Micromechanical Damage Model Research Articles

Micromechanical modeling of the progressive failure in short glass–fiber reinforced thermoplastics – First Pseudo-Grain Damage model

This paper presents a new micromechanical damage model, called “First Pseudo-Grain Damage” (FPGD) model, to predict the overall elasto-plastic behavior and damage evolution in short fiber reinforced thermoplastic materials typically produced by injection molding. The model combines mean-field homogenization theory with a continuum damage model, leading to a semi-analytical estimate of the composite incremental response that is convenient for the large scale simulation of composite structures. Each representative volume element (RVE) of the composite is decomposed into a set of pseudo-grains (PGs), which are two-phase composites with aligned fibers of the same aspect ratio. The PGs are homogenized individually according to a nonlinear Mori–Tanaka scheme. Then, a self-consistent scheme is applied to the aggregate of homogenized PGs. An anisotropic damage model is used at the PG level which enables accommodating arbitrary multiaxial and non-monotonic loading histories. Damage evolution inside PGs progressively affects the overall stiffness and strength of the RVE up to total failure. An evaluation of the proposed model against experimental data is conducted for short glass–fiber reinforced polyamide 6,6 (PA6,6). It is shown that the model yields satisfactory predictions of the response under uniaxial tension on samples with different fiber contents and under various loading directions relative to the main injection flow direction.

A nonlocal model of fracture by crazing in polymers

We derive and numerically verify scaling laws for the macroscopic fracture energy of polymers undergoing crazing from a micromechanical model of damage. The model posits a local energy density that generalizes the classical network theory of polymers so as to account for chain failure and a nonlocal regularization based on strain-gradient elasticity. We specifically consider periodic deformations of a slab subject to prescribed opening displacements on its surfaces. Based on the growth properties of the energy densities, scaling relations for the local and nonlocal energies and for the specific fracture energy are derived. We present finite-element calculations that bear out the heuristic scaling relations.

Brittle creep and subcritical crack propagation in glass submitted to triaxial conditions

AbstractAn experimental work is presented that aimed at improving our understanding of the mechanical evolution of cracks under brittle creep conditions. Brittle creep may be an important slow deformation process in the Earth's crust. Synthetic glass samples have been used to observe and document brittle creep due to slow crack‐propagation. A crack density of 0.05 was introduced in intact synthetic glass samples by thermal shock. Creep tests were performed at constant confining pressure (15 MPa) for water saturated conditions. Data were obtained by maintaining the differential‐stress constant in steps of 24 h duration. A set of sensors allowed us to record strains and acoustic emissions during creep. The effect of temperature on creep was investigated from ambient temperature to 70°C. The activation energy for crack growth was found to be 32 kJ/mol. In secondary creep, a large dilatancy was observed that did not occur in constant strain rate tests. This is correlated to acoustic emission activity associated with crack growth. As a consequence, slow crack growth has been evidenced in glass. Beyond secondary creep, failure in tertiary creep was found to be a progressive process. The data are interpreted through a previously developed micromechanical damage model that describes crack propagation. This model allows one to predict the secondary brittle creep phase and also to give an analytical expression for the time to rupture. Comparison between glass and crystalline rock indicates that the brittle creep behavior is probably controlled by the same process even if stress sensitivity for glass is lower than for rocks.

A nonlocal treatment technique based on the background cell concept for micro-mechanical damage modeling

In the present paper, a new nonlocal treatment for micro-mechanical damage modeling is introduced based on the background cell concept. The nonlocal damage variable in the modified GTN damage model is defined as the weighted porosity in analogy to the element-free Galerkin method. The evolution of the damage variable is related to the support domain surrounds the integration point. The efficient computational algorithm is taken from the regular background cell and implemented into the commercial finite element code ABAQUS via the user interface UMAT for both two-dimensional and three-dimensional problems. To verify the nonlocal damage model, extensive computational simulations of 2D and 3D cracked as well as holed specimens are presented and confirmed that the nonlocal damage overcomes mesh sensitivity and is computationally more efficient than other nonlocal treatment methods. The computational simulation of a compact-tension shear specimen reveals that the nonlocal damage model is able to predict mixed-mode crack growth independently of the element orientation.

A micromechanical damage and fracture model for polymers based on fractional strain-gradient elasticity

We formulate a simple one-parameter macroscopic model of distributed damage and fracture of polymers that is amenable to a straightforward and efficient numerical implementation. We show that the macroscopic model can be rigorously derived, in the sense of optimal scaling, from a micromechanical model of chain elasticity and failure regularized by means of fractional strain-gradient elasticity. In particular, we derive optimal scaling laws that supply a link between the single parameter of the macroscopic model, namely, the critical energy-release rate of the material, and micromechanical parameters pertaining to the elasticity and strength of the polymer chains and to the strain-gradient elasticity regularization. We show how the critical energy-release rate of specific materials can be determined from test data. Finally, we demonstrate the scope and fidelity of the model by means of an example of application, namely, Taylor-impact experiments of polyurea 1000 rods.

SEM in-situ study on the effect of offset-notch on basalt cracking behavior under three-point bending load

Three-point bending fracture tests of basalt with the different offset-notch locations were carried out by an in-situ observation with scanning electron microscope (SEM). These results indicated that the effects of offset-notch location on the crack initiation and propagation behaviors should be classified, the former is not obvious and the latter is sufficiently obvious. Most SEM images demonstrated that the micro-mechanical damage model can explain the influence of offset-notch location on crack propagation paths under a compressive stress, and especially the shear stress component exists. By means of the adjustment parameter λ, the influence of shear stress component contribution to the cracking criterion can be also estimated.

A two-scale time-dependent model of damage: Influence of micro-cracks friction

The aim of this paper is to present a micro-mechanical damage model for quasi-brittle materials that accounts for friction effects on microcracks . We use homogenization based on asymptotic developments to deduce the overall damage behavior starting from explicit descriptions of elementary volumes with micro-cracks. A time-dependent propagation criterion is assumed for the evolution of cracks at the small scale. An appropriate micro-mechanical energy analysis is proposed leading to a damage evolution law that accounts for friction effects, strain rate dependency, stiffness degradation , material softening and size effects. Numerical results are presented in order to illustrate the local and structural effective damage response. Mesh-independency is proved for the finite-element solutions, as a consequence of the regularizing effect of time.

Quantification of brittle-ductile failure behavior of ferritic reactor pressure vessel steels using the Small-Punch-Test and micromechanical damage models

Two German ferritic pressure vessel steels are examined in the brittle to ductile transition regime as a function of temperature and irradiation. The experiments are done by a miniaturized Small-Punch-Test in hot cells within the temperature range of −185°C up to 70°C. From the load–displacement curve of the SPT, the yield curves and parameters of both a non-local Gurson-Tvergaard-Needleman ductile damage model and a modified Beremin model are identified. The influence of temperature and irradiation on the model parameters is analyzed. All parameters are verified by comparison with results from standard test methods. The parameters, identified from SPT, are used to simulate the failure behavior in standard fracture mechanics specimens. In the upper shelf, the non-local GTN-model is applied to simulate crack resistance curves, from where the fracture toughness data could be successfully predicted. In the lower shelf, the Weibull-stress of the specimens was computed to find out the statistics of fracture toughness values. Finally, the modified Beremin model and the non-local ductile damage model were combined to evaluate the failure of fracture specimens in the brittle-ductile transition region. This way, an acceptable agreement with Master-curve data for non-irradiated steels could be achieved in the whole temperature range.

Multiscale finite element modelling of ductile damage behaviour of the human femur under dynamic loading

In this paper, we propose a new multiscale finite element methodology based on a recently developed micromechanical damage model for the modelling of the human bone behaviour under dynamic loading. The damage is carried out by the framework of the limit analysis based on the MCK (Monchiet, Charkaluk and Kondo) criterion. We first present the methodology allowing the estimation of elastic anisotropic properties of porous media by means of Mori–Tanaka homogenisation scheme. Then, we develop the formulation of the integrated yield criterion derived by considering trial velocity field inspired from the Eshelby inhomogeneous inclusion solution. The obtained micromechanical model is implemented via a User Material routine within the explicit dynamic code LS-DYNA©. The proposed micromechanical model has been applied successfully for the estimation of the mechanical properties of a human proximal femur under dynamic loading. From the obtained numerical results, it has been shown that the present model has improved the strength prediction of osteoporotic femurs by representing the failure risk in a more realistic approach.

A constitutive model for porous solids taking into account microscale inertia and progressive void nucleation

In the present paper, a micromechanical constitutive framework for ductile voided solids sustaining dynamic loading is proposed. The micro-inertia based model proposed by Jacques et al. (2012a) has been extended by taking void nucleation into account. To capture the combined effects of microscale inertia and void nucleation, a micro-mechanical model of damage is proposed. This model is based on three physical parameters: the porosity, the number of voids per unit volume and an internal variable aiming to represent the effect of void size heterogeneity. The evolution equations for these internal variables are derived and an application to the failure of an axisymmetric notched bar is presented.

A two-scale model for dynamic damage evolution

This paper presents a new micro-mechanical damage model accounting for inertial effect. The two-scale damage model is fully deduced from small-scale descriptions of dynamic micro-crack propagation under tensile loading (mode I). An appropriate micro-mechanical energy analysis is combined with homogenization based on asymptotic developments in order to obtain the macroscopic evolution law for damage.Numerical simulations are presented in order to illustrate the ability of the model to describe known behaviors like size effects for the structural response, strain-rate sensitivity, brittle–ductile transition and wave dispersion.

In-plane progressive matrix cracking analysis of symmetric cross-ply laminates with holes

Most of the previously performed damage analyses in composite laminates have been restricted to model the plain laminates without geometry discontinuities. In this study, a micromechanical damage model is combined with the finite element formulation and is implemented in the integration points to perform progressive damage analyses of composite laminates. A micromechanical damage model based on the stress transfer method is used to find the degradation of mechanical properties of composite laminates. Crack density is also used as an only state variable representing the damage in each Gauss point of every layer of the laminate. The strain energy and critical energy release rate criterion is also used to predict the damage initiation and evolution in each layer. A finite element discretization is used in conjunction with the user element definition capability of ABAQUS commercial software. To verify the developed procedure, a single element is analysed, and the obtained results are compared with available results in the literature. Progressive damage analyses are also performed for several symmetric cross-ply laminates with and without geometry discontinuity subjected to matrix cracking damage mechanism under in-plane loading conditions. The obtained mechanical response and variations of matrix crack density versus the applied load are also discussed.

Development of a micromechanical damage model for assessing lifetime due to cyclical mechanical loading

ABSTRACTThe safe assessment of temporary service load changes necessitates a fatigue analysis in general. Recent computation methods try to include the microcrack growth corresponding to fatigue in the assessment of the material damage. A new damage model, which is based on the development and evolution of microcracks, has been developed. The stochastic character of the initiation and growth of microcracks enables a more realistic description of the material damage. Within this scope the development of the model is presented and its correlation with experimental results is shown. Fatigue tests under uniaxial and torsional loadings were carried out with specimens made of austenitic stainless steel X6CrNiNffe1666‐bib‐0018–10 S (1.4550). The calculated results of the microcrack length distribution show for both uniaxial and multiaxial loading a good agreement with experimentally achieved data. Using the expectation value of the calculated surface microcrack distribution as the governing variable to predict the number of cycles to crack initiation NA, a good correlation between lifetime and local microcrack length distributions for complex loading conditions can be drawn.

Based on Micromechanical Damage of Experimental Study on 20 Steel Notched Specimen's Acoustic Emission Characteristics

Based on the Gurson-Tvergaard-Needleman micromechanical damage model, taking void growth ratio VG as the damage variable established acoustic emission (AE) quantitative evaluation model. Taking steel 20 notched bar specimens tensile process as example, get AE information from yield to fracture process. Using ABAQUS analyzed the meso-damage process during tensile process of the specimens, and get the numerical solution of meso-damage parameters. Based on AE testing and the results of Finite Element Simulation, established the quantitative evaluation formula of VG and AE cumulative hits N during 20 steel notched specimens tensile process. Result shows that, 20 steel from yield to fracture damage, the relationship between N and VG is divided into two stage, namely linear damage stage and nonlinear damage stage. When the N reaches 61, the material is at the transition stage from linear damage stage to nonlinear damage stage.

Micromechanical Modeling of Damage and Failure in Dual Phase Steels

Dual phase (DP) steels consisting of two phases, ferrite and dispersed martensite, offer an attractive combination of strength and stretchability, which is a result of the strong distinctions of these constituents in mechanical properties. However, the damage behavior in DP steels exhibits a rather complex scenario: voids are generated by the debonding of the hard phase from the matrix and the inner cracking of the hard phase in addition to by inclusions. The target of this study is to describe the initiation and evolution of damage in DP steel and develop a microstructure-based model which is capable of reflecting the underlying damage mechanisms. Both uniaxial and biaxial tensile tests are performed and the subsequent metallographic investigations are executed to reveal the mechanisms of damage initiation and evolution under different stress state condition and attention will be paid on the influence of various microstructural features on the initiation of damage. In finite element (FE) simulations, the microstructural features are taken into account by the representative volume elements (RVE). Different treatments of the constitutive behaviour of each constituent including isotropic hardening rule and crystallographically dependent configuration with crystal plasticity finite element method are investigated. Several numerical aspects are also discussed, such as RVE size, mesh size, element type, and boundary connections. In the end, the study is attempting to achieve a quantitative assessment of the cold formability of the investigated steel in a microscopic level based on microstructure information of material as well as to understand the damage mechanisms under different stress states condition which cause the macroscopic failure during plastic deformation.

Prediction of fracture behavior of beam-to-column welded joints using micromechanics damage model

Moment-resisting steel frames often fail by fracture failure of beam-to-column welded joints during a strong earthquake. This paper provides a numerical methodology based on micromechanics damage model instead of traditional fracture analytical methods to investigate the crack initiation and propagation of welded beam-to-column joints subjected to monotonic loading and ultra low cycle loading conditions. Firstly, parameters used in the micromechanics damage model for steel base metal, heat affected zone and weld metal were calibrated, respectively, against uniaxial tension test results and cycle test results of notched specimens. The evolution of void growth in the notched specimens under different loading conditions was compared. Secondly, fracture process of the welded joints subjected to tensile loading was simulated based on the micromechanics damage model. The predicted load displacement response agrees well with the other researcher's test results. Finally, the micromechanics damage model was applied numerically to investigate the ultra low cycle fatigue fracture behavior of the welded joints under constant amplitude as well as variable amplitude inelastic cyclic loading. According to the distribution and evolution of void in the welded joints obtained from finite element analysis, crack initiation and propagation were presented and the number of cycles to fracture was predicted. It is shown that the fatigue life predicted from finite element analysis based on micromechanics damage model agrees well with the other's test results.

Predicting lower bound damage curves for high‐strength low‐alloy steels

ABSTRACTHindered by the distinctive toughness requirements of the current European standards, the high‐strength low‐alloy (HSLA) steels are rarely applied to the pressure vessels industry. The reason is that the design rules specified by the standards define local plastic deformation as limit state. This results in an over‐conservative application of materials. To achieve an effective, economical and energy‐efficient use of HSLA steels, a strain‐based criterion, the damage curve, which considers crack initiation instead of the beginning of plastic deformation as limit state, is proposed in this study for the improved design rules. In the view of the interaction of microstructure and mechanical properties of materials, the new design rule is derived on the basis of the correlation of microstructural features of HSLA steels with the micromechanical damage models. The experimental verification of the result is furthermore investigated with sufficient agreement so that the general applicability of the procedure can be expected. However, further studies for a reliable parameter calibration are necessary.

Multiscale modeling for the simulation of damage processes at refractory materials under thermal shock

Refractory materials contain defects such as voids, microcracks or grain boundaries. Being exposed to high temperature gradients, strength and lifetime are essentially determined by these microscopic features. Bringing forward the understanding of micro–macro interactions, simulating damage patterns and predicting lifetime of refractory structures, a micromechanical damage model for thermomechanical dynamic loading conditions is presented. The material laws are formulated on the continuum level using appropriate homogenization methods. To combine fracture- and damage-mechanical approaches, submodels containing sharp crack tips are introduced at the ends of the damage zones. Also, conservation contour integrals are applied to damage zones yielding the energy release rates of equivalent crack configurations. Finite element simulations are presented showing wedge splitting tests exhibiting an extended R-curve behavior and cyclic thermal shock tests giving insight into evolving damage patterns. To quantify the thermal shock resistance of refractory ceramics, experiments suggested by Hasselman are simulated numerically supplying critical temperature slopes.

Three-dimensional quantitative in situ study of crack initiation and propagation in AA6061 aluminum alloy sheets via synchrotron laminography and finite-element simulations

Ductile crack initiation and propagation in AA6061 aluminum alloy for a fatigue precrack have been studied in situ via synchrotron radiation computed laminography, a technique specifically developed for three-dimensional imaging of laterally extended sheet specimens with micrometer resolution. The influence of the microstructure, i.e. due to the presence of coarse Mg2Si precipitates and iron-rich intermetallics, on the void nucleation process is investigated. Coarse Mg2Si precipitates are found to play a preponderant role in the void nucleation and ductile fracture process. Void growth and void coalescence are then observed and quantified by three-dimensional image analysis during crack initiation and propagation. Parameters for a Gurson–Tvergaard–Needleman micromechanical damage model are identified experimentally and validated by finite-element simulations.

Micromechanical-based criteria for the calibration of cohesive zone parameters

This paper presents a new micromechanical model for a collection of cohesive zone models embedded between each mesh of a finite element-type discretization. It aims to fully extend the previous linear results of Blal et al. (2012) [11] to the calibration of damageable cohesive parameters (cohesive peak stress, critical opening displacement, cohesive energy, etc). The main idea of the approach consists in replacing the underlying cohesive-volumetric discretization by an equivalent ‘matrix-inclusions’ composite. The overall behavior of this equivalent composite is estimated using homogenization schemes (Hashin–Shtrikman estimate and the modified secant method) and is given in a closed-form as function of both cohesive and bulk properties and the mesh density. In the particular case of a bilinear cohesive law a micromechanical damage model for quasi-brittle materials is derived. The corresponding local-to-global relationships are obtained for any overall triaxiality loading ratio.