Fracture criterion of a mixed-mode crack based on CED (Crack Energy Density)

The CED (Crack Energy Density) in an arbitrary direction, E_φ{symbol}, is defined as the quantity which has the meaning of strain energy area density in the plane containing a crack front line without any restriction on constitutive equation. We may expect that, as far as the opening type fracture occurs, a mixed mode crack begins to grow in the direction φ{symbol} where E_φ{symbol}^I (mode I contribution of E_φ{symbol}) takes the maximum value, E_{φ{symbol}max}^I, when E_{φ{symbol}max}^I reaches a critical value peculiar to a material (we call this criterion E_{φ{symbol}max}^I criterion). In this paper, the applicability of this E_{φ{symbol}max}^I criterion to elastic-plastic fractures is studied based on the fracture experiments on specimens of Aluminum alloy with a crack inclined to the loading axis and it is demonstrated that the onset and the direction of crack growth can be estimated by E_{φ{symbol}max}^I criterion in either case of fractures with relatively small yielding region and those with large yielding region. The applicability of E_{φ{symbol}max}^I criterion to elastic (quasi-elastic) fractures is also shown through the comparison of the result by E_{φ{symbol}max}^I criterion with the results by other criteria and experimental results.