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

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。     

基于局部位移场最小二乘拟合数字图像相关方法的剪切带应变测量

采用局部位移场最小二乘拟合数字图像相关方法测量了虚拟剪切带的应变,并将测量结果与中心差分方法的结果和理论解进行了对比,主要研究了计算窗口尺寸和子区尺寸的影响。研究发现:当子区尺寸较小且应变计算窗口尺寸较大时,局部位移场最小二乘拟合数字图像相关方法的测量结果接近于理论解;对于测量单轴压缩条件下低液限黏土试样破坏过程中的应变场,局部位移场最小二乘拟合方法的测量结果比中心差分方法测量结果更准确,有助于对剪切带应变的准确测量。     

基于环绕测点子区分割的数字图像相关方法剪切带宽度测量研究

提出了一种致力于改善狭窄、高应变梯度剪切带宽度测量精度的数字图像相关方法.通过对测点的原始子区的有限分割,使后代子区环绕在测点周围,以使一些后代子区位于简单变形区域,进而以最佳后代子区的结果作为测点结果.通过对比提出方法和粗-细方法的虚拟剪切带宽度测量结果,验证了提出方法的有效性,并从理论上分析了剪切带宽度测量误差.研...     

较大塑性变形下纳晶镍剪切带的演化模型

较大塑性变形下,采用TEM原位拉伸实验揭示了纳晶镍内剪切带演化的微观机制,优化了微观力学模型。结果表明:在纳米尺度范围内,随着晶粒尺寸的增加,应变软化的趋势越来越明显,剪切带宽度也随着增加;晶粒尺寸降低将导致纳晶材料中剪切带的产生提前;内部特征长度的值随着晶粒尺寸的增加呈现先增加后下降的特点;剪切带内的塑性应变分布为:在剪切带两个边界处应变为零,在剪切带中央剪切塑性应变达到最大值。     

较大塑性变形下纳晶镍剪切带的演化模型EI北大核心CSCD

较大塑性变形下,采用TEM原位拉伸实验揭示了纳晶镍内剪切带演化的微观机制,优化了微观力学模型。结果表明:在纳米尺度范围内,随着晶粒尺寸的增加,应变软化的趋势越来越明显,剪切带宽度也随着增加;晶粒尺寸降低将导致纳晶材料中剪切带的产生提前;内部特征长度的值随着晶粒尺寸的增加呈现先增加后下降的特点;剪切带内的塑性应变分布为:在剪切带两个边界处应变为零,在剪切带中央剪切塑性应变达到最大值。     

考虑应变梯度及刚度劣化的剪切带局部变形分析

基于梯度塑性理论,研究了应变软化阶段的刚度劣化对剪切带内部的局部应变及相对剪切位移的影响。剪切带被看作一维剪切问题,本构关系为线弹性及线性应变软化。考虑刚度劣化后,剪切带的弹性应变由弹性剪切模量、损伤变量及残余剪切模量确定。剪切带的非局部总应变由双线性的本构关系确定。将非局部总应变减去弹性应变,可得剪切带的非局部塑性应变。剪切带非局部塑性应变与流动应力及损伤变量等参数有关,此关系即为在经典弹塑性理论框架之内的考虑刚度劣化的屈服函数。将二阶应变梯度项引入该函数,可得剪切带内部的局部塑性剪切应变及局部总剪切应变的分布规律。对局部塑性剪切应变积分,得到了局部塑性剪切位移。结果表明:考虑了刚度劣化后,剪切带内部的弹性剪切应变及位移增加,而局部塑性剪切应变及位移降低。若不考虑刚度劣化,理论结果可蜕化为以前的结果。理论结果与岩石局部变形的观测结果在定性是一致的。     

剪切压电陶瓷块微位移测量及非线性修正

通过搭建的剪切压电陶瓷块微位移测量系统,进行了5个不同目标电压的剪切压电陶瓷微位移测量实验,对实验数据分别进行二阶、三阶、四阶最小二乘拟合后进行非线性修正实验,其中采用三阶最小二乘拟合进行修正时效果最好,其位移1 050 nm行程时最大非线性误差为3 nm。对所得三阶最小二乘拟合多项式的系数进行样条插值拟合,从而实现对不同目标位移的非线性修正,其中位移900 nm行程时最大非线性误差为4 nm,仅为原始非线性误差的11%。     

基于Timoshenko梁理论的钢-混组合梁动力刚度矩阵法

基于Timoshenko梁理论提出了适用于分析钢-混组合梁自振特性的动力刚度矩阵法,该计算模型中考虑了钢-混结合面剪切滑移、剪切变形和转动惯量的综合影响。动力刚度矩阵推导过程中未引入近似位移场或力场,因此,计算结果是准确的。与其他Timoshenko梁模型最大的不同是假设混凝土子梁和钢梁分别具有独立的剪切角,这个假设更加符合组合梁的实际运动,因此,计算结果更加准确。与已发表文章中的试验梁频率计算结果作对比分析;并讨论了不同剪力键刚度、跨高比时,剪切变形和转动惯量对钢-混组合梁自振频率的影响。结果表明:相对于已有的Euler-Bernoulli组合梁、子梁转角相同假设的Timoshenko组合梁模型,文中计算方法具有更高的计算精度,尤其是对于高阶频率;频率越高、剪力键刚度越大或跨高比越小,Euler-Bernoulli组合梁模型计算结果误差越大;对于1阶、2阶和3阶频率,高跨比分别大于10、18和25后,Euler-Bernoulli组合梁模型计算结果误差小于5%。     

基于能量原理的岩样单轴压缩剪切破坏失稳判据

利用能量原理对倾斜的剪切带-带外弹性岩石构成的系统的稳定性进行了研究。单轴压缩岩样沿轴向的变形被分解为两部分,带外弹性岩石压缩引起的变形和剪切带错动引起的变形。后者与剪切带的相对剪切变形具有简单的几何关系。系统的总势能由剪切带的弹性及耗散势能和带外弹性岩石对剪切带所作的外力功构成。剪切带的弹性及耗散势能与剪切带的体积有关系。剪切带的尺寸由梯度塑性理论确定。将系统的总势能对相对剪切变形求一阶导数(等于零),得到了弹性岩石的平衡条件。将总势能对相对剪切变形求二阶导数(小于零),得到了系统的失稳判据。它综合反映了岩石材料弹性及应变软化阶段本构参数(弹性模量及软化模量)、剪切带之外弹性岩石的尺寸、剪切带的尺寸及系统的结构形式(剪切带倾角)对系统稳定性的影响。失稳判据比以往所得到的失稳判据更严格,更精确,更具有广泛意义。     

数字图像相关技术在复合材料加筋曲板压缩试验中的应用

对复合材料自动铺丝和手工铺丝两种T型加筋曲板进行了单轴压缩试验，采用基于数字图像相关技术(Digital image correlation, DIC)的三维光学测量方法对该型加筋曲板的局部屈曲及后屈曲波形进行实时监测，并与传统应变、位移测量结果进行了对比分析。试验结果表明:DIC能够准确捕捉整个试验过程中的位移场，使用DIC设备观测到的屈曲模态与应变片数据反映的波形具有良好的一致性；不同于传统测量方法，DIC能够准确捕捉蒙皮在后屈曲阶段的屈曲模态转换的全过程；利用DIC技术能够对试验不同时间节点(即不同载荷水平)的屈曲模态进行清晰、直观的观测，因而能够较准确地获得结构的屈曲载荷，该载荷与由应变-载荷曲线确定的屈曲载荷相比，误差小于5%。采用ABAQUS有限元软件对试验过程进行了数值仿真分析，并通过与试验结果的对比表明了计算结果、DIC测量结果与传统方法测量结果三者具有良好的一致性。      

Displacement Discontinuity or Complex Shape of Sample: Assessment of Accuracy and Adaptation of Local DIC Approach

In this paper, we study the impact of a complex shape of sample and the appearance of a displacement discontinuity on performances of measurement by local Digital Image Correlation (DIC). Both cases are modelled from synthetic images into two parts: one with a speckle field and another part without speckle or two parts with similar speckle fields but with different kinematics. The accuracy of displacement measurements assessed for DIC subsets crossing the boundary between the two parts is lower than the one obtained without discontinuity and justifies adapting DIC method. A new local DIC process is presented in detail. It is an alternative way able to take into account any shape of sample and several curved lines of discontinuity in the same subset. Two experimental examples are presented: displacement and strain fields obtained by DIC and adapted DIC are compared. We can conclude that it is possible to lead a mechanical analysis until the limits of the sample and even during the appearance and the propagation of a crack.     

Assessment of Digital Image Correlation Measurement Accuracy in the Ultimate Error Regime: Main Results of a Collaborative Benchmark

We report on the main results of a collaborative work devoted to the study of the uncertainties associated with Digital image correlation techniques (DIC). More specifically, the dependence of displacement measurement uncertainties with both image characteristics and DIC parameters is emphasised. A previous work [Bornert et al. (2009) Assessment of digital image correlation measurement errors: methodology and results. Exp. Mech. 49, 353–370] dedicated to situations with spatially fluctuating displacement fields demonstrated the existence of an ‘ultimate error’ regime, insensitive to the mismatch between the shape function and the real displacement field. The present work is focused on this ultimate error. To ensure that there is no mismatch error, synthetic images of in‐plane rigid body translation have been analysed. Several DIC softwares developed by or in use in the French community have been used to explore the effects of a large number of settings. The discrepancies between DIC evaluated displacements and prescribed ones have been statistically analysed in terms of random errors and systematic bias, in correlation with the fractional part τ of the displacement component expressed in pixels. Main results are as follows: (i) bias amplitude is almost always insensitive to subset size, (ii) standard deviation of random error increases with noise level and decreases with subset size and (iii) DIC formulations can be split up into two main families regarding bias sensitivity to noise. For the first one, bias amplitude increases with noise while it remains nearly constant for the second one. In addition, for the first family, a strong dependence of random error with τ is observed for noisy images.     

Two‐scale shear band evolution by local partition of unity

We introduce a methodology to model shear band evolution in the quasi‐static regime using the extended finite element method. We enrich the finite element polynomial displacement field with a fine scale function, which models the high displacement gradient in the shear band. For this purpose we use a local partition of unity and a parameterized displacement enrichment based on closed form solutions for one‐dimensional shear bands. A stabilized consistent penalty method is used to circumvent locking in the regularized elasto‐viscoplastic plane‐strain regime and to guarantee element stability. The loss of stability of the boundary value problem is used as an indicator of shear band initiation point and direction. Shear band development examples are shown, illustrating the capabilities of the method to track shear band evolution and strains as high as 1000%. Copyright © 2005 John Wiley & Sons, Ltd.     

周期复合材料压电问题的双尺度数值模拟

利用渐近展开的方法对具有一般周期结构的复合材料中描述压电现象的电势与位移建立了二阶双尺度渐近展开式及边界层解, 得到了局部单胞内电场与位移场的相互耦合关系, 并给出了复合材料中电势与位移的双尺度结合边界层的有限元计算方法。数值算例表明了该方法的可行性与高效性。      

Theoretical Analysis on the Measurement Errors of Local 2D DIC: Part II Assessment of Strain Errors of the Local Smoothing Method–Approaching an Answer to the Overlap Question

In this paper, the strain error of subset‐based two‐dimensional digital image correlation (DIC) is theoretically derived. Analytical solutions are provided to estimate the strain error. A dimensionless factor is proposed, namely the overlap magnifier, which reveals the dependency of the strain error on the DIC regularisation parameters, that is, subset size, step size and strain window size. The derived equations are validated numerically and experimentally. The estimated random strain error is in good accordance with the experimental data. The proposed derivation can be readily extended to stereo DIC.     

Shear banding and strain softening in plane strain extension: physical modelling

Localization of deformation in systems of shear bands or normal faults, respectively, as a consequence of extensional loading can be observed on a wide range of spatial scales in soil and rock formations. A series of plane strain model experiments was achieved in natural (1 g) and increased (ng) gravity field (geotechnical centrifuge) with dry and moist sand as well as with dry and moist sand-clay mixtures. In these experiments, the geometry of the shear bands (inclination, width, spacing, sharpness) was detected by means of the digital image correlation (DIC) technique. Comparison with existing analytical approaches for the determination of the spacing of shear bands is presented briefly. The stress-strain behaviour of the materials was determined in a new biaxial test device, which allows for the performance of biaxial compression and extension tests. The evaluation focuses on the strain softening gradient, which is seen as a key parameter in the explanation of shear band spacing.     

Digital Image Correlation and Noise‐filtering Approach for the Cracking Assessment of Massive Reinforced Concrete Structures

This paper describes the use of Digital Image Correlation (DIC) techniques for the cracking assessment of reinforced concrete (RC) massive beams and walls. DIC is known to provide accurate and detailed information on displacement and strain fields. Non‐contact measurements can be used to evaluate concrete cracking of destructive tests carried out on a wide range of specimen scales. When applied to large RC structures tested outdoors or in difficultly controllable conditions, DIC‐based methods may lead to erroneous results. In this study a post‐processing procedure is presented to cope with noisy full‐field measurements. The proposed cracking assessment approach is validated on a large experimental campaign. Four points bending tests are carried out on RC beams: firstly on full‐scale rectangular beams and then on mock‐ups scaled down by 1/3. In addition, fours RC walls are tested under in‐plane cyclic shear up to failure. Digital images taken throughout the tests are processed by DIC techniques to provide in‐plane displacement and strain fields. Full‐field measurements are post‐processed by the noise‐filtering technique and the cracks patterns are identified. Crack widths are measured and compared with measurements obtained from conventional point‐based sensors (linear variable differential transformer LVDT and fibre‐optic FO transducers). The proposed DIC‐based post‐processing provides accurate estimation of cracks width for most of the tests. The analyses carried out on the two groups of RC beams show a scale‐effect on the cracks width.