Submicron deformation field measurements: Part 2. Improved digital image correlation

This is the second paper in a series of three devoted to the application of scanning tunneling microscopy (STM) to mechanics problems. In this paper, improvements to the digital image correlation method are outlined, a technique that compares digital images of a specimen surface before and after deformation to deduce its two-dimensional surface displacement field and strains. The necessity of using the framework of large deformation theory for accurately addressing rigid body rotations to reduce associated errors in the strain components is pointed out. In addition, the algorithm is extended to compute the three-dimensional surface displacement field from STM data; also, significant improvements are achieved in the rate as well as the robustness of the convergence. For (STM) topographs, the resolution yields 4.8 nm for the in-plane and 1.5 nm for the out-of-plane displacement components spanning an area of 10 m×10m.     

全局性能水准与构件局部损伤状态

传统的最大层间位移作为一个全局性的性能指标,超出给定的性能极限状态阈值就不能映射构件局部损伤状态。本文基于能量平衡原理,将塑性能量耗散和塑性铰的等效能相比得到累积塑性应变,将累积塑性应变这一反映局部损伤状态的损伤指标作为工程需求参数,假定一系列累积塑性应变阈值建立局部构件的易损性曲线族。以传统的最大层间位移作为反映全局性能水准的工程需求参数,建立结构全局性能极限状态下的易损性曲线。对比全局和局部易损性曲线,发现全局性能水准和局部构件损伤状态之间存在良好的相关性,通过易损性曲线的吻合程度可获得给定全局性能水准相对应的累积塑性应变阈值。进而也建立起全局性能指标与局部损伤状态的映射关系。基于累积塑性应变的机构易损性分析是一种更精确的易损性分析方法。     

Rough terrain profiling using digital image correlation

Road profiling is an important aspect of vehicle dynamics simulations especially over rough terrains. The accurate measurement of rough terrains allows for more accurate multi body simulations. Three dimensional road profiles are usually performed by utilising a line scan sensor which measures several points lateral to the road. The sensors range from simple road following wheels to LiDAR sensors. The obtained line scans are longitudinally stitched together using the orientation and position of the sensor to obtain a full three dimensional road profile. The sensor’s position and orientation therefore needs to be accurately determined in order to combine the line scans to create an accurate representation of the terrain. The sensor’s position and orientation is normally measured using an expensive inertial measurement unit or Inertial Navigation System (INS) with high sensitivity, low noise and low drift. This paper proposes a road profiling technique which utilises stereography, based on two inexpensive digital cameras, to obtain three-dimensional measurements of the road. The system negates the use of an expensive INS system to determine orientation and position. The data sets also require subsampling which can be computationally expensive. A simple subsampling routine is presented which takes advantage of the structure of the data sets to significantly speed up the process.     

Optimization of the forearm angle for arm wrestling using multi-camera stereo digital image correlation: A preliminary study

This study analyzes the function of different muscles during arm wrestling and proposes a method to analyze the optimal forearm angle for professional arm wrestlers. We built a professional arm-wrestling platform to measure the shape and deformation of the skin at the biceps brachii of a volunteer in vivo during arm wrestling. We observed the banding phenomenon of arm skin strain during muscle contraction and developed a model to evaluate the moment provided by the biceps brachii. According to this model, the strain field of the area of interest on the skin was measured, and the forearm angles most favorable and unfavorable to the work of the biceps brachii were analyzed. This study demonstrates the considerable potential of applying DIC and its extension method to the in vivo measurement of human skin and facilitates the use of the in vivo measurement of skin deformation in various sports in the future.     

Relating inhomogeneous deformation to local texture in zirconium through grain-scale digital image correlation strain mapping experiments

The effect of local texture on inhomogeneous plastic deformation is studied in zirconium subjected to uniaxial compression. Cross-rolled commercially pure Zr 702 plate that had a strong basal (0 0 0 1) texture through the plate thickness, and a non-basal texture in cross-section, was obtained. At a compressive strain rate of 1 s^?1, samples loaded either in the through-thickness or in-plane directions exhibited significant differences in yield strength, hardening response and failure mechanisms. These macroscopic differences are related to microstructural features by combining information from electron backscattered diffraction with real time in situ imaging and subsequent full-field strain measurements obtained using digital image correlation. Experimental results indicate that the through-thickness loaded zirconium samples, which show a strong basal-texture in the loading direction, do not deform homogeneously – implying the lack of a representative volume element. The detailed surface deformation fields provided by digital image correlation allow for a qualitative and quantitative analysis of the relationship between grain orientation and patterns of deformation bands that form as the precursors to development of an adiabatic shear band in the through-thickness loaded sample. For the in-plane loaded samples, inhomogeneities still exist at the microscale, but the collective behavior of several grains leads to a homogeneous response at the macroscale. It is observed that local texture for hcp polycrystals, which are significantly slip restricted, can directly affect both local and global response, even at low to moderate plastic strains.     

Calibration of constitutive models of steel beams subject to local buckling by using digital image correlation

It is proposed to identify the behavior of steel beams prior to and after the inception of local buckling by using digital image correlation. Full-field measurements are used to evaluate kinematic and static fields for determining constitutive laws. It enables for the detection of local buckling inception and the evaluation of the post-buckled behavior. Constitutive models are tuned by using measured Euler–Bernoulli kinematics.     

Performance of global look-up table strategy in digital image correlation with cubic B-spline interpolation and bicubic interpolation

Global look-up table strategy proposed recently has been proven to be an efficient method to accelerate the interpolation, which is the most time-consuming part in the iterative sub-pixel digital image correlation(DIC) algorithms. In this paper, a global look-up table strategy with cubic B-spline interpolation is developed for the DIC method based on the inverse compositional Gauss–Newton(IC-GN) algorithm.The performance of this strategy, including accuracy, precision, and computation efficiency, is evaluated through a theoretical and experimental study, using the one with widely employed bicubic interpolation as a benchmark. The global look-up table strategy with cubic B-spline interpolation improves significantly the accuracy of the IC-GN algorithm-based DIC method compared with the one using the bicubic interpolation, at a trivial price of computation efficiency.     

A study of localisation in dual-phase high-strength steels under dynamic loading using digital image correlation and FE analysis

Tensile tests were conducted on dual-phase high-strength steel in a Split-Hopkinson Tension Bar at a strain-rate in the range of 150–600/s and in a servo-hydraulic testing machine at a strain-rate between 10^?3 and 10⁰/s. A novel specimen design was utilized for the Hopkinson bar tests of this sheet material. Digital image correlation was used together with high-speed photography to study strain localisation in the tensile specimens at high rates of strain. By using digital image correlation, it is possible to obtain in-plane displacement and strain fields during non-uniform deformation of the gauge section, and accordingly the strains associated with diffuse and localised necking may be determined. The full-field measurements in high strain-rate tests reveal that strain localisation started even before the maximum load was attained in the specimen. An elasto-viscoplastic constitutive model is used to predict the observed stress–strain behaviour and strain localisation for the dual-phase steel. Numerical simulations of dynamic tensile tests were performed using the non-linear explicit FE code LS-DYNA. Simulations were done with shell (plane stress) and brick elements. Good correlation between experiments and numerical predictions was achieved, in terms of engineering stress–strain behaviour, deformed geometry and strain fields. However, mesh density plays a role in the localisation of deformation in numerical simulations, particularly for the shell element analysis.     

Three-dimensional displacement measurements using digital image correlation and photogrammic analysis

The application of digital image correlation and stereoscopic principles is used to determine three-dimensional displacements. Two pairs of stereo images of a speckled surface before and after deformation are digitized and correlated to determine the three-dimensional displacements. The images are interpolated so as to account for subpixel displacements. A sequential decision technique and a coarsefine search are employed to increase computer efficiency and decrease run time. Very accurate results are obtained, expecially when the magnification is increased. The effect of camera tilt is shown to be negligible. Theory and experimental verification are presented.     

Extended three-dimensional digital image correlation (X3D-DIC)

A correlation algorithm is proposed to measure full three-dimensional displacement fields in a three-dimensional domain. The chosen kinematic basis for this measurement is based on continuous finite-element shape functions. It is furthermore proposed to account for the presence of strong discontinuities, similarly to extended finite element schemes, with a suited enrichment of the kinematics with discontinuities supported by a (crack) surface. An optimization of the surface geometry is proposed based on correlation residuals. The procedure is applied to analyze one loading cycle of a fatigue-cracked nodular graphite cast iron sample by using computed tomography pictures. Subvoxel crack openings are revealed and measured. To cite this article: J. Réthoré et al., C. R. Mecanique 336 (2008).     

Deformation measurements by digital image correlation: Implementation of a second-order displacement gradient

This paper outlines the procedure for refining the digital image correlation (DIC) method by implementing a second-order approximation of the displacement gradients. The second-order approximation allows the DIC method to directly measure both the first- and second-order displacement gradients resulting from nonlinear deformation. Thirteen unknown parameters, consisting of the components of displacement, the first- and second-order displacement gradients and the gray-scale value offset, are determined through optimization of a correlation coefficient. The previous DIC method assumes that the local deformation in a subset of pixels is represented by a first-order Taylor series approximation for the displacement gradient terms, so actual deformations consisting of higher order displacement gradients tend to distort the infinitesimal strain measurements. By refining the method to measure both the first- and second-order displacement gradients, more accurate strain measurements can be achieved in large-deformation situations where second-order deformations are also present. In most cases, the new refinements allow the DIC method to maintain an accuracy of ±0.0002 for the first-order displacement gradients and to reach ±0.0002 per pixel for the second-order displacement gradients.     

A study of plastic zone formation by digital image processing

A simple experimental technique is presented to directly measure the plastic zone in engineering structural materials by using both digital image processing and optical techniques. Standard image processing procedures were performed on images obtainted from laser illumination of polished stainless steel specimens to obtain predictions of the onset and size of plastic zone formation. The finite element program, ANSYS, was used to obtain numerical solutions for comparison with the experimental data. It is shown that the experimental method discussed in this paper is capable of predicting plastic zone size as a function of loading.     

Analysis of strain localization during tensile tests by digital image correlation

This paper presents an imaging technique developed to study the strain localization phenomena that occur during the tension of thin, flat steel samples. The data are processed using digital speckle image correlation to derive the two in-plane components of the displacement vectors. The authors observe that the calculation of the intercorrelation function reveals a systematic error and propose a numerical method to limit its influence. Plastic incompressibility and thin-sheet assumptions are used to derive the third displacement component and, hence, the various strain and strain rate components. Numerous checks are presented at each step in processing the data to determine the final accuracy of the strain measurements. It is estimated that this accuracy is quite sufficient to track the inception and the development of localization. Examples of possible application are presented for mild steels whose strain localization mechanisms appear to be precocious and gradual.     

Identification of adhesive properties in GLARE assemblies using digital image correlation

An experimental-numerical methodology is introduced to identify the parameters of a cohesive law of an adhesive layer within a joined assembly on the basis of kinematic data provided by digital image correlation. Non-conventional experiments on joined samples were designed to generate within the assembly and the adhesive film complex strain and stress states close to those expected in-service and up to complete debonding. The modeling is developed with reference to the observed sub-domain in which the experimental boundary conditions are prescribed. The nonlinear behavior of the adhesive layer is described as a finite-thickness interface endowed with a mixed-mode cohesive law whose parameters are identified so as to match at best the measured displacement field.     

Evaluating the mechanical behavior of arterial tissue using digital image correlation

In this study, digital image correlation (DIC) was adopted to examine the mechanical behavior of arterial tissue from bovine aorta. Rectangular sections comprised of the intimal and medial layers were excised from the descending aorta and loaded in displacement control uniaxial tension up to 40 percent elongation. Specimens of silicon rubber sheet were also prepared and served as a benchmark material in the application of DIC for the evaluation of large strains; the elastomer was loaded to 50 percent elongation. The arterial specimens exhibited a non-linear hyperelastic stress-strain response and the stiffness increased with percent elongation. Using a bilinear model to describe the uniaxial behavior, the average minor and major elastic modulii were 192±8 KPa and 912±40 KPa, respectively. Poisson's ratio of the arterial sections increased with the magnitude of axial strain; the average Poisson's ratio was 0.17±0.02. Although the correlation coefficient obtained from image correlation decreased with the percent elongation, a correlation coefficient greater than 0.8 was achieved for the tissue experiments and exceeded that obtained in the evaluation of the elastomer. Based on results from this study, DIC may serve as a valuable method for the determination of mechanical properties of arteries and other soft tissues.     

Deformation analysis of a modular connection system by digital image correlation

Experimental Techniques -     

Surface deformation measurements of a cylindrical specimen by digital image correlation

Planar digital image correlation has been extended to measure surface deformations of cylindrical specimens without physical contact for high-temperature situations. A single CCD camera acquires the surface image patterns of a section of a specimen in the undeformed and deformed states to determine two-dimensional displacements on a projection plane. Axial, circumferential and shear deformations are determined through curvature transformation on the two-dimensional projection displacement field. The resolution of this technique was determined for a cylinder of 22.23-mm diameter to be 3.5 μm for the axial displacement, 0.05 percent for the axial and shear strains and 0.08 percent for the circumferential strain when correlation computations are carried out over a field of 5 mm×5 mm.     

Diffractography vs. holography—A stress analyst's comparison

Holographic interferometry provides an elegant and very sensitive displacement measurement means for the experimental stress analyst. Recently however, a related optical techniques, “diffractography”, has been developed which offers an alternative to holography in many cases, particularly in those experiments where information along one or more discrete lines is sufficient. This paper compares both approaches and presents new experimental data on deflections of a cantilever steel plate obtained using both techniques.