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Die wear during trimming of advanced high strength steel (AHSS) sheets deteriorates the edge quality of trimmed sheets. In this work, the mechanisms of AISI D2 steel trim die wear and their effects on plastic deformation and fracture behaviour of the sheared edge of DP980 steel sheet were examined. A mechanical press equipped with D2 inserts was used to trim DP980 sheets with a clearance of 0.14 mm (10%). Abrasion and microchipping were identified as the wear mechanisms operating at the upper die, with microchipping becoming more dominant after 60,000 trimming cycles. The burr height and the length of the burnish zone of sheared DP980 sheets increased linearly with the chipped die edge percentage. The shear strains in the shear effected zone (SAZ) were estimated using martensite displacements as metallographic markers in the ferrite matrix as a function of the depth beneath the sheared edge. The depth of SAZ, and the plastic strains at a given depth within the SAZ increased with the number of trimming cycles. Correlation of the local stress and strain values generated in the SAZ showed that a saturation flow stress was reached near the sheared edge. The damage in SAZ occurred in the form of crack formation at the martensite/ferrite interfaces and fracture of martensite. Die wear reduced the tensile ductility of the DP980 sheets, and the fracture mode in tension changed from ductile with localized neck to more brittle sheared edge fracture initiating from surface cracks after 60,000 cycles.

Numerical simulations of uniaxial tensile deformation of DP600 steel were carried out using a modified Rousselier ductile damage model at different strain rates ranging from 0.1 to 100 s−1. Since the original Rousselier model does not consider any secondary void nucleation or coalescence criteria, it was modified by including a strain-controlled void nucleation function, a coalescence criterion and a void growth acceleration function as the post-coalescence regime identifier. The predicted flow behaviour, the evolution of damage and critical strain and void volume fraction at the onset of coalescence were assessed to evaluate the performance of the proposed model at each strain rate. In addition, X-ray tomography analysis was employed to evaluate the void volume fraction predicted by each void coalescence criterion. The modified Rousselier model showed good agreement with the experimentally determined strain and void volume fraction at the onset of coalescence. Also, it could successfully predict the damage distribution and the final damage geometry of DP600 tensile specimens.

The formability of electro-hydraulically formed AA5182-O aluminium sheet was investigated by means of experimental testing and numerical modelling. The experimental results were compared with quasi-static, as-received forming limit curve (FLC) and were used to calibrate a finite element model of EHF. It is found that the formability improvement of AA5182-O sheets was insignificant when electro-hydraulically formed without a die. However, when specimens were electro-hydraulically formed with sufficient energy into 34 or 40° conical dies, the effective strain measured in safe grids increased by 40 and 70% respectively when compared with a conservative quasi-static FLC. Finite element simulation results suggested that a combination of different mechanical parameters contributed to the formability improvement. The increased strain rate in areas close to the apex of the speimen, the negative stress triaxiality just before specimens contact the die, and significant compressive through-thickness stress generated by high-velocity impact all contributed to the improvement of formability in electro-hydraulic die forming.

Dual phase (DP) steel sheets are increasingly being used for automotive applications due to relatively high strength and formability. In the current work, Marciniak formability tests were carried out to determine the forming limit curve (FLC) of DP600 steel sheet, and an extended version of Rousselier’s ductile damage model, which accounts for void nucleation, growth and coalescence was used to simulate the tests and predict strain localization and failure for three different strain paths: uniaxial tension, plane strain and biaxial tension. In addition, a combination of flat rolling and uniaxial tension tests were used to generate the extended flow curve of the material. Damage evolution in terms of Rousselier scalar damage variable and void volume fraction was assessed for each simulation condition. The FLC as well as neck and fracture morphologies and geometries were obtained from finite element simulations of the Marciniak tests and compared to experimental results. The sensitivity and dependency of the predicted necking limits, damage distribution and geometry predicted by the Rousselier damage model to the type of hardening model, strain path, void nucleation function and void coalescence criterion are discussed. The modified Rousselier model was shown to successfully predict the FLC, damage distribution and the final damage geometry of DP600 sheets.

Die wear during trimming of advanced high strength steel (AHSS) sheets adversely effects the edge quality of trimmed sheets. Due to the large size of the industrial scale dies, it is difficult to measure the wear at the trim edge of the die inserts as a function of the number of trimming cycles. In this work, an optical surface profilometry method was used to determine sliding wear and impact damage on AISI D2 die inserts used to trim 1.4-mm DP980 sheets through a semi-industrial scale trimming press. Reduced peak height (Spk) and reduced valley depth (Svk) were determined by establishing the bearing ratio curves in the damaged areas of the trim dies as a function of the number of trimming cycles up to 80,000 trimming cycles. The evolution of the total volumetric loss and wear rate on the sliding planes of the upper and lower dies showed a change in wear behaviour after 60,000 trimming cycles due to increased chipping. The sliding-induced percentage of total volumetric loss (SPOTV) decreased with the number of trimming cycles on the upper sliding plane revealing that the main damage mechanism changed from sliding-induced wear to impact fracture. The dominant damage mechanism on lower sliding plane was fracture induced as SPOTV on the lower sliding plane remained low constant value of 18% and evidenced by chipping observed on the trim die edge. The performance of trim dies could be improved by increasing the fracture toughness of the lower die and increasing the wear resistance of the upper die by applying proper coatings.

The objectives of this paper are to quantify the increase in formability of DP600 steel sheets in electrohydraulic die forming (EHDF). The conventional (quasi-static) and high strain rate forming limits of this sheet material were experimentally obtained from specimens deformed using Marciniak tests and EHDF tests, respectively. A numerical model of EHDF was developed in order to determine the strain path of sheet metal experiencing large strains. Forming limits obtained from EHDF specimens formed in plane strain into a V-shaped die indicated that, locally near the top edge of the specimen, more than 120% formability improvement was achieved. Moreover, a formability enhancement of more than 60% was achieved in EHDF in biaxial tension using a conical die, provided sufficient discharge energy was applied. It was found that the significant increases in formability in EHDF are associated with the high-velocity impact against the die wall and the consequent high effective strain rate.

In this study, damage mechanisms in AA5182-O aluminium sheets are investigated using quasi-static (QS) Marciniak tests and high strain-rate electro-hydraulic forming (EHF) process. The results confirm that void nucleation, growth and coalescence are the main damage mechanisms of AA5182-O at both high and low strain rates. The EDS analysis suggests that cracking of Al 3 (Fe-Mn) intermetallic particles is the main source of void nucleation, whereas Mg 2 Si particles do not majorly influence void formation. Void growth analysis suggests that specimens deformed under QS conditions contained more voids in areas away from the sub-fracture surface but specimens deformed at high strain rate exhibit more significant rate of void growth close to sub-fracture areas. Void formation is suppressed by increasing the applied energy in EHF. And more significantly, the growth of voids is suppressed due to the high-velocity impact of the sheet against the die which plays an important role in increasing formability of AA5182-O aluminium sheet in EHF process. When the void percentage increase remains less than about 0.5% AA5182-O can be formed safely. However, when the void percentage increases beyond 0.6–0.8% fracture becomes inevitable.

In the current research, the Rousselier ductile damage model was employed to model hardening, plastic instability and damage properties of DP600 during uniaxial tension in a wide range of strain rates (from 0.001 to 1000 s−1). Also, various well-known phenomenological hardening functions, such as Johnson–Cook and KHL as well as a modified version of Johnson-Cook and multiplicative combinations of Voce with other strain-rate hardening functions have been fitted to experimental flow curves via a new combination of non-linear regression and Markov chain Monte Carlo (MCMC) method. The effect of each hardening function on the evolution of the damage parameter, void volume fraction and strain distribution along the gauge length was evaluated throughout the deformation. Also, the onset of instability, geometry of the neck and final fracture were then assessed by comparing the numerical results with experimental data. It is found that the modified JC and Voce-modified JC models can predict the flow behaviour of DP600 more accurately. Additionally, it is shown that the strain hardening rate at large strain levels, as determined by the hardening models, has a considerable effect on the strain map along the specimen, onset of void growth, and progression of damage in the localized area. Keywords: Dual phase steel, Finite element, Modified Johnson–Cook, Markov chain Monte Carlo, Rousselier model, Ductile damage

There is a steady increase in the implementation of dual phase steels in stamped automotive components. Therefore, steel suppliers who develop dual phase steels are interested in predicting the microstructure-properties relationship for optimization of microstructural design. This goal is achievable by micromechanical modeling. The representative volume element (RVE) method has been a popular technique for micromechanical modeling of dual phase steels. It is generally considered that 2D modeling underestimates the flow curves and that 3D modeling predicts the experimental stress-strain curves more accurately. However, much of the research has focused on 2D modeling. This paper develops 3D micromechanical modeling of DP500 and bainite-aided DP600 steels by including statistical quantitative metallography data in the models. More than 3000 grains were analyzed in each steel. Hence, both volume fraction and morphology of martensite were statistically determined. This model predicted the ultimate tensile strength of these two dual phase steels with less than 0.5% error.

Electrohydraulic forming is a pulsed metal forming process that uses the discharge of electrical energy across a pair of electrodes submerged in fluid to form sheet metal at high velocities. Pulsed metal forming processes, including electrohydraulic forming, have been shown to increase the formability of sheet metals. Although significant formability enhancement has been reported for electrohydraulic die forming, there have been conflicting reports about the formability in electrohydraulic free forming (EHFF). Numerical modeling was used to design sheet metal specimen geometries to generate data for specific regions of the EHFF forming limit curve. The electrohydraulic free forming specimens were formed with the precise amount of input energy to cause a neck at the center of the gauge section. The quasi-static and EHFF forming limit curves for both AA5182-O and DP600 sheets were determined in accordance with the conventional North American formability evaluation method to allow for direct comparison. It was found that the forming limits in EHFF increased by approximately 5% major strain for DP600 and 8% major strain for AA5182, relative to their respective as-received FLC.

In this study, the tensile flow behaviour of AA5182-O sheet was experimentally obtained in different material directions (RD, DD, and TD) at strain rates ranging from 0.001 to 1000 s−1 and predicted by means of both phenomenological models and neural networks (NNs). Constants in Johnson–Cook (JC), Khan–Huang–Liang (KHL), and modified Voce were calculated using genetic algorithm (GA) and linear regression analysis and used to simulate the uniaxial tension tests. Two types of feed-forward back-propagation neural networks were also trained and validated to predict the rheological behaviour of the alloy without the limitations of a mathematical function. The weights and bias values of each network were then used to simulate uniaxial tensile deformation. Subsequently, the results were compared with experimental flow curves and accuracy parameters were calculated. It was found that the modified Voce constitutive equation was able to predict the flow behaviour of AA5182-O with better accuracy than JC and KHL models. Also, the NN was found to be the most accurate method of predicting the anisotropic rate-dependant behaviour of AA5182-O. Keywords: Phenomenological constitutive model, Genetic algorithm, Artificial neural network, 5000 series aluminium alloys, Moderate strain rates

A material model for more thorough analysis of plastic deformation of sheet materials is presented in this paper. This model considers the following aspects of plastic deformation behavior of sheet materials: (1) the anisotropy in yield stresses and in work hardening by using Hill’s 1948 quadratic yield function and non-constant stress ratios which leads to different flow stress hardening in different directions, (2) the anisotropy in plastic strains by using a quadratic plastic potential function and non-associated flow rule, also based on Hill’s 1948 model and r -values, and (3) the cyclic hardening phenomena such as the Bauschinger effect, permanent softening and transient behavior for reverse loading by using a coupled nonlinear kinematic hardening model. Plasticity fundamentals of the model were derived in a general framework and the model calibration procedure was presented for the plasticity formulations. Also, a generic numerical stress integration procedure was developed based on backward-Euler method, so-called multi-stage return mapping algorithm. The model was implemented in the framework of the finite element method to evaluate the simulation results of sheet metal forming processes. Different aspects of the model were verified for two sheet metals, namely DP600 steel and AA6022 aluminum alloy. Results show that the new model is able to accurately predict the sheet material behavior for both anisotropic hardening and cyclic hardening conditions. The drawing of channel sections and the subsequent springback were also simulated with this model for different drawbead configurations. Simulation results show that the current non-associated anisotropic hardening model is able to accurately predict the sidewall curl in the drawn channel sections.

Electrohydraulic forming (EHF) is a high energy rate forming process in which the strain rate in the sheet metal can vary from 5 × 10 2 to 10 5 s −1 depending on various factors. Several mechanisms have been reported to cause an improvement in formability in EHF such as material deformation mechanisms, inertial effects and the dynamic impact of the sheet against the die. EHF is a complex high speed forming process and experimental work alone is not sufficient to properly understand this process. To understand the variation of some influential variables in EHF, electrohydraulic die-forming (EHDF) and free-forming (EHFF) of DP590 dual phase steel were simulated in ABAQUS/Explicit by considering the fluid/structure interactions. Three-dimensional finite element simulations were conducted by modelling the water with Eulerian elements with a view to investigating the effect of released energy on the sheet deformation profile history, strain distribution, loading path and damage accumulation type. The Johnson–Cook constitutive material model was used to predict the sheet behaviour and the parameters in this model were calibrated based on experimental test results available for DP590 at various strain rates. The Johnson–Cook phenomenological damage model was also used to predict the ductile failure (damage accumulation) in both EHDF and EHFF. Predicted final strain values and damage accumulation type showed good agreement with the experimental observations.

Theoretical and experimental studies have shown that when a compressive stress is applied normal to the sheet surface its formability can be significantly improved. In forming processes such as hydroforming, the normal stress imposed at the surface of the sheet or tube can be very significant in specific locations and it is therefore necessary to account for this stress state when assessing the forming severity of industrial parts. It is also well known that the forming limit curve (FLC) can vary significantly in strain space as a result of non-linear strain paths. In this work, a numerical code based on the Marciniak and Kuczynski (MK) analysis (1967) was developed to predict the FLC of sheet metals by simultaneously accounting for the effects of strain path non-linearity and the normal stress. The FLC predicted with this code can be used to assess the forming severity of parts that are deformed under complex loading conditions in industrial metal forming processes. The predictive FLC model was validated using experimental data in which linear and bi-linear strain paths were applied to different steel and aluminum sheets or tubes under plane stress and three-dimensional stress conditions. This research work has two specific purposes: first, to investigate the influence of the magnitude of the prestrain in bi-linear loading on the sensitivity of the FLC to the normal stress, and second, to study the effect of the normal stress on the path dependence of the FLC. This work showed that, with increasing magnitudes of prestrain the influence of the normal stress on the formability of sheet metal will decrease, regardless of the loading path. Moreover, it was observed that even a significant normal stress will practically not affect the path dependence of the FLC.

AlSi10Mg is an interesting structural material due to its high specific mechanical properties, and good weldability which makes it a good candidate for additive manufacturing by selective laser melting. In this paper, the evolution of pores is visualized and quantified in an AlSi10Mg fabricated by selective laser melting using in-situ tension coupled with X-ray computed tomography. Graphical models were produced in order to visualize the evolution of pores, and the volume fraction, density, and mean diameter of pores were determined at each stage of deformation. Significant coalescence of pores was found during post-uniform elongation. Dimples on the fracture surfaces indicate ductile fracture.

The main objective of this paper is to develop a generalized finite element formulation of stress integration method for non-quadratic yield functions and potentials with mixed nonlinear hardening under non-associated flow rule. Different approaches to analyze the anisotropic behavior of sheet materials were compared in this paper. The first model was based on a non-associated formulation with both quadratic yield and potential functions in the form of Hill’s (1948) . The anisotropy coefficients in the yield and potential functions were determined from the yield stresses and r-values in different orientations, respectively. The second model was an associated non-quadratic model (Yld2000-2d) proposed by Barlat et al. (2003) . The anisotropy in this model was introduced by using two linear transformations on the stress tensor. The third model was a non-quadratic non-associated model in which the yield function was defined based on Yld91 proposed by Barlat et al. (1991) and the potential function was defined based on Yld89 proposed by Barlat and Lian (1989) . Anisotropy coefficients of Yld91 and Yld89 functions were determined by yield stresses and r-values, respectively. The formulations for the three models were derived for the mixed isotropic-nonlinear kinematic hardening framework that is more suitable for cyclic loadings (though it can easily be derived for pure isotropic hardening). After developing a general non-associated mixed hardening numerical stress integration algorithm based on backward-Euler method, all models were implemented in the commercial finite element code ABAQUS as user-defined material subroutines. Different sheet metal forming simulations were performed with these anisotropic models: cup drawing processes and springback of channel draw processes with different drawbead penetrations. The earing profiles and the springback results obtained from simulations with the three different models were compared with experimental results, while the computational costs were compared. Also, in-plane cyclic tension–compression tests for the extraction of the mixed hardening parameters used in the springback simulations were performed for two sheet materials.

The forming limit curve (FLC), a plot of the limiting principal surface strains that can be sustained by sheet metals prior to the onset of localized necking, is useful for characterizing the formability of sheet metal and assessing the forming severity of a drawing or stamping process. Both experimental and theoretical work reported in the literature has shown that the FLC is significantly strain-path dependent. In this paper, a modified Marciniak and Kuczynski (MK) approach was used to compute the FLC in conjunction with two different work-hardening models: an isotropic hardening model and a mixed isotropic–nonlinear kinematic hardening model, which is capable of describing the Bauschinger effect. Predictions of the FLC using the MK analysis have been shown to be dependent on the shape of the initial yield locus and on its evolution during work hardening; therefore the hardening model has an influence on the predicted FLC. In this investigation, published experimental FLCs of AISI-1012 low carbon steel and 2008-T4 aluminum alloy sheets that were subjected to various nonlinear loading paths were compared to predictions using both hardening models. The predicted FLCs were found to correlate quite well with experimental data and the effects of strain path changes and of the hardening model on predicted FLCs are discussed.

Experimental and numerical axial cutting of AA6061-T6 circular extrusions under both dynamic and quasi-static loading conditions were completed using single- and dual-cutter configurations to investigate load/displacement and collapse behaviour of the extrusions. Circular specimens with various wall thicknesses were considered for impact and quasi-static testing in this research. A steel cutter (AISI 4140) with four blades, having blade tip widths of 1.0 mm or 0.75 mm and blade lengths of 7 mm or 26.1 mm were used to cut through the extrusions. Straight and curved deflector profiles were used to flare the cut petalled sidewalls and facilitate the cutting system. Further quasi-static cutting tests using dual cutters were completed with or without the presence of a spacer to examine the load/displacement response as an adaptive energy absorption system. Results from the experimental impact tests illustrated that a higher peak cutting force, with a magnitude of approximately 1.09–1.98 times that of the force necessary under quasi-static testing conditions, was needed to initiate the cutting deformation mode. After this initial high force, the load/displacement responses were observed to be similar to those from the quasi-static tests with the exception of minor variations which resulted from material fracture that occurred on the petalled sidewalls during dynamic testing. Larger lengths of cutter blades and the curved deflector eased the flaring of the petalled sidewalls and reduced the occurrence of material fracture. The blade tip width had minor effects on the initial peak cutting force and mean cutting forces for extrusions under impact loading. The mean cutting force from the dynamic tests was determined to be 0.82–1.2 times that from the quasi-static experimental tests. Finally, quasi-static axial crushing of extrusions was completed to compare crashworthiness measures with the adaptive energy absorption system under the cutting deformation mode. A finite element model incorporating an Eulerian formulation was selected for the numerical model to simulate the cutting process. Simulation results generally agreed well with the experimental tests with a maximum over prediction of approximately 33% and 18% for the cutting force under impact and quasi-static loading, respectively.

A semi-implicit integration scheme was used to implement the Yoshida–Uemori two-surface model into the finite element method. Hill’s quadratic yield function was employed to account for the orthotropic behaviour of the metal sheet. The model was used to predict the cyclic simple shear response of DP-600. In order to evaluate the capability of the model for sheet metal forming, the model was used to simulate both the forming stage of a channel draw process in the presence of drawbeads and the subsequent springback stage. The results show that the model predicts the springback profile very well, especially at deeper drawbead penetrations.

The return mapping procedure was used to develop an algorithm for numerical implementation of Yoshida–Uemori two-surface plasticity model into a finite element program. A fully implicit integration scheme is utilized to integrate all plasticity equations. The algorithm was employed to develop user material subroutine (UMAT and VUMAT) for both ABAQUS-Standard and ABAQUS-Explicit codes. The numerical algorithm is quite general and is not limited to any particular yield function. However, as an example, the Yld2000-2d yield function was implemented in the subroutines in order to take the anisotropy of metal sheets into account. Finally, the subroutines were used to simulate the springback of a U-shape channel section. The channels were formed using two different drawbead penetrations and two different sheet materials, i.e. HSLA and AA6022-T43. The forming process and subsequent springback stage was simulated using the same yield function and three different hardening laws: (a) isotropic hardening, (b) a combined isotropic-nonlinear kinematic hardening and (c) the Yoshida–Uemori two-surface model. A comparison of the experimental and predicted channel sidewall profiles shows that the Yoshida–Uemori model generally improves the springback prediction compared to isotropic hardening and combined isotropic-nonlinear kinematic hardening.

In this paper an anisotropic material model based on non-associated flow rule and mixed isotropic–kinematic hardening was developed and implemented into a user-defined material (UMAT) subroutine for the commercial finite element code ABAQUS. Both yield function and plastic potential were defined in the form of Hill’s [Hill, R., 1948. A theory of the yielding and plastic flow of anisotropic metals. Proc. R. Soc. Lond. A 193, 281–297] quadratic anisotropic function, where the coefficients for the yield function were determined from the yield stresses in different material orientations, and those of the plastic potential were determined from the r-values in different directions. Isotropic hardening follows a nonlinear behavior, generally in the power law form for most grades of steel and the exponential law form for aluminum alloys. Also, a kinematic hardening law was implemented to account for cyclic loading effects. The evolution of the backstress tensor was modeled based on the nonlinear kinematic hardening theory (Armstrong–Frederick formulation). Computational plasticity equations were then formulated by using a return-mapping algorithm to integrate the stress over each time increment. Either explicit or implicit time integration schemes can be used for this model. Finally, the implemented material model was utilized to simulate two sheet metal forming processes: the cup drawing of AA2090-T3, and the springback of the channel drawing of two sheet materials (DP600 and AA6022-T43). Experimental cyclic shear tests were carried out in order to determine the cyclic stress–strain behavior and the Bauschinger ratio. The in-plane anisotropy (r-value and yield stress directionalities) of these sheet materials was also compared with the results of numerical simulations using the non-associated model. These results showed that this non-associated, mixed hardening model significantly improves the prediction of earing in the cup drawing process and the prediction of springback in the sidewall of drawn channel sections, even when a simple quadratic constitutive model is used.

The objective of this work is to predict the springback of Numisheet’05 Benchmark#3 with different material models using the commercial finite element code ABAQUS. This Benchmark consisted of drawing straight channel sections using different sheet materials and four different drawbead penetrations. Numerical simulations were performed using Hill's 1948 anisotropic yield function and two types of hardening models: isotropic hardening (IH) and combined isotropic-nonlinear kinematic hardening (NKH). A user-defined material subroutine was developed based on Hill's quadratic yield function and mixed isotropic-nonlinear kinematic hardening models for both ABAQUS-Explicit (VUMAT) and ABAQUS-Standard (UMAT). The work hardening behavior of the AA6022-T43 aluminum alloy was described with the Voce model and that of the DP600, HSLA and AKDQ steels with Hollomon's power law. Kinematic hardening was modeled using the Armstrong–Frederick nonlinear kinematic hardening model with the purpose of accounting for cyclic deformation phenomena such as the Bauschinger effect and yield stress saturation which are important for springback prediction. The effect of drawbead penetration or restraining force on the springback has also been studied. Experimental cyclic shear tests were carried out in order to determine the cyclic stress–strain behavior. Comparisons between simulation results and experimental data showed that the IH model generally overestimated the predicted amount of springback due to higher stresses derived by this model. On the other hand, the NKH model was able to predict the springback significantly more accurately than the IH model.

A biaxial testing apparatus was used to investigate the elastic-plastic behaviour of an 1145 aluminum sheet alloy. Flat cruciform specimens were deformed up to effective strains of approximately 0.15 in biaxial stretching, along seven different proportional strain paths. A finite element analysis of each test was carried out using four different phenomenological models of anisotropic plasticity. An iterative procedure was coupled with the numerical analyses in order to determine the anisotropic parameters in the various yield functions and thus obtain best fits to these functions. This method of numerically analyzing cruciform specimens leads to fairly accurate biaxial flow curves, as well as plastic work contours. The results are also compared with crystal plasticity simulations using a Taylor-type model.