Micromechanics-based Damage Model Research Articles

Quantification of damage evolution in stainless steel 316L based on 3D ex-situ X-ray CT and micro-damage model

Quantifying damage to improve the constitutive models that better account for damage prediction is of great importance in metal forming process. In this study, high-resolution micro-focus X-ray Computed tomography (CT) system, together with loading-unloading tensile test, were employed to quantify the 3D interactions of micro-voids evolution in the biocompatible alloy stainless steel 316L (SS316L). The specimen material was tensile deformed and interrupted at several strain intervals prior to failure, X-ray CT was then performed to quantify the damage evolution via the detected changing in size, number, distribution, and volume fraction of micro-voids (VFMV) after each specified strain increment. Thereby the nature of ductile damage, which involved the dynamic evolution mechanism of the nucleation, growth and coalescence of micro-voids, was revealed. Furthermore, an improved micromechanics-based damage (micro-damage) model considering large deformation condition was implemented into finite element (FE) package ABAQUS for the damage prediction. The damage of the specimen under tensile deformation with a wide range of stress states was predicted and a good agreement with experimental data was achieved in terms of damage distribution and evolution. It is concluded that the findings of this study not only reveal the dynamic evolution mechanism of the micro-voids in the damage process intuitively from the experimental point of view, but also provide more accurate material parameters for the theoretical damage modelling, so as to obtain more convincible damage prediction results in the metal forming process.

Enhancing understanding of fracture mechanisms in brittle rocks under static and cyclic loads: Experimental insights and theoretical model

The present study investigates the fatigue behavior of granite and red sandstone under coupled static and cyclic loading. Experimental results reveals a three-stage evolution trend for the deformation modulus, Young's modulus, peak strain, residual strain, dissipated energy as a function of the absolute cycle. Acoustic emission (AE) rate also exhibits a three-phase stage, including the initial phase, uniform velocity phase, and accelerated phase. To explain the mechanical responses and fracture mechanisms related to rock fatigue, this study built a micromechanics-based damage model that adopts a modified Paris law and considers both the effect of static stress and stress amplitude. The theoretical model successfully reflects the effect of static loading history and reproduces the three-stage evolution of residual strain during rock fatigue. The SIF deduced by the theoretical model exhibits a distinct behavior: it initially decreases during the first few cycles, stabilizes at a lower value, and subsequently undergoes a significant increase as it approaches the final cycles. The internal cause behind the three-stage evolution of crack growth rate, AE rate, and mechanical properties is attributed to subcritical crack growth during cyclic loading. Finally, the theoretical model successfully characterizes the effect of static stress and stress amplitude of cyclic loads on fatigue damage evolution.

Modeling the multiaxial fracture behavior of Ti–6Al–4V alloy sheets at a high temperature using improved damage modeling

In this study, the mechanical responses of Ti–6Al–4V alloy sheets at a high temperature under multi-axial loading were investigated using a micromechanics-based damage model within a continuum finite element (FE) framework. Tensile tests at three strain rates and a high temperature were conducted to analyze the plastic and ductile damage properties of the Ti–6Al–4V alloy sheets. Additionally, hot Nakajima tests were conducted on specimens with three different shapes to evaluate the improvement in formability at a high temperature. Moreover, the dimples on the fractured surfaces of the experimental samples were qualitatively analyzed. Simultaneously, corresponding FE simulations were conducted to predict the ductile damage behavior of the Ti–6Al–4V alloy sheets at a high temperature using a modified Gurson−Tvergaard−Needleman model. The predicted results and the displacements at the onset of failure were compared with the corresponding experimental data.

A micromechanical damage-healing model for encapsulation-based self-healing polymer composites under tensile loading

In this study, a novel micromechanics-based damage model is proposed for the damage evolution of a two-component microencapsulated-based self-healing polymer composite. In this way, a representative volume element (RVE) including an epoxy matrix with randomly distributed poly(methyl methacrylate) (PMMA) microcapsules is modeled in DigimatTM software and analyzed in Abaqus®. A new technique is developed to investigate the progressive damage by pre-inserted cohesive elements along all element boundaries of the epoxy matrix, PMMA shell, and capsule-matrix interfaces with the bilinear traction–separation law. Moreover, the impact of interface bonding strength, interface fracture energy, and PMMA microcapsules volume fraction on the load-carrying capacity of the RVEs under uniaxial tension loading was studied. The results indicated that the tensile strength of the self-healing polymer composite increased as the interfacial strength and fracture energy increased from 10 to 60 MPa and 100 to 1000 J/m2, respectively. Furthermore, the higher volume fraction of 5% PMMA microcapsules results in a lower load-carrying capacity of self-healing polymer composite with a strength of 4.9 N. A similar trend of Young’s modulus was observed for microcapsule-loaded epoxy composite compared to the pristine epoxy matrix. The micromechanical model has proper accuracy in predicting the tension behavior of self-healing composite in comparison to experimental results. Finally, two healing strategies are considered for the damaged RVE.

Stochastic fatigue life prediction in C/SiC composites at elevated temperature by micromechanics-based damage model

In this paper, a micromechanical approach is developed to predict the fatigue life and fracture process in different C/SiC composites subjected to different stochastic fatigue loading spectrums at elevated temperatures. Three types of stochastic fatigue load spectrums are considered in the fatigue life prediction at elevated temperature, that is, constant, increasing, and decreasing stochastic stress with cycles. Stress distribution between intact and broken fibers and the broken fibers fraction under stochastic fatigue loading spectrum are determined using the Global Load Sharing criterion considering multiple fatigue damage mechanisms at elevated temperatures. A new damage parameter of fatigue life degradation rate is developed to characterize the effect of stochastic loading on fatigue damage and fracture in C/SiC composites. Relationships between stochastic fatigue loading spectrum, broken fibers fraction, fatigue life, and fatigue life degradation rate in different C/SiC composite are established. Effects of stochastic fatigue loading spectrum type, stress level, and testing temperature on fatigue life degradation rate are discussed. The fatigue life degradation rate is very sensitive to the fiber preform, loading sequence, and testing temperature.

Fully-coupled continuum damage model for simulation of plasticity dominated hydrogen embrittlement mechanisms

The mechanical properties of steel are degraded due to the presence of hydrogen, also known as hydrogen embrittlement (HE). Simulations of hydrogen embrittlement at a continuum level can assist in characterizing the detrimental effect that is associated with the introduction of hydrogen regarding the structural integrity of steel structures. Such simulations require the implementation of both hydrogen diffusion and hydrogen assisted material degradation. The present study presents a framework for finite element simulations combining these aspects in a fully coupled way, with diffusion driven by hydrogen concentration, stress triaxiality gradient and plastic strain rate, and damage based on the ductile damage model known as the Complete Gurson Model (CGM). Hydrogen assisted degradation is modeled through acceleration of void growth, nucleation or coalescence, based on the HELP or HESIV mechanisms as underlying physical basis. The proposed model is the first fully-coupled continuum micromechanics-based damage model that accounts for the plasticity dominated HE mechanisms. The effect of element size and time increments is evaluated, establishing guidelines to use the model. Moreover, results of simulations of a tensile test on a hydrogen charged notched specimen are given, to provide an illustrative example of the capabilities of the framework. The well-known ductility loss due to hydrogen is observed in the simulation results.

Multi-scale modelling of progressive damage and failure behaviour of 2D woven SiC/SiC composites

In this paper, a multi-scale modelling approach has been developed to predict the progressive damage and failure behaviour of 2D woven SiC/SiC composites. At the tow scale, non-linear tow properties have been determined by a micromechanics-based damage model, in which two scalar damage variables were introduced to characterize the fibre-dominated and matrix-dominated damage, respectively. Based on periodic boundary conditions, a meso-scale unit cell model has been established to simulate the macroscopic stress-strain responses and progressive damage processes of the composite under uniaxial tensile, compressive and in-plane shear loadings, respectively. In the numerical method, the non-linear properties of constituent materials have been implemented by the user defined subroutine, USDFLD of the finite element package, Abaqus. The numerical results and their comparisons with experimental stress-strain curves have been presented. The failure mechanisms of the composite under each loading have been also discussed. The high efficiency and prediction accuracy of the model make it possible to analyse large scale woven composites.

Micromechanics-based damage model for liquid-assisted healing

This work presents a damage evolution framework including liquid-assisted healing. The model incorporates contributions from void size, void pressure, surface tension and liquid pressure. Experimental motivation for the damage-healing model is provided with in-situ melting experiments, where the evolution of the void distribution under monotonic tension is illustrated. The damage evolution is based on nucleation and growth of voids, which are modeled in a unified creep and plasticity framework. The proposed damage formulation introduces a void collective, which computes the void distribution in the material and allows to describe void collapse using the Rayleigh-Plesset equation. The necessary conditions for healing are discussed with use of model results. Particularly, the role of external load during healing, the dependence on liquid viscosity and surface tension are investigated.

An Integrative Model for the Dynamic Behavior of Brittle Materials Based on Microcracking and Breakage Mechanics

This study presents an enhanced integrative constitutive model for brittle materials subjected to dynamic loading by combining a micromechanics-based damage model and a breakage mechanics model. The damage model was used to describe microcracking, which captures the initial fragmentation of brittle solids due to growth of cracks until the material transforms into a granulated material. The dynamic behavior of the granulated material was described with a breakage mechanics model, which is activated when the damage level reaches a predefined critical threshold. The response of reference material boron carbide was simulated under confined/unconfined compression and ballistic impact loading conditions. The predictive capability of the integrative model was investigated by comparing the unconfined and confined simulation results with experimental data quantitatively and qualitatively. The simulations were also performed with an integrative model adopting a Drucker–Prager based two surface model to investigate the role of the granular material model on the macroscopic dynamic response. The two integrative models, which provided similar failure strength values under unconfined compression, predicted considerable different damage pattern in sphere impact simulations. A series of sensitivity simulations revealed that some critical granular model parameters strongly control the extent and spatial distribution of damage, and penetration resistance. The sphere impact simulations conducted with different impact velocities were able to reproduce various deformation features observed in previous experimental studies. The capability of the integrative model in capturing many aspects of the dynamic response of brittle materials under different loading conditions suggests that it can provide useful guidance for the design and development of next generation materials.

Influence of hierarchical porosity on the mechanical properties of porous woven composites under thermomechanical loading

The manufacturing process often results in hierarchical microstructures of porous woven composites, with pores and cracks in the matrix and fibers ranging from nanometers to hundreds of micrometers. This research is devoted to the mechanical behavior of porous woven composites with hierarchical pores of very different sizes under thermomechanical loading. A micromechanics-based damage model is developed within the continuum damage mechanics (CDM) considering the contribution of hierarchical pores for capturing the thermomechanical behaviour of porous woven composites. The predicted results of the proposed model are compared with available experimental results as well as other analytical methods to verify its correctness. The main advantages of the proposed model, comparing to the existing counterparts, are that the contributions of hierarchical pores can be examined on the material macroscopic mechanical responses, and the capability in characterizing the damage behaviour of matrix and fibers. This work can provide theoretical guidance for controlling the formation of hierarchical porosity during the manufacturing process.

A multi-mechanism constitutive model for the dynamic failure of quasi-brittle materials. Part II: Integrative model

In Part I, we established a model for amorphization during the failure of quasi-brittle materials. In this Part II, we present a multi-mechanism physics-based constitutive model which incorporates amorphization, microcracking and granular flow as basic deformation mechanisms. With this new integrative model, we investigate the interaction and competition of the different mechanisms. In the amorphization model we considered the initiation and evolution of amorphization bands. Microcracking is described with the micromechanics-based damage model developed in Tonge and Ramesh (2016a). Both amorphization and microcracking may introduce damage to the material, and granular flow is activated when the accumulated damage reaches some threshold value. Using boron carbide (BC) as the model material, we examine the response of a representative volume element (RVE) under different loading conditions and loading rates. We apply the full model to full simulations of plate impact and dynamic Vickers indentation into the material. Next, we simulate the sphere-on-cylinder impact experiments as an application of the integrative model. By comparing the simulation results with experiments and studying the influence of the various material parameters, we demonstrate the ability of the integrative model to capture the effects of multiple mechanisms and suggest some promising directions for material-design.

A micromechanics-based damage model for compressive behavior analysis of impacted composite laminates

The compressive strength of composite laminates decreases seriously after being subjected to impact loading, which is an important item to be considered in the usage of composite material. In this paper, a micromechanics-based damage model is proposed to study the compressive behavior of impacted composite laminates. The micro stresses of fiber and matrix are calculated by stress amplification factors and then used to judge the failure mechanisms according to corresponding physical failure criteria. A progressive damage model based on different failure statuses of constituents is established to study the degradation of material properties. The bi-linear cohesive model is used in the research of delamination onset and propagation. The compressive behaviors of quasi-isotropic composite laminates subjected to different impact energies are investigated by this proposed method. Good agreements in terms of structure responses, failure mechanisms, and residual compressive strengths are obtained between numerical results and experimental data. The matrix cracking and delamination caused by impact loading are responsible for the initiation and propagation of buckling, which leads to the final collapse of entire laminates. Based on the numerical investigations of material parameters, the increment of mode II interlaminar fracture toughness is capable of improving the residual compressive strength significantly.

A micromechanics-based damage model for non-woven fiber networks

Non-woven materials are fiber networks consolidated by different bonding techniques. It has been found that interfiber bond fracture is a major damage mechanism in non-wovens and strongly affects mechanical strength and toughness. In this article, we present a micromechanically based damage model for non-wovens. The model is built upon modeling single bond breaking processes and linking local damage events to macroscopic behaviors. In this model, a nonlinear term is introduced to describe non-affine deformation of fibers at a bond. The traction load on a bonded interface is determined by considering local force balance and network constraints. A bond breaks when its traction load exceeds a critical value, and this local information is used to update the global damage state through a classical continuum damage mechanics framework. Spatial correlation of damage in the network is modeled using a non-local averaging scheme. The proposed model is applied to a commercial non-woven series. The model is able to reproduce experimentally observed behaviors including elasticity, non-linear hardening, peak load and damage localization under uniaxial tensile loading as a function of network density. Damage states predicted by the numerical simulations match well with in-situ imaging results demonstrating the predictive capability of the model. The proposed model bridges non-woven microstructure and macroscopic behaviors and thus can serve as an effective tool for future studies of the mechanics of fiber networks.

Investigation of the effect of forming parameters in incremental sheet forming using a micromechanics based damage model

The incremental sheet forming (ISF) process is considered as a feasible solution for forming a variety of small batch and even customised sheet components. The quality of an ISF product is affected by various process parameters, e.g. sheet material, step-down, feed rate, tool diameter and lubricant. To produce an ISF part of sufficient quality and accuracy without defects, optimal parameters of the ISF process should be selected. In the present work, experiments and FE analyses were conducted to evaluate the influence of the main ISF process parameters including the step-down, feed rate and tool diameter on the formability and fracture of two types of pure Ti (grade 1 and 2). The Gurson–Tvergaard-Needleman (GTN) damage constitutive model with consideration of stress triaxiality was developed to predict ductile fracture in the ISF process due to void nucleation, growth and coalescence. It was found that the ISF parameters have varying degrees of effect on the formability and fracture occurrence of the two types of pure Ti, and grade 2 pure Ti sheet is more sensitive than grade 1 Ti sheet to the forming parameters due to low ductility.

Micro-voids quantification for damage prediction in warm forging of biocompatible alloys using 3D X-ray CT and RVE approach

This study aims to quantify the three-dimensional (3D) micro-voids for damage prediction in warm forging through non-destructive X-ray computed tomography (CT) and RVE approach. Typical biocompatible alloys, i.e., stainless steel 316 L (SS316L) and titanium alloy Ti-6Al-4V, were used as specimen materials in warm-forging a medical implant, i.e., a basal thumb implant. X-ray CT scanning was performed for both the preforms and forged components. Volumetric CT images were then reconstructed and the 3D micro-void distribution and evolution inside the materials were detected and analysed quantitatively. Furthermore, three typical local strain regions, i.e., the small tensile strain region (STSR), small compressive strain region (SCSR) and large compressive strain region (LCSR), were established as the 3D representative volume element (RVE) models for both SS316L and Ti-6Al-4V preforms. The spatial location, size and volume of each micro-void were obtained from defect analysis of the 3D CT images and considered explicitly for subsequent damage prediction. An improved thermo-mechanical coupled micromechanics-based damage (micro-damage) model, which considered the variation of volume fraction of micro-voids (VFMVs), was implemented into finite element (FE) package ABAQUS for localized damage prediction of the RVE models. The damage distributions of the RVE models at different strain levels were visualized and identified. Finally, the localized damage evolutions at both compressive and tensile deformations were predicted and found to match quite well with the findings acquired from CT scanning. Thus, the application of non-destructive X-ray CT measurement of micro-voids, incorporating the RVE approach, was able to play a significant role leading to a more reliable damage prediction in the warm forging process.

Micromechanics based damage model for predicting compression behavior of polymer concretes

In this study, the compressive behavior of polymer concrete (PC) is investigated using micromechanics-based representative volume element (RVE) concept. The RVE is composed of silica aggregates and epoxy matrix. The aggregate and matrix are modeled as linear elastic and elasto-plastic material, respectively. The interface between aggregates and matrix is modeled by employing a bilinear traction–separation law and its parameters are computed from Mohr–Coulomb failure criterion. RVE is modeled in Digimat software and imported into ABAQUS for damage analysis. Three types of boundary conditions, i.e., Dirichlet, periodic, and mixed are considered in the RVE modeling. The influences of aggregates shape, distribution, volume fraction, and interfacial parameters on the overall compressive behavior of PC are studied under uniaxial compression loading. In order to assess the micromechanical RVE model, standard cylindrical specimens of PC are manufactured and tested under uniaxial compression. Comparison of numerical and experimental results shows that: 1) the more the interfacial strength and fracture energy increases, the more the compressive strength of PC increases; 2) the compressive behavior of PC is highly dependent on aggregate volume fraction and distribution in comparison to aggregate shape, 3) the model has appropriate accuracy in predicting the compressive behavior of PC.

Micromechanics-based damage model for failure prediction in cold forming

The purpose of this study was to develop a micromechanics-based damage (micro-damage) model that was concerned with the evolution of micro-voids for failure prediction in cold forming. Typical stainless steel SS316L was selected as the specimen material, and the nonlinear isotropic hardening rule was extended to describe the large deformation of the specimen undergoing cold forming. A micro-focus high-resolution X-ray computed tomography (CT) system was employed to trace and measure the micro-voids inside the specimen directly. Three-dimensional (3D) representative volume element (RVE) models with different sizes and spatial locations were reconstructed from the processed CT images of the specimen, and the average size and volume fraction of micro-voids (VFMV) for the specimen were determined via statistical analysis. Subsequently, the micro-damage model was compiled as a user-defined material subroutine into the finite element (FE) package ABAQUS. The stress-strain responses and damage evolutions of SS316L specimens under tensile and compressive deformations at different strain rates were predicted and further verified experimentally. It was concluded that the proposed micro-damage model is convincing for failure prediction in cold forming of the SS316L material.

Damage modelling of epoxy material under uniaxial tension based on micromechanics and experimental analysis

Epoxy is a widely used thermosetting polymer in various engineering fields to develop composites. Studying its damage and fracture behaviour under various loading conditions is highly important. In this work, a micromechanics-based damage model is developed for understanding the damage initiation and growth in epoxy. To support this damage model, tests are performed for obtaining mechanical properties and to study the damage behaviour of epoxy. Diglycidyl ether of bisphenol A (DGEBA) resin with triethylenetetramine (TETA) hardener in 10:1 ratio are mixed and cured to make the epoxy. To give a physical meaning to damage, the model quantifies the damage as volume fraction of a spherical void in a unit representative volume element (RVE) of epoxy material. Degraded effective properties are computed for damaged RVE using standard mechanics-based micromechanical approach. A second-degree polynomial is established for effective stiffness with damage at any loading instance. This functional form of degraded stiffness in terms of damage is used in constitutive relations. A strain energy- based approach is used to compute thermodynamic forces, a state variable used for the evolution of damage. A damage evolution model is proposed with two material-specific parameters which are determined using experimental tests. The model is implemented by user material subroutine (UMAT) in commercial finite element software, Abaqus/Standard. The proposed model accurately captures the tensile behaviour of the epoxy material and gives capability to simulate an epoxy material’s damage behaviour from its initiation till failure or macrolevel rupture under uniaxial tensile loading. The developed model predicts the behaviour of the material in agreement with experimental results.

Scale effects in the static response of a one-dimensional quasi-brittle damage lattice

In this paper, we investigate the failure of a discrete elastic-damage axial system using both a discrete and an equivalent continuum approach. The microstructured damage chain consists of a one-dimensional damage lattice with direct nearest–neighbour interactions, which is composed of a series of periodic elastic-damage springs (axial lattice system treated in terms of discrete damage mechanics). We show that the damage lattice equations are equivalent to the centred finite difference formulation of a continuum damage mechanics (CDM) evolution problem. Such a discrete damage system reveals some scale effects on both the structural strength and stiffness. The nonlocal CDM in the hardening branch and cohesive damage model in the softening branch considered here are built using a continualisation procedure applied to the nonlinear difference equations of the lattice system. With this procedure, the difference equations to be solved are approximated by higher order differential equations. Using a rational asymptotic method, the continualised model appears to be equivalent to a nonlocal CDM model in the damage propagation zone. A finite length cohesive model is obtained in the softening range. A comparison of the discrete and the continuous problems for damage chains brings out the effectiveness of the new micromechanics-based nonlocal and cohesive continuum damage model, especially for capturing scale effects.

A unified micromechanics-based damage model for instantaneous and time-dependent behaviors of brittle rocks

This paper presents a unified micromechanics-based damage model for instantaneous and time-dependent inelastic behaviors of brittle rocks subjected to compressive stresses. The constitutive model is formulated in a combined homogenization/thermodynamics framework. The inelastic deformation is induced by frictional sliding along closed cracks, and strongly coupled with damage evolution by crack growth. Material degradation is described by a scalar-valued internal damage variable that is decomposed into two parts: an instantaneous part induced by applied stresses and a time-dependent part by subcritical cracking due to stress corrosion. Based on the system free energy determined with the Mori–Tanaka homogenization scheme, we propose a Coulomb-type friction criterion, which serves simultaneously as the yielding function and plastic potential, implying the use of an associated flow rule. An instantaneous damage criterion based on the conjugated force associated with the damage variable and a time-dependent damage criterion in terms of progressive evolution of microstructure are introduced. For the latter, an efficient computational algorithm is explored to solve numerically the strain history-dependent integration. As the first phase of validation, the proposed model is finally applied to simulate two typical brittle rocks, Dagangshan diabase and Xiangjiaba sandstone.