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.     

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。     

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.     

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.     

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.     

板料焊接变形测量的数字图像相关法应用研究

针对板料焊接时温度场的极不均匀性导致应变场的复杂性,提出一种基于数字图像相关法的全场、全过程分析板料焊接变形情况的方法。首先,对板料表面进行预处理;然后,利用高速相机拍摄板料焊接及冷却自由变形的全过程,通过数字图像相关技术计算所有图像中变形点的位移;最后,直观地获得板料焊接全场的变形规律。通过对Q235钢板进行氩弧堆焊实验表明,将一种新的3D-DIC技术应用于在线焊接变形中,能得到试件表面在整个焊接过程的全场变形数据,并且在高温焊缝区获得准确的变形规律。该方法攻克长期以来不能实时测量高温焊缝处应变的难题,为数值模拟理论提供验证手段,对揭示焊接变形机理、解决矫正变形问题等具有重要意义。     

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.     

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.     

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.     

Application of digital image analysis to strain measurement at elevated temperature

Digital imaging techniques are applied to the measurement of surface displacement and strain at elevated temperatures. A simple surface preparation using high temperature paint together with a CCD video camera for digital imaging serve as the basis for the measurements. Mathemetical correlation of the surface intensity pattern between reference and deformed states is used to measure local surface deformation. The method is non-contacting and full field. Displacement and strain measurements have been made at temperatures to 600°. Coefficients of thermal expansion of three metals have been measured using this technique and compared to strain gauge and handbook values. Limitations and potential extensions of the method are discussed.     

Equivalence of digital image correlation criteria for pattern matching

In digital image correlation (DIC), to obtain the displacements of each point of interest, a correlation criterion must be predefined to evaluate the similarity between the reference subset and the target subset. The correlation criterion is of fundamental importance in DIC, and various correlation criteria have been designed and used in literature. However, little research has been carried out to investigate their relations. In this paper, we first provide a comprehensive overview of various correlation criteria used in DIC. Then we focus on three robust and most widely used correlation criteria, i.e., a zero-mean normalized cross-correlation (ZNCC) criterion, a zero-mean normalized sum of squared difference (ZNSSD) criterion, and a parametric sum of squared difference (PSSD(ab)) criterion with two additional unknown parameters, since they are insensitive to the scale and offset changes of the target subset intensity and have been highly recommended for practical use in literature. The three correlation criteria are analyzed to establish their transversal relationships, and the theoretical analyses clearly indicate that the three correlation criteria are actually equivalent, which elegantly unifies these correlation criteria for pattern matching. Finally, the equivalence of these correlation criteria is further validated by numerical simulation and actual experiment.     

On the mechanical behavior of fiber-reinforced composites

In this paper, the derivation of the state potential is presented to model the mechanical behavior of fiber-reinforced composites. It allows matrixcracking, interfacial debonding and sliding to be accounted for in the framework of Continuum Damage Mechanics. An application is performed on a unidirectional SiC/SiC composite.     

Determination of three-dimensional displacement using two-dimensional digital image correlation

A novel method that uses a two-dimensional (2D) digital image correlation (DIC) based on a single CCD camera to measure three-dimensional (3D) displacement and deformation is proposed. Rigid-body displacement in 3D space consists of both in-plane and out-of-plane components. The presence of an in-plane displacement component results in a shift of the center of the image displacement vector, while the slope of the image displacement vector is related to the out-of-plane displacement component. Global DIC is employed to determine the displaced position of each point on an object based on a linear distribution characteristic of the displacement vector. Speckle images with deformation introduced by 3D displacement are generated to demonstrate the feasibility of the proposed method. In the 3D rigid-body displacement, both in-plane and out-of-plane displacement components are separated by determining the intercept and slope of the image displacement vector. In the 3D deformation, a zero order displacement (pure rigid-body displacement) mode is assumed in a small subset of pixels. Simulated and experimental results demonstrate that both in-plane and out-of-plane displacements can be accurately retrieved using the proposed method.     

Estimation of stress intensity factor by digital image correlation

A method of determining stress intensity factors using digital image correlation is presented. The experimental and analytical method is described with results for different specimen geometries given. Effects of using higher order terms in the series expansion are also investigated and presented.     

基于数字图像相关方法的CFRP层合板高温压缩性能实验研究

高温压缩性能是复合材料结构设计关键的力学参数,但是传统技术手段难以对其进行有效测量.通过搭建基于数字图像相关方法的高温实验系统,开展了复合材料的高温压缩实验,获得了130℃环境下CCF300/5228A碳纤维增强复合材料层合板0°和90°压缩性能、应力-应变曲线以及不同载荷情况下轴向应变分布及演化,并且与室温实验结果进行了对比.进一步通过扫描电镜进行了压缩试样的断口分析,结合实验结果,探讨了高温和铺层形式对压缩性能的影响.最后,通过实验验证了高温实验系统及相应实验方法的可行性和可靠性.结果表明:130℃环境下0°与90°压缩强度保持率分别为70.5％和62.6％,压缩模量保持率分别为88.0％和75.4％,说明由基体控制层合板的强度和模量对高温更敏感.