裂纹尖端应力场,应力强度因子

LINEAR ELASTIC FRACTURE MECHANICS (Contd.)
In the 1950s Irwin [7] and coworkers introduced the concept of stress intensity
factor, which defines the stress field around the crack tip, taking into account
• 应变；
表示形式；
• 应力应变关系；
• Westergaard应力函数；
• •
平衡方程；
•
平面应力和平面应变问题；
三种裂纹尖端的线性 弹性应力场解；
• 二维问题弹性解；
LINEAR ELASTIC FRACTURE MECHANICS (LEFM)
For LEFM the structure obeys Hooke’s law and global behavior is linear and if any local small scale crack tip plasticity is ignored The fundamental principle of fracture mechanics is that the stress field around a crack tip being characterized by stress intensity factor K which is related to both the stress and the size of the flaw. The analytic development of the stress intensity factor is described for a number of common specimen and crack geometries below. The three modes of fracture
In stress analysis each point, x,y,z, of a stressed solid undergoes the stresses; sx sy, sz, txy, txz,tyz. With reference to figure 2.3, when a body is loaded and these loads are within the same plane, say the x-y plane, two different loading
Mode I - Opening mode: where the crack surfaces separate symmetrically with respect to the plane occupied by the crack prior to the deformation (results from normal stresses perpendicular to the crack plane); Mode II - Sliding mode: where the crack surfaces glide over one another in opposite directions but in the same plane (results from in-plane shear); and Mode III - Tearing mode: where the crack surfaces are displaced in the crack plane and parallel to the crack front (results from out-of-plane shear).
sz = ν (sx+sy) where ν is Poisson's ratio.
crack length, applied stress s and shape factor Y( which accounts for finite size
of the component and local geometric features).
The Airy stress function.
s
s
thickness z-direction.
s
Plane Stress
Plane Strain
In the former case, the overall stress state is reduced to the three
components; sx, sy, txy, since; sz, txz, tyz= 0, while, in the latter case, a normal stress, sz, is induced which prevents the z displacement, ez = w = 0. Hence, from Hooke's law:
conditions are possible:
s
1. plane stress (PSS), when the
thickness of the body is
comparable to the size of the
y syy
Thickness
B
s
Thickness B
s
plastic zone and a free
断裂力学 第三讲
裂纹尖端应力场，应力强度因子
Baidu Nhomakorabea
问题
• 有哪几种典型的裂纹扩展形式？ • I、II、III型裂纹的裂纹尖端应力应变计位移的分布形式？ • 为什么用裂纹强度因子可以表征线弹性材料的断裂过程？ • 裂纹强度因子与能量释放率之间的关系
弹性理论简述
• 应力；
• Airy应力函数；
• 变形；
• Airy函数的复变函数
s
contraction of lateral surfaces
X
occurs, and, a
2. plane strain (PSN), when the
Crack Plane
sz sz sz sz
specimen is thick enough to avoid contraction in the