Chapter 4
Stress Intensity Factor- Calculation of Stress Field in the Vicinity of a Crack Tip
应力强度因子 - 计算裂纹尖端附近的应力场
Elastic behavior of material near crack tip is assumed. The assumption is valid for brittle materials. In many cases for ductile materials, the size of the plastic zone near crack tip is quite small so that its effect can be ignored.
假设材料在裂纹尖端附近具有弹性行为。该假设适用于脆性材料。在许多情况下,对于延展性材料,裂纹尖端附近的塑性区域的尺寸非常小,因此可以忽略其影响。
singularity near the crack tip will be derived.
将推导裂纹尖端附近的奇点。
Critical stress intensity factor as a measure of toughness of a material will be developed.
将开发临界应力强度因子作为材料韧性的量度。
Fundamental modes of cracks
裂纹的基本模式
Figure 4.1. The three modes of loading that can be applied to a crack
图 4.1.可应用于裂纹的三种加载模式
Mode I: The crack faces are pulled in a direction normal to the plane of the crack.
模式 I:将裂纹面沿垂直于裂纹平面的方向拉动。
Mode II: The crack faces are sheared in a direction normal to the crack front
模式二:裂纹面沿垂直于裂纹前沿的方向剪切
Mode III: The crack faces are sheared parallel to the crack front. This mode is also called “Tearing Mode”
模式III:裂纹面平行于裂纹前沿进行剪切。此模式也称为“撕裂模式”
※ Some Cracks can be represented by the combination of these fundamental modes.
※ 有些裂缝可以用这些基本模式的组合来表示。
Airy stress function formulation of plane problems
平面问题的空气应力函数公式
For cracks, most B.C.’s are traction B.C.’s.
对于裂缝,大多数 BC 是牵引 BC 的。
Most convenient when problems are formulated in terms of stresses
当问题以应力表述时最方便
In that case, the stresses must satisfy compatibility conditions as well as equilibrium equations.
在这种情况下,应力必须满足相容性条件以及平衡方程。
To reduce the number of equations to be solved, Airy stress function is introduced.
为了减少要求解的方程数量,引入了艾里应力函数。