ASM Metals HandBook Vol. 8 - Mechanical Testing and Evaluation

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plastic zone described in Eq 13. Cyclic plastic zones have been observed in several amorphous polymer

systems and are important in the inception of cracks under cyclic compression loading (Ref 13). Qualitatively,

it is easy to see that the size of the plastic zone increases with ΔK; therefore, process zone shielding

mechanisms are effective at high ΔK levels.

Contact shielding involves physical contact between mating crack surfaces because of the presence of

asperities, second-phase particles, and/or fibers. Premature contact between the crack surfaces occurs during

unloading at a stress intensity level known as K

, which is the closure stress intensity. The degree of shielding

caused by closure effects can be calculated:

ΔK

tip

= K

max

- K

(Eq 14)

where K

max

is the maximum stress intensity of the fatigue cycle. It should be noted from Eq 14 that the ΔK

tip

less than ΔK

, thus effectively lowering the stress intensity felt at the crack tip. Mechanisms such as contact

shielding and fiber bridging can contribute to this phenomenon. Contact shielding can arise from contact

between asperities or from fiber bridging in reinforced or blended polymers. Fiber bridging has been shown to

be a viable shielding mechanism in short fiber composites by Lang and his coworkers (Ref 19). In summary,

extrinsic shielding mechanisms can be utilized to improve resistance to fatigue crack propagation in

engineering polymers.

References cited in this section

10. G.C. Sih, Handbook of Stress Intensity Factors, Lehigh University Press, 1973

11. P.C. Paris, M.P. Gomez, and W.P. Anderson, Trends Eng., Vol 13, 1961, p 9

12. R.O. Ritchie, Proc. of the 5th Int. Conf., M.G. Yan, S.H. Zhang, and Z.M. Zheng, Ed., Pergamon Press,

1988, p 5

13. S. Suresh, Fatigue of Materials, 2nd ed., Cambridge University Press, 1998

14. A.G. Evans, Z.B. Ahmad, D.G. Gilbert, and P.W.R. Beaumont, Acta Metall., Vol 34, 1986, p 79

15. C.B. Bucknall and W.W. Stevens, in Toughening of Plastics, Plastics and Rubber Institute, London,

1978, p 24

16. R.W. Hertzberg, Deformation and Fracture Mechanics of Engineering Materials, 4th ed., Wiley, 1996

17. T.L. Anderson, Fracture Mechanics: Fundamentals and Applications, CRC Press, 1995

18. A.S. Argon, Proc. of 7th Int. Conf. on Advances in Fracture Research, K. Samala, K. Ravi-Chander,

D.M.R. Taplin, and P. Rama Rao, Ed., Pergamon Press, 1989

19. R.W. Lang, J.A. Manson, R.W. Hertzberg, and R. Schirrer, Polym. Eng. Sci., Vol 24, 1984, p 833

Fatigue Testing and Behavior of Plastics

Lisa A. Pruitt, University of California at Berkeley

Factors Affecting Fatigue Performance of Polymers

Molecular Variables. Polymers are sensitive to a number of molecular variables including molecular weight,

molecular weight distribution, crystallinity, chain entanglement density, and crosslinking (Ref 3, 5, 20, and 21).

In general, as the molecular weight of the polymer is increased, the fatigue resistance of the polymer is

enhanced. Some polymers (as mentioned earlier) are susceptible to craze nucleation that leads to subsequent

crack growth and fatigue failure. Figure 10(a) schematically illustrates the load bearing fibrils that comprise the

craze zone. Figure 10(b) shows a transmission electron micrograph of a craze preceding a fatigue crack in

polycarbonate (PC).

When a critical amount of damage has accumulated, the crack advances through the load bearing fibrils of the

craze zone. This advancement can occur by a void growth mechanism potentially enhanced by temperature,

chemical environment, or rupture of the highly stressed fibrils. The craze often advances in a discontinuous

manner and results in discontinuous crack growth in certain stress regimes (Ref 5). Kramer (Ref 22) has shown

that craze stability depends on numerous factors including the molecular weight and chain entanglement density

of the polymer. The stability or strength of the craze can be improved by increasing the molecular weight of the

polymer. Numerous studies indicate that increasing the molecular weight of the polymer increases craze

strength, creep rupture strength, and endurance limit under cyclic loading conditions (Ref 3, 5, 18, and 22).

Semicrystalline polymers provide improved fatigue resistance over glassy amorphous polymers. One

explanation is that the composite, two-phase structure, offers enhanced toughness. Improved strength is

provided by the more rigid crystalline phase, and ductility is provided by the more compliant amorphous phase.

Semicrystalline polymers provide higher fracture energies and can accommodate both amorphous and

crystalline modes of plasticity.

The arrangement of the crystallites within the amorphous phase or the polymer morphology is also important to

the resistance of fatigue. For example, branched versions of polyethylene offer decreased resistance, while very

high molecular weight versions of polyethylene with an enhanced level of tie molecules provide superior

resistance to fatigue crack propagation in comparison to generic linear polyethylene (Ref 3). In general,

semicrystalline polymers, such as nylon, polyacetal, and polyethylene, offer excellent resistance to fatigue

crack propagation and provide high S-N endurance limits (Ref 5). In comparison, amorphous glassy polymers

often suffer inferior fatigue strength due to a lack of shielding or toughening modes, because many amorphous

polymers are used below the glass transition temperature and are incapable of large amounts of ductile or

viscous deformation. Figure 11 shows a comparison of fatigue crack propagation behavior in the Paris regime

for several amorphous and semicrystalline polymers, and it is evident that the semicrystalline polymers offer

improved fatigue crack growth resistance.

Fig. 11 Comparison of fatigue crack propagation behavior in the Paris regime for several amorphous

and semicrystalline polymers. Note enhanced fatigue resistance of the semicrystalline polymers. Source:

Ref 5

Effect of Reinforcements. The addition of rubber particles to a ductile or brittle polymer provides a process

zone shielding mechanism involving massive shear banding of the matrix, which leads to improved fatigue

crack propagation resistance. The role of crack-tip shielding mechanisms on the crack growth rate regime has

been modeled by Ritchie (Ref 12). According to Ref 12, the occurrence of a process zone shielding mechanism

should change the slope (m) in the Paris regime but should not change the crack growth behavior at low crack

growth or near-threshold regime. Experimental support of this model has been given by Azimi et al. (Ref 23).

Figure 12 shows that the addition of rubber decreases the slope, m, and retards crack growth at high crack

growth rates due to toughening mechanisms. At low values of stress intensity range (ΔK), however, the crack

growth rates for the rubber-toughened epoxies are nearly identical to those of the unmodified (neat) resin. At

low ΔK levels, the process zone in front of the crack tip is small; the rubber reinforcements are not highly

stressed; hence, the crack grows with minimal plasticity in this regime. Conversely, at high ΔK levels, the

process zone is much larger than the size of the particles, and the rubber additions within this region are highly

stressed. The subsequent rubber particle cavitation causes significant additional plasticity in the matrix, and the

crack propagation rate is reduced.

Fig. 12 Fatigue crack propagation behavior for a rubber-toughened epoxy. The addition of rubber

decreases the slope, m, at high crack growth rates due toughening mechanisms and retarded crack

growth. CTBN, carboxy-terminated polybutadiene acrylonitrile rubber; MBS, methacrylate-butadiene-

styrene

Blending rubber-toughened polymers with a small amount of inorganic filler can also improve fatigue crack

propagation resistance. Azimi et al. (Ref 23) have studied several glass-filled, rubber-toughened blends, and

they believe the improved fatigue crack propagation resistance is the result of a synergistic interaction between

the hollow glass filler at the crack tip and the plastic zone triggered by the rubber particles. The synergistic

effect occurs by crack bridging via the glass phase and enhanced plasticity due to the presence of the rubber

particles.

An interesting distinction must be made between fatigue crack initiation and propagation studies. The addition

of rubber particles or reinforcements results in an increased resistance to crack propagation. However, this same

material often exhibits a decreased resistance to fatigue crack initiation or flaw inception. The second phase

addition serves as a nucleation site for crazes, voids, or shear bands and results in a decreased threshold for

crack inception. For example, high impact polystyrene studies (Ref 5) have shown an increased resistance to

crack propagation but a degraded resistance to crack inception when compared to the neat polystyrene resin.

Thus, designers need to have a clear understanding of the component design and loading environment when

making their material selection.

Mean Stress Effects. The fatigue response of a polymeric material is highly sensitive to the mean stress, σ

, of

the fatigue cycle:

(Eq 15)

Depending on the structure of the polymer and the micromechanisms of deformation, there are two distinct

responses to an increase in mean stress. For a nominal stress intensity range, some polymers exhibit an increase

in crack propagation rate while others show a decrease in crack growth rate. The published research on the

effects of mean stress and R-ratio covers a broad range of polymer classes including amorphous,

semicrystalline, crosslinked, and rubber-modified polymers (Ref 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, and 34).

Table 1 provides a summary of the effect of increased mean stress for several advanced polymer systems.

Table 1 Effect of increasing mean stress on polymer fatigue crack propagation

Polymer Reference

Increasing crack propagation rate with increasing mean stress

High density polyethylene 15

Nylon 5

High molecular weight PMMA 21, 25

Polystyrene 30, 35

Epoxy 24

Polyethylene copolymer 26

Decreasing crack propagation rate with increasing mean stress

Low density polyethylene 5

Polyvinyl chloride 34

Low molecular weight PMMA 21

Rubber-toughened PMMA 15

High impact polystyrene 15, 35

Acrylonitrile-butadiene-styrene 15

Polycarbonate 24, 32, 33, 44

Toughened polycarbonate copolyester 27

Increasing crack growth rates associated with an increased stress ratio or mean stress are observed in epoxy

resins, PMMA, HDPE copolymers, PS, PVC, and nylon. A number of different explanations and relationships

have been proposed to rationalize the effect of mean stress on fatigue crack propagation. Arad et al. (Ref 28)

suggested that the fatigue crack growth rates could be scaled to the stress intensity factor with the following

relationship:

(Eq 16)

where β depends on the loading environment, frequency, and material properties, and n is a material constant.

A micromechanistic explanation for this response to an increase in stress ratio or mean stress is also possible.

Polymers that become more prone to fracture with increasing mean stress are most likely affected by the

monotonic fracture process associated with the maximum portion of the loading cycle as it approaches a critical

stress intensity level. In general, these polymers are susceptible to crazing, chain scission, or crosslink rupture.

For these polymer types, an increase in mean stress results in faster crack propagation rates.

Remarkably, several polymer blends offer improved resistance to crack propagation as the mean stress is

increased (Ref 5). These polymers include ABS, HIPS, PC, low density or branched polyethylene, low

molecular weight PMMA, and rubber-toughened PMMA (Table 1). Hertzberg postulated that the strain energy

normally available for crack extension is consumed through deformation or structural reorganization ahead of

the crack tip. The use of strain energetics to describe fracture processes in polymers (Ref 1, 36) is formulated:

(Eq 17)

Here E is the total energy used by the solid to create a new unit area of surface through crack advance, E

is the

energy expended for an ideal elastic solid, C is a material constant that depends on the strain state of the

polymer, and ψ is the hysteresis ratio. The energy lost due to inelastic energy expenditure is captured by ψ. If

the energy loss is large, the amount of energy needed to cause fracture increases; hence, it is expected that the

crack growth rate will be reduced as ψ increases. Hertzberg and Manson (Ref 5) proposed that the effect of

mean stress on the fatigue crack propagation resistance of polymeric materials is directly linked to the

parameter, ψ. Thus, polymeric materials with a molecular structure susceptible to hysteretic losses or polymers

capable of structural reorganization are likely to be more resistant to fatigue crack propagation as the mean

stress is increased. These polymers have near tip processes that dissipate elastic energy ahead of the crack tip:

rubber toughening, orientation hardening, chain slip, and shear banding.

Variable amplitude fatigue plays an important role in the design of polymeric components subjected to

variations in the load cycle. Further, variable amplitude fatigue is a concern for components likely to experience

periodic or unanticipated tensile or compressive overloads. It is conventional to model the effect of variable

amplitude loading using the concept of cumulative damage (e.g., Palmgren-Miner mean accumulation rule).

While this concept has strength in crack initiation models, it does not capture the role of overload type or order

in the loading sequence and the subsequent effect on a propagating crack.

Application of a single tensile overload can extend the life of a cracked component by retarding the rate of

crack advance (Ref 13). This transient crack propagation behavior is often controlled by several mechanisms

including crack closure (Ref 37), residual compressive stresses upon unloading (Ref 31, 38, and 39), and crack-

tip blunting (Ref 40). The closure concept justifies the retardation of crack velocity in terms of residual

compressive stresses left in the plastically deformed wake of the advancing crack. The result is premature

contact between the crack faces while the specimen is still in the tensile portion of the fatigue cycle, and it

effectively reduces the stress intensity range driving the crack advance. This crack closure mechanism has been

proposed by Pitoniak et al. (Ref 41) to describe crack retardation in PMMA and by Murakami (Ref 42) for PC.

Blunting has been proposed to describe the reduced crack velocity following tensile overloads (Ref 43).

Although crack-tip blunting can temporarily affect the crack velocity subsequent to the overload, it does not

explain a prolonged regime of crack retardation. Pruitt et al.(Ref 44) have shown that the zone of residual

compressive stresses sustained at the crack tip upon unloading in amorphous polymers increases in size and

magnitude as the far-field tensile load is increased. These residual compressive stresses sustained at the crack

tip are believed to decrease the crack propagation rate following the tensile overload. The crack has to grow

through this zone of residual compression before it can return to its initial crack propagation rate for the ΔK

sustained prior to overload. This trend has been observed in numerous polymer systems (Ref 35, 44). Many

current life prediction models are formulated on the basis of residual compressive stresses for the

rationalization of crack retardation.

Compressive overloads can also be detrimental to the life of a structural component as the overload can result in

an enhanced rate of crack propagation. The application of fully compressive cyclic loads results in the inception

and growth of fatigue cracks ahead of stress concentrations and notches in polymers (Ref 39, 44). Figure 13

shows the nucleation and growth of a mode I fatigue crack in the plane of the notch as a result of cyclic

compression loading in HIPS. The source of this crack growth is the generation of a zone of residual tensile

stresses upon unloading from far-field compression. Permanent deformation ahead of the notch tip in polymers

can be induced by crazing, shear flow, chain reorientation, or a combination thereof (Fig. 14). In summary, the

application of compressive over-loads to polymers with stress concentrations can result in the generation of

residual tensile stresses and concomitant enhancement of crack velocity resulting in shortened component life.

Fig. 13 Optical micrographs showing the nucleation and growth of a mode I fatigue crack in the plane of

the notch as a result of cyclic compression loading in HIPS. (a) Crazing before fatigue cycling. (b)

Nucleation of fatigue crack after 15,000 cycles. (c) Crack growth after 20,000 cycles. (d) Crack growth

after 50,000 cycles. Source: Ref 43

Fig. 14 Schematic illustrating the possible mechanisms of permanent deformation ahead of the notch tip.

(a) Cyclic plastic zone typical of metals. (b) Cyclic damage zone typical of ceramics. (c) Craze or shear-

band zones typical of polymer. Source: Ref 43

Waveform and Frequency Effects. Many polymers, due to the viscoelastic nature, are highly sensitive to the

waveform or frequency of a fatigue test. Some crazeable polymers, such as PS, PMMA, and HIPS, exhibit

decreased crack propagation as the test frequency is increased, while materials such as PC, nylon, and

polysulfone exhibit no sensitivity (Ref 5). In crazeable polymers, the increased test frequency can diminish

chain disentanglement effects at the crack tip and result in a decreased rate of crack propagation. Wnuk (Ref

45) proposed that the crack propagation in a polymer could be described as the sum of the elastic and

viscoelastic contributions:

(Eq 18)

where K

is plane-strain fracture toughness, and the first term is the elastic contribution, which includes an

elastic compliance term, C

. The second term is the time-dependent contribution, which includes a creep

compliance term, C

, and the test frequency, ν.

Strain rate can also play a critical role in the fatigue response of time-dependent polymers. Hertzberg et al. (Ref

46) found strong sensitivity to waveform in PVC, PS, PMMA, and especially vinyl urethane. The square wave

provides a high strain rate in ramp-up, then it subjects the specimen to a longer period of peak load than a

triangular waveform with the same stress amplitude. This difference in load function can cause major

differences in fatigue crack propagation. For example, in vinyl urethane (VUR), the fatigue crack propagation

rate is reduced by a factor of 6 when switching from a triangular to a square wave loading function (Ref 47).

This behavior is attributed to the higher strain rate that dominates for very flexible polymers, such as VUR.

Another important factor is the amount of creep sustained at the peak load of the fatigue cycle. Polymers, such

as PMMA, that are susceptible to creep damage will generally perform poorly when tested under the square

waveform loading due to creep at peak load (Ref 46).

Environmental factors can play a critical role in the fatigue performance of engineering polymers. Many

amorphous polymers are known to be susceptible to chemically induced crazing (Ref 5). In such instances, the

crack inception values can be substantially reduced in the presence of aggressive media (Ref 5). For example,

PC is known to nucleate surface crazes in the presence of acetone vapor. Many rubbers are susceptible to

oxidation-induced embrittlement (Ref 48). Many medical polymers, such as orthopedic grade ultrahigh

molecular weight polyethylene (UHMWPE) or bone cement (PMMA), degrade due to oxidation embrittlement

and chain scission. These mechanisms are induced by ionizing modes of sterilization and subsequent aging (Ref

49, 50, 51, 52, 53, 54, 55, 56, 57, and 58). An example of the embrittling effect of gamma radiation sterilization

on the fatigue crack propagation resistance of medical grade UHMWPE used for total joint replacements is

provided in Fig. 15. While not all aggressive environments and effects on polymers are discussed here, it is

clear that care should be taken to conduct fatigue tests that mimic not only the mechanical loads but also the

chemical and aging environments that are most likely to be encountered in the lifetime of the device.

Fig. 15 Fatigue plot illustrating the devastating effect of gamma radiation sterilization on the fatigue

resistance of orthopedic grade ultrahigh molecular weight polyethylene used for total joint replacements

References cited in this section

1. E.H. Andrews, Testing of Polymers, W. Brown, Ed., Wiley, 1969, p 237

3. J.A. Sauer and G.C. Richardson, Int. J. Fract., Vol 16, 1980, p 499

5. R.W. Hertzberg and J.A. Manson, Fatigue of Engineering Plastics, Academic Press, 1980

12. R.O. Ritchie, Proc. of the 5th Int. Conf., M.G. Yan, S.H. Zhang, and Z.M. Zheng, Ed., Pergamon Press,

1988, p 5

13. S. Suresh, Fatigue of Materials, 2nd ed., Cambridge University Press, 1998

15. C.B. Bucknall and W.W. Stevens, in Toughening of Plastics, Plastics and Rubber Institute, London,

1978, p 24

18. A.S. Argon, Proc. of 7th Int. Conf. on Advances in Fracture Research, K. Samala, K. Ravi-Chander,

D.M.R. Taplin, and P. Rama Rao, Ed., Pergamon Press, 1989

20. A.J. Kinloch and F.J. Guild, in Advances in Chemistry Series 252: Toughened Plastics II: Novel

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21. T.R. Clark, R.W. Hertzberg, and N. Nohammadi, in 8th Int. Conf. Deformation, Yield and Fracture of

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22. E.J. Kramer and L.L. Berger, Advances in Polymer Science 91/92, H.H. Kausch, Ed., Springer-Verlag,

1990, p 1

23. H.R. Azimi, R.A. Pearson, and R.W. Hertzberg, J. Mater. Sci., Vol 31, 1996, p 3777

24. S.A. Sutton, Eng. Fract. Mech., Vol 6, 1974, p 587

25. B. Mukherjee and D.J. Burns, Mech. Eng. Sci., Vol 11, 1971, p 433

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30. J.A. Manson, R.W. Hertzberg, and P.E. Bretz, Advances in Fracture Research, D. Francois, Ed.,

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40. J.R. Rice, in Fatigue Crack Propagation, ASTM STP 415, ASTM, 1967, p 247

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Fatigue Testing and Behavior of Plastics

Lisa A. Pruitt, University of California at Berkeley

Fractography

One of the most useful tools in failure analysis is fractography, the study of fracture surfaces. Scanning electron

microscopy (SEM) can provide vast insight into failure mechanisms of polymers subjected to cyclic loading.

Analysis of the surface with SEM provides the site of crack inception. Discontinuous growth bands are often

encountered with polymers that undergo crazing. In such instances, the damage must accumulate before the

leading fiber can fail and the crack can advance. This results in discontinuous growth bands or markings that

are observed in fractography (Ref 5). Fractographic examination can also provide information on the formation

of discontinuous or continuous crack growth bands. Figure 16(a) shows the typical ductile mechanisms

observed in pristine UHMWPE, while Fig. 16(b) shows a typical brittle failure in acrylic-based bone cement.

Fractography can provide useful insight into the nature of fracture processes acting at the crack tip and is a

valid supplement for thorough fatigue characterization of engineering polymers (Ref 59).