J integral and COD fracture criteria in 40CrNiMo steel under mixed mode I+II loading

Abstract

By defining the J integral and crack opening displacement (COD) under mixed mode I + II loading, a mixed J integral fracture criterion is proposed and the relationship between the J integral and COD in 40CrNiMo steel is discussed. The mixed J integral J _M and its mode I and II components J _I and J _II were calculated by the finite element method, while the mixed COD and its mode I and II components CTOD and CTSD were measured using a duplicated grid. The critical values J _Mc and COD_c for mixed crack initiation were determined by a resistance curve. The results show that mode II loading lowers both J _Mc and COD_c for 40CrNiMo steel. The variation of J _Mcfrommode I tomode II loading is found to be in accordance with the linked equations J _Mc=J _Ii+J _IIi;(J _Ii/J _Ic)+(J _IIi/J _IIc)=1, where J _Icand J _IIcare the critical J integrals of pure mode I and II cracks,and J _Iiand J _IIiare the mode I and II components of J _Mc at arbitrary mixed K_I/K_II ratio respectively; the J _Mc value for a given K_I/K_II ratio can be obtained if J _Ic and J _IIc are known. Finally, under valid loads, J_M and the mixed COD satisfy the relation J _M=J _I+J _II=dσ₀CTOD+d _sτ₀CTSD. When unified by yield stress σ_y the relation becomes J _M=dσ_yCOD, where d _n, d _s and d are coefficients, and σ₀ and τ₀ are the tensile and shear stress at the crack tip strip respectively. While d _n and d _s vary with K_I/K_II ratio and materials, d was found to have a constant value of about 0.98.

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