Josef Jancar
Technical University Brno, Brno, Czech Republic
About 30% of total annual production of polymers are used in blends and about 80% of these blends are manufactured to improve toughness of the matrix poly- mer. Toughness of polymeric materials is very often the decisive parameter used in material selection for a wide variety of applications such as automotive, home appliances, construction, utilities, and sporting goods. Many products made of polymers are exposed to impact loading during their service life. High strain rates, low temperatures, and the presence of stress risers often lead to embrittlement of materials, even though they behave in a ductile manner at low strain rates or higher temperatures. The propensity of a material for brittle failure is thus of a great concern, especially in engineering applications.
Modification of commercial polymers to enhance their toughness has become a major new field of polymer science. The commercial success of HIPS and ABS led to the development of a whole new group of rubber-toughened plastics (1– 3). Chapter 1 provides trend data for the use of polypropylene (PP) resins as cost-effective replacement of engineering polymers. With the development of tailored polypropylene copolymers (see Chap. 2) and plastomers for impact modi- fication (see Chap. 7), composites of fillers and fibrous reinforcement can be effectively toughened to compete with polyamide type products.
Because impact modification of polypropylene blends and composites repre- sents an important area of commercial interest, material scientists seek an under- standing of the mechanisms underlying the attainment of desired toughness en-
158 Jancar
hancement. Most of these mechanisms also operate in the neat polymers; however, the incorporation of a secondary phase or component alters their modus operandi or introduces mechanisms that do not occur in the neat polymer.
6.1 DISSIPATION OF MECHANICAL ENERGY DUE TO
FRACTURE FAILURE
The major contributors to the dissipation of mechanical energy at the cross- sectional area of possible fractures are shear yielding and crazing mechanisms. Crazing is most important for glassy thermoplastics [polycarbonate (PC), high- impact polystyrene (HIPS), polymethyl methacrylate (PMMA), acrylonitrile-bu- tadiene-styrene (ABS)], and shear yielding is a major deformation mechanism in thermosets (epoxies, unsaturated polyesters) and semicrystalline thermoplas- tics with a sufficiently high degree of crystallinity (PP, polyanide 6 (PA6), PE). Shear yielding and crazing are not mutually exclusive to the given groups of materials. Very frequently, both modes of fracture can operate in the same speci- men at the same time. Furthermore, relative contributions will depend on test conditions (temperature, strain rate, crack tip radius) and on the structural vari- ables (crystalline morphology, tie molecules, molecular structure).
Frequently, a transition in major deformation mechanism from shear yielding to crazing or vice versa is accompanied by a sudden change in crack resistance. This is often referred to as a ductile brittle transition (DBT). Hence, low tempera- ture impact resistance of polypropylene-based materials is a key factor in material
selection for molded parts subjected the ambient temperatures as low as⫺40°C.
In this regard, plastomers described in Chapter 7 provide reduction of DBT well below end use requirements.
Additional dissipative processes arise from the presence of a secondary com- ponent in the polymer matrix or from interactions between the host polymer and the secondary particles. For a given polymer composite, there may exist inclusion cavitation, interfacial cavitation, particle deformation, and crack pinning by con- stituent particles.
6.2 MECHANISMS OF TOUGHNESS ENHANCEMENT IN
POLYMERS
It is generally accepted that the most effective dissipative processes are those involving large plastic deformation before crack initiation. These large plastic deformations take place in shear banding and crazing. However, extreme localiza- tion of plastic deformations into small volumes leads to macroscopic failure initi- ated from these areas of large plastic flow. This is even more pronounced in the
PP Impact Behavior 159
vicinity of pre-existing cracks or notches loaded at high strain rates or at low temperatures. An obvious method of increasing the amount of dissipated energy is the extension of the volume of a polymer involved in shear yielding or crazing (1,4,5). This is most effectively achieved by incorporating a secondary compo- nent of suitable elastic properties, inclusion size, and interfacial adhesion to the matrix. Most frequently used secondary components, or toughening agents, are elastomers, followed by thermoplastic inclusions and, in some instances, by rigid inorganic particles and reinforcements. This type of secondary inclusion controls the primary deformation mechanism on the microscopic scale. In the case of the brittle behavior of rigid thermosets, extension of shear yielding is achieved by reduction of the degree of cross-linking by increasing the molecular weight and flexibility of the chains between the cross-links. Among the toughening pro- cesses, nonexistent in neat polymers, the most important are crack pinning by rigid particles in thermosets, secondary component tearing, elastomer particle cavitation, and dewetting in rubber modified polymers.
6.2.1 Delocalization of Shear Banding
Extensive shear yielding at the crack tip is a major mechanical energy dissipation mechanism in many tough polymers. On the other hand, localized shear yielding (i.e., shear banding) is believed to be a precursor of brittle fracture in many poly- mers. It is now well established that a delocalization of shear banding can be achieved in many otherwise brittle polymers by incorporating a secondary discon- tinuous component. This phenomena is also described as the spreading of shear yielding over larger volume of a material at the crack tip. This especially occurs when the elastic modulus of the secondary polymer component is substantially lower than that of the matrix [4]. Newman and Strella (6) observed typical fea- tures of shear yielding in heterogeneous ABS terpolymer subjected to uniaxial tensile loading. The macroscopic features are necking, drawing, and orientation hardening. On the microscopic or structural level of individual rubber particles, it was found that the polymer matrix had undergone localized plastic deformation around virtually every single rubber particle. In the case of a pre-existing crack or defect, the same effect was observed for material within the crack tip plastic zone, which was, additionally, substantially greater than in the case of unmodified polymer.
The explanation of the effect of secondary component on the spreading of shear yielding (i.e., delocalization of shear banding) is based on a concept of local stress fields and stress concentrations in the matrix due to the presence of inclusions. This leads to a reduction of the external load needed to plastically deform the material. The original Goodier’s solution (7) for an isolated particle in an isotropic matrix resulted in a maximum stress concentration of about 1.9 at the equator of the inclusion (8). It should be borne in mind that this solution
160 Jancar
belongs to a class of analytical ‘‘single particle solutions.’’ These do not take into account possible stress fields interactions or overlaps in multiparticle systems (9). The solution for interacting particles (i.e., for volume fractions above 0.09) was obtained using the numerical finite element analysis (FEA) method (10–12). The results indicate that by an overlap of the stress fields of neighboring particles, stress concentration up to 6 can be achieved. The location of the maximum stress concentration moves away from the particle surface and its actual position de- pends on the spatial packing of the inclusions. It was also shown that there is not much of a difference in stress fields between elastomer inclusion and a void (13). Additional consideration should be given to the fact that a morphology of a semicrystalline matrix can be affected substantially when the interinclusion distance becomes of the order of lamella size.
The stresses around the particle have the character of triaxial tension only in the case of perfect interfacial adhesion. This is exemplified by rubber-toughened epoxies, ABS, and toughened nylons due to a comparable bulk modulus between matrix and elastomer. In such a case, elastomer particle cavitation occurs. Micro- shear bands were observed in rubber-toughened PVC initiated at an angle of 55–
64°with respect to the direction of the applied stress (14). Additionally, the au-
thors have observed cavities in the rubber particles aligned in the planes of shear microbands. This explains a cause for the generation of stress whitening in this material. For ABS, it has been shown that the mechanism of delocalized shear yielding can lead to similar cavitation without crazing. Donald and Kramer (15) studied the effect of particle size on the deformation mechanism in ABS and
found that in the case of 0.1-µm diameter inclusions, crazing is suppressed and
shear deformation promoted by particle cavitation. In the system with 1.5-µm
diameter inclusions, crazing was the major deformation mechanism for energy dissipation.
It is now believed that the process of particle cavitation relieves the local buildup hydrostatic tension caused by constant volume shear banding. This allows additional enhancement of shear yielding in both thermosets and thermo- plastics (16). Hence, soon after development of some initial shear yielding, the local triaxial constrains are relieved by cavitation even in relatively thick speci- mens. Similar explanations were proposed for PC/PE, PC/MBS (17), and rubber- modified epoxies (18–23). In polymers or under test conditions favoring crazing as a major deformation mechanism, cavitation and voiding of the rubber particles leads to a premature craze breakdown and it is damaging to the polymer. 6.2.2 Crazing in Semicrystalline Polymers Subjected to Impact
Jang et al. (24–27) studied extensively craze formation in semicrystalline poly- mers, namely in virgin and rubber-modified polypropylene. They studied the ef- fects of injection-molding conditions on PP morphology and its relation to craz- ing at low temperatures and high strain rates. Their investigation characterized
PP Impact Behavior 161
the effects of various thermoplastic elastomer impact modifiers on crystallization, fusion, and crystalline morphology of molded polypropylene specimens. Jang and coworkers found that crazes are formed preferentially in the core of the injection- molded test specimen, where a regular spherulitic structure existed. The surface ‘‘skin’’ and ‘‘shear’’ zones, which are characterized by oriented molecules and oriented spherulitic growth, respectively, contained little or no crazes. This effect was ascribed to the molecular orientation effect, which is known to prevent craze formation and growth (28). However, no consideration was given to the possibil- ity that in addition to the orientation of molecules or spherulites, the surface layers are in the plane stress state, which favors shear yielding rather than dilata- tional crazing.
Despite some evidence of crazing, it was proposed (25) for semicrystalline polymers that shear yielding is the main deformation mechanism under usual conditions and crazing is a minor component of plastic deformation in these poly- mers, operating at very low temperatures and/or high strain rates in amorphous regions. For a given temperature, a critical strain rate appears to exist above which crazing dominates and below which shear yielding is dominant (29–30). This hypothesis is verified experimentally by observation of appreciable increase in shear yield strength of polymers with decreasing temperature and/or increasing the strain rate. On the other hand, the triaxial type of crazing stress is relatively unaffected by these test conditions. It is believed (31) that the specimen either shear yields if a shear component of the stress field exceeds the shear yield strength or crazes if the triaxial tension exceeds the craze formation stress. Wu (32) measured the energy dissipation contributions from crack formation, crazing, and shear yielding in rubber modified nylon-66. The energy consumed by forma- tion of new surfaces during impact loading was five orders of magnitude smaller
than that dissipated by crazing and shear yielding at 23°C. Crazing dissipates
about 25% of the total energy and shear yielding dissipates the remaining 75%, mostly in the form of heat, causing an increase in temperature within the stress-
whitened zone by about 10°C. The crazing energy contribution can be further
assigned to energy stored in craze fibrils (60%) and energy used to during fibril formation (40%).
Crazes in PP were found to be morphologically similar to those occurring in glassy polymers. They exhibit high reflectivity, large area-to-thickness ratio, and substantial planarity. Craze planes were usually perpendicular to the direction
of principal tensile stress, although local deviations of up to 15° existed. It is
assumed that these deviations are due to local order (i.e., crystalline structure and superstructure). Moreover, crazes in PP have a larger tendency to bifurcate or branch off compared with crazes in glassy polymers. They propagate through spherulites, and their length is not restricted to one spherulite diameter nor do they growth preferentially in the radial direction. As was shown by Friedrich (33), crazing can be affected substantially by alterations of the crystalline structure. If most crazes develop at the interfaces between large spherulites, the measured
162 Jancar
fracture toughness is low. Distinct fracture-resistance values exist for crazes de- veloped within larger spherulites or at the boundaries of the smaller ones. This phenomenon could be one of the possible mechanisms to explain how elastomers can affect crack resistance of semicrystalline polymers when added to modify crystalline morphology.
As in the crazing in rubber-modified glassy polymers, it appears reasonable to assume that a critical rubber particle size domain also exists for rubber-modi- fied semicrystalline polymers. Jang et al. (25) observed that for elastomer parti-
cles of diameter, D, smaller than about 0.5µm, no crazes were initiated. It was
suggested (26) that the loss of craze nucleation efficiency of small particles was due to the small size of the stress concentration region being insufficient to ac- commodate the formation of a craze (i.e., to achieve critical porosity for craze
nucleation) (17). The critical size, found to be 0.5µm for PP modified with EPR,
ethylene-propylene-diene rubber (EPDM), or styrene-butadiene rubber (SBR), will vary, however, depending on a particular matrix/rubber pair. One reason for such a variation can be the change in the rubber-to-matrix modulus ratio that affects the stress concentration ability (34,35).
The actual morphology of crazes in PP consists of fibrils spanning the craze surfaces and, in addition to these, of interconnecting fibrils randomly oriented in respect to the principal stress direction (26). Apparently, a large number of voids exist in these crazes, distinguishing them from the crazes observed in glassy polymers. One can speculate on the reasons for the observed differences. For example, from concepts concerning the proposed role of weakly bonded rubber particles as the only stress raisers, experimental observations suggest that these particles do not act as craze terminators in any case. But at present, there is no conclusive explanation to explain this observation.
6.2.3 Crack Bridging and Particle Tearing
Crack bridging by elongated elastomer inclusions was the first model attempting to explain rubber toughening in HIPS (36). It was also suggested as a possible toughening mechanism in thermoplastic-modified epoxies (37). The contribution of crack bridging and particle tearing to the total energy dissipated during fracture of rubber-modified polymers was shown to be negligible because of the very low shear modulus of the elastomer (38). Several authors (39–41) presented experi- mental data suggesting that crack bridging and particle tearing operates in thermo- plastic-modified epoxies; however, the understanding of this phenomenon is far from being complete.
In the case of thermoplastic-modified epoxies, the proposed role of elongated rigid plastic particles is to span the two fracture surfaces and apply tractions that effectively reduce stress intensity factor applied at the crack tip (42). Additional contribution to the energy dissipation is assumed from the plastic deformation of the inclusions (43). Pearson and Yee (44) suggested that the contribution to
PP Impact Behavior 163
the overall toughness from this mechanism in thermoplastic-modified epoxies is between limits given by the case of rubber-modified (37) and glass-filled epoxy resin (45).
The model of Ahmad et al. (37) predicts that the size of the particle affects the total tear energy consumed. In particular, toughness improvements should be greater for larger particles, which contradicts the rubber-toughening concept in PP. Additionally, increases in particle stiffness and tear energy should result in enhanced crack resistance. Two to three orders of magnitude larger elastic moduli of thermoplastics compared with common elastomers can conceivably increase the importance of this toughening mechanism. Moreover, when the secondary polymer possesses large deformability, the increase in tear energy also enhances contribution from this mechanism. As was shown by Cecere and McGrath (46) and Raghava (47), increase in molecular weight of the secondary thermoplastic polymer led to improvement in toughness in agreement with expected increase in deformation to break with increasing molecular weight. Rose’s model (48) explains the observed maximum on toughness versus filler volume fraction by considering the ratio between the ease of circumventing the particle and matrix cracking.
6.3 CHARACTERIZATION OF THE IMPACT BEHAVIOR OF
POLYPROPYLENE
The presence of a super molecular structure, namely crystalline regions and their aggregates, substantially complicates the failure mechanisms in semicrystalline thermoplastics (e.g., polypropylene under impact loading compared with glassy polymers). As described in Chapter 2, degree of crystallinity, spherulite size and shape, lamellae thickness and size, and crystallographic structure of the basic unit are primary structural variables that affect deformation behavior of polypropylene resins. Chemical structure of the chain, molecular weight and weight distribution, molecular relaxation, and related molecular properties are defined as secondary variables. This group of molecular characteristics influence toughness through their effect on the crystalline structure and mechanical response of amorphous regions in semicrystalline plastics. The occurrence of an isothermal transition under adiabatic conditions in these materials also plays a role in determining the amount of material fracture toughness. In addition, all standard impact tests have the specimen and leading geometry as variables embodied in the measured values via control over the state of stress.
In Section 6.8, a detailed analysis of the most frequently used impact tests (i.e., Charpy and Izod impact tests) is used to characterize fracture toughness. Temperature, strain rate, crack tip curvature, specimen thickness, annealing, aging, irradiation, and environmental effects are discussed as test variables using the framework of fracture mechanics.
164 Jancar
A detailed discussion of dynamic effects during the uniaxial impact test is presented and a simple way of accounting for them using the lumped weight model proposed by Williams (49) [i.e., within the frame of linear elastic fracture mechanics (LEFM)]. This model provides a firm basis for understanding signifi- cance of experimental data obtained using standard impact tests. Using proce- dures based on LEFM, one can separate the effects of the test geometry from geometry-independent material properties. This is, however, a time consuming and tedious procedure.
To extend the applicability of this method from brittle to quasibrittle materi- als, a concept of small scale yielding is applied. This approach allows incorpora- tion of general views on both structural and test variables affecting the resulting impact behavior.
6.4 LINEAR ELASTIC FRACTURE MECHANICS
One of the major impulses for a great scientific effort were seemingly inexplicable failures of the Liberty ships during WWII. This resulted in the creation of a new scientific discipline—fracture mechanics. The U.S. Navy was the major research sponsor in this area during the 1940s and 1950s. This effort was built on a previ- ous discovery by Griffith (50) that the strength of materials is a stochastical pa- rameter depending on the distribution of defects that are always present in any material. The inherent material strength is controlled by the size of these defects, mode of loading, and material properties. Most of the initial effort was devoted to studies of metals (51–54) using the concepts of linear elastic behavior before