Study on the behavior of elastic-plastic fracture under mixed I+II mode loading in aluminum alloy Ly12-J-integral analysis

Abstract

The elastic-plastic fracture behavior of aluminum alloy Ly12 under mixed I+II mode loading was studied by finite element method and fracture test. A mixed mode elastic-plastic fracture criterion of J-integral was proposed by using the J-resistance curve, and the maximum fracture effective plastic strain ε_p max of different mixed ratios at crack tip were also calculated. The results show that

(1) the initiation J-integral values of different mixed ratios have the equation

$$\left\{ \begin{gathered} J_{MC} = J_{Ii} + J_{{\text{II}}i} \hfill \\ J_{{\text{I}}i} /J_{{\text{I}}C} + J_{{\text{II}}i} /j_{{\text{II}}C} = 1, \hfill \\ \end{gathered} \right.$$

where J _Ii and J _IIi are the mode I and mode II components of the mixed initiation J-integral J _MC at a constant ixed ratio, respectively;

(2) the relation between the J _MC and mixed ratio K _I/K _II is

$$J_{MC} = K_{\text{I}}^{\text{2}} J_{{\text{I}}C} /(K_{\text{I}}^{\text{2}} + \alpha K_{{\text{II}}}^{\text{2}} ) + \alpha K_{{\text{II}}}^{\text{2}} ) + \alpha K_{{\text{II}}}^{\text{2}} J_{{\text{II}}C} /(K_{\text{I}}^{\text{2}} + \alpha K_{{\text{II}}}^{\text{2}} ),$$

α = J _IC /J _IIC ;

(3) J _MC increases with an increasing of mode II component, J _IIC is twice of J _IC for Ly12; and

(4) the maximum fracture effective plastic strain ɛ _{p max} and stress triaxiality σ _m /σ of different mixed ratios at crack tip satisfy the formula of

$$\varepsilon _p {\text{ max exp(3}}\sigma _m {\text{/2}}\sigma {\text{)}} = {\text{constant, }}$$

where the constant is about 9.52 for Ly12. The relation with double parameters, ɛ _{p max} and σ_m/σ, can be used as the local fracture or damage mechanics parameter under mixed mode I+II loading.