Nanoscale deformation measurement of microscale interconnection assemblies by a digital image correlation technique

The continuous miniaturization of microelectronic devices and interconnections demand more and more experimental strain/stress analysis of micro-?and nanoscale components for material characterization and structure reliability analysis. The digital image correlation (DIC) technique, with the aid of scanning probe microscopes, has become a very promising tool to meet this demand. In this study, an atomic force microscope (AFM) was used to scan and digitally image micro-interconnection assemblies in a micro-thermoelectric cooler. AFM images of the scan region of interest were obtained separately when the microelectronic device was operated before and after the cooling and heating stages. The AFM images were then used to obtain the in-plane deformation fields in the observed region of the micro-assembly. AFM image correlation is performed for nanoscale deformation analysis using the authors' AFM-DIC program. The results show that the observed region was subjected to cyclic strains when the device worked between its cooling and heating stages, and cyclic strain in the vertical direction was found to be a significant deformation mode. The thermally induced deformation behavior of the micro-assembly device was modeled by finite element analysis (FEA). Both thermal-electric analysis and thermal stress analysis were conducted on a 3D finite element model of the device. It is shown that the experimental results were able to validate the finite element analysis results.     

Measurement of resistance curves in the longitudinal failure of composites using digital image correlation

This paper presents a new methodology to measure the crack resistance curves associated with fiber-dominated failure modes in polymer–matrix composites. The crack resistance curves not only characterize the fracture toughness of the material, but are also the basis for the identification of the parameters of the softening laws used in the numerical simulation of fracture in composite materials. The proposed method is based on the identification of the crack tip location using Digital Image Correlation and the calculation of the J-integral directly from the test data using a simple expression derived for cross-ply composite laminates. It is shown that the results obtained using the proposed methodology yield crack resistance curves similar to those obtained using Finite Element based methods for compact tension carbon–epoxy specimens. However, it is also shown that, while the Digital Image Correlation based technique mitigates the problems resulting from Finite Element based data reduction schemes applied to compact compression tests, the delamination that accompanies the propagation of a kink-band renders compact compression test specimens unsuitable to measure resistance curves associated with fiber kinking.     

On image gradients in digital image correlation

In digital image correlation (DIC), the unknown displacement field is typically identified by minimizing the linearized form of the brightness conservation equation, while the minimization scheme also involves a linearization, yielding a two‐step linearization with four implicit assumptions. These assumptions become apparent by minimizing the non‐linear brightness conservation equation in a consistent mathematical setting, yielding a one‐step linearization allowing a thorough study of the DIC tangent operator. Through this analysis, eight different image gradient operators are defined, and the impact of these alternative image gradients on the accuracy, efficiency, and initial guess robustness is discussed on the basis of a number of academic examples and representative test cases. The main conclusion is that for most cases, the image gradient most common in literature is recommended, except for cases with: (1) large rotations; (2) initial guess instabilities; and (3) costly iterations due to other reasons (e.g., integrated DIC), where a large deformation corrected mixed gradient is recommended instead. Copyright © 2015 John Wiley & Sons, Ltd.     

基于数字图像相关方法的气凝胶复合材料各向异性热变形测量

在热防护材料及结构高温力学性能研究中,测量其在热载荷与机械载荷作用下产生的变形是重要且基础的工作。基于数字图像相关方法,建立了可实现800℃变形测量的非接触式测量系统。针对陶瓷纤维增强SiO_2气凝胶复合材料,从面外和面内两个材料方向,以25℃为参考温度,试验测量了材料加热至300~800℃范围内不同温度时产生的热变形。研究结果表明,在此试验系统基础上的变形测量方法可用来测量此类热防护材料的高温变形。陶瓷纤维增强SiO2气凝胶复合材料的高温热变形具有明显的各向异性,面外方向上表现为"收缩",面内方向上表现为"膨胀"。SiO_2气凝胶基体中的颗粒团聚以及增强纤维在面内方向上的铺层分布是导致热变形各向异性的主要原因。     

采用数字图像相关方法的莫来石纤维增强气凝胶复合材料力学试验

基于V型缺口试样双轨剪切法设计了面内剪切试验方案,开展了莫来石纤维增强气凝胶复合材料的室温面内剪切和弯曲性能试验,采用数字图像相关方法对试样表面的位移场和应变场进行测量,并分析了力学行为和破坏模式。结果表明:设计的试验方案可以在测试区域获得均匀的剪切应变场,适用于莫来石纤维增强气凝胶复合材料的面内剪切性能测试。试验获得的面内剪切模量和强度分别为248 MPa和0.95 MPa,弯曲模量和强度分别为294 MPa和2.08 MPa。面内剪切载荷下,试样的裂纹萌生于缺口尖端附近,并沿两缺口连线方向扩展。根据弯曲正应变场的分布特点,发现试样中性层与几何对称面不重合,验证了该材料拉压模量不同的性质。采用数字图像相关方法获得的中性层位置和理论计算值比较接近,相对误差在10%左右。     

动态断裂韧性实验中DIC技术应用研究

高速冲击动态断裂韧性的加载和测试技术一直是近年关注的热点,随着计算机和光学传感器的发展,采用数字图像相关方法测量材料的动态断裂韧性已成为重要选择。该文基于分离式Hopkinson压杆原理的加载技术,通过高速摄影机拍摄高速冲击下三点弯曲试样裂纹的起裂和扩展,运用数字图像相关技术分析裂尖场的散斑图像,计算得到相应的应变场变化,试样外表面处于平面应力状态,其裂尖应变场呈现"0"型,而非试样对称面所处于的平面应力状态下呈"8"型。结果表明,DIC技术可以应用于动态断裂韧性实验,也证明裂尖场粘贴的应变片测量试样起裂的有效性。     

基于数字图像相关的钢纤维增强水泥基复合材料的冲击损伤特性

本文采用数字图像相关（DIC）技术对钢纤维增强水泥基复合材料三点弯落球冲击试验过程中试件表面位移场和应变场进行计算与研究,基于开裂点附近位移变化确定初裂冲击次数,并对全场水平应变值进行统计分析,得到冲击过程的损伤程度因子（D_f）表征曲线,进一步探讨纤维掺量对试件弯曲冲击损伤的影响规律。试验结果表明：钢纤维的掺入对水泥基材料破坏次数的提高较初裂次数更明显;D_f曲线能够较好反映冲击荷载作用下试件弯曲冲击破坏各阶段;试件弯曲冲击损伤过程经历缓慢、加速、再缓慢三个阶段;纤维掺量越多,D_f曲线发展越缓慢,冲击损伤三阶段中的再缓慢阶段所占比例越大,即钢纤维增韧作用主要表现在三阶段损伤过程中的再缓慢阶段。     

Global and local coordinates in digital image correlation

Digital image correlation (DIC) is commonly used to measure specimen displacements by correlating an image of a specimen in an undeformed or reference configuration and a second image under load. To establish the correlation between the images, numerical techniques are used to locate an initially square image subset in a reference image. In this process, choosing appropriate coordinates is of fundamental importance to ensure accurate results. Both global and local coordinates can be used in shape functions. However, large rigid body rotations and deformations are accurately obtained by using global rather than local shape functions. In addition, points located after displacement may not be at an integer pixel distance from the original position. Hence subpixel displacement estimation methods such as interpolation or fitting of correlation coefficients are essential. A solution using the least-squares method is employed by choosing proper coordinates, and the feasibility of using local coordinates is demonstrated and validated with a mathematical model. Both simulated and experimental results show that the proper choice of coordinates does ensure the reliability and improve the accuracy of measurements in DIC.     

基于数字图像相关技术的木纤维/高密度聚乙烯复合材料界面力学行为

以木纤维/高密度聚乙烯(WF/HDPE)复合材料界面应变为研究对象,采用数字图像相关技术(DIC)探究WF(质量分数为10wt%~40wt%)及改性聚磷酸铵(mAPP)阻燃剂(质量分数为10wt%~25wt%)对WF/HDPE复合材料应变分布及传递的演变规律,并结合力学性能测试和SEM对其拉伸性能、冲击性能、界面结合进行分析。结果表明:随着WF添加量从10wt%增至30wt%,WF/HDPE复合材料应变传递较为平稳,由受力两端向复合材料轴中心均匀传递,当WF添加量为30wt%时,高应变在复合材料上约1/2区域得到了有效传递,此时,复合材料的拉伸强度和冲击强度分别达21.5 MPa和10.22 kJ/m2。但当WF添加量增加至40wt%时,WF/HDPE复合材料的拉伸承载端部出现应力集中,阻碍了其内部应变的均匀传递。mAPP阻燃剂加剧了WF与HDPE界面间的脱粘行为,削弱了WF与HDPE之间的机械啮合作用力。当mAPP阻燃剂添加量从10wt%增加至25wt%时,WF/HDPE复合材料开始出现多个分散的高应变区域,全场应变传递出现不规则分布。当mAPP阻燃剂添加量达25wt%时,WF/HDPE复合材料应变分布呈两极化趋势,导致复合材料的拉伸强度和冲击强度分别降低为15.5 MPa和5.49 kJ/m2。      

Spatiotemporal regularization for digital image correlation: Application to infrared camera frames

The spatiotemporal response of a stainless steel plate undergoing cyclic laser shock is recorded with an infrared camera, and digital image correlation is used to analyze both displacement and temperature fields. Two very challenging difficulties are addressed: (i) large gray‐level variations (due to temperature changes) and (ii) convection effects affecting images. To this aim, a spatiotemporal regularization is designed exploiting a numerical model of the test. The thermomechanical space‐time predictions are first processed through Karhunen‐Loève decomposition to extract dominant temporal and spatial modes. The temporal modes are then inserted in a spatiotemporal digital image correlation framework to estimate the experimental spatial modes that account for both gray‐level variations (and hence temperature) and displacement fields. It is shown that with only 3 modes, the full thermomechanical response of the material is captured. The temporal regularization issued from the model also allows the spurious effect of convection to be filtered out. Due to the drastic decrease in the number of degrees of freedom because of data reduction, the number of analyzed frames can be reduced from 50 down to 6 to capture the thermomechanical response, thereby leading to enhanced efficiency.     

AFM image reconstruction for deformation measurements by digital image correlation

The scanner drift of the atomic force microscope (AFM) is a great disadvantage to the application of digital image correlation to micro/nano-scale deformation measurements. This paper has addressed the image distortion induced by the scanner drifts and developed a method to reconstruct AFM images for the successful use of AFM image correlation. It?presents such a method, that is to generate a corrected image from two correlated AFM images scanned at the angle of 0° and 90° respectively. The proposed method has been validated by the zero-deformation test. A buckling test of a thin plate under AFM has also been demonstrated. The in-plane displacement field at the centre point of the buckling plate has been successfully characterized by the application of the image correlation technique on reconstructed AFM images.     

Buckling of fibers in fiber-reinforced composites

Elastic stability of fibers in fiber-reinforced composite materials subject to compressive loading is studied. The transversal buckling mode is considered, and two limiting cases, the dilute and non-dilute composites are analyzed. In the case of a non-dilute composite, the cylindrical model and the lubrication approximation are applied. The original problem is reduced to a problem of stability of a rod on elastic foundation. Through the solution of this problem a simple formula for the buckling load is obtained. In the case of a dilute composite, the solution of a problem of stability of a compressed rod in elastic plane is used. On the basis of the obtained solutions in two limiting cases the interpolation formulae are derived. These formulae describe buckling of fiber in the fiber-reinforced composite for any value of the fiber volume fraction. Comparison with known numerical and experimental results is carried out, and the sufficient accuracy of the derived formulae is demonstrated.     

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。      

Time‐resolved integrated digital image correlation

This paper discusses a method that provides the direct identification of constitutive model parameters by intimately integrating the finite element method (FEM) with digital image correlation (DIC), namely, directly connecting the experimentally obtained images for all time increments to the unknown material parameters. The problem is formulated as a single minimization problem that incorporates all the experimental data. It allows for precise specification of the unknowns, which can be, but are not limited to, the unknown material properties. The tight integration between FEM and DIC enables for identification while providing necessary regularization of the DIC procedure, making the method robust and noise insensitive. Through this approach, the versatility of the FE method is extended to the experimental realm, enhancing the analyses of existing experiments and opening new experimental opportunities. Copyright © 2015 John Wiley & Sons, Ltd.     

Error evaluation technique for three-dimensional digital image correlation

Three-dimensional (3D) digital image correlation (DIC) is one of the most popular techniques used in engineering for strain and deformation measurement. However, the error analysis of 3D DIC, especially which kind of parameters dominates the error of 3D coordinate reconstruction in any kind of configuration, is still under study. In this paper, a technique that can be used for error determination of reconstruction is presented. The influence from the system calibration and image correlation to the error is theoretically analyzed. From numerical experiments of one-dimensional line and two-dimensional plane, the evaluation procedure is validated to be flexible. A typical test with standard objects is also conducted. With this technique, once a 3D DIC system is set up and images of objects with speckles and calibration boards are recorded, the error of the configuration can be immediately evaluated. The standard deviation of every point in the world coordinate can be determined by statistical analysis.     

Extended digital image correlation with crack shape optimization

The methodology of eXtended finite element method is applied to the measurement of displacements through digital image correlation. An algorithm, initially based on a finite element decomposition of displacement fields, is extended to benefit from discontinuity and singular enrichments over a suited subset of elements. This allows one to measure irregular displacements encountered, say, in cracked solids, as demonstrated both in artificial examples and experimental case studies. Moreover, an optimization strategy for the support of the discontinuity enables one to adjust the crack path configuration to reduce the residual mismatch, and hence to be tailored automatically to a wavy or irregular crack path. Copyright © 2007 John Wiley & Sons, Ltd.     

Application of digital image correlation method for analysing crack variation of reinforced concrete beams

The Digital Image Correlation (DIC) method is a fast-growing emerging technology that provides a low-cost method for measuring the strain of an object. In this study, the feasibility of using this method to observe cracks developed in reinforced concrete beams will be explored so that a practical application can be proposed. The DIC method has been applied for analysing the field of surface displacement and strain; it is not applicable for measuring non-continuous field of displacement. However, if a singular point (i.e., crack points) can be considered as the area of concentrated strain by imitating the treatment of micro-cracks using the finite element method, the region of concentrated strain field based on analyses of digital images can be applied for determining the locations of cracks. Laboratory results show that cracks developed in reinforced cement beams can be observed with a good precision using the von Mises strain field, and that smaller grids lead to clearer crack images. In addition to identifying visible cracks, the DIC image analysis will enable researchers to identify minute cracks that are not visible to naked eyes. Additionally, the DIC method has more accuracy and precision than visual observation for analysing crack loadings so that earlier warnings can be realized before cracks develop in the specimen.