The practice of attempting validation of crack-propagation laws (i.e., the laws of Head, Frost and Dugdale, McEvily and Illg, Liu, and Paris) with a small amount of data, such as a few single specimen test results, is questioned.It is shown that all the laws, though they are mutually contradictory, can be in agreement with the same small sample of data. It is suggested that agreement with a wide selection of data from many specimens and over many orders of magnitudes of crack-extension rates may be necessary to validate crack-propagation laius. For such a wide comparison of data a new simple empirical law is given which fits the broad trend of the data.

The crack extension in a large plate subjected to general plane loading is examined theoretically and experimentally. It is found that under skew-symmetric plane loading of brittle materials the “sliding” or the crack extension in its own plane does not take place, instead crack grows in the direction approximately 70 deg from the plane of the crack. This is very nearly the direction perpendicular to the maximum tangential stress at the crack tip, which is 70.5 deg. The hypothesis that the crack will grow in the direction perpendicular to the largest tension at the crack tip seems to be verified also by cracked plates under combined tension and shear. In spite of the fact that “sliding” and “tearing” modes of crack extension do not take place in brittle materials it is shown that one can still talk about critical stress intensity factors in plane shear and transverse bending of plates. It is also shown that, in general plane loading, the fracture criterion in terms of stress intensity factors is an ellipse.

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In this paper the plane elasticity problem for a nonhomogeneous medium containing a crack is considered. It is assumed that the Poisson's ratio of the medium is constant and the Young's modulus E varies exponentially with the coordinate parallel to the crack. First the half plane problem is formulated and the solution is given for arbitrary tractions along the boundary. Then the integral equation for the crack problem is derived. It is shown that the integral equation having the derivative of the crack surface displacement as the density function has a simple Cauchy type kernel. Hence, its solution and the stresses around the crack tips have the conventional square-root singularity. The solution is gi.ven for various loading conditions. The results show that the effect of the Poisson's ratio and consequently that of the thickness constraint on the stress intensity factors are rather negligible. On the other hand, the results are highly affected by the parameter a describing the material nonhomogeneity in E{x} = Eoexp(sx).

Abstract.In this paper a pair of Gauss-Chebyshev integration formulas for singular integrals are developed. Using these formulas a simple numerical method for solving a system of singular integral equations is described. To demonstrate the effectiveness of the method, a numerical example is given. In order to have a basis of comparison, the example problem is solved also by using an alternate method.