Anisotropic Damage Constitutive Model Research Articles

Effects of strain rate and bedding on shale fracture mechanisms

Anisotropic shale is commonly distributed in nature and undergoes both dynamic compressive and tensile load in geological engineering. In this article, the coupling effects of strain rate and bedding structures on the fracture mechanisms of shale are investigated using a split Hopkinson pressure bar (SHPB) system. The tension–compression comparative study is conducted. The Brazilian disc method is modified, and a unified strain rate measurement method is established to comprehensively analyze shale’s fracture-related properties, including moduli, strength and energy dissipation. The results indicate that the energy dissipated by shale fracture is strongly related to its strength. The strain rate and bedding affect the anisotropic strength and dissipated energy by changing the crack density and crack propagation mode. At low or medium strain rates, the bedding orientation of shale determines the direction of crack propagation. However, at high strain rates, microcracks in different directions are widely activated in the shale, which increases the fracture degree and decreases the difference in fracture toughness between the shale’s matrix and bedding planes. This also leads to a decrease in anisotropy and causes the bedding planes to lose control over the direction of crack propagation. Additionally, the dynamic tensile strength of shale increases faster than the compressive one with the strain rate, leading to a reduction in the proportion of tensile failure under impact load. Based on the experimental findings, a new anisotropic damage constitutive model is developed to characterize the dynamic properties of shale. This model reflects the anisotropic damage evolution behaviors and aligns well with experimental results, offering a theoretical foundation for predicting shale’s dynamic fracture behavior. In addition to shale, the developed experimental methods and theoretical models can also be applied to the fracture analysis of other brittle transversely isotropic materials.

A Statistical Anisotropic Damage Constitutive Model for Shale Including the Effects of Confining Pressure and Strain Rate

A Statistical Anisotropic Damage Constitutive Model for Shale Including the Effects of Confining Pressure and Strain Rate

Anisotropic damage constitutive model of AA5754 aluminum alloy considering warm forming history

A multipath two-stage loading test for AA5754 aluminum alloy is carried out. In the first loading stage, the tensile tests of big samples were conducted with different preforming conditions. Then small samples were cut off from the pre-strained big samples. In the second loading stage, the mechanical properties of small samples were measured, and the influence of preforming factors such as prestrain value, temperature, strain rate and stress state on the mechanical properties of the sheets has been studied. With increasing prestrain, the yield stress of the sheet increases and the failure strain decreases linearly. The higher the preforming temperature is, the lower the yield strength of the sheet is under the same prestrain, and the greater the hardening index and failure strain. Moreover, the mechanical properties of the sheet are not sensitive to the forming strain rate and stress state. In addition, a transient softening effect appeared during the two-stage loading test. A damage constitutive model considering the history of warm forming is established by VUMAT subroutine of ABAQUS commercial software. The parameters of the constitutive model are determined by the two-stage loading experimental data and a genetic algorithm. This model can describe the transient softening and Bauschinger effect of AA5754 aluminum alloy after preforming at different temperatures. Good agreement is also observed between the stress-strain responses of AA5754 aluminum alloy after warm preforming and the predictions of the model.

Modeling the anisotropic plasticity and damage of AA7075 alloy in hot forming

The theory of unified visco-plastic damage constitutive equations has been frequently used to model the thermal flow behavior and damage evolution of various materials. But the anisotropic properties of materials were generally neglected in the previous studies. In this paper, a novel damage correction formula was proposed, which was expressed as a function of loading path and loading direction and used as a multiplier of a continuum damage model. By integrating a set of unified visco-plastic damage constitutive equations, the Yld2004-18p criterion and the damage correction formula, an improved anisotropic damage constitutive model was established. Anisotropic plasticity and anisotropic damage of AA7075 alloy under hot forming conditions can be properly modeled by this model. Material constants included in the three integrated functions were determined respectively based on different experimental data. The calibrated model is capable to accurately predict the forming limit curves of AA7075 alloy for different forming temperatures, strain rates and loading directions. The model was then numerically implemented in hot Nakajima simulations. The simulation results were evaluated comprehensively from the aspects of limit strain point, punch force- displacement curve, major strain field and fracture position. For further verification of the established model, hot forming simulation of a B-pillar was conducted and compared with a real B-pillar of AA7075 alloy fabricated via an industrial hot stamping process. It is concluded the anisotropic damage constitutive model can be numerically applied to accurately predict the plastic deformation and damage-induced fracture of AA7075 alloy under hot forming conditions.

A Statistical Damage Constitutive Model of Anisotropic Rock: Development and Validation

The damage constitutive model is of great significance to research the stress-strain relationship and damage evolution of rock under loading in engineering. In order to investigate the effect of anisotropic characteristic on the stress-strain relationship and damage evolution, a statistical damage constitutive model of anisotropic rock under true triaxial condition was developed. In this study, the plane which existed perpendicular to the coordinate axis was extracted from representative volume element (RVE) of rock. The extracted plane was assumed to be composed of abundant mesoscopic elements whose failure strength satisfied the Weibull distribution. According to the number of failure elements on the plane in each direction under loading, the anisotropic damage variable was established based on the proposed concept of areal damage. A statistical damage constitutive model of anisotropic rock was developed by using strain equivalent hypothesis and generalized Hooke constitutive model. Subsequently, the parameters in the anisotropic damage constitutive model were determined by the method of total differential. Thus, the damage evolution of anisotropic rock under various stress conditions can be conveniently evaluated by the anisotropic damage model. The model was validated based on the tests of rocks under the stress conditions of conventional triaxial and true triaxial, respectively. Moreover, for the purpose of studying the influence of parameters on the model, sensitivity analyses of mechanical parameters and model parameters were carried out. The results of statistical damage constitutive clearly demonstrate the stress-strain and damage evolution of anisotropic rock under various stress conditions.

Development and validation of an anisotropic damage constitutive model for C/SiC composite

Due to damage coupling and anisotropic evolution, constitutive models of Ceramic Matrix Composites are generally deficient in the description of material behavior under complex load conditions. This paper studied the mechanical behavior of a PIP prepared 3k carbon fabric plain woven C/SiC material under complex stress states. The phenomenon and mechanism of the anisotropy damage were analyzed. A constitutive model was proposed considering the anisotropy damage effect by load ratio functions, and only scalar damage variables were used to maintain a simple formulation. The constitutive model was validated against tensile tests of hat-shaped CMC components, and a FEM model of the experiments was established. The comparisons of strain results between the experiments and the FEM simulation showed good agreement under different loads. The model can be employed to facilitate structural analysis and design where material non-linearity is important.

Strong discontinuity analysis of a class of anisotropic continuum damage constitutive models – Part II: Concrete material application

On the basis of the strong discontinuity analysis, a discrete model expressed in terms of traction vector-displacement jump has been constructed from a continuous model expressed in terms of stress–strain law. In the first part of the paper, this approach has been extended to a class of anisotropic continuum damage constitutive models [1]. In this second part of the paper, the proposed class of discrete anisotropic damage constitutive models is particularized. More precisely, a micromechanical-based anisotropic damage constitutive model is derived. This model accounts in a natural manner for particular crack families orientation. The aims of this paper are (i) to illustrate the capabilities of the proposed discrete enhanced model in reproducing the induced anisotropy appearing in quasi-brittle materials when cracking and (ii) to assess the numerical robustness of the time integration scheme. For this purpose, two numerical examples at the material point level are exposed after a brief presentation of the time integration scheme. The correspondence between the continuous and the discrete model as well as the induced anisotropy features are emphasized.

Damage Theoretical Analysis of 2.5D C/SiC Composites under Tensile and Shear Loading

An anisotropic damage constitutive model is developed to describe the damage behavior of C/SiC composites. Different kinematic and isotropic hardening functions were employed in damage yield function to describe accurately the damage nonlinear hardening. The damage variable is defined by the principle of energy equivalence. The degradation of stiffness and the unrecoverable deformation induced by micro-crack propagation were considered in this model. The constants of constitutive model are identified and the damage evolution processes under tensile and shear loading. Uniaxial tension and shear tests have been used to valid the constitutive model to C/SiC composites.

Continuum damage mechanics based modeling progressive failure of woven-fabric composite laminate under low velocity impact

A continuum damage mechanics (CDM) meso-model was derived for both intraply and interply progressive failure behaviors of a 2D woven-fabric composite laminate under a transversely low velocity impact. An in-plane anisotropic damage constitutive model of a 2D woven composite ply was derived based on CDM within a thermodynamic framework, an elastic constitutive model with damage for the fibre directions and an elastic-plastic constitutive model with damage for the shear direction. The progressive failure behavior of a 2D woven composite ply is determined by the damage internal variables in different directions with appropriate damage evolution equations. The interface between two adjacent 2D woven composite plies with different ply orientations was modeled by a traction-separation law based interface element. An isotropic damage constitutive law with CDM properties was used for the interface element, and a damage surface which combines stress and fracture mechanics failure criteria was employed to derive the damage initiation and evolution for the mixed-mode delamination of the interface elements. Numerical analysis and experiments were both carried out on a 2D woven glass fibre/epoxy laminate. The simulation results are in agreement with the experimental counterparts, verifying the progressive failure model of a woven composite laminate. The proposed model will enhance the understanding of dynamic deformation and progressive failure behavior of composite laminate structures in the low velocity impact process.

Theoretical Formulation of a Coupled Elastic—Plastic Anisotropic Damage Model for Concrete using the Strain Energy Equivalence Concept

An anisotropic damage constitutive model for concrete is developed within the framework of elastoplasticity and continuum damage mechanics. The transformation from the effective (undamaged) to the damaged configuration in the elastic regime is obtained by using the hypothesis of elastic strain energy equivalence. Damage in plasticity is accounted for by developing a new formulation relating the plastic strains rate tensors in the effective and damaged configurations. Two anisotropic damage criteria are introduced to account for the different concrete behavior effects under tensile and compressive loadings. The total stress is decomposed into tensile and compressive components in order to satisfy these damage criteria. The plasticity yield criterion presented in this work accounts for the spectral decomposition of the stress tensor and will be used simultaneously with the damage criteria. The transformation of stresses from the effective to the damaged configuration is achieved by using a fourth order transformation tensor that is based on second order tensile and compressive damage tensors. Expressions are derived for the elastoplastic tangent operator in the effective and damaged configurations. The formulations are derived consistently based on sound thermodynamic principles.

The application of a homogenized overall and local anisotropic damage constitutive model to unidirectional and cross-ply CFCC with oblique loading directions

A homogenized anisotropic damage constitutive model is proposed to describe the mechanical behavior of continuous fiber-reinforced ceramic matrix composites (CFCC) for different loadings direction and laminate stacking sequences. An overall fourth-order damage effect tensor is introduced to account for the overall damage of the composites. In addition, two local (matrix and fiber) fourth-order damage effect tensors are introduced to analyze the local effects of damage experienced in both matrix and fibers. The overall and local damage tensors are correlated through a homogenization procedure. New expressions are derived for the stress and strain concentration factors of the damaged composite. The model is simulated by macro-microscopic finite element method (FEM). As applications of the model, unidirectional and cross-ply CFCC laminates with oblique loading directions are analysed to discuss the effects of fiber arrangement and orientation on the macroscopic mechanical behavior.

A Homogenization Procedure for the Numerical Simulation of Mechanical Behavior of CFCC by Considering the Overall and Local Anisotropic Damage

An anisotropic damage constitutive model was presented to characterize mechanical behavior of continuous fiber-reinforced ceramic matrix composites (CFCC) with two-scale damage. An overall fourth-rank damage effect tensor was introduced to account for the overall damage of the composite system. In addition, two local (matrix and fiber) fourth-rank damage effect tensors were introduced to account for the local effects of damage experienced by both the matrix and fibers. The overall and local damage tensors were correlated together using homogenization procedure. In terms of the homogenization methods, the effective elastic properties were obtained, and the stress and strain concentration factors were derived for damaged composites. The model was applied in detail to the unidirectional laminate that was subjected to uni-axial tension. The results were compared well with experimental data. The effects of important parameters such as the fiber volume fraction and the damage material parameters on the nonlinear behavior of the composites were investigated. The model provided a useful tool for understanding the overall dependence of stress-strain behavior on all the underlying constituent material properties.

Crack tip superblunting: experiment, theory and numerical simulation

Experimental revelation ofsuperblunting along plane strain predominant crack tip segment is reported here for modified polyproplene. As elucidated by a heuristic model of progressive circumferential cold-draw, the formation of superblunting crack tip depends critically on the ratio between the cold-draw propagation speed and the loading speed, and contributes significantly to the material toughening, especially for the improvement in impact toughness. Detailed numerical calculations are conducted based on a hyperelastic-viscoplastic and anisotropic damage constitutive model at finite deformation. The simulated results recapitulate the essential features of crack tip superblunting.