Micromechanical Damage Model Research Articles

Use of a modified Gurson model approach for the simulation of ductile fracture by growth and coalescence of microvoids under low, medium and high stress triaxiality loadings

Abstract In the paper the modified Gurson model is developed for the simulation of damage growth and ductile fracture under low, medium and high stress triaxiality loadings. A new coalescence criterion is introduced based on a simple assumption that singular value of the effective stress triggers the coalescence of microvoids in materials. According to the introduced approach the void coalescence described by means of the modified Gurson model is not only determined by the so-called critical, constant void volume fraction but also by the stress triaxiality ratio. Computational simulations have been carried out for Al 2024–T351 aluminum specimens. In order to find some improvements of micromechanical damage models, two different approaches have been compared for modeling the shear driven microvoid coalescence under low stress triaxiality loadings.

Modelling of plastic flow localisation and damage development in friction stir welded 6005A aluminium alloy using physics based strain hardening law

Plastic flow localisation and ductile failure during tensile testing of friction stir welded aluminium specimens are investigated with a specific focus on modelling the local, finite strain, hardening response. In the experimental part, friction stir welds in a 6005A-T6 aluminium alloy were prepared and analysed using digital image correlation (DIC) during tensile testing as well as scanning electron microscopy (SEM) on polished samples and on fracture surfaces. The locations of the various regions of the weld were determined based on hardness measurements, while the flow behaviour of these zones was extracted from micro-tensile specimens cut parallel to the welding direction. The measured material properties and weld topology were introduced into a 3D finite element model, fully coupled with the damage model. A Voce law hardening model involving a constant stage IV is used within an enhanced Gurson type micro-mechanical damage model, accounting for void nucleation, growth and coalescence, as well as void shape evolution. The stage IV hardening, observed in Simar et al. (2010), was found to increase the stiffness during plastic flow localisation as well as to postpone the onset of fracture as determined by the void coalescence criterion. Furthermore, the presence of a second population of voids was concluded to strongly affect the fracture strain of the high strength regions of the welds. This modelling effort links the microstructure and process parameters to macroscopic parameters relevant to the optimisation of the welds.

A micromechanical constitutive model for dynamic damage and fracture of ductile materials

This paper proposes a detailed theoretical analysis of the development of dynamic damage in plate impact experiments for the case of high-purity tantalum. Our micro-mechanical model of damage is based on physical mechanisms (void nucleation and growth). The model is aimed to be general enough to be applied to a variety of ductile materials subjected to high tensile pressure loading. In this respect, the work of Czarnota et al. (J Mech Phys Solids 56:1624–1650, 2008) has been extended by introducing the concept of nucleation law and by entering a nonlinear formulation of the elastic response based on the Mie-Gruneisen equation of state. This later aspect allows us to consider high impact velocities. All model parameters are directly assessed by experimental measurements to the exception of the nucleation law which is characterized by the way of an inverse identification method using three free-surface velocity profiles (at low, intermediate and high impact velocities). It is shown that the nucleation law can be consistently determined in the range of operating pressures. The nucleation law being identified, the development of internal damage happens to be a natural outcome of the modelling. The model is applied to predict damage development and free-surface velocity profiles for various test conditions. The variety and the quality of results support the physical basis (in particular micro-inertia effects) upon which the proposed model of dynamic damage is based.

Micromechanics of high-temperature damage in dual-phase stainless steel

High-temperature ductility of dual-phase stainless steels is investigated using a micromechanics approach of damage and fracture. Two different microstructures are studied with either a lamellar or a globular morphology of the ferrite phase, the latter being twice as ductile as the former at 1150 °C. The high-temperature damage evolution is characterized at different loading rates using notched round cylindrical bars producing different stress triaxialities, supplemented by fractographic analysis. The experimental observations have generated an advanced elasto-viscoplastic micromechanical damage model for both microstructures. With a detailed account of the process of nucleation, growth and coalescence of voids, the model properly captures the effect of stress triaxiality, strain rate, and morphology of the ferritic phase on the high-temperature ductility. The key factor controlling the loss of ductility in the lamellar microstructure is the constraint induced by the harder austenite layer on the softer ferrite zones.

On a class of micromechanical damage models with initial stresses for geomaterials

Abstract In this paper, we extend a class of micromechanical damage models by including initial stresses. The proposed approach is based on the solution of the Eshelby inhomogeneous inclusion problem in the presence of a pre-stress (in the matrix), adapted for elastic voided media. The closed form expression of the corresponding energy potential is used as the basis of various isotropic damage models corresponding to three standard homogenization schemes. These models are illustrated by considering isotropic tensile loadings with different initial stresses. Finally, still in the isotropic context, we provide an interpretation of the macroscopic damage model formulated by Halm and Dragon (1996) by briefly connecting it to the present study.

Micromechanical damage modeling and simulation of punch test

In order to verify the validity and applicability of the porous plasticity model for the simulation of non-local plastic fractures, punch tests are carried out for round steel plates of JIS G3131 SPHC. Incremental tensile coupon tests for the material are also conducted to obtain the plastic mechanical properties. Material parameters required for the porous plasticity model are identified through parametric numerical simulations of the coupon tests. It is proved that that force vs. indentation curves from punch test simulations using the porous plasticity model with the identified material parameters show good agreement with punch test results. It is also verified that simulated fracture shapes in the punch specimens are almost similar to the experimental ones in which fracture occurs along the circumferential edge of indenter where the hydrostatic stress develops highly.

Micromechanical modeling of interface damage of metal matrix composites subjected to off-axis loading

A three dimensional micromechanics based analytical model is presented to investigate the effects of initiation and propagation of interface damage on the elastoplastic behavior of unidirectional SiC/Ti metal matrix composites (MMCs) subjected to off-axis loading. Manufacturing process thermal residual stress (RS) is also included in the model. The selected representative volume element (RVE) consists of an r × c unit cells in which a quarter of the fiber is surrounded by matrix sub-cells. The constant compliance interface (CCI) model is modified to model interfacial de-bonding and the successive approximation method together with Von-Mises yield criterion is used to obtain elastic–plastic behavior. Dominance mode of damage including fiber fracture, interfacial de-bonding and matrix yielding and ultimate tensile strength of the SiC/Ti MMC are predicted for various loading directions. The effects of thermal residual stress and fiber volume fraction (FVF) on the stress–strain response of the SiC/Ti MMC are studied. Results revealed that for more realistic predictions both interface damage and thermal residual stress effects should be considered in the analysis. The contribution of interfacial de-bonding and thermal residual stress in the overall behavior of the material is also investigated. Comparison between results of the presented model shows very good agreement with finite element micromechanical analysis and experiment for various off-axis angles.

Coupled Micromechanical Model of Moisture-Induced Damage in Asphalt Mixtures

The combined effect of moisture and mechanical loading on asphalt mixtures has been recognized as one of the main causes of premature deterioration of flexible pavements. This paper presents a micromechanical model of moisture-induced damage in asphalt mixtures. The model couples the effect of moisture diffusion and mechanical loading to quantify the level of damage within the mixtures. The mechanical properties of the materials are defined as a function of the amount of moisture content. The cohesive zone modeling technique is used to simulate adhesive damage at the aggregate-mastic interfaces. Damage is evaluated based on the location and time for crack initiation and propagation at the aggregate-mastic interfaces and on the level of strains and stresses within the bulk of the mastic. Results show that micromechanical models provide a better understanding of moisture damage mechanisms in asphalt mixtures and can guide the development of continuum damage models.

A micromechanical model for inelastic ductile damage prediction in polycrystalline metals for metal forming

Abstract This paper deals with micromechanical modeling of ductile damage and its effects (coupling) on the plastic behavior of FCC polycrystalline metallic materials. The ‘fully coupled’ constitutive equations are written in the framework of rate-dependent polycrystalline plasticity where a ‘ductile’ damage variable has been introduced at a crystallographic slip system (CSS) scale in order to describe the material degradation by initiation, growth and coalescence of microdefects inside the aggregate. Both, theoretical and numerical (FEA) aspects of the proposed micromechanical coupled model are presented. The ability of the obtained model to predict the plastic strain localization, due to the ductile damage effect, in the classical tensile test is carefully analyzed. Application is also made to the fracture prediction in deep drawing of a cylindrical cup using a thin sheet. Finally, some concluding remarks and perspectives are pointed out.

A micromechanical damage model for rocks and concretes under triaxial compression

Based on analysis of deformation in an infinite isotropic elastic matrix containing an embedded elliptic crack, subject to far field triaxial compressive stress, the energy release rate and a mixed fracture criterion are obtained by using an energy balance approach. The additional compliance tensor induced by a single closed elliptic microcrack in a representative volume element and its in-plane growth is derived. The additional compliance tensor induced by the kinked growth of the elliptic microcrack is also obtained. The effect of the microcracks, randomly distributed both in geometric characteristics and orientations, is analyzed with the Taylor’s scheme by introducing an appropriate probability density function. A micromechanical damage model for rocks and concretes under triaxial compression is obtained and experimentally verified.

Micromechanical modeling of damage and fracture of unidirectional fiber reinforced composites: A review

An overview of methods of the mathematical modeling of deformation, damage and fracture in fiber reinforced composites is presented. The models are classified into five main groups: shear lag-based, analytical models, fiber bundle model and its generalizations, fracture mechanics based and continuum damage mechanics based models and numerical continuum mechanical models. Advantages, limitations and perspectives of different approaches to the simulation of deformation, damage and fracture of fiber reinforced composites are analyzed.

A Micromechanical Damage Model for Carbon Fiber Composites at Reduced Temperatures

Fiber-reinforced composites are seeing increased use in civil infrastructure applications where they may be exposed to moisture, sub-ambient temperatures (below —40°C in northern regions), and reduced-temperature (freeze— thaw) thermal cycling. These environments may induce internal damage in the composite due to residual stresses caused by mismatches in coefficients of thermal expansion between the constituents. In this study, a micromechanical damage model is presented for the prediction of matrix crack development in a unidirectional carbon/epoxy composite resulting from exposure to sub-ambient temperatures. Two thermal loadings are considered: cool-down from the cure temperature of the composite (121°C) to 25°C (▵T= -96°C) and to -50°C (▵T=-171°C). A finite element model is utilized to determine the internal stresses due to differences in the CTE of the constituents, and a shear-lag model is developed to predict subsequent crack spacing in the matrix. The influence of fiber spacing (or fiber volume fraction) is addressed. Model predictions indicate that, at 25°C, the internal stresses are not large enough to cause matrix cracking in this composite. However, at -50°C, the longitudinal tensile stress in the matrix exceeds the strength of the epoxy at most typical fiber volume fractions, which will result in matrix cracking. The shear-lag model was used to predict the subsequent crack spacing, and demonstrated a strong dependence on service temperature and fiber spacing. The model predictions provide good qualitative agreement with experimental observations, and indicate that the development of damage in a composite should be considered in the design of composite structures for reduced temperature environments.

3D Micromechanics and Effective Moduli for Brittle Composites with Randomly Located Interacting Microcracks and Inclusions

An innovative 3D, statistical micromechanical framework is proposed for brittle composites with interacting microcracks and interacting inclusions based on the concept of the ensemble—volume average and pairwise interactions. To account for the effect of 3D interactions among constituents, an approximate analytical solution of a micromechanical formulation is presented to accommodate all possible first-order and second-order ensemble—volume averaged perturbations due to the existence and interactions of randomly located microcracks and inclusions. In particular, explicit analytical solutions for the interactions between penny-shaped microcracks and spherical inclusions are systematically derived. The proposed pairwise interacting and first-order micromechanical damage models are compared to illustrate the influence of constituent interactions on effective elastic-damage moduli of composites. This framework provides a viable methodology to accommodate statistical, micromechanical, and interacting aspects of randomly distributed microcracks and inclusions.

Micromechanical damage model for rocks and concretes subjected to coupled tensile and shear stresses

Based on the analysis of the deformation in an infinite isotropic elastic matrix with an embedded elliptic crack under far field coupled tensile and shear stresses, the energy release rate and a mixed fracture criterion are obtained using an energy balance approach. The additional compliance tensor induced by a single opening elliptic microcrack in a representative volume element is derived, and the effect of microcracks with random orientations is analyzed with the Taylor’s scheme by introducing an appropriate probability density function. A micromechanical damage model for rocks and concretes is obtained and is verified with experimental results.

English

The micromechanical model of damage and fracture of elastovisoplastic materials is suggestedand applied to studying the processes of damage and fracture. The model describes the scale effectin processes of damage and localization of plastic strain in adiabatic shear bands. For the integrationof the suggested equations the new splitting method was used. It was shown that it has significantadvantages compare to existing iterative methods. The possibilities of the model suggested for thedescription of the plastic strain localization are illustrated by several examples.

On damage modelling in unsaturated clay rocks

The aim of this paper is to present the main problems encountered in the modelling of damage in an unsaturated quasi-brittle rock mass. Micromechanical damage models are based on a physical definition of damage, related to fracturing. Phenomenological formulations are less straightforward, but offer huge modelling possibilities by means of economical computation processes. Due to the dissipative aspect of damage, the Inequality of Clausius–Duhem (ICD) has to be satisfied. Strain softening and crack localization are regularized by means of a non-local formulation, founded on microstructure concepts, homogenisation and space averaging or gradient-enhancement. In an unsaturated damaged porous medium, suction effects combine with mechanical loading and fracturing, which induces complex couplings. On the one hand, Continuum Damage Mechanics well represents stiffness degradation for dry materials. On the other hand, fracture network models give a good estimation of complex flows. It is difficult to reconcile both theories. A new mixed model, HHMD, is proposed. It is a fully coupled formulation, involving independent state variables.

Damage evolution and fracture events sequence in various composites by acoustic emission technique

Three composites materials, Glare 2 fiber metal laminates, graphite/epoxy (Gr/Ep) and carbon/carbon (C/C) have been tested mechanically under quasi-static loading in uniaxial and bending modes using uniform and notched specimens. Acoustic emission (AE) technique was utilized in tracking the damage accumulation profile during loading up to fracture in terms of AE counts rate and cumulative. In addition wavelet transforms was used to process AE signals in order to obtain both frequencies and time information on the main failure mechanism and the sequential events during fracture process. This was supported by light and electron microscopies characterizations. The mechanical and acoustical responses were examined with respect to orientation and temperature effects for the Glare 2, exposure temperature effect for the Gr/Ep and porosity degree effect for the C/C. Manifestly, the AE results demonstrate different damage build-up profiles and point to a transition in failure micro-mechanisms with respect to the influence of each parameter (temperature, orientation, and density) on the specific composite tested. For the Gr/Ep, the wavelet transforms indicate the sequence of events in the fracture process, from fiber breaks followed by debonding and ending with matrix cracking. In some cases, it has been observed that the damage accumulation profile in terms of AE resembled the dependency of the crack density versus the strain predicted by a micro-mechanical damage model.

Damage and size effects in elastic solids: A homogenization approach

The paper presents a new procedure to construct micro-mechanical damage models able to describe size effects in solids. The new approach is illustrated in the case of brittle materials. We use homogenization based on two-scale asymptotic developments to describe the overall behavior of a damaged elastic body starting from an explicit description of elementary volumes with micro-cracks. An appropriate micro-mechanical energy analysis is proposed leading to a damage evolution law that incorporates stiffness degradation, material softening, size effects, unilaterality, different fracture behaviors in tension and compression, induced anisotropy. The model also accounts for micro-crack nucleation and growth. Finite element solutions for some numerical tests are presented in order to illustrate the ability of the new approach to describe known behaviors, like the localization of damage and size-dependence of the structural response. Based on a correct micro-mechanical description of the energy dissipation associated with failure, the model avoids significant mesh dependency for the localized damage finite element solutions.

Investigating Morphology Evolution of Damage by a Cellular Automaton Modelling

A two-dimensional cellular automaton (CA) model is developed to simulate damage and fracture morphology evolution on the mesoscale in materials. The plastic convection of damage is mapped onto the CA lattice, and initiation, propagation and coalescence of damage are simulated with a local rule-based scheme of a probability cellular automaton. The model includes known physical distinctions of fracture behavior between microcracks and microvoids, and they are characterized by modifying the probability rule of the cellular automaton. The simulations provide visual insight to understand how those physical processes dynamically progress and they affect the damage evolution in materials. The modeling can be used to link micromechanical models to continuum damage models.

Micromechanics-based Interfacial Debonding Model for Damage of Functionally Graded Materials with Particle Interactions

A micromechanical damage model is developed for two-phase functionally graded materials (FGMs) considering the interfacial debonding of particles and pair-wise interactions between particles. Given an applied mechanical loading on the upper and lower boundaries of an FGM, in the particle—matrix zones, interactions from all other particles over the representative volume element (RVE) are integrated to calculate the homogenized elastic fields. A transition function is constructed to solve the elastic field in the transition zone. The progressive damage process is dependent on the applied loading and is represented by the debonding angles which are obtained from the relation between particle stress and interfacial strength. In terms of the elastic equivalency, debonded, isotropic particles are replaced by perfectly bonded, orthotropic particles. Correspondingly, the effective elasticity distribution in the gradation direction is solved. The computational implementation is discussed and numerical simulations are provided to illustrate the capability of the proposed model.