BIFURCATION OF CRACK PATTERN IN ARRAYS OF 2-DIMENSIONAL CRACKS

Theoretical calculations based on simple arrays of two-dimensional cra cks demonstrate that bifurcation of crack growth patterns may exist. T he approximation used involves the 'dipole asymptotic' or 'pseudo-trac tion' method to estimate the local stress intensity factor. This leads to a crack interaction parametrized by the crack length/spacing ratio lambda = a/h. For parallel and edge crack arrays under far field tens ion, uniform crack growth patterns (all cracks having same size) yield to nonuniform crack growth patterns (bifurcation) if lambda is larger than a critical value lambda(cr). However, no such bifurcation is fou nd for a collinear crack array under tension. For parallel and edge cr ack arrays, respectively, the value of lambda(cr) decreases monotonica lly from (2/9)(1/2) and (2/15.096)(1/2) for arrays of 2 cracks, to (2/ 3)(1/2)/pi and (2/5.032)(1/2)/pi for infinite arrays of cracks. The cr itical parameter lambda(cr) is calculated numerically for arrays of up to 100 cracks, whilst discrete Fourier transform is used to obtain la mbda(cr) for infinite crack arrays. For infinite parallel crack arrays under uniaxial compression, a simple shear-induced tensile crack mode l is formulated and compared to the modified Griffith theory. Based up on the model, lambda(cr) can be evaluated numerically depending on mu (the frictional coefficient) and c(0)/a (c(0) and a are the sizes of t he shear crack and tensile crack, respectively). As an iterative metho d is used, no closed form solution is presented. However, the numerica l calculations do indicate that lambda(cr) decreases with the increase of both mu and c(0)/a.