A Framework for Modeling of Stress-Strain Hysteresis Response of Brittle Matrix Composites under Fatigue Loading

摘要

All brittle matrix composites (BMCs), including unidirectional fiber-reinforced, cross-ply laminated, and woven fabric ones, normally exhibit characteristic stress-strain hysteresis-loop behaviors with progression of matrix microcracking under monotonically and cyclic loading. These characteristic behaviors include gradual change and/or abrupt kinks in secant modulus during loading, unloading or reloading path of a hysteresis loop, and overall change in hysteresis loop shapes under progressive cyclic loading. Through the analyses using a shear-lag model, it has been shown that the hysteresis is caused by irreversible internal friction in the debonded interfacial area, and the interfacial debonding in turn is induced by transverse matrix microcracking. However, that the shear-lag model over-simplifies the real condition, for example, by assuming a complete crack in matrix, which is equivalent to the complete loss of normal-load-carrying capability of matrix due to the imposed periodicity condition of a unit cell representing the composite. However, during the progressive damage process, matrix with microcracking may continue to hold a residual strength due to irregularity of a microcrack network and other physical factors. More recently, Yang and Mall have considered the effects of residual strength of a damaged constituent by incorporating a generally nontrivial cohesive force across crack surfaces in a unit-cell representation. This was referred to as a cohesive-shear-lag model, as an alternate to the shear-lag model. When the cohesive force diminishes, the cohesive-shear-lag model reduces to a shear-lag model. Yang and Mall have further generalized the cohesive-shear-lag model by incorporating damages in both weak and strong constituents for the application to the all class of BMCs undergoing transverse microcracking, interfacial debonding and frictional sliding. They have applied the cohesive-shear-lag model to the CMCs and validated the idea of introducing a residual strength to damaged constituent. The present work, as a extension to the previous works, is intended to examine detailed features of a stress-strain hysteresis loop predicted by the cohesive-shear-lag model and to investigate how its features are affected by the deformation/damage processes in BMCs under progressive loading.