Nano-scale Three-dimensional Crack Propagation Considering Surface Effect

On the macroscopic scale,the fracture toughness of cracked thin plate is strongly dependent on the thickness of thin plate,and the main mechanism has been discussed by three-dimensional constraint theory.However,the main factors affecting the fracture performance of cracked plates with nanometer thickness are not clear at present.In this study,surface effect are introduced into the theoretical model to characterize the fracture behavior of cracked metal plates with nanometer thickness.According to the principle of virtual work,the formulas of stress field and stress intensity factor(SIF)at crack tip are derived.Compared with the results of molecular dynamics simulation,finite element simulation and Gurtin&Murdoch surface model,the predicted values of our theoretical model are closer to those of numerical simulation.The effect of nano-scale surface effect on the crack propagation behavior of single crystal aluminum under cyclic fatigue loading is also studied.The results show that the crack propagation rate of the model with small thickness is faster than that of the model with large thickness.These studies have important guiding significance for understanding the fracture behavior and fatigue mechanism of cracked metal plates with nanometer thickness.The main research contents are as follows:(1)Combining classical elastic fracture mechanics theory and virtual work principle,based on the surface energy density theory of Chen-Yao,the surface effect is a function of body surface energy density and surface relaxation parameters,and the expression of stress field at the tip of type I crack considering surface effect is derived.Based on this expression,the normalized SIF decreases with the thin plate thickness decreasing,which indicates that the nano-scale surface effect can effectively improve the fracture toughness of cracked thin plate.In addition,the results show that the influence of surface effect on SIF is obvious only when the thin plate thickness is less than 10nm.(2)Molecular dynamics and finite element method were used to establish single crystal aluminum and single crystal copper crack plates with different thickness to calculate their SIF.In molecular dynamics,linear extrapolation is used to obtain the SIF,while the surface effect of the finite element model is achieved by applying surface traction perpendicular to the crack surface.The results show that the normalized SIF results in the numerical model have the same trend as the theoretical prediction.In addition,the influence of temperature in molecular dynamics and the traction region of the crack surface on SIF,T stress and out-of-plane constraint factor T_z is also discussed.Temperature has little influence on normalized stress intensity factor k_Ⅰ,T stress and out-of-plane constraint factor T_z,and the influence of surface traction distribution area on stress field distribution,T stress and out-of-plane constraint factor T_z is also not obvious,but has significant influence on SIF.(3)The influence of surface effect on fatigue crack propagation of three single crystal aluminum crack plates with different thickness was studied.The results show that the surface effect can improve the material strength,and the small thickness plate has slower dislocation emission rate.In addition,the fatigue crack propagation rate increases with the decrease of the thickness,and the crack tends to close in the plate with large thickness.Temperature has a certain effect on the thin plate of small thickness while the large one is not sensitive to temperature.