crazing in two polystyrene/polybutadiene block copolymers

Crazing in Two Polystyrene/Polybutadiene Block Copolymers

A. S. ARGON,* R. E. COHEN,+ B. Z. JANG,t and J. B. VANDER SANDE,t Massachusetts Insti tute of Technology, Cambridge, Massachusetts 02139

Synopsis

Crazing was investigated in two commercial polystyrene/polybutadiene block copolymers made by the Phillips Petroleum Co. and marketed under the trade names of KRO-1 and KRO-3 resins. The two block copolymers each with 23% polyhutadiene (PB), have radically different microstructure and radically different crazing behavior, leading to strains to fracture of 0.1 and 1.0, respectively. Of these, the KRO-1 Resin has a phase microstructure that consists of randomly wavy and often interconnected rods of PB of 20 nm diameter surrounded by polystyrene (PS). The microstructure of KRO-3 Resin consists of lamellae of P B with 20 nm thickness and large aspect ratio which range in packing from regular aligned lamellar domains with randomly varying misorientation in the annealed material, to randomly corrugated and wavy sheets in the as-received material. Crazes in KRO-1 Resin have well delineated planar shapes with a conventional, tufty craze matter structure which suggests growth by the now well-established meniscus instability mechanism proposed by one of us. In KRO-3 Resin, on the other hand, crazing involves profuse cavitation if the PB lamellae, giving rise to less well delineated zones of cavitational growth dispersed over the volume and suggests a mechanism of craze growth by stable, interfacial cavitational degradation in a process zone ahead of the craze tip. The measured stress and temperature dependences of craze velocities in these two polymers is in partial support of the suggested mechanisms which are also developed in outline.

INTRODUCTION

Below their glass transition temperatures many glassy polymers exhibit a brittle behavior when tested in tension in ordinary laboratory air. In these polymers, fracture is preceded by crazing. Such polymers are called “crazable.” A few glassy polymers, such as polycarbonate, and some polyimides do not craze and are tough under comparable conditions. These polymers are under normal conditions “not crazable.” Even though a great deal is known about the kinetics of nucleation and growth of crazes in crazable glassy polymers, there is currently inadequate understanding of the molecular specificity of the phenomenon to permit predictivestatements on which polymers are crazabie and which are not. That brittleness in crazable glassy polymers can be alleviated by the incorpo- ration of rubbery heterogeneities has been known for a long time. It is now also known that such toughening is a result of either profuse crazing initiated and controlled by particulate heterogeneities or of distortional plasticity with or without microscopic shear localization.’ Different heterogeneous polymers under different stress and temperature are known to exhibit a different mixture of these processes during normal tensile behavior. The considerations that govern the contributions of one or the other of these mechanisms of inelastic

* Department of Mechanical Engineering. + Department of Chemical Engineering. * Department of Materials Science and Engineering.

Journal of Polymer Science: Polymer Physics Edition, Vol. 19, 253-272 (1981) IC) 1981 John Wiley & Sons, Inc. 0098-1273/81/0019-0253$02.00

254 ARGON ET AL.

behavior to the work of fracture are usually complicated not only by important interactions between them but also by the fact that in the final analysis crazing itself occurs by distortional plasticity on a finer scale.2 In general it is found that under relatively high strain rates of laboratory tension experiments and impact, crazing is by far the major contributor to toughness in nearly every case.l Through accumulated industrial experience it has been established that many factors are important in assuring adequate toughness in a heterogeneous polymer among which the size, shape, volume fraction and internal constitution of rubbery particles together with the character, chemistry, and thickness of their interfaces play important roles.’J According to such experience it is normally rationalized that for a given volume fraction of heterogeneity, optimum toughness is achieved for a given particle size (ca. 2-5 pm), that is small enough to maximize the volume fraction of craze matter in the stretched polymer, but also large enough to initiate crazes from interfaces of such particles. With regard to the latter point it has been proposed that the precursor events that result in the formation of a craze nucleus require a certain minimum volume element over which the concentrated stress must be relatively uniform.:'^^ According to current experience, particle sizes much less than 0.5 pm become ineffective in nucleating crazes. For a variety of such reaons it is of interest to explore the behavior of styrene-butadiene block copolymers that permit the manipulation of the size, shape, and nature of the interface a t constant volume fraction of particle, by means of different equilibrium ternary mixtures with additional hom~polymer,~ and by means of different solvent extraction rates6 that result in nonequilibrium microstructures. Here we report the results of an experimental investigation on the mechanism of toughness in two commercial resins, manufactured by the Phillips Petroleum Company. A preliminary communication of some early results of this study has already been made earlier.7

EXPERIMENTAL PROCEDURE

Material and Microstructure

Two commerical polystyrene/polybutadiene (PS/PB) block copolymers made by the Phillips Petroleum Company under the designation of “K” resins and labeled as KRO-1 and KRO-3 have been investigated. The chemistry, molecular weight distribution and some mechanical properties of these materials were described by Fodor et a1.,8 some of which, relevant to our discussion here, are given in Table I. These materials were obtained in 0.38-mm-thick sheets from the manufacturer. Routine NMR measurements showed that polybutadiene (predominantly 1,3 addition) makes up about 23% of the weight of both polymers. Measurements by DTA-TMA show two distinct transitions near -90 and 95°C for both polymers corresponding to the PB and PS, respectively. A weak diffuse intermediate transition, however, is also observed at room temperature which may relate to an interfacial material.

Annealing experiments performed on as-received sheets at 105OC showed that they contracted in the longitudinal direction and expanded in the transverse direction by roughly equal amounts while undergoing an increase in the thickness dimension of the order of 12%. These dimensional changes were complete within a period of about 30 min in KRO-3 resin and 40 min in KRO-1 resin. Although

CRAZING IN BLOCK COPOLYMERS 255

the retained orientation due to initial processing must be termed small, it had measurable effects on craze growth as will be discussed below.

The surface perfection of the as-received sheets was adequate for most experiments. In a few instances, however, in craze growth experiments where high surface perfection is essential, some samples were metallographically polished with 0.1 pm alumina suspension in distilled water.

Since an important goal was to relate the crazing behavior of these polymers to their microstructure the latter was examined in considerable detail by both conventional transmission electron microscopy (TEM) performed on Phillips EM-200 and EM-300 microscopes, and scanning transmission electron microscopy (STEM) performed on a VG-5 microscope. In all cases, the PB phase microstructure was fixed by the now conventional OsO4 treatment prior to microtomy.

Figures l(a) and l(b) show the microstructures of the as-received and annealed samples of KRO-1 Resin. This structure is best described as an interconnected space network of randomly wavy rods of PB of 20 nm diameter surrounded by

Fig. 1. STEM micrographs of the microstructure of KRO-1 resin (a) in as-received form and (b) in annealed form.

256 ARGON ET AL.

a matrix of PS. In the as-received sheet, the PB microstructure has a readily discernable orientational strain which is removed upon annealing.

Figures 2(a) and 11 show in turn two different views of the KRO-3 microstructure in the as-received sheet. Of these, Figure 2(a) is a transverse section through the oriented phase structure while Figure 11 is nearly parallel to it in a strained and partially cavitated sample. Figure 2(b) shows in turn the microstructure in an annealed sample of KRO-3 resin where it is in the form of regular but randomly misoriented domains of parallel lamellae. These different views of the KRO-3 resin structure suggest that it is composed of layers or lamellae of large aspect ratio of PB of 20 nm thickness which are either piece-wise straight in the annealed sheet or corrugated and aligned in the oriented sheet-all surrounded by a majority phase of PS.

Fig. 2. (a) STEM micrograph of the microstructure of as-received KRO-3 resin (dark field) and (b) TEM micrograph of the annealed microstructure of KRO-3 resin; note gray regions where section departed from being perpendicular to the microstructure.


A number of different techniques were used in the crazed samples to accen- tuate the microstructural details in microtomy. Most specimens containing crazes were fixed in Os04 solutions in their extended states held by mechanical clamps to prevent craze recovery and alteration of craze matter during the long periods of fixing of the order of several days. Crazed specimens were microtomed a t room temperature in several different directions to reveal the morphology of the craze matter. The preferred sectioning procedure was along planes containing the tensile axis and along directions approximately 45" to the tensile axis. These sections intersect craze planes at right angles and placefhe outlines of the craze planes at 45" in the section with either the marks left by the imperfections in the knife or by the chatter marks often left parallel to the knife front. In addition to these, sections were also made nearly normal to the tensile axis. Such sections intersect craze planes at very shallow taper angles and are sometimes useful in providing a unidirectional magnification of the craze structure, particularly a t its border with solid polymer.

Testing Procedure

Strip specimens with reduced gauge sections for tension experiments were produced by cutting the sheets to size, with a sharp surgical blade, while they were clamped between two parts of a metal template. For stress-strain experiments in tension, no further preparation was necessary. For craze growth rate measurements, where suppression of spurious crazing from the imperfections of the cut edges is essential, the edges of the specimens as well as their flat surfaces were metallographically polished with 0.1 pm alumina suspension in water.

In experiments on craze structure determination where the mode of testing is not a key factor, specimens were often clamped in a vice and carefully extended by hand to quickly achieve desired densities of crazes. Controlled stress-strain experiments a t room temperature were performed with a floor model Instron machine with conventional laboratory extension rate of 10-4-10-3 sec-I. Craze growth rate measurements in dry laboratory air were carried out at both room temperature (20°C) and at -20°C on a specially constructed constant load maintaining frame and utilized a photomicrographic craze length recording procedure described earlier by Argon and Salama.2

EXPERIMENTAL RESULTS

Stress-Strain Experiments

Load extension curves for both KRO-1 and KRO-3 resins showed relatively abrupt yielding behavior without a significant yield drop and were substantially flat to final fracture. The measured yield stresses and strains to fracture are listed in Table I. Crazing, readily discernible as the development of a translucent sheen, and eventual whitening, accompanied yielding. The principal component of inelastic strain was axial with very little contraction in the lateral direction and in the thickness dimension-indicating that the platic strain was substantially due to the production of craze matter. Beyond such coarse observations, however, no accurate determination of the dimensions of the straining specimen was made which would be necessary to determine the specific combination of

258 ARGON ET AL.

TABLE I Some Physical and Mechanical Properties of KRO-1 and KRO-3 Resins at 2OoC

KRO-1 KRO-3

m w 1.79 X lo5 a

Weight fraction PB 0.23 Yield stress (MPa) 20.95 E (MPa) 1269 ' f 0.09 P (MPa) 92.72

m" 1.32 x 105 a

2.17 X lo5 a

1.06 X lo5 a

0.23 21.0

1474 1.10

107.54

a Fodor et al. (ref. 8).

dilatational (crazing) strain and distortional strain.l In the hand-stretching experiments, a marked loss of bending stiffness in the plastically extended specimens was readily felt, indicating further that the majority of the plastic straining was by means of crazing. The fact that the load-extension curves were substantially horizontal indicates a large degree of stability in the deforming specimen that is compatible with early nucleation of crazes followed by their growth-and, of course, orientation hardening in the tufty craze matter produced. Thus, apparently, an expected strain softening due to cavitation is continuously balanced by orientation hardening in the craze matter.

Craze Morphology

Surfaces of crazed KRO-1 and KRO-3 samples were coated with a very thin layer of vapor deposited gold to make them conducting and more reflective for study in the scanning electron microscope (SEM), or for viewing in the light microscope by reflected light. Examinations of such crazed surfaces with both the light microscope and the SEM has indicated that the crazes in KRO-1 are relatively straight and have straight edges on the scale of 20 nm-the limit of resolution of the SEM. A typical example is shown in Figure 3(a) where the fine craze microstructure in the dilated lower craze is just resolvable with the SEM. On the other hand, the outlines of the crazes on the surfaces of KRO-3 were significantly wavy having also rough edges on a scale of 0.1 pm. A typical example is shown in Figure 3(b) revealing a coarse scale craze microstructure. Figures 3(a) and 3(b) show that although crazes in KRO-1 and KRO-3 are vented to the atmosphere, these openings can be abruptly terminated as at ( A ) in Figure 3(a), or can be interrupted by solid bridges as a t ( B ) in Figure 3(b). Outside of this detail, however, it is clear that the resolution of the SEM is insufficient to discern the details of the craze matter structure.

Figure 4 shows crazes in annealed KRO-1 in transmission electron microscopy (TEM) in a microtomed section normal to the craze plane. A larger magnification view of a representative region in such a craze is shown in Figure 5. Both figures show a well defined and sharply bordered craze zone and a tufty craze structure very similar to that in single phase PS. The craze thickness, which is in the range of 0.5 pm, is close to thicknesses of simple crazes in the PS ho- mopolymer, but is now many times the scale of the block copolymer phase wave length. This and other results on craze growth suggest that the KRO-1 block copolymer is acting as a new quasicontinuum phase. In Figure 6, a taper section


Fig. 3. (a) SEM micrograph of surface relief of craze in KRO-I resin showing sharply delineated craze zone; (b) SEM micrograph of surface relief and internal structure of craze in KRO-3 resin showing rough borders and fragmentation.

at an angle of the order of 5" with the craze plane is shown in as-received KRO-1. In spite of the distortion, undoubtedly produced by the microtome knife, the section shows the craze tufts and the interspersed cavities roughly in cross section. There is no significant extension across the craze borders which are now indistinct due to the overlap produced by the taper section and the nearly parallel nature of the cut to the craze plane. Comparison of the annealed background microstructure of the crazed sample in Figures 4 and 5 with that in Figure l(a) of the undeformed sample, and the corresponding pair of Figure 6 and Figure l(b) shows no significant elongation due to the straining that resulted in the crazes. This is taken as further confirmation that the measured inelastic strain in the tension experiments is almost entirely due to crazing with only negligible accompanying distortional plastic flow. In KRO-1 Resin, the well defined nature of crazes, their

260 ARGON ET AL.

Fig. 4. TEM micrograph of crazes in KRO-1 resin showing sharply delineated structure.

sharpness of border and the observed sensitivity of craze initiation to surface perfection all indicate that the favored sites of craze initiation are surface imperfections. There is little evidence of craze initiation in the interior from either of the two phases or their interface.

Figure 7 shows a relatively low magnification micrograph of crazes in a sample of stretched KRO-3 resin, microtomed normal to the craze planes. The micrograph shows two important features. First, the crazes appear fragmented as a multiplicity of thin, cavitated zones; and second, the craze matter is filled with a dense collection of black dots. A closer inspection of this structure shown in Figure 8 demonstrates that the black dots are broadened regions of PB phase

Fig. 5. T E M micrograph of a craze in KRO-1 resin showing the conventional tufty craze matter structure.

CRAZING IN BLOCK COPOLYMERS 26 1

Fig. 6. STEM micrograph of a craze in KRO-1 resin in a taper section.

and are taken to signify an early stage of cavitational breakdown in the PB phase that has resulted in a preferential fixing by the 0 ~ 0 4 . Furthermore, several clear examples of cavitation inside the PB phase can also be discerned as shown in the areas marked “C.” Examination of other areas as shown in Figure 9 reveals readily additional isolated darkened spotty regions inside the PB phase away from already cavitated craze zones such as in region “A.” These are clear indi- cations that unlike in KRO-1 Resin there is considerable isolated internal cavitation in KRO-3, and preferentially in the PB phase. Once a critical amount of such cavitation is concentrated in a zone, large scale delamination, drawing, and tuft formation follows as is shown in Figure 10. In the oriented sheets, an- other form of diffuse cavitation is observed as is shown in Figure 11 that is very reminiscent of the incipient fracture process in heavily oriented crystalline polymers undergoing fibril fracture as has been studied in detail by Peterlin.g

Craze Growth Rates

Craze length as a function of time under constant applied tensile stress was measured a t both room temperature and at -2OOC in specimens of unannealed sheet but with carefully polished surfaces. The craze length was recorded photographically and was subsequently measured from film. Figures 12(a) and 12(b) show typical results of craze length at room temperature plotted against time in KRO-1 and KRO-3 resin. Clearly, the craze length is a linear function of time. The results of such measurements at different stress levels are given in Table 11. All the reported measurements relate to noninteracting crazes relatively far apart from each other.

Some experiments on craze growth were also performed on annealed sheets a t a stress level off of the yield strength. There too the craze growth was found to be a linear function of time but was 26% faster in KRO-1 resin and 34% faster in KRO-3 resin compared with the unannealed polymers. The reduced growth rate in the unannealed sheets is attributed to the orientational alignment of the PS phase in them.

262 ARGON ET AL.

Fig. 7. TEM micrograph of a crazed KRO-3 resin showing dispersed cavitation and delocalized cavitated regions acting as crazes.

DISCUSSION

Microstructure and Stiffness of the Resins

In both KRO-1 and KRO-3 resins, the PB phase is quasirandomly dispersed in the PS. Hence, the shear modulus of the composite polymer should be obtainable by the well known self-consistent method of modulus averaging for composites which is based on Eshelby’s method of obtaining the homogeneous concentrations of stress and strain inside ellipsoidal heterogeneities. In the case of the K resins, the PB rubbery phase can be idealized to be of ellipsoidal shape and to have a shear modulus that is negligible in comparison with that of the majority phase of PS. The self-consistent problem of randomly dispersed soft ellipsoidal heterogeneities in a matrix of much higher deformation resistance has recently been considered by Chen and Argonlo in a general sense to include even nonlinear responses of the two phases. Their result, however, for linear response of two incompressible phases, one of which (at a small volume fraction c ) has negligible shear deformation resistance, is particularly simple and can be stated as

(1) E,. = Eps[l - ( 8 / 1 5 ~ ) ~ ( ~ / b ) ]


Fig. 8. TEM micrograph of a craze in KRO-3 Resin. Note the dark regions inside the PB phase, resulting from accelerated fixing with OsO4 due to early forms of cavitation in this phase. Note particularly regions marked C showing clear examples of splitting inside the PB phase.

where E, and Eps are the Young’s moduli of the block-copolymer composite and the majority phase of polystyrene, and alb is the major to minor axis ratio of the included ellipsoidal heterogeneity. The experimentally measured composite Young’s moduli for KRO-1 and KRO-3 at room temperature are given in Table I while the Young’s modulus for PS at room temperature is 3300 MPa.” The aspect ratios alb for the K resins that is compatible with these measured moduli can be obtained from eq. (1) and are 15.75 for KRO-1 and 14.17 for KRO-3, respectively. Although these values must be slightly in error because only the PB phase is incompressible, we find the calculated aspect ratios quite reasonable particularly for KRO-3 Resin vis-A-vis its structure shown, e.g., in Figure 2 ( c ) . For KRO-1 Resin, where the PB phase appears to be in the form of a micronet- work forming snaky cylinders, the computed aspect ratio of 15.75 is taken only as “reasonable” for an unrealized equivalent ellipsoidal phase form. Based on this understanding, however, we estimate the Young’s moduli of the resins a t -20°C to be E = 1389 MPa for KRO-1, and E = 1613 MPa for KRO-3 by merely scaling them parallel to the temperature dependence of the shear modulus of PS given by Wall et al.”

264 ARGON ET AL.

Fig. 9. TEM micrograph of a craze in KRO-3 resin with observable enhanced fixing with OsO4 inside PB in regions A , away from the craze indicating incipient dispersed nonlocalized cavitation inside PB.

Craze Nucleation and Growth

Argon3J2 has proposed that craze initiation in single-phase polymers such as PS goes through an incubation stage in which a critical concentration of porosity is produced by at least a limited amount of inhomogeneous plastic flow around surface or interface stress concentrations-provided the volume element in which the stresses are concentrated is of a sufficiently large size to permit such plastic flow to develop. Experiments and theoretical considerations based on conventional heterogeneous polymers such as HIPS and ABS have indicated that when particle sizes become smaller than about 0.5 pm, the size of the volume element in the region of stress concentration is smaller than what is r eq~ i red . ' , ~*~ On this basis, we expect that the phase wave length in the K resins is too small to initiate crazes in the interior of the polymer. The fact that crazes form from the free surfaces in these polymers-at least initially-is in agreement with this expectation. There is no evidence that in KRO-1 crazes initiate anywhere but at the free surfaces. In KRO-3, on the other hand, we have shown, as indicated in Figure 7 and particularly in Figure 8, that cavitation occurs in the PB phase which is responsible for the delocalization of the cavitation process and the less distinct nature of the crazes themselves. The reason for this difference between


Fig. 10. TEM micrograph of a craze in KRO-3 resin with a craze tip zone of developing cavitational degradation blending in smoothly with the craze.

the two polymers is likely to be in the difference of their phase form. In KRO-1, where the PB phase is in the form of a snaky, circular, cylindrical object, the internal concentration of negative pressure in the PB phase will be lower than that in the ellipsoidal and sheetlike form of the KRO-3 resin. The experimental results, however, demonstrate that this quasihomogeneous dispersion of the

Fig. 11. STEM micrograph of highly aligned microstructure in as-received KRO-3 resin. Note dispersed quasihomogeneous cavitation inside PB lamellae.

266 ARGON ET AL.

(8) 7 -

6 - I 0

- I

z -

- N KRO-3

um=1382MPo T=20°C

-

-

19 2 0 2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 3 0 ~ 1 0 ~ TIME, SEC

Fig. 12. (A) Craze length vs. time relation for three crazes in as-received KHO-1 resin temperature; (B) craze length vs. time relation for two crazes in as-received KRO-3 resin temperature; u- = 13.82 MPa.

at room at room

cavitation is not undesirable, as it imparts to the KRO-3 resin a level of toughness, an order of magnitude above that of KRO-1.

The difference in the dispersion of the cavitation process in these two polymers has also important consequences on the mechanism of craze growth. In KRO-1 resin, the apparent higher integrity of the PB phase results in sharply delineated crazes having a relatively conventional tufty craze matter structure. We expect that crazes in this resin grow by the now well established mechanism of the Taylor meniscus instability proposed by Argon and Salama,* which has now been veri- fied by direct stereoimaging in the electron microscope by Donald and Kramer.13 The craze velocity governed by this mechanism of craze growth is2 (Appendix A)

- 0.133 1 - u y = - P


TABLE I1 Craze Velocities in KRO-1 and KRO-3 Resins

KRO-1 KRO-3 u- (MPa) daldt (cm sec-I) u, (MPa) daldt (cm sec-‘)

11.01 13.82 16.32 18.37 19.33 21.44

33.58 44.00 46.11 49.07

T = 293 K 3.28 x 8.39 x 10-6 5.70 x 2.17 x 10-4 3.5:3 x 10-4 3.58 x lo-:{

8.90 x 10-6 2.60 x 10-5 3.70 x 1.10 x 10-4

T = 253 K

13.81 16.68 17.41 18.42 21.18

23.02 23.02 26.87 29.91

1.02 x 10-6 9.65 X 2.71 x 4.04 X 6.89 x 10-4

2.15 X 3.50 x 10-6 2.72 x 3.21 x 10-5

51.46 1.16 x 10-4

/3 = A/ 1 +-- (A - 1) ( io:; ) (4)

In eq. (2), P is a modulus parameter involving the shear modulus p and the Poisson’s ratio Y of the composite polymers; 0 is a function of the extension ratio X and the tensile orientation hardening rate d Yld X in units of the initial yield strength Yo of the polystyrene in the block copolymer composite in the craze matter; (r, is the applied tensile stress; D 1 and B are derived material constants relating to the principal meniscus wave length and the distortional plastic flow process that is involved in the meniscus convolution. For homo-PS, these quantities have been found to be 2.77 X lo5 m/sec and 1.57 eV, respectively,2 but are expected to be different in the composite resins. The measured craze velocities in KRO-1 at both room temperature and -20°C are plotted in Figure 13, appropriately, on semilogarithmic coordinates suggested by the form of eq. (2), where P has utilized the shear moduli obtainable from the Young’s moduli presented in Table I and discussed in the preceding section. We have for ref- erence also plotted the corresponding craze velocity data for a mineral-oil-free polystyrene (DOW 686 PS) investigated by Argon and Salama.2 Clearly, the trend in the two polymers is very similar and even suggests the possible presence of a stress shift that will give superposition. As discussed by Argon and Salama2 for the case of homo-PS, here too it is possible to adjust the parameter /3 to obtain agreement between theory and experimental results for the room-temperature craze growth measurements. The results vary to some degree based on the choice of the magnitude of the preexponential constant D1 and the uncertainty about the plastic flow process in the composite polymer but indicate that 0 must be of order 2, which for an extension ratio of X = 10, as is suggested from Figure 5, indicates further that the normalized orientation hardening rate, (l/Yo)(d Y/d A) of the PS in the craze matter is of order 0.5. These are all in acceptable ranges. The experimental and theoretical results for -20°C are more difficult to reconcile but suggest much higher orientation hardening rates for the same extension ratios.

The mechanism of craze growth in KRO-3 resin must be modeled differently based on the propagation of a degradation zone in front of the craze which, as

268

10-3

0

V

u

<> \

\

10-4

V W In \ I u 2 10-5 c

- - be -

10-6

lo-’-

ARGON ET AL.

I I I 1 I - 293OK -

- /DOW ~ / ; 686 P S I KRO- I 253°K -

-

-

-

-

I I I I

/ I -

I I

I I / 2 9 3 O ~ I /253°K

-

I I I / 1 I I I 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

it travels along with the craze, progressively converts strained but sound polymer at the border of a plastic process zone A to fully cavitated polymer at the craze tip. A model of this type has been developed by Anderson and Bergkvist’* for a crack propagating by degrading matter in front of it from a maximum deformation resistance equal to om to zero at the crack tip, according to a simple traction-displacement law shown in Figure 14. As is shown in Appendix B, when this model of Anderson and Bergkvist is transposed into one relevant to KRO-3, with the assumption that the polymer begins to degrade by cavitation inside the PB phase upon yielding, i.e., when om = Y, we obtain an expression for craze velocity that is identical to that of eq. (2). The proportionality constant D, however, is given by

where 6 is the thickness of the cavitating zone ahead of the craze plane that must be approximately equal to the phase wave length of the resin, y is the ratio of the strain cc for cavitation to the yield strain c y , and p has the same meaning as defined by eq. (4). In eq. (5), io is the preexponential factor in the strain rate expression for distortional plastic flow in the yield theory of Argon and Besso- nov,15 and has a magnitude of typically sec-’. Based on this model, the measured craze velocities have been plotted in Figure 15 on the same semilogarithmic axes as for KRO-1 resin. The results a t 2OoC are nearly identical with


" t

Fig. 14. (a) Traction-displacement law for a degrading continuum; adapted to crazing in KRO-3 resin; (b) traction distribution in front of a craze.

those for KRO-1, while the shift of the results for -2OOC is distinctly different from that for KRO-1, and is in keeping with the increased plastic resistance with decreasing temperature for the PS component of the composite polymer. A reasonably good fit of the theoretical form given by eqs. (2) and (5) to the experimental data for 2OoC can be obtained by values of 0, A, and (l/YO)(dY/dA) that are rather similar to those of KRO-1. In view of the much more complex

I O - ~ I I I I I I -

- -

0

\ I 3 < 10-5 -

0 V \

-v

253'K

KRO-3

- I .> \

t? - 10-6

I I 1 I I I n ni nr, n- n A nti nc n7 " "., ".L ".I v.7 ".I "." "..

Fig. 15. Dependence of craze velocity in KRO-3 as a function of normalized stress at 253 and 293 K.

270 ARGON ET AL.

nature of the cavitational localization in this polymer, however, this apparent agreement is less convincing beyond demonstrating some validity for the model of craze propagation by diffuse interfacial cavitation. It is essential to reem- phasize here that craze propagation in homogeneous polymer is normally very difficult by cavity nucleation ahead of the craze as has been shown by Argon and Salama.2 In the KRO-3 resin, however, this becomes the favored mechanism because of the existence of weak PB phases with adverse aspect ratios that makes cavitation in them relatively easy.

We note finally that the craze stresses reported in these experiments and listed in Table I1 produce large inelastic strains-albeit cavitational-and therefore constitute craze yield stresses. They are a very large fraction of the modulus parameter P which is the athermal plastic resistance of the polymer in very high strain rate experiments. Thus, these polymers have very remarkably stable crazing behavior on a normalized basis when they are compared with single phase glassy polymers.

This research has been supported by the National Science Foundation through the Center for Materials Science and Engineering at M.I.T. initiated under Grant No. DMR 76-80895 and continuing under DMR 78-24185.

APPENDIX A: CRAZE GROWTH IN KRO-1 RESIN

Argon and Salama’ have given a simple expression for steady-state craze growth in homogeneous polymer by the meniscus instability. This expression given in eq. (2) needs some clarification for adaptation to a heterogeneous polymer such as a KRO-1 resin. As sketched out in Figure 16, it is assumed that solid polymer is drawn out from the craze flank along the surface S - S under an average craze face traction that for long crazes must be equal to the distant boundary traction u,.’ This is possible by virtue of the concentration of‘ pressure in regions P by anology to the pressure concentration in the shoulder region of a necked bar as has been shown by Argon, Im, and Needleman.16 In the drawn tufts a t poink T far away from the surface S - S , however, the polymer must support the same average traction after having undergone a certain amount of orientation hardening. If the rise of true tensile plastic resistance of‘ PS due to orientation hardening can be given as

d Y dX

Y,) + - ( A - 1)

where Yo is the initial yield stress of PS, then overall force equilibrium at plane S-S and across the tufts of cross sectional area A requires that

“m “m

I I I I I

I

I d Y + Yo (I + dX (X-1)) I - c )

Fig. 16. Idealized craze border in a KRO-1 resin.


in eq. (7), c represents the volume fraction of PB, and the factor (1 - c ) is introduced to represent the fact that at the highly drawn state of matter of the craze tufts some of the PB will have ruptured and will not contribute to the load carrying capacity ofthe craze matter as Figure 5 clearly indicates. In KRO-1 resin we assume that initially the plastic resistance results entirely from the plastic resistance of PS and that the PB phase supports pressure but offers no shear resistance and in addition serves to concentrate the applied stress in the PS to some extent. Therefore we assume that the craze growth law by the mechanism of interface convolution must he stated in terms of the plastic resistances of the PS phase a?d then recast in terms of the applied stresses by using the results of eq. (7). That is, the ratio Y / Y for PS in the following equation (8) for the steady craze growth rate must be replaced by the expression given in eq. (9),

da D1 dt Y/P [ hxT[ (:TI] exp -- 1 - 7 _ = -

where pc = [0.133/(1 - v)]pC is a modulus parameter for the composite polymer.

APPENDIX B: CRAZE GROWTH IN KRO-3 RESIN

We model the growth of a craze in KRO-3 resin by the formation and steady propagation of a cavitational degradation zone ahead of the craze by adapting to a craze the model of Anderson and Berkgvist14 for the growth of a crack by a degradation zone of thickness 6, in which the tractions first rise to urn with a strain oft , and then decrease to zero when the average strain across 6 reaches t; as shown in Figure 14. In the case of a craze, the traction need drop to only u- with a total average strain t, of cavitation. Anderson and Bergkvist show that this degradation profile will undergo a reverse mapping onto the crack (craze) tip defining a process zone length A within which the cavitation goes from its full value a t the crack (craze) tip under a traction of urn to the incipient value a t the border of the zone A away from the craze tip under a traction urn. Then the steady-state craze growth rate should be

(10) da A ~ -=- dt Cc - c.,

where

i = ioexpl- ( R / ~ T ) [ I - (~/E)”/fi] l (11)

where K ,

*(Y - urnp A =

by linear elastic crack mechanics.

factor of According to Anderson and Bergkvist the crack (craze) will advance a t a critical stress intensity

where 0 is the ratio of the slope of the decreasing portion of the traction displacement law to the in- creasing portion, i.e.,

where we have equated urn to Y , the tensile plastic resistance, and t.s to fy, the yield strain. Then substitution of eqs. (11)-(14) into (10) together with the use of eq. (9) from Appendix A gives for the craze velocity

where

272 ARGON ET AL.

where y = C J C . ~

References

1. C. B. Bucknall, Toughened Plastics, Applied Science, London, 1977. 2. A. S. Argon and M. M. Salama, Philos. Mag., 36, 1217 (1977). 3. A. S. Argon, Pure Appl . Chem., 43,247 (1975). 4. C. B. Bucknall, J. Mater., 4 214 (1969). 5. H. Kawai, T . Soen, T. h u e , T. Ono, and T. Uchida, Mem. Fac. Eng. Kyoto Uniu., 33(4), 383

6. R. E. Cohen and F. S. Bates, J. Polym. Sci. Polym. Phss. Ed., 18,2143 (1980). 7. A. S. Argon, R. E. Cohen, B. Z. Jang, and J. Vander Sande, “Crazing in a New Type HIPS and

in Two K-Resins,” in Toughening of Plastics, Plastics and Rubber Institute, London, 1978, p. 16-1.

8. L. M. Fodor, A. G. Kitchen, and C. C. Biard, Am. Chem. Soc. Prepr. Diu. Org. Coat. Plast. Chem., 34(1), 130 (1974).

9. A. Peterlin, in The Solid S ta te of Polymers, P. H. Geil, E. Baer, and Y. Wada, eds., Marcel Dekker, New York, 1974, p. 83.

(1971).

10. I. W. Chen and A. S. Argon, Acta Metall., 27,749 (1979). 11. R. A. Wall, J. A. Sauer, and A. E. Woodward, J . Pol-vm. Sci., 35,281 (1959). 12. A. S. Argon and J. A. Hannoosh, Philos. Mag., 36,1195 (1977). 13. A. M. Donald and E. J . Kramer, Philos. Mag., to appear. 14. H. Anderson and H. Bergkvist, J. Mech. Phys. Solids, 18, l (1970). 15. A. S. Argon and M. I. Bessonov, Philos. Mag., 35,917 (1977). 16. A. S. Argon, J. Im, and A. Needleman, Metall. Trans., 6A, 815 (1975).

Received June 4,1980 Accepted July 30,1980

crazing in two polystyrene/polybutadiene block copolymers

Documents