考虑一阶和二阶位移梯度的数字图像相关方法在剪切带测量中的比较  

A COMPARISON OF DIC METHODS CONSIDERING THE FIRST- AND SECOND-ORDER DISPLACEMENT GRADIENTS IN SHEAR BAND MEASUREMENTS

作　　者：王学滨[1] 杜亚志[1] 潘一山[1] 

机构地区：[1]辽宁工程技术大学力学与工程学院,辽宁阜新123000

出　　处：《工程力学》2013年第7期282-287,共6页Engineering Mechanics

基　　金：国家自然科学基金项目(50974069);国家重点基础研究发展计划项目(2010CB226803);辽宁省高等学校优秀人才支持计划项目(LJQ2011030)

摘　　要：当剪切带中存在二阶位移梯度或应变梯度时,研究了两种数字图像相关(DIC)方法在测量位移、应变及应变梯度中的表现。以基于梯度塑性理论的剪切带的位移解作为基础,通过Matlab仿射变换制作了具有不同平均剪切应变和应变梯度的虚拟剪切带。通过对其计算和分析得到了下列结果:当剪切带的平均剪切应变和应变梯度较高时,与只考虑一阶位移梯度的DIC方法相比,考虑二阶位移梯度的DIC方法优势明显,获得的位移、应变及应变梯度结果与理论解比较吻合,由于DIC方法测量的是平均应变,因此,剪切带中心的峰值应变将被低估;当剪切带的平均剪切应变和应变梯度较低时,剪切带中心的峰值应变可能被高估,受标准偏差的影响,考虑二阶位移梯度的DIC方法没有优势。基于上述研究结果,在单向压缩应力控制加载条件下,对砂样从开始加载至宏观裂纹出现之前变形过程中的3种应变场的4种结果进行了分析。由于应变不超过0.25,因而考虑二阶位移梯度的DIC方法的结果并无优势。In the existence of the second-order displacement gradient or strain gradient in a shear band, the differences between two kinds of digital image correlation （DIC） methods in measurements of the displacement, strain and strain gradient are investigated. Based on the theoretical solution of displacement in a shear band, which is based on gradient-dependent plasticity, fictitious shear bands with different averaged shear strains and strain gradients are generated using an affine transform in Matlab. The following results are obtained through calculation. When the averaged shear strain and corresponding gradient are higher in a shear band, compared with the DIC method only considering the first-order displacement gradient, the DIC method considering the second-order displacement gradient has obvious advantages and the calculated displacement, strain and strain gradient agree well with the theoretical solutions. However, the highest strain at the central region of the shear band is underestimated due to the fact that the measured strain is the averaged strain in DIC methods. When the averaged shear strain and corresponding gradient are lower, the highest strain in a shear band may be overestimated due to the influence of standard deviation. No advantage is found in the DIC method consideringthe second-order displacement gradient under this condition. Based on these results obtained, four kinds of results of three kinds of strain fields from the initial loading to pre-fracturing within a sand specimen are analyzed in uniaxial compression and stress-controlled loading. The maximum strain is found to be less than 0.25 and then the results obtained by the DIC method considering the second-order displacement gradient have no advantage.

关 键 词：剪切带 二阶位移梯度 砂样 数字图像相关方法 一阶位移梯度 仿射变换 梯度塑性理论 

分 类 号：TU451[建筑科学—岩土工程]