7 The Theory of Rubber Toughening
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of Brittle Polymers C. G. B R A G A W Plastics Department, Ε. I. du Pont de Nemours & Co., Wilmington, Del. The technology of ABS and impact polystyrene resins shows that incorporation of a dispersed rubber phase of appropri ate properties can raise impact toughness by an order of magnitude, apparently by increasing the energy-absorbing volume in the resin. Principal existing theories of the tough ening of brittle plastics by rubber dispersion are considered; all appear quite limited in ability to explain known phe nomena and have substantial difficulties. It is proposed that the mechanism whereby rubber dispersions greatly increase energy-absorbing volume is by causing cracks and/or crazes to branch dynamically at rubber sites through the Yoffe mechanism (35). The theory explains anomalous morpho logical evidence and is supported by evidence from a variety of physical measurements.
"Qolymers such as poly (methyl methacrylate) ( P M M A ) and polystyrene are brittle on a macro scale, but on a micro scale they are enor mously tough. Crack propagation in these materials requires 3 Χ 10 to 2 χ 10 ergs/cm of new crack surface (5), far more than the theoretical value of —-450 ergs/cm (5) calculated assuming that fracture involves breakage of molecules oriented perpendicular to the crack surface. The formation of interference colors at the crack surface indicates the pres ence of a low density oriented (crazed) layer at the crack surface (6, 18), and this layer is commonly thought to have absorbed the energy measured. Assuming 2μ as the upper limit of layer thickness (18), it is calculated that the deforming layer i n the plastic absorbs 5 Χ 10 ergs/gram. This is about half the average specific energy dissipation i n a tough, ductile steel (yield stress 48,000 psi, ultimate elongation 3 1 % ). The apparent brittleness of P M M A , polystyrene, and styrene/acrylonitrile copolymer ( S / A N ) arises because energy absorption is confined A
5
e
2
2
8
86 In Multicomponent Polymer Systems; Platzer, N.; Advances in Chemistry; American Chemical Society: Washington, DC, 1971.
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7.
BRAGAW
Rubber Toughening of Polymers
87
to thir^ layers of the order of a micron (18). In the case of rubbertoughened P M M A , polystyrene, S / A N , and P V C , deformation occurs i n millimeter-thick layers, and macro energy absorption is usefully high. This layer is most readily marked by blushing. Evidence of large defor mations i n matrix material in ABS-type resins is (a) tensile bars elongate and neck permanently—this permanence requires permanent deformation of the S / A N matrix since it is the only continuous phase and constitutes x
1
(8)
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If we postulate that the energy required to break a specimen is simply surface energy (neglecting kinetic and elastic strain energies), then Impact Energy « 2 y A
c
(9)
where γ is the effective surface energy associated with a unit area of crazed or cracked surface. Combining Equations 8 and 9, impact strength, to a first approximation, is predicted to be an exponential with base 2. This crude derivation has neglected important processes such as coop erative stress relief, craze recombination, failure to branch at every par ticle, etc. Experimental data on the effect of rubber content on impact strength are shown i n Figure 9. Data are for specimens containing two different types of rubber. Base 2 exponentials fit the data well; we have been unable to find nonexponential functions which fit as well.
Summary Existing studies of the fracture of apparently brittle plastics such as polystyrene or styrene/acrylonitrile copolymer indicate that the polymers are actually enormously tough in very thin layers near crack or craze interfaces. Because the energy-absorbing volume is so low i n these poly mers, their engineering usefulness has been limited. The technology of A B S and impact polystyrene resins shows that incorporation of a dispersed rubber phase of appropriate properties can raise impact tough ness by an order of magnitude, apparently by increasing the energyabsorbing volume i n the resin. Principal existing theories of the tough ening of brittle plastics by rubber dispersion a l l appear quite limited i n ability to explain known phenomena and have substantial difficulties. It is proposed that the mechanism whereby rubber dispersions greatly increase energy-absorbing volume is one which causes cracks and/or crazes to branch dynamically at rubber sites through the Yoffe mechanism (35). This theory explains existing morphological information (25, 33), strain and strain rates effects, need for interphase adhesion, and depend ence of toughness on rubber particle size and size distribution, rubber content and temperature.
In Multicomponent Polymer Systems; Platzer, N.; Advances in Chemistry; American Chemical Society: Washington, DC, 1971.
106
M U L T I C O M P O N E N T P O L Y M E R SYSTEMS
Acknowledgments The author thanks H . A . Davis and R. P. Schatz for optical and electron micrographie measurements, and O. J . Cope for assistance i n chemical and physical characterization of rubbers and resins.
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R E C E I V E D October 31,
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In Multicomponent Polymer Systems; Platzer, N.; Advances in Chemistry; American Chemical Society: Washington, DC, 1971.
