Finite element analysis of the three-dimensional stress state at bi-material edges and corners

When a multi-material structure fails, failure often initiates at free edges and corners where the material interface intersects the stress-free edge. The importance of understanding the crack initiation mechanism requires a rational and standardized approach to characterize the crack initiation process. Establishing the precise methodology and the selection of the proper analysis technologies for failure analysis are essential for multi-material structures and devices.; The traditional fracture mechanics approach combined with enriched elements has been widely used to compute the singular stress field and stress intensity factors in the vicinity of a crack front. Since the existence of a prior crack is not required for the enrichment scheme, a "fracture-mechanics-like" analytical approach, based on the enrichment scheme, has been developed to analyze the three-dimensional stress state and the edge/corner stress intensity factors at the singular edge front without cracks. The closed, explicit expressions for the asymptotic displacement field around the singular sites have been derived and integrated into the enriched edge and corner elements to determine the edge/corner stress intensity factors in the enrichment scheme.; Accuracy of this fracture-mechanics-like approach has been verified by comparisons with certain interfacial crack problems. This fracture-mechanics-like approach has been used to determine the edge stress intensity factors for a series of adhesively-bonded butt joints; the numerical results are compared favorably with those available in the literature.; The 3D stress states in the vicinity of corner points for a series of geometries have been examined by this approach. It is concluded that the highest stress occurs at the corner point for all cases. As the half corner expansion angle gamma becomes larger, the highest normal stress increases. This implies that small gamma angles at the corner may be good choices for geometry design. Investigations have found that the normalization treatment has no effect on the resulting normal stress and the displacement distributions but it changes the value of the corner stress intensity factors dramatically. This comparison means that the three-dimensional stress state can be predicted accurately if the correct corner stress singularities are embedded into the displacement formulation for the enriched corner elements.