Anisotropic Damage Model Research Articles

Cyclic behaviour of 3D-woven composites in tension: Experimental testing and macroscale modelling

Composites with 3D-textile reinforcement present several engineering advantages. However, their intricate yarn architecture also creates a material with a number of nonlinear behaviours and features, which need to be understood in order to enable their efficient use. To demonstrate the anisotropic development of such non-linear behaviours, and how they depend on loading mode, tensile samples of a 3D-woven layer-to-layer angle interlock carbon-fibre reinforced epoxy composite are tested experimentally (data shared publicly). More specifically, specimens are cut and tested at orientations of 0°, 15°, 30°, 45° and 90° relative to the direction of the warp yarns. The samples are tested cyclically by loading and unloading them at progressively higher displacement values. By monitoring the reduction in stiffness and the development of permanent strains it is possible to identify material parameter values used to calibrate an anisotropic macroscale elasto-plastic damage model. The model shows promising agreement with the experimental results.

Invariant-based interpretation of anisotropic damage induced by cyclic loading

Damage of quasi-brittle materials appears as micro-cracks and is represented by a tensorial internal variable. Established anisotropic damage models are dedicated to monotonic –possibly multiaxial– loading. Additionally, the effective visualization and the interpretation of anisotropic damage are challenging. In materials with heterogeneous meso-structure, e.g., concrete, the damage field, and the corresponding induced anisotropy are heterogeneous as the orientation depends on the local mechanical state. The post-processing can be performed in the principal damage basis, but this basis can be a field that varies spatially and temporally. The present work addresses both problems: (i) the enhancement of an anisotropic damage model to tackle cyclic and alternate loading on quasi-brittle materials and (ii) the interpretation of the damage-induced anisotropy due to complex loading, such as alternate and non proportional ones. In the proposed model, the strain-based damage criterion function, more precisely the consolidation function, is constructed to be dependent on the so-called active damage. We define different invariant-based indicators of the anisotropy of both the damage and the effective elasticity tensors. These indicators are assessed for homogeneous and heterogeneous fields representing an aggregate embedded in a mortar matrix.

A microcrack-based anisotropic damage model for concrete under mechanical loading and calcium leaching

In underground construction, concrete is always subjected to triaxial stress and calcium ion leaching, which results in anisotropic damage to concrete and reduce the durability of the structure. To capture the anisotropic damage properties of concrete subjected to mechanical-chemical coupling effects and predict the durability of underground concrete structure accurately, a microcrack-based anisotropic damage model is proposed. The mechanical damage, reflecting the density and direction of the microcracks caused by mechanical loading, is defined by a second-order tensor. The degree of chemical damage is defined by the amount of solid calcium phase lost in the concrete. Considering oriented microcrack and the influence of chemical damage on fracture toughness, the anisotropic mechanical damage evolution law of microcrack was established by linear fracture mechanics. A phenomenological chemical model governed by a diffusion law considering the variation of diffusion coefficient with stress induced microcracks is defined to describe the calcium dissolution process. The simulation results are in good agreement with the experimental results. Compared with the traditional elastoplastic damage model, the maximum creep error is only 0.114 ‰.

A Thermodynamically Consistent Anisotropic Continuum Damage Mechanics Model With Damage-Dependent Equivalent Strain

Abstract This paper proposes a new thermodynamically consistent anisotropic continuum damage mechanics model that the degradation of material is described by a set of damage variables. We adopt a set of novel equivalent strains which are functions of both the strain and the damage state variables as well. A viscous stabilization method is considered to improve the convergence during the material softening. The evolution of damage state variables is updated through a Newton–Raphson iterative process. The expression of the consistent tangent stiffness matrix is also derived. A smoothed exponential damage evolution shape function with rescaling regularization method is proposed to describe the material softening process and the mesh dependency phenomenon is relieved. Several sets of numerical examples including three-point-bending of a notched beam, uniaxial tension of unnotched and notched plate of composite material with multiple layups are presented to verify the anisotropic damage models.

A tensorial energy-release-rate based anisotropic damage-plasticity model for concrete

This paper proposes an anisotropic damage model for concrete to capture its plasticity and damage behavior effectively. Utilizing the framework of continuum damage mechanics, the model considers the influence of plastic Helmholtz free energy on damage evolution. This approach explicitly deduces damage-related thermodynamic forces without resorting to assumptions such as strain equivalence or energy equivalence. The proposed model employs tensile and compressive damage tensors to describe the development of anisotropic damage in concrete. The solution for plastic strain utilizes the empirical plasticity model. Furthermore, a unified evolutionary criterion for isotropic and anisotropic damage is also established, incorporating damage yield functions and orthogonal flow laws. Numerical simulations are conducted to validate the model’s ability to reproduce typical nonlinear behaviors of concrete structures under various load conditions.

Stress redistribution and stress triaxiality effect on the fatigue life of notched Ni-based single crystal superalloy at 760℃

The multiaxial stress state caused by geometric discontinuities will result in significant differences in the fatigue performance compared to the uniaxial stress state. It is crucial importance to research the notch fatigue behaviors of nickel-based single crystal (Ni-SX) superalloys at high temperature. This study investigated the impact of stress redistribution and stress triaxiality on the fatigue life of notched Ni-based single crystal superalloy at 760℃. The high temperature fatigue tests were carried out on the specimens under different stress ratios and the stress amplitudes under the same life conditions were obtained. A novel anisotropic damage model, incorporating the influence of stress triaxiality is proposed coupled with crystal plasticity theory. Based on experimental findings, an evaluation of the test parameters was conducted.The results showed that Mises stress, maximum principal stress, normal stress of principal stress along the loading direction, maximum principal strain, and strain along the loading direction were inadequate in reflecting the significant variations of samples observed among different stress ratios. However, the stress triaxiality at the unloading valley exhibited a high sensitivity to changes in fatigue life. To evaluate the fatigue life of notched specimens under different stress ratios, an improved Basquin’s type life prediction model was proposed, utilizing the stress triaxiality at the unloading valley. The proposed model demonstrates a favorable normalization trend for the fatigue life of notched specimens subjected to various stress concentration factor (SCF) conditions.

Damage and fracture initiation under shear and compression stress states in the aluminum alloy EN AW6082-T6

The present paper deals with the experimental and numerical analysis of damage and fracture behavior of ductile metals under combined compression and shear loading. Biaxial experiments with the H-specimen using a pneumatic downholder during compression loading and corresponding numerical simulations are discussed. A thermodynamically consistent anisotropic continuum damage model using damage strains is presented. During the experiments strain fields in critical areas of the specimens are monitored by digital image correlation (DIC) technique also showing evolution of deformation in thickness direction of thin sheets. Corresponding numerical simulations reveal the stress states and details of inelastic deformation behavior.

Influence of crystal orientations on the creep fracture of a nickel-based single crystal superalloy

Due to the anisotropy of the modulus of face-centered cubic cells, the nickel-based single crystal alloys exhibits substantial anisotropy at high temperatures. Their creep properties, especially the creep rupture lives, are related to the actuation of the slip system and the magnitude of the shear stress on the slip plane. The creep orientation sensitivity has been analyzed through creep experiments, as well as the microstructure and morphology of the fracture. On the macroscale, the necking sections of [001], [011] and [111] orientations are circular, elliptical and circular, respectively. Meanwhile, on the microscopic scale, the damage evolution caused by the expansion of the internal micropores in the single crystal alloy under the three orientations shows fourfold symmetry, double symmetry and triple symmetry, respectively. Based on the crystal plasticity theory, an anisotropic creep constitutive model and damage model are established to reflect the difference in creep deformation and damage evolution caused by orientation. The numerical simulations of the whole creep process of a second generation nickel-based single crystal superalloy show that the creep constitutive model and damage model can simulate the deformation and damage of the specimen under different orientations, and the creep life can be obtained.

Anisotropic damage state modeling based on harmonic decomposition and discrete simulation of fracture

This study proposes an anisotropic damage state modeling of the effective (damaged) elasticity tensor E˜ as a function of damage based on (i) a discrete element model for quasi-brittle material and (ii) a decomposition of the elasticity tensor in covariants. A procedure is proposed to measure the evolution of effective elasticity tensors computed by a beam-particle model. Various multiaxial damaging loadings allow us to constitute a dataset of around 76 000 effective elasticity tensors (our virtual testing reference set). We then cross-identify the anisotropic/tensorial damage state for the whole dataset. A detailed analysis of the dataset, using the distance to orthotropy as a guideline, justifies representing the induced micro-cracking by a single second-order damage variable D, even in the final stages with strong micro-cracks interaction. To formulate the damage state coupling, we use a reconstruction formula of orthotropic elasticity tensors in terms of invariants and (tensor) covariants. Thanks to this formula, some parts of the effective elasticity tensors E˜ (such as the dilatation part) are modeled exactly from the single damage variable. Constitutive equations are proposed for the remaining parts of E˜ (such as its generalized shear modulus and fourth-order harmonic part) using physical assumptions from micro-mechanics and a sparse data driven approach. The proposed anisotropic damage state coupling E˜(D) accurately models the damaged elasticity tensors in multiaxial loading, proportional or non-proportional, up to high damages. The present study firstly highlights the need for an anisotropic damage model for quasi-brittle materials and, secondly, offers a methodology to formulate the damage state coupling by explicit formulas introducing at most two dedicated parameters: the (optional) nonlinear shear-damage coupling parameter m and the harmonic prefactor h.

A Regularised Anisotropic Elastoplastic Damage and Viscoplastic Model and Its Hydromechanical Application to a Meuse/Haute-Marne URL Drift

A Regularised Anisotropic Elastoplastic Damage and Viscoplastic Model and Its Hydromechanical Application to a Meuse/Haute-Marne URL Drift

An anisotropic damage model for finite strains with full and reduced regularization of the damage tensor

AbstractThe modeling of damage as an anisotropic phenomenon enables the consideration of arbitrarily oriented microcracks at the material point level. Yet, the incorporation of material softening into structural simulations still requires a regularization of for example, the degrading variable. There exist different possibilities for a regularization in case of anisotropic damage with varying numbers of nonlocal degrees of freedom corresponding to for example, the symmetric integrity tensor , the principal traces of the damage tensor or a scalar damage hardening variable. Here, we propose a finite strain formulation with a symmetric second order damage tensor of which all six independent components are regularized with a corresponding nonlocal degree of freedom. Due to the significant increase in computational cost caused by the full regularization of the damage tensor, alternative approaches for a reduced regularization with fewer nonlocal degrees of freedom are discussed. Thereafter, the results of a numerical example using the model with full regularization are presented.

An anisotropic nonlinear multiscale damage model for mechanical behavior of a composite laminate with matrix cracks

An anisotropic nonlinear multiscale damage model for mechanical behavior of a composite laminate with matrix cracks

A large strain anisotropic ductile damage model — Effective driving forces and gradient-enhancement of damage vs. plasticity

A novel anisotropic ductile damage model at finite strains is proposed in this work. The model is formulated based on the fictitious configuration concept and includes deformation induced evolution of anisotropic damage properties. As a key contribution, different effective driving forces for both, plasticity and damage are elaborated in the context of a so-called two-surface formulation, i.e. the consideration of two admissible (but not independent) domains — one related to plastic flow and one related to damage evolution. The investigations include the introduction of effective stresses driving plastic flow on the one hand, and effective driving forces related to the evolution of anisotropic damage on the other. In addition and as an alternative to the introduction of effective driving forces, contributions influencing the respective threshold values related to plastic flow and damage evolution are proposed. Specification of the underlying constitutive equations together with the introduction of a suitable algorithmic implementation allows the model to predict experimentally observed material behaviour. Moreover, fundamental properties of the model are discussed by means of non-proportional loading paths generated by combinations of loading under uniaxial tension and simple shear. In view of the simulation of inhomogeneous boundary value problems, the implementation of the model into a finite element formulation is discussed. Since softening, respectively material degradation and necking phenomena, may results in mesh-dependent simulation results, an appropriate regularisation must be included in the model. In this work, gradient-enhancements in the form of a so-called micromorphic approach are included. In particular, gradients of scalar-valued hardening variables related to plasticity and damage are accounted for. A detailed analysis of the necessity of these gradient-enhancements of both, damage and plasticity is carried out based on the proposed multi-surface anisotropic ductile damage model. It turns out that gradient-enhanced regularisation of the damage contribution alone is not sufficient to regularise the problem (and vice versa, i.e. gradient-enhanced regularisation of the plasticity contribution alone is not sufficient as well) but contributions related to both phenomena, i.e. damage and plasticity, need to be regularised.

Numerical and experimental studies on crack nucleation and propagation in thin films

The prediction of damage and cracking patterns in ceramic thin films plays a vital role in the optimal design thereof. In this study, we focus on developing a numerical framework to predict fracture in ceramic thin films. For accurate and efficient modeling, the fracture energy and the material strength (ultimate stress) are taken into account by the cohesive phase-field damage model. Moreover, we argue that the orientation of the grain morphology induces a preferential direction for the crack which serves as a weak spot for crack initiation and propagation. A novel equivalent fracture energy is introduced into the formulation to account for the effects of microstructure on the cracking behavior of thin films. On the experimental side, tensile tests on (V,Al)N and (V,Al)(O,N) thin films deposited on ductile substrates are performed. It has been shown that this approach is a fast and efficient tracking tool for determining the mode-I fracture properties. To evaluate the accuracy of the anisotropic cohesive phase-field damage model proposed in this study, the crack patterns and crack density values of two chemically different thin films are compared for both numerical and experimental setups. This work provides new insights into the effect of different material parameters on the damage behavior of thin films. The key parameters can be summarized as the ultimate strength, fracture energy as well as the existing residual stress within the film.

A thermodynamically consistent anisotropic damage model for metallic glasses

AbstractThe recent success in manufacturing large‐size, also called bulk metallic glasses (BMGs) using 3D‐printing based on laser powder bed fusion (LPBF) opens an avenue for the broad application of this material class. To explore the great potential of both as‐cast and 3D‐printed BMGs, a comprehensive understanding and an accurate prediction of the plastic deformation and damage behaviour of this material class are indispensable. In this study, we develop a thermodynamically consistent anisotropic damage model incorporating tension‐compression asymmetry (TCA) to describe the unique inelastic deformation and damage behaviours of metallic glasses. The widely observed normal stress sensitivity and plastic dilatancy in metallic glasses are considered by using an extended Mohr‐Coulomb criterion in the constitutive description. Furthermore, a second‐order damage tensor is adopted for describing the anisotropic damage behaviour. By augmenting the Helmholtz free energy function to be dependent on the gradient of the free volume concentration and the gradient of the nonlocal damage parameter, the governing equations for the corresponding internal variables are derived within the framework of finite deformation. The damage localisation and mesh dependency are correspondingly alleviated. The simulation result shows that the shear band patterns are in good agreement with the experimental observations from literature.

Reducing internal variables and improving efficiency in data-driven modelling of anisotropic damage from RVE simulations

Reducing internal variables and improving efficiency in data-driven modelling of anisotropic damage from RVE simulations

A general continuum damage model for soft composites

Soft composites, including filled rubbers, nanocomposite gels, double network hydrogels, and multiple network elastomers, all exhibit stress-softening behavior in loading–unloading cycles, also denoted as the Mullins effect. Though qualitatively this damage behavior shows similar features, the details still vary with material types. In this work, we provide a general approach towards modeling the Mullins effect for soft composites based on continuum damage mechanics. We start with formulating a one-dimensional damage model. A logarithmic damage variable is employed, while a damage potential function is adopted to obtain the evolution law for the damage variable. We then extend the one-dimensional damage model to three-dimensions. The eight-chain type micro–macro transition is used to formulate an isotropic damage model. An anisotropic damage model is constructed based on the full network model, while a new micro–macro mapping is used to determine the micro stretch from the macro deformation. With this new mapping, the full network model appears in a consistent format in that the free energy, dissipation, and stress are respectively given by the average of their directional micro counterparts. In the current approach, two constitutive functions need to be determined: the elastic free energy density and the stored energy limit. Simple forms of these two constitutive functions are provided with only a small set of model parameters. The resulting models are then successfully applied to describe the stress response in loading–unloading cycles and the anisotropic response of predeformed materials for different kinds of soft composites.

A Continuum Damage-Based Anisotropic Hyperelastic Fatigue Model for Short Glass Fiber Reinforced Polyamide 66

A phenomenological 3D anisotropic nonlinear fatigue damage model has been developed for a short glass fiber-reinforced polyamide. The model is formulated within the framework of continuum damage mechanics and is based on a proposed anisotropic hyperelastic strain energy function. The proposed model accounts for the effects of fiber content and nonlinear material behavior. The mechanical behavior of polyamide reinforced with 20% and 30% wt short glass fiber has been experimentally investigated under quasi-static and fatigue loading. Fatigue tests under bending loading are carried out on rectangular specimens cut in the parallel and perpendicular direction to the mold flow direction. The proposed fatigue damage model allows predicting the fatigue damage of composite materials reinforced with short fiberglass, considering fiber orientation and fiber content. The model is used to predict the damage evolution and the number of cycles to failure, and good agreement between predicted values and experimental data is observed.

A fracture energy–based viscoelastic–viscoplastic–anisotropic damage model for rate-dependent cracking of concrete

A fracture energy–based viscoelastic–viscoplastic–anisotropic damage model for rate-dependent cracking of concrete

An Anisotropic Damage Model of Quasi-Brittle Materials and Its Application to the Fracture Process Simulation

Accurate predictions of the failure behaviors of quasi-brittle materials are of practical significance to underground engineering. In this work, a novel anisotropic damage model is proposed based on continuous damage mechanics. The anisotropic damage model includes a two-parameter parabolic-type failure criterion, a stiffness degradation model that considers anisotropic damage, and damage evolution equations for tension and shear, respectively. The advantage of this model is that the degradation of elastic stiffness only occurs in the direction parallel to the failure surface for shear damage, avoiding the interpenetration of crack surfaces. In addition, the shear damage evolution equation is established based on the equivalent shear strain on the failure face. A cyclic iterative method based on the proposed anisotropic damage model was developed to numerically simulate the fracture process of quasi-brittle materials. The developed model and method are important because the ready-made finite element software is difficult to simulate the anisotropic damage of quasi-brittle materials. The proposed anisotropic damage model was tested against a conventional damage model and validated against two benchmark experiments: uniaxial and biaxial compression tests and Brazilian splitting tests. The results demonstrate that the proposed anisotropic damage model simulates the mesoscale damage mode, macroscale fracture modes, and strength characteristics more effectively and accurately than conventional damage models.