In creeping solids,plane stress and plane strain solutions for asymptotic singular crack-tip fields have been first put forward by Riedel and Rice with C^(*)as the dominating parameter and developed by Xiang and Guo into three-dimensional solution(3D)for stationary cracks under the domination of C^(*)with the constraint factor Tz.However,how to characterize the 3D crack-tip fields under creep damage-induced quasistatic growing conditions remains challenging.In this study,we reveal that,for 3D quasistatic growing cracks,the leading singular solution can effectively characterize the crack-tip stress distributions with relative errors less than 10.8%for relative creep time up to 0.8 in various specimens with finite thickness.For a given relative time,Tz distributions can be unified by the equivalent thickness concept,Beq.The results show that C^(*)-T_(z) can effectively quantify both the load and constraint effects on the crack-tip fields.Such geometry independent dominance can considerably simplify the treatments of load and constraint effects,thereby promoting the application of fracture mechanics in high-temperature damage tolerance designs.
In this paper,the Discrete Least Squares Meshless(DLSM)method is developed to determine crack-tip fields.In DLSM,the problem domain and its boundary are discretized by unrelated field nodes used to introduce the shape functions by the moving least-squares(MLS)interpolant.This method aims to minimize the sum of squared residuals of the governing differential equations at any nodal point.Since high-continuity shape functions are used,some necessary treatments,including the visibility criterion,diffraction,and transparency approaches,are employed in the DLSM to introduce strong discontinuities such as cracks.The stress extrapolation and J-integral methods are used to calculate stress intensity factors.Three classic numerical examples using three approaches to defining discontinuities in the irregular distribution of nodal points are considered to investigate the effectiveness of the DLSM method.The numerical tests indicated that the proposed method effectively employed the approaches to defining discontinuities to deal with discontinuous boundaries.It was also demonstrated that the diffraction approach obtained higher accuracy than the other techniques.
Nanoscale defects,including cracks,circular holes,and the triangular-shaped defects,often occur in the growth of boron nitride nanosheets(BNNS).In this study,the fracture behavior of chiral BNNS with different crack-tip shapes and the interactions of nanoscale crack-defects are studied using molecular dynamics(MD)simulations and finite element(FE)analysis.Both MD and FE results indicate that the fracture strength of BNNS with two cracktips(t=2)is significantly higher than that with one cracktip(t=1),in which the difference in zigzag(ZZ)direction is more obvious than that in armchair(AC)direction,mainly due to the fact that the change of bond angles near the cracktips is more substantial in the ZZ direction than those in the AC direction.Our results show that the fracture strength of BNNS strongly depends on crack-tip shapes,chiral angles,the defect-to-cracktip spacing and deflection angles.Checking against the current MD simulations and FE analysis shows the present results are reasonable.This study should be of great importance for enhancing the fracture performance of BNNS by modulating their crack-tip shapes and the interactions of nanoscale crack-defects.
大多数工程材料显示出脆性特征(例如,复合材料),而脆性材料中的裂纹已公认为是工程结构破坏的主要原因,裂纹尖端应力场必然是建立断裂判据的基础。因此,本文重点讨论I + II + III混合型加载下的裂纹尖端应力,采用线弹性力学方法解决正交异性材料典型应力边值问题。首先确定三维空间问题的弹性力学基本方程,基于复变函数理论求解控制方程。接着利用应力函数和坐标变换求解基本方程。最终获得了混合型加载下正交异性材料裂纹尖端附近的应力分量通解。