旋转梯度对平面裂纹的影响及其尺度效应

INFLUENCE OF ROTATION GRADIENT ON PLANE CRACK AND ITS SCALE EFFECT

将移动最小二乘无网格方法和弹性偶应力理论结合在一起,建立弹性偶应力理论的移动最小二乘无网格方法离散模型。首先研究偶应力理论下的小圆孔应力集中问题,确定该方法的基本参数,解决算法实施的关键技术。在此基础上,针对不同的特征长度,研究平面应力情况下中心I型裂纹尖端的强度因子和正应力分布、单边和双边I型裂纹尖端应力强度因子、最大剪应力以及复杂受力状态下中心斜裂纹初始扩展问题。与此同时,研究剪力和裂隙压力对尺度效应的影响。结果表明:偶应力对I型裂纹尖端的剪应力影响显著,对I型裂纹尖端正应力影响甚微;对平面斜置裂纹的弯折扩展有显著的影响,破裂角度、破裂步长、扩展载荷表现出显著的尺度效应;水平剪力明显加剧了尺度效应,裂隙压力对尺度效应的影响甚微。

The moving least square meshless method and the couple stress theory were combined together.Discrete model of moving least square meshless method was derived based on couple stress theory.First,stress concentration of the circular hole was studied under couple stress theory.The basic parameters of the method were determined;and the key technology of the algorithm application was also solved.On this basis,as for the plane stress problems,stress intensity factor and normal stress near crack tip of the central crack-I,stress intensity factor and the maximum shear stress of single and two boundary crack-I,and initial rupture of oblique central crack were studied with different characteristic lengths.Meanwhile,influence of shear force and fracture pressure on scale effect were presented.The results show that the couple stress has a significant influence on shear stress at crack-I tip,little influence on normal stress at crack-I tip.The couple stress has a significant influence on oblique crack bending propagation for plane stress problem.For oblique crack,the crack propagation angles,steps and loads show remarkable scale effect.The horizontal shear may intensify the scale effect.The fracture pressure has little influence on scale effect.