Three-dimensional stress fields near notches and cracks

Abstract

Structures with notches have a tendency to develop critical crack growth because of the stress concentration. The strength of the structures with stress gradient usually shows strong three-dimensional (3D) effects even under in-plane loading. The commonly twodimensional (2D) models for fracture assessments of bodies with notches and cracks may lead to inaccurate predictions when in-plane loading is applied to certain 3D geometries. In the paper, the recent researches on the 3D effects of stress concentrations at notches and 3D stress fields of cracks are summarized. A new concept of equivalent thickness of the point on the crack front line is proposed based on the detailed analyses of the 3D out-ofplane stress fields of cracks, and then new empirical formulae of the 3D out-of-plane stress constraint factor T z of I-II mixed-mode cracks are obtained by use of the equivalent thickness. Combining the T z with the in-plane constraint parameters T or Q, the 3D multi-parameter descriptions of the stress field in front of various types of cracks using K -T z , J -T z , K -T -T z and J -Q-T z combination can be formulated.

Formulization of Three-Dimensional Stress and Strain Fields at Elliptical Holes in Finite Thickness Plates

“…For the finite thickness plate, 0 ≤ T z ≤ ν, where ν is Poisson's ratio of the material. The third parameter is the equivalent thickness B eq of the point on the crack front line empirically defined by She et al [39]:…”

三维裂纹端部应力场的三参数描述及等效厚度概念

“…基 于这一点, 曲线裂纹上某一点 P 处的等效厚度可以由 其具有相同 T z 分布的穿透直裂纹板的厚度来确定, 如图 12 所示. 图 13-16 分别给出了穿透直裂纹 [36] (图 13)、 四分 之一椭圆角裂纹 [40] (图 14), 半椭圆表面裂纹 [41] (图 15) 以及内埋裂纹 [42] (图 16)的等效厚度研究结果, 其中 t 为椭圆形状比(t=a/c). 下面分别给出各种裂纹的裂纹 前沿线上某点的等效厚度 B eq .…”

“…最初 的 B eq 被经验地定义为裂纹前沿线的切线与结构表面 的交点与切点的最短距离的两倍, 如图 10 所示. 后 来, 对于含有穿透直裂纹的平板, She 等人[36] 研究了 三维约束从板的中心面到表面的变化, 并基于约束 等效的原则, 提出了一种基于离面应力约束因子 T z 的等效厚度的定义, 如图 11 所示. 对于厚度为 B eq 的 穿透直裂纹(如图 11(b)), 中面上 T z 沿着 r 方向的分布 (z=0,     可以通过以下公式进行描述[36] :…”

Determination of effect of elliptic notches and grooves on stress concentration factors on notched bar in tension and grooved shaft under torsion

“…Stress field and stress concentration factor in 3D models of elliptic holes in flat rectangular bars were also studied numerically by Yang (2009), Zhao et al (2008, Snowberger (2008), Pedersen et al (2007) etc. Yang (2009) showed that the plane stress condition of 3D models is approximately achieved by the 2D ones when the plate thickness tends to zero.…”