Growth from a straight crack subjected to arbitrary remote loading

Abstract

Growth from straight cracks is studied, both for loading in pure mode I or II and for mixed mode loading. Small scale yielding and a plane condition are assumed. Growth is assumed to take place in either mode I or mode II. Loss of directional stability sometimes occurs even from cracks that seem destined for continued growth straight forward. A striking example is the case of collinear cracks under symmetric remote loading growing toward each other: before coalescence they deflect from their straight paths and avoid each other instead of running together tip to tip as expected. One single crack growing in mode I under symmetric loading conditions might suffer from loss of directional stability. Directional stability is here defined to prevail if the angle formed by the straight line between the crack tips and the original crack direction eventually decreases during growth. This is shown to be the case if, and only if, the principal stress perpendicular to the original crack is the largest of the two in-plane stresses. Another, although less logical, candidate for definition of directional stability is also discussed. It concentrates on the position of the crack tips rather than on the main direction of the crack and it is in this case assumed that directional stability prevails if the crack tips eventually move closer toward the line along the original crack. This definition leads to directional stability when the principal stress in the original crack direction is smaller than the fraction 1 − π/4 of the other in-plane stress. For a crack under mixed mode loading conditions an abrupt deviation from the straight path is expected. Comparison of theoretically obtained values of the mode I and II stress intensity factors at the tips of the crack, after introduction of an infinitesimal disturbance, with experimental results indicates that mode I growth is preferred before mode II in the absence of a confining pressure, at least if the ratio between the critical mode II and I stress intensity factors is larger than 0.38–0.81, depending on the load situation. Thus also a straight crack, originally directed favourably for extension straight forward in mode II, will exhibit directional instability and mode I growth will take over after kink formation at the tips of the crack. Eventually the growth approaches a direction perpendicular to the largest in-plane principal stress.