Three-Dimensional Elastic Stress Fields near Crack Front in Finite Thickness Plates
Yang Zheng(1), Huo Chunyong(1), Guo Wanlin(1,2) Wang Yanfei(3)
(1,Xi'an Jiaotong University, Xi'an 710049, China) (2,Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China)
(3,Henan University of Science & Technology, Luoyang 471039, China)

Abstract: 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 T_z  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 T_z   in creases with increasing B and closing to the middle plane. The T_z   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.
Keywords: crack, stress intensity factor, out-of-plane stress constraint factor.