NONLINEAR STRESS-STRAIN CURVES FOR SOLIDS CONTAINING CLOSED CRACKS WITH FRICTION

Solutions for the uniaxial stress-strain response of a body containing a distribution of non-interacting nonlinear cracks are derived. First , building on energy formalisms outlined by previous workers, general solutions are derived for the body containing cracks with dissipative tractions al their surfaces, in either tension or compression loading. The special case of a body in compression loading with sliding closed cracks governed by a general friction law is then considered as a cas e study. The friction law contains two shear resistance terms: a ''fri ction coefficient'' term proportional to the resolved normal compressi on stress across the crack plane; and a ''cohesion'' term representing the intrinsic shear resistance of the closed crack. Inclusion of the latter term is critical to the existence of a well-defined yield point in the stress-strain curve. It is assumed that the cracks do not exte nd at their ends during the loading-unloading-reloading cycle; they ar e, however, allowed to undergo reverse sliding during the unloading. T wo crack distributions are considered: all cracks aligned, leading to linear expressions for both the elastic and quasi-plastic stress-strai n regions; and cracks randomly oriented, with more complex (but noneth eless tractable) expressions for the quasi-plastic regions. The result ant nonlinear stress-strain curves exhibit cyclic hysteresis, to an ex tent dependent on friction and crack configuration parameters. Illustr ative stress-strain curves are generated for selected ranges of these controlling parameters. An outcome of the analysis is the potential li nk to microstructural variables, via the crack configuration parameter , offering the prospect for predictions of damage accumulation in real microstructures. The model also offers the prospect of accounting for fatigue properties, via attrition of the frictional resistance at the sliding crack surfaces. (C) 1997 Elsevier Science Ltd. All rights res erved.