Craze branching

Sonic Modulus. If crack or craze branching is the operative mech-nism in toughening, toughness should be directly related to the difference in sonic speeds in matrix and dispersed phases. Experiments to confirm this effect were undertaken using three commercial ABS resins. These were selected to represent the three main rubber types encountered commercially an acrylonitrile/butadiene copolymer rubber, a butadiene rubber with grafted styrene/acrylonitrile copolymer, and a block polymer of... 

Test results, plotted in Figures 5, 6, and 7, show that impact strengths vary with difference in sonic speed in the way predicted by the crack/ craze branching theory. 

Rubber Particle Size and Shape. If rubber particles act as crack or craze branch points along an advancing crack in matrix polymer, impact strength should depend on the frequency with which branch points are encountered. If C = rubber phase volume fraction, N = number of dispersed particles, and d = average particle diameter, N C -r (P, N is maximized as C increases or d decreases. The probability of an advancing crack hitting a particle as it advances an incremental distance is proportional to cross sectional area Nd2, which equals C/d. Again, C... 

Unlike the normalized craze branch data, the normalized shear data do not fall on the same lifetime curve. More interestingly, but perhaps fortuitously, almost all... 

When the lifetime data were plotted with stresses normalized by the corresponding uniaxial tensile yield stresses (Fig. 31), the craze branch data again fell within a narrow lifetime band. As with PC, the normalized shear branch did not map out a narrow band of shear lifetimes, but instead showed very similar fatigue lifetimes, despite the wide range of normali d stresses from 0.5 to 0.8. 

Based on this combination of theory and experiment, Bragaw (1970, 1971) has proposed that rubber particles can serve as nuclei for crack (or craze) branches because of their lower sound velocity the proposal has been supported by Grancio (1971). Now the modulus of typical plastics is... 

In an isotropic medium, cracks do not move faster than half the shear wave velocity Vu so the implications of the 0.8V curve in Figure 4 were not explored. In the two-phase ABS system, however, one can imagine cracks or crazes propagating rapidly in the matrix (V /2 <—B20 meters/sec), and thence into the rubber particle [at 23°C, polybutadiene (V /2 /—29 meters/sec)] where violent branching would occur. 

If Vt 1240 meters/sec in the matrix and branching will occur in the rubber at 29 meters/sec, we calculate A/Co = 0.047. Thus, branching can occur after a matrix crack acceleration distance of only 2 to 5/x (assuming a Griffith crack length of 50-100fi) hence, ample room for the development of fast cracks or fast crazes exists in the ABS structure. Note that the expressions for craze instability, acceleration, and speed (Equations 1, 6, 7) show that the macro strain rate of the specimen is irrelevant— fast cracks and crazes propagate in specimens strained even at slow creep rates. 

Experimental Evidence. Morphology. Figure 3 (33) shows in phase contrast microscopy the development of crack or craze patterns around rubber particles in a toughened polystyrene. The lack of dependence of crack inclination on direction of stress is especially marked in this micrograph, and can be explained only by reference to dynamic branching rather than to crack or craze nucleation by stress raisers. Schmitt and Keskkula refer to the lines as craze cracks and cracks. ... 

Rubber Content. In the theories of toughening where the role of rubber particles is (a) to absorb energy directly or (b) to induce matrix yielding through stress concentration or hydrostatic tension effects, energy absorption should increase linearly with the number of rubber particles (proportional to rubber content if particle size is invariant). On the other hand, if dynamic craze/crack branching is the operative mechanism, evidence of an exponential law may be expected. The exponential form of the law may be derived as follows. 

Besides crystallinity itself, the kind and amount of side chains is of importance for crazing. A schematic investigation of the influence of chain branches was performed in PE that were introduced via copolymerization [84], A long-chain branched low-density polyethylene (PE-LD) was compared to a linear low-density polyethylene (PE-LLD) with different short chains [85]. Type and concentration of the copolymers were chosen in order to attain the same density of 0.920 g/cm3 and melt flow rate of 25 g/10 min for all polymers. The ESC resistance was measured in a long-term tensile test of notched specimens at 50 °C in 10% Igepal solution. 

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