A finite element technique for determining mode I stress intensity factors: Application to no-slip bimaterial crack problems

A comparative finite element technique, using conventional finite elements, is presented for the determination of mode I stress intensity factors in two-dimensional crack problems. Given a crack problem to be solved and an auxiliary crack problem for which the mode I stress intensity factor K_I is readily available, it is argued that the ratio of K_Is for these two problems can be approximated by the ratio of corresponding crack opening displacements near the crack tips, as obtained from finite element solutions. The geometry and loading of the auxiliary problem need not be related to those of the problem to be solved; however, it is essential that the mesh configurations around the crack tips be identical so that numerical errors inherent to the finite element discretization process be the same for the two problems. The validity of this technique is checked for several two-dimensional problems for cracks in homogeneous material whose solutions are available in the literature. Then, it is verified that the method applies to problems of no-slip cracks at a bimaterial interface, in which the no-slip condition is enforced by including no-slip blocks along the crack faces. Finally, this technique is used to predict the stress intensity factors for a four-point bending specimen with an edge no-slip crack at the bimaterial interface.