K. Bose et al., STABLE CRACK-GROWTH ALONG A BRITTLE DUCTILE INTERFACE - II - SMALL-SCALE YIELDING SOLUTIONS AND INTERFACIAL TOUGHNESS PREDICTIONS/, International journal of solids and structures, 36(1), 1999, pp. 1-34
The problem bf a crack growing steadily and quasi-statically along a b
rittle/ductile interface under plane strain, mixed mode, and small sca
le yielding conditions is considered. The ductile material is assumed
to be characterized by the J(2)-flow theory-of plasticity with linear
strain hardening, while the brittle material is assumed to be linear e
lastic. A displacement-based finite element method, exploiting the con
vective nature of the problem; is utilized to solve the relevant bound
ary value problem. In Part I of this work, the corresponding asymptoti
c problem was solved. This paper addresses the full-field problem in o
rder to validate the asymptotic solutions, and to explore the physical
implications of the results. The numerical full-field results are fou
nd to be in good agreement with the analytical asymptotic solutions. I
n particular, the full-field results strongly Suggest that the stress
fields in the vicinity of the crack tip are variable-separable of the
power singular type; and also that the mode mix of the near-tip stress
fields is, to a large extent, independent of the applied elastic;node
mix; The amplitude (the plastic stress intensity factor) and the regi
ons of validity of the asymptotic fields are estimated from the full-f
ield results, and are observed to be strongly dependent on the, applie
d mode mix. The-remote elastic loading fields appear to influence the
near-tip fields, primarily, through the plastic stress intensity facto
r. The present work also explores the suggestion made by Bose and Pont
e Castafieda (1992) that the solutions to the small scale yielding pro
blem may be used in the context of a standard crack growth criterion,
requiring that continued growth take place. with a fixed near-tip crac
k opening profile, to obtain theoretical predictions:for the dependenc
e of interfacial toughness on the applied mode mix. Based on the numer
ical results, predictions for mixed made toughness of the brittle/duct
ile interface are reported. The results, which are in qualitative agre
ement with available experimental data and also with some recent theor
etical results, predict-a strong dependence of interfacial toughness o
n mode mix, This suggests that ductility provides the main operating m
echanism for explaining the dependence of interfacial toughness on-the
mode mix of the applied loading fields, during steady crack growth. (
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