T-stress evaluation for curved crack problems

SummaryA general formulation for evaluating the T-stress at tips of a curved crack is introduced. In the formulation, a singular integral equation with the distribution of dislocation along the curve is suggested. The left-hand side of the equation is composed of a singular integral and a regular integral, and the right-hand side is the applied traction. An explicit formula for T-stress at the crack tip is first obtained in this paper. From the solution for the singular integral equation, the stress intensity factors and the T-stress at the crack tips can be evaluated. The T-stress is composed of two portions: (a) the relevant stress at the prospective site of the crack tip in the uniform field without crack and (b) the value of a regular integral in the singular integral equation. An effective method, the curve length method, is used to solve the singular integral equation. The arc crack with known solution is taken as an example to examine the suggested method. Several numerical examples are presented. The influence of the curvature to T-stress is addressed.

[1]  F. Erdogan,et al.  On the numerical solution of singular integral equations , 1972 .

[2]  Yan Chen,et al.  Closed form solutions of T-stress in plane elasticity crack problems , 2000 .

[3]  M. Williams,et al.  On the Stress Distribution at the Base of a Stationary Crack , 1956 .

[4]  Bhushan Lal Karihaloo,et al.  Higher order terms of the crack tip asymptotic field for a notched three-point bend beam , 2001 .

[5]  J. Rice,et al.  Slightly curved or kinked cracks , 1980 .

[6]  Morton Lowengrub,et al.  Some Basic Problems of the Mathematical Theory of Elasticity. , 1967 .

[7]  Solveig Melin,et al.  The influence of the T-stress on the directional stability of cracks , 2002 .

[8]  K. B. Broberg,et al.  A note on T-stress determination using dislocation arrays , 2005 .

[9]  X. Y. Lin,et al.  Complex potentials and integral equations for curved crack and curved rigid line problems in plane elasticity , 2006 .

[10]  J. Hancock,et al.  Two-Parameter Characterization of Elastic-Plastic Crack-Tip Fields , 1991 .

[11]  J. Rice,et al.  Limitations to the small scale yielding approximation for crack tip plasticity , 1974 .

[12]  J. Knott.  Mechanics of Fracture , 1983 .

[13]  N. Muskhelishvili.  Some basic problems of the mathematical theory of elasticity , 1953 .

[14]  K. W. Schuler,et al.  Shock pulse attenuation in a nonlinear viscoelastic solid , 1973 .

[15]  A. J. Carlsson,et al.  Influence of non-singular stress terms and specimen geometry on small-scale yielding at crack tips in elastic-plastic materials , 1973 .

[16]  Y. Chen.  Solution of integral equation in curve crack problem by using curve length coordinate , 2004 .

[17]  Theo Fett,et al.  Stress intensity factors and T-stress for internally cracked circular disks under various boundary conditions , 2001 .

[18]  Y. Z. Chen,et al.  Stress intensity factors for curved and kinked cracks in plane extension , 1999 .

[19]  T. Cook,et al.  On the numerical solution of singular integral equations , 1972 .

[20]  Solveig Melin.  On singular integral equations for kinked cracks , 1986, International Journal of Fracture.