Uncoupled Damage Model Research Articles

Predictive mechanical property and fracture behavior in high-carbon steel containing high-density carbides via artificial RVE modeling

The mechanical properties and fracture behavior of high-carbon steel are closely related to the microstructural characteristics. This work developed the artificial representative volume element (RVE) model to explore the effects of microstructural characteristics on mechanical properties and fracture behavior of high-carbon steel containing high-density carbides under uniaxial tension. A series of RVEs with different ferrite grain sizes, particle volume fractions, and particle sizes were generated based on the RSA algorithms. The mechanism-based plasticity model and the three uncoupled damage models were implemented into the RVE modeling. The model parameters were calibrated by the corresponding simulation between in-situ μ DIC and microstructure-based RVE simulation. The predicted mechanical properties and fracture strain from the RVE simulation were in good agreement with the experimental results. Simulated results from a series of RVEs quantified the effects of ferrite grain sizes, particle volume fractions, and particle sizes on strength, elongation, and damage evolution of high-carbon steel containing high-density carbides: strength increases with increasing particle volume fraction while elongation decreases, as well as excessively large or small grain and particle size were not favored to improve elongation. These results were attributed to the damage and internal stress partition.

Experiment and prediction of the strain-range dependent ultra-low-cycle fatigue based on micromechanical cyclic void growth model

Under severe seismic action, the local stress concentration region in steel structures is prone to the ultra-low-cycle fatigue (ULCF) under high triaxiality and irregular cyclic deformation with intensively varying strain amplitudes. It emphasizes the necessity of the jointed effects of the stress triaxiality and strain range incorporated in the ULCF life prediction. Given the limited relevant studies in terms of the underlying micro-mechanisms, this paper focuses on experimental and modeling studies of the combined effects of stress triaxiality and strain range on the ULCF failure, based on Gurson-Tvergaard-Needleman (GTN) microvoid evolution theories. Monotonic tensile tests on three types of notched round bars suggest that fracture strain decreases with increasing triaxiality. Cyclic tests on two types of notched bars under various strain ranges confirm the combined effects of stress triaxiality and strain range. Given a specific triaxiality, the ULCF damage accumulation rate increases linearly as the tensile plastic strain range ramps up. For the same tensile plastic strain range, higher triaxiality results in a greater damage accumulation rate. In the modeling studies, the consistency of the GTN and uncoupled damage models has been proven in terms of ULCF failure of structural steel. Based on GTN theories, a new micromechanical cyclic void growth model (GCVGM) is proposed, considering the detailed processes of void nucleation, growth, and coalescence under monotonic and cyclic loadings. Moreover, the joint effects of stress triaxiality and strain range can be explicitly described within a unified framework, without additional empirical assumptions. Based on experimental and simulation results, the proposed GCVGM shows significant advantages over conventional models in accurately predicting ULCF failure under various loading protocols, with low average errors of 2.73 % and −0.91 % for two types of notched bar specimens, respectively.

Response of thin walled transversely stiffened clamped circular plates under uniform impulsive loads

Paper presents numerical models based on detailed characterization of various uncoupled damage models in a finite element analysis (FEA) setup to assess large deformations and observed ductile fracture failure modes of fully clamped circular plates as well as transversely stiffened circular plates in cross stiffened configurations under uniform impulsive loads. The numerical schemes have been based on a detailed definition of the constitutive properties based on inverse FEA simulations of the uniaxial tension test for the calibration of material and failure parameters. Experiments have been conducted using two types of freshly prepared mild steel uniaxial tension test specimens covering the envisaged range of stress tri-axialities to establish the steel plate material and fracture characteristics necessary for the calibration of the presented phenomenological damage models. Published results based on extensive experimental works by various authors on response of thin walled clamped circular plates under transversely applied uniform air blast loads, manifesting in large plastic deformations, thinning and tearing under various ductile fracture modes, have been used in the performance assessment of presented numerical models and procedure, which incorporate different damage models including temperature effects due to plastic dissipation. Based on evaluated performance of the discussed failure models within the FEA setup, a hybrid damage model with a tri-axiality based two part ductile fracture locus has been proposed, which shows very good correlation with the published experimental results, presented in terms of non-dimensional parameters over a wide range of impulsive loading. The validated numerical setup using the proposed hybrid damage model has also been used to predict the effect of transverse cross stiffened configurations of flat bar stiffeners on large deformations and ductile fracture of clamped circular plates under transverse uniform impulsive blast loads, along with some key insights in the evolution of plastic zones and damage progression.

Ductile fracture modelling of steel plates under tensile and shear dominated states

The prediction of ductile fracture is highly related to the stress and strain states in the plastic stage. For steel plates in the engineering structure, despite many stress-strain equations based on the von Mises criterion developed, it is found that the finite element (FE) analysis using true stress-strain relation calibrated by the uniaxial tensile tests cannot properly describe the shear behaviour of steel plates. In this paper, the combined linear and power stress-strain law with a shear plastic factor is proposed to characterize the mechanical behaviour of steel plates under shear dominated state. Then, Bao-Wierzbicki (BW) criterion, an uncoupled damage model, is adopted to predict the tensile and shear dominated fracture of steel plates. The uniaxial tensile and shear tests of steel plates are carried out to calibrate relevant parameters in the true stress-strain relation and ductile fracture model. Furthermore, single-bolt connections subjected to tensile and shear dominated states are designed and tested. Parallel FE simulations are performed to validate the ductile fracture model with the calibrated stress-strain relations. FE results regarding these specimens show a good agreement with the corresponding experimental results. The uncoupled damage model integrated with the proposed stress-strain relation is verified to be suitable to simulate the ductile fracture of steel plates under tensile and shear dominated states.

Large deformations and failure of clamped circular steel plates under uniform impulsive loads using various phenomenological damage models

Paper presents numerical models based on a detailed characterization of various uncoupled damage models in a finite element analysis (FEA) setup to assess their results and comparative performance in simulation of structural response and failure of clamped circular plates subjected to a wide range of uniform impulse loading. The significance of numerical modeling of ductile fracture in simulating the various observed modes of failure in steel structures under intense blast loading has also been presented along with an overview of various phenomenological damage models in the published domain. Numerical schemes presented in the paper are founded on a detailed and well-defined material model using mechanical uniaxial tension tests (UTT) and its inverse FEA simulations. Elaborate UTT experiments have been conducted to establish the mechanical strength and ductile fracture characteristics of a particular grade of mild steel for its usage in the calibration of the discussed damage models. Relative performance of various simple as well as complex phenomenological damage models in simulating/ predicting the experimentally observed structural response and different failure modes of fully clamped circular steel plates over a broad range of uniform impulsive loads has also been presented. Published results based on extensive experimental works by various authors on response of thin walled clamped circular plates under transversely applied uniform air blast loads, manifesting in plastic deformations of large magnitude, inception of thinning and tearing under various ductile fracture modes, have been utilized in the validation of the numerical model and procedure. Based on the evaluated performance of the discussed numerical models, a hybrid damage model adopted within the FEA setup has been proposed, demonstrating a very good correlation of numerical predictions with experiments. The validated FEA setup incorporating the calibrated hybrid damage model has further been gainfully utilized towards critical insights in the evolution of plastic deformations, progression of damage and their correlation with experimentally observed failure modes over a wide range of loading, involving varying stress states and tri-axiality.

Prediction of Behaviour of Thin-Walled DED-Processed Structure: Experimental-Numerical Approach.

Additive manufacturing (AM) becomes a more and more standard process in different fields of industry. There is still only limited knowledge of the relationship between measured material data and the overall behaviour of directed energy deposition (DED)-processed complex structures. The understanding of the structural performance, including flow curves and local damage properties of additively manufactured parts by DED, becomes increasingly important. DED can be used for creating functional surfaces, component repairing using multiple powder feeders, and creating a heterogeneous structure with defined chemical composition. For thin parts that are used with the as-deposited surface, this evaluation is even highly crucial. The main goal of the study was to predict the behaviour of thin-walled structures manufactured by the DED process under static loading by finite element analysis (FEA). Moreover, in this study, the mechanical performance of partly machined and fully machined miniaturized samples produced from the structure was compared. The structure studied in this research resembles a honeycomb shape made of austenitic stainless steel AISI 316L, which is characterized by high strength and ductility. The uncoupled damage models based on a hybrid experimental-numerical approach were used. The microstructure and hardness were examined to comprehend the structural behaviour.

A comparative study of three forms of an uncoupled damage model as fracture judgment for thin-walled metal sheets

Ductile fracture always occurs in plastic forming processes of thin-walled metal sheets. Damage models, both coupled and uncoupled ones, have been extensively developed to predict fracture of the sheets. Among these, uncoupled damage models, owing to their simple form are widely used. While for an uncoupled damage model, there exist three forms for its fracture prediction: (1) damage threshold (DT), which is related to the damage accumulation; (2) fracture strain (FS), which is always a function of stress triaxiality and Lode parameter; (3) fracture forming limit diagram (FFLD), which is always related to the principal strains. However, for an uncoupled damage model, its three forms (DT, FS and FFLD) for fracture prediction have never been compared before, and thus scholars have always been confused about how to choose the right form of the three in different loading processes. To clarify this confusion, two popular uncoupled damage models of the MMC4 and DF2016 are embedded into an anisotropic yield function first. Then the above-mentioned three forms of the two models are separately applied for fracture prediction in shear test, dog-bone specimen tensile test, hole specimen tensile test, notched specimen tensile test, bulging test in proportional loadings, and a complex non-proportional loading process of spin forming, respectively. Finally, the predicted results with these three forms are systematically compared and a new explanation for their applicability under different stress states is displayed.

Prediction of deformation and failure anisotropy for thin magnesium sheets under mixed-mode loading

The plastic deformation and the failure behavior of a third generation magnesium AZ31 sheet is studied under quasi-static tensile, compressive, and mixed mode loading conditions at room temperature. While the deformation anisotropy is found to be less pronounced compared to previously investigated rolled sheets of this alloy, a strong dependence of the failure strain on the sheets orientation is experienced. This failure anisotropy is further studied and quantified using mixed-mode tests realized using a modified Arcan fixture. The irreversible deformation is modeled in the framework of finite elements using two coupled anisotropic plastic potentials. The model parameters are calibrated using the global force-elongation record of the tested samples. For the prediction of failure, an uncoupled damage model based on transformation of strain rates is developed and applied. It is shown that this model is able to predict the observed edge failure of notched specimens with good accuracy. The model predictions for the smooth tensile tests are analyzed in detail by full-field FE analyses to understand the interaction between strain localization and predicted damage evolution.

Determination of Fracture Limit Line in Principal Strain Space by Shear Tests

The main goal of this paper was to define a new limit line, which expands Forming Limit Curve (FLC) more precisely Fracture Forming Limit Curve (FFLC). The new limit line was defined by damage models transformed from triaxiality-fracture strain space to the major/minor strain space and we focused on the shear area. Because FLC and FFLC have some limitations, for example, some Advanced High Strength Steels (AHSS) fractures before thinning. Another limitation can be seen on the left side of the diagrams in the shear region, where the part can break in the process without crossing the FLC or FFLC. The different shapes of samples were used for finding a new line of the FFLC and Deep Drawing Test (DDT) was used for verification. The fracture points from measurement were used for calibration of simple uncoupled damage models. The simple model means model, which is calibrated based on one or two measurements (tensile test or tensile test + shear test). This paper was used an Advanced High Strength Steel (AHSS) DP1000 sheet with a thickness of 0.8 mm for the experiments.

Ductile failure prediction of pipe-ring notched AISI 316L using uncoupled ductile failure criteria

The goal of this work is to predict ductile failure of pipe-ring notched AISI 316L specimens, where notches mimic the geometry of corrosion defects. Uncoupled damage models are used to that end. The Johnson-Cook and Lou-Huh criteria are calibrated.The uncoupled damage models are calibrated using experimental results from testing pipe-ring notched specimens. Calibration was achieved using a hybrid experimental-numerical approach. Six notch shapes are studied. Experimental matrices are designed to determine these shapes, and the pipe-ring notched specimen is inspired from the literature.Calibration of the uncoupled damage models require a ductile crack initiation indicator. The first indicator was based on the derivative curves of the force versus the connectors displacement curve. The second was based on the raw images of the gage section. The third was based on a percentage of the connectors displacement at fracture.Results show that ductile fracture depends on the Lode paramater. As a consequence, the Lou-Huh criterion is more effective at predicting ductile fracture than the Johnson-Cook criterion.

Comparison of two uncoupled ductile damage initiation models applied to DP900 steel sheet under various loading paths

Accurate prediction of the fracture occurrence of high strength materials is always the hot spot in the research field of metal-forming process. Appropriate material model is the key issue which can accurately describe the mechanical forming behavior under different forming conditions. However, advanced fully coupled damage/behavior models are heavy to use by engineers and have a high cost in term of calculation consuming time. In this paper, a simple uncoupled damage approach, designed to be easy to use for engineers and accurate as well, is investigated. Two uncoupled damage models, which consider the effect of the Lode angle and the hydrostatic pressure, combing three typical hardening rules, are selected and applied to the damage prediction of DP900 dual-phase steel. The hardening properties and forming limit strains under different loading paths of DP900 are investigated and studied throughout a variety of mechanical experiments, including the uniaxial tensile test, the pre-notched tensile tests with three notched radii, and the butterfly tests. Finally, the prediction accuracy of the used models for DP900 is compared and discussed.

Aluminium plates with pre-formed slits subjected to blast loading

The dynamic response of thin, perforated aluminium plates subjected to blast loading was studied both experimentally and numerically. Two different blast intensities were used and the plates were pre-cut with four horizontal and vertical slits prior to testing. The applied AA6016-T4 plates had an exposed area of 0.3 m x 0.3 m and a thickness of 1.5 mm. Special focus was placed on the dynamic response and failure characteristics of the plates. Uniaxial tensile tests were conducted in three different directions to determine the material behaviour and material parameters were found by inverse modelling using the optimization tool LSOPT. Finally, numerical simulations were performed in the finite element code Abaqus/Explicit where the plates were uniformly loaded with time-dependent pressure histories from similar tests on massive plates. The material behaviour was assumed to follow the J2 flow theory of plasticity and an uncoupled damage model was used in combination with element erosion to predict material failure. The numerical results were in good agreement with the experimental observations and predicted both the dynamic response and the complete tearing of the centre part of the plates.

Application of the critical plane approach to the torsional fatigue assessment of welds considering the effect of residual stresses

This study aims to investigate how the welding residual stresses affect the fatigue life of steel tubular joints. A single pass weld with filler material is created on the tubular specimens made of structural steel S355J2H. At first, welding residual stresses are calculated numerically by means of FE simulations. The validity of the results is verified experimentally by means of diffraction measurement techniques. Then, an uncoupled damage model based on the critical plane approach is utilized in order to calculate the fatigue life and the initial crack orientation. The as-welded specimens were subjected to cyclic torsional loading with constant stress amplitudes. The Fatemi-Socie (FS) damage parameter is used which is interpreted as the cyclic shear strain damage modified by the normal stress to include the crack closure effect. The stable portion of welding residual stresses is accounted for by the normal stress term of the model. It was observed that despite the common understandings about the critical weld notches, the crack initiation sites under torsional loading have been shifted from the weld toe and from the surface to the heat affected zone and beneath the surface where high tensile residual stresses exist. Then the initial cracks propagated toward the surface whose orientations were influenced by the presence of compressive residual stresses on the surface.It was generally found that the Fatemi-Socie parameter is capable of torsional fatigue damage assessment of welded tubular specimens which contain residual stresses since this critical plane parameter is based on the maximum shear strain plane.

Comparison of Damage Models in Numerical Simulations of Fillet Welds under Quasi-static and Impact Loading

Finite element (FE) simulations can be a powerful tool for predicting the response of fillet welds subjected to various types of loading. This requires that the fillet welds are modelled adequately, which can be a great challenge. Capturing the correct evolution of material damage and failure in the welds can be particularly difficult. This paper investigates two approaches to model damage in fillet welds of steel that are subjected to quasi-static and impact loading. One approach uses a shear-modified Gurson model, whereas the other employs an extended Cockcroft-Latham failure criterion, which is uncoupled from the constitutive equations. In both cases, a linear elastic-thermoviscoplastic constitutive relation is used. The two approaches produce practically the same global force-deformation response up to the instant the first elements are eroded. Thus, coupling damage with the constitutive relations has minor effect on this part of the response. Both damage models yield a decent agreement in terms of maximum force and weld deformation at failure when comparing the quasi-static tests with the respective simulations. On the other hand, noticeable discrepancies with the experimental results are observed for the simulations of the impact tests. However, the simulations using the extended Cockcroft-Latham criterion gave weld deformations at failure that were in better agreement with the experiments than the shear-modified Gurson model. In conclusion, an uncoupled damage model may be sufficient for predicting the global response of fillet welds.

Application of Uncoupled Damage Models to Predict Ductile Fracture in Sheet Metal Blanking

The use of uncoupled damage models has been widely used over the years for the prediction of ductile fracture in engineering applications. Nevertheless, its applicability in the prediction of failure has been shown to be limited in the wide range of loading conditions encountered in different manufacturing processes. In order to enhance the formulation of former damage models, the Lode angle has been recently used to characterize the stress states along with the stress triaxiality. This new family of damage models has been demonstrated to give excellent results when proportional loading paths are considered, but its efficiency in more complex applications still need further analysis. To this end, a comparative study of former and recently developed uncoupled damage models is performed in this work. The identification of material parameters is done considering simple mechanical tests under different conditions. Then, the models are used to predict the onset and propagation of cracks during blanking, where numerical predictions are compared with experimental results. Finally, the selected damage models presented a remarkable overall performance in the range of clearances under study.

Micromechanics-Based Damage Analysis of Fracture in Ti5553 Alloy with Application to Bolted Sectors

A physics-based, uncoupled damage model is calibrated using cylindrical notched round tensile specimens made of Ti5553 and Ti-6Al-4V alloys. The fracture strain of Ti5553 is lower than for Ti-6Al-4V in the full range of stress triaxiality. This lower ductility originates from a higher volume fraction of damage sites. By proper heat treatment, the fracture strain of Ti5553 increases by almost a factor of two, as a result of a larger damage nucleation stress. This result proves the potential for further optimization of the damage resistance of the Ti5553 alloy. The damage model is combined with an elastoviscoplastic law in order to predict failure in a wide range of loading conditions. In particular, a specific application involving bolted sectors is addressed in order to determine the potential of replacing the Ti-6Al-4V by the Ti5553 alloy.

Prediction of fretting fatigue crack initiation and propagation lifetime for cylindrical contact configuration

A fretting fatigue failure scenario can be explained by accumulation of damage, which leads to formation of initial macro-cracks at the contact interface and propagation of macro-cracks to sudden rupture of bulk material. The main aim of this study is estimating these two portions by means of a numerical modelling approach. For this purpose, an uncoupled damage model based on a thermodynamic potential function is used to model the crack initiation lifetime. In order to model crack propagation part a linear-elastic fracture mechanics approach under mixed-mode loading conditions has been considered. The crack propagation direction is defined based on experimental observation and compared with some available criteria in the literature, which are usually used for proportional loading conditions. The estimated results are compared with observed experimental lifetime and show good agreement.

Identification methodology and comparison of phenomenological ductile damage models via hybrid numerical–experimental analysis of fracture experiments conducted on a zirconium alloy

The present study details the methodology of the identification process of uncoupled damage formulations proposed by Bai and Wierzbicki (B&W model – Bai and Wierzbicki (2008) and Modified Mohr–Coulomb – Bai and Wierzbicki (2010)) as well as the Lemaitre and enhanced Lemaitre coupled damage models. These uncoupled models were first implemented in the Finite Element (FE) software Forge2009®, then their parameters identifications were carried out. These identifications involve two steps: identification of hardening law parameters and identification of damage parameters. In the first step, the method to obtain the coefficient of a non-linear friction law in compression test is also presented. The second step differs between the above-mentioned models: the identification of uncoupled models is carried out through the experimental fracture strains of different loading paths, while the identification of Lemaitre’s model is based on the softening effect of damage. The latter model is enhanced by accounting for the influence of the Lode parameter to improve its ability to predict fracture in shear loading. The results show that, among the studied models, the proposed enhanced Lemaitre model gives overall best results in terms of fracture prediction for all the tests. The proportionality of studied loading paths is also discussed. It is shown that the compression is not suitable to identify the parameters of the studied uncoupled damage models.

Research on sheet metal semicutting process using coupled and uncoupled damage model

An axisymmetric finite element model was created using ABAQUS software to study the evolution of the ductile damage in the process of sheet metal semicutting. A modified Gurson–Tvergaard–Needleman (GTN) porous material model and a modified Rice–Tracey ductile fracture model which takes into account the influence of stress triaxiality and deviatoric stress tensor on material damage, were introduced and the improvements of them were verified based on a single element uniaxial tension test and different tensile tests with notched specimens. After that, both of them were used for elastoplastic sheet metal semicutting analysis. By analysing the distributions of hydrostatic stress, equivalent stress, equivalent strain, stress triaxiality and fracture of sheet metal in the process of semicutting parts based on simulation and the corresponding experimental results, some phenomenon related to void nucleation, growth and coalescence in the sheet metal semicutting process was discussed.

Description of numerical techniques with the aim of predicting the sheet metal blanking process by FEM simulation

A numerical formulation of the blanking process in 2D is presented in this article. A finite element software called BlankForm has been developed to simulate the blanking process. Several approaches to model ductile damage and fracture have been investigated and are presented in this paper. In particular, some details are provided about a discrete cracking method that has been developed to take the propagation of one or several cracks into account. Our formulation is evaluated on an axisymmetric blanking experiment. The importance of remeshing is demonstrated. Coupled and uncoupled damage models are benchmarked, and two methods for fracture simulation are analysed, namely the previous discrete cracking method, and a widely used method in blanking applications, the element kill method. It is shown that more realistic results are obtained when the discrete cracking method is used.