Damage Evolution Model Research Articles

Rate and confinement effects on the tensile strength of asphalt binder

Asphalt binder is a viscoelastic material that works as a glue to bind the aggregate particles to form an asphalt concrete composite. Fatigue cracking is a predominant form of distress in the asphalt pavements that is primarily dictated by the ability of the asphalt binder to resist tensile loads. The motivation of this study was to quantify the tensile strength of the asphalt binder under a confined state of stress that is similar to what the binder experiences in an asphalt concrete mixture. A poker chip geometry was used to simulate the confined state. Laboratory tests were performed on binders of different grades by varying the film thickness, rate of loading and modes of loading. These three factors influence the stress–strain behavior and failure stress of the confined asphalt binder films. Within the linear viscoelastic limit and before damage is induced, the differences due to the rate and mode of loading could be successfully explained and unified using modified correspondence principle. Beyond this limit, the differences due to rate and mode of loading could be successfully explained and unified using a power law damage evolution model following the methodology referred to as the viscoelastic continuum damage model. Examination of the failure surfaces and true internal stresses within the poker chip geometry reveals that tensile failure occurs in the form of cavitation as long as a certain degree of confinement is achieved.

Modeling and Simulation of Damage Evolution during Crevice Corrosion

In this paper we report a computational method for determining the spatial and temporal evolution of damage during crevice corrosion. The model uses the potentiodynamic polarization data for nickel (Ni) in sulfuric acid and assumes well-mixed solution chemistry inside and outside the crevice, consistent with a pure IR model. Damage, potential and current profiles as well as other characteristic features of the crevice corrosion process are predicted. We describe for the first time how changing IR inside the crevice results in propagation away from the initiation site both toward the mouth and deeper into the crevice. To validate the model predictions we compare damage profiles from our model for Ni crevice corrosion with published experimental results. Since the model calculates the true crevice gap in real time, the results provide unique insight into the critical length to gap ratio necessary to propagate IR controlled crevice corrosion.

A Lattice-spring Model for Damage Evolution in Cement Paste

To understand better the fracture processes in cement-based materials, it is essential to predict the evolution of damage in cement paste. A recently proposed site-bond model is developed further to take into account the key microstructure data, such as pore size distribution, porosity, and size distribution and volume fraction of anhydrous cement grains obtained from high resolution X- ray tomography. The grains are associated with lattice sites linked by deformable bonds. The bonds are bundles of elastic-brittle springs, resisting normal and shear relative displacements between grains with potential for failure. The model length scale and thence spring constants are controlled by grain statistics. The spring failure properties are controlled by pore statistics. Macroscopic damage develops by a succession of local failures, represented by spring removal. The model is used to simulate the stress-strain response and damage in cement paste under uniaxial tensile loading. The influence of porosity on tensile strength and damage evolution is estimated in a quantitative manner. The predictions of the model are in a very good agreement with the available experimental data.

New model for creep damage analysis and its application to creep crack growth simulations

A creep damage model from the micromechanics viewpoint is presented in the paper. In order to mitigate the difficulty of calibrating many parameters in the existing damage evolution models, a simple creep ductility exhaustion approach is employed to account for the accumulation of the creep damage. Two-dimensional and three-dimensional numerical analyses of creep crack growth based on the new creep-damage model and/or Liu-Murakami model are carried out. When the damage parameter reaches a critical value, the load carrying capacity of each damaged element approaches zero and thus crack growth can be characterised by a completely damaged element zone ahead of the initial crack tip. The finite element simulation results obtained are compared favourably with experimental data for the compact tension specimen for 316 stainless steel and bending cracked plate for T91 steel at elevated temperatures. The comparisons show the excellent capability of the proposed model in predicting the crack growth rate and progressive crack profiles. In addition, the influences of the plasticity and mesh size are discussed in this paper.

Environmental creep intergranular damage and multisite crack evolution model for engineering alloys

In this paper a sub-grain size finite element meshing technique has been developed to employ in a combined creep continuum damage and environmentally assisted time dependent material depletion and crack growth model. The model can cover a wide range of failures allowing crack paths for intergranular and transgranular cracking as well as surface oxidation and depletion due to corrosion. It has been customised to predict time and stress induced intergranular surface damage and cracking for isotropic metallic grain structures which undergo oxidation at the surface and are under creep loading regime. It is shown that creep crack growth predictions using a remaining ductility multiaxial failure strain constraint-based model coupled with a time-dependent environmentally assisted corrosion/oxidation rate dependent parameter can realistically assess damage and cracking rates for the engineering alloys shown. Material depletion and multiple intergranular crack paths are modelled by assuming weaker grain boundaries having realistically a reduced critical damage index of a factor of 2 less than that of the grains. A probabilistic random crack extension criterion is also proposed which allows for statistically varying random damage and surface crack growth development during each run using the same input properties. This method can take into account the level of scatter that exists in the material characterisation test data and in long term component oxide and crack damage measurements. The results for a sample rectangular block under tension using representative material creep and oxidation properties are used to predict and compare the relative extent of creep to environmental damage under different loading conditions.

An alternative to the Kelvin decomposition for plane anisotropic elasticity

In this paper, we propose an alternative tensorial decomposition to the Kelvin's one (introduced by Kelvin in 1856) for plane anisotropic elasticity using the polar formalism (introduced by Verchery in 1979). In the first part of the paper, a parallel between the two approaches is proposed. Thanks to it, some new results are found; namely, the projectors introduced have a direct interpretation in terms of material symmetry and are intrinsic for any type of symmetry considered, that is, they do not depend on any elastic modulus for any type of symmetry, unlike in the Kelvin decomposition. The introduction of what we call, in the paper, the polar projectors, stresses and strains gives a new insight into the polar formalism. The results proposed in this paper will hopefully be useful in some cases, for example, in the modeling of anisotropic damage evolution in solids. Copyright © 2013 John Wiley & Sons, Ltd.

Topological sensitivity analysis for elliptic differential operators of order 2m

The topological derivative is defined as the first term of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of a singular domain perturbation. It has applications in many different fields such as shape and topology optimization, inverse problems, image processing and mechanical modeling including synthesis and/or optimal design of microstructures, fracture mechanics sensitivity analysis and damage evolution modeling. The topological derivative has been fully developed for a wide range of second order differential operators. In this paper we deal with the topological asymptotic expansion of a class of shape functionals associated with elliptic differential operators of order 2m, m⩾1. The general structure of the polarization tensor is derived and the concept of degenerate polarization tensor is introduced. We provide full mathematical justifications for the derived formulas, including precise estimates of remainders.

Simulation of microstructural damage evolution during very high cycle fatigue (VHCF) using the boundary element method

AbstractA simulation model for damage evolution in slip bands under VHCF condition is presented. By use of a numerical method it is applied to a real simulated microstructure of AISI304. It considers orientations of slip systems as well as individual anisotropic elastic properties in each grain. The numerical method is the two‐dimensional boundary element method which is based on two integral equations and implies fundamental solutions for anisotropic elastic solids. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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.

A Model of Damage Evolution During Crevice Corrosion of Nickel Base Alloys

not Available.

Numerical modelling of ductile damage evolution in tensile and bending tests of timber structures

The characteristic values for strength and stiffness of all sorts of timber products are based on the assumption of a linear relation between stress and strain prior to failure and consequently verification of the load-bearing capacity of individual members in a construction is also based on a similar linear relation. Such an approach is very conservative and ill suited for performance-based design, which requires a full analysis of the structure with the possibility of moment and/or stress redistribution within parts of the structure. The development of material models that encompass the complex behaviour of wood is therefore necessary. The present work presents a model formulated within the frameworks of plasticity and continuum damage mechanics (CDM). It applies the classical flow theory of plasticity to formulate ductile failure of wood in compression and damage mechanics for the brittle failure modes. It takes into account the orthotropic elastic behaviour, the plastic anisotropic isotropic hardening, the isotropic ductile damage, and the large plastic deformations. The model was used to predict the initiation and growth of ductile damage in tensile and bending tests on different timbers types. Good agreement was found between the predictions of the model and the experimental results.

Research on damage evolution and damage model of 316LN steel during forging

The tensile tests and unloading tensile experiments of 316LN steel were conducted. The damage evolution processes were investigated by optical microscope. The fracture was studied using a Scanning Electron Microscope (SEM) and optical microscope, of which, the chemical compositions were analyzed by Energy Dispersive Spectrometer (EDS). The results show that voids nucleate by decohesion of Al2O3 inclusions–matrix interface and mainly along the grain boundary, especially, at triangular grain boundary junctions. The tensile processes were simulated by Deform2D under different deformation conditions. The critical damage values were obtained. The model between the critical damage value, temperature and strain rate was established by regression analysis. A combination of numerical simulation and upsetting experiments was applied for verifying the accuracy and reliability of critical damage value. These damage values can be used to predict the initiation of voids during 316LN steel hot forging. So, they have important instructional effects on designing forging technology of 316LN steel.

Modeling of damage in unidirectional ceramic matrix composites and multi-scale experimental validation on third generation SiC/SiC minicomposites

The purpose of this paper is to experimentally validate a 1D probabilistic model of damage evolution in unidirectional SiC/SiC composites. The key point of this approach lies in the identification and validation at both local and macroscopic scales. Thus, in addition to macroscopic tensile tests, the evolution of microscopic damage mechanisms – in the form of matrix cracks and fiber breaks – is experimentally analyzed and quantified through in-situ scanning electron microscope and computed tomography tensile tests. A complete model, including both matrix cracking and fiber breaking, is proposed on the basis of existing modeling tools separately addressing these mechanisms. It is based on matrix and fiber failure probability laws and a stress redistribution assumption in the vicinity of matrix cracks or fiber breaks. The identification of interfacial parameters is conducted to fit the experimental characterization, and shows that conventional assumptions of 1D probabilistic models can adequately describe matrix cracking at both macro- and microscopic scales. However, it is necessary to enrich them to get a proper prediction of ultimate failure and fiber break density for Hi-Nicalon type S fiber-reinforced SiC/SiC minicomposites.

Fatigue Damage Model of Limestone Based on Dynamic Elastic Modulus Attenuation Rule

For exploring the attenuation law of limestone dynamic elastic modulus (DEM) under fatigue cyclic loading, 24 limestone specimens were used to conduct dynamic uniaxial cyclic compressive tests under different loading frequencies and stress amplitudes on MTS Test System. The tests results confirmed that the decrease of DEM goes through three different stages with the increase of cyclic numbers. And, there is no distinct correlation between three-stage evolution rule of DEM and frequencies as well as stress amplitudes. The degeneration of DEM is caused by accumulation of micro-cracks and damage increase in rock specimen. Thus, based on attenuation rule of DEM, a fatigue damage evolution model which can depict the first two stages of limestone fatigue damage development was proposed.

Analysis of the Necking Behaviors with the Crystal Plasticity Model Using 3-Dimensional Shaped Grains

Without initial imperfection and damage evolution model, it is difficult to analyze the necking behavior by finite element analysis with continuum theory. Moreover, the results are greatly dependent on the size of the initial imperfection. In order to predict necking phenomenon without geometric imperfection, in this study, a crystal plasticity model was introduced in the 3-dimensional finite element analysis of tensile test. Grains were modeled by an octahedron and different orientations were allocated to each grain. Damage model was also used to predict the sudden drop of load carrying capacity after necking and to reflect the void nucleation and growth on the severely deformed region. Well-known Cockcroft-Latham damage model was used. Void nucleation, growth and coalescence behavior during necking were predicted reasonably.

Multiscale Modeling of Damage Evolution in Viscoelastic Bituminous Mixtures Subjected to Cyclic Loading

This study presents a multiscale computational model and its application to predict damage dependent mechanical behavior of bituminous mixtures subjected to cyclic loading. Two length scales (global and local) are two-way coupled in the model framework by linking a homogenized global scale to a heterogeneous local scale representative volume element. Based on the unique two-way coupled multiscaling and the use of the finite element technique incorporated with the material viscoelasticity and cohesive zone fracture, the model approach can successfully account for the effect of mixture heterogeneity, material viscoelasticity, and damage accumulation due to cracks in the small scale on the overall performance of larger scale mixtures or structures. This step requires only the properties of individual constituents. To demonstrate the model and its features, bending beam fatigue testing of a bituminous mixture, which is composed of elastic aggregates and viscoelastic bitumen, is simulated by altering the mixture's constituent properties. The model clearly presents progressive damage characteristics with repetitive loading cycles and the analysis clearly demonstrates the sensitivity of the approach to constituent material properties. The multiscale model presented herein is expected to drastically reduce time-consuming and expensive fatigue tests, which, when performed in the traditional manner, require many replicates and do not define the cause of microstructural fatigue, damage, and failure.

Damage evolution law of coal-rock under uniaxial compression based on the electromagnetic radiation characteristics

Based on electromagnetic radiation characteristics, the present research studied the damage evolution of rock under uniaxial compression. Besides, this research built the coal-rock damage evolution model considered residual strength. The applicability and accuracy of the model were verified through experiments. The results show that coal-rock damage evolution consists of four periods. The first period is from the beginning of compression to nearly 20% of the stress peak value, during which the damage variable changes stably about 0.1, and accordingly a few of electromagnetic radiation signals emerge. The second period is from about 20% to 70% of the stress peak value. The damage has stable development, and the parameter of electromagnetic radiation characteristics turns larger continuously with the increase of stress. The third period is when the damage has accelerated development, the coal-rock was broken which result from sharp increasing of the damage variable, meanwhile a great quantity of electromagnetic radiation signals emerge. The fourth period is after the coal-rock fracture, during which the damage variable corresponding to the parameter of electromagnetic radiation characteristics has a stable development. This research has great academic and realistic significance for further studies the electromagnetic radiation characteristics of coal-rock under loading and damage and the forecasting of coal-rock dynamic disasters.

Experimental and numerical investigation for ductile fracture of Al-alloy 5052 using modified Rousselier model

In this paper, the ductile fracture of Al-alloy 5052 is studied by experiments and simulations using a modified Rousselier model. Although tension failure has been successfully predicted by the classical Rousselier model, its predictive capability on shear failure was seldom discussed. A modified Rousselier model was proposed by incorporating the recent extended damage evolution model by Nahshon and Hutchinson. The modified Rousselier model can capture both tension and shear failure. A stress integration algorithm based on the general backward-Euler return algorithm for this constitutive model was developed and implemented into finite element model by the user defined material subroutine VUMAT in the ABAQUS/Explicit. The tensile tests of smooth round bar and notched round bars with different sizes were carried out to investigate the mechanical behavior of Al-alloy 5052. Consequently, the material parameters of the classical Rousselier model were identified by an inverse method using these experimental data. A shear test was also performed to calibrate the new shear damage coefficient in the modified Rousselier model. For the shear test, the simulations show that although shear failure can be predicted by the Rousselier model, the ductility was over-estimated. However, the modified Rousselier model can give more accurate results. The simulations on uniaxial tension of the round bars also confirm that the modified Rousselier model can well predict the cup-cone fracture mode. The results indicate that the Lode parameter in the new damage evolution model is important to capture the cup-cone fracture mode transition.

A VANISHING VISCOSITY APPROACH TO A RATE-INDEPENDENT DAMAGE MODEL

We analyze a rate-independent model for damage evolution in elastic bodies. The central quantities are a stored energy functional and a dissipation functional, which is assumed to be positively homogeneous of degree one. Since the energy is not simultaneously (strictly) convex in the damage variable and the displacements, solutions may have jumps as a function of time. The latter circumstance makes it necessary to recur to suitable notions of weak solution. However, the by-now classical concept of global energetic solution fails to describe accurately the behavior of the system at jumps. Hence, we consider rate-independent damage models as limits of systems driven by viscous, rate-dependent dissipation. We use a technique for taking the vanishing viscosity limit, which is based on arclength reparametrization. In this way, in the limit we obtain a novel formulation for the rate-independent damage model, which highlights the interplay of viscous and rate-independent effects in the jump regime, and provides a better description of the energetic behavior of the system at jumps.

Damage evolution model of strain hardening cementitious composites under the uniaxial stress state

The deformation and damage behaviors of strain hardening cementitious composites (SHCC) under the uniaxial stress state were investigated in this paper. Two ductile failure-based constitutive models were introduced to describe the uniaxial tension and compression properties of SHCC only using a few parameters. The computation method of model parameters was developed to ease the simulation procedures. Damage evolution of the SHCC was simulated by the formulation of continuum damage mechanics subsequently. The results show that the proposed models fit the stress-strain curves reasonably well, and the damage variables show different growth rules under uniaxial tension and compression. It is concluded that the proposed method can not only simply simulate the constitutive behavior of SHCC with the reasonable accuracy but also capture the characteristic of material degradation.