Modelling and simulation of short fatigue cracks

Abstract: The growth of short fatigue cracks deviates from the behaviour of long fatigue cracks even if subjected to the same nominal driving force. The influence from the microstructure is pronounced, while crack closure effects may not be that important as for longer cracks. The objective of this thesis is to study the local conditions for crack growth for two different short crack problems, and to develop methods to model the cases of interest. The questions at issue together with the smallest relevant length in each problem govern the choice of the methods. The first part of the thesis, addresses the problem of a short edge crack in a ductile crystalline body subjected to varying loading. The crack growth mechanism is assumed to be blunting and resharpening, and is modelled by the emission and annihilation of discrete dislocations at the crack tip. The emitted discrete dislocations move along preferred slip planes if the lattice friction is overcome. These discrete dislocations represent the plastic deformation in an otherwise linear elastic material. A boundary element approach is used to model the crack, through distributing dislocation dipoles along the crack line. Detailed investigations of a short edge crack growing in mode I have show that the competition between the increasing global stress due to crack advance and the increasing shielding effect on the crack tip from the dislocations in the plastic zone is crucial for crack growth. The spreading of plasticity into neighbouring grains is simulated by letting dislocations nucleate at the grain boundaries. For the first few cycles, only minor differences between crack growth rates are found for the cases with and without grain boundary nucleation. The influence of the distance between the crack tip and the grain boundary is found to be more pronounced. A study of short crack growth during up to 5000 cycles shows that a crack can both accelerate and decelerate before it is arrested. In the second part of the thesis, interfacial fracture is considered with the focus on interface cracks emanating from stress concentrations developed at the edges of an interface. A method is presented for obtaining the complex stress intensity factor for an interface crack in a bimaterial from finite element calculations using a minimum number of computations. A crack closure integral method for homogeneous materials is modified to include mismatch in material properties. This is achieved through direct calculations from the nodal forces and displacements near the tip computed by a single finite element analysis. The influence of thickness and edge angle of the coating on the energy release rate and the mode mixity is investigated for a short edge crack at the interface of a thermal barrier coating system. It is concluded that a reduction of the edge angle of a thick coating results in a decrease of the risk for crack propagation.