DVC中内部散斑质量评价及计算体素点的优化选择

数字体图像相关方法(digital volume correlation, DVC)是一种可测量物体内部三维全场变形的先进实验力学测试技术, 通过分析由体图像成像设备(如X-ray CT)获取的物体变形前后的三维体图像, DVC可获得物体内部具有亚体素精度的三维变形信息. 在应用DVC测量内部变形时, 被测试样体图像的内部散斑质量对其测量精度有着重要影响. 本文从DVC算法位移测量误差的理论分析和数值模拟实验两方面证实了DVC的位移测量误差与计算子体块的灰度梯度平方和(sum of square subvolume intensity gradient, SSSIG)值呈负相关关系, 即: 计算子体块的SSSIG值越大, 其位移测量精度越高, 因此SSSIG可用于体图像内部散斑质量的定量评价. 尽管直接增加计算子体块尺寸可以增加SSSIG, 但是较大计算子体块内更多的计算点会导致计算量的显著增加. 为此, 本文进一步提出一种计算体素点优化选择方法, 该方法通过将计算子体块中灰度梯度较小的体素点剔除出计算, 以实现在增大计算子体块尺寸的同时不会显著增加计算量. 模拟和真实实验结果显示了该计算体素点优化选择方法的有效性.      

数字体图像相关方法中基于迭代最小二乘法的物体内部变形测量

本文提出一种基于迭代最小二乘法的亚体素位移测量算法.该算法模型结合了符合实际情况的线性灰度变化模型和线性位移映射函数,采用仅需变形后体图像一阶灰度梯度的迭代最小二乘法计算亚体素位移和位移梯度.由于该算法采用的模型符合实际情况,因而具有更高的位移测量精度和更广泛的适用性.此外,由于仅需变形后体图像的一阶灰度梯度,无需计算...     

Digital Image Correlation with Self-Adaptive Gaussian Windows

A novel subpixel registration algorithm with Gaussian windows is put forward for accurate deformation measurement in digital image correlation technique. Based on speckle image quality and potential deformation states, this algorithm can automatically minimize the influence of subset sizes by self-adaptively tuning the Gaussian window shapes with the aid of a so-called weighted sum-of-squared difference correlation criterion. Numerical results of synthetic speckle images undergoing in-plane sinusoidal displacement fields demonstrate that the proposed algorithm can significantly improve displacement and strain measurement accuracy especially in the case with relatively large deformation.     

橡胶材料弹性模量数字图像相关测定法

利用数字图像相关方法测量了小应变下柔性橡胶的弹性模量.用CCD相机记录单轴压缩实验中圆柱体橡胶试样表面人工散斑图像,作为数字图像相关测量技术中的变形信息载体.分析了镜头畸变对位移测量的影响,运用数字图像相关法得出小应变范围内像胶的应力应变曲线,计算出橡胶的弹性模量.并与采用千分表所得到的结果进行了比较,两者符合较好.实...     

Measurement of Local Thermal Deformations in Heterogeneous Microstructures via SEM Imaging with Digital Image Correlation

It is challenging to measure accurately and with high spatial resolution the local thermal strains in heterogeneous microstructures due of the complex nature of the thermal deformations and local boundary conditions. In the enclosed study, a digital image correlation (DIC) based, thermal strain mapping technique is described that is able to probe thermal deformations with sub-micron spatial resolution and sub-nanometer displacement accuracy for both homogeneous and heterogeneous materials, including cross-sections of IC packages. The full-field thermal deformation maps of different materials within a nanostructured IC chip cross-section are established from room temperature up to 160 °C, uncovering the heterogeneous nature of the specimen while accurately measuring the highly non-uniform displacement and strain fields across the multiple material constituents. As described in this work, the DIC-enabled technique is capable of high resolution mapping of local thermo-mechanical deformations in heterogeneous materials, providing a methodology that can improve our understanding of complex material systems under controlled thermal-environmental conditions.     

The effect of the multi-axiality of compressive loading on the accuracy of a continuum model for layered materials

Two methods of analysis of the internal instability of layered materials are discussed: the continuum approach and the piecewise-homogeneous medium model. Based on the results obtained within the scope of the model of a piecewise-homogeneous medium and the 3-D stability theory, the accuracy of a continuum theory is examined for incompressible non-linear materials undergoing large deformations. Two different loading conditions are compared: biaxial and uniaxial compression. The effect of the multi-axiality of loading on the accuracy of the continuum theory is determined for the particular model of hyperelastic layers described by the Treloar’s potential (i.e. by a neo-Hookean type potential), which is a simplified version of the Mooney’s elastic potential.     

聚氨酯(PU)在力学性能测试中的摩擦效应与变形均匀性研究

作为防弹玻璃夹层材料,PU的动态力学性能一直受到学者们的关注。为准确表征其动态力学性能,本文采用ABAQUS有限元软件对不同摩擦系数下的单轴压缩试验进行数值仿真,分析试样加载端面的摩擦效应和几何尺寸对单轴压缩试验结果的影响;结合高速摄影技术(HSP)与数字图像相关技术(DIC)观测到试样在拉伸试验中的动态变形场和应变场,探讨标距段的应力均衡性;同时对PU材料在不同应变率下的单轴压缩、拉伸力学性能进行测试。结果表明:压缩试样的端面摩擦效应限制横向变形,影响了试样内部的受力分布,使得测量得到的应力值偏大;试样长径比越小,端面摩擦效应的影响越大;在单轴动态拉伸试验中,板状拉伸试样的标距段选取应当考虑两端倒角尺寸。通过测试PU的拉、压力学性能,发现材料具有显著的应变率敏感性。     

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.     

数字图像相关方法在闭孔泡沫铝压缩试验中的应用

为了了解相对密度与胞孔结构对闭孔泡沫铝力学性能的影响,本文采用放大成像及数字图像相关技术对两种不同密度的泡沫纯铝试样进行了实验研究.利用数字图像相关方法对泡沫纯铝变形前后的图像进行相关计算,获得了弹性范围内静态压缩情况下闭孔泡沫铝材料表面的全场变形及局部孔结构的变形,同时根据试验结果计算了试件的名义弹性模量.实验结果表明泡沫铝整体孔结构的变形与泡沫金属材料相对密度有关,而单个孔结构的变形主要与孔壁面光滑程度和皱褶有关.实验结果还表明图像相关方法能够有效地应用于闭孔泡沫金属的力学性测量和评估的研究.     

Capturing anisotropic constitutive models with WYPiWYG hyperelasticity; and on consistency with the infinitesimal theory at all deformation levels

The elastic nonlinear behavior of fiber-reinforced materials and soft biological tissues is analyzed using anisotropic hyperelastic models. Frequently, these models are not compatible with the corresponding infinitesimal theory, but some of them may be modified to accommodate that theory in the limit. WYPiWYG hyperelasticity is compatible with the infinitesimal theory at all deformation levels and capable of capturing exactly a complete set of experimental data, which reproduces all deformation modes at every strain level, under homogeneous deformations. In this work we study the relevance of recovering the infinitesimal theory at every deformed configuration and also the performance of the WYPiWYG method in predicting the behavior of anisotropic materials at large strains under nonhomogeneous deformations.     

High-Resolution Deformation Mapping Across Large Fields of View Using Scanning Electron Microscopy and Digital Image Correlation

This paper details the creation of experimental and computational frameworks to capture high-resolution, microscale deformation mechanisms and their relation to microstructure over large (mm-scale) fields of view. Scanning electron microscopy with custom automation and external beam control was used to capture 209 low-distortion micrographs of 360 μm?×?360 μm each, that were individually correlated using digital image correlation to obtain displacement/strain fields with a spatial resolution of 0.44 μm. Displacement and strain fields, as well as secondary electron images, were subsequently stitched to create a 5.7 mm × 3.4 mm field of view containing 100 million (7678?×?13,004) data points. This approach was demonstrated on Mg WE43 under uniaxial compression, where effective strain was shown to be relatively constant with respect to distance from the grain boundary, and a noticeable increase in the effective strain was found with an increase in the basal Schmid factor. The ability to obtain high-resolution deformations over statistically relevant fields of view enables large data analytics to examine interactions between microstructure, microscale strain localizations, and macroscopic properties.     

Mechanical Properties of Ballistic Gelatin at High Deformation Rates

The characterization of soft or low impedance materials is of increasing importance since these materials are commonly used in impact and energy absorbing applications. The increasing role of numerical modeling in understanding impact events requires high-rate material properties, where the mode of loading is predominantly compressive and large deformations may occur at high rates of deformation. The primary challenge in measuring the mechanical properties of soft materials is balancing the competing effects of material impedance, specimen size, and rate of loading. The traditional Split Hopkinson Pressure Bar approach has been enhanced through the implementation of polymeric bars to allow for improved signal to noise ratios and a longer pulse onset to ensure uniform specimen deformation. The Polymeric Split Hopkinson Pressure Bar approach, including the required viscoelastic bar analysis, has been validated using independent measurement techniques including bar-end displacement measurement and high speed video. High deformation rate characterization of 10% and 20% ballistic gelatin, commonly used as a soft tissue simulant, has been undertaken at nominal strain rates ranging from 1,000 to 4,000/s. The mechanical properties of both formulations of gelatin exhibited significant strain rate dependency. The results for 20% gelatin are in good agreement with previously reported values at lower strain rates, and provide important mechanical properties required for this material.     

Full 3D Measurement of Strain Field by Scattered Light for Analysis of Structures

The studies of structures with complex geometry or non-plane loading impose generally taking into account the mechanical volume effects. Mechanical data at the core of materials can be obtained by using special devices, generally from X-ray tomography. In this paper, we present an original volume investigation technique for transparent materials. This technique, easier to implement, does not require any complex device. It is based on scattered light by randomly distributed marks and provides three-dimensional images allowing the use of correlation technique, extended to three dimensions. The accuracy of measurement is evaluated for an imposed rigid body translation and a mechanical homogeneous loading in small and large strains. In conclusion, an example of application is presented concerning a local mechanical loading of compression in which we make a comparison with a finite element simulation.     

Micro- and Nanoscale Deformation Measurement of Surface and Internal Planes via Digital Image Correlation

The digital image correlation (DIC) technique is successfully applied across multiple length scales through the generation of a suitable speckle pattern at each size scale. For microscale measurements, a random speckle pattern of paint is created with a fine point airbrush. Nanoscale displacement resolution is achieved with a speckle pattern formed by solution deposition of fluorescent silica nanoparticles. When excited, the particles fluoresce and form a speckle pattern that can be imaged with an optical microscope. Displacements are measured on the surface and on an interior plane of transparent polymer samples with the different speckle patterns. Rigid body translation calibrations and uniaxial tension experiments establish a surface displacement resolution of 1 μm over a 5×6 mm scale field of view for the airbrushed samples and 17 nm over a 100×100 μm scale field of view for samples with the fluorescent nanoparticle speckle. To demonstrate the capabilities of the method, we characterize the internal deformation fields generated around silica microspheres embedded in an elastomer under tensile loading. The DIC technique enables measurement of complex deformation fields with nanoscale precision over relatively large areas, making it of particular relevance to materials that possess multiple length scales.     

Constitutive equations for thermomechanical deformations of glassy polymers

Poly-Carbonate (PC) and Poly-Methyl-Methacrylate (PMMA) are lightweight and mechanically tough transparent glassy polymers. Their mechanical behavior at low to moderate strain rates has been well characterized; however, that at high strain rates needs additional work. We propose two modifications to existing pressure-dependent viscoplastic constitutive equations that enable one to simulate better mechanical deformations of PC and PMMA at high strain rates. First, the elastic moduli are taken to depend upon the current temperature and the current effective strain rate. Second, two internal variables are introduced to better characterize the strain softening of the material at high strain rates. A technique to find values of newly introduced material parameters is described. We compute the local temperature rise due to energy dissipated during plastic deformations. The true axial stress vs. the true axial strain curves in uniaxial compression from numerical simulations of the test configurations at high strain rates using the proposed constitutive equations are found to agree well with the experimental results available in the literature.     

Specimen Size and Strain Rate Effects on the Compressive Behavior of Concrete

Three high-performance concrete (HPC) materials with different specimen geometries were characterized using Kolsky compression bar techniques to study the strain rate and specimen size effects on their uniaxial compressive strength. A large-diameter Kolsky bar and recently established annular pulse shaping technique were used to achieve dynamic stress equilibrium and constant strain-rate deformation in the experiments. A complimentary effort was conducted using a 19-mm-diameter Kolsky compression bar to understand the strain rate and specimen size effects on failure strength and dynamic increase factor (DIF) for concrete. It was found that, for all three concrete materials investigated, the failure strength is highly dependent on the specimen geometry, however such a relationship is not apparent for the DIF. The DIF observed in this study shows significantly lower values compared to historical data, which may indicate the importance of well-controlled dynamic testing conditions on the accuracy and validity of experimental results for concrete materials.     

Critical Evaluation of a Constitutive Model for Glassy Polycarbonate

Polycarbonate (PC) is an important amorphous glassy polymer whose intrinsic uniaxial response exhibits all the features like strain softening and hardening at large deformations characteristic of this class of materials. Polycarbonate is significantly ductile and is capable of sustaining large plastic deformation. Constitutive models of PC, in order to be useful, should be able to faithfully model its elastic as well as plastic behaviour with as few undetermined parameters as possible. We assess the efficacy of a particular model of glassy polymers by fitting its parameters through usual uniaxial tensile and compressive tests and then using those parameters to model a fracture specimen in 3-dimensions. A range of experimental techniques like digital image correlation, photoelasticity and x-ray tomography are used to make careful quantitative comparisons with computer simulations. Our results indicate that in view of the small scale yielding situation prevalent in PC specimens even at high loads, a faithful prediction of the elastic parameters are sufficient for reproducing most global responses and deformation fields away from the crack. However, to predict fracture initiation, the deformation state within the small but significant fracture process zone needs to be reproduced. This cannot be done unless the entire uniaxial response is modelled to a reasonable degree of accuracy.     

Towards High Performance Digital Volume Correlation

We develop speed and efficiency improvements to a three-dimensional (3D) digital volume correlation (DVC) algorithm, which measures displacement and strain fields throughout the interior of a material. Our goal is to perform DVC with resolution comparable to that achieved in 2D digital image correlation, in time that is commensurate with the image acquisition time. This would represent a significant improvement over the current state-of-the-art available in the literature. Using an X-ray micro-CT scanner, we can resolve features at the 5 micron scale, generating 3D images with up to 36 billion voxels. We compute twelve degrees-of-freedom at each correlation point and utilize tricubic spline interpolation to achieve high accuracy. We improve the algorithm’s speed and robustness through an improved coarse search, efficient implementation of spline interpolation, and using smoothing splines to address noisy image data. For DVC, the volume of data, number of correlation points, and work to solve each correlation point grow cubically. We therefore employ parallel computing to handle this tremendous increase in computational and memory requirements. We demonstrate the application of DVC using simulated deformations of 3D micro-CT scans of polymer samples with embedded particles forming an internal pattern.     

Constitutive equations in finite elasticity of rubbers

A constitutive model is derived for the elastic behavior of rubbers at arbitrary three-dimensional deformations with finite strains. An elastomer is thought of as an incompressible network of flexible chains bridged by permanent junctions that move affinely with the bulk material. With reference to the concept of constrained junctions, the chain ends are assumed to be located at some distances from appropriate junctions. These distances are not fixed, but are altered under deformation. An explicit expression is developed for the distribution function of vectors between junctions (an analog of the end-to-end distribution function for a flexible chain with fixed ends). An analytical formula is obtained for the strain energy density of a polymer network, when the ratio of the mean-square distance between the ends of a chain and appropriate junctions is small compared with the mean-square end-to-end distance of chains. Stress–strain relations are derived by using the laws of thermodynamics. The governing equations involve three adjustable parameters with transparent physical meaning. These parameters are found by fitting experimental data on plain and particle-reinforced elastomers. The model ensures good agreement between the observations at uniaxial tension and the results of numerical simulation, as well as an acceptable prediction of stresses at uniaxial compression, simple shear and pure shear, when its parameters are found by matching observations at uniaxial tensile tests.     

On the local nature of the strain field calculation method for measuring heterogeneous deformation of cellular materials

A strain field calculation method based on the optimal local deformation gradient technique has been developed to calculate the ‘local’ strain tensor of cellular materials using cell-based finite element models. The local nature and accuracy of this method may be strongly dependent on the cut-off radius, which is introduced to collect the effective nodes for determining the optimal local deformation gradient of a node. Two different schemes are first analyzed to determine the suitable cut-off radius by characterizing the heterogeneous deformation of Voronoi honeycombs under uniaxial compression and we suggest that in Scheme 1, the cut-off radius defined based on the reference configuration is about 1.5 times the average cell radius; in Scheme 2, the cut-off radius defined based on the current configuration is about 0.5 times the average cell radius. Then, Scheme 3, a combined scheme of the two former schemes, is further suggested. It is demonstrated that the optimal cut-off radius in Scheme 3 characterizes the local strain reasonable well whether the compression rate is low or high. Finally, the strain field calculation method with the optimal cut-off radius is applied to reveal the evolution of the heterogeneous deformation of two different configurations of double-layer cellular cladding under a linear decaying blast load. The 2D fields and the 1D distributions of local engineering strain are calculated. These results interpret the shock wave propagation mechanisms in both claddings and provide useful understanding in the design of a double-layer cellular cladding.