TECHNICAL REVIEW
Some Unsolved Problems in Failure of Polymers Under Stress Roger P. Kambour Corporate Research and Development, General Electric Co., Schenectady, NY IE301
Failure is reviewed for tilled and unfilled crystallizing and noncrystallizing rubbers, thermoplastic elastomers, and crystalline and glassy thermoplastics. Understanding of rupture of unfilled noncrystollizing rubbers is good because deviations from linear viscoelastic behavior over the entire stress-strain curve a r e small. Conventionally reinforced rubbers, crystallizable rubbers, and thermoplastic elastomers show successively greater departures a t high strain from the viscoelastic behavior of unfilled noncrystallizing rubbers; correspondingly, failure is increasingly complex. Both ductile and brittle failure modes a r e important in plastics. In crystalline plastics understanding of ductile failure is made difficult by the many deformation mechanisms operative in o complex microstructure; in glossy polymers Understanding the various deformation mechanisms is hampered by an uncertainty about the nature of segmental packing and its response to stress. Crazing is an important, incompletely understood feature of brittle failure in both glassy and crystalline polymers. Finally, environmental effects a r e discussed briefly, particularly in regard to corrosion fatigue.
Room P. KAMBOUR i s Manager, Polymer Studies Unit at lhe General Electric Research and Development Center, Schenectady, N Y . He received his B A degree from Amherst College (f954)and his PhD in chemistry from the U n i w sity of New Hampshire (1960). His research interests are in the structure and properties of crazes and mechanism of fracture in glassy polymers, diffusion swelling and cystallization in polymers, morphology and properties of block copolymers, and the relaxation behavior and impact strength ofpolymer systems. Dr. Kambour i s a member of the A C S and Sigma X i , a Fellow of the American Physical Society, and i s on &he Edilorial Advisory Board of Polymer Engineering and Science. I n 1968 he was recipient of the Union Carbide Chemicals Award of the ACS Division of Organic Coatings and Plastics.
T h e strengths of all real materials lie orders of magnitude below the strengths of their ideal counterparts. The strength of an ideal solid would he the force per unit cross section needed to overcome the aggregate strength of all chemical bonds that lie across a given cross-sectional plane. The source of this weakness of the course is the nonuniform distribution of stress arising in all real bodies as a result of adventitious flaws or mechanical heterogeneities that preexist in the bodies or develop under stress. For the last half century there have been two philosophically distinct groups of theories of the strengths of real solids. The critical stress theories spring from the work of Inglis 140 Ind.
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(1913) who related the stress existing a t the tip of a crack in an elastic body t o the applied stress S,the elastic modulus of the material, and the geometry of the crack. In its simplest form the critical applied stress for fracture S, can be expressed as
S, =
LTi,(p/4
C)'/Z
where cc is the true strength of the material a t the crack tip (Le., the ideal strength), p is the radius of curvature of the crack tip, and c the length of the crack. See Berry (1964) for a lucid exposition of this approach. Subsequent r e f i n e ments have considered how microheterogeneities in the material and its nonelastic behavior around the crack tip serve to increase the effective value of p , thus reducing the stressconcentrating ability of the crack and raising the macroscopic strength S,. Other treatments have incorporated an environment dependence of vc. The second group of theories of strength based on the classical work of Griffith (1921, 1924) may be termed fracture energy theories. According to Griffith, a crack in an ideally elastic solid will not propagate until the energy required to break the chemical bonds involved is equaled or exceeded by the reduction in stored elastic energy when the crack grows by an incremental amount. The so-called Griffith equations for the strength of flawed, ideally elastic bodies resulted from combining this concept with the Inglis expression for the stress-concentrating ability of a crack of known length and radius of curvature, e%.,
S, = (2 E y / s c ) l ' z where E is the elastic modulus, and y the so-called fracture surface energy-the energy required to create unit area of new solid surface. See Berry (1964) for a discussion of the derivation of this equation. Subsequent developmentsnotably those of Irwin (1939, 1958)-have enlarged the concept of the energy term to include other energy demands
t h a t must be met during crack propagation. I n this framework it is recognized that for most materials, the energy dissipated in viscous and plastic deformation processes in the region ahead of the crack tip usually exceeds the true fracture surface energy y by several orders of magnitude. Curiously, of all common solid materials only those lying at the extremes of modulus and extensibility are known to fracture in ways t h a t can be treated simply b y either of the above classes of failure theory: These materials are inorganic glasses and conventional unfilled, noncrystallizing rubbers. I n the first case ultimate extension is small and, moreover, nearly entirely elastic. As a result, crack propagation energies for glass determined from experiment are not much larger than true surface energies. I n the case of unfilled noncrystallizing rubbers, of course, ultimate extension is large. At low speeds deformation is again almost entirely elastic, and a suitable formulation of the Griffith criterion serves to predict failure. At higher rates of extension, deformation is no longer purely elastic but rather viscoelastic. However, such viscoelasticity is nearly linear all the way to the breaking point, and i t has been possible to make suitable modifications in the Griffith framework to account for the time-dependent aspects of strength. See Smith (1969) for a comprehensive review of the theories of the strength of rubber. These materials, glass and noncrystallizing unfilled rubbers, are notoriously defective in strength properties-glass because of its lack of toughness and unreinforced rubber because of its generally low tensile strength. By contrast, most engineering materials are useful because they have a balance of strength and toughness as their structures are heterogeneous and deformable in one way or another. Some of these materials are bimaterial composites like fiber-reinforced plastics or carbon black-reinforced rubber. Others, like polypropylene, are single-component materials containing a hard phase (e.g., crystalline) and a soft phase (e.g., rubbery-amorphous). Natural rubber and glassy plastics like polystyrene are members of a third class that might be termed potential composites: Although initially homogeneous, they develop mechanical heterogeneities under high stress. I n all these cases the structural heterogeneities serve to blunt cracks or to dissipate strain energy and thus to postpone fracture to higher stresses and/or longer times. Most of the unsolved problems in the strength of polymeric materials have to do with these various heterogeneous materials-although they are the most useful materials, the very heterogeneities t h a t make them useful cause their strength properties to be the most difficult to treat by the simple failure theories previously outlined. Elastomers
This section deals with unsolved problems in the rupture of unfilled noncrystallizing single-phase rulcanizates, x i t h reinforcement effects caused by particulate fillers and by strain-induced crystallization, and finally with elastomeric block polymers. Discussion here draws heavily on the excellent and comprehensive review of the failure of elastomers by Smith (1969). Noncrystallizing Single-phase Gum Vulcanizates. All of the prominent failure theories for rubbers are based 011 the two failure criteria discussed in the introduction: the critical energy criterion of Griffith and the critical stress criterion. Theories of Greensmith (1964) and Knauss (1963, 1965) based on the Griffith criterion assume that a preexisting
"crack" will propagate under stress when the energy dissipated in forming a new crack surface is equaled or exceeded by the decrease of elastic energy stored in the specimen. Specifically, the crack propagates when T = 2 KCW where W is the stored energy density, C is the crack length, K is a constant, and T is the crack propagation energy. I n the theory of Greensmith, T and W are time-independent material constants. I n the treatment of Knauss, W is dependent on time through the viscoelastic behavior of t'he material. The theory of Bueche and Halpin (1964) starts from a stress criterion: Crack propagation occurs when the stress a t the crack tip is high enough to break chain bonds. [See also Halpin (1964, 1965).] But this stress is again dependent on time by reason of the viscoelastic properties of the material. If the testing time is long compared to the longest relaxation time in the material, the molecular extension keeps pace with the increase in stress, and failure occurs a t maximum possible chain extension. Both theories can be fitted to experimental failure through adjustment of parameters unavoidably empirical. This comes about because of a lack of detailed knowledge about what really happens in the material around the crack tip as failure progresses: what the spatial distribution of broken chains is and what the nonlinear viscoelastic effects are in the interrelationship of stress and strain. As long as nonlinear effects are not excessive and are confined largely to the crack tip region, the time-temperat'ure dependence of true tensile strength and of ultimate elongabion can often be reduced by the log scale shifting procedures commonly applied to linear viscoelastic phenomena. As with linear phenomena time-temperature reduction of failure data works well only when no structural change occurs with time, temperature, or extension and when all relaxation times have the same temperature dependence. TTnder these conditions, moreover, the time effects associated with the specific kind of test (creep, stress relaxation, constant st'rain rate) can be eliminated by eliminating the time scale itself: By plotting true stress a t break vs. elongation a t break on a log-log plot, Smit'h (1969) developed the now famous failure envelope. For many conventional gum vulcanizates the failure envelope lies just inside the estimated equilibrium stress-strain curve t h a t would obtain if failure did not intervene. Finally, through a procedure that accounts for differences in crosslink density and in sbatistical segment length, t'hese equilibrium stress-strain curves and the failure envelopes can be normalized for many materials. The universal failure envelope that results is a reflection of the success of the statistical thermodynamic theory of rubber elasticity and linear viscoelasticity theory in treating the mechanics of real rubbers. Thus, for conventional noncryst'allizing gum vulcanizates, tensile failure can be rationalized quite \yell in terms of lowst,ress behavior. By comparison, effects of reinforcement and crystallization make these t,reatments difficult. These and other difficulties make treatment' of failure in elastomeric block polymers even more difficult. Reinforcement Effects by P a r t i c d a t e Fillers. As noted in the introduction, elasbomers having no reinforcing mechanisms are relatively weak except under restricted test conditions-those that correspond to the region of maximum strain in the failure envelope. Reinforcement occurs under three conditions: Particulat,e fillers are added, strain-induced crystallization occurs a t high extensions, or the material is a block polymer, part of which is segregated into glaLLG wv or crystalline domains. Ind. Eng. Chem. Prod. Res. Develop., Vol. 1 1 , No. 2 , 1972
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According to Smith (1969), the primary viscoelastic change seen on adding a filler like carbon black or silica gel is a reduction of the number of short relaxation times and a n increase in the number of long ones. This is reflected in a shift of position and a change in shape of the middle section of the failure envelope. The greater the reinforcement, the more this section is shifted toward higher strengths and lower elongations. Polymer chains are adsorbed more or less strongly to the filler surface, but just how this causes the changes in the relaxation time spectrum is not known for sure in spite of a great amount of attention in the past. I n the Bueche-Halpin theory of failure, the effects of carbon black are seen primarily in the parameter q that is supposed to indicate the number of filaments that rupture in the slow growth period of the crack. These authors suggest that this may indicate a n increase in tortuosit’y of the crack because it must pass around filler particles. It also seems likely t,hat many short-chain segments that bridge between neighboring part’iclesmay break, but the ability of the particles to redistribute t’he load over the set of chain segments adsorbed to their surfaces tends to stabilize the local situation. Yim and St. Pierre (1970) have carried out studies in which controlled and characterized changes of the adsorptive characteristics of the filler surface are brought about with the intent of relatiiig these to reinforcing behavior. This appears to be one approach worthy of much more exploitation. *\ related approach of considerable interest is the use by Xorton and Healy (1968) of glassy polymer latex particles as reinforcing agents. These are spherical and their size can be controlled. I n addition, their mechanical properties can be varied: I n the foremost example of this approach to date, polystyrene spheres have been added to polybutadiene to form a model for comparison with the styrene-butadienestyrene block polymers discussed in the next section. Failure data from the model system form a reasonably good failure envelope. Smith (1970) suggested t h a t reinforcement here arises from the deformation of the latex particles a t high extensions. If so, this system is an example of one for which a failure envelope can be formed in spite of the fact that the reinforcing mechanism (glassy polymer deformation) is not linearly viscoelastic, and thus should not be amenable to time-temperature reduction, the theoretical basis of failure envelope formation. However, the correctness of proposed mechanism could be verified by the use of polystyrene particles crosslinked by divinylbeiizene incorporation; these particles being much more rigid should not reinforce well if the proposed mechanism is correct. I n any case, this discussion serves to point up some of the degrees of freedom inherent in particulate polymer fillers. Another point about fillers that the present author a t least does not understand is that they often change the shift factor ( a T ) dependence on temperature from the W L F type to the Xrrhenius type (Smith, 1969). W L F dependence is understood to occur when viscosity is controlled by free volume, and the latter changes with temperature. A priori, there appears to be no obvious reason why filler incorporation should prevent free volume in a material above its T ofrom being temperature dependent. Indeed, the effect of fillers on free volume is small enough that they have only a niinor influence on T,. Reinforcement by Strain-Induced Crystallization. Several rubbers (e.g. , natural rubber, polychloroprene, polydimethylsiloxane) crystallize a t high extensions. Crystallization brings severe departures of failure data from the simple failure envelope even when the crystallinity developed is 142 Ind. Eng. Chem. Prod. Res. Develop., Vol. 1 1 , No. 2, 1972
confined to the immediate region of the crack tip. As summarized by Smith (1969) resistance to crack propagation is augmented by two factors: the increase in length of material in the stress direction owing t o the morphology of the crystalline phase and to the inherently greater resistance to cracking of the crystals themselves. I n unfilled butyl rubber, strain-induced crystallization occurs rather slowly, probably reflecting, according to Smith (1964), the low growth rates of crystallization a t lower temperatures in the absence of stress. Strain-induced crystallization is prominent a t low temperatures but disappears rather abruptly as room temperature is approached. By contrast, in natural rubber strain-induced crystallization occurs rapidly but in gradually decreasing amounts up to about 100°C. The departures of failure data for these materials from their respective failure envelopes differ markedly because of these contrasting crystallization characteristics. Phenomena like these have been studied for many years, particularly in natural rubber. There are many unsolved questions, however, dealing with the nucleation and growth kinetics of strain-induced crystallization, of quantitative stress configurations a t the crack tips, and the mechanisms of crack propagation through the crystallized material. [See A n d r e w (1964, 1968) for more detail.] Elastomeric Block Polymers. Block polymers containing three or more blocks per molecule that segregate to form domains that are glassy or crystalline a t ambient temperature constit’ute high strength, high elongation rubbery materials if the content of elastomeric blocks exceeds 60-70%‘,. Styrenebutadiene-styrene SBS triblock polymers and polyesterpolyurethane multiblock polymers are well-known commercial examples. hside from the electron microscopy of Beecher et al. (1969) and time-temperature reduced failure data developed by Smith (1970) for one SRS material, little systematic information has been developed on the failure of these materials. The relative novelty of this class of rubbers, their rapid proliferation, and their internal complexities make failure of these materials a wide-open, exceedingly complex problem in a burgeoning field. Several aspects make these materials the most varied and challenging of elastomers. First, their morphologies change with composition and forming history in ways that markedly affect stress-strain behavior (Wilkes and Stein, 1969; Kambour, 1970a). The stress-strain response, even a t low elongation, is often more or less nonlinear involving as i t can the breakup of the domain network. Deformation in the SBS mat,erials involves large deformations of the spheroidal elements of the domain netIvork. The spectrum of relaxation behavior of these glassy elements augments considerably the relaxation capability of the rubbery phase a t long times-high temperatures. But since the relaxation behavior of the two parts of the material are so different, time-temperature reduction should not succeed in unifying failure data from the entire temperature range of utility into a single failure envelope. llultisequence block polymers containing many short blocks offer additional challenges. Usually block lengths are too short for the application of random flight statistics to the individual block, and thus chain configurations are difficult to assess. When the two blocks are dissimilar enough, domain formation can persist down to sequence lengths of two or three repeat units, as evidenced in the work of Harrell (1970) b y the continued manifestation of a domain melting point. Large-scale deformation of these materials would then appear to involve a “hopping” of blocks in a repeated fashion from one domain to t,he next. The blocks are often small enough,
however, to make electron microscopic study of even the undeformed structure a difficult job. Crystalline Thermoplastics
By comparison with conventional crosslinked, noncrystallizing gum rubbers, our understanding of the strength of glassy and crystalline plastics is in a n earlier state in its evolutionary development. Its progress is made difficult b y several differences from rubbers: the complexities of morphology in crystalline polymers; uncertainties relating to the morphology (or its lack) in glassy materials; and the departure from linear viscoelastic response at low strains. I n brief, there are vast gaps in our knowledge of the continuum t h a t must exist between chain structure, morphology and its changes under stress, and the mechanics of failure. A vast amount of work has been done on the morphology and viscoelasticity of crystalline polymers in the last 15 years; yet, a swirl of controversy surrounds many aspects of these subjects even in the case of the most deceptively simple of these materials, polyethylene. Today, there is fairly wide agreement t h a t chain-folded morphology carries over from solution-grown single crystals to bulk-crystallized materials. T h e demonstration by Keith et al. (1966) and Vadimsky et al. (1969) of the existence of intercrystalline links and their importance in transmitting stress between lamellae is a relatively recent development. However, spatial frequency of these links in bulk-crystallized polymer and the nature of the stress distributions around them in various stages of respc’iise to stress are currently totally unknown. I n spite of the hundreds of papers published on the lowstress relaxation behavior of crystalline polymers, our knowledge of the irecise segmental motions involved is actually quite limited. h review of these limits is outside the scope of this discussion, and those interested can only be referred to McCrum et al. (1967) for a n excellent and comprehensive review. Most of the work in the field is still aimed a t cataloging the sources of these motions in terms of specific chemical groups and for crystalline materials, in terms of morphological features (e.g., Crystalline or noncrystalline, folds, row vacancy or other crystal defect). I n only a few cases have specific, quantitative models for the motions involved been advanced (e.g., Hoffman et al., 1966). Yet, many of these processes are prominent in influencing or dominating creep, stress relaxation a t intertnediate stresses, and even ultimate elongation in strength tests. Cnder intermediate stresses the spherulites in crystalline polyniers distort through interlamellar slip and lamellar buckling and a t high stresses disintegrate into blocks of folded-chain material with extended-chain polymer in between. [See Kambour and Robertson (1970, 1972) for a review of this subject.] Further drawing proceeds with more conversion of folded-chain to extended-chain material. These changes proceed through a host of mechanisms, the specific set of which varies from one polymer to the next. Again, most of the activity in this area of study is still primarily concerned with a determination of what happens in a given polymer, with quantitative descriptions of the mechanisms of these motions in terms of molecular and lattice structures and dynamics being subjects for the future. These segmental motions figure heavily in the ultimate properties of crystalline plastics: High strength and elongation require usually that mechanisms of flow exist t h a t serve to keep the stress distribution well enough equalized to delay the nucleation and growth of the voids that are the precursors of fracture. “Brittle” Failure. As with most materials so-called brittle
failure in crystalline plastics appears to involve a large amount of plastic deformation on a localized scale around the crack tip. According to Cooney (1964) and Prevorsek (1966), some of this deformation is conventional shear deformation. However, i t is beginning to be understood that extensive amounts of flow accompanying void formation often occur beyond crack tips in forms reminiscent of crazes in glassy polymers. These craze-like bodies have been seen by Harris and Ward (1970) in polyethylene terephthalate because of their lightreflecting character. I n polypropylene Kambour (1970b) found t h a t the application of stress to sharp cracks above O°C or so produces extremely noticeable stress-whitening beyond the crack tip before propagation commences. Microscopic examination shows t h a t the whitening arises from a multitide of tortuous craze-like regions of deformation extending beyond the crack tip, each craze having a sponge-like character. h s has been observed by van Schooten (1960) for the propagation of cracks in oxidatively embrittled polypropylene, these “crazes” exhibit a tendency to run preferentially along spherulite boundaries and spherulite radii. Xothing more is known about these bodies, the character of the polymer webbing in them, or the details of how they propagate. Considering the richness of detail already known about crystalline polymer morphology and its deformation processes, the brittle fracture in general and these craze-like bodies in particular would seem to be a fertile ground for study. Detergent and Solvent Cracking of Polyolefins. T e n to 15 years ago, that polyethylene was peculiarly susceptible to stress cracking in detergents and their solutions in water as dilute as 0.01% constituted a painful industrial problem and a scientific puzzle as tough as the veritable Gordian knot. The eventual switch from branched to linear polyethylene solved the industrial problem, but the scientific puzzle remained, in spite of dozens of papers on the subject. From the most thoughtful and systematic of these (Pelagatti and Baretta, 1959; Lander, 1960; Rogers, 1962; Isaacsen et al., 1963), we draw the following salient points: Crack locus is along spherulite boundaries and radii as with other types of cracking. However, cracks develop preferentially in those spherulites a t the boundaries or “shoulders” of regions of cold drawing (where the change from the lamellar to extended-chain morphology change is just beginning) ; low-polymer molecular weight and broad distribution make for greater susceptibility (the reason for this is not known, although today me may speculate t h a t it involves the density of intercrystalline links) ; in resins of low molecular weight, cracking susceptibility is greater in small molecule organic liquids than in detergents, but the reverse is true for high molecular weight polymers, suggesting that the respective mechanisms are not quite the same; agents of limited solubility absorbed to saturation are often much more effective cracking agents than those of higher saturation solubility absorbed to the same degree, suggesting that the tendency to cluster or recondense internally in microvoids may be important to cracking efficiency. These points suggest t h a t the agents interfere with t h e reorganization of polymer into sound continuous extendedchain material as i t is drawn out of lamellar crystals. Clustering of solvent molecules or detergent-stabilized water molecules in voids that might normally be formed only temporarily would tend to stabilize them and prevent the rehealing of t h e polymer structure. This point is clearly speculative. T h e main thrust of the discussion is to point out how little is yet known about the mechanism(s) of this complex problem. Ind. Eng. Chem. Prod. Res. Develop., Vol. 1 1 , No. 2, 1972
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Glassy Polymers
Brittle Failure. The last dozen years have provided a noticeable advance in our understanding of how cracks initiate and propagate in glassy polymers. According to Berry (1964), crazes initiate a t low stresses and grow with time. Kambour and Russell (1971) have found that as stress is increased andl’or time progresses, the spongy structure of the craze tends to coarsen, and according to Murray and Hull (1969), eventually a macroscopic hole forms. The hole grows in size slowly until the stress a t its edge has increased to the point where the hole can propagate rapidly through the remainder of the preexistent craze and then into the region beyond the boundary of the original craze. As it propagates further, however, it is always preceded b y the formation of more craze material beyond the running crack tip, and indeed, Kambour (1966) has termed the whole fracture process craze formation and breakdown. Now the ease of craze formation varies considerably from one glassy polymer to the next, but why this is so remains a mystery. All materials exhiblt a threshold value of applied strain below which crazing will not occur under the ambient conditions; termed the critical strain ecJ it appears, a t least for polystyrene, to be the best criterion for craze initiation, according to M‘ang et al. (1971). Xom eC rises roughly linearly with decreasing temperature from a low value near T,, as first pointed out by Ziegler and Brorvn (1955). But even when the differences in T,-TteSt are accounted for, there remain between different polymers wide differences in ec that are not understood. h good example of this is provided by contrasting the behavior of polymethylmethacrylate and polystyrene: Why are the et's equal to 1.20 and 0.35%, respectively, a t room temperature when their To’sare essentially the same? Plastic flow plays a large part in crazing, but, for example, the yield stress of Pl‘IhIX is higher than that of PS by only 30% a t room temperature. Of undoubted significance, 11e believe, is that in P M X i under constant applied strain, craze initiation will proceed only during the first 10 min; in PS crazing initiates a t ever lower strains until the 10-hr point is reached. P M M h undergoes much more homogeneous stress relaxation than does PS, and this may compete with and limit the crazing process to short times (see Kambour and Robertson, 1970,1972). Tied u p with the above question is the molecular one: Is there some kin! of chain-packing feature on a scale between 10 and 100 A that leads to the crazing phenomenon so characteristic of glassy polymers? We would like to work down through the continuum level of treatment to a n understanding of crazing in terms of chain structure. The unanswered questions are: Do glassy polymers exhibit any kind of packing order as Yeh and Geil (1967), for example, believe, and if so, how does this order relate to hole initiation? If not, then how should me viex this “perfectly” disordered state? The great advantage that order provides is a standard state against which defects can be defined. “Perfect” disorder on the other hand implies a random fluctuation of neighboring chain-segment directions; if so, are these fluctuations related to the ease of hole formation, and, in turn, are they strongly influenced by chemical structure of the polymer chain? Another question concerns the kinetics of the viscous processes involved in craze formation and craze breakdown. As reviewed by Kambour and Robertson (19’70, 19’72), these kinetics differ in several ways; for example, stress-temperature- and molecular-veight dependences. Studying the break144 Ind.
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down process independent of the formation process is difficult; therefore, aside from realizing that these differences exist and are of foremost importance in determining the amount of craze material and its spatial distribution a t a crack tip, little is further understood about the kinetics of either process. Ductile Failure. The secoiid, more desirable and less common mode of failure, is that of shear yielding-homogeneous flow under the shear component of applied stress. X favorite qualitative rationale for shear f l o ~has been that applied stress increases free volume enough to lower T , to the test temperature. This view is open to several criticisms, but perhaps the most serious one from a chemist’s point of view is that there appears to be no way to make a connection to the molecular level. h more successful approach is that of Robertson who assumes that an energy criterion controls flow: When stress is high enough, the number of chain bonds in the high-energy state is great enough for the solid to become fluidized. The great appeals of this approach are that T , remains a constant, the direction of flow is a natural outcome, and the temperature dependence of yield stress can be calculated from an expression having no adjustable parameters. Several questions remain to be answered, the foremost of which relates to the cooperative nature of shear flo~v.PF‘hile a given polymer yields rather uniformly throughout a t higher temperatures, a t lower temperatures the flow becomes more and more sharply concentrated in shear bands, according to Argon et al. (1968), Robertsoi; (1968), and Rowden and Jukes (1970). Bands 100 to 1000 A thick have been frequently seen, and the boundaries seem to be sharply defined. The existence of these bands implies that flow has a cooperative aspect to it that becomes more prominent the lower the temperature. The nature of this cooperativeness remains essentially unknown. To the extent that it is intramolecular, it depends on the nature of molecular packing in the glass which, as discussed before, remains speculative. Rubber Modification. Incorporation of rubber, either by blocking or grafting procedures, in glassy polymers is well known to bring about increased toughness. Bucknall (1967) and coworkers have discovered that craze initiation a t the rubber-glass interface and growth between particles are the sole sources of this toughness in rubber-modified polystyrene. I n .;ins shear deformation appears to play a significant role as well, according to more recent work (Bucknall, 1970). These facts imply t h a t both modes of flow can be influenced by the presence of rubber particles and, moreover, that the extent to which one mode is favored to the exclusion of the other depends on specifics of the structure. I n addition to the properties of the unmodified glassy matrix, i t appears likely that the size, composition, and/or internal structure of the rubber particles play a role in influencing the mode of flow. .\side from speculation of this nature, little further information appears to exist in print as to the experimental facts of the situation. h systematic investigation of these effects is needed as \vel1 as a theoretical mechanics treatment of the influence of rubber particle size a t constant composition on the relative ease of shear flow and crazing. Fatigue and Environmental Fatigue. Failure of plastics under cyclic stress conditions has received little attention, particularly in regard to environmental (e+, solvent) effects, Most of the reported studies have dealt with plots of log of number of cycles to failure vs. applied stress. A few have focused on the two modes of failure (ductile and brittle) that have been observed, ductile failure being associated
largely with heat generation produced by high-amplitude straining at rapid rates (Higuchi and Imai, 1970). With increase in temperature, yield stress is exceeded eventually. A brief report by Marshall e t al. (1970) of t h e effect of fatigue on polystyrene suggests t h a t crazing and crack propagation can be markedly changed by cyclic stress. In this study 3000-Hz cyclic stress applied to a preformed crack brought about a marked sharpening of the crack tip. T h e sharpened crack propagated with a much reduced fracture energy. The implication here is t h a t craze breakdown is much more sensitive t o cyclic stressing than are craze initiation and growth. Recently, Marshall and Williams (1971) reported preliminary results of a corrosion fatigue study of a glassy polymer. Growth and breakdown of crazes in PMMA loaded in methanol a t various frequencies show features t h a t differ from those seen under static loading conditions. Some of t h e differences may be caused b y viscoelastic effects related to the cyclic flow of liquid in and out of the craze as the craze is alternately extended and compressed. These examples serve to indicate how little is yet known about effects of fatigue on the mechanisms of crack propagation. As plastics find wider use as structural materials, this subject will undoubtedly assume greater and greater importance. Summary
Based on historical precedent, we can expect each of these problems to meet one of several fates: to be resolved as a result of future improvements in our understanding of basic polymer morphology, its mechanisms of deformation, interfacial interactions, and so on; to be laid to rest through the application of new experimental techniques t h a t open u p new perspectives on these problems; to become obsolete as adventitious or empirical innovations bring solutions t o the practical problems through materials replacement (as has actually happened with polyethylene stress cracking). At the same time new problems will continue to be recognized. Materials innovators continue to spawn new kinds of polymers and polymer composites. And polymeric materials continue to find new uses in new environments and under new combinations of stress and stress history. Given the continued expansion in the utilitarian importance of polymeric materials, the number of important unsolved problems in the failure of polymeric materials under stress will undoubtedly sho\T- a net increase with time. Literature Cited
Andrews, E. H., “Fracture in Polymers,” American Elsevier, New York, NY, 1968. Andrews, E. H., Proc. Roy. SOC.,A , 277, 562 (1964). Argon, A. S., Andrews, R. D., Godrick, J. A., Whitney, W., J . A d . Phus.. 39. 1899~~-(1968). ~, Beech&; J. F:, hlarker, L., Bradford, R. D., Aggarwal, S. L., J . Polym. Sci. C , 26, 117 (1969). Berry, J. P., “Fracture Processes in Polymeric Solids,” B. Rosen, Ed., Interscience, New York, NY, 1964, Chap. 2. Bowden, P. B., Jukes, J. A., Int. Conf. on the Yield, Deformation and Fracture of Polymers, Cambridge University, Cambridge, England, March 1970.
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