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Micromechanical Modeling of Damage Mechanisms in Dual-Phase Steel Under Different Stress States
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.
... 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. ...
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%.
... Damage begins at low strains in the ferrite phase, specifically at interfaces with other phases and in trapped ferrite surrounded by martensite as well. Also, micro-crack initiation occurs at higher strain in the thin martensite phase due to strain or shear band growth and at the boundary between the phases [17,18]. The dominant deformation-induced damage mechanisms in DP800 using panoramic imaging techniques and machine learning methods are statically studied. ...
Dual-phase (DP) steels are widely used in the automotive industry due to their exceptional performance. It offers excellent strength, ductility, formability, and weldability. However, there is a high risk of edge cracking, particularly in materials like DP1000 steel, caused by residual damage from blanking, such as microcracks and burrs, which needs further investigation. In this study, the transformative potential of laser-polishing on DP1000 steel was investigated. The goal was to reduce edge crack sensitivity and enhance edge formability. In this work, laser-polished samples produced by various pre-manufacturing techniques such as sawing, punching, and waterjet cutting were examined. Various evaluations were performed on laser-polished samples. Those included white-light-confocal microscopy, scanning electron microscopy, and Electron Backscatter Diffraction (EBSD) analysis. Those evaluations aimed to analyze the microstructural transformation, surface roughness, and micro grain size distribution resulting from laser-polishing. Laser-polishing is a process in which the edge of the sample is remelted locally. Hence, residual damage vanishes, and surface defects disappear, which should be beneficial for edge formability. On the other hand, the cooling rate during re-solidification is high, leading to high strength and reduced ductility compared to the initial DP steel. Therefore, hole expansion tests were conducted to evaluate the edge formability of the steel. The results indicated a significant improvement in the hole expansion ratio of the laser-polished samples compared to samples with conventional manufactured edges. These findings will help to assess the advantages and limitations of laser-polishing in sheet material manufacturing.
... 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. ...
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. ...
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. ...
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. ...
A modified 9Cr-1Mo steel having lath martensitic microstructure has been subjected to the hot-rolling at three different temperatures followed by a normalization at 1025°C to form different crystallographic textures after thermomechanical processing. The samples hot-rolled at 875°C, 1000°C and 1050°C showed major texture components as Goss (i.e. {110}<001>), Cube (i.e. {001}<01¯0>) and Gamma (i.e. {111}<1¯1¯2>), respectively. Next, these samples have been uniaxial tensile tested at quasi-static strain rate at room temperature, and tensile properties are evaluated. The results indicated almost similar strength levels for Goss and Cube oriented specimens, and significantly reduced strength for Gamma oriented samples. However, the Cube and Goss oriented samples showed different strain hardening rates owing to the occurrence of deformation induced twinning and anti-twinning phenomenon as revealed by the Visco-plastic self-consistent polycrystal plasticity simulations. Simulation results were validated with experimental observations using high-resolution transmission electron microscopy. Anisotropic parameters have also been simulated considering the difference in initial crystallographic orientations. Study of deformation micro-mechanism at different length scale of martensitic units (e.g., prior-austenite grain, martensitic packets, blocks, sub-blocks, and laths) revealed negligible rotations at the prior-austenite grain level, whilst the lattice rotations were found to be significant at martensitic sub-block (i.e. variant) length scale. The investigation indicated that some specific types of martensitic variants generally participated in large lattice rotation during deformation for differently textured samples.
... 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. ...
A novel modification of Weng’s secant approach to modeling the elastoplastic stress-strain response of tailor-tempered 22MnB5 steel with heterogeneous material properties when subjected to plastic deformation is described. In the tailored tempering process (TTP) of high-strength boron-manganese steel, different distributions of mechanical properties in the same component can be realized. The elastoplastic constitutive relation is an urgent issue when developing components with customized material properties. The capabilities of classical mixture rule methods and improved homogenization methods to describe the mechanical behavior of inhomogeneous products containing various volume fractions of constituent phases are extensively studied. Weng’s secant model is modified by using the exponential function instead of the power law relation to calculate the flow stress of tailor-tempered 22MnB5 steel. To correctly predict the higher hardness of the bainite around martensite than that inside the bainite structure, which is due to plastic deformation of the surrounding local bainite induced by the volume expansion accompanying martensite transformation, the phase boundary considering the hardening of surrounding local bainite is introduced into the secant model. Furthermore, Vickers hardness parameters instead of phase volume control parameters are used in the modified secant method. The predictability of the overall response obtained using the novel micromechanical-based secant method shows good agreement with experimentally obtained elastoplastic deformation behaviors.
... 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] . ...
The paper is concerned with the effect of punch angle (0°, 4°, 8°, 16°), sheet thickness (0.8, 2 mm), and punch speed (25, 37.5 mm / min) on the force formation and noise in the blanking of DP600 dual-phase steel sheet. The blanking experiments were carried out in a modular blanking die. The blanking force and noise variables were obtained simultaneously during the blanking using a load cell and noise measuring device, respectively. It was determined that the blanking force significantly decreased with an increasing punch angle, while noise formation decreased. The increase in the punch speed slightly increased the amount of noise while it did not affect the blanking force significantly.
... 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. ...
A modified 9Cr-1Mo steel having lath martensitic microstructure has been subjected to the hot-rolling at three different temperatures followed by a normalization at 1025 °C to form different crystallographic textures after thermomechanical processing. The samples hot-rolled at 875 °C, 1000 °C and 1050 °C showed major texture components as Goss (i.e. {110}<001>), Cube (i.e. {001}<0-10>) and Gamma (i.e. {111}<-1-12>), respectively. Next, these samples have been uniaxial tensile tested at quasi-static strain rate at room temperature, and tensile properties are evaluated. The results indicated almost similar strength levels for Goss and Cube oriented specimens, and significantly reduced strength for Gamma oriented samples. However, the Cube and Goss oriented samples showed different strain hardening rates owing to the occurrence of deformation induced twinning and anti-twinning phenomenon as revealed by the Visco-plastic self-consistent polycrystal plasticity simulations. Simulation results were validated with experimental observations using high-resolution transmission electron microscopy. Anisotropic parameters have also been simulated considering the difference in initial crystallographic orientations. Study of deformation micro-mechanism at different length scale of martensitic units (e.g., prior-austenite grain, martensitic packets, blocks, sub-blocks, and laths) revealed negligible rotations at the prior-austenite grain level, whilst the lattice rotations were found to be significant at martensitic sub-block (i.e. variant) length scale. The investigation indicated that some specific types of martensitic variants generally participated in large lattice rotation during deformation for differently textured samples.
Dual-phase (DP) steels are characterized by their good formability and interesting material properties, which primarily originate from their unique composition, combining the ductile ferrite phase with the hard martensite phase. At the microscale, DP steels exhibit various fracture mechanisms that need to be investigated through proper plasticity and failure models. These mechanisms include interface decohesion between ferrite–martensite and ferrite–ferrite phases, as well as martensite cracking, depending on the steel's microstructure. In this study, crystal plasticity and cohesive zone frameworks are employed together with a ductile failure model in 3D polycrystalline Representative Volume Element simulations to address the multiscale characteristics of the fracture mechanisms in DP steels. The analysis requires an extensive parameter identification procedure, which is presented in detail. The obtained results demonstrate the framework's capability to effectively identify the primary failure mechanisms correlated with crucial microstructural features, including crystallographic orientation, morphology, volume fraction, and stress triaxiality. Findings indicate that an increase in the connectivity of the martensitic phase induces a shift from ferrite–ferrite decohesion to ferrite–martensite decohesion and martensite cracking. Similarly, as the volume fraction of martensite increases, decohesions become constrained, making martensite cracking the main failure mode. The numerical observations regarding triaxiality highlight that as stress triaxiality increases, the predominant failure mechanism is changed from martensite cracking and ferrite–martensite decohesion to ferrite–ferrite decohesion.
A mathematical model is developed to consider the impact of microstructural parameters, including the volume fraction and the average particle size of martensite, on the flow stress and strain‐hardening behavior of dual‐phase microstructure. In this regard, the micromechanical approach is applied for partitioning the stress and strain in ferrite and martensite. Martensite carbon content and geometrically necessary dislocations, generated from austenite‐to‐martensite transformation, and strain accommodation at the ferrite–martensite interface, are involved to modify the partitioned stress of martensite and ferrite, respectively. Having partitioned stress in each phase, the global stress is estimated as the function of steel chemical composition, ferrite grain size, martensite particle size, aspect ratio, and volume fraction. To evaluate the applicability of the proposed model, four dual‐phase steels containing 12, 25, 34, and 48% volume fractions of martensite are prepared from the intermediate quenching process, and then after the strain‐hardening stages are investigated. Comparing the experimental result and model output reveals that the presented model shows good predictive capabilities to identify strain‐hardening stages and estimate the inverse of the strain‐hardening exponent.
The morphology distribution of microstructure has an important influence on the match of the strength and plasticity of dual-phase pipeline steel. Bainite and PF dual-phase steels with layered and network morphology were obtained by combining the Thermomechanical Control Process (TMCP) and inter-critical isothermal heat treatment. A novel experimental-numerical methodology studied the effect of phase distribution characters on the deformability of PF and bainite dual-phase pipeline steel. The plastic damage features and microscopic strain and stress distribution in both network and layered microstructure were clarified. The obvious differences in the microstructure evolution for both samples were captured by a quasi-situ tensile test. The PF phase in the network morphology sample was believed the main deformation phase, but the deformation of the PF phase in the layered morphology sample was restrained. Two three-dimensional (3D) crystal plasticity finite element models (CPFEMs) were established based on the electron backscatter diffraction (EBSD) data. The simulation results indicated that the strain field in layered microstructure was more uniform than that in network microstructure, and the continuous internal stress relaxation (ISR) in the bainite phase led to plastic damage at low tensile strain level; The strain field in network microstructure mainly existed in the PF phase, the deformation of the PF phase can be fully utilized. When changing the tensile x-direction of the layered microstructure to the z-direction, the strain field showed an obvious anisotropy, and loading in the z-direction increased the risk of interlaminar crack formation.
As a result of their heterogeneous two-phase microstructure, dual-phase (DP) steels reveal various damage mechanisms leading to the nucleation of voids, microcracks, and other defects at all stages of deformation. Defects may also preexist in the microstructure due to thermomechanical processing of the material. The literature has ample evidence that DP steels, while offering a good compromise between ductility and strength, are sensitive to these types of preexisting defects. However, the quantitative dependency of mechanical properties of DP steels on such preexisting defects is still to be explored. In this paper, a systematic statistical analysis of this sensitivity is carried out using an idealized microstructural model of randomly generated two-phase volume elements with embedded preexisting defects. The proposed model also enables a methodological study probing the influence of mechanical phase contrast (i.e., the hardness difference between the constituent phases) and volume fractions. It is observed that high phase contrast microstructures are less sensitive to initial defects since the inherent extreme heterogeneity of the microstructure leads to the nucleation of new damage incidents irrespective of the presence of preexisting defects. At constant contrast, the volume fraction of the hard phase has less influence. These conclusions are insensitive to the precise type of defect considered.
Shear cutting is a proven process for chip-less separation of metals and used as a cost-effective production method. The process design of shear cutting is usually based on time and cost intensive experimental tests. Therefore, numerical depiction of the process offers great potential to reduce these practical tests. An important aspect hereby is the representation of temperature dependency of the material. However, the classical Modified-Mohr-Coulomb (MMC) failure model does not depict this effect directly. Therefore, the objective of this paper is to investigate the temperature dependency of MMC failure model for simulating shear cutting. The required data is obtained from tensile tests on miniaturised specimens under variation of temperature on dual-phase steel DP1000, using an additional optical measurement system. To determine stress triaxiality, Lode angle parameter and plastic strain at failure, the experimental tests are simulated using the Finite-Element simulation program ABAQUS. The MMC failure surfaces are fitted using the least squares method in Matlab. With this approach, temperature dependent MMC failure model was built to be used for shear cutting simulation of DP1000 steel.
This paper studies the plastic deformation, localization and the ecking behavior of polycrystalline dual phase (DP) steels, with di�erent martensite volume fractions, and ferrite orientation distributions, through crystal plasticity finite element method. The grain structure of the full size micron-scale polycrystalline samples is built through Voronoi tesselation and the specimens are deformed under uniaxial loading condition. For the modelling of martensite phase J2 plasticity with isotropic hardening is employed
while in randomly oriented ferrite grains the crystal plasticity theory works. The material parameters are identified with respect to
uniaxial tensile experimental data using a fully periodic RVE with enough number of ferrite grains. The attention is focused on the
e�ect of the martensite morphology and the ferrite orientation distribution on the formation of the shear bands and then the necking
of the sample.
Damage models, particularly the Gurson-Tvergaard-Needleman (GTN) model, are widely used in numerical simulation of material deformations. Each damage model has some constants which must be identified for each material. The direct identification methods are costly and time consuming. In the current work, a combination of experimental, numerical simulation and optimization were used to determine the constants. Quasi-static and dynamic tests were carried out on notched specimens. The experimental profiles of the specimens were used to determine the constants. The constants of GTN damage model were identified through the proposed method and using the results of quasi-static tests. Numerical simulation of the dynamic test was performed utilizing the constants obtained from quasi-static experiments. The results showed a high precision in predicting the specimen's profile in the dynamic testing. The sensitivity analysis was performed on the constants of GTN model to validate the proposed method. Finally, the experiments were simulated using the Johnson-Cook (J-C) damage model and the results were compared to those obtained from GTN damage model.
The use of high performance materials such as high strength steel grades, aluminium and magnesium alloys has raised the difficulty to accurately predict structural crash behaviour: these materials are generally more prone to rupture than mild steel, and predicting rupture is still very difficult to achieve. In this paper certain facts behind metal rupture prediction are exposed together with the classical ways they have been approached in the past. A new "hybrid two parameter" model approach is proposed. These are models that include not only a measure of "damage" within the material but also a measure of the critical volume" to be saturated with damage before the damage evolves to an 'initial' crack. The way this approach is manifested through the new E-W material rupture model in PAM CRASH is shown. Academic examples are presented with this new modelling capability and they are compared favourably with the existing academic literature evidence. Finally, pre-industrial application examples are shown to support the potential of the new E-W model to predict rupture phenomena in car body crash: aluminium car body parts, statically and dynamically loaded. (A) For the covering abstract see ITRD E121867.
A plate of dual phase steel was produced from low carbon steel with intercritical annealing treatment. Its optically determined surface microstructure was utilized to construct three different microstructural models. To describe the ductile damage in the ferritic matrix, the Gurson-Tvergaard-Needleman model was used with the failure in the martensite phase being ignored. The numerical results obtained for the mechanism of void initiation and coalescence were compared with the experimental observations. The numerical results obtained from the randomly extruded 3D model showed a significantly better agreement with the experimental ones than those obtained from the 2D model or the uniformly extruded 3D model.
The ductile damage mechanisms dominating in modern high-strength steels have emphasised the significance of the onset of damage and the subsequent damage evolution in sheet metal forming processes. This paper contributes to the modelling of the plasticity and ductile damage behaviour of a dual-phase steel sheet by proposing a new damage mechanics approach derived from the combination of different types of damage models. It addresses the influence of stress state on the plasticity behaviour and onset of damage of materials, and quantifies the microstructure degradation using a dissipation-energy-based damage evolution law. The model is implemented into ABAQUS/Explicit by means of a user material subroutine (VUMAT) and applied to the subsequent numerical simulations. A hybrid experimental and numerical approach is employed to calibrate the material parameters, and the detailed program is demonstrated. The calibrated parameters and the model are then verified by experiments at different levels, and a good agreement between the experimental and numerical results is achieved.
The flow behavior of dual-phase (DP) steels is modeled on the finite-element method (FEM) framework on the microscale, considering the effect of the microstructure through the representative volume element (RVE) approach. Two-dimensional RVEs were created from microstructures of experimentally obtained DP steels with various ferrite grain sizes. The flow behavior of single phases was modeled through the dislocation-based work-hardening approach. The volume change during austenite-to-martensite transformation was modeled, and the resultant prestrained areas in the ferrite were considered to be the storage place of transformation-induced, geometrically necessary dislocations (GNDs). The flow curves of DP steels with varying ferrite grain sizes, but constant martensite fractions, were obtained from the literature. The flow curves of simulations that take into account the GND are in better agreement with those of experimental flow curves compared with those of predictions without consideration of the GND. The experimental results obeyed the Hall-Petch relationship between yield stress and flow stress and the simulations predicted this as well.
A reliable prediction of ductile failure in metals is still a wide-open matter of research. Among different models, Gurson-Tvergaard-Needleman (GTN) has been used extensively. One major issue is the accurate identification of GTN model parameters, which it is not possible to perform experiments for their evaluation. In the present paper a novel inverse procedure aimed to estimate the material parameters of the GTN porosity-based plastic damage model by means of RSM method is represented. The results showed good agreement between experimental and predicted forming limit diagrams when determined GTN parameters were utilized. FE-simulation by means of Abaqus software used to predict FLDs. © 2011 Published by Elsevier Ltd. Selection and peer-review under responsibility of ICM11
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.
Theoretical and experimental studies have shown that stress triaxiality is the key parameter controlling the magnitude of the fracture strain. Smooth and notched round bar specimens are mostly often used to quantify the effect of stress triaxiality on ductile fracture strain. There is a mounting evidence (Bai and Wierzbicki, 2008, "A New Model of Metal Plasticity and Fracture With Pressure and Lode Dependence," Int. J. Plast., 24(6), pp. 1071-1096) that, in addition to the stress triaxiality, the normalized third deviatoric stress invariant (equivalent to the Lode angle parameter) should also be included in characterization of ductile fracture. The calibration using round notched bars covers only a small range of possible stress states. Plane strain fracture tests provide additional important data. Following Bridgman's stress analysis inside the necking of a plane strain specimen, a closed-form solution is derived for the stress triaxiality inside the notch of a flat-grooved plane strain specimen. The newly derived formula is verified by finite element simulations. The range of stress triaxiality in round notched bars and flat-grooved specimens is similar, but the values of the Lode angle parameter are different. These two groups of tests are therefore very useful in constructing a general 3D fracture locus. The results of experiments and numerical simulations on 1045 and DH36 steels have proved the applicability of the closed-form solution and have demonstrated the effect of the Lode angle parameter on the fracture locus.
A steel containing 0.32 wt.% C, 0.88 wt.% Mn, 0.99 wt.% Si, 0.9 wt.% Ni, and 0.9 wt.% Cr was intercritically annealed at different
temperatures from 775 to 870 °C and quenched in oil to produce dual-phase steel microstructure. Tensile testing of these samples
gave a series of strengths and ductilities. The tensile strength increased with the increased annealing temperatures and the
martensite percentage increased with a reduction in ductility. Microvoids were formed near the fracture surfaces. The morphology
of the microvoids changed with the martensite percentage from decohesion of the martensite particles to the intergranular
and transgranular cracks, which defined the ultimate fracture mode of the specimens. The change in the morphology of microvoids
may be due to a high percentage of carbon in the steel, which produced stresses in the matrix (ferrite) during phase transformation.
The Mohr–Coulomb (M–C) fracture criterion is revisited with an objective of describing ductile fracture of isotropic crack-free
solids. This criterion has been extensively used in rock and soil mechanics as it correctly accounts for the effects of hydrostatic
pressure as well as the Lode angle parameter. It turns out that these two parameters, which are critical for characterizing
fracture of geo-materials, also control fracture of ductile metals (Bai and Wierzbicki 2008; Xue 2007; Barsoum 2006; Wilkins
etal. 1980). The local form of the M–C criterion is transformed/extended to the spherical coordinate system, where the axes
are the equivalent strain to fracture [`(e)]f{\bar \varepsilon_f} , the stress triaxiality η, and the normalized Lode angle parameter [`(q)]{\bar \theta} . For a proportional loading, the fracture surface is shown to be an asymmetric function of [`(q)]{\bar \theta}. A detailed parametric study is performed to demonstrate the effect of model parameters on the fracture locus. It was found
that the M–C fracture locus predicts almost exactly the exponential decay of the material ductility with stress triaxiality,
which is in accord with theoretical analysis of Rice and Tracey (1969) and the empirical equation of Hancock and Mackenzie
(1976), Johnson and Cook (1985). The M–C criterion also predicts a form of Lode angle dependence which is close to parabolic.
Test results of two materials, 2024-T351 aluminum alloy and TRIP RA-K40/70 (TRIP690) high strength steel sheets, are used
to calibrate and validate the proposed M–C fracture model. Another advantage of the M–C fracture model is that it predicts
uniquely the orientation of the fracture surface. It is shown that the direction cosines of the unit normal vector to the
fracture surface are functions of the “friction” coefficient in the M–C criterion. The phenomenological and physical sound
M–C criterion has a great potential to be used as an engineering tool for predicting ductile fracture.
Recent development of damage plasticity theory shows the critical plastic strain at fracture for ductile solids depends on the pressure and the Lode angle on the octahedral plane along the loading path. The determination of the fracture strain envelope is usually a difficult and time consuming process. This is due to the experimental difficulties in maintaining a constant pressure and Lode angle at the fracture site, which is further complicated by the coupled nature of the parameters to be calibrated and the geometrical localization of the deformation. The fracture strain envelope is one of the key ingredients of the damage plasticity theory and relates to the accuracy of predicted results. In the present paper, the Lode angle dependence and the pressure sensitivity functions for the fracture strain envelope are derived from the hardening rule of the matrix using Tresca type fracture condition and Drucker–Prager formula, respectively. Quantitative analyses of Clausing’s and Bridgman’s test data are presented. Then a pressure modified maximum shear stress condition is adopted as fracture initiation condition to examine their joint effects on the fracture strain envelope. The relationship of the strain hardening, the pressure sensitivity and the Lode angle dependence are examined and verified by existing experimental results. We show that within the moderate range of stress triaxiality, the pressure modified maximum shear condition can be used as the fracture stress envelope for ductile metals within the framework of damage plasticity. The present method reduces significantly the amount of work to calibrate the material parameters for ductile fracture.
Slant ductile rupture is one of the common failure modes in the pressure vessel and piping industry. Such failure in tubing and casing can be the result of excessive internal pressure and/or axial loading. The underlying physics of ductile rupture is essential in predicting the fracture modes and the crack propagation path for ductile metals. The slant fracture phenomenon is studied numerically by adopting a recently developed damage plasticity theory. The damage plasticity theory incorporates all three stress invariants in a nonlinear damaging process of the material. The numerical integration algorithm for the new model is presented for small strain case. Three applications of different loading conditions are shown to illustrate its effectiveness in predicting ductile fracture. Emphasis is given to the influencing factors to slant fracture and the shear nature of the crack pattern in these applications. These numerical solutions are in good agreement with the experimental observations.
The fracture of ductile solids has frequently been observed to result from the large growth and coalescence of microscopic voids, a process enhanced by the superposition of hydrostatic tensile stresses on a plastic deformation field. The ductile growth of voids is treated here as a problem in continuum plasticity. First, a variational principle is established to characterize the flow field in an elastically rigid and incompressible plastic material containing an internal void or voids, and subjected to a remotely uniform stress and strain rate field. Then an approximate Rayleigh-Ritz procedure is developed and applied to the enlargement of an isolated spherical void in a nonhardening material. Growth is studied in some detail for the case of a remote tensile extension field with superposed hydrostatic stresses. The volume changing contribution to void growth is found to overwhelm the shape changing part when the mean remote normal stress is large, so that growth is essentially spherical. Further, it is found that for any remote strain rate field, the void enlargement rate is amplified over the remote strain rate by a factor rising exponentially with the ratio of mean normal stress to yield stress. Some related results are discussed, including the long cylindrical void considered by F.A. McClintock (1968, J. appl. Mech. 35, 363), and an approximate relation is given to describe growth of a spherical void in a general remote field. The results suggest a rapidly decreasing fracture ductility with increasing hydrostatic tension.
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.
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.
Micromechanical analyses of various materials under high cycle fatigue (HCF) loading have been investigated previously. Experimental findings have shown that failure due to HCF occurred with different pattern comparing to the other loading conditions. The current work tries to carry out both experiments and simulations at micro scale. In this research, scanning electron microscopy (SEM) and metallography images of the specimens are taken to investigate the failure and deformation patterns in dual phase (DP) steel under high cycle fatigue loading. Failure mechanisms of DP steels are also predicted using a real representative volume element (RVE) and microstructural finite element (FE) modeling. The linear damage accumulation rule (Miner's damage rule) is used to determine the material degradation due to fatigue loading. The cyclic loading is implemented in the FE model of the microstructure by developing ANSYS parametric design language (APDL) code to obtain the damage, failure pattern and fatigue life of the RVE. It is also shown that the finite element modeling of the real RVE considering both plasticity and fatigue damage leads to acceptable compatibility between the obtained cracking patterns from SEM images (experiments) and finite element predictions.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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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On the effect of the third invariant of the stress deviator on ductile fracture
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Massachusetts Institute of Technology, Cambridge, MA (USA); 2005.
Standard Test Method for Determining Volume Fraction by Systematic Manual Point Count
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Stress state dependent damage modeling with a focus on the lode angle influence
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Basaran M. Stress state dependent damage modeling with a focus on the lode angle influence, Ph.D. thesis, Aachen: Shaker; 2011.
Modelling the mechanical properties of multiphase steels based on microstructure
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