 117–145

3 M.A Fonte and M.M Freitas, Semi-Elliptical Crack Growth Under Rotating or Reversed Bending

Combined with Steady Torsion, Fatigue Fract Eng Mater Struct., Vol 20, 1997, p 895–906

4 M Endo and Y Murakami, Effects of an Artificial Small Defect on Torsional Fatigue Strength of

Steels, J Eng Mater Technol (Trans ASME), Vol 109, 1987, p 124–129

5 M.W Brown and K.J Miller, Biaxial Cyclic Deformation Behavior of Steels, Fatigue Eng Mater Struct., Vol 1, 1979, p 93–106

Multiaxial Fatigue Testing

Yukitaka Murakami, Kyushu University, Japan

Testing of Specimens Containing Notches or Cracks

Rectangular plate specimens containing an inclined central or edge crack are used for crack propagation tests in mixed-mode loading (Ref 6, 7, and 8) The axial load is applied through the pins attached to the holes at the grips A notch or crack is introduced by a saw or razor If a fatigue crack is introduced in a wide plate by preliminary tension-compression fatigue, a specimen such as that shown in Fig 9 can be prepared by cutting the plate (Ref 6, 7, and 8)

Fig 9 Rectangular plate specimens containing an inclined center crack Dimension are in mm Source: Ref 7

Cruciform Specimen The type of specimen shown in Fig 10 is used to investigate the effect of plastic zone size or yielding at the tip of a crack The stress intensity factor has the same value under the combination of an identical stress, σy, and a different stress, σx However, the size of the yield zone at the crack tip is dependent on the value of the stress, σx, in the direction of the crack line

Fig 10 Cruciform specimen containing a central crack Dimension are in mm Source: Ref 9

Three-Point and Four-Point Bending Specimens with a Crack In three-point bending (Fig 11a), not only shear

force but also bending moment is always induced at the crack and, accordingly, we have both KI and KII On the

other hand, in four-point bending, one can control the magnitude of bending moment at the crack by changing

the location of loads This can be done in such a way that there is only a KII stress state at the crack tip (Ref 10)

Fig 11 Three-point and four-point bending specimens, (a) Three-point and four-point bending specimens with an offset crack Source: Ref 10 (b) Four-point bending specimens with a semielliptical edge crack Source: Ref 11

The specimens shown in Fig 11(b) are variations of four-point bending specimens with edge cracks (Ref 11) However, it must be noted that the shear stress component is always zero at the free surface

Compact Tension Shear Specimen The compact tension specimen shown in Fig 12 is used in combination

with a jig that can control the direction of loadings and thus the combination of KI and KII (Fig 13) (Ref 12)

Fig 12 Shape and dimension of compact tension shear specimen w, width; t, thickness; a, crack length

Source: Ref 12

Fig 13 Position of loading device (a) Mode I (α = 0°), (b) Mixed mode (0° < α < 90°), (c) Mode II (α =

90°) F, force Source: Ref 12

Compact Shear Specimen The compact shear specimen (Ref 13, 14) shown in Fig 14 is used in the equilibrium loading system (Fig 15a), though the mode is not pure mode II If the distance between the pins of load application is small, the component of mode I is relatively small compared to the component of mode II The specimen of the type in Fig 15(b) is for the mode III test, but it also has a problem in that the mode I component is always induced in the system

Fig 14 Shape and dimension of compact shear specimen Dimension are in mm ρ, notch root radius Source: Ref 14

Fig 15 Loading apparatus (a)Mode II type, (b) Mode III type Source: Ref 14

Mode II Crack Growth Specimen (Ref 15, 16) The mode II threshold stress intensity factor range, ΔKIIth, is an important material property with respect to rolling contact fatigue resistance However, the measurement of

ΔKIIth in the laboratory is very difficult because a crack that has been growing in mode II can easily switch to mode I growth during the test A method of measuring ΔKIIth has been developed and applied to various steels (Ref 15, 16)

Figure 16 shows the basic model of measurement method in which a specially designed double-cantilever specimen is used Figure 16 shows stress distributions and the normal and shear stress at the position without a slit In principle, neither tensile nor compressive stress of σx exists on the neutral axis, and so a mode II fatigue crack is expected to grow along this section The specimen (Fig 17) has a chevron notch and side grooves

Figure 18(a) shows the setup for the mode II fatigue crack growth test In this test, two identical specimens are used as a pair so that a conventional closed-loop type tension-compression servomechanical fatigue machine can be used Figure 18(b) shows the detail of attaching one specimen to the testing machine Ceramic cylinders are inserted between cantilevers to share the applied load equally to each lever

Fig 16 Basic model of mode II crack growth test P, force

Fig 17 Shape and dimension of mode II crack growth specimen Dimensions are in mm

Fig 18 Mode II crack growth testing machine, (a) Setup of mode II crack growth testing machine (b) Detail of mode II crack growth testing machine with one specimen in place

Circumferentially Notched Cylindrical Specimen This type of specimen is used to investigate the behavior of

mode III crack growth under torsional loading (Fig 19) Although the nominal stress intensity factor, KIII, is known, the exact value is difficult to estimate due to the friction between mating crack surfaces A typical morphology of the fracture surface under these conditions is termed “factory roof” morphology (Ref 17)

Fig 19 Circumferentially notched torsion specimen for mode III fatigue crack propagation Dimensions

are in mm ro, outer radius; rN , radius of notch Source: Ref 17

Tubular Specimen Containing a Slit This type of specimen is used to investigate the fatigue crack growth behavior and approximately two-dimensional, mixed-mode stress condition under torsion coupled with tension-compression A typical initial notch (Fig 20) is usually introduced The width of slit must be very small, because the initial geometry of the slit strongly influences the initial direction of crack growth

Fig 20 Tubular specimen containing a slit for combined torsion and tension-compression fatigue test Dimensions are in mm Source: Ref 18

Solid Cylindrical Specimen Containing a Small Hole or Initial Crack The effects of artificial small defects on torsional fatigue strength can be studied by introducing an artificial small hole (Ref 4) Figure 21 shows the shape and dimension of a drilled hole

Fig 21 Shape and dimension of a small hole introduced on the surface of torsional fatigue test specimen

(Geometry of specimen is shown in Fig 4.) d, diameter Source: Ref 4

If a fatigue crack is introduced by a preliminary tension-compression fatigue test, crack growth behavior and threshold condition under mixed-mode loading can be studied Initial small semielliptical cracks ranging from

200 to 1000 μm in length are introduced by preliminary tension-compression fatigue using a specimen containing holes of 40 um diameter (Fig 22) Crack growth behavior from the initial small crack, such as crack branching (Ref 1) and kinking (Ref 19), can be investigate The threshold condition of a small crack can be studied based on the mixed-mode fracture mechanics analysis of a semielliptical crack (Fig 3)

Fig 22 Initial small surface crack introduced by tension-compression fatigue test using the specimens containing holes of 40 μm (Geometry of specimen is shown in Fig 7.) Source: Ref 1

References cited in this section

1 Y Murakami and K Takahashi, Torsional Fatigue of a Medium Carbon Steel Containing an Initial Small Surface Crack Introduced by Tension-Compression Fatigue: Crack Branching, Non-Propagation

and Fatigue Limit, Fatigue Fract Eng Mater Struct., Vol 21, 1998, p 1473–1484

4 M Endo and Y Murakami, Effects of an Artificial Small Defect on Torsional Fatigue Strength of

Steels, J Eng Mater Technol (Trans ASME), Vol 109, 1987, p 124–129

6 S Iida and A.S Kobayashi, Crack-Propagation Rate in 7075-T6 Plates under Cyclic Tensile and

Transverse Shear Loadings, J Bas Eng (Trans ASME), Ser D, Vol 91, 1969, p 764–769

7 K Tanaka, Fatigue Crack Propagation from a Crack Inclined to the Cyclic Tensile Axis, Eng Fract Mech., Vol 6, 1974, p 493–507

8 A Otsuka, K Mori, and T Miyata, The Condition of Fatigue Crack Growth in Mixed-Mode Condition,

Eng Fract Mech., Vol 7, 1975, p 429–439

9 H Kitagawa, R Yuuki, and K Tohgo, A Fracture Mechanics Approach to High-Cycle Fatigue Crack

Growth Under In-Plane Biaxial Loads, Fatigue Eng Mater Struct., Vol 2, 1979, p 195–206

10 H Gao, M.W Brown, and K.J Miller, Mixed-Mode Fatigue Thresholds, Fatigue Eng Mater Struct.,

Vol 5, 1982, p 1–17

11 K Tohgo, A Otsuka, and M Yoshida, Fatigue Behavior of a Surface Crack under Mixed Mode

Loading, Fatigue '90, Proc of the 4th International Conf on Fatigue and Fatigue Thresholds, Vol 1,

Materials and Component Engineering Publication, 1990, p 567–572

12 H.A Richard and K Benitz, A Loading Device for the Creation of Mixed Mode in Fracture Mechanics,

Int J Fract., Vol 22, 1983, p R55–R58

13 D.L Jones and D.B Chisholm, An Investigation of the Edge-Sliding Mode in Fracture Mechanics, Eng Fract Mech., Vol 7, 1975, p 261–270

14 K Komai and E Usuki, Fractographic Study on Mode II and Mode III SCC Crack Growth in Al-Zn-Mg

Alloy, J Soc Mater Sci., Jpn., Vol 33, 1984, p 921–926

15 Y Murakami and S Hamada, New Method for the Measurement of Mode II Fatigue Threshold Stress

Intensity Factor Range ΔKIIth, Fatigue Fract Eng Mater Struct., Vol 20, 1997, p 863–870

16 Y Murakami, C Sakae, and S Hamada, Mechanism of Rolling Contact Fatigue and Measurement of

ΔKIIth for Steels, Proc of Engineering Against Fatigue, A.A Balkema, Rotterdam, 1999

17 H Nayeb-Hashemi, F.A McClintock, and R.O Ritchie, Effect of Friction and High Torque on Fatigue

Crack Propagation in Mode III, Metal Trans A, Vol 13A, 1982, p 2197–2204

18 A.T Yokobori, Jr., T Yokobori, K Sato, and K Syoji, Fatigue Crack Growth under Mixed Mode I and

II, Fatigue Fract Eng Mater Struct., Vol 8, 1985, p 315–325

19 Y Murakami and K Takahashi, Crack Branching and Threshold Conditions of Small Cracks in Biaxial

Fatigue, Proc of the 12th Biennial Conf on Fracture, ECF 12, EMAS Publishing, Vol 1, 1998, p 67–72

Multiaxial Fatigue Testing

Yukitaka Murakami, Kyushu University, Japan

Summary

Since no standard testing method exists, it is important to choose a testing method suitable for a purpose of each testing Various testing methods available for biaxial and multiaxial fatigue testing are summarized as follows Biaxial fatigue testing machines, in which cyclic torsion is coupled with tension-compression loading, have been widely used because these testing machines can be applied to study the following:

• Mode III crack growth behaviors under cyclic torsion by using circumferentially notched cylindrical specimens

• Crack growth behaviors under approximately two-dimensional mode I and by using a tubular specimen with a slit

• Effects of small fatigue crack or defect under biaxial loading if an initial small crack is introduced by preliminary tension-compression fatigue testing

Triaxial Testing In addition, biaxial fatigue testing (cyclic torsion with tension-compression) can be combined with the application of internal or external pressure for tubular specimens or cylindrical specimens The influence of complex three-dimensional stress conditions can be investigated However, these triaxial testing machines are very complicated and expensive

Notched Plate and Precracked Bending Specimens Rectangular plate specimens with an inclined notch or a crack and three-point or four-point bending specimens with a crack are used to investigate crack growth under mixed mode I and II It must be noted that the stress intensity factors cannot be kept constant during the test, because crack growth mode shifts from mode II or III to mode I

The cruciform specimen permits a wide variation of stress intensity factors, KI and KII However, testing machines for this type of specimen are complex, and preparation of specimens is not easy High compressive loads cannot be applied to the specimen because of the possibility of buckling

Compact Specimen The compact tension-shear (CTS) specimen is used to investigate the crack growth under mixed mode I and II, including pure mode II, loadings The compact shear (CS) specimen is also used to investigate the crack growth under mode II and mode III However, it is very difficult to achieve pure mode II crack growth by these specimens because crack growth mode easily switches from mode II to mode I Thus, mode of loading is not necessarily the same as mode of crack growth

Double Cantilever Specimen Mode II crack growth plays an important role in crack growth under rolling

contact fatigue The values of ΔKIIth for various steels can be measured using the specially designed double cantilever specimen A conventional closed-loop tension-compression fatigue testing machine can be used in the system

Multiaxial Fatigue Testing

Yukitaka Murakami, Kyushu University, Japan

References

1 Y Murakami and K Takahashi, Torsional Fatigue of a Medium Carbon Steel Containing an Initial Small Surface Crack Introduced by Tension-Compression Fatigue: Crack Branching, Non-Propagation

and Fatigue Limit, Fatigue Fract Eng Mater Struct., Vol 21, 1998, p 1473–1484

2 A Ono, “Fatigue of Steel under Combined Bending and Torsion,” Mem Coll Eng., Kyushu Imp Univ., Vol 2, 1921, p 117–145

3 M.A Fonte and M.M Freitas, Semi-Elliptical Crack Growth Under Rotating or Reversed Bending

Combined with Steady Torsion, Fatigue Fract Eng Mater Struct., Vol 20, 1997, p 895–906

4 M Endo and Y Murakami, Effects of an Artificial Small Defect on Torsional Fatigue Strength of

Steels, J Eng Mater Technol (Trans ASME), Vol 109, 1987, p 124–129

5 M.W Brown and K.J Miller, Biaxial Cyclic Deformation Behavior of Steels, Fatigue Eng Mater Struct., Vol 1, 1979, p 93–106

6 S Iida and A.S Kobayashi, Crack-Propagation Rate in 7075-T6 Plates under Cyclic Tensile and

Transverse Shear Loadings, J Bas Eng (Trans ASME), Ser D, Vol 91, 1969, p 764–769

7 K Tanaka, Fatigue Crack Propagation from a Crack Inclined to the Cyclic Tensile Axis, Eng Fract Mech., Vol 6, 1974, p 493–507

8 A Otsuka, K Mori, and T Miyata, The Condition of Fatigue Crack Growth in Mixed-Mode Condition,

Eng Fract Mech., Vol 7, 1975, p 429–439

9 H Kitagawa, R Yuuki, and K Tohgo, A Fracture Mechanics Approach to High-Cycle Fatigue Crack

Growth Under In-Plane Biaxial Loads, Fatigue Eng Mater Struct., Vol 2, 1979, p 195–206

10 H Gao, M.W Brown, and K.J Miller, Mixed-Mode Fatigue Thresholds, Fatigue Eng Mater Struct.,

Vol 5, 1982, p 1–17

11 K Tohgo, A Otsuka, and M Yoshida, Fatigue Behavior of a Surface Crack under Mixed Mode

Loading, Fatigue '90, Proc of the 4th International Conf on Fatigue and Fatigue Thresholds, Vol 1,

Materials and Component Engineering Publication, 1990, p 567–572

12 H.A Richard and K Benitz, A Loading Device for the Creation of Mixed Mode in Fracture Mechanics,

Int J Fract., Vol 22, 1983, p R55–R58

13 D.L Jones and D.B Chisholm, An Investigation of the Edge-Sliding Mode in Fracture Mechanics, Eng Fract Mech., Vol 7, 1975, p 261–270

14 K Komai and E Usuki, Fractographic Study on Mode II and Mode III SCC Crack Growth in Al-Zn-Mg

Alloy, J Soc Mater Sci., Jpn., Vol 33, 1984, p 921–926

15 Y Murakami and S Hamada, New Method for the Measurement of Mode II Fatigue Threshold Stress

Intensity Factor Range ΔKIIth, Fatigue Fract Eng Mater Struct., Vol 20, 1997, p 863–870

16 Y Murakami, C Sakae, and S Hamada, Mechanism of Rolling Contact Fatigue and Measurement of

ΔKIIth for Steels, Proc of Engineering Against Fatigue, A.A Balkema, Rotterdam, 1999

17 H Nayeb-Hashemi, F.A McClintock, and R.O Ritchie, Effect of Friction and High Torque on Fatigue

Crack Propagation in Mode III, Metal Trans A, Vol 13A, 1982, p 2197–2204

18 A.T Yokobori, Jr., T Yokobori, K Sato, and K Syoji, Fatigue Crack Growth under Mixed Mode I and

II, Fatigue Fract Eng Mater Struct., Vol 8, 1985, p 315–325

19 Y Murakami and K Takahashi, Crack Branching and Threshold Conditions of Small Cracks in Biaxial

Fatigue, Proc of the 12th Biennial Conf on Fracture, ECF 12, EMAS Publishing, Vol 1, 1998, p 67–72

Introduction to Mechanical Testing of Components

Introduction

TESTING OF COMPONENTS requires an understanding of service conditions and mechanical testing and design While there are many types of components tests for a multitude of products, the articles in this Section focus primarily on the basic principles for some common types of engineering components These articles provide an overview of the typical test methodology, developed by national organizations such as ASTM, as well as industry-specific organizations, test apparatus, procedures, test sample preparation, data collection, and interpretation Using standard test methods provides for consistent test results

The mechanical evaluation of components requires an engineer to use many sources of information It also requires an understanding of service conditions, design, and manufacturing variables All these variables can make it difficult to validate components The following overviews briefly summarize some general factors in the design and manufacture of components Additional information is also provided in the article“Overview of Mechanical Properties and Testing for Design” in this Volume The remaining articles in this Section describe tests for common types of fabricated components and the modeling of metal deformation

Introduction to Mechanical Testing of Components

Overview of Component Testing

Brian Klotz, Component Test Resources, General Motors Corporation

Testing of components involves a series of processes to validate the product for usage Computer systems are playing a dominating role in the design of components and simulating how they react under different environments Design engineers use three-dimensional modeling software to design components This software allows the engineer to create a three-dimensional image of the component to scale He or she can then manipulate the image to identify design concerns, match to models of mating parts to check for interference, and manufacture the component right from the model This design model can also be used to generate a finite-element analysis (FEA) model The FEA model can show an engineer how the design reacts under various loading conditions If areas of the design are suspect, design changes can be made and reevaluated easily While FEA models provide an engineer the ability to improve component designs without making a physical part, further test simulations to evaluate durability need to be developed to accurately predict the total capability of a component The use of physical tests is required to develop these simulations

An understanding of the operating environment in which the component must function establishes the basis for testing the component The environment may include cyclic or static loading, vibration concerns, thermal variations, or many others Duplicating or simulating this environment becomes a challenge at a component level While elaborate test systems can be produced to incorporate multiple environments, in most instances the basic component design functionality is all that need be evaluated Developing tests to perform the evaluations typically involves developing a set of fixtures to hold the component and impart the loading into the part on some type of test stand Design of fixtures is critical to the repeatability of the overall testing The loading characteristics the component experiences in its application must be understood in order for a test to be developed

Once the test environment is understood, fixtures developed, and the component design manufactured, a test can be performed on the component The testing is done either to correlate the output of the FEA model or validate the component design and manufacturing Testing done to compare the results from math-based FEA models to real-life test results allows engineers the ability to further develop the capability of the models to predict design concerns This type of testing typically requires less samples and can provide long-term cost

benefits to an organization This iterative process of design analysis and testing ultimately leads to product designs that may require no component testing, only testing as part of an assembly to validate the system Testing done to validate the component design and manufacturing requires knowledge of the duty cycle in which the component must operate In order to develop component-level validation tests, test procedures and methods must be correlated to this duty cycle, and the test stand must be able to duplicate these load inputs Validation tests require multiple samples to be subjected to duty-cycle loading Results of these tests are then evaluated using statistical methods in order to determine whether they meet the product design requirements This method of testing can be very costly if several redesigns must be done

Introduction to Mechanical Testing of Components

Overview of Mechanical Properties for Component Design

Henry E Fairman, MQS Inspection, Inc

The ultimate result of performing mechanical tests is to provide information that may be used in the design and manufacture of components Design of components requires an understanding of the materials properties and how they will be used by the component The manufacturing process that is used to produce the part also must

be considered during the design process because manufacturing methods influence materials properties and the selection of appropriate mechanical testing methods to ensure that the component will meet its required life cycle

This overview briefly reviews the relationship of mechanical properties in the process of mechanical design As previously noted, detailed materials properties and design methodologies are required for a wide variety of applications that encompass factors such as:

• Load-bearing capability to meet the desired service condition

• Capability of the design to meet the required lifetime

• Effect of service (environmental) conditions on the design

• Performance requirements such as minimum weight, stiffness, and life-cycle cost

• Size and shape factors

A significant part of the design process is also the experience based on the performance of similar components The design process also uses predictive models, which may be a simple model or a more complex model developed by the FEA method

Introduction to Mechanical Testing of Components

General Mechanical Behavior

One key aspect of product and process design is a basic understanding of fundamental mechanical behavior, which is described in the first two articles of this Volume (“Introduction to the Mechanical Behavior of Metals” and “Introduction to the Mechanical Behavior of Nonmetallic Materials”) In general, fine-grained materials have better mechanical and fatigue properties than coarse-grained materials Components that have a mixture of fine- and coarse-grained materials will generally have properties similar to those of the coarse-grained material Coarse-grained materials exhibit the lowest properties with the exception of creep and stress rupture, where single-grained materials have exhibited superior properties at elevated temperature

Nonuniform microstructures will affect the mechanical properties of the material or component For example, the center of 8 in carbon or alloy bar produced by the strand casting process will exhibit different mechanical

properties than samples taken from the center, midradius, and outer diameter when tested in the longitudinal direction Samples taken from the transverse direction will also have different properties than the longitudinal samples will have Impact and fracture testing results are significantly impacted by the sample direction

Mechanical working such as the rolling or drawing of materials can significantly improve the mechanical properties of the materials, raising the yield and ultimate strengths along with reducing the ductility values Age hardening of metals generally raises the yield and ultimate strengths of materials The fatigue properties are not generally significantly improved by age hardening

Heat treating processes that result in transformation hardening, such as occurs with carbon and alloy steels, will raise the mechanical and fatigue properties of these alloys It changes the creep properties by only a small degree because the principal effect is in the initial stage of creep deformation

Introduction to Mechanical Testing of Components

Properties and Design for Static Loads

Tension and compression testing are common test methods as described in detail in the articles “Uniaxial Tension Testing” and “Uniaxial Compression Testing” in this Volume Property data present in the literature are normally based on specimens machined from raw materials and represent ideal data for the materials Typical stress-strain data for a variety of alloys are provided in Fig 1 In the elastic region, stress and strain are

proportional by Hooke's law (σ = Eε) In the plastic region, work hardening is described by a power law:

σ = Ke n

(Eq 1)

where K is the strength coefficient and n is the strain-hardening exponent Typical stress-strain properties

values are shown in Tables 1 and 2 (Ref 1) for selected steels and aluminum alloys, respectively, for monotonic loads Tables 1 and 2 also list cyclic stress-strain properties, as described later General properties related to monotonic stress-strain behavior are described briefly here

Table 1 Monotonic and cyclic stress-strain properties of selected steels

GPa 10 6 ksi MPa ksi MPa ksi MPa ksi

Strain hardening exponent

SAE950X As-received, 146 HB 207 30 391 56.7 510 74.0 800 116.0 0.15 74 978 141.8 1.34 SAE980X Prestrained, 225 HB 193 28 576 83.5 695 100.8 992 143.9 0.13 68 1219 176.8 1.15

(S′y )

Cyclic strength exponent

(K′)

Cyclic true fracture stress (σ′ f ) Alloy Condition (a)

MPa ksi MPa ksi

Cyclic strain hardening exponent

(n′) MPa ksi

b Cyclic true fracture strain(ε′ f )

(a) Q&T, quenched and tempered

(b) E, elastic modulus; Sy, yield strength; Su, tensile strength; σf, true fracture stress; εf, true fracture strain;

%RA, percent reduction in area K and n per Eq 1

(c) S′y cyclic yield strength; K′ cyclic strength coefficient; n′ cyclic strain hardening exponent; see also Eq 3 for definitions of b and c

Source: Ref 1

Table 2 Monotonic and cyclic stress-strain properties of selected aluminum alloys

Elastic modulus

(E)

Yield strength

(Sy )

Tensile strength

(Su )

Strength coefficient

(K)

True fracture stress (σ f ) Alloy Condition

GPa 10 6 ksi MPa ksi MPa ksi MPa ksi

Strain hardening exponent

(S′y )

Cyclic strength exponent

(K′)

Cyclic true fracture stress (σ′ f ) Alloy Condition

MPa ksi MPa ksi

Cyclic strain hardening exponent

(n′) MPa ksi

b Cyclic

true fracture strain (ε′ f )

Fig 1 Typical stress-strain curves for selected metals

Ultimate strength refers to the maximum stress that a material can withstand before failure occurs The ultimate

strength is related to the materials composition, mechanical working, and heat treatment The term ultimate tensile strength is synonymous with tensile strength, which is the accepted ASTM term for the maximum stress

obtainable before fracture of the specimen

Yield strength is commonly defined as the load at which a given amount of plastic strain has occurred The yield strength is related to the materials composition, mechanical working, and heat treatment

Elastic limit (or proportional limit) is the load at which plastic deformation begins to take place Removal of the load allows the material to return to its initial shape This property of materials is not commonly used in the design of components

Modulus of elasticity is the ratio of stress to strain below the elastic limit The modulus is a measure of material

rigidity or stiffness for loading under tension, compression, or shear The tensile modulus of elasticity (E), in

principle, is roughly equivalent to the modulus in compressive The shear modulus (or the modulus of rigidity,

G) is related to the tensile modulus as follows:

(Eq 2)

where μ is Poisson's ratio

The moduli are usually characteristic for a given materials family such as aluminum, steel, and so on Table 3 (Ref 2) provides data on the relative stiffness of a number of materials Tensile moduli range from 45 to 207 GPa (6.5 × 106 to 30 × 106 psi) for common metallic materials

Table 3 Comparison of the stiffness of selected engineering materials

Material Modulus of

elasticity (E), GPa

Density (ρ), mg/m 3

E/ρ × 10 -5 E1/2/ρ × 10-2 E1/3/ρ

Epoxy-62% aramid fibers 82.8 1.38 60 20.6 146.6

Source: Ref 2

Dynamic Modulus Modulus can also be determined from resonant vibrations with piezoelectric or electromagnetic transducers ASTM standards C 1198 and C 1259 describe test method for determining the dynamic elastic module of advanced ceramics These standards also form the basis for two recent additions to ASTM standards:

• ASTM E 1875-98; Standard Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio by Sonic Resonance

• ASTM E 1876-98; Standard Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio by Impulse Excitation

These two standards are almost verbatim versions of C 1198 and C 1259, which are generic and need not be confined to advanced ceramics, but are applicable to all elastic materials

In resonant methods, Young's modulus, sheer modulus, and Poison's ratio can all be computed from the resonant frequencies of prismatic bar, rods, or slabs Dynamic methods of measuring elastic moduli are related

to adiabatic conditions; whereas, static methods are isothermal For ceramic materials (Ref 3), the adiabatic values can be of the order of 0.1% higher than isothermal values (Ref 4)

ASTM C 1198 is a clone of two earlier ASTM standards (C 848 and C 623) that are suitable for ceramic whitewares, and glass and glass-ceramics, respectively Rather than using the tables and graphs in the earlier standards, the newer standard C 1198 uses the original equations for relating the elastic constants to the resonance frequencies Although recommended sizes for flat and round specimens are given, the equations are sufficiently general that a wide size range can be used The equations include the conventional polynomial correction factors to reflect the finite specimen thicknesses, but simplified equations are also provided for instances where the length-to-thickness ratio of the specimens is greater than 20 Specimen flatness and parallelism are critical; but, with proper care, accuracies and precisions of better than 1% are feasible C 1198 is

primarily intended to be used with monolithic, or whisker-or particulate-reinforced ceramics There is some potential for its use on continuous-fiber reinforced ceramics

ASTM C 1259 describes a similar but more modern methodology for measuring the same properties as C 1198 except that impulse rather than continuous excitation is used to resonate the specimen The fundamental resonant frequency of a rectangular-shaped specimen is measured following mechanical excitation by a singular elastic strike with an impulse tool The resulting vibrations are monitored and transformed into electrical signals The signals are analyzed and the properties calculated with a knowledge of the mass and dimensions of the specimen

JIS Standard R 1602 also uses the resonance frequency method, but goes further by incorporating several alternate procedures These include measurements of the static deflection of a beam in bending (with proper corrections for machine compliance), the strain in a strain-gauged specimen loaded in flexure, or the longitudinal-wave velocity in an ultrasonically pulsed specimen The elevated temperature standard JIS R 1605 incorporates the resonance frequency or ultrasonic pulse methods to compute dynamic elastic moduli Both Japanese standards prescribe specimen length to thickness ratios of 20 or greater The same simplified formulas

as given in ASTM C 1198 are used

Elongation and reduction of area are ductility measurements determined during static mechanical testing and are related to the plastic deformation that takes place between the elastic limit and the ultimate strength of a material These properties are useful when evaluating ductility during deformation such as extrusion, forging,

or drawing

Poisson's ratio, μ, is the ratio between axial strain to lateral strain during tensile loading It usually has a value

of approximately 0.3 for most metallic materials For some materials with anisotropic crystal structures (such as the hcp structure of titanium α or α-β alloys with a preferred or textured crystal orientation), Poisson's ratio may depend on orientation

Design of components for tensile loads normally uses the “fail-safe” concept of design in which a safety factor

is applied to either the yield strength or the ultimate strength of the material Design using cast materials typically uses the ultimate strength, whereas design using wrought materials uses the yield strength Design that anticipates rapid loading often utilizes the ratio of yield strength to ultimate strength A material having a ratio above 0.75 often will fail due to its inability to undergo plastic deformation under load

Flexural Modulus and Strength For ceramics and polymer materials, modulus and strength is often evaluated

by flexural testing In the case of ceramics, bend testing eliminates the gripping problems associated with the tension testing of ceramics

Flexural testing by either three-point or four-point loading is the traditional method for evaluating the uniaxial strength ceramics The method is applicable for purposes of material development, and sometimes design However, for design purposes, tension testing is generally preferred (Ref 5)

Standards for the flexural testing of ceramics include:

• ASTM C 1161-90 Standard Test Method for Flexural Strength of Advanced Ceramics at Ambient Temperature

• ASTM C 1211-92 Standard Test Method for Flexural Strength of Advanced Ceramics at Elevated Temperature

• MIL STD 1942 Flexural Strength of Advanced Ceramics at Ambient Temperatures

• JIS R 1601 Testing Method for Flexural Strength (Modulus of Rupture) of High-Performance Ceramics

• JIS R 1604 Elevated Temperature Testing Method for Flexural Strength

• EN 843-1 Monolithic Ceramics, Mechanical Properties at Room Temperature, Part 1: Determination of Flexural Strength

The latter standard has been adopted by the European Community and supercedes previous European Standards (DIN 51-110 Part 1 and AFNOR B41-104) There are many similarities between these standards The specimen and fixture sizes are quite comparable and many tolerances and specifications are identical Nevertheless, there are some differences that are of concern as discussed in Ref 5 For example, the U.S and European standards require the load rollers to be free to rotate to eliminate friction error, but the JIS standard does not

Although the flexure test is a simple method, significant errors (>5%) can occur from twisting, misalignment, and frictional constraints (Ref 3) Flexure testing of continuous-fiber, ceramic matrix composites must be

viewed with considerable caution because the failure mode could be tension fracture, shear fracture, compression failure, or buckling

Hardness testing is a very common mechanical test applied to materials Hardness testing is used extensively in quality control, where data can be collected that relate the mechanical properties of a given material, its microstructure, and processing methods

Over the years, many researchers have endeavored to relate hardness values obtained from mechanical testing

to the properties of the material This has proved to be difficult because the shape of the indenters, loads, and rate of loading interact with each material in a different manner For example, an annealed material will work harden during the test differently than the same material that has received various degrees of cold work Materials such as carbon and alloy steels, which are strengthened by different processes (such as annealing, normalizing, and hardening), have different work-hardening behavior that influences indentation results Likewise, cast aluminum alloys have similar hardness values to the wrought alloys yet possess significant different mechanical properties Therefore, the correlation of strength and hardness (much like the conversion

of hardness readings for different hardness scales) depends on the material, its condition, and the underlying strengthening mechanisms

More information on the factors and variation of strength-hardness correlations are discussed in the article

“Selection and Industrial Applications of Hardness Tests” in this Volume In fact, Fig 15(b) in that article illustrates an example of an inverse correlation of tensile strength and hardness for a line pipe steel The explanation of this unexpected result is not clear, but it demonstrates the need for caution and empirically derived analysis when estimating mechanical strength from hardness

References cited in this section

1 M.R Mitchell, Fundamentals of Modern Fatigue Analysis for Design, Fatigue and Fracture, Vol 19, ASM Handbook, ASM International, 1996, p 231

2 M.M Farag, Properties Needed for the Design of Static Structures, Materials Selection and Design, Vol

20, ASM Handbook, ASM International, 1997, p 510

3 C.R Brinkman and G.D Quinn, Standardization of Mechanical Properties Tests for Advanced Ceramics, in Mechanical Testing Methodology for Ceramic Design and Reliability, Marcel Dekker,

1998, p 353–386

4 R Morrell, Handbook of Properties of Technical and Engineering Ceramics, Vol 1, Her Majesty's

Stationary Office, London, 1989

5 G.D Quinn and R Morrell, “Design Data for Engineering Ceramics: A Review of the Flexure Test,” J

Am Ceram Soc., Vol 74 (No 9), 1991, p 2037–2066

Introduction to Mechanical Testing of Components

Properties and Design for Dynamic Loads

Mechanical design is commonly based on static loading of a component However, there are many components that see an initial dynamic load followed by static or cyclic loading Typical examples are explosive fasteners driven into concrete walls, the torsion spring used in overhead door mechanisms, dies for metal-forming operations, and aircraft landing gears Impact tests and fracture toughness tests are the most common tests performed to demonstrate how materials behave under dynamic loads These types of tests are performed to use standard test specimens and often bear no relationship to the complex shapes present in components The rate of loading is also kept to standard conditions

Impact testing of materials provides information on how a material will perform under dynamic loading The data obtained from impact testing provide no values that can be used in the designing of components The data

do provide comparative information between different materials as well as the difference between lots of materials and/or heat treatment The data are often plotted as a function of temperature because many materials

exhibit a loss in impact strength as the temperature is lowered This point is defined as the transition

temperature (Fig 2)

Fig 2 Ductile-brittle temperature transition bcc, body-centered cubic; fcc, face-centered cubic

The most common impact tests are the Charpy and Izod tests, in which the notched specimen is struck by a hammer The notch concentrates the stresses so that plastic flow is minimized, and almost all of the energy is used to fracture the specimen Other less-common impact tests are the tensile and torsional impact tests, which measure the performance of materials under these conditions

The tensile impact test provides comparative information on the differences between various materials and lots

of materials It also can be used to predict the forming characteristics of materials being fabricated by energy forming methods The torsional impact test provides information on how tubular cross sections of various materials will perform under load The most common application of these data is for shafts that are rapidly brought up to an operating speed and supplement the torsional fatigue data on these sections The test is rarely performed on solid specimens due to the more complex stress state that exists in this geometry

high-Fracture toughness testing evaluates the ability of a material to withstand fracture in the presence of cracks When fracture toughness is used as design criteria, the designer must be aware that the failure of the component will occur at nominal stresses below the design stresses for the given material Cracks, discontinuities, and microscopic features such as inclusions and other anomalies are often present in components and should be accounted for in the design process

The design philosophy for fracture toughness falls into four categories:

• Infinite-life design: This philosophy assumes that the component has no defects that will affect the life

of the component This philosophy incorporates the traditional design method that uses the fatigue (endurance) limit of the material

• Safe-life design: This approach uses a design stress based on the number of cycles at the working stress

that the component must carry to perform its task

• Fail-safe design: This design philosophy assumes that the structure will continue to support its load

after the failure of a single component of the structure Fail-safe designs often include the presence of cracks

• Damage-tolerant design: This approach was developed by the U.S Air Force and incorporates the

detection of cracks along with the crack growth rate of the material Based on life histories, the remaining life of the component is determined

Introduction to Mechanical Testing of Components

Properties and Design for Cyclic Loads

In the real world, very few components are subject to static tensile, compression, and bending loads The common approach for design of components in fatigue is the design-life approach, where data obtained from

cyclic testing are presented as an S-N curve The data from S-N testing are often combined in a constant-life

fatigue diagram, which combines the alternating stress conditions with the cycles to failure One of the advantages of such a diagram is that the effect of different loading conditions is easily seen in this type of diagram Figure 3 (Ref 6) shows a typical constant-life diagram for alloy steel This type of diagram can be

used to construct S-N diagrams for the expected loading of the component

Fig 3 Constant-life diagram for alloy steels The data in this type of representation can be used to create

an S-N curve for any level of mean stress Note the presence of safe-life, finite-life lines on this plot This

plot This diagram is for average test data for axial loading of polished specimens of AISI 4340 steel (ultimate tensile strength, UTS, 125 to 180 ksi) and is applicable to other steel (e.g., AISI 2330, 4130, and 8630) Source: Ref 6

External and internal notches significantly reduce the fatigue properties of materials For example, precipitation-hardened metals exhibit lower fatigue properties than would be expected from their yield/tensile properties Ceramics and glasses contain internal defects, which reduce their expected fatigue strengths The operating environment can produce external defects such as corrosion pits or stress corrosion cracks, which can serve as initiation sites for fatigue to occur

Fatigue life data are also expressed in terms of a strain-based fatigue, which is divided into an elastic cycle) component and a plastic (low-cycle) component as follows (Ref 1):

(high-(Eq 3)

where Nf is the number of cycles to failure, σ′f is the cyclic true fracture, ε′f is the true fracture strain, and b and

c are constants for a given material Values for selected steels and aluminum alloys are listed in Tables 1 and 2,

respectively

Use of published fatigue data and stress concentrations combined with appropriate calculations and rate of loading provide only an approximation of the useful life of a component If repeated failures of a component occur, a statistically designed, factorial test program should perform to validate the design assumptions Data obtained from strain gage measurements are useful in the design of the experiment

Tension-tension (axial) fatigue commonly occurs in press frames, bolted assemblies, and components subjected

to thermal stresses In the case of a press frame, it would be a zero to maximum tensile loading condition The bolted joint normally has a preload applied so that the loading of the bolt is between a mean and maximum tensile stress A bridge that undergoes thermal expansion will have both compressive and tensile loading, with the mean stress being that of the ambient temperature at time of construction Many materials exhibit a good correlation of axial fatigue strength with their yield and/or ultimate strengths and typically have a ratio of 0.3 to 0.5 to these properties

Bending fatigue results in the outer surface being subjected to alternating tensile and compressive stresses in varying ratios with the limiting strength being in the tensile direction Common components subjected to bending fatigue include flapper-type valves and gear teeth The stresses are given by:

where M is the bending moment, c is the distance from the center of the section to the outside surface, and I is

the moment of inertia of the section

Since the maximum stress is at the surface, processes such as shot peening and carburizing that produce compressive stresses are often used to improve the properties of the material

Rotating bending fatigue tests have been performed for many years, and the bulk of fatigue data presented in the literature were produced by the R.R Moore rotating bending fatigue machine In this type of loading, a given point on the outside diameter of the specimens is subjected to alternating tensile or tensile-compressive stress each time it undergoes a 360° rotation The effects of various stress concentrations on rotating bending endurance limits are also readily available These data are widely used for shafts that are subjected to varying degrees of misalignment and are the predominate failure modes for these components

Torsional fatigue data are less commonly reported in the literature These are the predominate failure modes of compression springs and shafts that are connected to drive gears For steels, the ratio between rotating bending and torsional endurance limits is typically 0.8

Fatigue crack growth rates are directly related to the material's crystal structure, stress level, rate of loading, and stress concentrations present in the component The field of fracture mechanics has provided significant data on

the growth rate of fatigue cracks under axial loading where fracture toughness (KIc) has been determined for a wide variety of materials

References cited in this section

1 M.R Mitchell, Fundamentals of Modern Fatigue Analysis for Design, Fatigue and Fracture, Vol 19, ASM Handbook, ASM International, 1996, p 231

6 D.W Cameron and D Hoeppner, Fatigue Properties in Engineering, Fatigue and Fracture, Vol 19, ASM Handbook, ASM International, 1996, p 19

Introduction to Mechanical Testing of Components

Mechanical Properties and Design for High Temperature

Creep properties of materials are those in which a material continues to elongate under constant load at the working temperature of a component Creep damage usually results in fracture, and creep properties of metallic materials are significant in such diverse applications as a toaster heating element, automobile exhaust system

components, high-temperature steam lines, furnaces and burners, and jet engine turbine components It is of major importance for polymers, which exhibit creep at or just above room temperature

Stress-rupture testing is also used to evaluate the creep resistance of materials In this test, the sample is subjected to a constant load, and the time to fracture is measured as it varies with stress and temperature It is often used as an acceptance test for high-temperature materials since it can be performed more rapidly than creep testing can Creep fatigue results when cyclic loading occurs at elevated temperatures where creep damage can occur It is directly related to the crack growth properties of the material, and is discussed in the article “Creep Crack Growth Testing” in this Volume In general, materials are classed as being either creep-ductile materials (iron-base materials fall within this group) or creep-brittle materials (this group includes high-temperature aluminum alloys, titanium alloys, nickel-base high-temperature alloys, and ceramics)

Creep of Ceramics Ceramics also exhibit creep behavior Use of advanced ceramics for elevated temperature applications may involve the need for constitutive laws in order to predict deformation or strain up to a specified limit as established by design Similarly creep-rupture models may also be required Bending test data obtained at temperatures within the creep range are not suitable for establishing these laws because of difficulties in interpretation of specimen behavior (Ref 5) Therefore, to formulate these laws, data must be generated in both pure tension or compression in accordance with established standards

ASTM C 1291 is a new standard that covers determination of the elevated-temperature time-dependent deformation tensile (creep) and stress-rupture properties of monolithic ceramics Creep time-to-failure is also included in this test method This method is only suitable for monolithic ceramics This test is not suitable for continuous fiber-reinforced ceramic composites, which do not behave as isotropic, homogeneous materials Specimens (dogbone flats or rounds) are subjected to uniform stress in the gage area, where creep deformation

is measured by either optical or mechanical extensometers (Ref 7, 8, and 9) Optical extensometers provide good stability, while mechanical devices may have advantages in terms of accuracy and ease of use

References cited in this section

5 G.D Quinn and R Morrell, “Design Data for Engineering Ceramics: A Review of the Flexure Test,” J

Am Ceram Soc., Vol 74 (No 9), 1991, p 2037–2066

7 H Pih and K.C Liu, “Laser Diffraction Methods for High Temperature Strain Measurements,” Exp Mech., March 1991, p 60–64

8 K.C Liu and J.L Ding, “A Mechanical Extensometer for High Temperature Tensile Testing of

Ceramics,” J Test Eval., Sept 1993, p 406–413

9 J.Z Gyekenyesi and P.A Bartolotta, “An Evaluation of Strain Measuring Devices for Ceramic

Composites,” J Test Eval., Vol 20, 1992, p 285–295

Introduction to Mechanical Testing of Components

Applications Factors in Mechanical Performance

Application of materials properties along with the operating stresses calculated from traditional mechanics yields only a best-case scenario for the performance of a component Design shape, environmental effects and surface degradation, the manufacturing method, and the condition of the material all play significant roles in the design process

Part Shape In almost all cases, engineering components and machine elements have to incorporate design features that introduce changes in their cross section For example, shafts must have shoulders to take thrust loads at the bearings and must have keyways or splines to transmit torques to or from pulleys and gears mounted on them Under load, such changes cause localized stresses that are higher than those based on the