Applicability of CED (crack energy density) to mixed mode fracture problem

The CED (Crack Energy Density), ε_φ{symbol}, in an arbitrary direction is defined and has a consistent meaning without any restriction on constitutive equation. In general, ε_φ{symbol} can be divided into the contributions of each mode and the maximum value, ε^I_{φ{symbol}max}, of ε^I_φ{symbol} for mode I is expected to play the most important role in mixed mode fracture problems. In this paper, ε_φ{symbol} and ε^I_φ{symbol} for specimens under tension with a crack inclined to the loading axis are evaluated by path-independent integrals and the method based on the relationship between ε_φ{symbol} and load-displacement curves through elastic finite element analyses, and a practical method to evaluate ε^I_{φ{symbol}max} is proposed through comparison of the results with theoretical ones. Subsequently, ε^I_{φ{symbol}max} corresponding to an experimental result of ductile fracture is evaluated by the above proposed method through elastic-plastic finite element analyses and the applicability of CED (ε^I_{φ{symbol}max}) to a mixed mode fracture problem is demonstrated.