Theoretical study on damage bifurcation of unstable failure process of quasi-brittle materials

来源期刊：中国有色金属学报(英文版)2009年增刊第3期

论文作者：王忠昶 赵德深 杨庆

文章页码：811 - 818

Key words：isotropic damage; orientation of localization; maximum hardening modulus; bifurcation; uniaxial sample

Abstract: To obtain the damage effect in the process of elasto-plasticity deformation of quasi-brittle materials, the isotropic damage loading-unloading function and damage variable were introduced to non-continuous bifurcation. The critical bifurcation orientation and its corresponding hardening modulus for quasi-brittle materials were derived considering the effect of stiffness degradation and volumetric dilatancy under the assumption of isotropic damage. The relationships of localized orientation angle and maximal hardening modulus dependent on degree of damage and initial Poisson’s ratio of rock were explored. Comparative analyses were conducted to study the bifurcation of uniaxial tension-compression samples under the conditions of plane stress and plane strain. It is shown that as the initial Poisson’s ratio or degree of damage increases, the localization orientation angle of the plane uniaxial compression sample tends to be initiated to decrease. However, the localization orientation angle of the plane uniaxial tension sample tends to be initiated to increase. The sum of orientation angle under tension and compression conditions is 90°. There are plane stress and plane strain cases of the maximum hardening modulus that is independent of the uniaxial compression and tension.

基金信息：the National Natural Science Foundation of China
Science and Technology Research Foundation of Key Laboratory of Education Department of Liaoning Province, China