Diffraction Assisted Image Correlation: A Novel Method for Measuring Three-Dimensional Deformation using Two-Dimensional Digital Image Correlation

Digital Image Correlation (DIC) provides a full-field non-contact optical method for accurate deformation measurement of materials, devices and structures. The measurement of three-dimensional (3D) deformation using DIC in general requires imaging with two cameras and a 3D-DIC code. In the present work, a new experimental technique, namely, Diffraction Assisted Image Correlation (DAIC) for 3D displacement measurement using a single camera and 2D-DIC algorithm is presented. A transmission diffraction grating is placed between the specimen and the camera, resulting in multiple images which are then used to obtain apparent in-plane displacements using 2D-DIC. The true in-plane and out-of-plane displacements of the specimen are obtained from the apparent in-plane displacements and the diffraction angle of the grating. The validity and accuracy of the DAIC method are demonstrated through 3D displacement measurement of a small thin membrane. This technique provides new avenues for performing 3D deformation measurements at small length scales and/or dynamic loading conditions.     

Spherical indentation analysis of stress relaxation for thin film viscoelastic materials

The mechanical testing of thin layers of soft materials is an important but difficult task. Spherical indentation provides a convenient method to ascertain material properties whilst minimising damage to the material by allowing testing to take place in situ. However, measurement of the viscoelastic properties of these soft materials is hindered by the absence of a convenient yet accurate model which takes into account the thickness of the material and the effects of the underlying substrate. To this end, the spherical indentation of a thin layer of viscoelastic solid material is analysed. It is assumed that the transient mechanical properties of the material can be described by the generalised standard linear solid model. This model is incorporated into the theory and then solved for the special case of a stress relaxation experiment taking into account the finite ramp time experienced in real experiments. An expression for the force as a function of the viscoelastic properties, layer thickness and indentation depth is given. The theory is then fitted to experimental data for the spherical indentation of poly(dimethyl)siloxane mixed with its curing agent to the ratios of 5:1, 10:1 and 20:1 in order to ascertain its transient shear moduli and relaxation time constants. It is shown that the theory correctly accounts for the effect of the underlying substrate and allows for the accurate measurement of the viscoelastic properties of thin layers of soft materials.     

Three-dimensional Full-field Measurements of Large Deformations in Soft Materials Using Confocal Microscopy and Digital Volume Correlation

A three-dimensional (3-D) full-field measurement technique was developed for measuring large deformations in optically transparent soft materials. The technique utilizes a digital volume correlation (DVC) algorithm to track motions of subvolumes within 3-D images obtained using fluorescence confocal microscopy. In order to extend the strain measurement capability to the large deformation regime (>5%), a stretch-correlation algorithm was developed and implemented into the Fast Fourier Transform (FFT)-based DVC algorithm. The stretch-correlation algorithm uses a logarithmic coordinate transformation to convert the stretch-correlation problem into a translational correlation problem under the assumption of small rotation and shear. Estimates of the measurement precision are provided by stationary and translation tests. The proposed measurement technique was used to measure large deformations in a transparent agarose gel sample embedded with fluorescent particles under uniaxial compression. The technique was also employed to measure non-uniform deformation fields near a hard spherical inclusion under far-field uniaxial compression. Introduction of the stretch-correlation algorithm greatly improved the strain measurement accuracy by providing better precision especially under large deformation. Also, the deconvolution of confocal images improved the accuracy of the measurement in the direction of the optical axis. These results shows that the proposed technique is well-suited for investigating cell-matrix mechanical interactions as well as for obtaining local constitutive properties of soft biological materials including tissues in 3-D.     

Effects of large deformation and material nonlinearity on spherical indentation of hyperelastic soft materials

Up to now, the indentation of hyperelastic soft materials has not been completely understood. In this paper, the spherical indentation on hyperelastic soft solids was systematically investigated through theoretical analysis and finite element method (FEM). The validation and application of the Hertzian load-displacement relation for indentation of hyperelastic soft materials were clarified, the effects of large deformation and material nonlinearity on spherical indentation of hyperelastic soft materials were analyzed and discussed. It was found that the complicated indentation behaviors of hyperelastic soft solids mainly depended on the coupling interactions of large deformation and material nonlinearity. Besides, we proposed two new nonlinear elastic contact models to separate the effects of large deformation and material nonlinearity on spherical indentation responses of hyperelastic soft solids. Our efforts might help to enhance the understanding of hyperelastic indentation problems and provided necessary instructions for the mechanical characterization of hyperelastic soft materials.     

Sampling Moiré Method for Accurate Small Deformation Distribution Measurement

In this paper, a novel accurate deformation distribution measurement technique by using sampling moiré method is proposed. The basic principle and an experimental result of a steel beam in symmetric three-point bending are reported. In this method, the measurement area of a target is attached with an adhesive tape of a known pitch grating firstly. An ordinary CCD camera is installed on a fixed point to record the image during deformation. The captured image is analyzed by performing easy image processing, i.e., thinning-out and linear interpolation, to obtain the multiple phase-shifted moiré patterns. Then, the phase distribution of the moiré pattern can be calculated using phase-shifting method. Finally, the deformation distribution is calculated by the grating pitch times the phase difference of before deformation and after deformation. The experimental results in symmetric three-point bending test show that the displacement of the steel beam at loading point agree well with those obtained by an accurate displacement sensor. The average error of displacement measurement is less than 4 μm when 2 mm grating pitch is used, and it corresponds to 1/500 of the grating pitch accuracy. This indicates that noncontact deformation distribution measurement is possible by simple and easy procedure with high accuracy, high speed, and low cost for the structural evaluation of infrastructures.     

基于SHPB的球形压痕实验方法

提出一种基于霍普金森压杆装置的动态球形压痕实验方法,通过将硬质合金小球置于2个试件中间,实现加载过程中2个试件的同时压入,以得到准确的压痕力与位移的关系。利用有限元软件ABAQUS/Explicit对该实验方法进行了数值模拟,从实验结果的可行性、准确性等方面,对新实验方法与传统的动态压痕实验方法进行了比较;采用新方法对铝合金材料进行了实验,并得到了压入力-位移曲线等关系。研究结果表明:采用新实验方法能得到较准确的结果,能较真实地描述压痕过程。     

二维材料力学行为的压痕测试

准确了解二维材料的力学性能对于推动其应用具有重要意义, 无基底压痕技术是目前最广泛采用的二维材料力学性能测试方法之一, 本文综述了二维材料压痕研究的最新进展以及所面临的问题, 并对将来的研究工作进行了展望.无基底压痕技术是将二维材料转移到带有沟槽或柱形孔的基底上, 制备二维材料"梁"和"鼓"模型, 然后利用原子力显微镜测量其在压针作用下的载荷--位移关系, 最后通过基于连续介质薄膜导出的压痕响应分析模型拟合实验结果, 估算出二维材料的弹性模量和本征强度.由于二维材料的厚度远小于连续介质薄膜, 来自于压头以及基底孔侧壁的范德华力对二维材料的压痕响应具有显著影响, 造成二维材料与传统压痕分析模型中的基本假设不符, 导致不能准确预测二维材料的弹性模量; 另外, 由于传统压痕模型无法准确描述二维材料在大变形下的非线性行为, 以及由缺陷等引起的应力集中, 导致由压痕测试表征的二维材料(特别是多晶二维材料)本征强度具有较大的偏差. 因此, 一方面需要正确了解由压痕技术获得的二维材料力学性能, 另一方面还需对目前的研究方法做进一步的改进和完善.      

Indentation tests investigation of mechanical behavior of two-dimensional materials

准确了解二维材料的力学性能对于推动其应用具有重要意义, 无基底压痕技术是目前最广泛采用的二维材料力学性能测试方法之一, 本文综述了二维材料压痕研究的最新进展以及所面临的问题, 并对将来的研究工作进行了展望.无基底压痕技术是将二维材料转移到带有沟槽或柱形孔的基底上, 制备二维材料"梁"和"鼓"模型, 然后利用原子力显微镜测量其在压针作用下的载荷--位移关系, 最后通过基于连续介质薄膜导出的压痕响应分析模型拟合实验结果, 估算出二维材料的弹性模量和本征强度.由于二维材料的厚度远小于连续介质薄膜, 来自于压头以及基底孔侧壁的范德华力对二维材料的压痕响应具有显著影响, 造成二维材料与传统压痕分析模型中的基本假设不符, 导致不能准确预测二维材料的弹性模量; 另外, 由于传统压痕模型无法准确描述二维材料在大变形下的非线性行为, 以及由缺陷等引起的应力集中, 导致由压痕测试表征的二维材料(特别是多晶二维材料)本征强度具有较大的偏差. 因此, 一方面需要正确了解由压痕技术获得的二维材料力学性能, 另一方面还需对目前的研究方法做进一步的改进和完善.     

软材料接触力学问题的实验研究

针对硫化硅橡胶在刚性压头作用下的大变形接触问题,研究了橡胶类软材料接触区区域变形场的实验测量技术。为了研究硫化硅橡胶与刚性体在试件内部接触的大变形问题,本文提出了一种体内数字栅云纹实验技术,给出了该技术的原理和实现方法。然后运用数字图像处理方法得到了橡胶材料大变形位移u场、v场,并结合橡胶材料在压头作用下的理论分区模型,分析了软材料接触区域的大变形场,讨论了接触区域的变形分区规律,并初步给出了接触区域应变计算方法。     

Centrosymmetric 3D Deformation Measurement using Grid Method with a Single-Camera

This study proposes an effective method to measure centrosymmetric 3D static and dynamic deformations from the microscale to macroscale using grid method with a single camera. The camera was tilted at a particular angle and used to observe specimen grids in order to acquire coupling fields of both in-plane and out-of-plane displacement. This study also analyzes the decoupling methods of these two displacement types, and a systematic deduction of a theoretical equation for 3D deformation analysis was conducted based on the method. The sensitivity of morphology measurement was then evaluated and the elimination of noise and rotational errors was discussed. The efficiency and accuracy of this technique was verified through a microscale static feasibility test and a high-speed impact experiment that simulated an underwater explosion. The proposed approach uses minimal equipment, is simple and convenient, and can be used to measure centrosymmetric 3D deformation in multi-scale both statically and dynamically. In addition, this method avoids the non-synchronization problem of a pair of high-speed cameras in high-speed 3D measurements.     

A robust hyper-elastic beam model under bi-axial normal-shear loadings

In this paper, a simple and robust constitutive model is proposed to simulate mechanical behaviors of hyper-elastic materials under bi-axial normal-shear loadings in the finite strain regime. The Mooney–Rivlin strain energy function is adopted to develop a two-dimensional (2D) normal-shear constitutive model within the framework of continuum mechanics. A motion field is first proposed for combined normal and shear deformations. The deformation gradient of the proposed field is calculated and then substituted into right Cauchy–Green deformation tensor. Constitutive equations are then derived for normal and shear deformations. They are two explicit coupled equations with high-level polynomial non-linearity. In order to examine capabilities of the developed hyper-elastic model, uniaxial tensile responses and non-linear stability behaviors of moderately thick straight and curved beams undergoing normal axial and transverse shear deformations are simulated and compared with experiments. Fused deposition modeling technique as a 3D printing technology is implemented to fabricate hyper-elastic beam structures from soft poly-lactic acid filaments. The printed specimens are tested under tensile/compressive in-plane and compressive out-of-plane forces. A finite element formulation along with the Newton–Raphson and Riks techniques is also developed to trace non-linear equilibrium path of beam structures in large defamation regimes. It is shown that the model is capable of predicting non-linear equilibrium characteristics of hyper-elastic straight and curved beams. It is found that the modeling of shear deformation and finite strain is essential toward an accurate prediction of the non-linear equilibrium responses of moderately thick hyper-elastic beams. Due to simplicity and accuracy, the model can serve in the future studies dealing with the analysis of hyper-elastic structures in which two normal and shear stress components are dominant.     

基于体视显微镜的测量系统标定研究

微观三维变形测量系统在工程上有广泛的应用。本文构建了体视显微镜双相机微观图像采集与测量系统,可以实现对微小物体形貌、位移、变形的全场测量。微观三维变形的测量精度与成像系统的畸变模型存在密切的关系。本文采用了考虑多种不确定情况的畸变模型,能很好地表达体视显微镜测量系统的成像误差,并设计了点阵式标定模板和精密的平动平台,实现了基于Tsai标定的自动标定算法。实验表明,体视显微镜测量系统可以在各种放大倍数下稳定工作,标定的精度得到很大的提高,并给出了在不同放大倍数下对规则圆柱体的形貌和直径的测量结果。     

A mechanics prediction of the behaviour of mono-crystalline silicon under nano-indentation

This paper uses a new constitutive model developed recently by the authors to analyse the multi-phase transformations in mono-crystalline silicon when subjected to nano-indentation. The finite element method is employed to the integration of the stress–strain relationship. A very good agreement is reached with the experimental measurements, with an accurate prediction of the observed pop-in and pop-out and detailed phase transformation events in loading and unloading. It was found that due to the change of microstructures, the material in the deformation zone could experience a local unloading during indentation loading or undergo a local loading during indentation unloading. The phase transformation events during indentation are closely related to the variation of both the deviatoric and hydrostatic stress components.     

基于频闪栅线投影的三维微结构高频动态测试系统

在微电子机械系统(MEMS)中,执行器的动作主要通过微结构的微小变形来实现,故其动态变形测试具有十分重要的意义.本文采用栅线投影测量和频闪成像技术,研制了一套三维微结构高频动态测试系统,可以实现高速10MHz频率的动态变形测量.由于在频闪测量中,光源照明信号与器件激励信号需严格同步,本文采用直接数字频率合成和现场可编程...     

Numerical and experimental indentation tests considering size effects

A series of nanoindentation experiments with maximum depths varying from 1200 to 2500 nm were conducted to study indentation size effects on copper, aluminium alloy and nickel. As expected, results from classical plasticity simulation deviate significantly from experimental data for indentation at micron and submicron levels. C⁰ continuity finite element analysis incorporating the conventional theory of mechanism-based strain-gradient (CMSG) plasticity has been carried out to simulate spherical and Berkovich indentation tests at micron level where size effect is observed. The results from both numerical and actual spherical and Berkovich indentation tests demonstrate that materials are significantly strengthened for deformation at this level and the proposed approach is able to provide reasonably accurate results.     

A method to determine Young＇s modulus of soft gels for cell adhesion

A convenient technique is reported in this note for measuring elastic modulus of extremely soft material for cellular adhesion. Specimens of bending cylinder under gravity are used to avoid contact problem between testing device and sample, and a beam model is presented for evaluating the curvatures of gel beams with large elastic deformation. A self-adaptive algorithm is also proposed to search for the best estimation of gels＇ elastic moduli by comparing the experimental bending curvatures with those computed from the beam model with preestimated moduli. Application to the measurement of the property of polyacrylamide gels indi- cates that the material compliance varies with the concentrations of bis-acrylamide, and the gels become softer after being immersed in a culture medium for a period of time, no matter to what extent they are polymerized.     

Stress measurement of SS400 steel beam using the continuous indentation technique

An analytical model is presented for determining surface residual stress using continuous indentation. The elastic residual stress is assumed to have no influence on contact area or hardness and to be uniform over a volume that is several times larger than the indentation mark. A step-by-step analysis for the residual-stress-induced load difference at a given depth is outlined here and such concepts as stress interaction, stress-sensitive contact morphology, and reversible contact recoveries during a stress relaxation are described. Finally, the proposed method is applied to the interpretation of the continuous indentation results obtained from an SS400 steel beam in which controlled bending stresses are generated. The stress estimated, however, showed a high scatter due to plastic pile-up deformation. When the optically measured contact area is used as an alternative of the contact area calculated from the unloading curve, the re-evaluated stress agrees well with the already known applied stress.     

数字图像相关方法在桥梁裂缝变形监测中的应用

本文结合工程实际背景分析了数字图像相关方法应用在桥梁裂缝变形监测中的可行性及优越性。根据桥梁裂缝变形的特点采用数字图像处理技术中的位移梯度法进行所选区域的相关匹配搜索并对相关系数的计算公式加以改进。使实验过程得以简化。计算结果全场化、直观化。本文对数字图像处理软件的测量精度和在实际测量中的测试误差进行了分析和研究。证明该软件能够更加精确地测定裂缝在各种荷载作用下的变形量值．实际的桥梁测试也验证了该方法的可行性和优越性。若图像记录设备的分辨率是12．47pixel／mm(0．0802ram／pixel)。本文所涉及到的桥梁裂缝边缘的位移测试精度为0．000802mm。     

A numerical approach to spherical indentation techniques for material property evaluation

In this work, some inaccuracies and limitations of prior indentation theories, which are based on experimental observations and the deformation theory of plasticity, are investigated. Effects of major material properties on the indentation load-deflection curve are examined via finite element (FE) analyses based on incremental plasticity theory. It is confirmed that subindenter deformation and stress-strain distribution from deformation plasticity theory are quite dissimilar to those obtained from incremental plasticity theory. We suggest an optimal data acquisition location, where the strain gradient is the least and the effect of friction is negligible. A new numerical approach to indentation techniques is then proposed by examining the FE solutions at the optimal point. Numerical regressions of obtained data exhibit that the strain-hardening exponent and yield strain are the two key parameters which govern the subindenter deformation characteristics. The new indentation theory successfully provides a stress-strain curve and material properties with an average error of less than 3%.     

三维电子束云纹法

三维电子束(3D电子束)云纹法是一种微尺度三维变形测量方法。该方法通过在试件表面制作高密度光栅,结合双目视觉立体成像技术,在SEM中形成两个角度的电子束云纹图,即可分析获得三维变形信息。考虑到离面变形与面内变形计算时的相互耦合关系,本文对现有的3D电子束云纹法进行了进一步发展,系统推导了3D电子束云纹法的通用理论公式。利用变形前后不同角度拍摄的电子束云纹图,可分别迭代计算出面内变形、离面变形和形貌等信息。对全息光栅鼓泡变形的验证实验证明了本文发展的3D电子束云纹法理论的正确性。