Stress Analysis of Cracks

Most of the crack problems that have been solved are based on two-dimensional, linear elasticity (i.e., the infinitesimal or small strain theory for elasticity). Some three-dimensional problems have also been solved however, they are limited principally to axisymmetric cases. Complex variable techniques have served well in the solution of these problems. To gain a better appreciation of the problems of fracture and crack growth, it is important to understand the basic assumptions and ramifications that underlie the stress analysis of cracks. 

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H. Tada, P. Paris and G. Irwin, The Stress Analysis of Cracks Handbook, Del Research Corporation, St Louis, 1973 (for Tabulation of Stress Intensities). 

Tada H., Paris P.C. and Irwin G.R. (2000). The Stress Analysis of Cracks Handbook. Professional Engineering Publishing, London. 

Tada, H., Paris, P. C, Irwin, G. R. Stress analysis of cracks handbook. Del Research Corporation 1973... 

The functions fi(y) and fzix) depend on the boundary conditions and cannot be chosen arbitrarily. It will be shown later, for example, that for a cracked plate under remote biaxial tension, the boundary condition on shearing stresses (r y = 0 at infinity) requires that the sum of the last two terms be zero. As such, the derivatives must be equal to a constant of opposite sign, which leads to fi(y) = Ay and fiix) = -Ax. Here, the contribution of/i(y) and/2(x) to the u and v displacements represents rigid body rotation and is not considered further in the stress analysis of cracked bodies. It should be noted that the constant A cannot be arbitrarily neglected. 

Tada H, Paris P C and Irwin G R (1985) in The stress analysis of cracks handbook, 2nd edition, Paris Productions Incorporated, St. Louis, MO, p. 2.16. 

Paris P C and Sih G C (1964) Stress analysis of cracks, Fracture Toughness Testing and its Applications, ASTM STP S81, American Society for Testing and Materials, pp. 30-83. 

Tada, H., 1985, Handbook for Stress Analysis of Cracks, 2nd ed., Del. Research Corp., 1985. 

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