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.

A B S T R A C T This paper deals with the general problem of crack extension in a combined stress field where a crack can grow in any arbitrary direction with reference to its original position. In a situation, when both of the stress-intensity factors, kl, kz are present along the crack front, the crack may spread in any direction in a plane normal to the crack edge depending on the loading conditions. Preliminary results indicate that the direction of crack growth and fracture toughness for the mixed problem of Mode I and Mode II are governed by the critical value of the strain-energy-density factor, Scr. The basic assumption is that crack initiation occurs when the interior minimum of S reaches a critical value designated S¢,. The strain-energy-density factor S represents the strength of the elastic energy field in the vicinity of the crack tip which is singular of the order of 1/r where the radial distance r is measured from the crack front. In the special case of Mode I crack extension So, is related to k~c alone as So, =(x -1)kx2¢/8~. In general, S takes the quadratic form a 11 k 1 + 2al 2 k lk2 + a2z k z whose critical value is assumed to be a material constant. The analytical predictions are in good agreement with experimental data on the problem of an inclined crack in plexiglass and aluminum alloy specimens. The result of this investigation provides a convenient procedure for determining the critical crack size that a structure will tolerate under mixed mode conditions for a given applied stress.

The general equations for crack-tip stress fields in anisotropic bodies are derived making use of a complex variable approach. The stress-intensity-factors, which permit concise representation of the conditions for crack extension, are defined and are evaluated directly from stress functions. Some individual boundary value problem solutions are given in closed form and discussed with reference to their companion solutions for isotropic bodies.It is found that an elastic stress singularity of the order r -~ is always present at the crack tip in a body with rectilinear anisotropy (r being the radial distance from the crack front). This result and some additional consideration of the crack-tip stress fields imply that it is possible to extend current fracture mechanics methods to the representation of fracture conditions for anisotropic bodies with craektike imperfections.

The in-plane extension of two dissimilar materials with cracks or fault lines along their common interface is considered. A method is offered for solving such problems by the application of complex variables integrated with the eigenfunction-expansion technique presented in an earlier paper. The solution to any problem is resolved to finding a single complex potential resulting in a marked economy of effort as contrasted with the more laborious conventional methods which have not yielded satisfactory results. Boundary problems are formulated and solutions are given in closed form. The results of these evaluations also give stress-intensity factors (which determine the onset of rapid fracture in the theory of Griffith-Irwin) for plane problems.

A general survey of the results of elastic stress analyses of cracked bodie is the basic objective of this work. The stress-intensity-factor method ofs representing results is stressed and compared with other similar methods. All three modes of crack-surface displacements are considered, as well as specialized results applicable to plate and shell bending. Results for various media (for example, anisotropic, viscoelastic, or nonhomogeneous) are contrasted with the analysis of homogeneous isotropic media. The accuracy of the representation of the crack-tip stress fields by stress-intensity factor methods is discussed, pointing out some limitations of applicability. Methods of estimating and approximate analysis for stress-intensity factors in complicated practical circumstances are also discussed.