Abstract Surface shape and surface displacement measurements for non-planar specimens are obtainable using a stereo vision system with digital image correlation (StereoDIC). The surface measurements can be employed with appropriate local surface fitting methods to extract full-field estimates for surface strains on the specimen surface. Since StereoDIC provides a dense set of 3D surface position measurements, Xi, for the entire field of view in the stereo vision system, it has been shown that these measurements will have inherent variability. This variability will propagate into any optimally defined local surface representation, including the surface's local unit vectors, such as the surface normal, n; a surface tangent, t, and the cross product, b = n x t. Once the unit vectors are estimated at surface position, Y, the surface representation at this point can be used with the orthogonal unit vectors n, b and t to obtain a set of local surface strains at Y, with variability in the initial surface shape measurements propagating into variations in the strain estimates. In the enclosed work, the authors develop a set of equations for local strain variability due to inaccuracies in the local unit vectors n, b, and t. Results are reported for the case where the unit vectors are obtained assuming a local planar fit to an N x N set of measurements Xi, and strains are determined along the two estimated in-plane directions b and t. Simulations show that the resulting strains have variability that is a strong function of the estimated normal, n. Specifically, simulations show that the estimated local strains have errors that are a strong function of both the direction of nand variability in the estimated normal, n, relative to the stereo system bisector, even if the surface strains in the original directions are exact. Experimental studies for cylindrical specimens are shown to be in agreement with the trends predicted by the simulations, demonstrating the potential importance of surface normal estimation in experimental studies.

中文翻译：

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表面法向变化对 StereoDIC 中局部表面应变测量的影响

摘要 使用具有数字图像相关性的立体视觉系统 (StereoDIC) 可以获得非平面试样的表面形状和表面位移测量值。表面测量可以与适当的局部表面拟合方法一起使用，以提取试样表面表面应变的全场估计值。由于 StereoDIC 为立体视觉系统中的整个视场提供了一组密集的 3D 表面位置测量值 Xi，已经表明这些测量值将具有固有的可变性。这种可变性将传播到任何优化定义的局部表面表示中，包括表面的局部单位向量，例如表面法线，n；表面切线 t 和叉积 b = nx t。一旦单位向量在表面位置 Y 被估计，在这一点上的表面表示可以与正交单位向量 n、b 和 t 一起使用，以获得 Y 处的一组局部表面应变，初始表面形状测量值的可变性传播为应变估计值的变化。在所附的工作中，由于局部单位向量 n、b 和 t 的不准确，作者开发了一组用于局部应变变异性的方程。结果报告的情况是，假设对 N x N 组测量值 Xi 进行局部平面拟合而获得单位向量，并且沿两个估计的平面内方向 b 和 t 确定应变。模拟表明，由此产生的应变具有可变性，这是估计的正常值 n 的强函数。具体来说，模拟表明，即使原始方向的表面应变是精确的，估计的局部应变具有误差，这些误差是估计法线 n 的方向和可变性的强函数，相对于立体系统平分线。圆柱形试样的实验研究表明与模拟预测的趋势一致，证明了表面法线估计在实验研究中的潜在重要性。