Stress fields round indentations in poly(methyl methacrylate)

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Abstract
The authors discuss the stress field in the neighbourhood of an indentation made by a steel ball in poly(methyl methacrylate), the special characteristics of which have been described by Puttick (1973). These results suggest that the deformation in the interior of the solid approximates to that round a spherical cavity expanded by internal pressure in a plastic-elastic medium, as proposed for other materials both by Marsh (1964) and by Johnson (1970). The approximations required to apply ideal plastic-elastic theory to polymers are discussed, and Hill's solution (1950) of the equilibrium equation for the expanded cavity is modified to take into account the sensitivity of the yield stress of PMMA to strain rate and hydrostatic pressure; the result gives the indentation pressure in terms of the radius of the plastic zone. The latter dimension is experimentally determined by measuring the indentation pressure, so that the scale of the stress field in the interior is known. The state of plane stress in the surface is interpreted in terms of the plastic-elastic expansion of a hole in a plate. The tensile component of the stress field thus derived appears to explain well the orientation, shape and size of the stable cracks initiated at such indentations.

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