Draw-bend Tests Research Articles

Crystal plasticity-based finite element simulations of load reversals and hat-shaped draw-bending for predicting the springback behavior of dual-phase steel sheets

This work is concerned with predicting geometrical shape changes in sheet metal forming using a multi-level simulation framework that considers the directionality of deformation mechanisms acting at the single-crystal level and microstructural evolution. The multi-level model is an elasto-plastic self-consistent (EPSC) homogenization of single-crystal behavior giving the constitutive response at each finite element (FE) material point. Numerical solution of a boundary value problem over geometry is then obtained using continuum finite elements at the macro-level. First, a set of model parameters for the evolution of slip resistance of ferrite and martensite and backstress are established by fitting a comprehensive set of mechanical data for dual-phase (DP) steels 590, 780, and 1180 using one-element model. Next, the potential of the FE-EPSC modeling framework is illustrated by carrying out a set of hat-shaped draw-bending simulations of the steel sheets. The evolution of geometry after hat-shaped draw-bending and springback is predicted and verified with experimental measurements for as-received DP 780. In doing so, the role of accounting for backstress is revealed as critical for the accurate prediction of the part geometry. The same process simulation involving a pre-strained sheet of DP 780 is compared with a corresponding experiment to reveal the role of strain hardening and residual stress on the subsequent part shape changes after the hat-shaped draw-bending test and springback. Finally, the same process simulations involving DP 590 and DP 1180 are performed to confirm the effect of strength on the geometrical shape changes of the sheets after springback.

Density-based topology optimization integrated with genetic algorithm for optimizing formability and bending stiffness of 3D printed CFRP core sandwich sheets

To expand the application ranges of sandwich sheets from conventional 2D flat panel types to 3D complex shapes and simultaneously improve the specific bending stiffness , a novel topology optimization strategy that can optimize the bending stiffness while maintaining good formability was proposed. In the proposed approach, the density-based topology optimization was integrated with the multi-stage genetic algorithm (GA) to optimize the repeatable unit cell of the core structure of sandwich sheets. Two optimization schemes were adopted, in which one optimizes the formability and the other one optimizes the bending stiffness while fulfilling potential failure constraints. The failure constraints on core shear failure and face buckling were theoretically deduced to mathematically formulate the topology optimization problem, which was solved by the adaptive multi-stage GA to increase the possibility of generating physically meaningful and additively manufacturable topologies. For the experimental evaluations of mechanical properties and formability, the final optimal topologies under volume fraction constraints of 50% and 62.5% were additively manufactured using carbon fibre reinforced nylon. Comparing the sandwich topologies obtained by two optimization schemes, the bending stiffness of sandwich topologies with the core density of 50% and 62.5% are improved by 41.58% and 41.49%, while the energy absorption capabilities are improved by 13.60% and 29.40% respectively. L-bending and draw-bending tests indicate the improved formability of topologically optimized sandwich sheets. The proposed approach is capable of designing formable sandwich sheets with improved bending stiffness, which is expected to expand the application envelope of sandwich sheets with better mechanical properties. • Topology optimization of sandwich sheets that can not only be bent without failure but also have optimal bending stiffness. • Integration of density-based topology optimization with multi-stage genetic algorithm. • Theoretical core shear failure and face buckling constraints on sandwich sheets during bending. • Improved bending stiffness and formability of topologically optimized sandwich sheets with 3D printed CFRP cores.

Fracture Investigation in Draw Bending of AZ31B Sheets using Fuzzy Logic Prediction

Automotive and aircraft industries are facing an increased demand of light-weighted materials for reducing fuel consumption and CO2 emissions. Magnesium alloy sheets are considered in manufacturing components of complex geometries and with flexible processes. Fracture investigation of AZ31B alloy sheets is of interest in continuous bending processes to achieve better formability. Certain forming processes of AZ31B sheets are restricted due to its limited ductility at room temperature. Draw bending of AZ31B sheets provides us the necessary forming state to investigate fracture limits. Our investigation relies on data extracted from draw bending tests organised according to a design of experiments plan. The experimental studies were conducted for different punch radii, traverse speeds and rolling directions. The predicted fracture behavior via Fuzzy Logic provides essential data to the setup procedures needed for our subsequent research, which is focusing on reducing the limitations of AZ31B sheets formability.

Modeling of nonlinear elastoplastic behavior after stress reversal for high strength steel

Material characteristics have significant impact on simulation of sheet metal forming. The accuracy of springback prediction depends on the estimation of strain recovery after die release. It is well known that the experimentally obtained unloading behavior for steel sheets is nonlinear stress-strain relationship, and the response during unloading and reloading shows a hysteresis loop. This behavior should be modeled by a material model and considered in FE-simulations for accurate predictions. In this study, the in-plane stress reversal tests for high strength steel were carried out to observe the elastoplastic behaviors after stress reversal. A material model that considers the nonlinear behavior was newly developed and implemented into the FEM software. The accuracy of springback prediction with the developed material model was validated by the draw bending tests and its springback simulations. The simulations with the developed material model show better agreement with the experimentally measured springback profile as compared to the other material models.

Time-dependent springback of a commercially pure titanium sheet

Abstract Time-dependent springback of a commercially pure titanium sheet was investigated experimentally from the viewpoints of strain rate, holding time at the bottom dead center before unloading, and elapsed time after unloading. A draw-bending test showed that the amount of springback decreased linearly with the holding time before unloading when plotted on logarithmic scale and increased with the elapsed time after unloading. To investigate the mechanism of these results, stress relaxation and creep tests were conducted. The variation of the amount of springback with the holding time corresponded well with that of the stress during stress relaxation. On the other hand, the in-plane anisotropy in the evolution of the amount of springback with the elapsed time did not correspond with that of creep strain. The mechanism of the in-plane anisotropy in the elapsed-time dependency was discussed in terms of the stress relaxation and creep behaviors.

Thermal deformation behavior and mechanism of intermetallic alloy Ti2AlNb

The deformation behavior and mechanism of Ti2AlNb-based alloy were experimentally investigated at elevated temperatures. Firstly, the stress–strain relationships at different temperatures and strain rates were investigated via uniaxial tensile testing. Then, formability data, as determined by examining the deep drawing and bending abilities, were obtained through limiting draw ratio (LDR) and bending tests. Finally, metallographic experiments and fracture morphology investigations were conducted to examine the thermal deformation mechanism of the alloy. The results showed that as the temperature increased, the total elongation increased from 13.58% to 97.82% and the yield strength decreased from 788 to 80 MPa over the temperature range from 750 to 950 °C at a strain rate 0.001 s−1. When the temperature reached 950 °C, the strain rate was found to have a great influence on the deformation properties. The plastic formability of the sheet metal was significantly improved and a microstructural transformation of O to B2 and α2 occurred in this temperature region, revealing the deformation mechanism of its plasticity.

Prediction of springback in anisotropic sheet metals: The effect of orientation and friction

In this paper, springback of anisotropic sheet based on the modified form of the asymmetric non-quadratic yield function (YLD96) for plane stress conditions due to Barlat et al. (Yield function development for aluminium alloy sheets. J Mech Phys Solids 1997; 45: 1727–1763), suitable for describing mixed (isotropic and kinematic) hardening in aluminium alloy sheets under the Bauschinger Effect was compared with the results of tests. Simulation of uniaxial tensile and cyclic tests including both nonlinear isotropic and nonlinear kinematic hardening showed the necessity of including the Bauschinger effect in the constitutive equations at both small and large strains. Following the application to prediction of springback in draw bending of these alloys oriented in the rolling direction, draw-bending tests on AA2024-O and AA7075-O alloy sheets are described. The springback parameters of specimens with axes oriented at 45° and 90° to the rolling direction were measured and compared with prediction based on the modified form of the YLD96, which captured the hardening response at small and large strains when combined with the mixed hardening model, predicting springback in very good agreement with experimental results. The number of components of back stress used in this model depends on the nature of the nonlinear behaviour of the material. For alloys AA2024-O and AA7075-O, excellent agreement with experiments required the use of up to three nonlinear components of back stress. Prediction suggested values of friction consistent with published values and showed that friction inversely affected the radius of sidewall curl, but was not sensitive to lower and upper opening angle. This was consistent with the findings of Carden et al. (Measurement of springback. Int J Mech Sci 2002; 44: 79–101), although those authors also reported that very low friction may increase springback in their proposed draw-bending test. The results confirmed the efficacy of the yield surface model based on YLD96, modified to include nonlinear isotropic and nonlinear kinematic hardening, for predicting deformation subject to the Bauschinger effect.

Macro and Micro Structuring of Deep Drawing's Tools for Lubricant Free Forming

In today's industry waste avoidance and efficient use of resources is becoming more significant due to economic and environmental requirements. Decreasing usage of lubricants in forming processes such as deep drawing offers a high potential regarding these efforts. A radical approach, which leads to the highest savings, is the realization of a complete lubricant free deep drawing process – the lubricant free forming. The approach in this paper is to find out a method for eliminating the lubrication in deep drawing process, by means of macro structured tool, in order to control of the friction forces and the material flow and also coating them with an adapted coating film. This paper presents an overview of the basic process principles and first analytical and experimental results. Based on initial FE simulations, a macro structured tool for deep drawing is simulated to be compared with conventional tools. The required punching force, change in sheet thickness during the process and also shear stress on the flange are compared in these simulations. Because the draw edge radius is the most critical part of deep drawing regarding the frictional force, draw bend test is used to enable the analysis of this area. Hence a cylindrical specimen, which is already coated with tetrahedral amorphous carbon (ta-C), is used. Through Direct Laser Interface Pattering, it is possible to change the surface properties of the ta-C films selectively by local graphitization, delamination or by removal. The paper presents results of experimental and numerical investigations with the special tool set carried out with blanks made of steel DC04. The results will be discussed regarding the process limits and the potential for future applications.

이동경화 모델에 기반한 MS1470 강판의 스프링백 예측

Spring-back of MS1470 steel sheets was numerically predicted using a non-linear kinematic hardening material behavior based on the Yoshida-Uemori model. From uniaxial tension and uniaxial tension-compression-tension data as well as the uniaxial tension-unloading-tension data, the parameters of the Yoshida-Uemori model were obtained. For the numerical simulations, the Yoshida-Uemori model was implemented into the commercial finite element program, ABAQUS/Explicit and ABAQUS/Standard using the user-defined material subroutines. The model performance was validated against the measured spring-back from the benchmark problems of NUMISHEET 2008 and NUMISHEET 2011, the 2-D draw bending test and the S-rail forming test, respectively.

Extension of quasi-plastic–elastic approach to incorporate complex plastic flow behavior – application to springback of advanced high-strength steels

Materials modeling and numerical formulations were conducted to describe the complex material behavior upon strain path change in order to enhance the prediction accuracy of springback in advanced high strength steels (AHSS). An approach without kinematic hardening rule, or the homogeneous anisotropic hardening (HAH) model, was incorporated to the newly conceived quasi-plastic–elastic strain (QPE) formulations. The HAH model is able to capture complex plastic flow behavior of sheet metals such as the Bauschinger effect, transient behavior, work-hardening stagnation and permanent softening. The QPE approach was developed to reproduce the nonlinear elastic behavior during unloading and reloading. The two models were independently validated for predicting springback, with better performance than conventional constitutive models. In this study, the two models are combined and extended to enhance the prediction capability of springback in AHSS. For this purpose, fully implicit numerical algorithms were re-formulated to link the two modeling approaches using general anisotropic yield function and hardening for shell element. The original model was only valid for continuum isotropic element with analytical stress integration procedure. Simulations of 2D draw bending test were performed to validate the developed approach for two AHSS, DP780 and TRIP780, sheets. The springback prediction was significantly improved if most of the complex material behavior relating to elasticity and plasticity were taken into account in the finite element simulations.

The Draw-Bend Fracture Test and Its Application to Dual-Phase and Transformation Induced Plasticity Steels

Unpredicted sheet forming failures of dual-phase (DP) steels can occur in regions of high curvature and with little apparent necking. Such failures are often referred to as “shear fractures”. In order to reproduce such fractures in a laboratory setting, and to understand their origin and the inability to predict them, a novel draw-bend formability (DBF) test was devised using dual displacement rate control. DP steels from several suppliers, with tensile strengths ranging from 590 to 980 MPa, were tested over a range of rates and bend ratios (R/t) along with a TRIP (transformation induced plasticity) steel for comparison. The new test reliably reproduced three kinds of failures identified as types 1, 2, and 3, corresponding to tensile failure, transitional failure, and shear fracture, respectively. The type of failure depends on R/t and strain rate, and presumably on the initial specimen width, which was constant in this study. Two critical factors influencing the lack of accurate failure prediction were identified. The dominant one is deformation-induced heating, which is particularly significant for advanced high strength steels because of their high energy product. Temperature rises of up to 100 deg. C were observed. This factor reduces formability at higher strain rates, and promotes a transition from types 1 to 3. The second factor is related to microstructural features. It was significant in only one material in one test direction (of 11 tested) and only for this case was the local fracture strain different from that in a tensile failure. Alternate measures for assessing draw-bend formability were introduced and compared. They can be used to rank the formability of competing materials and to detect processing problems that lead to unsuitable microstructures.

Determination of pressure-dependent friction coefficient from draw-bend test and its application to cup drawing

Friction under lubricated conditions is known to depend on pressure, and experimental determination of this dependence has typically quantified pressure as a uniform value over the contact area. However, non-uniform pressure distributions at the contact interfaces of draw-bend tests have been reported from various experiments and simulations. A previous study by the authors had evaluated the conventional methodology, which assumes uniform pressure distribution to estimate friction coefficients from draw-bend friction tests, and has concluded that the conventional methodology is only valid for measuring an average friction coefficient over the pressure range, which exists in a specific draw-bend system. In this paper, a new methodology to determine friction coefficients from draw-bend friction tests considering the pressure non-uniformity is suggested. In the methodology, contact pressure maps obtained from simulations, instead of the uniform pressure assumption, are included in the analysis of test data to measure the pressure dependency of friction coefficient. The proposed method is applied to friction measurement of aluminum sheets with anisotropic mill-finish surface and friction coefficients were obtained as functions of contact pressure, sliding velocity and sliding direction. Lastly, the obtained friction data were implemented into a finite element code, and circular cup drawing experiments and simulations were performed to validate the methodology.

Finite element modeling using homogeneous anisotropic hardening and application to spring-back prediction

A finite element (FE) implementation of the recently proposed constitutive model (Homogeneous yield function-based anisotropic hardening model or HAH; doi:10.1016/j.ij-plas.2011.03.003 in International Journal of Plasticity) that describes the plastic behavior of materials subjected to multiple strain path changes was developed. A complete formulation based on the return-mapping algorithm for the yield function was proposed. In particular, a multi-step Newton–Raphson method was introduced to calculate the gradient of the HAH model for the stress integration procedure. In addition to the numerical aspects, the theoretical proofs of the stability and convexity of the HAH model were discussed. For verification purpose, simple finite element simulations were conducted and the results were compared to those obtained from various constitutive models. Finally, mechanical characterization and U-draw bend experiments were performed on DP590 and TRIP590 steel sheet samples. The springback was quantified using the parameters defined at the NUMISHEET (1993) benchmark. Simulations of the 2D draw-bend test were performed with the FE code and the HAH constitutive description for DP590 and TRIP590 steel sheet samples. All the predicted springback values for these materials were in good agreement with experimental data.

The shear fracture of dual-phase steel

Unexpected fractures at high-curvature die radii in sheet forming operations limit the adoption of advanced high strength steels (AHSS) that otherwise offer remarkable combinations of high strength and tensile ductility. Identified as “shear fractures” or “shear failures,” these often show little sign of through-thickness localization and are not predicted by standard industrial simulations and forming limit diagrams. To understand the origins of shear failure and improve its prediction, a new displacement-controlled draw-bending test was developed, carried out, and simulated using a coupled thermo-mechanical finite element model. The model incorporates 3D solid elements and a novel constitutive law taking into account the effects of strain, strain rate, and temperature on flow stress. The simulation results were compared with companion draw-bend tests for three grades of dual-phase (DP) steel over a range of process conditions. Shear failures were accurately predicted without resorting to damage mechanics, but less satisfactorily for DP 980 steel. Deformation-induced heating has a dominant effect on the occurrence of shear failure in these alloys because of the large energy dissipated and the sensitivity of strain hardening to temperature increases of the order of 75 °C. Isothermal simulations greatly overestimated the formability and the critical bending ratio for shear failures, thus accounting for the dominant effect leading to the inability of current industrial methods to predict forming performance accurately. Use of shell elements (similar to industrial practice) contributes to the prediction error, and fracture (as opposed to strain localization) contributes for higher-strength alloys, particularly for transverse direction tests. The results illustrate the pitfall of using low-rate, isothermal, small-curvature forming limit measurements and simulations to predict the failure of high-rate, quasi-adiabatic, large-curvature industrial forming operations of AHSS.

Springback evaluation of friction stir welded TWB automotive sheets

Springback behavior of automotive friction stir welded TWB (tailor welded blank) sheets was experimentally investigated and the springback prediction capability of the constitutive law was numerically validated. Four automotive sheets, aluminum alloy 6111-T4, 5083-H18, 5083-O and dual-phase DP590 steel sheets, each having one or two different thicknesses, were considered. To represent mechanical properties, the modified Chaboche type combined isotropic-kinematic hardening law was utilized along with the non-quadratic orthogonal anisotropic yield function, Yld2000-2d, while the anisotropy of the weld zone was ignored for simplicity. For numerical simulations, mechanical properties previously characterized [1] were applied. For validation purposes, three springback tests including the unconstrained cylindrical bending, 2-D draw bending and OSU draw-bend tests were carried out. The numerical method performed reasonably well in analyzing all verification tests and it was confirmed that the springback of TWB as well as of base samples is significantly affected by the ratio of the yield stress with respect to Young’s modulus and thickness.

Finite element analysis of the influence of the restraining force in the draw bend test

Draw restraining force is used in sheet metal forming processes to regulate material flow and control springback in the parts. In this paper, the influence of draw restraining force on springback behaviour of dual phase steels is investigated, through numerical simulations of the draw bend test. Three grades of dual phase steels are submitted to different normalized back forces in the range from 0.5 to 1.1 of the initial yield stress. All simulations were performed with the DD3IMP in-house code. The study highlights the importance of an accurate modelling of the isotropic work hardening of dual phase steels for an accurate springback prediction.

Springback Characteristics of Magnesium Alloy Sheet AZ31B in Draw-Bending

In this study, we carried out a two-dimensional draw-bending test on an AZ31B magnesium alloy sheet at various forming temperatures and blank holding forces, and the springback characteristics of the Mg alloy sheet were systematically examined. The amount of springback decreased with increasing temperature and blank holding force. The decrease in the amount of springback caused by the increase in temperature was much larger than that caused by the increase in blank holding force, which indicated that increasing temperature was much more effective for decreasing the amount of springback than increasing blank holding force. The amount of springback became negligible at 200°C and above. This result was attributable to the following factors: (a) flow stress decreased rapidly as temperature increased, (b) reverse bending on the sidewall arose at 150°C and above, and (c) fine grains due to dynamic recrystallization were formed at 200°C and above. Microstructure evolution during the draw-bending test was also observed with particular focus on twinning, and its effects on springback characteristics were studied in detail.

Springback and time-dependent springback of 1Cr18Ni9Ti stainless steel tubes under bending

In this paper, the springback and time-dependent springback of 1Cr18Ni9Ti stainless steel tubes subject to bending is explored. Rotary draw bending tests have been carried out and marked time-dependent springback has been observed. A novel model in which time-dependent springback is associated with strain hardening is presented as an attempt to analyze this behavior. Using this model, the formulae of time-dependent springback, time-independent springback and total springback are derived. In addition, finite element analysis has been performed to investigate the stress distribution as well as to calculate the magnitude of springback. Comparison between analytical and experimental results shows good agreement.

Formability of advanced high strength steels

Novel draw-bend tests of 3 dual-phase (DP) steels utilizing velocity control of both actuators revealed three patterns of failure depending on draw speed, draw speed ratio, and R/t ratio. Shear failure occurs preferentially for smaller R/t and higher deformation rates. During draw bend tests, the temperature rises are significant, up 100°C before necking, with consequent loss of strength in affected regions. A novel 1-D constitutive equation relating flow stress to strain, strain rate, and temperature was developed based on tensile tests. FE simulations using the measured constitutive response predicted the types of failures accurately, without introducing damage mechanics. The deformation-induced heating is a critical part of the failure process.

Springback prediction of TWIP automotive sheets

In an effort to reduce the weight of vehicles, automotive companies are replacing conventional steel parts with light weight alloys and/or with advanced high strength steels (AHSS) such as dual-phase (DP), twinning induced plasticity (TWIP), and transformation induced plasticity (TRIP) steels. The main objective of this work is to experimentally and numerically evaluate the macro-performance of the automotive TWIP sheet in conjunction with springback. In order to characterize the mechanical properties, simple tension and tension-compression tests were performed to determine anisotropic properties, as well as the Bauschinger, transient, and permanent softening behaviors during reverse loading. For numerical simulations, the anisotropic yield function Yld2000-2d was utilized along with the combined isotropic-kinematic hardening law based on the modified Chaboche model. Springback verification was performed for the unconstrained cylindrical bending and 2D draw bending tests.