3차 등매개 유한요소를 이용한 이종재료 접합면에 수직인 균열의 응력확대계수 평가

Evaluation of stress intensity factor for a crack normal to bimaterial interface using cubic isoparametric finite elements

When a crack meets bimaterial interface stress singularity depends on the elastic constants of the adjacent materials. In the present study we are going to describe the finite element formulation for problems with a crack to be embedded in the stiffer material$({\mu}_2/{\mu}_1)$. The cubic isoparametric singular element, represented by adequately shifting the mid-side nodes adjacent to the crack tip is constructed to enclose the crack tip. An alternative method to obtain the optimal position of the mid-side nodes of cubic isoparametric elements is presented. In addition, a proper definition for the stress intensity factors of a crack normal to bimaterial interface is provided. It is based upon near a tip displacement solutions. Models for numerical analysis are two dimensional elastic bodies with a through crack under plain strain. The results obtained are compared with the previous solutions.