This article presents a constitutive model for dense sand that exhibits a post-peak strain-softening behavior. This model combines elements of plasticity with damage mechanics to simulate the stress–strain behavior. The post-peak stress drop is captured by the elasto-damage formulation, while the plasticity is superimposed beyond the elastic range. The total strain increment is composed of an elasto-damage strain increment and a plastic strain increment. The elasto-damage strain increment is found using the elasto-damage formulation, while the plastic strain increment is found using either the Drucker–Prager classical plasticity model or as a function of the damage strain. To calibrate this model, an experimental program was conducted on dense sand at different relative densities. The various physical and mechanical properties of the sand were determined. Both triaxial compression tests and hydrostatic tests were performed under different confining pressures, in order to obtain the model parameters at various conditions. These parameters were used to calibrate the model, which was coded in FORTRAN computer programs to simulate the stress–strain behavior of dense sand. The model was verified and found to be a good predictor of the response of dense sand for the selected stress path.

FEM results of softening materials are well known to show pathological mesh dependency. The main goal of this work is to revisit and propose efficient nonlocal damage gradient enhanced formulations able to avoid mesh dependency in the context of elastoplastic damage models with destination to industrial applications. This formulation is presented and studied for simple tension tests, with various spatial discretizations. Numerical aspects and implementation in ABAQUS-standard environment are discussed. The structure of the nonlocal element needed for those formulations is presented. For a given set of meshes, the ability of the proposed formulation to control the size of the necking zone is studied. In the same time the independence of the global dissipation to the mesh size is checked. Theoretical and practical limits of the proposed approach are highlighted.

A model for simulating fatigue damage accumulation and the fatigue failure process in metals is presented. The simulation is achieved by modeling material behavior with a series of nonlinear mechanical springs with randomized behavior. With each applied stress, a certain number of springs rupture. The damage accumulation process is modeled by the number of springs that have ruptured during the entire stress application cycle. When a sufficiently large number of springs rupture, the entire system is considered to have failed. This constitutes fatigue failure. This article follows two previous publications by the first two authors and extends the model further by incorporating additional random variables, investigating the significance of uncertainty in the spring behavior and simulation of the hysteresis behavior of metals during the fatigue damage accumulation process. Results similar to (1) the Wöhler S–N curve and (2) the hysteresis loss versus the number of stress cycle relationship, observed in laboratory testing of metal specimens, are presented.

Fully coupled thermo-elasto-visco-plastic-damage constitutive equations based on the state variables under large plastic deformation are developed for metal forming simulation. Relevant numerical aspects concerning both the global resolution strategy as well as the local integration scheme are discussed. The model is implemented into ABAQUS/Explicit using the Vumat user subroutine and used in connection with a 2D adaptive mesh facility. Application is made to the orthogonal metal cutting resulting in chip formation and segmentation or breaking. This example is studied in order to examine the ability of this adaptive fully coupled approach to predict qualitatively the formation and the segmentation of the chip compared to the classical procedure, which neglects the damage effect.

An experimental study has been carried out to determine the critical damage parameter based on the concept of entropy flow. The fatigue damage is either a cumulative process that progresses toward a maximum tolerable damage, or is an irreversible progression of cyclic plastic strain energy that reaches its critical value at the onset of fracture. In the present study, irreversible heat dissipation in terms of entropy is utilized to experimentally determine the degradation of different specimens subjected to low cyclic bending fatigue. An experimental correlation between entropy and damage is proposed. It is shown that the cyclic energy dissipation in the form of thermodynamic entropy can be effectively utilized to determine the critical damage value.

A new conical splay test is developed to assess the mechanisms of damage evolution in a range of stress states representative of hot rolling. The test consists of a bulk forming operation between open dies, during which plastic deformation occurs across a gradient of stress states from near-uniaxial tension to highly compressive. The transition between tensile and compressive stress state allows the microstructure to be accurately linked to the corresponding stress state. FE simulation of the new test is used to analyze the stress-state history during deformation. A low-carbon free-cutting steel, which is prone to edge cracking during hot rolling, is studied and the modes of damage evolution are discussed.

A simple quantitative method is presented which is applicable to any type of fatigue testing that uses sinusoidal strain/stress input and which will work for experimentally identifying points of failure due to fatigue damage of any kind of material being tested. The present work utilizes strain-controlled bending beam fatigue test on asphalt mixtures to demonstrate the efficacy of this method. Distortions in the hysteresis loop or waveform are tracked to pinpoint the appearance of initial microcracks and final point of complete failure due to fatigue damage. Relationship between output signals for consecutive cycles with reference to initial stable cycle is used for computing ‘R²’. The ‘R²’ drops sharply from initial stable value of 1 to less than 0.5 and eventually to almost 0 with increasing loading cycles. The number of cycles determined from the fitted equation at ‘R²’ = 1 marks the point of first fatigue failure N_fff and ‘R²’ = 0 marks the point of complete fatigue failure N_cff.

This article proposes an elastic-plastic damage model that combines micromechanical modeling with continuum damage mechanics to predict the stress–strain response of injection-molded long-fiber thermoplastics. The model accounts for distributions of orientation and length of elastic fibers embedded in a thermoplastic matrix whose behavior is elastic-plastic and damageable. The elastic-plastic damage behavior of the matrix is described by the modified Ramberg–Osgood relation and the 3D damage model in deformation assuming isotropic hardening. Fiber/matrix debonding is accounted for using a parameter that governs the fiber/matrix interface compliance. A linear relationship between this parameter and the matrix damage variable is assumed. First, the elastic-plastic damage behavior of the reference aligned fiber composite containing the same fiber volume fraction and length distribution as the actual composite is computed using an incremental Eshelby–Mori–Tanaka mean field approach. The incremental response of the latter is then obtained from the solution for the aligned-fiber composite by averaging over all fiber orientations. The model is validated against the experimental stress–strain results obtained for long-glass-fiber/polypropylene specimens.

This manuscript presents a new multiscale framework for the analysis of failure of thin heterogeneous structures. The new framework is based on the asymptotic homogenization method with multiple spatial scales, which provides a rigorous mathematical basis for bridging the microscopic scales associated with the periodic microstructure and thickness, and the macroscopic scale associated with the in-plane dimensions of the macrostructure. The proposed approach generalizes the Caillerie–Kohn–Vogelius elastostatic heterogeneous plate theory for failure analysis when subjected to static and dynamic loads. Inelastic fields are represented using the eigendeformation concept. A computationally efficient n-partition computational homogenization model is developed for simulation of large scale structural systems without significantly compromising on the solution accuracy. The proposed model is verified against direct 3D finite element simulations and experimental observations under static and dynamic loads.

The 2D extended homogenization model based on molecular chain network theory is employed to investigate the micro-to macroscopic mechanical behavior of polymer with randomly distributed voids under macroscopic compaction. A parametric study is performed to quantify the effect of the volume fraction of voids and the macroscopic stress triaxiality of loading conditions on the compaction behavior of porous polymer. The results suggest that the onset of localized shear band at the ligament between voids leads to the macroscopic yield of porous polymer. Furthermore, the microscopic localized shear deformation behavior is promoted in the polymer with high-volume fraction of voids under high macroscopic stress triaxiality loading condition, which results in the early appearance of the macroscopic yield. After the macroscopic yield, a remarkable strain hardening is shown in the macroscopic response of porous polymer under high macroscopic stress triaxiality loading condition, which is due to the onset and propagation of a large number of shear bands at the ligaments between voids. On the other hand, microscopic buckling develops at the narrowest ligament in the polymer with high-volume fraction of voids under high macroscopic stress triaxiality loading condition, which leads to the relative low macroscopic deformation resistance. Furthermore, to develop the macroscopic constitutive model of polymer with high-volume fraction of voids under high macroscopic stress triaxiality loading condition, a modified Gurson model is proposed which takes account of microscopic buckling and gives a good agreement with the unit cell computational results.

Majority of the available high-cycle fatigue (HCF) criteria have been proposed based on definition of an equivalent stress. Although these criteria have shown good agreements with results of the fatigue tests performed in particular conditions, majority of them do not consider all effects that have to be taken into account: mean normal and shear stresses, phase shift and different or random frequencies of the stress components, relative time locations of the extrema of the time histories of the stress components, etc. In the present article, based on the microscopic fatigue failure observations reported by some prominent references, new HCF criteria are proposed in three categories to overcome the mentioned shortcomings: (1) critical plane approach; (2) energy approach; and (3) integral approach. A relevant fatigue life assessment algorithm is also proposed and results of the prominent criteria are compared with results of the proposed criteria as well as the experimental results prepared by the author. To introduce a comprehensive study, the criteria are evaluated for components with complicated geometries under proportional, nonproportional, and random loadings. Results reveal that predictions of the proposed energy and integral approaches are more accurate.

Detailed experimental observations and numerical simulations are presented for the evaluation of residual properties of high-strength concrete specimens after exposure to high temperatures. Heated and nonheated notched four-point bending specimens were tested at ambient conditions approximately 1 month after exposure to the high temperature. Residual strength and post-peak response were monitored using a closed-loop load frame, and the fracture process zone was observed using Electronic Speckle Interferometry. The symmetric over-nonlocal formulation of a microplane model was used for interpreting the experimental investigation. The size-effect results were used to identify the true tensile strength and the initial fracture energy corresponding to the peak and the initial post-peak slope of a linear cohesive crack law. This study reveals that the material ductility increases with the thermal damage, which is explained by the increase of the fracture process zone size and the characteristic length.

Detailed un-standard experiments of fracture toughness in which SENB specimens of five different thicknesses were included, were carried out to investigate the size effect on the ductile and brittle fracture. It is found that the fracture toughness on the upper shelf increases with the size of the specimens, which have the similar geometry and then decreases gradually to the plane strain fracture toughness. The ductile fracture toughness increases with the size in the range of 4–16 mm for the increment of the plastic deformation zone size and plastic fracture strain under general yielding conditions, and then drops down from 16–22 mm for the increase of the high-stress triaxiality zone and the plastic deformation zone size not changing much which is less than the residual ligament width. While the fracture toughness of the lower shelf increases with the thickness in the range of 4–8 mm for the plastic deformation zone size increasing under small-scale yielding conditions, and then drops down from 8 to 22 mm for the increase of the high out-of-plane constraint. Theoretical analysis with the primary definition of the fracture toughness J integral, the constraint level and the plastic deformation volume was performed to investigate the different size effects for different temperatures. Finite Element Analysis simulations with continuum damage model to get the distribution and variety of the stress triaxiality as an important factor of fracture strain and fracture toughness.

The main purpose of this paper is to demonstrate that besides the stress triaxiality parameter, the Lode angle, which can be related to the third invariant of the deviatoric stress tensor, also has an important effect on ductile fracture. This is achieved by conducting a series of micromechanics analyses of void-containing unit cells and experimental-numerical studies of carefully designed specimens experiencing a wide range of stress states. As a result, a fracture criterion is expressed in terms of the equivalent failure strain as a function of the stress triaxiality and the Lode angle (or the third invariant of the stress deviator) and this function is calibrated for a DH36 steel plate.

Many anisotropic damage models have been proposed for different materials, ductile as well as quasi-brittle. The main drawback of the corresponding analyzes is that a large number of material parameters is often introduced, leading to identification difficulties and also to model complexity and associated numerical difficulties. It is also sometimes difficult to ensure the continuity of the stresses if the quasi-unilateral effect of microcracks closure and the dissymmetry tension/compression are represented. In order to solve those difficulties, one proposes to write the damage models in a specific nonstandard thermodynamics framework. The damage states are represented by a symmetric second-order tensor and the damage rate is assumed governed by a positive second-order tensor having a clear meaning: the absolute or the positive value of the plastic strain rate tensor for ductile materials, the positive part of the total strain tensor in quasi-brittle materials. Such a nonstandard feature makes the proof of the the positivity of the intrinsic dissipation necessary. This important proof is given in the considered framework for any damage law ensuring (anisotropic) damage increase and for any case, 3D, proportional or nonproportional. This extends then to induced anisotropy the isotropic case property of a positive damage rate as a sufficient condition for the thermodynamics second principle to be fulfilled. Altogether with the fact that the thermodynamics potential can be continuously differentiated, the example of an anisotropic damage model for concrete (build in this framework) is given. It allows for robust finite element implementation. Both space (classical nonlocal with internal length, nonlocal with internal time) and time regularizations (visco- or delay-damage) are used and applied to quasi-static and dynamic cases. Examples on concrete and reinforced concrete structures are given.

Performance-based design approach of special moment-resistant reinforced concrete (RC) framed structures demands a thorough understanding of axial force–bending moment (P–M) yield interaction of RC elements, particularly when the structure is subjected to seismic loads. Latest design approach includes desirable features of both ultimate strength and working stress to ensure a suitable ductile deformation response. This demands a detailed understanding of nonlinear response of P–M interaction. A complete set of analytical expressions for P–M yield interaction are proposed in a closed form by defining the limit boundary with ten sub-domains based on Euro Code currently in prevalence. P–M interaction relationships are also verified for plastic flow-rule in two main sections namely: (i) tension failure resulting in yielding of steel; and (ii) compression failure resulting in crushing of concrete. The conventional limit P–M domain is described based on Euro Code as long as the plastic strain increment becomes nearly normal to the yield domain over the part of bending response in the presence of axial force. The verified flow rule shows a close agreement in all sub-domains of tension failure, while does not qualify in few of the sub-domains of crushing failure. Practical examples of RC sections are chosen to illustrate the influence of different parameters namely: (i) cross-section dimension; (ii) percentage of tension and compression reinforcements; and (iii) properties of constitutive materials on the P–M boundary. Mathematically developed P–M interaction model is capable of identifying the damage mechanism of different sub-domains in RC sections; damage identification is made on the basis of strain profile of concrete and reinforcing steel.

Numerical simulation by finite element analysis was used to investigate the relationship between the strength of glass fiber reinforced plastic (GFRP) and fiber length. Load speed dependability was also investigated, since thermoplastic resin used for GFRP exhibits much nonlinear stress–strain behavior and strong dependency on load speed. For this purpose, we conducted a periodic-cell simulation to address the effect of composite microstructure, matrix viscoplasticity, and microscopic damage (fiber break and matrix crack). When the fiber length was varied, the damage pattern was divided into two patterns: fiber-avoiding propagation and fiber-breaking modes of the matrix crack from fiber ends. When the matrix crack easily propagated in a fiber-avoiding way for shorter fiber lengths, the rate-dependent effect of the matrix was significant. Moreover, we considered the length at which the fracture mode changed based on this analysis, and compared it with the conventional critical length given by Kelly. Since the conventional critical length does not ensure improved composite strength, the consideration of the damage mode transition is essential for selecting the appropriate fiber length for strength improvement.

The coupled computational procedure of the induction heating, the thermal conduction, the thermal elasto-viscoplastic damage, and the phase transformation analysis has been developed for the induction hardening analysis of steel machine parts. The validity of the proposed computational procedure has been illustrated by conducting the induction hardening analysis of a circular bar and a notched circular bar.

Cohesive zone models (CZMs) are being increasingly used to describe local fracture and failure behaviors in a number of material systems. The idea of the cohesive approach is to include a complex behavior around the crack front into the simple cohesive model for crack propagation analysis. Many cohesive laws have been proposed and there are a few rate-depend cohesive zone models. To describe the damage and failure phenomena on the interface, damage-based cohesive zone model (DCZM) is the most reasonable. Therefore, the aim of this article is to develop the phenomenological rate-depend cohesive zone model based on damage mechanics. Based on the internal variable theory of thermodynamics, a continuum interface constitutive model relating interface traction with interface separation has been developed. By introducing an interface damage variable, an evolution equation was derived to characterize the degradation of interfacial rigidity with interface debonding. This constitutive relation is applied to the matrix cracking in composites materials and the shear stress distribution, interface damage evolution, pullout stress, and pullout works were discussed. These results show that the proposed model qualitatively explain the experimental results and is useful for the prediction of the damage states, remaining strength and life time of the rate-depend bonding interface

In the present article, columnar specimens of lead zirconate titanate (PZT) were subjected to static compressive stress, and the characteristics of fracture under compression were clarified. The fracture tests were interrupted at certain intervals, and resonance and anti-resonance frequencies and electrostatic capacity were measured by means of an impedance analyzer with the compressive stress unloaded. The interruption and measurement were repeated with the maximum stress increased up to the fracture. The material properties of the specimens such as the electromechanical coupling coefficient, the dielectric constant, the elastic coefficient, and the piezoelectric constant were evaluated based on the resonant properties, and the variation of the material properties in the process of the fracture were clarified experimentally. An elastic coefficient was also evaluated from stress–strain relations during the compression fracture tests, and the difference in the elastic coefficient depending on the method of evaluation was discussed. Furthermore, internal damage developed in the specimens during the compression fracture tests was evaluated based on the variation of the elastic coefficients indirectly as a scalar damage variable on the basis of the continuum damage mechanics. Features of the damage development and the dependence of the quantitative value of the damage variables on the evaluation method of the elastic coefficient were discussed. SEM micrographs of the fracture surface were observed and the causes of the damage were investigated

Fracture in concrete is determined by excessive cracking. Numerical analysis of concrete fracture is either based on smeared crack method or discrete crack method. Smeared crack method is easier to implement than the discrete crack method but is therefore less accurate and applicable only for specific problems. We study fracture of concrete by a simplified meshless discrete crack method. The method exploit the advantages of smeared crack method and maintains the accuracy of discrete crack method. The discrete crack is modeled by set of crack segments that can be arbitrarily placed in the meshless discretization. Neo-Hooke material is used in the bulk material and cohesive zone model once the discrete crack occurs. We demonstrate for mode-I and mixed mode failure the accuracy of the meshless discrete crack method.

In order to clarify the elasto-viscoplastic deformation behavior and strength of rubber blended semi-crystalline polymer, micro- to mesoscopic mechanical behavior was modeled by using large deformation finite element homogenization method. In this model, dimension of mesostructure is identified by the volume fraction of interface region around the rubber particles. The effects of strain rate and the size of rubber particles on the mesoscopic true stress–strain relation, strain rate distribution in mesoscopic area, and change in mesoscopic morphology with deformation are investigated by numerical simulation of uniaxial tensile deformation of semi-crystalline polymer with nonuniformly distributed rubber particles. A series of computational simulations clarified that mechanical behavior of blend polymer is strongly affected by the size of rubber particles. Mesoscopic true stress–strain relationship shows softening for blend polymer with large rubber particles, which is closely related to the distribution of strain rate on mesoscopic scale. When the rubber particles are large, local strain rate is highly concentrated in the ligament area between adjacent rubber particles, while it distributes in larger area of semi-crystalline polymer matrix in case of small rubber particles. The difference in these localized deformation leads to characteristic change in the size and shape of rubber particles with straining. Nonuniform deformation in mesoscopic area caused by heterogeneous rubber particle distribution is emphasized by high strain rate and large rubber particles. Furthermore, maximum mean stress generated in semi-crystalline polymer matrix is very high when the size of rubber particles is smaller than or ligament thickness is larger than a specific value. The specific thickness corresponds to the critical value for brittle-ductile transition of rubber blended semi-crystalline polymer obtained by impact test

Elastic–plastic constitutive equation of hard metal for cold forging tools such as WC-Co cemented carbide with anisotropic damage is proposed to predict a precise service life of cold forging tools. A second rank symmetric damage tensor is introduced in order to express the anisotropic material damage and damage-induced stress unilaterality, namely a salient difference in uniaxial behavior between tension and compression. The conventional framework of irreversible thermodynamics is used to derive the constitutive equation. The Gibbs potential is formulated as a function of stress tensor, damage tensor, isotropic hardening variable, and kinematic hardening variable tensor. The elastic-damage constitutive equation, conjugate forces of damage, isotropic hardening, and kinematic hardening variable is derived from the potential. For the kinematic hardening variable, the superposition of three kinematic hardening laws is employed in order to improve the cyclic behavior of the material. For the evolution equation of the damage tensor, the damage is assumed to progress by fracture of the Co matrix–WC particle interface and by the mechanism of fatigue, i.e., the accumulation of microscopic plastic strain in matrix and particles. By using the constitutive equations, calculation of uniaxial tensile, and compressive test is performed and the results are compared with the experimental ones in the literature. Furthermore, finite element analysis on the behavior of cemented carbide as a die-insert of cold forward extrusion die set was carried out. The proposed constitutive equation was implemented to commercial FE software MSC.Marc2005 using User Subroutines. It is found that the anisotropic damage component can describe the different failure modes of the die-insert, namely fatigue crack and forced rupture.

This study pays attention to reveal material properties that control a resistance curve for ductile crack growth (CTOD-R curve) on the basis of the mechanism for ductile crack growth, so that the R-curve could be numerically predicted only from those properties. Crack growth tests using 3-point bend specimens with a fatigue pre-crack are conducted for two steels that have different ductile crack growth resistance, whereas both steels have the same mechanical properties in terms of strength and work hardening. Observation of crack growth behaviors provides that different mechanisms between ductile crack initiation from fatigue pre-crack and subsequent growth process can be applied. It is shown that two types of ductile properties of steel associated with ductile damage can mainly influence CTOD-R curve; one is a resistance of ductile crack initiation estimated with critical local strain for ductile cracking from a surface of notch root, and the other one is a stress triaxiality dependent ductility obtained with circumferentially notched round-bar specimens. The damage model for numerically simulating the R-curve is proposed taking the above two ductile properties into account, where the ductile crack initiation from crack-tip is in accordance with local strain criterion, and the subsequent crack growth triaxiality dependent damage criterion. The proposed model accurately predicts the measured different R-curves between two steels used that have the same ‘strength properties’, and also the stress triaxiality dependence of R-curve.

In order to clarify the elasto-viscoplastic deformation behavior and strength of rubber blended semi-crystalline polymer, micro- to mesoscopic mechanical behavior was modeled by using large deformation finite element homogenization method. In this model, dimension of mesostructure is identified by the volume fraction of interface region around the rubber particles. The effects of strain rate and the size of rubber particles on the mesoscopic true stress–strain relation, strain rate distribution in mesoscopic area, and change in mesoscopic morphology with deformation are investigated by numerical simulation of uniaxial tensile deformation of semi-crystalline polymer with nonuniformly distributed rubber particles. A series of computational simulations clarified that mechanical behavior of blend polymer is strongly affected by the size of rubber particles. Mesoscopic true stress–strain relationship shows softening for blend polymer with large rubber particles, which is closely related to the distribution of strain rate on mesoscopic scale. When the rubber particles are large, local strain rate is highly concentrated in the ligament area between adjacent rubber particles, while it distributes in larger area of semi-crystalline polymer matrix in case of small rubber particles. The difference in these localized deformation leads to characteristic change in the size and shape of rubber particles with straining. Nonuniform deformation in mesoscopic area caused by heterogeneous rubber particle distribution is emphasized by high strain rate and large rubber particles. Furthermore, maximum mean stress generated in semi-crystalline polymer matrix is very high when the size of rubber particles is smaller than or ligament thickness is larger than a specific value. The specific thickness corresponds to the critical value for brittle-ductile transition of rubber blended semi-crystalline polymer obtained by impact test.

This article discusses the delayed fracture and localized polarization switching near a crack tip in three-point bending piezoceramics under electromechanical loading. We have used finite element analysis to study delayed fracture experiments with single-edge precracked-beam method. A nonlinear finite element analysis was employed to calculate the fracture mechanics parameters such as energy release rate for the permeable, impermeable, and open crack face boundary conditions. Recent proposed energetically consistent boundary conditions were also considered. The effects of applied electric field and localized polarization switching on the fracture mechanics parameters were then examined.

A crack initiates at an interface edge between submicron thick films and leads to the malfunction of microelectronic devices. In this study, the cohesive zone model method with a cohesive law based on the damage mechanics concept is developed to simulate the creep crack initiation at an interface edge between tin and silicon films. Experiments on delamination at the Sn/Si interface using a micro-cantilever bend specimen were conducted. The cohesive law is applied to the elements in the UEL user subroutine in the finite element code ABAQUS. The parameters characterizing the cohesive law are calibrated by fitting displacement-time curves obtained by experiments and FEM simulations. It is revealed that the order of stress singularity increases with time and has a significant jump in its value at the crack initiation.

The past 20 years have seen substantial work on the modeling of ductile damage and fracture. Several factors explain this interest. (i) There is a growing demand to provide tools which allow to increase the efficiency of structures (reduce weight, increase service temperature or load, etc.) while keeping or increasing safety. This goal is indeed first achieved by using better materials but also by improving design tools. Better tools have been provided which consist (ii) of material constitutive equations integrating a physically-based description of damage processes and (iii) of better numerical tools which allow to use the improved constitutive equations in structural computations which become more and more realistic. This article reviews the material constitutive equations and computational tools, which have been recently developed to simulate ductile rupture.

Modern approaches to the modeling of composites are no longer limited to the use of a single approach for the whole structure or for all the degradation mechanisms. On the contrary, modern advances enable the definition of truly multiscale models in order to describe the degradation. Thus, homogenized models can be rigorously deduced from the underlying micromechanics. In the past few years, LMT-Cachan has made a number of contributions to the three key points of these multiscale approaches: (1) the improvement of the reference model on the fine scale, (2) the definition of a controlled correspondence between the scales, and (3) the definition of the associated homogenized model. Here, the complete approach is formalized as a modeling pyramid. Each mechanism of degradation is described on the more relevant scale within an ‘hybrid micromechanical model’. Based on the reference modeling, constitutive laws can be transfered within the unique framework of damage mechanics for being applied within commercial softwares. As an illustration, we focus more specifically on the homogenized law obtained for transverse cracking. The constitutive law and the material parameters issued from the homogenization, which define the model on the higher scale, are reviewed. Their identification is studied in detail. An important key point of the pyramidal approach appears here. Since it allows the interpretation of every quantity on different scales (both at the micromechanical and at the mesomechanical scales), the most relevant scale can be used for the identification of a chosen property. We limit ourselves to a ‘classical’ identification. We mean by classical identification a procedure based on straight specimens. This process, to a certain extent, uses a parametric simulation of the nonlinear model based on a finite element representation of the test samples. The complete model is then used for the simulation of an industrial sample with hole. That example emphasizes the interest of underlying micromechanial variables for experimental validation.

The deformation and damage mechanisms of sheets aluminium alloy 2198 are investigated experimentally and numerically. Mechanical tests in three different orientations are carried out on smooth and U-notched flat specimens. The material's microstructure is characterized to obtain the second phase area content, the morphology of particles and the void volume fraction. The fracture surfaces of the different specimens are examined using scanning electron microscopy. Smooth specimens loaded in the longitudinal and transversal orientation exhibit a slanted fracture surface, which has an angle of about 45° with respect to the loading direction. Samples loaded in 45°-orientation fail in a flat manner. Notched specimens show a V-shaped fracture surface. Failure initiates here at the notch root. It is shown that primary voids are first initiated at intermetallic particles. Void growth is promoted and rupture is caused by shear failure between regions of cavities. Finite element calculations are performed to simulate the orientation-dependent deformation and damage behavior. A phenomenological yield criterion combined with a porosity-based isotropic damage model allows for the quantitative prediction of specimen's failure for different triaxialities. An interaction of deformation and damage evolution can be demonstrated. The deficit of the von Mises yield criterion for this kind of metallic materials becomes evident.

A micromechanical model for predicting the strain increment required to bring a damaged material element from the onset of void coalescence up to final fracture is developed based on simple kinematics arguments. This strain increment controls the unloading slope and the energy dissipated during the final step of material failure. Proper prediction of the final drop of the load carrying capacity is an important ingredient of any ductile fracture model, especially at high stress triaxiality. The model has been motivated and verified by comparison to a large set of finite element void cell calculations.

In this study, void coalescence with and without a plastic prestrain history is studied using stress-controlled axisymmetric unit cell models. In addition to spherical voids, both oblate and prolate voids are considered. In the case with prestrain history a uniaxial prestrain up to 10% was applied and the material is thereafter subjected to loadings with constant stress triaxiality. It is found that the microscopic position of the maximum axial stress in void ligament can be taken as an indicator for void coalescence. In the beginning of plastic loading the maximum axial stress occurs at the edge close to the void. With the increase of plastic deformation, the position of maximum axial stress shifts from the void edge to cell boundary and coalescence starts when the position appears at the boundary. It is shown that a prestrain history significantly reduces the void coalescence strain. The prestrain effect on void coalescence depends strongly on the initial void shape. Prestrain history induces both strain hardening and void shape change. The effect of prestraininduced void shape change on coalescence strain is relatively small while the effect of prestrain-induced local hardening is significant.

Evolutionary statistical characters of fatigue damage are investigated on the smooth surface samples of 1Cr18Ni9Ti welded metal. Previous effective short fatigue crack (ESFC) criterion by Zhao et al. is employed with a local viewpoint of fatigue damage. Main attentions are paid to three kinds of ESFC data, i.e., density values of ESFCs, dominant ESFC (DESFC) lengths, and growth rates of DESFC. Six possible statistical models, i.e., normal, lognormal, extreme maximum value, extreme minimum value, two-parameter Weibull, and three-parameter Weibull, are compared to examine their validity for describing these three kinds of data. In the comparisons, three aspects of the statistical models are considered synthetically, i.e., total fit effect, consistency with fatigue physics, and safety of prediction in right tail region. Results reveal that there is a significant damage character of the micro-structural short crack (MSC) stage and the physical short crack (PSC) stage. The variation coefficient of the data increases in MSC stage, and then decreases in PSC and long crack (LC) stages. Extreme minimum value distribution is the appropriate model for describing the density values of ESFCs and the DESFC lengths. While extreme maximum value distribution is the reasonable model for the growth rates of DESFC. Fatigue damage is subject to an evolutionary random process from an initially chaotic (nonordered) state, to an independent state, and finally to a loading history-dependent state.

Predicting the energy absorption of composite structures requires a constitutive model that is capable of representing post-peak softening and irreversible strains, i.e., a coupled damage-plasticity model. The development of such models requires a general damage-plasticity framework. This article examines the merits and limitations of the continuum damage mechanics (CDM) framework and the plasticity framework. Based on the physical evidence of damage accumulation process in composites and the fundamentals of the two theories, a simple coupling method was proposed. This method employs a perfect plastic flow rule within a CDM framework. The capability of this method was examined by incorporating plasticity into the Matzenmiller-Lubliner-Taylor (MLT) model, a classic CDM model for composites. The coupled MLT-plasticity model was implemented as a user defined material law in explicit finite element code LS-DYNA®, and subsequently numerical tests were conducted. It was demonstrated that the proposed method can extend an existing composite CDM model into a coupled damage-plasticity model seamlessly with only a few extra parameters, while retaining its computational efficiency. The capability of the coupled CDM-plasticity model in energy absorption prediction was validated in axial impact simulations of a composite tube reinforced with 1-ply carbon fiber tri-axial braid.

The size-effect predictions from double-K fracture criterion, characterized by two parameters: the initiation toughness and the unstable toughness, are compared with the fictitious crack model or cohesive crack model for practical (laboratory) size range of three-point bend test notched specimens. Both the fracture models, although, adopt different crack propagation criteria, they yield indistinguishable crack initiation and unstable fracture loads for usual laboratory size specimens. Notable difference in the predicted crack initiation and unstable fracture loads are observed for asymptotic large size specimens and these loads are more conservative than those obtained using the fictitious crack model by ~20 and 22%, respectively.

Corrosion is one of the most damaging mechanisms in many engineering structures. To better understand how corrosion growth process takes place in AA 2024-T3 materials, research is being conducted to capture and systematically characterize the corrosion process, and develop simulation models. The objective of this study is to systematically investigate the degradation of major chemical elements (Al and Cu) in AA 2024-T3 as a function of the exposure time and electrochemical parameters during the corrosion process through experiments and develop an artificial neural network (ANN) model for the analysis and prediction. Experiments were conducted on AA 2024-T3 specimens under controlled electrochemical conditions. The chemical element map was developed through energy dispersive spectrometry technique for evaluation purposes. Based on the experimental data, an ANN model is developed for the analysis and prediction of degradation of major chemical elements at various exposure time and electrochemical parameters during the corrosion process. A very good performance of the neural network is achieved after training and validation with the experimental data. The degradation of the major chemical elements and material loss at various electrochemical parameters as a function of time was studied through ANN analysis.

Prediction of ductile failure onset in fracture-free materials has instigated several research works in the last few years. The literature shows basically two general approaches: (i) post-processed fracture indicators and (ii) damage-based material modeling. The former has shown successful to predict failure initiation in specific forming operations, whereas the latter has proved greater potential in assessing failure processes under general stress–strain paths. This work extends an existing isotropic damage model to account for separately tensile and compressive stress effects. Material modeling is based on finite strain elastoplasticity fully coupled to the damage evolution law. An assessment of some post-processed failure indicators is also presented. The damage model and fracture criteria are verified against tensile tests of notched specimens (tensile-dominant stress states) and the upsetting test of cylindrical billets (compressive-dominant stress states).

Characters of fatigue damage of smooth-surface samples are experimentally drawn through investigation on evolutionary crack sizes, density values, and growth rates of 1Cr18Ni9Ti welded metal. Previous effective short fatigue crack (ESFC) criterion, which consists of three interrelated concepts, i.e., ESFCs, dominant ESFC (DESFC), and density of ESFCs, is employed with a viewpoint of damage localization. Results reveal that the damage is subject to micro-structural short crack (MSC), physical short crack (PSC), and long crack (LC) stages. ESFCs and DESFC contribute to fatigue damage directly. The ESFCs sizes increase randomly and competitively, and exhibit a sudden increase when the ESFCs coalesce with each other to form the DESFC. But the DESFC size always increases stably. With the DESFC size increasing and the crack tips transferring, the non-ESFCs, in the form of the density of ESFCs, contribute to fatigue damage indirectly at the initial district of DESFC and then the crack tip districts. The density always increases in MSC stage. After reaching the maximum value at the transition point between MSC and PSC stages, it decreases rapidly in PSC stage, and then, tends to a saturation value in LC stage. The growth rates of ESFCs decrease randomly in MSC stage and then wave around the dominant growth rate in PSC stage. While the growth rate of DESFC shows a stable decrease in MSC stage and a constant increase in PSC stage. The behavior of DESFC is the result of the interactive and evolutionary collective action of short cracks, and therefore it is a reasonable description and quantification for the fatigue damage of smooth-surface samples.

This paper describes a method for predicting locations in a two-phase material where effective elastic strain is concentrated above a specified threshold value by virtue of the local arrangement of phases and a specified set of boundary conditions. This prediction is made entirely based on knowledge of the material properties of the phases, their spatial arrangement, and the boundary conditions, and does not require numerical solution of the equations of elasticity. The example problem is a 2D idealization of a fiber- or particle-reinforced composite in which the fibers/particles are randomly placed in the matrix and the boundary conditions correspond to uniaxial extension. The method relies on a moving window implementation of a decision tree classifier that predicts, for all points in the material, whether the effective elastic strain will exceed a specified threshold value. The classifier operates on a set of attributes that are the coefficients of a series expansion of a discretized version of the phase geometry. The basis vectors appearing in this series expansion of the phase geometry are derived from a principal components analysis of a set of training samples for which the mechanical response is calculated using finite element analysis. These basis vectors allow the accurate representation of the phase geometry with many fewer parameters than is typical, and, because the training samples contain information regarding the mechanical response of the material, also allow prediction of the response using a classifier that takes a relatively small number of input attributes. The predictive classifier is tested on simulated two-phase material samples that are not part of the original training set, and correctly predicts whether efffective elastic strain will be elevated above a specified threshold with greater than 90% accuracy.