混合モードき裂の最大エネルギー解放率の解析的近似式の提唱

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抄録

Use of some mixed mode fracture criterion becomes necessary when reliability evaluation of ceramic components is made based on flaw distributions, since most components are subjected to multi-axial stresses in service conditions. The maximum energy release rate criterion is one of the wellknown criteria for mixed mode fracture. In the case of a mixed mode crack, the energy release rate, G, takes a maximum value, G_max, when the crack extends in a certain direction. The maximum energy release rate criterion (G_max criterion) assumes that unstable crack extension occurs when G_max reaches a certain critical value. Unfortunately, a reliable analytical expression of G_max in terms of the stress intensity factors has not yet been obtained. This is an obstacle to analytical treatments based on G_max criterion. Thus, it was attempted in this paper to derive an analytical expression of G_max for a two-dimensional crack. The approximate analytical expression G_max=(K_I²+3K_II²+K_I√K_I²+6K_II²)/2E' was obtained, where K_I(>0) and K_II are the mode I and mode II stress intensity factors, and E'=E for plane stress and E'=E/(1-ν²) for plane strain with E and ν being usual elastic constants. From comparison of this expression with the exact value of G_max evaluated numerically, it was shown that the proposed expression is quite accurate. It was also shown that the expression of G_max given by Hellen and used by Lamon for reliability evaluation of ceramic components is not adequate.