有限厚度板穿透裂纹前缘附近三维弹性应力场分析

通过三维有限元计算来研究有限宽度、有限厚度含有穿透裂纹板的裂纹前缘应力场，从中找出应力强度因子与板的厚度、裂纹长度之间的关系，同时还分析了裂尖的三维约束程度和三维约束区的大小。分析结果表明：应力强度因子沿厚度的分布是不均匀的，应力强度因子的最大值及其位置与厚度有关；有限厚度板中面应力强度因子(KI)m-p及最大应力强度因子(KI)max均大于平面应力或平面应变的应力强度因子。对有限厚度裂纹问题，按平面应力或平面应变来考虑是不安全的；板中面的应力强度因子(KI)m-p及最大应力强度因子(KI)max是厚度B／a的函数；板的中面离面约束系数Tx最大，自由面(z=B)Tx=0。沿厚度方向裂尖附近的离面约束系数Tx也是z／B和B／a的函数，随着厚度的增加离面约束系数Tx增大，离中面越近离面约束系数Tx越大。Tx随着x的增大急剧减小，三维约束影响区域大小大约为板厚的一半，且裂纹长度a／W对应力强度因子沿厚度变化规律及Tx影响区域大小影响较小。

Three-Dimensional Elastic Stress Fields near Crack Front in Finite Thickness Plates

The problems considered here are the finite width plates in different thickness with through-thickness crack subjected to a uniaxial tension. Detailed three-dimensional finite element computations are performed to investigate the stress field near the crack front. From analysis result the relations between the stress intensity factors and the plate thickness, the crack length are gotten. The scale of the constraint area and the constraint grade are also analyzed. The Stress Intensity Factors (SIF) are not uniform through the thickness. The value and location of maximum SIF depend on the plate thickness. Both the SIF in the middle plane (K I) m-p and the maximum SIF (K I ) max are greater than the one of the plane stress or the plane strain. So it is not safety that the problems of finite thickness are considered as the plane stress or plane strain one. The SIF in the middle plane, the value and location of maximum SIF along the crack front are the functions of B/a. The out-of-plane stress constraint factors Tz has the maximum value on the mid-plane and is zero on the free plane. The out-of-plane stress constraint factors are the functions of B/a and z/B. The Tz increases with increasing B and closing to the middle plane. The Tz decreases with increasing the distance from crack tip rapidly. The size of the three-dimensional effect zone is about the half of the thickness, and the length of crack (a/W) affects the SIF distribution through the thickness and the size of the three-dimensional effect zone lightly.