Analysis of a multiaxial test on a C/C composite by using digital image correlation and a damage model

The “planar” digital image correlation technique needs a single CCD camera to acquire the surface patterns of a zone of a specimen in the underformed and deformed states. With these two images, one can determine in-plane displacement and strain fields. The digital image correlation technique used herein is based on Fast Fourier Transforms, which are very effective in reducing the computation cost. Its performance is assessed and discussed on artificial signals and in a real experimental situation. The technique is utilized to analyze experimental results of a plane shear experiment and validate a damage meso-model describing different degradations in a C/C composite material.     

Digital image processing for non-linear system identification

Emerging digital image processing techniques demonstrate their potential applications in engineering mechanics, particularly in the area of system identification involving non-linear characteristics of mechanical and structural systems. The objective of this study is to demonstrate the proof-of-concept that the techniques permit the identification non-intrusively and remotely. First, the efficacy of the digital image processing method is shown by identifying the friction behavior between two solids that are assumed to be governed by the Coulomb friction model. The inverse analysis is carried out to validate the proposed method of identifying model parameters. Studies further illustrate that the digital imaging procedure and inverse analysis algorithms developed for the friction problem can be extended for identification of non-linear mechanical and structural characteristics. One illustration utilizes the second example, where relative motion between a model structure and a shaking table is measured by digitally processing the analogue image provided by a video tape recorded during a shaking table test of a model structure base isolated by a hybrid isolation device consisting of friction and elastomeric components. Third, constitutive relationship for a non-linear elastomeric membrane is identified by digitally processing images of its deformed states under tension. The relationship is postulated to follow the Mooney-Rivlin function. Schemes developed are verified with iterative non-linear finite-element program that is valid in the finite deformation range. Emerging cost-effective hardware and software systems for high-performance data acquisition and processing are quite promising to the implementation of the techniques by removing most, if not all, of its existing limitations.     

Digital speckle correlation for strain measurement by image analysis

This paper is concerned with small strain measurement utilizing the numerical processing of digital images. The proposed method has its theoretical basis in digital signal analysis and, from a methodological point of view, it can be considered as an extension to digital images of the wellknown white light speckle photography technique. That conventional method is based on the analysis of photographic plates that are exposed twice (before and after the specimen deformation) with the image of a random speckle pattern that has been previously printed on the test piece surface. The digital speckle correlation advantages consist of requiring a very simple specimen preparation and, mainly, of allowing the strain field computation just by numerical elaboration of the acquired images. In this paper, the theoretical basis of the technique and some valuable improvements to the known analogous methodologies are presented. Finally, test results for an application of digital speckle correlation are shown and advantages and disadvantages of the technique are elaborated. In addition, further developments in this area are discussed.     

Effects of material anisotropy and inhomogeneity on cavitation for composite incompressible anisotropic nonlinearly elastic spheres

The effects of material anisotropy and inhomogeneity on void nucleation and growth in incompressible anisotropic nonlinearly elastic solids are examined. A bifurcation problem is considered for a composite sphere composed of two arbitrary homogeneous incompressible nonlinearly elastic materials which are transversely isotropic about the radial direction, and perfectly bonded across a spherical interface. Under a uniform radial tensile dead-load, a branch of radially symmetric configurations involving a traction-free internal cavity bifurcates from the undeformed configuration at sufficiently large loads. Several types of bifurcation are found to occur. Explicit conditions determining the type of bifurcation are established for the general transversely isotropic composite sphere. In particular, if each phase is described by an explicit material model which may be viewed as a generalization of the classic neo-Hookean model to anisotropic materials, phenomena which were not observed for the homogeneous anisotropic sphere nor for the composite neo-Hookean sphere may occur. The stress distribution as well as the possible role of cavitation in preventing interface debonding are also examined for the general composite sphere.     

On a finite-strain viscoplastic law coupled with anisotropic damage: theoretical formulations and numerical applications

Based on a dissipation inequality at finite strains and the effective stress concept, a Chaboche-type infinitesimal viscoplastic theory is extended to finite-strain cases coupled with anisotropic damage. The anisotropic damage is described by a rank-two symmetric tensor. The constitutive law is formulated in the corotational material coordinate system. Thus, the evolution equations of all internal variables can be expressed in terms of their material time derivatives. The numerical algorithm for implementing the material model in a finite element programme is also formulated, and several numerical examples are shown. Comparing the numerical simulations with experimental observations indicates that the present material model can describe well the primary, secondary and tertiary creep. It can also predict the anisotropic damage modes observed in experiments correctly.     

An energy-based anisotropic yield criterion for cellular solids and validation by biaxial FE simulations

The initial yield surface of 2D lattice materials is investigated under biaxial loading using finite element analyses as well as by analytical means. The sensitivity of initial yield surface to the dominant deformation mode is explored by using both low- and high-connectivity topologies whose dominant deformation mode is either local bending or strut stretching, respectively. The effect of microstructural irregularity on the initial yield surface is also examined for both topologies. A pressure-dependent anisotropic yield criterion, which is based on total elastic strain energy density, is proposed for 2D lattice structures, which can be easily extended for application to 3D cellular solids. Proposed criterion uses elastic constants and yield strengths under uniaxial loading, and does not rely on any arbitrary parameter. The analytical framework developed allows the introduction of new scalar measures of characteristic stresses and strains that are capable of representing the elastic response of anisotropic materials with a single elastic master line under multiaxial loading.     

A simple framework for full-network hyperelasticity and anisotropic damage

A formulation of a constitutive behaviour law is proposed for hyperelastic materials, such that damage induced anisotropy can be accounted for continuously. The full-network approach with directional damage is adopted as a starting point. The full-network law with elementary strain energy density based on the inverse Langevin is chosen as a reference law which is cast into the proposed framework. This continuum formalism is then rewritten using spherical harmonics to capture damage directionality. The proposed formalism allows for an efficient (and systematic) expansion of complex non-linear anisotropic constitutive laws. A low order truncated expression of the resulting behaviour is shown to reproduce accurately the stress-strain curves of the exact behaviour laws.     

A plasticity and anisotropic damage model for plain concrete

A plastic-damage constitutive model for plain concrete is developed in this work. Anisotropic damage with a plasticity yield criterion and a damage criterion are introduced to be able to adequately describe the plastic and damage behavior of concrete. Moreover, in order to account for different effects under tensile and compressive loadings, two damage criteria are used: one for compression and a second for tension such that the total stress is decomposed into tensile and compressive components. Stiffness recovery caused by crack opening/closing is also incorporated. The strain equivalence hypothesis is used in deriving the constitutive equations such that the strains in the effective (undamaged) and damaged configurations are set equal. This leads to a decoupled algorithm for the effective stress computation and the damage evolution. It is also shown that the proposed constitutive relations comply with the laws of thermodynamics. A detailed numerical algorithm is coded using the user subroutine UMAT and then implemented in the advanced finite element program ABAQUS. The numerical simulations are shown for uniaxial and biaxial tension and compression. The results show very good correlation with the experimental data.     

Damage and fracture evaluation of granular composite materials by digital image correlation method

This paper presents the applications of digital image correlation technique to the mesoscopic damage and fracture study of some granular based composite materials including steelfiber reinforced concrete, sandstone and crystal-polymer composite. The deformation fields of the composite materials resulted from stress localization were obtained by the correlation computation of the surface images with loading steps and thus the related damage prediction and fracture parameters were evaluated. The correlation searching could be performed either directly based on the gray levels of the digital images or from the wavelet transform (WT) coefficients of the transform spectrum. The latter was developed by the authors and showed higher resolution and sensitivity to the singularity detection. Because the displacement components came from the rough surfaces of the composite materials without any coats of gratings or fringes of optical interferometry, both surface profiles and the deformation fields of the composites were visualized which was helpful to compare each other to analyze the damage of those heterogeneous materials. The project supported by the National Natural Science Foundation of China (10125211 and 10072002), the Scientific Committee of Yunnan Province for the Program of Steel Fiber Reinforced Concrete, and the Institute of Chemical Materials, CAEP at Mianyang     

Fatigue damage of APC-2 composite assessed from material degradation and non-destructive evaluation data

Quasi-isotropic 45° APC-2 specimens are fatigued under constant amplitude stress reversal load condition. Fatigue induced degradation of the mechanical properties is correlated to data obtained from non-destructive evaluation. C-scan readings were used to define a generic damage severity factor D. It refers to the current fatigue damage state and accounts for the varying severity of damage at the different specimen locations. Analytical expressions are developed to relate D to the axial stiffness, residual strength and interlaminar shear strength. An indication of damage tolerance can thus be made for evaluating the integrity of structural components.     

Digital image correlation techniques for measuring tyre-road interface parameters: Part 1 – Side-slip angle measurement on rough terrain

This paper presents inexpensive methods whereby the vehicle side-slip angle can be measured accurately at low speeds on any terrain using cameras. Most commercial side-slip angle sensor systems and estimation techniques rely on smooth terrain and high vehicle speeds, typically above 20 km/h, to provide accurate measurements. However, during certain in-situ tyre and vehicle testing on off-road conditions, the vehicle may be travelling at speeds slower than required for current sensors and estimation techniques to provide sufficiently accurate results. Terramechanics tests are typical case in point. Three algorithms capable of determining the side-slip angle from overlapping images are presented. The first is a simple fast planar method. The second is a more complex algorithm which can extract not only the side-slip angle but also its rotational velocities and scaled translational velocities. The last uses a calibrated stereo-rig to obtain all rotations and translational movement in world coordinates. The last two methods are aimed more at rough terrain applications, where the terrain induces motion components other than typical predominant yaw-plane motion. The study however found no discernible difference in measured side-slip angle of the methods. The system allows for accurate measurement at low and higher speeds depending on camera speed and lighting.     

框架结构损伤的检测诊断与评估方法研究

通过构造以损伤参数为未知量的超定非线性方程组,提出了3种改进的框架结构损伤的检测、诊断、评估方法——改进的一阶迭代法、改进的混合迭代法、改进的动静结合法。通过对框架结构损伤识别的数值模拟分析可以得出:在单柱或梁发生20%及以下损伤的情况下,动静结合法、一阶迭代法、混合迭代法均能较好地识别出损伤的位置与程度。在求解40%及以上的损伤或者多处梁柱损伤时,一阶迭代法和混合迭代法分别只经过25次迭代和22次迭代就达到设定的10-8迭代误差而收敛停止计算,均能准确地识别出损伤单元的位置与损伤程度;与一阶迭代法相比,混合迭代算法由于采用了精确度较高的二阶非线性解析解作为迭代修正的初值,因而迭代修正精度更高,收敛性更好;动静结合法由于结合了结构的动态信息和静态信息,识别精度与混合迭代算法接近且减少了运算时间,并且通过提高计算中所使用的模态阶数可大大提高其识别精度。     

Quasi-static tensile deformation and fracture behavior of a highly particle-filled composite using digital image correlation method

Polymer bonded explosives (PBXs) are highly particle-filled composite materials. This paper experimentally studies the tensile deformation and fracture behavior of a PBX simulation by using the semi-circular bending (SCB) test. The deformation and fracture process of a pre-notched SCB sample with a random speckle pattern is recorded by a charge coupled device camera. The displacement and strain fields on the observed surface during the loading process are obtained by using the digital image correlation method. The crack opening displacement is calculated from the displacement fields, the initiation and propagation of the crack are analyzed. In addition, the damage evolution and fracture mechanisms of the SCB sample are analyzed according to the strain fields and the correlation coefficient fields at different loading steps.     

On the coupling of anisotropic damage and plasticity models for ductile materials

In this contribution various aspects of an anisotropic damage model coupled to plasticity are considered. The model is formulated within the thermodynamic framework and implements a strong coupling between plasticity and damage. The constitutive equations for the damaged material are written according to the principle of strain energy equivalence between the virgin material and the damaged material. The damaged material is modeled using the constitutive laws of the effective undamaged material in which the nominal stresses are replaced by the effective stresses. The model considers different interaction mechanisms between damage and plasticity defects in such a way that two-isotropic and two-kinematic hardening evolution equations are derived, one of each for the plasticity and the other for the damage. An additive decomposition of the total strain into elastic and inelastic parts is adopted in this work. The elastic part is further decomposed into two portions, one is due to the elastic distortion of the material grains and the other is due to the crack closure and void contraction. The inelastic part is also decomposed into two portions, one is due to nucleation and propagation of dislocations and the other is due to the lack of crack closure and void contraction. Uniaxial tension tests with unloadings have been used to investigate the damage growth in high strength steel. A good agreement between the experimental results and the model is obtained.     

Mixed numerical–experimental technique for orthotropic parameter identification using biaxial tensile tests on cruciform specimens

This paper presents a mixed numerical–experimental method for the identification of the four in-plane orthotropic engineering constants of composite plate materials. A biaxial tensile test is performed on a cruciform test specimen. The heterogeneous displacement field is observed by a CCD camera and measured by a digital image correlation (DIC) technique. The measured displacement field and the subsequently computed strain field are compared with a finite element simulation of the same experiment. The four independent engineering constants are unknown parameters in the finite element model. Starting from an initial value, these parameters are updated till the computed strain field matches the experimental strain field. Two specimen geometries are used: one with a centered hole to increase the strain heterogeneity and one without a hole. It is found that the non-perforated specimen yields the most accurate results.