改进扩展数字图像相关方法及其应用研究
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摘要
数字图像相关方法是实验力学领域中最常用的测试方法之一，具有广阔的工程应用前景。扩展数字图像相关方法的形函数选取扩展有限元位移模式，一定程度上突破了传统数字图像相关方法不适用于不连续变形场测试的局限性，扩大了方法的适用范围。本文的主要研究内容就是对扩展数字图像相关方法的算法进行改进，以进一步提高方法精度，扩大其工程应用范围。
本文提出的改进扩展数字图像相关方法主要对方法进行了如下三点优化和改进：首先，提出了单单元的相关方案和核区的数据后处理方法，与整体相关方案相比，本文方法可有效减少子区间误差传递，一定程度上提高方法测试精度。其次，提出了环形模板的整像素位移搜索方法，及改进扩展数字图像相关方法中Newton-Raphson算法(N-R算法)迭代初值的选择方案。利用环形模板搜索得到的整像素位移为N-R算法提供迭代初值，减少了迭代不收敛现象的出现。另外，由于环形模板具有旋转不变性，而双线性位移模式又能完全描述刚体转动，因而，结合环形模板整像素位移搜索的改进扩展数字图像相关方法可以测试含任意转角的变形。再次，提出了子区优选法，利用相关系数的值来确定最优子区的尺寸和位置，使材料弹性常数、裂纹尖端变形场等力学参量的测试更精确。
本文利用模拟散斑图及实验对改进扩展数字图像相关方法的测试精度进行分析。对于单单元相关方案，单个子区变形场的测试精度即表明了方法的测试精度。精度分析结果表明：当子区所选形函数的位移假设能够完全描述子区真实变形时，大的子区可以减少随机误差进而提高测试精度，且具有较少节点的单元类型对应较高的测试精度；形函数选取裂纹贯穿单元位移模式来测试裂纹贯穿子区变形场时，其测试精度低于分别利用基于常规单元位移模式的改进扩展数字图像相关方法测试裂纹两侧的连续变形场；基于四节点矩形单元位移假设的改进扩展数字图像相关方法测试符合其变形假设的位移场时，最大绝对误差出现在节点处，且当给定位移接近整像素或半像素时，测试误差较小。
最终将本文提出的改进扩展数字图像相关方法应用到工程实际问题的测量中：测试了手机导光板的弹性常数；分析了纸浆模塑托盘跌落试验中的弹塑性变形；测试了聚氨酯试件的大挠度变形及挠曲线；测试了金属材料的裂纹区域变形场；测试了聚碳酸酯材料的平面应变断裂韧性；分析了手机液晶面板的弯曲破坏行为。
Digital image correlation (DIC) method is one of the most commonly used testmethods in experimental mechanics. It proves to be a very promising test method forengineering application. Standard DIC is not applicable to measure the discontinuousdeformation field directly. However, the displacement mode of extended finiteelement method (FEM), which is chosen as the shape function of extended digitalimage correlation (X-DIC) method, could break the application limitations of standardDIC in the discontinuous deformation field measurement. The main content of thispaper is to improve the algorithm of X-DIC, with the aim to improve themeasurement accuracy of X-DIC and enlarge its engineering application scales.
This paper improved and optimized X-DIC method in three aspects. Firstly,single-element correlation scheme and core area method for post-processing ofmeasured results are proposed. Compared to the integral correlation scheme, theproposed method could reduce the error transfer between the subset effectively andimprove the measurement accuracy to some extent. Secondly, ring template isproposed for estimating the integer pixels displacement. And the scheme of the initialvalue selection for the Newton-Raphson iterative method of improved X-DIC is alsoproposed. The above-mentioned work could reduce the non-convergence phenomenonin the iterative procedure. What’s more, the ring template possesses the rotationinvariance and the bi-linear displacement hypothesis could describe the rigid bodyrotation completely, which make improved X-DIC could measure the deformationincluding rigid body rotation with arbitrary angle. Thirdly, the selection scheme of theoptimum subset is proposed as well. Correlation coefficient is used to determine thesize and the location of the optimum subset, which makes the measurement of theelastic constants and the deformation of the crack tip and other mechanical parameterswith higher accuracy.
Simulated images and experiments are used to analysis the measurementaccuracy of improved X-DIC. For single-element correlation scheme, themeasurement accuracy of single subset could represent the measurement accuracy ofimproved X-DIC. Some conclusions are reached through the accuracy analysis: if thedisplacement hypothesis of the shape function could describe the actual deformation of the subset completely, the subset with large size could reduce the random error andimprove the measurement accuracy, and subset with fewer nodes would get highermeasurement accuracy; when the displacement mode of the cracked element is chosenfor the shape function to measure the discontinuous deformation, the measurementaccuracy is lower than that of using conventional element to measure the deformationfield on each side of the crack respectively; when improved X-DIC based on thefour-node quadrilateral element displacement hypothesis is used to measure thedeformation which is in accordance with this hypothesis, the maximum absolute errorwill be located on the node of the subset; and as the given displacement approachesthe integer pixels or half pixels, the measurement error gets minor.
At last, improved X-DIC is used to solve the practical engineering problems: theelastic constants of the light guide plate of mobile phone are measured; theelastic-plastic deformation of the molded pulp pallet in the dropping test isinvestigated; large deflection deformation of the polyurethane specimen is measured;the deformation in the region near the crack of the metal specimen is measured; theplane strain fracture toughness of polycarbonate is measured; and the bendingdestruction behavior of the liquid crystal faceplate used for mobile phone is studied.
本文提出的改进扩展数字图像相关方法主要对方法进行了如下三点优化和改进：首先，提出了单单元的相关方案和核区的数据后处理方法，与整体相关方案相比，本文方法可有效减少子区间误差传递，一定程度上提高方法测试精度。其次，提出了环形模板的整像素位移搜索方法，及改进扩展数字图像相关方法中Newton-Raphson算法(N-R算法)迭代初值的选择方案。利用环形模板搜索得到的整像素位移为N-R算法提供迭代初值，减少了迭代不收敛现象的出现。另外，由于环形模板具有旋转不变性，而双线性位移模式又能完全描述刚体转动，因而，结合环形模板整像素位移搜索的改进扩展数字图像相关方法可以测试含任意转角的变形。再次，提出了子区优选法，利用相关系数的值来确定最优子区的尺寸和位置，使材料弹性常数、裂纹尖端变形场等力学参量的测试更精确。
本文利用模拟散斑图及实验对改进扩展数字图像相关方法的测试精度进行分析。对于单单元相关方案，单个子区变形场的测试精度即表明了方法的测试精度。精度分析结果表明：当子区所选形函数的位移假设能够完全描述子区真实变形时，大的子区可以减少随机误差进而提高测试精度，且具有较少节点的单元类型对应较高的测试精度；形函数选取裂纹贯穿单元位移模式来测试裂纹贯穿子区变形场时，其测试精度低于分别利用基于常规单元位移模式的改进扩展数字图像相关方法测试裂纹两侧的连续变形场；基于四节点矩形单元位移假设的改进扩展数字图像相关方法测试符合其变形假设的位移场时，最大绝对误差出现在节点处，且当给定位移接近整像素或半像素时，测试误差较小。
最终将本文提出的改进扩展数字图像相关方法应用到工程实际问题的测量中：测试了手机导光板的弹性常数；分析了纸浆模塑托盘跌落试验中的弹塑性变形；测试了聚氨酯试件的大挠度变形及挠曲线；测试了金属材料的裂纹区域变形场；测试了聚碳酸酯材料的平面应变断裂韧性；分析了手机液晶面板的弯曲破坏行为。
Digital image correlation (DIC) method is one of the most commonly used testmethods in experimental mechanics. It proves to be a very promising test method forengineering application. Standard DIC is not applicable to measure the discontinuousdeformation field directly. However, the displacement mode of extended finiteelement method (FEM), which is chosen as the shape function of extended digitalimage correlation (X-DIC) method, could break the application limitations of standardDIC in the discontinuous deformation field measurement. The main content of thispaper is to improve the algorithm of X-DIC, with the aim to improve themeasurement accuracy of X-DIC and enlarge its engineering application scales.
This paper improved and optimized X-DIC method in three aspects. Firstly,single-element correlation scheme and core area method for post-processing ofmeasured results are proposed. Compared to the integral correlation scheme, theproposed method could reduce the error transfer between the subset effectively andimprove the measurement accuracy to some extent. Secondly, ring template isproposed for estimating the integer pixels displacement. And the scheme of the initialvalue selection for the Newton-Raphson iterative method of improved X-DIC is alsoproposed. The above-mentioned work could reduce the non-convergence phenomenonin the iterative procedure. What’s more, the ring template possesses the rotationinvariance and the bi-linear displacement hypothesis could describe the rigid bodyrotation completely, which make improved X-DIC could measure the deformationincluding rigid body rotation with arbitrary angle. Thirdly, the selection scheme of theoptimum subset is proposed as well. Correlation coefficient is used to determine thesize and the location of the optimum subset, which makes the measurement of theelastic constants and the deformation of the crack tip and other mechanical parameterswith higher accuracy.
Simulated images and experiments are used to analysis the measurementaccuracy of improved X-DIC. For single-element correlation scheme, themeasurement accuracy of single subset could represent the measurement accuracy ofimproved X-DIC. Some conclusions are reached through the accuracy analysis: if thedisplacement hypothesis of the shape function could describe the actual deformation of the subset completely, the subset with large size could reduce the random error andimprove the measurement accuracy, and subset with fewer nodes would get highermeasurement accuracy; when the displacement mode of the cracked element is chosenfor the shape function to measure the discontinuous deformation, the measurementaccuracy is lower than that of using conventional element to measure the deformationfield on each side of the crack respectively; when improved X-DIC based on thefour-node quadrilateral element displacement hypothesis is used to measure thedeformation which is in accordance with this hypothesis, the maximum absolute errorwill be located on the node of the subset; and as the given displacement approachesthe integer pixels or half pixels, the measurement error gets minor.
At last, improved X-DIC is used to solve the practical engineering problems: theelastic constants of the light guide plate of mobile phone are measured; theelastic-plastic deformation of the molded pulp pallet in the dropping test isinvestigated; large deflection deformation of the polyurethane specimen is measured;the deformation in the region near the crack of the metal specimen is measured; theplane strain fracture toughness of polycarbonate is measured; and the bendingdestruction behavior of the liquid crystal faceplate used for mobile phone is studied.
引文
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