浙江大学：《材料力学》课程PPT教学课件（教案讲稿）第七章 应力应变分析强度理论 Analysis of Stress and Strain Failure Criteria

第七章应力应变分析强度理论 Chapter7 Analysis of Stress and Strain Failure Criteria

Chapter7

Analysis of stress-state and strain-state)< 第七章应力和应变分析强度理论 Chapter7 Analysis of Stress and Strain Strength Theories §7-1应力状态概述 (Concepts of stress-state) §7-2平面应力状态分析-解析法 (Analysis of plane stress-state) D§7-3平面应力状态分析-图解法 (Analysis of plane stress-state) D§7-4三向应力状态分析

就分 nalysis of stress-state and strain-state四 §7-5平面应变状态分析 (Analysis of plane strain-state) D§7-6广义胡克定律 (Generalized Hooks law) §7-7复杂应力状态的变形比能 (Strain-energy density in general stress-state §7-8强度理论( Failure criteria) □§7-9莫尔强度理论 (Mohr's failure criterion)

就分 nalysis of stress-state and strain-state四 §7-1应力状态概述 (Introduction of stress-state) 、应力状态的概念( Concepts of stresses-state) 请看下面几段动画 1.低碳钢和铸铁的拉伸实验 (A tensile test of low-carbon steel and cast iron) 2低碳钢和铸铁的扭转实验 (A torsional test of low-carbon steel and cast iron)

就分 nalysis of stress-state and strain-state四 低碳钢和铸铁的拉伸 低碳钢 铸铁 (low-carbon steeD (cast-iron) ? 塑性材料拉伸时为什么会出现滑移线?

就分 nalysis of stress-state and strain-state四 低碳钢和铸铁的扭转 低碳钢 铸铁 (low-carbon steeD) (cast-iron) 为什么脆性材料扭转时沿45°螺旋面断开?

就分 nalysis of stress-state and strain-state四 3.重要结论( Important conclusions) (1)拉中有剪,剪中有拉; (2)不仅横截面上存在应力斜截面上也存在应力 (3)同一面上不同点的应力各不相同; (4)同一点不同方向面上的应力也是各不相同 哪一个面上? 应力 哪一点? 哪一点? 哪个方向面? 4.一点的应力状态( state of stresses of a given point) 过一点不同方向面上应力的情况,称之为这一点的应力状 态( state of stresses of a given point),亦指该点的应力 全貌

就分 nalysis of stress-state and strain-state四 二、应力状态的研究方法( The method for investigating the state of stress) 1.单元体( Element body) 2.单元体特征( Element characteristic (1)单元体的尺寸无限小每个面上应力均匀分布 (2)任意一对平行平面上的应力相等a2 3主单元体( Principal body) 各侧面上切应力均为零的单元体 用 o2

就分 nalysis of stress-state and strain-state四 4.主平面( Principal plane) 切应力为零的截面 5主应力( Principal stress 主面上的正应力 说明:一点处必定存在这样的一个单元体,三个相互垂直的面 均为主平面,三个互相垂直的主应力分别记为a1,,G且规定按 代数值大小的顺序来排列,即 用

 1   2   3

就分 nalysis of stress-state and strain-state四 、应力状态的分类 The classification of stresses-state) 1空间应力状态( Triaxial stress-state or three-dimensional stress-state 个主应力G1,a2,O3均不等于零 2平面应力状态( Biaxial stress-state or plane stress-state 个主应力G1,O2,O中有两个不等于零 3单向应力状态( Uniaxial stress-state or simple stress-state 三个主应力a1,02,G中只有一个不等于零 3 用理