Coupled Damage Model Research Articles

Ductile fracture prediction using enhanced CDM model with Lode angle-dependency for titanium alloy Ti-6Al-4V at room temperature

Abstract Fully coupled ductile damage model considering strength-differential (SD) effect is proposed for simulation of metal forming processes for Ti-6Al-4V. The developed constitutive equations are based on non-associative plasticity theory under thermodynamically-consistent framework. The third stress invariant is added to Hill48 criterion to capture the SD effect. Lode angle-dependent enhanced fully coupled damage model is proposed to account for the loading path sensitivity on ductile damage initiation and growth. A detailed material parameters identification procedure is presented. The proposed model is implemented into the FE code Abaqus/Explicit through user defined subroutine VUMAT. The numerically predicted results obtained with the proposed model are compared to experimental data of Ti-6Al-4V and good agreement is observed.

A multi-scale fatigue–creep coupled damage model for steel structures under extreme cyclic loading and temperature

In order to compute the process from the damage accumulation to failure of steel structures under extreme cyclic loading and temperature, a multi-scale fatigue–creep damage model has been developed. Based on the balance of micro-crack number density theory, the multi-scale fatigue damage model has been established using generalized self-consistent method. In the fatigue damage model, the scatter of micro-crack length is expressed by two-parameter Weibull distribution and the interaction among micro-cracks has been studied. In turn, the multi-scale fatigue–creep damage model has been developed by considering the nonlinear coupling of fatigue damage and creep damage. The validity of the developed model has been verified by comparing the predicted damage evolution curves with experimental damage data. The developed model enables to more accurately study the fatigue degradation of steel structures than the phenomenological damage models. Fatigue–creep damage analysis on steel turbine blades under different extreme operating condition are performed using the developed model.

Micromechanical modeling of short crack nucleation and growth in high cycle fatigue of martensitic microstructures

High cycle fatigue (HCF) is a frequently limiting failure mechanism of machine elements and modern high strength steels. Present day design rules rely on semi-empirical methods, guidelines and utilization of macroscopic analysis means in origin, such as fracture mechanics. The resulting challenge is that short crack regime, critical for HCF in terms of lifetime of components and products, is somewhat poorly handled. This is an outcome of the fact that the present means and methodologies do not explicitly account for effects arising from material microstructure, an oversight micromechanics aims to rectify.Micromechanical modeling operating on fatigue at the scale of material microstructure necessitates the introduction of suitable means to describe the mechanisms of cyclic plastic deformation and microstructural morphologies, considered critical for HCF especially at the early stages of micro-crack nucleation and damage evolution towards and within the short crack regime. In current work, a crystal plasticity based approach with combined hardening is utilized to capture the respective deformation response utilizing full field modeling. The modeling is carried out for both simplified prior austenite grain like microstructures as well as complex imaging based martensitic quenched and tempered steel microstructural models. A fully coupled damage modeling scheme is introduced to track damage nucleation and evolution at the scale of the studied microstructures. Crack closure is included within the approach to track behavior of microstructure scale defects under, e.g., fully reversed loading, more realistically. Model calibration is addressed and application cases involving damage and crack growth both under monotonic and cyclic loading are presented.The results demonstrate how the coupling of damage to crystal plasticity modeling can be utilized to identify and track the evolution of microstructure scale damage mechanisms in complex martensitic microstructures. Interactions between strain localization and damage accumulation are presented as well as transition from micro-cracking to short crack growth. The results show that the proposed approach can interpret the intricate dependencies and relations between complex microstructures, their (cyclic) deformation mechanisms and evolution of damage, the outcomes regarding crack formation and behavior are found to be in line with similar experimental studies.The proposed framework for modeling damage in polycrystalline microstructures is quite general in its capabilities. By solely introducing a suitable crystal plasticity based deformation model and a damage model describing nucleation and softening can plastic slip and damage interactions be studied in complex microstructures, and in principle, on any system where similar constitutive models are utilizable. The exploitation of the resulting micromechanical modeling and simulation capabilities lies both in simulation driven design of fatigue resistant components and high strength steels.

A coupled damage model and a semi-analytical contact solver to simulate butterfly wing formation around nonmetallic inclusions

This paper presents a damage modeling approach to simulate the formation of butterfly wings in rolling contact fatigue coupled with a fast method for solving 3D contact problems with the presence of a spherical heterogeneity. The damage model is implemented in a semi-analytical model using the Eshelby’ s equivalent inclusion method in the contact solver. The proposed technique can easily include the effects of heterogeneous inclusions to the homogeneous solution in the contact algorithm. Contact pressure and subsurface stress field computation time is kept small due to the use of 3D and 2D Fast Fourier Transforms. Cuboidal inclusions with the same size as the discretization of the half-space are superimposed to represent the microstructural alterations during butterfly wings formation.

Experimental Studies on the Influences of Chemical Corrosion on the Mode I Fracture Toughness of Sandstone

Abstract Chemical corrosion in coal mines substantially affects the mechanical properties of rocks such as sandstone and may trigger the instability of roadways. In this article, the effects of chemical corrosion on the Mode I fracture toughness of sandstone are investigated using semicircular bending tests. The two experimental factors involved in this article are the pH value of the soaking solution and the soaking time. Based on the peak load and the shape parameters of specimens, the Mode I fracture toughness of sandstone under chemical corrosion is estimated as a function of the pH value of the soaking solution and the soaking time. In soaking tests, the relationships between the pH value of the soaking solution and the soaking time and the relative quality and porosity of sandstone are determined. The results indicate that chemical corrosion weakens the mechanical properties of sandstone specimens but enhances the ductility of sandstone specimens. The Mode I fracture toughness of sandstones decreases with an increase in the soaking time. The Mode I fracture toughness of sandstones initially increases but then decreases with an increase in the pH value. When the pH value is 7, the Mode I fracture toughness of sandstone attains the maximum value. The damage to sandstone specimens shares the same mechanical mechanism as the deterioration of the Mode I fracture toughness of sandstone. The results are significant for establishing a coupling damage model for the mechanical–hydrochemical behaviors of rocks.

Failure prediction on steel sheet under different loading paths based on fully coupled ductile damage model

It is well known that the ductile damage evolution on sheet metal under complex loading conditions is highly dependent on the complexity of the applied loading path. In this study, a fully coupled ductile damage model including the effect of Lode angle and microcracks closure together with the mixed nonlinear isotropic and kinematic hardenings is used to simulate the fracture occurrence of the chosen low carbon steel. Various mechanical tests including the uniaxial tensile tests, the pre-notched tensile tests with four notched radii, the butterfly specimen tests under different loading paths, and deep drawing tests are performed on the chosen low carbon steel sheet to calibrate and validate the proposed model. The influence of the Lode angle on damage evolution is investigated throughout various numerical simulations. These results showed the wide capabilities of the proposed fully coupled damage model on the prediction of ductile fracture under the wide range of loading conditions.

Loading and unloading test of hard rock and its elastoplastic damage coupling model

Loading and unloading test of hard rock and its elastoplastic damage coupling model

A Nonlinear Creep Damage Coupled Model for Rock Considering the Effect of Initial Damage

The experimental results show that initial damage has a clear effect on the creep behavior of rock. However, among the current creep models for rock, few consider the effect of the initial damage state. In the present study, a new nonlinear creep damage model for rock is proposed based on multi-loading creep tests of sandstone with different initial damage levels. The new model is composed of four components, a Hooke body, a Kelvin body, an improved viscous element, and a new nonlinear visco-plastic damage component. The creep damage model can not only describe the three typical creep stages (primary creep, secondary creep and tertiary creep) but also show the effect of initial damage on the creep failure stress. The parameters of the nonlinear creep damage model are obtained using the nonlinear least squares method. A unified set of creep parameters is proposed to predict the creep behavior of sandstone in different initial damage states. The agreement between the experimental data and numerical prediction demonstrates the applicability of the proposed model.

Numerical Investigation to Influence of Perforation Angle on Hydraulic Fracturing Process

Considering the heterogeneous characteristics of rock in a meso-scale, a flow–stress–damage coupling model was created based on the finite element method firstly. Then the hydraulic fracturing process of the heterogeneity rockmass under different perforation angles were investigated by the RFPA2D-flow software. The numerical simulation results show that the maximum principle stress controls the fracture propagation direction no matter how perforation angle changes. With the increase of the perforation angle, a turning fracture becomes more obvious and the turning distance bigger. The best perforation angle area is from 0° to 30°. Above results are of some significance to hydraulic fracturing tests and engineering practice.

Damage constitutive models of concrete under the coupling action of freeze–thaw cycles and load based on Lemaitre assumption

In cold environments, concrete structures are subjected to a combined action of load, freeze–thaw cycles, and salt attack. The performance degradation of some concrete structures in such areas is serious, thus shortening their service life. In this study, a macro-mesoscopic coupling damage model was established to determine the durability of concrete under the coupling action of freeze–thaw cycles and load based on the Lemaitre strain equivalent assumption. Meanwhile, the an indoor accelerated test was conducted to verify the rationality of the model. Results indicated that the damage in different kinds of concrete under freeze–thaw cycles and load can be predicted by the theoretical model. The structural coupling damage was determined by the meso-damage caused by the freeze–thaw cycles and the macro-damage caused by the applied load, which showed a nonlinear superposition relationship. The evolution laws of coupling damage were entirely different because of the freeze–thaw cycles and strain. The coupling damage and peak strain increased with the increase in number of freeze–thaw cycles but the variation range of damage and peak stress decreased. The peak strain can be the critical point of the coupling damage when the number of freeze–thaw cycles was constant. The growth of coupling damage was not significant before the peak strain. When the deformation approached the peak strain, the coupling damage increased considerably, and the concrete was destroyed rapidly.

Coupled Field Numerical Model of Lithium Ion Battery Damage

Nail penetration test is commonly used to study the internal short-circuits, but the test results usually have poor reproducibility and offer limited insight. This paper deals with a possibility of numerical simulation of damage lithium ion battery by penetration of sharp object (for example by car crash).

Coupled constitutive model of damage affected two-phase continuum

A broad class of metastable materials, including selected alloys (e.g. stainless steels) used for applications in radiation environment (particle accelerators), is characterized by simultaneous occurrence of the plastic strain driven phase transformation and evolution of nano/micro damage. Plastic flow in such materials is usually accompanied by dynamic evolution of microstructure, resulting from the strain induced fcc-bcc phase transformation. Two-phase continuum is composed of austenitic matrix (fcc) and martensitic inclusions (bcc), represented by type Eshelby ellipsoidal entities embedded in ductile matrix. The matrix remains entirely plastic, and contains micro-cracks and micro-voids representing ductile damage. On the other hand, the inclusions are characterized by much higher yield stress and their behavior is generally brittle. Thus, brittle damage develops in the inclusions. The origin of damage is mechanical (manufacturing and load induced defects), and related to the source of radiation (primary or secondary particles flux). Among the lattice defects induced by radiation, the clusters of nano/micro voids are accounted for. The constitutive model takes into account the evolution of mechanically and radiation induced nano/micro damage in the presence of microstructure evolution, reflected by the plastic strain driven dynamic change of proportions between the matrix and the inclusions. The model is multiscale since the processes that occur at different scales (micro, meso, macro) are addressed, and coupled, since both phenomena: phase transformation and damage are described by coupled equations. Application to irradiated corrugated shells, components of thermo-mechanical compensation systems, are presented.

Numerical and Experimental Validation of a New Damage Initiation Criterion

Most commercial finite element software packages, like Abaqus, have a built-in coupled damage model where a damage evolution needs to be defined in terms of a single fracture energy value for all stress states. The Johnson-Cook criterion has been modified to be Lode parameter dependent and this Modified Johnson-Cook (MJC) criterion is used as a Damage Initiation Surface (DIS) in combination with the built-in Abaqus ductile damage model. An exponential damage evolution law has been used with a single fracture energy value. Ultimately, the simulated force-displacement curves are compared with experiments to validate the MJC criterion. 7 out of 9 fracture experiments were predicted accurately. The limitations and accuracy of the failure predictions of the newly developed damage initiation criterion will be discussed shortly.

Formability prediction for AHSS materials using damage models

Advanced high strength steels (AHSS) are seeing an increased use, mostly due to lightweight design in automobile industry and strict regulations on safety and greenhouse gases emissions. However, the use of these materials, characterized by a high strength to weight ratio, stiffness and high work hardening at early stages of plastic deformation, have imposed many challenges in sheet metal industry, mainly their low formability and different behaviour, when compared to traditional steels, which may represent a defying task, both to obtain a successful component and also when using numerical simulation to predict material behaviour and its fracture limits. Although numerical prediction of critical strains in sheet metal forming processes is still very often based on the classic forming limit diagrams, alternative approaches can use damage models, which are based on stress states to predict failure during the forming process and they can be classified as empirical, physics based and phenomenological models. In the present paper a comparative analysis of different ductile damage models is carried out, in order numerically evaluate two isotropic coupled damage models proposed by Johnson-Cook and Gurson-Tvergaard-Needleman (GTN), each of them corresponding to the first two previous group classification. Finite element analysis is used considering these damage mechanics approaches and the obtained results are compared with experimental Nakajima tests, thus being possible to evaluate and validate the ability to predict damage and formability limits for previous defined approaches.

Coupling damage and reliability modeling for creep and fatigue of solder joint

Solder joint often plays a crucial role in the normal operation of electronic equipment due to its unique material properties and harsh working condition, making it very important to carry out the accurate reliability analysis of solder joint. The low-cycle fatigue due to temperature cycling and the creep brought by continuous high temperature are two dominant failure modes of the solder joint. Current modeling methods for these two mechanisms mainly focus on failure process of each mechanism separately, with little consideration of the coupling relationship in the material properties. This paper introduces a coupling damage model considering both low-cycle fatigue and creep. The coupling relationship between these two failure mechanisms is investigated with the effects of creep strain rate on the ductility and the effects of damage on mechanical properties of solder joint. The analysis of the former mechanism concerns the fatigue parameter of Coffin-Manson model, while the latter one focuses on the applied stress increasing with the accumulation of damage. Further, considering that creep degradation rate would increase once the cumulative damage reaches a trigger threshold, a generalized cumulative damage model is developed. Based on this assumption, a reliability model for solder joint considering the uncertainty of model parameters is then proposed. Finally, a case study of a lead-free solder joint is given to validate this method.

Modified Johnson-Cook Plasticity Model with Damage Evolution: Application to Turning Simulation of 2XXX Aluminium Alloy

AbstractMechanical properties of the metals and their alloys are influenced by the material grain size at microscale. In the present study, the Johnson-Cook (JC) material model is modified to incorporate the effect of material's grain size along with the plasticity coupled damage model. 2D finite element (FE) simulations of turning process of an aerospace grade aluminium alloy 2024 (AA2024) were performed with different grain sizes using a commercial FE software, ABAQUS/Explicit. FE simulation results were compared with the published experimental data on turning process of AA2024. The proposed modified JC material model successfully simulated the increase in cutting force as a function of grain size refinement.

Numerical prediction of ductile failure in the blanking process by means of uncoupled and coupled phenomenological damage models

Fracture prediction in blanking has gained great attention due to increasing requirements of high-quality products. In this work, the predictive capabilities of different uncoupled and coupled damage models, recently implemented in a fully implicit homemade FE code, for blanking process are compared. Some advanced models considered here include damage sensitivity to both triaxiality and Lode angle in their formulation. The material characterization is based on the history of internal variables during loading, where different mechanical tests are considered. Finally, numerical and experimental results are compared for a wide range of different geometries of blanking.

Application of Coupled Damage and Beremin Model to Ductile-Brittle Transition Temperature Region Considering Constraint Effect

For nuclear safety, fracture evaluation of reactor pressure vessels (RPV) under neutron irradiation is key issue. Fracture toughness from a CT specimen is used as a material constant for fracture evaluation, but it is well known that it has a large constraint, which causes lower toughness than that of flawed structures, such as a RPV with a surface flaw. In ductile to brittle transition temperature (DBTT) region ferritic steel which is material of RPV has a large scatter and it becomes important to know the accurate scatter of an irradiated material because of less margin of RPV’s integrity after a long term operation. In this paper to establish a more precise fracture evaluation method in DBTT region for an irradiated RPV with a postulated surface flaw, a coupled model of damage mechanics for ductile fracture and Beremin model for cleavage fracture was applied for correction of the effect of a small ductile growth on the stress-strain field. To confirm the validity of the method, as the first trial, fracture tests using CT specimens were performed in several temperature conditions. The temperature dependence of the parameters of Beremin models were investigated as well.

Numerical Modelling of Damage Evolution in Ingot Forging

The ingot forging process is numerically simulated applying both the Shima-Oyane porous plasticity model as a coupled damage model and the uncoupled normalized Cockcroft & Latham criterion. Four different cases including two different lower die angles (120o and 180o) and two different sizes of feed (400mm and 800mm) are analysed. Comparison of the simulation results with recommendations in literature on ingot forging, indicates the normalized Cockcroft & Latham damage criterion to be the most realistic of the two.

A damage-based failure model for coarsely meshed shell structures

This paper presents a fast and reliable method for failure prediction of coarsely meshed shell structures. The method is especially relevant when investigating the impact performance of offshore structures, typically stiffened panel structures where the size of the structure limits the possible detailing level during analysis.The method combines a local instability criterion with post-necking damage in order to numerically model the failure process in large shell elements. The failure model is based on power law plasticity with the stress-based Bressan–Williams–Hill (BWH) local instability criterion and a coupled damage model after incipient necking. The BWH criterion gives a robust estimation of incipient necking for coarsely meshed shell structures. After necking starts, a mesh-size dependent damage model is coupled to the element strength for material softening until failure, assuming that the strain localization occurs locally inside the element within a virtual neck. The model is incorporated in the explicit FE code LS-DYNA.The material model formulation is validated against experiments at several levels; from formability tests with varying strain states to medium and large scale impact experiments, giving a robust prediction of energy dissipation and material failure in the structure with low mesh dependency.The material model is calibrated from a single uniaxial test, and gives robust and consistent simulation results in which details of the localized necking phenomenon is included in the behavior of large shell elements. Thus, it is readily used for structural design of offshore structures in order to assess the technical safety level of the structure against collisions in all phases of the design process.