Volume 20 - Materials Selection and Design Part 11 potx

Source: Ref 49 In addition to the determination of the Weibull shape and scale parameters discussed previously, analysis of dependent reliability in brittle materials necessitates accu

47 R.R Wills and R.E Southam, Ceramic Engine Valves, J Am Ceram Soc., Vol 72 (No 7), 1989, p

1261-1264

48 J.R Smyth, R.E Morey, and R.W Schultz, "Ceramic Gas Turbine Technology Development and Applications," Paper 93-GT-361, presented at the International Gas Turbine and Aeroengine Congress and Exposition (Cincinnati, OH), 24-27 May 1993

Design with Brittle Materials

Stephen F Duffy, Cleveland State University; Lesley A Janosik, NASA Lewis Research Center

Life Prediction Using Reliability Analyses

The discussions in the previous sections assumed all failures were independent of time and history of previous thermomechanical loadings However, as design protocols emerge for brittle material systems, designers must be aware of several innate characteristics exhibited by these materials When subjected to elevated service temperatures, they exhibit complex thermomechanical behavior that is both inherently time dependent and hereditary in the sense that current behavior depends not only on current conditions, but also on thermomechanical history The design engineer must also be cognizant that the ability of a component to sustain load degrades over time due to a variety of effects such as oxidation, creep, stress corrosion, and cyclic fatigue Stress corrosion and cyclic fatigue result in a phenomenon called subcritical crack growth (SCG) This failure mechanism initiates at a preexisting flaw and continues until a critical length is attained

At that point, the crack grows in an unstable fashion leading to catastrophic failure The SCG failure mechanism is a dependent, load-induced phenomenon Time-dependent crack growth can also be a function of chemical reaction, environment, debris wedging near the crack tip, and deterioration of bridging ligaments Fracture mechanism maps, such

time-as the one developed for ceramic materials (Ref 49) depicted in Fig 9, help illustrate the relative contribution of various failure modes as a function of temperature and stress

Fig 9 Fracture mechanism map for hot-pressed silicon nitride flexure bars Fracture mechanism maps help

illustrate the relative contribution of various failure modes as a function of temperature and stress Source: Ref

49

In addition to the determination of the Weibull shape and scale parameters discussed previously, analysis of dependent reliability in brittle materials necessitates accurate stress field information, as well as evaluation of distinct parameters reflecting material, microstructural, and/or environmental conditions Predicted lifetime reliability of brittle material components depends on Weibull and fatigue parameters estimated from rupture data obtained from widely used tests involving flexural or tensile specimens Fatigue parameter estimates are obtained from naturally flawed specimens ruptured under static (creep), cyclic, or dynamic (constant stress rate) loading For other specimen geometries, a finite element model of the specimen is also required when estimating these parameters For a more detailed discussion of time-

time-dependent parameter estimation, the reader is directed to the CARES/Life (CARES/Life Prediction Program) Users and

Programmers Manual (Ref 50) This information can then be combined with stochastic modeling approaches and

incorporated into integrated design algorithms (computer software) in a manner similar to that presented previously for time-independent models The theoretical concepts upon which these time-dependent algorithms have been constructed and the effects of time-dependent mechanisms, most notably subcritical crack growth and creep, are addressed in the remaining sections of this article

Although it is not discussed in detail here, one approach to improve the confidence in component reliability predictions is

to subject the component to proof testing prior to placing it in service Ideally, the boundary conditions applied to a component under proof testing simulate those conditions the component would be subjected to in service, and the proof test loads are appropriately greater in magnitude over a fixed time interval This form of testing eliminates the weakest components and, thus, truncates the tail of the strength distribution curve After proof testing, surviving components can

be placed in service with greater confidence in their integrity and a predictable minimum service life

Need for Correct Stress State

With increasing use of brittle materials in high-temperature structural applications, the need arises to accurately predict thermomechanical behavior Most current analytical methods for both subcritical crack growth and creep models use elastic stress fields in predicting the time-dependent reliability response of components subjected to elevated service temperatures Inelastic response at high temperature has been well documented in the materials science literature for these material systems, but this issue has been ignored by the engineering design community However, the authors wish to emphasize that accurate predictions of time-dependent reliability demand accurate stress-field information From a design engineer's perspective, it is imperative that the inaccuracies of making time-dependent reliability predictions based on elastic stress fields are taken into consideration This section addresses this issue by presenting a recent formulation of a viscoplastic constitutive theory to model the inelastic deformation behavior of brittle materials at high temperatures

Early work in the field of metal plasticity indicated that inelastic deformations are essentially unaffected by hydrostatic stress This is not the case for brittle (e.g., ceramic-based) material systems, unless the material is fully dense The theory presented here allows for fully dense material behavior as a limiting case In addition, as pointed out in Ref 51, these materials exhibit different time-dependent behavior in tension and compression Thus, inelastic deformation models for these materials must be constructed in a manner that admits sensitivity to hydrostatic stress and differing behavior in tension and compression

A number of constitutive theories for materials that exhibit sensitivity to the hydrostatic component of stress have been proposed that characterize deformation using time-independent classical plasticity as a foundation Corapcioglu and Uz (Ref 52) reviewed several of these theories by focusing on the proposed form of the individual yield function The review includes the works of Kuhn and Downey (Ref 53), Shima and Oyane (Ref 54), and Green (Ref 55) Not included is the work by Gurson (Ref 56), who not only developed a yield criteria and flow rule, but also discussed the role of void nucleation Subsequent work by Mear and Hutchinson (Ref 57) extended Gurson's work to include kinematic hardening

of the yield surfaces

Although the previously mentioned theories admit a dependence on the hydrostatic component of stress, none of these theories allows different behavior in tension and compression In addition, the aforementioned theories are somewhat lacking in that they are unable to capture creep, relaxation, and rate-sensitive phenomena exhibited by brittle materials at high temperature Noted exceptions are the recent work by Ding et al (Ref 58) and the work by White and Hazime (Ref 59) Another exception is an article by Liu et al (Ref 60), which is an extension of the work presented by Ding and

coworkers As these authors point out, when subjected to elevated service temperatures, brittle materials exhibit complex thermomechanical behavior that is inherently time dependent and hereditary in the sense that current behavior depends not only on current conditions, but also on thermomechanical history

The macroscopic continuum theory formulated in the remainder of this section captures these time-dependent phenomena

by developing an extension of a J2 plasticity model first proposed by Robinson (Ref 61) and later extended to sintered powder metals by Duffy (Ref 62) Although the viscoplastic model presented by Duffy (Ref 62) admitted a sensitivity to hydrostatic stress, it did not allow for different material behavior in tension and compression

Willam and Warnke (Ref 63) proposed a yield criterion for concrete that admits a dependence on the hydrostatic component of stress and explicitly allows different material responses in tension and compression Several formulations

of their model exist, that is, a three-parameter formulation and a five-parameter formulation For simplicity, the overview

of the multiaxial derivation of the viscoplastic constitutive model presented here builds on the three-parameter formulation The attending geometrical implications have been presented elsewhere (Ref 64, 65) A quantitative assessment has yet to be conducted because the material constants have not been suitably characterized for a specific material The quantitative assessment could easily dovetail with the nascent efforts of White and coworkers (Ref 59)

The complete theory is derivable from a scalar dissipative potential function identified here as Under isothermal conditions, this function is dependent on the applied stress ij and internal state variable ij:

The stress dependence for a J2 plasticity model or a J2 viscoplasticity model is usually stipulated in terms of the deviatoric

components of the applied stress, S ij = ij - ( ) kk ij , and a deviatoric state variable, a ij = ij - ( ) kk ij For the viscoplasticity model presented here, these deviatoric tensors are incorporated along with the effective stress, ij = ij -

ij, and an effective deviatoric stress, identified as ij = S ij - a ij Both tensors, that is, ij and ij, are utilized for notational convenience

The potential nature of is exhibited by the manner in which the flow and evolutionary laws are derived The flow law is derived from by taking the partial derivative with respect to the applied stress:

(Eq 54)

The adoption of a flow potential and the concept of normality, as expressed in Eq 54, were introduced by Rice (Ref 66)

In his work, the above relationship was established using thermodynamic arguments The authors wish to point out that

Eq 54 holds for each individual inelastic state

The evolutionary law is similarly derived from the flow potential The rate of change of the internal stress is expressed as:

(Eq 55)

where h is a scalar function of the inelastic state variable (i.e., the internal stress) only Using arguments similar to Rice's,

Ponter, and Leckie (Ref 67) have demonstrated the appropriateness of this type of evolutionary law

To give the flow potential a specific form, the following integral format proposed by Robinson (Ref 61) is adopted:

(Eq 56)

where , R, H, and K are material constants In this formulation is a viscosity constant, H is a hardening constant, n and

m are unitless exponents, and R is associated with recovery The octahedral threshold shear stress K appearing in Eq 56 is

generally considered a scalar state variable that accounts for isotropic hardening (or softening) However, because

isotropic hardening is often negligible at high homologous temperatures (T/Tm 0.5), to a first approximation K is taken

to be a constant for metals This assumption is adopted in the present work for brittle materials The reader is directed to Ref 68 for specific details regarding the experimental test matrix needed to characterize these parameters

The dependence on the effective stress ij and the deviatoric internal stress a ij is introduced through the scalar functions

F = F ( ij, ij ) and G = G (a ij, ij) Inclusion of ij and ij will account for sensitivity to hydrostatic stress The concept

of a threshold function was introduced by Bingham (Ref 69) and later generalized by Hohenemser and Prager (Ref 70)

Correspondingly, F is referred to as a Bingham-Prager threshold function Inelastic deformation occurs only for those stress states where F ( ij, ij) > 0

For frame indifference, the scalar functions F and G (and hence ) must be form invariant under all proper orthogonal transformations This condition is ensured if the functions depend only on the principal invariants of ij , a ij ij, and ij;

that is, F = F ( 1, 2, 3), where 1 = ii, 2 = ( ) ij ij, 3 = ( ) ij jk ki , and G = G ( 1, 2, 3), where I1 =

aii , J2 = ( )a ijaij , J3 = ( ) a ijajkaki These scalar quantities are elements of what is known in invariant theory as an integrity

basis for the functions F and G

A three-parameter flow criterion proposed by Willam and Warnke (Ref 63) serves as the Bingham-Prager threshold

function, F The William-Warnke criterion uses the previously mentioned stress invariants to define the functional

dependence on the Cauchy stress ( ij) and internal state variable ( ij) In general, this flow criterion can be constructed from the following general polynomial:

(Eq 57)

where c is the uniaxial threshold flow stress in compression and B is a constant determined by considering

homogeneously stressed elements in the virgin inelastic state ij = 0

Note that a threshold flow stress is similar in nature to a yield stress in classical plasticity In addition, is a function

dependent on the invariant J3 and other threshold stress parameters that are defined momentarily The specific details in

deriving the final form of the function F can be found in Willam and Warnke (Ref 63), and this final formulation is stated

here as:

(Eq 58)

for brevity The invariant 1 in Eq 58 admits a sensitivity to hydrostatic stress The function F is implicitly dependent on

3 through the function r( ), where the angle of similitude, , is defined by the expression:

(Eq 59)

The invariant 3 accounts for different behavior in tension and compression, because this invariant changes sign when the direction of a stress component is reversed The parameter characterizes the tensile hydrostatic threshold flow stress For the Willam-Warnke three-parameter formulation, the model parameters include t, the tensile uniaxial threshold stress, , the compressive uniaxial threshold stress, and , the equal biaxial compressive threshold stress

A similar functional form is adopted for the scalar state function G However, this formulation assumes a threshold does not exist for the scalar function G and follows the framework of previously proposed constitutive models based on

Robinson's viscoplastic law (Ref 61)

Employing the chain rule for differentiation and evaluating the partial derivative of with respect to ij, and then with respect to ij, as indicated in Eq 54 and 55, yields the flow law and the evolutionary law, respectively These expressions are dependent on the principal invariants (i.e., 1, 2, 3, 1, 2, and 3) the three Willam-Warnke threshold parameters (i.e., t, c, and bc), and the flow potential parameters utilized in Eq 56 (i.e., , R, H, K, n, and m) These

expressions constitute a multiaxial statement of a constitutive theory for isotropic materials and serve as an inelastic deformation model for ceramic materials

The overview presented in this section is intended to provide a qualitative assessment of the capabilities of this viscoplastic model in capturing the complex thermomechanical behavior exhibited by brittle materials at elevated service temperatures Constitutive equations for the flow law (strain rate) and evolutionary law have been formulated based on a threshold function that exhibits a sensitivity to hydrostatic stress and allows different behavior in tension and compression Furthermore, inelastic deformation is treated as inherently time dependent A rate of inelastic strain is associated with every state of stress As a result, creep, stress relaxation, and rate sensitivity are phenomena resulting from applied boundary conditions and are not treated separately in an ad hoc fashion Incorporating this model into a nonlinear finite element code would provide a tool for the design engineer to simulate numerically the inherently time-dependent and hereditary phenomena exhibited by these materials in service

Life Prediction Reliability Models

Using a time-dependent reliability model such as those discussed in the following section, and the results obtained from a finite element analysis, the life of a component with complex geometry and loading can be predicted This life is interpreted as the reliability of a component as a function of time When the component reliability falls below a predetermined value, the associated point in time at which this occurs is assigned the life of the component This design methodology presented herein combines the statistical nature of strength-controlling flaws with the mechanics of crack growth to allow for multiaxial stress states, concurrent (simultaneously occurring) flaw populations, and scaling effects With this type of integrated design tool, a design engineer can make appropriate design changes until an acceptable time

to failure has been reached In the sections that follow, only creep rupture and fatigue failure mechanisms are discussed Although models that account for subcritical crack growth and creep rupture are presented, the reader is cautioned that currently available creep models for advanced ceramics have limited applicability because of the phenomenological nature of the models There is a considerable need to develop models incorporating both the ceramic material behavior and microstructural events

Subcritical Crack Growth. A wide variety of brittle materials, including ceramics and glasses, exhibit the

phenomenon of delayed fracture or fatigue Under the application of a loading function of magnitude smaller than that which induces short-term failure, there is a regime where subcritical crack growth occurs and this can lead to eventual component failure in service Subcritical crack growth is a complex process involving a combination of simultaneous and synergistic failure mechanisms These can be grouped into two categories: (1) crack growth due to corrosion and (2) crack growth due to mechanical effects arising from cyclic loading Stress corrosion reflects a stress-dependent chemical interaction between the material and its environment.Water, for example, has a pronounced deleterious effect on the strength of glass and alumina In addition, higher temperatures also tend to accelerate this process Mechanically induced cyclic fatigue is dependent only on the number of load cycles and not on the duration of the cycle This phenomenon can

be caused by a variety of effects, such as debris wedging or the degradation of bridging ligaments, but essentially it is based on the accumulation of some type of irreversible damage that tends to enhance crack growth Service environment, material composition, and material microstructure determine if a brittle material will display some combination of these fatigue mechanisms

Lifetime reliability analysis accounting for SCG under cyclic and/or sustained loads is essential for the safe and efficient utilization of brittle materials in structural design Because of the complex nature of SCG, models that have been developed tend to be semiempirical and approximate the behavior of SCG phenomenologically Theoretical and experimental work in this area has demonstrated that lifetime failure characteristics can be described by consideration of the crack growth rate versus the stress intensity factor (or the range in the stress intensity factor) This is graphically depicted (see Fig 10) as the logarithm of crack growth rate versus the logarithm of the mode I stress intensity factor Curves of experimental data show three distinct regimes or regions of growth The first region (denoted by I in Fig 10) indicates threshold behavior of the crack, where below a certain value of stress intensity the crack growth is zero The

second region (denoted by II in Fig 10) shows an approximately linear relationship of stable crack growth.The third region (denoted by III in Fig 10) indicates unstable crack growth as the materials critical stress intensity factor is approached For the stress-corrosion failure mechanism, these curves are material and environment sensitive This SCG model, using conventional fracture mechanics relationships, satisfactorily describes the failure mechanisms in materials where at high temperatures, plastic deformations and creep behave in a linear viscoelastic manner (Ref 71) In general, at high temperatures and low levels of stress, failure is best described by creep rupture, which generates new cracks (Ref 72) The creep rupture process is discussed further in the next section

Fig 10 Schematic illustrating three different regimes of crack growth

The most-often-cited models in the literature regarding SCG are based on power-law formulations.Other theories, most notably Wiederhorn's (Ref 73), have not achieved such widespread usage, although they may also have a reasonable physical foundation Power-law formulations are used to model both the stress-corrosion phenomenon and the cyclic fatigue phenomenon.This modeling flexibility, coupled with their widespread acceptance, make these formulations the most attractive candidates to incorporate into a design methodology A power-law formulation is obtained by assuming the second crack growth region is linear and that it dominates the other regions Three power-law formulations are useful for modeling brittle materials: the power law, the Paris law, and the Walker equation The power law (Ref 71, 74) describes the crack velocity as a function of the stress intensity factor and implies that the crack growth is due to stress corrosion For cyclic fatigue, either the Paris law (Ref 75) or Walker's (Ref 76, 77) modified formulation of the Paris law

is used to model the SCG The Paris law describes the crack growth per load cycle as a function of the range in the stress intensity factor The Walker equation relates the crack growth per load cycle to both the range in the crack tip stress

intensity factor and the maximum applied crack tip stress intensity factor It is useful for predicting the effect of the

R-ratio (the R-ratio of the minimum cyclic stress to the maximum cyclic stress) on the material strength degradation

Expressions for time-dependent reliability are usually formulated based on the mode I equivalent stress distribution

transformed to its equivalent stress distribution at time t = 0 Investigations of mode I crack extension (Ref 78) have

resulted in the following relationship for the equivalent mode I stress intensity factor:

where Ieq ( , t) is the equivalent mode I stress on the crack, Y is a function of crack geometry, a ( , t) is the

appropriate crack length, and represents a spatial location within the body and the orientation of the crack In some models (such as the phenomenological Weibull NSA and the PIA models), represents a location only Y is a function of

crack geometry; however, herein it is assumed constant with subcritical crack growth Crack growth as a function of the equivalent mode I stress intensity factor is assumed to follow a power-law relationship:

is a material/environmental fatigue parameter, KIc is the critical stress intensity factor, and Ieq ( , tf) is the equivalent

stress distribution in the component at time t = tf The dimensionless fatigue parameter N is independent of fracture criterion B is adjusted to satisfy the requirement that for a uniaxial stress state, all models produce the same probability of failure The parameter B has units of stress2 × time

Because SCG assumes flaws exist in a material, the weakest-link statistical theories discussed previously are required to predict the time-dependent lifetime reliability for brittle materials An SCG model (e.g., the previously discussed power law, Paris law, or Walker equation) is combined with either the two- or three-parameter Weibull cumulative distribution function to characterize the component failure probability as a function of service lifetime The effects of multiaxial stresses are considered by using the PIA model, the Weibull NSA method, or the Batdorf theory These multiaxial reliability expressions were outlined in the previous section on time-independent reliability analysis models, and, for brevity, are not repeated here The reader is directed to see the previous section or, for more complete details, to consult Ref 50

Creep Rupture. For brittle materials, the term creep can infer two different issues The first relates to catastrophic failure of a component from a defect that has been nucleated and propagates to critical size This is known as creep rupture to the design engineer Here, it is assumed that failure does not occur from a defect in the original flaw population Unlike SCG, which is assumed to begin at preexisting flaws in a component and continue until the crack reaches a critical length, creep rupture typically entails the nucleation, growth, and coalescence of voids which eventually form macrocracks, which then propagate to failure The second issue related to creep reflects back on SCG as well as creep rupture, that is, creep deformation This section focuses on the former, while the latter (i.e., creep deformation) is discussed in a previous section

Currently, most approaches to predict brittle material component lifetime due to creep rupture employ deterministic methodologies Stochastic methodologies for predicting creep life in brittle material components have not reached a level

of maturity comparable to those developed for predicting fast-fracture and SCG reliability One such theory is based on the premise that both creep and SCG failure modes act simultaneously (Ref 81) Another alternative method for characterizing creep rupture in ceramics was developed by Duffy and Gyekenyesi, (Ref 82), who developed a time-dependent reliability model that integrates continuum damage mechanics principles and Weibull analysis This particular approach assumes that the failure processes for SCG and creep are distinct and separable mechanisms

The remainder of this section outlines this approach, highlighting creep rupture with the intent to provide the design engineer with a method to determine an allowable stress for a given component lifetime and reliability This is accomplished by coupling Weibull theory with the principles of continuum damage mechanics, which was originally developed by Kachanov (Ref 83) to account for tertiary creep and creep fracture of ductile metal alloys

Ideally, any theory that predicts the behavior of a material should incorporate parameters that are relevant to its microstructure (grain size, void spacing, etc.) However, this would require a determination of volume-averaged effects of microstructural phenomena reflecting nucleation, growth, and coalescence of microdefects that in many instances interact This approach is difficult even under strongly simplifying assumptions In this respect, Leckie (Ref 84) points out that the difference between the materials scientists and the engineer is one of scale He notes the materials scientist is interested in mechanisms of deformation and failure at the microstructural level and the engineer focuses on these issues at the component level Thus, the former designs the material and the latter designs the component Here, the engineer's viewpoint is adopted, and readers should note from the outset that continuum damage mechanics does not focus attention

on microstructural events, yet this logical first approach does provide a practical model, which macroscopically captures the changes induced by the evolution of voids and defects

This method uses a continuum-damage approach where a continuity function, , is coupled with Weibull theory to render

a time-dependent damage model for ceramic materials The continuity function is given by the expression:

to use a scalar state variable for damage because only uniaxial loading conditions were considered The incorporation of a continuum-damage approach within a multiaxial Weibull analysis necessitates the description of oriented damage by a second-order tensor

Life-Prediction Reliability Algorithms

The NASA-developed computer program CARES/Life (Ceramics Analysis and Reliability Evaluation of

Structures/Life-Prediction program) and the AlliedSignal algorithm ERICA have the capability to evaluate the time-dependent reliability

of monolithic ceramic components subjected to thermomechanical and/or proof test loading The reader is directed to Ref

39 and Ref 40 for a detailed discussion of the life-prediction capabilities of the ERICA algorithm The CARES/Life

program is an extension of the previously discussed CARES program, which predicted the fast-fracture

(time-independent) reliability of monolithic ceramic components CARES/Life retains all of the fast-fracture capabilities of the CARES program and also includes the ability to perform time-dependent reliability analysis due to SCG CARES/Life

accounts for the phenomenon of SCG by utilizing the power law, Paris law, or Walker equation The Weibull cumulative distribution function is used to characterize the variation in component strength The probabilistic nature of material strength and the effects of multiaxial stresses are modeled using either the PIA, the Weibull NSA, or the Batdorf theory Parameter estimation routines are available for obtaining inert strength and fatigue parameters from rupture strength data

of naturally flawed specimens loaded in static, dynamic, or cyclic fatigue Fatigue parameters can be calculated using either the median value technique (Ref 85), a least squares regression technique, or a median deviation regression method

that is somewhat similar to trivariant regression (Ref 85) In addition, CARES/Life can predict the effect of proof testing

on component service probability of failure Creep and material healing mechanisms are not addressed in the CARES/Life

code

Life-Prediction Design Examples

Once again, because of the proprietary nature of the ERICA algorithm, the life-prediction examples presented in this

section are all based on design applications where the NASA CARES/Life algorithm was utilized Either algorithm should

predict the same results cited here However, at this point in time comparative studies utilizing both algorithms for the

same analysis are not available in the open literature The primary thrust behind CARES/Life is the support and

development of advanced heat engines and related ceramics technology infrastructure This U.S Department of Energy (DOE), and Oak Ridge National Laboratory (ORNL) have several ongoing programs such as the Advanced Turbine Technology Applications Project (ATTAP) (Ref 48, 86) for automotive gas turbine development, the Heavy Duty Transport Program for low-heat-rejection heavy-duty diesel engine development, and the Ceramic Stationary Gas Turbine

(CSGT) program for electric power cogeneration Both CARES/Life and the previously discussed CARES program are

used in these projects to design stationary and rotating equipment, including turbine rotors, vanes, scrolls, combustors, insulating rings, and seals These programs are also integrated with the DOE/ORNL Ceramic Technology Project (CTP) (Ref 87) characterization and life prediction efforts (Ref 88, 89)

The CARES/Life program has been used to design hot-section turbine parts for the CSGT development program (Ref 90)

sponsored by the DOE Office of Industrial Technology This project seeks to replace metallic hot-section parts with uncooled ceramic components in an existing design for a natural-gas-fired industrial turbine engine operating at a turbine rotor inlet temperature of 1120 °C (2048 °F) At least one stage of blades (Fig 11) and vanes, as well as the combustor liner, will be replaced with ceramic parts Ultimately, demonstration of the technology will be proved with a 4000 h engine field test

Fig 11 Stress contour plot of first-stage silicon nitride turbine rotor blade for a natural-gas-fired industrial

turbine engine for cogeneration The blade is rotating at 14,950 rpm Courtesy of Solar Turbines Inc

Ceramic pistons for a constant-speed drive are being developed Constant-speed drives are used to convert variable engine speed to a constant output speed for aircraft electrical generators The calculated probability of failure of the piston is less than 0.2 × 10-8 under the most severe limit-load condition This program is sponsored by the U.S Navy and ARPA (Advanced Research Projects Agency, formerly DARPA, Defense Advanced Research Projects Agency) As depicted in Fig 12, ceramic components have been designed for a number of other applications, most notably for aircraft auxiliary power units

Fig 12 (a) Ceramic turbine wheel and nozzle for advanced auxiliary power unit (b) Ceramic components for

small expendable turbojet Courtesy of Sundstrand Aerospace Corporation

Glass components behave in a similar manner as ceramics and must be designed using reliability evaluation techniques The possibility of alkali strontium silicate glass CRTs spontaneously imploding has been analyzed (Ref 91) Cathode ray tubes are under a constant static load due to the pressure forces placed on the outside of the evacuated tube A 68 cm (27 in.) diagonal tube was analyzed with and without an implosion protection band The implosion protection band reduces the overall stresses in the tube and, in the event of an implosion, also contains the glass particles within the enclosure Stress analysis (Fig 13) showed compressive stresses on the front face and tensile stresses on the sides of the tube The

implosion band reduced the maximum principal stress by 20% Reliability analysis with CARES/Life showed that the

implosion protection band significantly reduced the probability of failure to about 5 × 10-5

Fig 13 Stress plot of an evacuated 68 cm (27 in.) diagonal CRT The probability of failure calculated with

CARES/Life was less than 5.0 × 10 -3 Courtesy of Philips Display Components Company

The structural integrity of a silicon carbide convection air heater for use in an advanced power-generation system has been assessed by ORNL and the NASA Lewis Research Center The design used a finned tube arrangement 1.8 m (70.9 in.) in length with 2.5 cm (1 in.) diam tubes Incoming air was to be heated from 390 to 700 °C (734 to 1292 °F) The hot

gas flow across the tubes was at 980 °C (1796 °F) Heat transfer and stress analyses revealed that maximum stress gradients across the tube wall nearest the incoming air would be the most likely source of failure

Probabilistic design techniques are being applied to dental ceramic crowns, as illustrated in Fig 14 Frequent failure of some ceramic crowns (e.g., 35% failure of molar crowns after three years), which occurs because of residual and functional stresses, necessitates design modifications and improvement of these restorations Thermal tempering treatment is being investigated as a means of introducing compressive stresses on the surface of dental ceramics to improve the resistance to failure (Ref 92) Evaluation of the risk of material failure must be considered not only for the service environment, but also from the tempering process

Fig 14 Stress contour plot of ceramic dental crown, resulting from a 600 N biting force Courtesy of University

of Florida College of Dentistry

References cited in this section

39 J.C Cuccio, P Brehm, H.T Fang, J Hartman, W Meade, M.N Menon, A Peralta, J.Z Song, T Strangman, J Wade, J Wimmer, and D.C Wu, "Life Prediction Methodology for Ceramic Components of Advanced Heat Engines, Phase I," ORNL/Sub/89-SC674/1/V1, Vol 1, Final Report, Oak Ridge National Laboratory, March 1995

40 J.C Cuccio, P Brehm, H.T Fang, J Hartman, W Meade, M.N Menon, A Peralta, J.Z Song, T Strangman, J Wade, J Wimmer, and D.C Wu, "Life Prediction Methodology for Ceramic Components of Advanced Heat Engines, Phase I," ORNL/Sub/89-SC674/1/V2, Vol 2, Final Report, Oak Ridge National Laboratory, March 1995

48 J.R Smyth, R.E Morey, and R.W Schultz, "Ceramic Gas Turbine Technology Development and Applications," Paper 93-GT-361, presented at the International Gas Turbine and Aeroengine Congress and Exposition (Cincinnati, OH), 24-27 May 1993

49 G.D Quinn, Fracture Mechanism Maps for Advanced Structural Ceramics: Part 1; Methodology and

Hot-Pressed Silicon Nitride Results, J Mater Sci., Vol 25, 1990, p 4361-4376

50 N.N Nemeth, L.M Powers, L.A Janosik, and J.P Gyekenyesi, "CARES/Life Prediction Program

(CARES/Life) Users and Programmers Manual," TM-106316, to be published

51 T.-J Chuang, and S.F Duffy, A Methodology to Predict Creep Life for Advanced Ceramics Using

Continuum Damage Mechanics, Life Prediction Methodologies and Data for Ceramic Materials, STP 1201,

C.R Brinkman and S.F Duffy, Ed., ASTM, 1994, p 207-227

52 Y Corapcioglu and T Uz, Constitutive Equations for Plastic Deformation of Porous Materials, Powder Technol., Vol 21, 1978, p 269-274

53 H.A Kuhn and C.L Downey, Deformation Characteristics and Plasticity Theory of Sintered Powder

Metals, Int J Powder Metall., Vol 7, 1971, p 15-25

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55 R.J Green, A Plasticity Theory for Porous Solids, Int J Mech Sci., Vol 14, 1972, p 215

56

A.L Gurson, Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I Yield Criteria

and Flow Rules for Porous Ductile Media, J Eng Mater Technol., Vol 99, 1977, p 2-15

57 M.E Mear and J.W Hutchinson, Influence of Yield Surface Curvature on Flow Localization in Dilatant

Plasticity, Mech Mater., Vol 4, 1985, p 395-407

58 J.-L Ding, K.C Liu, and C.R Brinkman, A Comparative Study of Existing and Newly Proposed Models

for Creep Deformation and Life Prediction of Si3N4, Life Prediction Methodologies and Data for Ceramic Materials, STP 1201, C.R Brinkman and S.F Duffy, Ed., ASTM, 1994, p 62-83

59 C.S White, and R.M Hazime, Internal Variable Modeling of the Creep of Monolithic Ceramics,

proceedings of the 11th Biennial Conference on Reliability, Stress Analysis, and Failure Prevention, O

Jadaan, Ed., American Society of Mechanical Engineers, 1995

60 K.C Liu, C.R Brinkman, J.-L Ding, and S.Liu, Predictions of Tensile Behavior and Strengths of Si3N4

Ceramic at High Temperatures Based on a Viscoplastic Model, ASME Trans., 95-GT-388, 1995

61 D.N Robinson, "A Unified Creep-Plasticity Model for Structural Metals at High Temperature," ORNL/TM

5969, Oak Ridge National Laboratory, 1978

62 S.F Duffy, A Unified Inelastic Constitutive Theory for Sintered Powder Metals, Mech Mater., Vol 7, 1988,

p 245-254

63 K.J Willam and E.P Warnke, Constitutive Model for the Triaxial Behaviour of Concrete, Int Assoc Bridge Struct Eng Proc., Vol 19, 1975, p 1-30

64 L.A Janosik and S.F Duffy, A Viscoplastic Constitutive Theory for Monolithic Ceramic Materials I,

paper 15, Proceedings of the Physics and Process Modeling (PPM) and Other Propulsion R&T Conference, Vol I, Materials Processing, Characterization, and Modeling; Lifing Models, CP-10193, National

Aeronautics and Space Administration, 1997

65 L.A Janosik and S.F Duffy, A Viscoplastic Constitutive Theory for Monolithic Ceramics I, paper No GT-368, International Gas Turbine Congress, Exposition, and Users' Symposium (Birmingham, UK), American Society of Mechanical Engineers, 10-13 June 1996

96-66 J.R Rice, On the Structure of Stress-Strain Relations for Time-Dependent Plastic Deformation in Metals, J Appl Mech., Vol 37, 1970, p 728

67 A.R.S Ponter and F.A Leckie, Constitutive Relationships for Time-Dependent Deformation of Metals, J Eng Mater Technol (Trans ASME), Vol 98, 1976

68 L.A Janosik, "A Unified Viscoplastic Constitutive Theory for Monolithic Ceramics," Master's thesis, Cleveland State University, Cleveland, OH, 1997, to be published

69 E.C Bingham, Fluidity and Plasticity, McGraw-Hill, 1922

70 K Hohenemser and W Prager, Ueber die Ansaetze der Mechanik Isotroper Kontinua, Z Angewandte Mathemat Mech., Vol 12, 1932 (in German)

71 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

72 S.M Wiederhorn and E.R Fuller, Jr., Structural Reliability of Ceramic Materials, Mater Sci Eng., Vol 71,

1985, p 169-186

73 S.M Wiederhorn, E.R Fuller, and R Thomson, Micromechanisms of Crack Growth in Ceramics and

Glasses in Corrosive Environments, Met Sci., Aug-Sept 1980, p 450-458

74 S.M Wiederhorn, Fracture Mechanics of Ceramics, R.C Bradt, D.P Hasselman, and F.F.Lange, Ed.,

Plenum, 1974, p 613-646

75 P Paris and F Erdogan, A Critical Analysis of Crack Propagation Laws, J Basic Eng., Vol 85, 1963, p

528-534

76 K Walker, The Effect of Stress Ratio During Crack Propagation and Fatigue for 2024-T3 and 7075-T6

Aluminum, Effects of Environment and Complex Load History on Fatigue Life, STP 462, ASTM, 1970, p

1-14

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

SiC-Whisker-Reinforced Alumina Ceramic Composite: Long and Small Crack Behavior, J Am Ceram Soc., Vol 75 (No

83 L.M Kachanov, Time of the Rupture Process Under Creep Conditions, Izv Akad Nauk SSR, Otd Tekh Nauk, Vol 8, 1958, p 26

84 F.A Leckie, Advances in Creep Mechanics, Creep in Structures, A.R.S Ponter and D.R.Hayhurst, Ed.,

Springer-Verlag, 1981, p 13

85 K Jakus, D.C Coyne, and J.E Ritter, Analysis of Fatigue Data for Lifetime Predictions for Ceramic

Materials, J Mater Sci., Vol 13, 1978, p 2071-2080

86 S.G Berenyi, S.J Hilpisch, and L.E Groseclose, "Advanced Turbine Technology Applications Project (ATTAP)," Proceedings of the Annual Automotive Technology Development Contractor's Coordination Meeting (Dearborn, MI), 18-21 Oct 1993, SAE International

87 D.R Johnson and R.B Schultz, "The Ceramic Technology Project: Ten Years of Progress," Paper

93-GT-417, presented at the International Gas Turbine and Aeroengine Congress and Exposition (Cincinnati, OH), 24-27 May 1993, American Society of Mechanical Engineers

88 J Cuccio, "Life Prediction Methodology for Ceramic Components of Advanced Heat Engines," Proceedings of the Annual Automotive Technology Development Contractor's Coordination Meeting (Dearborn, MI), 18-21 Oct 1993

89 P.K Khandelwal, N.J Provenzano, and W.E.Schneider, "Life Prediction Methodology for Ceramic Components of Advanced Vehicular Engines," Proceedings of the Annual Automotive Technology Development Contractor's Coordination Meeting (Dearborn, MI), 18-21 Oct 1993

90 M van Roode, W.D Brentnall, P.F Norton, and G.P Pytanowski, "Ceramic Stationary Gas Turbine Development," Paper 93-GT-309, presented at the International Gas Turbine and Aeroengine Congress and Exposition (Cincinnati, OH), 24-27 May 1993, American Society of Mechanical Engineers, 24-27 May

1993

91 A Ghosh, C.Y Cha, W Bozek, and S Vaidyanathan, Structural Reliability Analysis of CRTs, Society for Information Display International Symposium Digest of Technical Papers, Vol XXIII, 17-22 May 1992,

Society of Information Display, Playa Del Ray, CA, p 508-510

92 B Hojjatie, Thermal Tempering of Dental Ceramics, Proceedings of the ANSYS Conference and Exhibition,

Vol 1, Swanson Analysis Systems Inc., Houston, PA, 1992, p I.73-I.91

Design with Brittle Materials

Stephen F Duffy, Cleveland State University; Lesley A Janosik, NASA Lewis Research Center

References

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33 D.J Thomas and R.C Wetherhold, Reliability of Continuous Fiber Composite Laminates, Comput Struct.,

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34 J.L Palko, "An Interactive Reliability Model for Whisker-Toughened Ceramics," Master's thesis, Cleveland State University, Cleveland, OH, 1992

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37 J.P Gyekenyesi and N.N Nemeth, Surface Flaw Reliability Analysis of Ceramic Components with the

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38 J.P Gyekenyesi, SCARE: A Postprocessor Program to MSC/NASTRAN for the Reliability Analysis of

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39 J.C Cuccio, P Brehm, H.T Fang, J Hartman, W Meade, M.N Menon, A Peralta, J.Z Song, T Strangman, J Wade, J Wimmer, and D.C Wu, "Life Prediction Methodology for Ceramic Components of Advanced Heat Engines, Phase I," ORNL/Sub/89-SC674/1/V1, Vol 1, Final Report, Oak Ridge National Laboratory, March 1995

40 J.C Cuccio, P Brehm, H.T Fang, J Hartman, W Meade, M.N Menon, A Peralta, J.Z Song, T Strangman, J Wade, J Wimmer, and D.C Wu, "Life Prediction Methodology for Ceramic Components of Advanced Heat Engines, Phase I," ORNL/Sub/89-SC674/1/V2, Vol 2, Final Report, Oak Ridge National Laboratory, March 1995

41 C Baker and D Baker, Design Practices for Structural Ceramics in Automotive Turbocharger Wheels,

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42 C.J Poplawsky, L Lindberg, S Robb, and J Roundy, "Development of an Advanced Ceramic Turbine Wheel for an Air Turbine Starter," Paper 921945, presented at Aerotech '92, Anaheim, CA, Society of Automotive Engineers, 5-8 Oct 1992

43 J.H Selverian, D O'Neil, and S Kang, Ceramic-to-Metal Joints: Part I-Joint Design, Am Ceram Soc Bull., Vol 71 (No 9), 1992, p 1403-1409

44 J.H Selverian and S Kang, Ceramic-to-Metal Joints: Part II-Performance and Strength Prediction, Am Ceram Soc Bull., Vol 71 (No 10), 1992, p 1511-1520

45 C.L Snydar, "Reliability Analysis of a Monolithic Graphite Valve," presented at the 15th Annual Conference on Composites, Materials, and Structures (Cocoa Beach, FL), American Ceramic Society, 1991

46 J.A Salem, J.M Manderscheid, M.R Freedman, and J.P Gyekenyesi, "Reliability Analysis of a Structural Ceramic Combustion Chamber," Paper 91-GT-155, presented at the International Gas Turbine and Aeroengine Congress and Exposition, Orlando, FL, 3-6 June 1991

47 R.R Wills and R.E Southam, Ceramic Engine Valves, J Am Ceram Soc., Vol 72 (No 7), 1989, p

1261-1264

48 J.R Smyth, R.E Morey, and R.W Schultz, "Ceramic Gas Turbine Technology Development and Applications," Paper 93-GT-361, presented at the International Gas Turbine and Aeroengine Congress and Exposition (Cincinnati, OH), 24-27 May 1993

49 G.D Quinn, Fracture Mechanism Maps for Advanced Structural Ceramics: Part 1; Methodology and

Hot-Pressed Silicon Nitride Results, J Mater Sci., Vol 25, 1990, p 4361-4376

50 N.N Nemeth, L.M Powers, L.A Janosik, and J.P Gyekenyesi, "CARES/Life Prediction Program

(CARES/Life) Users and Programmers Manual," TM-106316, to be published

51 T.-J Chuang, and S.F Duffy, A Methodology to Predict Creep Life for Advanced Ceramics Using

Continuum Damage Mechanics, Life Prediction Methodologies and Data for Ceramic Materials, STP 1201,

C.R Brinkman and S.F Duffy, Ed., ASTM, 1994, p 207-227

52 Y Corapcioglu and T Uz, Constitutive Equations for Plastic Deformation of Porous Materials, Powder Technol., Vol 21, 1978, p 269-274

53 H.A Kuhn and C.L Downey, Deformation Characteristics and Plasticity Theory of Sintered Powder

Metals, Int J Powder Metall., Vol 7, 1971, p 15-25

54 S Shima and M Oyane, Plasticity Theory for Porous Metals, Int J Mech Sci., Vol 18, 1976, p 285

55 R.J Green, A Plasticity Theory for Porous Solids, Int J Mech Sci., Vol 14, 1972, p 215

56

A.L Gurson, Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I Yield Criteria

and Flow Rules for Porous Ductile Media, J Eng Mater Technol., Vol 99, 1977, p 2-15

57 M.E Mear and J.W Hutchinson, Influence of Yield Surface Curvature on Flow Localization in Dilatant

Plasticity, Mech Mater., Vol 4, 1985, p 395-407

58 J.-L Ding, K.C Liu, and C.R Brinkman, A Comparative Study of Existing and Newly Proposed Models

for Creep Deformation and Life Prediction of Si3N4, Life Prediction Methodologies and Data for Ceramic Materials, STP 1201, C.R Brinkman and S.F Duffy, Ed., ASTM, 1994, p 62-83

59 C.S White, and R.M Hazime, Internal Variable Modeling of the Creep of Monolithic Ceramics,

proceedings of the 11th Biennial Conference on Reliability, Stress Analysis, and Failure Prevention, O

Jadaan, Ed., American Society of Mechanical Engineers, 1995

60 K.C Liu, C.R Brinkman, J.-L Ding, and S.Liu, Predictions of Tensile Behavior and Strengths of Si3N4

Ceramic at High Temperatures Based on a Viscoplastic Model, ASME Trans., 95-GT-388, 1995

61 D.N Robinson, "A Unified Creep-Plasticity Model for Structural Metals at High Temperature," ORNL/TM

5969, Oak Ridge National Laboratory, 1978

62 S.F Duffy, A Unified Inelastic Constitutive Theory for Sintered Powder Metals, Mech Mater., Vol 7, 1988,

p 245-254

63 K.J Willam and E.P Warnke, Constitutive Model for the Triaxial Behaviour of Concrete, Int Assoc Bridge Struct Eng Proc., Vol 19, 1975, p 1-30

64 L.A Janosik and S.F Duffy, A Viscoplastic Constitutive Theory for Monolithic Ceramic Materials I,

paper 15, Proceedings of the Physics and Process Modeling (PPM) and Other Propulsion R&T Conference, Vol I, Materials Processing, Characterization, and Modeling; Lifing Models, CP-10193, National

Aeronautics and Space Administration, 1997

65 L.A Janosik and S.F Duffy, A Viscoplastic Constitutive Theory for Monolithic Ceramics I, paper No GT-368, International Gas Turbine Congress, Exposition, and Users' Symposium (Birmingham, UK), American Society of Mechanical Engineers, 10-13 June 1996

96-66 J.R Rice, On the Structure of Stress-Strain Relations for Time-Dependent Plastic Deformation in Metals, J

Appl Mech., Vol 37, 1970, p 728

67 A.R.S Ponter and F.A Leckie, Constitutive Relationships for Time-Dependent Deformation of Metals, J Eng Mater Technol (Trans ASME), Vol 98, 1976

68 L.A Janosik, "A Unified Viscoplastic Constitutive Theory for Monolithic Ceramics," Master's thesis, Cleveland State University, Cleveland, OH, 1997, to be published

69 E.C Bingham, Fluidity and Plasticity, McGraw-Hill, 1922

70 K Hohenemser and W Prager, Ueber die Ansaetze der Mechanik Isotroper Kontinua, Z Angewandte Mathemat Mech., Vol 12, 1932 (in German)

71 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

72 S.M Wiederhorn and E.R Fuller, Jr., Structural Reliability of Ceramic Materials, Mater Sci Eng., Vol 71,

1985, p 169-186

73 S.M Wiederhorn, E.R Fuller, and R Thomson, Micromechanisms of Crack Growth in Ceramics and

Glasses in Corrosive Environments, Met Sci., Aug-Sept 1980, p 450-458

74 S.M Wiederhorn, Fracture Mechanics of Ceramics, R.C Bradt, D.P Hasselman, and F.F.Lange, Ed.,

Plenum, 1974, p 613-646

75 P Paris and F Erdogan, A Critical Analysis of Crack Propagation Laws, J Basic Eng., Vol 85, 1963, p

528-534

76 K Walker, The Effect of Stress Ratio During Crack Propagation and Fatigue for 2024-T3 and 7075-T6

Aluminum, Effects of Environment and Complex Load History on Fatigue Life, STP 462, ASTM, 1970, p

1-14

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

SiC-Whisker-Reinforced Alumina Ceramic Composite: Long and Small Crack Behavior, J Am Ceram Soc., Vol 75 (No

83 L.M Kachanov, Time of the Rupture Process Under Creep Conditions, Izv Akad Nauk SSR, Otd Tekh Nauk, Vol 8, 1958, p 26

84 F.A Leckie, Advances in Creep Mechanics, Creep in Structures, A.R.S Ponter and D.R.Hayhurst, Ed.,

Springer-Verlag, 1981, p 13

85 K Jakus, D.C Coyne, and J.E Ritter, Analysis of Fatigue Data for Lifetime Predictions for Ceramic

Materials, J Mater Sci., Vol 13, 1978, p 2071-2080

86 S.G Berenyi, S.J Hilpisch, and L.E Groseclose, "Advanced Turbine Technology Applications Project (ATTAP)," Proceedings of the Annual Automotive Technology Development Contractor's Coordination Meeting (Dearborn, MI), 18-21 Oct 1993, SAE International

87 D.R Johnson and R.B Schultz, "The Ceramic Technology Project: Ten Years of Progress," Paper

93-GT-417, presented at the International Gas Turbine and Aeroengine Congress and Exposition (Cincinnati, OH), 24-27 May 1993, American Society of Mechanical Engineers

88 J Cuccio, "Life Prediction Methodology for Ceramic Components of Advanced Heat Engines," Proceedings of the Annual Automotive Technology Development Contractor's Coordination Meeting

(Dearborn, MI), 18-21 Oct 1993

89 P.K Khandelwal, N.J Provenzano, and W.E.Schneider, "Life Prediction Methodology for Ceramic Components of Advanced Vehicular Engines," Proceedings of the Annual Automotive Technology Development Contractor's Coordination Meeting (Dearborn, MI), 18-21 Oct 1993

90 M van Roode, W.D Brentnall, P.F Norton, and G.P Pytanowski, "Ceramic Stationary Gas Turbine Development," Paper 93-GT-309, presented at the International Gas Turbine and Aeroengine Congress and Exposition (Cincinnati, OH), 24-27 May 1993, American Society of Mechanical Engineers, 24-27 May

1993

91 A Ghosh, C.Y Cha, W Bozek, and S Vaidyanathan, Structural Reliability Analysis of CRTs, Society for Information Display International Symposium Digest of Technical Papers, Vol XXIII, 17-22 May 1992,

Society of Information Display, Playa Del Ray, CA, p 508-510

92 B Hojjatie, Thermal Tempering of Dental Ceramics, Proceedings of the ANSYS Conference and Exhibition,

Vol 1, Swanson Analysis Systems Inc., Houston, PA, 1992, p I.73-I.91

Design with Plastics

G.G Trantina, General Electric Corporate Research and Development

Introduction

THE KEY to any successful part development is the proper choice of material, process, and design matched to the part performance requirements The ability to design plastic parts requires knowledge of material properties performance indicators that are not design or geometry dependent rather than material comparators that apply only to a specific geometry and loading Understanding the true effects of time, temperature, and rate of loading on material performance can make the difference between a successful application and catastrophic failure Examples of reliable material performance indicators and common practices to avoid are presented in this article Simple tools and techniques for predicting part performance (stiffness, strength/impact, creep/stress relaxation and fatigue) integrated with manufacturing concerns (flow length and cycle time) are demonstrated for design and material selection

Engineering plastics are now used in applications where their mechanical performance must meet increasingly demanding requirements Because the marketplace is more competitive, companies cannot afford overdesigned parts or lengthy, iterative product-development cycles Therefore, engineers must have design technologies that allow them to create productively the most cost-effective design with the optimal material and process selection

The design-engineering process involves meeting end-use requirements with the lowest cost, design, material, and process combination (Fig 1) Design activities include creating geometries and performing engineering analysis to predict part performance Material characterization provides engineering design data, and process selection includes process/design interaction knowledge In general, the challenge in designing with structural plastics is to develop an understanding not only of design techniques, but also of manufacturing and material behavior

Fig 1 Design-engineering process The goal is to meet the end-use requirements the first time with the lowest

cost

Engineering thermoplastics exhibit complex behavior when subjected to mechanical loads Standard data sheets provide overly simplified, single-point data that are either ignored or, if used, are probably misleading Some databases provide engineering data (Ref 1) over a range of application conditions and knowledge-based material selection programs have been written (Ref 2) A methodology for optimal selection of materials and manufacturing conditions to meet part performance needs is being developed This methodology is clarified in this article by describing and demonstrating simple tools and techniques for the initial prediction of part performance, leading to the optimal selection of materials and process conditions Related coverage is provided in the articles "Effects of Composition, Processing, and Structure on Properties of Engineering Plastics" and "Design for Plastics Processing" in this Volume Detailed information about many

of the concepts described in this article can be found in Engineering Plastics, Volume 2 of the Engineered Materials

Handbook published by ASM International

Design with Plastics

G.G Trantina, General Electric Corporate Research and Development

Mechanical Part Performance

There are a wide variety of part performance requirements Some, such as flammability, transparency, ultraviolet stability, electrical, moisture, and chemical compatibility, as well as agency approvals, are specified as absolute values or simplified choices However, mechanical requirements such as stiffness, strength, impact, and temperature resistance cannot be specified as absolute values For example, a part may be required to have a certain stiffness maximum deflection for a given loading condition The part geometry (design) and the material stiffness combine to produce the part stiffness Thus, it is impossible to select a material without some knowledge of the part design Similarly, the part may be required to survive a certain drop test and/or a certain temperature/time/loading condition Again, it is impossible

to select a material or design a part by using traditional, inadequate, single-point data such as notched Izod or heat distortion temperature (HDT) In addition, it is important to consider the effects of the design and material selection of a part on its fabrication (see the article "Relationship between Materials Selection and Processing" in this Volume)

Considerations such as flow and cycle time should be quantitatively included in the design and material-selection process Simple yet extremely useful tools and techniques for the initial prediction of part performance are presented here

The design process for thermoplastic part performance can be divided into two categories based on time-independent and time-dependent material behavior (Fig 2) For time-independent material behavior, elastic material response is used to predict the displacement of a part under load The maximum load occurs when the strength of the material is reached as fully plastic yielding for ductile materials or brittle failure for glass-filled materials Time-dependent material behavior becomes important for three types of loading: monotonic loading at a given strain-rate until failure occurs, constant load for a period of time, or cyclic load In the first case strain-rate-dependent material behavior becomes important; for constant load or displacement, time-dependent deformation or stress relaxation becomes an important design consideration; for cyclic loading, fatigue failure is an important consideration In the next five sections, stiffness, strength, impact, creep/stress relaxation, and fatigue behavior will be related to part performance More details of these important design issues can be found in Ref 3

Fig 2 Design for thermoplastic part performance (a) Time-independent (b) Time-dependent

Part Stiffness. Many thermoplastic parts are platelike structures that can be treated as a simply supported plate, possibly reinforced with ribs A procedure intended to provide quick, approximate solutions for the stiffness of laterally loaded rib-stiffened plates has been developed (Ref 4) The computer program employs the Rayleigh-Ritz energy method and is capable of including the geometric nonlinearities associated with the large-displacement response typical of low-

modulus materials such as thermoplastics The program allows the user to input the important parameters of specific plate structures (length, width, thickness, number of ribs, rib geometry), the boundary conditions (simply supported, clamped, point supported), and the loading (central point, uniform pressure, torsion loading) With the capability of multiple rib pattern definitions, the user can quickly determine the load-deflection response for different designs to select the one that

is most effective for the specific application This tool has been validated with finite element results An example demonstrating the prediction of the nonlinear load displacement response is shown in Fig 3

Fig 3 Nonlinear pressure-deflection response for a 254 by 254 mm (10 by 10 in.) plate with a thickness of 2.5

mm (0.1 in.) and a material with a modulus of 2350 MPa (340 ksi)

Strength and Stiffness of Glass-Filled Plastic Parts. An accurate characterization of the strength and stiffness of glass-filled thermoplastics is necessary to predict the strength and stiffness of components that are injection molded with these materials The mechanical properties of glass-reinforced thermoplastics are generally measured in tension using end-gated, injection-molded ASTM type I (dog-bone) specimens (Ref 3) However, the gating and the direction of loading of these molded specimens yields nonconservative stiffness and strength results caused by the highly axial orientation of glass that occurs in the direction of flow (and loading) during molding

Previous studies (Ref 5) have shown that injection-molded, glass-reinforced thermoplastics are anisotropic; that is, stiffness and strength values in the cross-flow direction are substantially lower than in the flow direction The tensile stiffness and strength were measured by using dog-bone specimens that were cut in both the flow and ross-flow direction from edge-gated plaques of various thicknesses The ratio of the cross-flow/flow tensile modulus and strength of 30% glass-filled polybutylene terephthalate (PBT), 30% glass-filled modified polyphenylene oxide (M-PPO), and 50% glass-filled (long-glass fibers) nylon are plotted versus specimen thickness in Fig 4 and 5 It is important to note the strong dependence of the cross-flow/flow ratio on specimen thickness and the small values of this ratio for small specimen thicknesses These data clearly indicate that material selection and design for glass-filled materials that are based on injection-molded bars of a given thickness could be totally misleading cross-flow properties could be only 50% of flow properties (small specimen thicknesses), and unless the thickness of the specimen is the same as the thickness of the part, the data could not be used for predicting part performance However, for most parts (thickness less than 4 mm) with glass loadings of 30% or greater, a simple mold-filling analysis coupled with an anisotropic stress analysis with the cross-flow stiffness of 60% of the flow stiffness provides a reasonable prediction of part performance (Ref 3)

Fig 4 Ratio of cross-flow/flow tensile modulus as a function of specimen thickness PBT, polybutylene

terephthalate; M-PPO, modified polyphenylene oxide

Fig 5 Ratio of cross-flow/flow ultimate stress as a function of specimen thickness

Part Strength and Impact Resistance. A number of test methods such as Izod (notched beam) and Gardner/Dynatup (disk) are available for measuring impact resistance (Ref 3) Such tests should not only measure the amount of energy absorbed, but also determine the effects of temperature on energy absorption Additionally, they should

be able to identify strain-rate-dependent transitions from ductile to brittle behavior They should be applicable to a wide variety of geometric configurations Unfortunately, these techniques provide only geometry-specific, single-point data for

a specific temperature and strain rate Also, each test provides a different ductile/brittle transition Energy absorption, however measured, is made up of many complex processes involving elastic and plastic deformation, notch sensitivity, and fracture processes of crack initiation and propagation

The prediction of strength and impact resistance of plastic parts is probably the most difficult challenge for the design engineer Tensile stress-strain measurements as a function of temperature and strain rate provide one piece of useful information Most unfilled engineering thermoplastics exhibit ductile behavior in these tensile tests, with increasing strength (maximum stress) as displacement rate increases and/or temperature decreases However, stress-state effects

must be added to the tensile behavior because the three-dimensional stress state created by notches, radii, holes, thick sections, and so forth increase the potential of brittle failure

Ductile-to-brittle transitions in the fracture behavior of unfilled thermoplastics occur with increasing strain rates, decreasing temperatures, and increasingly constrained stress states Figure 6 shows three common mechanical test techniques:uniaxial tension, biaxially stressed disks (usually clamped on the perimeter and loaded perpendicularly with a hemispherical tup), and notched beams loaded in bending These three tests provide uniaxial, biaxial, and triaxial states of stress Typical part geometries and loadings exhibit combinations of these states of stress Thus, no one test is sufficient for part design and material selection Furthermore, there are two competing failure modes: ductile and brittle (Fig 6) With increasingly constrained stress states (uniaxial biaxial triaxial), the tendency for brittle failure tends to increase Brittle failure occurs when the brittle failure mechanism occurs prior to ductile deformation (Fig 6)

Fig 6 Impact test methods exhibiting various states of stress (a) Tensile test uniaxial stress state (b)

Dynatup test biaxial stress state (c) Notch Izod test triaxial stress state (d) Competing failure modes

The calculation and measurement of the ductility ratio (Ref 6) is a method to characterize the ductility of a material for a relatively severe state of stress, for example, a beam with a notch radius of 0.25 mm (0.010 in.) The ductility ratio is

defined as the ratio of the failure load in the notched-beam geometry (Pfailure) to the maximum ductile, load-carrying capability in an unnotched-beam geometry where the height of the unnotched beam is equal to the net section height of the notched-beam geometry:

(Eq 1)

where:

be plotted as a function of strain rate at different temperatures to create fracture maps such as the one shown for polycarbonate (PC) in Fig 7 This information is useful for material-selection and initial part design considerations

Fig 7 Fracture map for polycarbonate

Creep/Stress Relaxation Time/Temperature Part Performance. Polymers exhibit time-dependent deformation (creep and stress relaxation) when subjected to loads This deformation is significant in many polymers, even

at room temperature, and is rapidly accelerated by small increases in temperature Hence, the phenomenon is the source of many design problems Development and application of methods are needed for predicting whether a component will sustain the required service life when subjected to loading, as the useful life of the part could be terminated by excessive deformation or even rupture For most practical applications of polymers, predictive methods must account for part geometry, loading, and material behavior

A common measure of heat resistance is the heat distortion temperature (HDT) For this test, bending specimen 127 by 12.7 mm (5 by 0.5 in.) with a thickness ranging from 3.2 to 12.7 mm (0.125 to 0.5 in.) is placed on supports 102 mm (4 in.) apart, and a load producing an outer fiber stress of 0.46 or 1.82 MPa (66 or 264 psi) is applied The temperature in the chamber is increased at a rate of 2 °C/min (3.6 °F/min) The temperature at which the bar deflects an additional 0.25 mm (0.010 in.) is called the HDT or sometimes the deflection temperature under load (DTUL) Such a test, which involves variable temperature and arbitrary stress and deflection is of no use in predicting the structural performance of a thermoplastic at any temperature, stress, or time In addition, it can be misleading when comparing materials A material with a higher HDT than another material could exhibit more creep at a lower temperature Also, some semicrystalline materials exhibit very different values of HDT at 0.46 and 1.82 MPa (66 and 264 psi) For example, with PBT, the HDT

at 0.46 MPa (66 psi) is 154 °C (310 °F), and the HDT for 1.82 MPa (264 psi) is 54 °C (130 °F) The question of which HDT to use for comparison with another material that has the same HDT for both stress levels naturally arises Another approach that is often used to account for the change in material modulus with temperature is the use of dynamic mechanical analysis (DMA) data (Ref 7) Although this approach may be a more useful indication of instantaneous

modulus variation with temperature than HDT, it is unable to account for the time-dependent nature of most applications For purposes of predicting part performance and for material selection, tensile creep data are the desired measurements

To be useful for preliminary part design and material selection, creep data must be converted to simple information such

as "deformation maps." A simple method is summarized where linear elastic part deformations are simply magnified by the use of deformation maps thus accounting for time and temperature effects

A deformation map is produced directly from creep data (Ref 8) For a given temperature, T, the measured dependent strain, (t) is divided by the applied stress, , to determine the creep compliance, J, as:

Thus, a deformation map in time and temperature space can be produced from creep data with lines of constant

compliance and modulus (Fig 8) Thus, the design process involves calculating the linear elastic part deformation using E

and then magnifying that deformation by for the time of loading and ambient temperature When a constant

displacement is applied to a part, the calculated linear elastic stress using E is then reduced by Ê for the time of interest

and ambient temperature Thus, the deformation map provides a simple method to predict the time-dependent performance of plastic parts As shown in Fig 8, the deformation map provides the material response that can be combined with a linear elastic, time-independent analysis (in this case a finite-element stress analysis) to predict the time-dependent deformation Validation of this approach is demonstrated by comparing it to experimentally measured part deformations (Fig 8)

Fig 8 Deformation map (a) used to predict PC part deformation at 82 °C (180 °F) Ê = E(T,t)/2350 MPa (b)

Comparison of cathode-ray-tube housing creep prediction

Fatigue-Cycle-Dependent Part Performance. An understanding of the deformation and fracture behavior of plastics subjected to cyclic loading is needed to predict the lifetime of structures fabricated from thermoplastics This fatigue behavior is of concern because failure at fluctuating load levels can occur at much lower levels than failure under monotonic loading A significant amount of information exists on the fatigue behavior of plastics Unfortunately, very little has been documented about the application of this understanding to the prediction of the fatigue behavior of plastic parts

There are two distinct approaches to treating and measuring the fatigue of polymers The first approach is the traditional

measurement of the number of cycles to failure (N) as a function of the fluctuating load or stress (S), that is, S-N The

"load" that is controlled is the minimum and maximum force or displacement in tension or bending The fluctuations have

a certain frequency and waveform From a design viewpoint, it is difficult to predict part performance with these data because an enormous number of variables must be taken into consideration as well as various environmental conditions and a wide variety of materials

The second approach to treating the fatigue of plastics is cyclic crack propagation The use of fracture mechanics in cyclic fatigue involves the measurement of the amount of crack growth per cycle as a function of the stress-intensity factor The fundamental addition here is the treatment of the crack length and thus an improved understanding of a fatigue

mechanism However, the same large number of variables that apply to the traditional fatigue (S-N) approach apply to the

crack propagation approach In addition, the design engineer is challenged with determining the initial or inherent flaw size

Even though cycle-dependent part performance is not well understood, a general design-engineering approach can be applied to the fatigue of plastic parts First, for material selection an awareness of the fatigue performance of numerous plastics is necessary Materials should be compared under identical test conditions to determine their relative fatigue performance This preliminary selection should be based on the general assessment of the relative fatigue performance, taking into account the overall severity of the part loading Next, the part loading conditions should be determined and related to the appropriate laboratory data This task is probably the most important, yet the most difficult due to the large number of variables involved Establishing whether the part will experience load-controlled or displacement-controlled cyclic loadings is possibly the most significant factor Next, the effects of frequency, waveform, and load level and type must be assessed to determine if part temperature will increase, leading to thermal fatigue, or if mechanical failure will occur with little or no temperature increase Other conditions that should be considered or matched from the laboratory specimen to the component include environmental effects (e.g., temperature), stress state, stress concentrations, and mean stress Finally, appropriate laboratory tests or full-scale component tests should be conducted These laboratory tests must

be carefully planned to achieve correspondence to the actual service conditions

Fracture mechanics can be used to provide an approach to predicting the fatigue lifetime of components The important additional feature is an understanding of crack growth through measurement of the amount of crack growth per cycle

(da/dN) as a function of the cyclic range of stress-intensity factors ( K) Despite the fact that plastics are time-dependent

materials, and that linear fracture mechanics only apply strictly to elastic materials, it appears that crack propagation rates

in many polymers can be correlated with K

During the fatigue process, the stress amplitude ( ) usually remains constant and failure occurs as the result of crack

growth from an initial, subcritical size to a critical size related to the fracture toughness (Kc) of the material The lifetime

of a component is thus dependent on the initial crack size, the rate of crack growth, and the critical crack size The relation takes the power-law form:

(Eq 7)

where A and n are material constants varying with temperature, environment, and frequency The stress-intensity factor

range is given as:

where Y is a crack and structural geometry factor and a is crack length Typical crack propagation curves for a number of

plastics (Ref 9) are shown in Fig 9

Fig 9 Fatigue crack propagation behavior ABS, acrylonitrile-butadiene-styrene; PC, polycarbonate; M-PPE,

modified polyphenylene ether

Fatigue lifetime of plastic parts can be calculated for design purposes by integrating the crack-growth rate expression (Eq 7) after substitution of Eq 8:

This expression can be used to predict the fatigue lifetime of a component with an initial defect of known size

The fatigue lifetime (number of cycles-to-failure) of a part is strongly dependent on the applied load S-N curves have

been generated for a number of thermoplastics (Ref 10) at room temperature with a standard tensile specimen with a net cross section of 12.7 by 3.2 mm (0.5 by 0.125 in.) The tensile load was varied from a very small load (nearly zero) to

various maximum loads (stresses) A sinusoidal waveform with a frequency of 5 Hz was used Very little or no specimen

heating occurred By choosing S-N curves for the same materials polycarbonate (PC), modified polyphenylene ether PPE), and acrylonitrile-butadiene-styrene (ABS) whose fatigue crack propagation behavior is displayed in Fig 9, the S-N

(M-data can be combined with the crack propagation (M-data to compute the initial crack lengths (Eq 10) The final crack length

af is computed from the fracture toughness of these materials Thus, over the range of stresses for the S-N curves, the

initial crack lengths can be computed Ideally, these crack lengths would be independent of applied stress level However,

while there is some variation, the average crack length was computed and used in Eq 10 to "predict" the measured S-N

data from the crack growth rate data These results are shown in Fig 10 for PC, M-PPE, and ABS These data and this

approach indicate the similarity of the S-N and crack growth rate methods of predicting part lifetime and suggest a method

of utilizing both types of data

Fig 10 S-N data compared to crack growth prediction (a) PC; ai = 0.013 mm (b) M-PPE; ai = 0.32 mm (c)

ABS; ai = 0.23 mm

References cited in this section

3 G.G Trantina and R.P Nimmer, Structural Analysis of Thermoplastic Components, McGraw-Hill, 1994

4 K.C Sherman, R.J Bankert, and R.P Nimmer, "Engineering Performance Parameter Studies for

Thermoplastic, Structural Panels," 1989 ANTEC Conf Proc., Society of Plastics Engineers, p 640-644

5 G Ambur and G.G Trantina, Structural Failure Prediction with Short-Fiber Filled Injection Molded

Thermoplastics, 1988 ANTEC Conf Proc., Society of Plastics Engineers, p 1507

6 J.T Woods and R.P Nimmer, Design Aids for Preventing Brittle Failure in Polycarbonate and

Polyetherimide, 1996 ANTEC Conf Proc., Society of Plastics Engineers, p 3182-3186

7 M.P Sepe, Material Selection for Elevated Temperature Applications: An Alternative to DTUL, 1991 ANTEC Conf Proc., Society of Plastics Engineers, p 2257-2262

8 O.A Hasan and G.G Trantina, Use of Deformation Maps in Predicting the Time-Dependent Deformation

of Thermoplastics, 1996 ANTEC Conf Proc., Society of Plastics Engineers, p 3223-3228

9 R.W Hertzberg and J.A Manson, Fatigue of Engineering Plastics, Academic Press, 1990

10 G.G Trantina, Material Properties for Part Design and Material Selection, 1996 ANTEC Conf Proc.,

Society of Plastics Engineers, p 3170-3175

Design with Plastics

G.G Trantina, General Electric Corporate Research and Development

Manufacturing Considerations

Flow Length Estimation. The ability to manufacture plastic parts using the injection-molding process is governed by the material behavior, part geometry, and processing conditions Estimating the flow length of the resin into a mold of a

given thickness is an important manufacturing consideration for the design engineer An example is given here of a generic tool (Ref 11) capable of analyzing radial flow and quantifying effects of material, geometry, or process changes This tool, Diskflow, is composed of a numerical flow analysis, automatic mesh generator, and menu-driven pre- and postprocessors No knowledge of simulation techniques is required, though a knowledge of injection molding is needed when interpreting the results

Diskflow utilizes modeling techniques common to most commercial analyses (see the article "Computational Fluid Dynamics" in this Volume), yet is much faster due to the radial flow assumption and subsequent numerical methods Modeling, postprocessing, and computer analysis time have been minimized, reducing total analysis time This analysis cannot replace three-dimensional filling analyses as it does not yield any information regarding knit-line and gas trap locations, cavity pressure and temperature distributions, or more complex mold geometries, but it does yield significant results regarding design feasibility, material performance, and process effects

Diskflow uses complete viscosity versus shear rate and temperature data fit with a modified Cross model with Landel-Ferry (WLF) temperature dependence when available If this advanced model is not available, the Arrhenius model is employed Mold and melt temperatures can be chosen if default values are not adequate The mold geometry is defined in terms of a nominal wall thickness and cavity radius that can be calculated by entering cavity volume or projected area The sprue is defined by entering the sprue type (hot or cold) and then entering the length, upper diameter, and lower diameter

Williams-For flow length estimation, an initial flow rate is assumed constant subject to some user-specified maximum pressure limit that mimics the capability of a molding machine As the mold fills at a constant volumetric flow rate, the injection pressure rises due to the increasing flow resistance When the injection pressure attains the user-specified maximum, the analysis switches over to a second phase in which the injection pressure is maintained at a constant value and the flow rate is allowed to vary; the flow rate eventually decays to zero at which point a final flow length is attained The flow length may be defined as the farthest distance that a polymeric material travels in a mold of some nominal wall thickness given a set of processing conditions The flow length capability examines the feasibility of manufacturing a desired design: if the distance from the gate to the corner of the part is greater than the predicted flow length, then the part may not be manufacturable Figure 11 shows the dependence of flow length on wall thickness for a maximum injection pressure of 103.5 MPa (15 ksi) for PC This information is useful for assessing manufacturability in the early stages of design and material selection

Fig 11 Flow length versus wall thickness predicted by Diskflow mold-filling analysis Material, unfilled PC; mold

temperature, 82 °C; melt temperature, 335 °C; maximum injection pressure, 103.4 MPa

Cycle Time Estimation. The molding of thermoplastics consists of injecting a molten polymer into the cooled mold cavity The injected resin is held in the cavity until the part solidifies (by heat transfer) The time for the melt to cool until

it solidifies to the extent that the part can be removed from the mold and retain its dimensions is generally the majority of the total cycle time The large impact of the cooling time on the total processing cost is obvious

During the cooling phase, heat conduction is the prime mechanism of heat transfer The development of a simplified mold-cooling program allows designers and molders to evaluate materials and process parameters in a rapid, convenient, and cost-efficient manner Plastic parts are usually thin, and thus a one-dimensional, transient heat conduction analysis is adequate to approximate the cooling of the real part The main assumption is that the mold surface is kept at a constant temperature throughout the cooling phase Comparing calculated minimum cooling times for different material part geometries (i.e., thickness) and processing conditions help optimize the material-selection process

Thermal material properties are strong functions of temperature Because the thermoplastic material experiences a wide range of temperatures during the cooling phase, temperature-dependent material data such as specific heat and thermal conductivity are used for the computations To perform the analysis the injection temperature, mold temperature, ejection temperature, material, and thickness must be chosen The program uses a one-dimensional finite-difference scheme to calculate temperature through the thickness as a function of time When the center of the plate reaches the specified ejection temperature, the analysis is stopped and the results are displayed graphically By performing the analysis for a range of part thicknesses, cooling time curves can be produced (Fig 12) These curves can then be used to estimate cycle times in the early stages of material selection and design

Reference cited in this section

11 D.O Kazmer, "Development and Application of an Axisymmetric Element for Injection Molding

Analysis," 1990 RETEC Conf Proc

Design with Plastics

G.G Trantina, General Electric Corporate Research and Development

Design-Based Material Selection

Design-based material selection (Ref 12, 13) involves meeting the part performance requirements with a minimum system cost while considering preliminary part design, material performance, and manufacturing constraints (Fig 13) Some performance requirements such as transparency, Food and Drug Administration (FDA) approval, or flammability rating are either met by the resin or not Mechanical performance such as a deflection limit for a given load are more complicated requirements Time- and temperature-reduced stiffness of the material is determined from the deformation map Part design for stiffness involves meeting the deflection limit with optimal rib geometry and part thickness combined with the material stiffness This part geometry can be used to compute the part volume that when multiplied by the material cost provides the first part of the system cost The second half of the system cost is the injection-molding machine cost multiplied by the cycle time This total system cost is a rough estimate used to rank materials/designs that meet the part performance requirements In addition, the manufacturing constraint of flow length for the part thickness must be considered The entire process is summarized in Fig 13

Fig 13 Design-based material-selection process

Example 1: Materials Selection for Plate Design

A simple example is presented to illustrate the design-based material-selection process A 254 by 254 mm (10 by 10 in.) simply supported plate is loaded at room temperature with a uniform pressure of 760 Pa (0.11 psi) The maximum allowable deflection is 3.2 mm (0.125 in.) Using the program Ribstiff, described previously in the part stiffness section, the nonlinear load-displacement response of the plate can be computed Through iteration, it is determined that a PC plate with a thickness of 2.5 mm (0.1 in.) satisfies the requirements (Fig 3) From Fig 11, the flow length is 320 mm (12.5 in.) Thus, the plate could be filled with a center gate or from the center of an edge From Fig 12, the in-mold cooling time is

10 s The volume of the plate is 0.00016 m3 (10 in.3)

A second design can be produced by designing a rib-stiffened plate Again, through iteration, a 1.5 mm (0.060 in.) thick plate with 10 ribs in each direction with a rib height of 4.5 mm (0.18 in.) and a rib thickness of 1.5 mm (0.060 in.) would meet the deflection requirement From Fig 11, the flow length is about 175 mm (7 in.) Thus, because a center-gated plate would have a flow length of 175 mm (7 in.), the part would probably fill if the ribs would serve as flow leaders to aid the flow However, it is generally not recommended to push an injection-molding machine to its limits because this will exaggerate inconsistencies in the material and the process A more thorough three-dimensional process simulation should

be performed to determine the viability of this design before it is chosen From Fig 12, the in-mold cooling time is about

4 s, a considerable savings (6 s/part) in cycle time as compared to the plate with no ribs In addition, the volume of the ribbed plate is 0.00013 m3 (8 in.3), a saving of 20% on material as compared to the plate with no ribs The system cost of the ribbed plate is computed to be 73% of the plate with no ribs (Fig 1) Because the ribs would produce a constrained, three-dimensional stress state, consideration of impact would be important for high rates of loading and low temperature (Fig 7) The fracture map shows a tendency for brittle behavior with PC at low temperature and high loading rates for notched or constrained geometries

If time/temperature performance were added to this example as a requirement, the optimal material may change or the initial design would need to be modified If the same load were applied to the plate for 1000 h at a temperature of 79 °C (175 °F), the PC plate would exhibit a deformation as if its material stiffness were about 40% of the room-temperature modulus (Fig 8) Simply increasing the thickness of the plate with no ribs to 3.5 mm (0.136 in.) would provide a design that would meet the deflection requirements The penalty would be a 40% increase in material usage and an additional 8 s added to the cycle time Choosing a material with more temperature resistance or initial stiffness is an option

Example 2: Materials Selection for an Electrical Enclosure

The usefulness of this process can be demonstrated through another design example In this case, a very simple five-sided box is chosen The box is used as an electrical enclosure and must meet flammability requirements This limits the number of candidate materials to examine more closely Also, this enclosure is not painted and, therefore, the resin must

be unfilled to maintain acceptable aesthetics It is unribbed to minimize sink marks on the exposed surfaces Finally, it must support a uniform load across its surface without deflecting more than 2.5 mm The enclosure is a 300 mm wide by

450 mm long by 100 mm high box (Fig 14)

Fig 14 Geometry of enclosure example

A series of analyses is performed using three resins to see how they perform under different conditions These resins are representative of what is currently used in electrical enclosures (computer housings, office equipment, etc.) They are an unfilled M-PPO resin, an unfilled ABS resin, and an unfilled PC-ABS resin blend

To examine the relative performance of each resin, the application requirements are varied in loading, environment, and manufacturing First, the uniform load is varied from 150 to 1200 Pa Next, the ambient temperature the enclosure must withstand for 1000 h under load is varied from 20 to 80 °C Finally, the gating scenario is changed from edge gated to center gated to multiple gates

Using a center-gated box at 40 °C for 1000 h, the uniform load is varied from 150 to 1200 Pa The Design-Based Material Selection Program determines for each resin the optimal wall thickness to support the load at the lowest variable system cost for each loading case Figure 15(a) compares the normalized cost of the enclosure for each resin as the load is increased As can be seen from this graph, the PC-ABS and M-PPO are virtually equivalent in cost, while the ABS is about 30% more expensive While this may seem counterintuitive (ABS is less expensive per pound than PC-ABS or M-PPO), it is easily explained by examining Fig 15(b), wall thickness versus loading At this elevated temperature and long time (40 °C, 1000 h), the ABS requires significantly more material to support the required load within the specified 2.5

mm deflection than either the PC-ABS or the M-PPO This added material far outweighs the price advantage of ABS

Fig 15 Loading variation for 40 °C and 1000 h

The cooling time is another factor that will increase the variable system cost of the ABS resin enclosure As the wall thickness increases, the time to cool the part to ejection temperature will increase The cooling time is also influenced by the thermal properties of each resin Figure 16 contains a graph of the cooling time versus wall thickness for the three example materials based on one-dimensional transient heat-transfer analyses The wall thickness for each resin to support

600 Pa at a deflection of no more than 2.5 mm is indicated on the graph From this graph, it can easily be seen that, in this case, the cooling time for each resin will be very different

Fig 16 Cooling time versus wall thickness

Using a center-gated box that must support a 300 Pa load within a 2.5 mm deflection of 1000 h, the temperature was varied from 20 to 80 °C Figure 17(a) compares the normalized cost of these three resins as the temperature is increased Initially, at 20 °C these resins have very similar variable system costs As the temperature increases, the creep performance of each resin decreases Figure 17(b) shows the creep modulus for each resin as the temperature changes The creep modulus of the ABS resin decreases rapidly as temperature increases The M-PPO maintains its stiffness longer, but eventually decreases rapidly while the PC-ABS performs better, because of the high creep resistance of the PC component of the blend

Fig 17 Temperature variation

The wall thickness to support the load must increase as temperature increases because the creep modulus decreases This,

in turn, increases the part volume and the cooling time, affecting the variable system cost As the temperature increases, the cost rises to high levels (ABS at 80 °C, 1000 h) If the application must withstand these temperature extremes, a higher-performance thermoplastic may be a better choice

The process to manufacture this enclosure can influence how the enclosure will be designed and what material will be used Using a box that must support a 150 Pa load within a 2.5 mm deflection in a 40 °C environment for 1000 h, the gating scenario is varied choosing three common configurations (Fig 18) edge gate, center gate, and four gates The minimum flow length necessary to fill the part is determined for each case based on the geometry of the enclosure and the gate position The minimum flow length necessary to fill the part is determined for each case based on the geometry of the enclosure and the gate position The minimum wall thickness to allow each material to achieve this flow length, determined using the radial flow injection molding simulation, is then used as a lower bound on the thickness optimization and is shown in Fig 19(b) Figure 19(a) details the normalized cost versus minimum flow length (i.e., gating scenario) Initially, as the flow length increases (from four gates to center gate) the normalized cost does not change The

wall thickness necessary to support the load within the specified deflection is greater than the minimum wall thickness dictated by the flow length constraint As the flow length increases from the center-gated to the edge-gated case, the normalized cost increases because the wall thickness is now dictated by the manufacturing constraint rather than the loading condition The gate placement now dictates the wall thickness that is necessary to fill the part

Fig 18 Examples of gating scenarios

Fig 19 Gating variation

There are other considerations that a design engineer can use to help determine the best material for an application The strength of a resin over a range of temperatures may aid the engineer in determining if the part will fail under load The impact performance of the resin, as indicated by the ductility ratio, can also be quite important While it only indicates the impact performance for one specific geometry, and cannot be used in design, it does provide useful comparative information

References cited in this section

12 G.G Trantina, P.R Oehler, M.D Minnichelli, Selecting Materials for Optimum Performance, Plast Eng.,

Aug 1993, p 23-26

13 P.R Oehler, C.M Graichen, and G.G Trantina, Design-Based Material Selection, 1994 ANTEC Conf Proc., Society of Plastics Engineers, p 3092-3096

Design with Plastics

G.G Trantina, General Electric Corporate Research and Development

the combination of S-N data and crack growth rate data is useful because it provides two options: to use the S-N data

directly or to use the initial defect size with the crack growth rate data In either case, with the vast number of parameters that affect fatigue behavior, having more information is useful The design methods and material data summarized here provide the design engineer with more effective and efficient techniques to select materials and design plastic parts

Design with Plastics

G.G Trantina, General Electric Corporate Research and Development

of Mechanical Engineers, July 1986

3 G.G Trantina and R.P Nimmer, Structural Analysis of Thermoplastic Components, McGraw-Hill, 1994

4 K.C Sherman, R.J Bankert, and R.P Nimmer, "Engineering Performance Parameter Studies for

Thermoplastic, Structural Panels," 1989 ANTEC Conf Proc., Society of Plastics Engineers, p 640-644

5 G Ambur and G.G Trantina, Structural Failure Prediction with Short-Fiber Filled Injection Molded

Thermoplastics, 1988 ANTEC Conf Proc., Society of Plastics Engineers, p 1507

6 J.T Woods and R.P Nimmer, Design Aids for Preventing Brittle Failure in Polycarbonate and

Polyetherimide, 1996 ANTEC Conf Proc., Society of Plastics Engineers, p 3182-3186

7 M.P Sepe, Material Selection for Elevated Temperature Applications: An Alternative to DTUL, 1991 ANTEC Conf Proc., Society of Plastics Engineers, p 2257-2262

8 O.A Hasan and G.G Trantina, Use of Deformation Maps in Predicting the Time-Dependent Deformation

of Thermoplastics, 1996 ANTEC Conf Proc., Society of Plastics Engineers, p 3223-3228

9 R.W Hertzberg and J.A Manson, Fatigue of Engineering Plastics, Academic Press, 1990

10 G.G Trantina, Material Properties for Part Design and Material Selection, 1996 ANTEC Conf Proc.,

Society of Plastics Engineers, p 3170-3175

11 D.O Kazmer, "Development and Application of an Axisymmetric Element for Injection Molding

Analysis," 1990 RETEC Conf Proc

12 G.G Trantina, P.R Oehler, M.D Minnichelli, Selecting Materials for Optimum Performance, Plast Eng.,

Aug 1993, p 23-26

13 P.R Oehler, C.M Graichen, and G.G Trantina, Design-Based Material Selection, 1994 ANTEC Conf Proc., Society of Plastics Engineers, p 3092-3096

Design with Composites

R.J Diefendorf, Clemson University

Introduction

THE QUEST for improved performance has caused designers to search for materials with lower density, higher modulus, and higher theoretical strength than the common engineering metals There are a number of elements and compounds, all centered around carbon in the periodic table, that have lower density and high modulus and strength All are brittle ceramic materials with the exception of beryllium The specific modulus (modulus/density) provides an indication of performance for a stiffness-limited application and for pure tensile applications in which weight is important (Fig 1) The theoretical tensile strength of a brittle material is approximately 0.2 of the elastic modulus, so the same materials that have high modulus have the potential for high strength Practically, many of these materials have been made in fiber form with high tensile strength, although with much lower strength than the theoretical values (Fig 2) The ranking is more complicated for compressive loading as the failure mechanism may vary, but the general formula is (modulus)n/density,

where n = or While the value of the modulus can be less important because of the fractional exponent, the density always is factored to the first power The common engineering metals cannot match, on the basis of specific modulus and strength, the decrease in structural weight that can be achieved with these ceramic materials

Fig 1 Specific modulus (modulus/density) of selected materials for structural applications Note the constancy

of the common engineering metals and the high values for low-density ceramics Source: Ref 1

Fig 2 Specific strength (strength/density) of selected materials for structural applications Values are for

high-strength wires Materials with high specific moduli are often observed to have high specific high-strength also Source: Ref 1

A high specific modulus and strength is insufficient to be a useful engineering material Designers resist using brittle materials, because of poor impact, little damage tolerance, and difficulties with machining and assembly that may raise local stresses to high values Structural integrity often depends on withstanding these high local stresses Ductile metals yield and redistribute the stress, but composite materials exhibit a lower ductility Stress analysis is often very good at the global scale, but is apt to be poorer in localized areas The application of finite element analysis has decreased problems with stress concentrations, but providing the ceramic material with a pseudoductile behavior would be a breakthrough Fiber-reinforced composite materials can provide better impact resistance and a more "graceful failure," or more yielding strain before failure Additional information about performance characteristics of brittle materials is provided in the article "Design with Brittle Materials" in this Volume

Reference

1 R.J Diefendorf and E.W Tokarsky, High Performance Carbon Fibers, Polym Sci Eng., Vol 15 (No 3),

1975, p 151

Design with Composites

R.J Diefendorf, Clemson University

Fiber-Reinforced Composite Materials

Fibers can be made in small diameter with desirable microstructures, such that very high strength can be obtained High loads can be carried by using a plurality of these high-strength fibers Damage tolerance is also achieved, as the loss of a few fibers does not decrease the overall load-bearing capability much However, if there is no coupling among a bundle of parallel fibers, fiber fractures accumulate with increasing load until the remaining fibers fail ("bundle strength") (Ref 2) (Fig 3a) There are two problems: (1) no load is carried by a broken or discontinuous fiber, and (2) fibers buckle at very low loads in compression because of their small diameter Man learned many centuries ago that twisting the continuous fiber bundle into a yarn provides a frictional force among the fibers that also allows discontinuous fibers to be used Multiple breaks in a single fiber could even be generated in a yarn during loading However, improving the compressive strength requires better fiber stabilization than coupling by friction The problem is that in a strongly coupled system, failure of the whole structure occurs when the first fiber fails a very low strength (Fig 3b.) Noncatastrophic failure requires that the bond strength between the fiber and matrix be sufficiently low that when the fiber fractures, the fiber debonds from the matrix to arrest crack propagation by blunting (Fig 3c) Damage tolerance is provided by the redundancy in load-carrying members Localized impact may fracture a few fibers, but the load carried by the fractured fibers will be transferred through the matrix to the remaining fibers

Fig 3 Interfacial bonding A bundle of fibers (a) usually will have about 70 to 80% of the average tensile

strength determined on a single fibers With a very strong bond between fiber and matrix (b), the whole composite will fail in a brittle manner when the very weakest fiber in the composite fails Tensile strength is low An optimal interfacial strength (c) will produce multiple fractures in each filament, and the tensile strength will equal or even exceed the average fiber tensile strength Source: Ref 3

The whole basis for fiber-reinforced composites is that some of the potential strength and modulus are traded for a measure of damage tolerance and a more graceful failure The penalty is that the strength transverse to the fiber bundle is low The strength and modulus of a uniaxial fiber-reinforced composite is high in only one direction Of course, fibers could be oriented in different directions to provide the required stiffness and strengths, but space is not necessarily filled very efficiently Woven fabrics often are used to replace uniaxial plies or are added locally to improve transverse properties For triaxially stressed parts, composites usually do not offer improved performance compared to the engineering metals (There are important applications in which the engineering metals cannot be used, and composites are attractive.) Fortunately, structural elements are usually stressed predominantly in one (beams) or two directions (plates), and not three directions For uniaxially and biaxially stressed elements, the performance levels possible with composites cannot be matched by other materials

References cited in this section