数字图像相关法测量局域变形场中形函数和模板尺寸的影响

数字图像相关法测量均匀变形场已被普遍接受, 其测量结果可与应变片测量结果比较. 然而, 在工程测量中, 针对局域变形场(应变高度集中, 如波特文-勒夏特利埃带、试件缺口附近和裂纹尖端等), 应变片受限于其尺寸, 其测量结果是接触面内的平均应变值. 此时, 采用数字图像相关法能够测量这些局域变形场. 但形函数和模板尺寸等计算参数对计算结果影响很大, 这也导致使用者很难判断计算结果的可靠性. 论文通过对合金拉伸实验获得的不同应变梯度的波特文-勒夏特利埃带和模拟生成的带的计算分析, 发掘了形函数和模板尺寸作用于计算结果的深层机制, 证明了二阶形函数比一阶形函数更适用于高度非均匀的局域变形场. 提出了在局域应变场测量中, 当一阶和二阶形函数计算结果的相对误差小于10% 时, 二阶形函数的结果是可靠的判据. 

INFLUENCE OF SHAPE FUNCTIONS AND TEMPLATE SIZE IN DIGITAL IMAGE CORRELATION METHOD FOR HIGHLY INHOMOGENEOUS DEFORMATIONS

Digital image correlation (DIC) method and its reliability and accuracy are commonly accepted in the measurements of affine deformations since it obtains comparable results with strain gauges. However, in engineering measurements, there are always substantial local deformations with high strain gradients such as the Portevin-Le Chatelier (PLC) bands, deformations near gaps and crack tips. In these situations, because the results within the contact areas are smoothed, strain gauges are restricted. Here DIC method can be employed to solve this problem. Problems that the calculation parameters (the order of shape functions, template size, etc.) seriously impact on the results and often make it difficult to get reliable results. In this paper, the deep mechanism that how the shape functions and the size of the templates impact on the accuracy of DIC results is discovered via analyzing PLC bands with different gradients in tensile tests and simulated bands. Second-order shape functions are more suitable than first-order shape functions to describe local deformations according to the simulation results. A gist is proposed that the results of second-order shape functions are reliable and accurate when the relative error between first- and second-order shape functions is less than 10%.