Nonlinear effects in interfacial fracture

by Geubelle, Philippe H.

Abstract (Summary)
The issue of the non-coplanar quasi-static propagation of a crack in homogeneous and bimaterial sheets is investigated. Through a preliminary linear analysis, it is shown that the interface crack kinking problem is confronted, in most practical cases, with difficulties which do not arise in the homogeneous situation: the crack path as predicted by the maximum energy release rate criterion cannot be determined uniquely and an additional length parameter, absent in the homogeneous case, needs to be specified to assure uniqueness. Following that development, the assumption of small deformations is relinquished and it is shown how the size of the nonlinear zone imparts possibly the physical significance of the additional length parameter. The analysis is performed numerically in the homogeneous and bimaterial cases within the framework of the nonlinearly elastic theory of plane stress and using a "boundary-layer" approach. Material and geometrical nonlinearities are combined through the use of the Generalized Neo-Hookean (GNH) model. As the length of the crack extension becomes comparable to the size of the nonlinear zone, a transition is observed between the value of the energetically most favorable kink angle predicted by the linear theory and a unique "nonlinear" value which is found to be independent of the crack extension length and the far-field loading conditions. The results of the crack propagation analysis are related to those of a detailed asymptotic analysis of the structure of the near-tip stress and deformation fields for the GNU class of hyperelastic materials. The investigation addresses a) the symmetric (mode I) and non-symmetric (mixed-mode) homogeneous situations, b) the rigid substrate case and c) the general bimaterial problem which allows for an arbitrary choice, on both sides of the interface, of the three material parameters characterizing the GNH model. The asymptotic analysis allows to quantify the effect of the "hardening" characteristics on the blunting of the crack and the associated stress and strain singularities, and shows that the near-tip fields corresponding to a general nonsymmetric loading are, in the homogeneous situation, related to those of the symmetric (mode I) case through a rotation which depends on the material characteristics and the far-field loading conditions. A somewhat similar property is obtained in the bimaterial problem, where the existence of a non-oscillatory and "contact-free" solution is confirmed for all material combinations.
Bibliographical Information:

Advisor:Guruswami Ravichandran; James K. Knowles; Wolfgang Gustav Knauss

School:California Institute of Technology

School Location:USA - California

Source Type:Master's Thesis



Date of Publication:03/04/1993

© 2009 All Rights Reserved.