裂縫在塑流模式彈塑性材料中之 J 積分閉合正解

Abstract

本文旨在將塑流理論彈塑性模式引入裂縫分析，在塑性狀態時利用勞侖茲群理論導出閉合正解，在彈性狀態時則使用彈性正解。 在第一模態下透過此模式的導入，將Irwin的塑性模式改為塑流理論完全彈塑性模式。首先，第二章先進行線彈性裂縫分析，第三章則在塑流理論完全彈塑性模式下，提供塑性狀態彈塑性解及彈性卸載解，使J積分的使用不再侷限於不可卸載的材料。第四章則延伸到著名的Prandtl-Reuss彈塑性材料模式，將第三章作為偏差部分並添加線彈性作為體積部分，第五章延伸至第三模態。

This thesis aims to introduce flow elastoplastic model in crack analysis, utilizing the Lorentz group theory to derive closed-form solutions in the plastic state and elastic solutions in the elastic state. By incorporating this model in the first mode, Irwin's plasticity model is replaced by the flow elastoplastic model. Chapter 2 first conducts linear elastic fracture analysis, while Chapter 3 provides the automatic on-off shift capability of elastoplastic solution and elastic unloading solution for the flow model of perfect elastoplasticity, allowing the use of the J-integral beyond deformation plastic materials suffering from lacking unloading. Chapter 4 extends to the Prandtl-Reuss model by interpreting Chapter 3 to be the deviatoric part and adding linear elasticity to be the volumetric part.The third mode is considered in chapter 5 .