Multi-parameter average strain energy density factor criterion applied on the bi-material notch problem

Abstract

The stress field near a bi-material notch tip has the singular character. The power of singularity is lower in comparison to the case of a crack. The stress field can be described by the asymptotic stress series, in which each term contains generalized stress intensity factor and stress term exponent. The terms can be either singular or non-singular depending on the value of stress term exponent. The exponents are determined as solution of eigenvalue problem and depend on material properties and local geometry. The factors are calculated by analytical-numerical approaches and depend on global geometry and applied loading. The singular terms become unbounded when approaching the bi-material notch tip while the non-singular terms vanish. The non-singular terms increase precision in stress description on larger distances from the notch tip. The crack initiation conditions from the notch tip can be assessed by the average strain energy density factor (SEDF) criterion. In the case of bi-material notch problem, the crack can initiate in the direction of global minimum, the local minimum or the interface. The actual crack initiation load is calculated for each of abovementioned directions considering the individual fracture toughnesses. Contrary to the case of a crack, the direction of minimum of SEDF changes in dependence on the distance from the tip, therefore the average value over specific distance is used. The multi-parameter criterion considers singular and non-singular stress terms. Therefore in cases, when the specific distance is large, the non-singular terms provide means to improve precision of prediction of crack initiation parameters.