Article

# Micromechanical Modeling of Damage Mechanisms in Dual-Phase Steel Under Different Stress States

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## Abstract

In this paper, the fracture behavior and micro-damage evolution in DP600 and DP980 steels were studied using experimental and numerical methods. First, four specimens with different loading conditions were tested to investigate the influence of the stress state on the fracture behavior and in-situ tensile tests were carried out in order to evaluate damage evolution in the two steels. Afterwards, 3D RVEs based on random martensite phase distribution were generated for both materials and a VUMAT subroutine was utilized to include the modified Mohr-Coulomb (MMC) damage model in the ferrite phase and predict the macroscopic fracture strain under complex loading conditions. Finally, damage mechanism in the RVE was compared to the in-situ test. It was observed that damage initiation mechanism in DP steels is dependent on the size of ferrite phases. In DP steels with large ferrite phases, strain localization in the middle of the phase caused damage initiation, whereas for steels with smaller ferrite grains, such as DP980, strain localization in the boundary of two phases is the dominant damage initiation mechanism. Furthermore, damage occurred by formation of voids, initiation of micro-cracks near the voids, and propagation and coalescence of these micro-cracks. Also, the response surface methodology can be used to calibrate parameters of the MMC damage model and the resulting FE model can accurately predict the stress-strain curve and fracture strain for all considered loading conditions, except for the shear loading condition. Finally, the proposed micromechanical FE model can be used to predict the same damage mechanisms as the in-situ tensile test.

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... Their promising properties can be attributed to their microstructure, which consists of hard martensite islands and a soft ferrite matrix. This microstructure leads to high formability, continuous yielding behavior, high strength, high strain hardening rate, and low yield stress-to-tensile strength ratio [2]. ...
... , (2) where and ∆ are the thickness of the interface and entropy of fusion between the phases, respectively. Additionally, the parameters and represent the liquidus line slop for component and the diffusion matrix, respectively, and is related to the partition coefficient. ...
... The material properties of the ferrite and martensite phases are essential factors to consider. It is well known that they change with the process parameters [33,34], but to simplify the process, the flow curves were taken from DP600 steel, as shown in Figure 4, which was reported in a previous study [2]. Damage in the martensite phase was ignored, and the Johnson-Cook damage model was used for the ferrite phase. ...
Article
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A comprehensive approach to understand the mechanical behavior of materials involves costly and time-consuming experiments. Recent advances in machine learning and in the field of computational material science could significantly reduce the need for experiments by enabling the prediction of a material's mechanical behavior. In this paper, a reliable data pipeline consisting of experimentally validated phase field simulations and finite element analysis was created to generate a dataset of dual-phase steel microstructures and mechanical behaviors under different heat treatment conditions. Afterwards, a deep learning-based method was presented, which was the hybridization of two well-known transfer-learning approaches, ResNet50 and VGG16. Hyper parameter optimization (HPO) and fine-tuning were also implemented to train and boost both methods for the hybrid network. By fusing the hybrid model and the feature extractor, the dual-phase steels' yield stress, ultimate stress, and fracture strain under new treatment conditions were predicted with an error of less than 1%.
... The geometrically necessary dislocation (GND) build-up around the phase boundaries are indicators of such strain localizations [21,22]. Finally, the local state of stress-strain is expected to decide the damage initiation [13,31,32]. In summary, it is clear that multiple characterization tools plus plasticity modeling are required for effective exploration of mechanical behavior in complex multi-phase microstructures. ...
... Different damage micro-mechanisms have been reported in different DP steels [12][13][14][15][16][17][18]. Cheloee Darabi et al. [19,20] observed damage initiation at low strains in the middle of the large ferrite phase, at the interfaces between phases, and at the trapped ferrite phase surrounded by martensite. Also, the micro-crack initiation was detected at higher strains at the thin martensite phase due to strain or shear band growth, and at the boundary between the phases. ...
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In the present work, the microstructural damage behavior of two DP1000 steel test subjects through various stress states was studied to thoroughly learn the interaction between microstructure, damage evolution, and edge stretchability. In addition, microstructural changes at the fracture sites and fracture surfaces were observed using a scanning electron microscope. The distinctive mechanical and damage behaviors of the materials were revealed. However, the steels were slightly different in chemical composition, microstructural characteristics, and yield stress. The results showed that when microstructural and mechanical properties of phases were more similar, i.e., the microstructure was more homogenous, the damage was initiated by cracking at ferrite-martensite interfaces, and it propagated along the loading direction. This allowed the material to represent high local formability and significant necking. In contrast, by increasing the dissimilarity between ferrite and martensite phases, damage propagated by the shear linking of the voids hindered local deformation of the material and led it to sudden fracture after negligible necking. These distinct damage evolutions noticeably influenced the materials’ edge stretchability. Since higher local formability favors the edges with higher resistance to cracking, the hole expansion ratio increases, as clearly observed throughout the current study.
... Based on the type, number, and volume fraction of phases, different micro, and macro-mechanically approaches have been proposed to model the damage and fracture behavior during the plastic deformation of multi-phase steels. Micromechanical concepts of crystal plasticity (Dakshinamurthy & Ma, 2018;Kadkhodapour et al., 2011;Tasan et al., 2014) and Representative Volume Elements (RVE) (Aghaei & Ziaei-Rad, 2020;Ahmadi et al., 2020;Cheloee Darabi et al., 2021;Paul, 2012;Sun et al., 2009;Yerra et al., 2013) have been developed in DP steels. In addition, damage mechanics as a specific method for modeling the plastic behavior coupled with damage growth in the material has been implemented in the subject. ...
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In this paper, a new constitutive model for plastic behavior of the metastable austenitic stainless steels at cryogenic temperatures is presented. The constitutive model is a phenomenological hyperelastic-based large deformation model developed in the framework of continuum damage mechanics considering the dissipative phenomena of strain-induced phase transformation and damage growth during plastic deformation. To solve the coupled nonlinear set of equations, incremental equations and the related implicit integration method have been developed. Numerical analysis is performed by implementing the constitutive model in a UMAT subroutine in ABAQUS/STANDARD. In addition, experiments have been conducted to identify the material model parameters for AISI304 steel at the 77K temperature. In addition to calibration, the constitutive model was validated via a tensile test of a notched sample. Also, the model has been compared with the experimental data at 4.2 K available in the literature. The results show that the model is well able to predict the hardening behavior, martensite evolution, and damage growth during the plastic deformation until the fracture with acceptable accuracy.
... The second type (type II) is notified in the bainite phase shown in Figure 22c,e. With the growth of deformation bands, the martensite phase cannot bear plastic deformation anymore [49], and the third type of void initiation (type III) forms due to the failure in the martensite phase, as illustrated in Figure 21b. In Figure 21, the microstructure is martensite as matrix and bainite as inclusion, and martensite forms a continuous network around bainite grains. ...
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Hot stamping components with tailored mechanical properties have excellent safety-related performance in the field of lightweight manufacturing. In this paper, the constitutive relation and damage evolution of bainite, martensite, and mixed bainite/martensite (B/M) phase were studied. Two-dimensional representative volume element (RVE) models were constructed according to microstructure characteristics. The constitutive relations of individual phases were defined based on the dislocation strengthening theory. Results showed that the damage initiation and evolution of martensite and bainite phases can well described by the Lou-Huh damage criterion (DF2015) determined by the hybrid experimental–numerical method. The calibrated damage parameters of each phase were applied to the numerical simulation, followed by the 2D RVE simulations of B/M phase under different stress states. To study the influence of martensite volume fraction (Vm) and distribution of damage evolution, the void nucleation and growth were evaluated by RVEs and verified by scanning electron microscope (SEM). Three types of void nucleation modes under different stress states were experimentally and numerically studied. The results showed that with the increase of Vm and varying martensite distribution, the nucleation location of voids move from bainite to martensite.
... The mechanism of void initiation and void growth in DP800 steel was explored earlier (Kadkhodapour et al., 2011b(Kadkhodapour et al., , 2011a, where uniaxial tensile tests and subsequent simulations revealed higher strain localization in ferrite as compared to martensite, and preferential void 4 initiation in martensitic regions resulted in final failure. Moreover, their group looked into the different aspects of micro-mechanism of damage in DP steels under complex loading condition (Cheloee Darabi et al., 2021b), or due to hydrogen embrittlement (Asadipoor et al., 2021) or because of different state of stress conditions (Cheloee Darabi et al., 2021a), where strain localization, formation of voids and subsequent nucleation of crack were modelled. ...
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... Yalçinkaya et al. [39] developed a crystal plasticity finite element (CPFE) framework and used 3D RVE with a Voronoi inlay to investigate the effect of microstructure parameters on the initiation and expansion of local plastic deformation of dual-phase steel. Darabi et al. [40] generated a 3D RVE model with a random distribution of martensite and predicted the fracture characteristics and microstructure evolution of two dual-phase steels under complex loading conditions. Park et al. [41] combined the microscale RVE model with the dislocation accumulation formula and used it as an alternative to the crystal plasticity method to analyze the hardening of grain boundaries and local nonuniform plastic deformation behavior of ferrite-bainite steel. ...
Article
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... For this reason, the use of advanced highstrength steel sheets in automobiles has increased considerably in recent years. Among the materials called advanced high-strength steels developed in this context, dual-phase steels have an important place with their superior mechanical properties [1][2][3][4][5][6] . ...
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... The mechanism of void initiation and void growth in DP800 steel was explored earlier (Kadkhodapour et al., 2011b(Kadkhodapour et al., , 2011a, where uniaxial tensile tests and subsequent simulations revealed higher strain localization in ferrite as compared to martensite, and preferential void 4 initiation in martensitic regions resulted in final failure. Moreover, their group looked into the different aspects of micro-mechanism of damage in DP steels under complex loading condition (Cheloee Darabi et al., 2021b), or due to hydrogen embrittlement (Asadipoor et al., 2021) or because of different state of stress conditions (Cheloee Darabi et al., 2021a), where strain localization, formation of voids and subsequent nucleation of crack were modelled. ...
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Monotonic deformation behavior of ferrite-martensite dual phase steels with martensite volume of 13-43% have been analyzed in the current investigation using micromechanics based finite element simulation on representative volume elements. The effects of martensite volume fraction on the strain partitioning behavior between soft ferrite matrix and hard martensite islands in dual phase steels during tensile deformation have been investigated. As a consequence of strain incompatibility between hard martensite and soft ferrite phases, inhomogeneous deformation and finally deformation localization occur during tensile deformation. Restricted local deformation in ferrite phase caused by the adjacent martensite islands triggers the local stress triaxiality development. As the martensite volume fraction increases, the local deformation restrictions in ferrite phase also increases and which results in higher stress triaxiality development. Similarly the strain partitioning behavior between ferrite matrix and martensite island is also influenced by the volume fraction of martensite. The strain partitioning coefficient increases with increasing martensite volume fraction.
Article
Dual phase (DP) steels, which have an intricate microstructure, consist of ferrite and martensite phases and because of interaction between the ferrite and martensite phases, those have complex behaviors. In this study, the flow curves of two heat-treated DP steels, DP800 and DP980, were compared with those of the 2D and 3D micromechanical models based on actual microstructure under symmetric and periodic boundary conditions. The effects of martensite phase distributions on the flow curves of 2D and 3D micromechanical models were investigated. Moreover, two different microstructures of DP980 with two different distributions of martensite phases were compared together to investigate the effect of martensite phase distribution in 2D and 3D micromechanical models on the stress-strain curve of DP980. Also, an in-situ tensile setup test was employed in order to investigate the initiation of localized strain patterns in the ferrite phase. The stress-strain curve, localization patterns and initiation of slip bands obtained from 2D and 3D micromechanical models were compared with the experimental results. The numerical results revealed that the stress-strain curves obtained from 3D models in comparison with 2D models are in closer agreement with experimental data.
Article
Chapter
This chapter contains detailed theoretical analysis and experimental data on the relationship of structure parameters of dual-phase steels (volume fraction and hardness of martensite, ferrite grain size, structure morphology) and various mechanical properties such as yield and tensile strength, strain hardening, elongation. Various facture characteristics including resistance to crack initiation and propagation, as well as resistance to fatigue hydrogen embrittlement are summarized. The main features of intercritical annealing (enrichment of austenite by carbon and transformations in cooling affected by pre-existing austenite-ferrite interfaces) are discussed. Individual steps of the processing, including formation of austenite phase, its growth, decomposition, and final tempering of ferrite-martensite mixture, are described. This chapter summarizes various effects of steel composition on processes during the heating in the intercritical temperature range, including kinetics austenitization, recrystallization of initial structure and morphology of the formed austenite-ferrite mixture. Effects of chemical composition on tensile properties, behavior at aging, and tempering, are presented.
Article
A microstructure-based approach by means of representative volume elements (RVEs) is employed to evaluate the flow curve of DP steels using virtual tensile tests. Microstructures with different martensite fractions and morphologies are studied in two- and three-dimensional approaches. Micro sections of DP microstructures with various amounts of martensite have been converted to 2D RVEs, while 3D RVEs were constructed statistically with randomly distributed phases. A dislocation-based model is used to describe the flow curve of each ferrite and martensite phase separately as a function of carbon partitioning and microstructural features. Numerical tensile tests of RVE were carried out using the ABAQUS/Standard code to predict the flow behaviour of DP steels. It is observed that 2D plane strain modelling gives an underpredicted flow curve for DP steels, while the 3D modelling gives a quantitatively reasonable description of flow curve in comparison to the experimental data. In this work, a von Mises stress correlation factor σ3D/σ2D has been identified to compare the predicted flow curves of these two dimensionalities showing a third order polynomial relation with respect to martensite fraction and a second order polynomial relation with respect to equivalent plastic strain, respectively. The quantification of this polynomial correlation factor is performed based on laboratory-annealed DP600 chemistry with varying martensite content and it is validated for industrially produced DP qualities with various chemistry, strength level and martensite fraction.
Article
As-hot-rolled, ferrite-martensite dual-phase steels of rather simple composition can be produced by the “Dual Phase Rolling (DPR) process” which involves a low finish rolling temperature and a very low coiling temperature. Laboratory DPR experiments have been carried out using C-Mn steels and those with Cr or Si additions, to examine the effects of alloying and processing factors on the structure and mechanical properties of the processed steels. Major results obtained are as follows: (1) To attain a sufficiently low yield-to-tensile strength ratio, the final finish pass temperature should be at about Ar3 point which varies depending on the composition, so as to bring about early separation of the alpha phase from the gamma phase before cooling starts. The coiling after a rapid cooling should be done at a temperature lower than 200°C, almost regardless of the steel composition, to suppress auto-tempering of the transformed martensite and aging of the ferrite. (2) Both Cr and Si additions enhance the hardenability of partitioned austenite, allowing a relaxed cooling rate to obtain the martensite phases. However, Cr addition is prone to hinder the early phase separation making the gamma-to-alpha transformation sluggish. Silicon addition accelerates the phase separation, so that a wide range of finishing temperature is available.
Article
Dual-phase steels show complex damage mechanisms that complicate the prediction of sheet formability. The ductile crack initiation locus (DCIL) has been developed as a failure criterion to better describe the characteristic forming behaviour in dual-phase steels. It displays the equivalent plastic strain at a critical combination of stress triaxiality and Lode angle with four damage parameters. Due to the high experimental complexity of the determination of these parameters and the missing link to the microstructure, an alternative numerical approach is of great interest. In this study, the micromechanical Gurson-Tvergaard- Needleman (GTN) model was employed to predict the damage parameters of a dual-phase steel. An adequate calibration procedure of the GTN parameters was defined with the consideration of the link between microstructural features and mechanical behaviours. After the determination of the GTN parameters, tensile tests of different specimens expressing different stress states were simulated using the GTN model. An overall good agreement was obtained for the force-displacement response. However, due to the exclusion of the Lode angle effect of the GTN model, the limitation of the capability of predicting the damage parameters in the whole stress state was also indicated and discussed.
Article
Local deformation and damage mechanisms have been studied for a commercial DP600 steel using in-situ tensile testing inside a scanning electron microscope (SEM) in combination with Digital Image Correlation (DIC). Different gauge geometries have been used to study damage evolution processes during tensile testing up to final failure. Strain distributions have been measured within the ferrite and martensite phases, together with the corresponding strain values for identified damage initiation mechanisms. According to the strain maps, large plastic deformation with strain values as large as 4.5 have been measured within the ferrite phase. Severe deformation localization and slip band formation were observed within the ferrite grains. The DIC results show that martensite in the studied material is plastically deformable with a heterogeneous strain distribution within the islands with values of up to 0.9 close to the phase boundaries. Failure of the martensite islands occurs mostly due to micro-crack initiation at the boundaries with the ferrite followed by crack propagation towards the centre of the islands. As for the ferrite matrix, it is found that its interface with the martensite is strong and cohesive. Localized damage in the matrix occurs by sub-micron void formation within the ferrite adjacent to the interface as opposed to the separation along the phase boundary itself or in the central regions of the ferrite grains A mechanism has been proposed to explain the deformation and damage evolution in the microstructure of the studied DP600 steel up to the final fracture.
Article
Dual-phase steels (DP) are well suited for automotive application due to their attractive mechanical properties, such as high strength and good formability. These properties are achieved by the dispersion of hard martensite particles in the soft and ductile ferrite matrix. The current work aims to predict the mechanical properties of dual-phase steels. A microstructure based approach by means of representative volume element (RVE) was employed for this purpose. Available and novel routines were used to create the 2D RVEs from the real microstructures. Periodic and homogeneous boundary conditions were imposed. Dislocation based model was implemented to predict the flow behaviour of the single phases. Computational first order homogenization strategy was employed to obtain the true stress–true strain curves from the RVE calculations. The implementation of the periodic boundary condition results in a better agreement with the converged effective value compared to the displacement boundary condition. Equiaxed microstructures show higher strength and work hardening compared to that of the banded microstructures. In the same fraction of martensite, the yield stress of DP steels decreases by increasing the aspect ratio of martensite bands.
Article
In this paper, we examine the key factors influencing ductile failure of various grades of dual phase (DP) steels using the microstructure-based modeling approach. Various microstructure-based finite element models are generated based on the actual microstructures of DP steels with different martensite volume fractions. These models are, then, used to investigate the influence of ductility of the constituent ferrite phase and also the influence of voids introduced in the ferrite phase on the overall ductility of DP steels. It is found that with volume fraction of martensite in the microstructure less than 15%, the overall ductility of the DP steels strongly depends on the ductility of the ferrite matrix, hence pre-existing micro-voids in the microstructure significantly reduce the overall ductility of the steel. When the volume fraction of martensite is above 15%, the pre-existing voids in the ferrite matrix does not significantly reduce the overall ductility of the DP steels, and the overall ductility is more influenced by the mechanical property disparity between the two phases. The applicability of the phase inhomogeneity driven ductile failure of DP steels is then discussed based on the obtained computational results for various grades of DP steels, and the experimentally obtained scanning electron microscopy (SEM) pictures of the corresponding grades of DP steels near fracture surface are used as evidence for result validations.
Article
Classical metal plasticity theory assumes that the hydrostatic pressure has no or negligible effect on the material strain hardening, and that the flow stress is independent of the third deviatoric stress invariant (or Lode angle parameter). However, recent experiments on metals have shown that both the pressure effect and the effect of the third deviatoric stress invariant should be included in the constitutive description of the material. A general form of asymmetric metal plasticity, considering both the pressure sensitivity and the Lode dependence, is postulated. The calibration method for the new metal plasticity is discussed. Experimental results on aluminum 2024-T351 are shown to validate the new material model.From the similarity between yielding surface and fracture locus, a new 3D asymmetric fracture locus, in the space of equivalent fracture strain, stress triaxiality and the Lode angle parameter, is postulated. Two methods of calibration of the fracture locus are discussed. One is based on classical round specimens and flat specimens in uniaxial tests, and the other one uses the newly designed butterfly specimen under biaxial testing. Test results of Bao (2003) [Bao, Y., 2003. Prediction of ductile crack formation in uncracked bodies. PhD Thesis, Massachusetts Institute of Technology] on aluminum 2024-T351, and test data points of A710 steel from butterfly specimens under biaxial testing validated the postulated asymmetric 3D fracture locus.
Article
Ductile failure of metals is often treated as the result of void nucleation, growth and coalescence. Various criteria have been proposed to capture this failure mechanism for various materials. In this study, ductile failure of dual phase steels is predicted in the form of plastic strain localization resulting from the incompatible deformation between the harder martensite phase and the softer ferrite matrix. Microstructure-level inhomogeneity serves as the initial imperfection triggering the instability in the form of plastic strain localization during the deformation process. Failure modes and ultimate ductility of two dual phase steels are analyzed using finite element analyses based on the actual steel microstructures. The plastic work hardening properties for the constituent phases are determined by the in-situ synchrotron-based high-energy X-ray diffraction technique. Under different loading conditions, different failure modes and ultimate ductility are predicted in the form of plastic strain localization. It is found that the local failure mode and ultimate ductility of dual phase steels are closely related to the stress state in the material. Under plane stress condition with free lateral boundary, one dominant shear band develops and leads to final failure of the material. However, if the lateral boundary is constrained, splitting failure perpendicular to the loading direction is predicted with much reduced ductility. On the other hand, under plane strain loading condition, commonly observed necking phenomenon is predicted which leads to the final failure of the material. These predictions are in reasonably good agreement with experimental observations.
Article
Multiphase steels have become a favoured material for car bodies due to their high strength and good formability. Concerning the modelling of mechanical properties and failure behaviour of multiphase steels, representative volume elements (RVE) have been proved to be an applicable approach for describing heterogeneous microstructures. However, many multiphase steels exhibit inhomogeneous microstructures which result from segregation processes during continuous casting. These segregations lead to a formation of martensite bands in the microstructure causing undesirable inhomogeneities of material properties. The aim of this work is to develop an FE evaluation procedure for predicting a microcrack formation provoked by banded martensitic structures. A micromechanism based damage curve was applied as a failure criterion for the softer ferritic matrix in the microstructure in order to simulate the propagation of cracks resulting from the failure of martensitic bands. The parameters of the damage curve were determined by in situ miniature bending tests and tensile tests with notched samples. The presented approach provides the basis for an assessment criterion of the component safety risk of multiphase steels with inhomogeneous microstructures.
Article
In the present work, a unified formulation has been applied to predict the tensile curves of ferrite, pearlite, bainite and martensite. This model produces a Voce type of equation that has been successfully applied to fit the experimental tensile curves obtained with the above mentioned microstructures. This allows testing the model over the broad range of tensile strengths that are associated to the different microstructures produced by the transformation of the austenite. The results are treated in a unified way and discussed in terms of a characteristic size for each microstructure type and the size variations within each range.
Article
The evolution of local plastic deformation in a dual-phase (DP) steel has been studied using Digital Image Correlation (DIC) and in-situ tensile testing inside a scanning electron microscope. Tests were performed using specially designed samples to study the initiation and evolution of damage in DP1000 steel by measuring the strains at the scale of the microstructure. Micrographs have been analysed using DIC at different stages throughout a tensile test to measure local strain distributions within the ferrite–martensite microstructure. The results show progressive localisation of deformation into bands orientated at 45° with respect to the loading direction. Strain magnitudes are higher in the ferrite phase with local values reaching up to 120%. Several mechanisms for damage initiation are identified and related to the local strains in this steel. The procedure used and the results obtained in this work may help the development of models aimed at predicting the properties of new generation automotive steels.
Article
We study the ultimate ductility and failure modes of a commercial transformation-induced plasticity (TRIP) 800 steel under different loading conditions with an advanced microstructure-based finite-element analysis. The representative volume element (RVE) for the TRIP 800 under examination is developed based on an actual microstructure obtained from scanning electron microscopy. The ductile failure of the TRIP 800 under different loading conditions is predicted in the form of plastic strain localization without any prescribed failure criteria for the individual phases. This indicates that the microstructure-level inhomogeneity of the various constituent phases can be the key factor influencing the final ductility of the TRIP 800 steel under different loading conditions. Comparisons of the computational results with experimental measurements suggest that the microstructure-based modeling approach accurately captures the overall macroscopic behavior of the TRIP 800 steel under different loading and boundary conditions.
Article
In this paper, a macroscopic orthotropic yield criterion, which can describe both the anisotropy of a material and the yielding asymmetry between tension and compression, is introduced. The yield function is expressed in terms of the principal values of the stress deviator, ensuring insensitivity to the hydrostatic pressure. Application of the proposed criterion to magnesium and titanium alloy sheets shows that this model can capture very well the complex behavior of these materials.
Article
In this paper void coalescence is regarded as the result of localization of plastic flow between enlarged voids. We obtain the failure criterion for a representative material volume (RMV) in terms of the macroscopic equivalent strain (Ec) as a function of the stress triaxiality parameter (T) and the Lode angle (θ) by conducting systematic finite element analyses of the void-containing RMV subjected to different macroscopic stress states. A series of parameter studies are conducted to examine the effects of the initial shape and volume fraction of the primary void and nucleation, growth, and coalescence of secondary voids on the predicted failure surface Ec(T,θ). As an application, a numerical approach is proposed to predict ductile crack growth in thin panels of a 2024-T3 aluminum alloy, where a porous plasticity model is used to describe the void growth process and the expression for Ec is calibrated using experimental data. The calibrated computational model is applied to predict crack extension in fracture specimens having various initial crack configurations and the numerical predictions agree very well with experimental measurements.
Article
The influence of martensite morphology and its geometrical distribution in ferrite matrix on the mechanical properties and fracture mechanisms of Fe-Mn-C dual phase steels has been studied experimentally. Special attention has been paid to the determination of the fracture mechanisms. Examination of the repolished longitudinal sections of fractured specimens by scanning electron microscopy has revealed that, according to their different morphologies and dispersions, the main mechanism of void formation in these dual phase steels can change from martensite cracking to decohesion at the ferrite/martensite interface. These two features, in turn, can determine the failure mechanisms of the specimen: cleavage or ductile ‘cup and cone’ fracture. In addition, the observed mechanical properties have been related to these modes of fracture.
Article
Dual phase (DP) steels having a microstructure consists of a ferrite matrix, in which particles of martensite are dispersed, have received a great deal of attention due to their useful combination of high strength, high work hardening rate and ductility. In the present work, a microstructure based micromechanical model is developed to capture the deformation behavior, plastic strain localization and plastic instability of DP 590 steel. A microstructure based approach by means of representative volume element (RVE) is employed for this purpose. Dislocation based model is implemented to predict the flow behavior of the single phases. Plastic strain localization which arises due to incompatible deformation between the hard martensite and soft ferrite phases is predicted for DP 590 steel. Different failure modes arise from plastic strain localization in DP 590 steel are investigated on the actual microstructure by finite element method.
Article
Finite element (FE) analysis was employed to investigate the casting microcrack and micropore growth in nickel-base single-crystal superalloys DD3. Based on the finite deformation rate-dependent crystallographic constitutive equation, the simulations of casting microcrack and micropore growth in three-dimensional unit cell model were carried out in a range of parameters including stress triaxiality, Lode parameter and type of activated slip systems. The FE results show that the stress triaxiality has profound effects on growth behavior, and the Lode parameter is also important for the casting microcrack and micropore growth. The type of operative slip systems has remarkable effect on casting microcrack and micropore growth, so the life of single-crystal component is associated with the type of activated slip systems, which is related to Schmid factor and the number of activated slip systems. The growth comparison between microcrack and micropore reveals that when the material is subjected to large deformation, the growth rate of microcrack is faster than that of micropore, i.e. microcrack is more dangerous than micropore; the microcrack is easier to result in brittle fracture than micropore. The stress triaxiality and Lode parameter have strong influence on the growth of microcrack and micropore.
Article
The stress triaxiality is, besides the strain intensity, the most important factor that controls initiation of ductile fracture. In this study, a series of tests including upsetting tests, shear tests and tensile tests on 2024-T351 aluminum alloy providing clues to fracture ductility for a wide range of stress triaxiality was carried out. Numerical simulations of each test was performed using commercial finite element code ABAQUS. Good correlation of experiments and numerical simulations was achieved. Based on the experimental and numerical results, the relation between the equivalent strain to fracture versus the stress triaxiality was quantified and it was shown that there are three distinct branches of this function with possible slope discontinuities in the transition regime. For negative stress triaxialities, fracture is governed by shear mode. For large triaxialities void growth is the dominant failure mode, while at low stress triaxialities between above two regimes, fracture may develop as a combination of shear and void growth modes.
Article
The finite element is an interesting way to study the mechanical behaviour of multi-phase materials. In this article, we show that three-dimensional modelling is necessary for this purpose. A two dimensional (2D) simulation proves unsatisfactory, especially because of the mechanical and geometrical restrictions imposed by the 2D description of the microstructure.
Article
A detailed analysis of the microstructure and failure mechanism of a dual-phase steel material as a function of strain was conducted. Accordingly, three tensile tests were performed and interrupted at different strain levels in order to investigate void nucleation, void growth and void coalescence. Scanning electron microscopy analysis revealed that void nucleation occurs by ferrite grain-boundary decohesion in the neighborhood of martensite grains. Further, void initiation could be observed between closely situated martensite grains. Martensite morphology and distribution has a significant impact on the accumulation of damage. The mechanism of failure was found to be influenced by deformation localization due to microstructural inhomogeneity. Based on the experimental observations and simulation results, a model describing the failure mechanism is proposed for dual-phase steel material.
Article
All damage and failure models, describing either the evolution of microvoids, the development of shear bands or local rupture, rely on the knowledge of the hardening function at large plastic strains which, then, becomes an essential prerequisite for any failure prediction.The phenomenon of ductile failure is analyzed here by focusing on its relationship with the variables for the stress--strain characterization, and by discussing the influence of plastic strain, stress triaxiality and Lode angle parameters on both the above aspects of materials behavior.Failure predictions are presented for different metals and different combinations of load-specimen geometry, according to three theories (the Tresca criteria and two models by Wierzbicki et al.) and to a procedure previously developed for the stress--strain characterization in the post-necking range.Experimental tests are performed by pulling tensile specimens and notched flat samples up to failure, then finite elements simulations are used to calculate the required failure-related variables within the volume of failing specimens; the results of the failure calculations are compared each other and with experimental data, and a discussion about the peculiarities of the methods used for predicting failure is also provided.
Article
This paper considers fracture characteristics of OFHC copper, Armco iron and 4340 steel. The materials are subjected to torsion tests over a range of strain rates, Hopkinson bar tests over a range of temperatures, and quasi-static tensile tests with various notch geometries. A cumulative-damage fracture model is introduced which expresses the strain to fracture as a function of the strain rate, temperature and pressure. The model is evaluated by comparing computed results with cylinder impact tests and biaxial (torsion-tension) tests.
Article
This paper scrutinizes the reliability of indentation-based damage quantification, frequently used by many industrial and academic researchers. In this methodology, damage evolution parameters for continuum damage models are experimentally measured by probing the deformation-induced degradation of either hardness or indentation modulus. In this critical assessment the damage evolution in different sheet metals was investigated using this indentation approach, whereby the obtained results were verified by other experimental techniques (scanning electron microscopy, X-ray microtomography and highly sensitive density measurements), and by finite element simulations. This extensive experimental–numerical assessment reveals that the damage-induced degradation of both hardness and modulus is at least partially, but most likely completely, masked by other deformation-induced microstructural mechanisms (e.g. grain shape change, strain hardening, texture development, residual stresses and indentation pile-up). It is therefore concluded that hardness-based or modulus-based damage quantification methods are intrinsically flawed and should not be used for the determination of a damage parameter.
Automotive Steels: Design, Metallurgy, Processing and Applications explores, 7-Dual-phase steels
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