Measurement and modeling of simple shear deformation under load reversal: Application to advanced high strength steels
Introduction
Advanced high strength steels (AHSS) have been replacing conventional low strength steels for automotive parts because of weight saving and improved crash performance. However, it is a challenge to successfully introduce AHSS because of their inferior formability and larger springback compared to conventional steels. Especially, springback, the undesirable elastic recovery in a formed part when forming loads are removed, should be compensated to allow the assembly of a component.
In order to understand and predict the mechanics of springback for AHSS, there have been numerous approaches using finite element (FE) simulations [1], [2], [3], [4], [5], [6], [7], [8]. The FE approach can reduce the development cost and time significantly by suggesting manufacturing modifications without resorting to numerous experimental trial-and-error steps. Therefore, it is important to increase the accuracy of FE simulations to provide results similar to those obtained in real forming processes.
For this purpose, a reliable constitutive model that properly describes the elastic–plastic response of a sheet metal is necessary. In particular, for an accurate prediction of springback, various constitutive models, which capture the complex material behavior during strain path changes, have been proposed. This is because bending and unbending with a superimposed stretch, which occur in a typical process involving load reversal and the Bauschinger effect, influence the springback behavior significantly. The Bauschinger effect, which is characterized by a lower yield stress and higher strain hardening rate upon load reversal, was successfully captured by advanced constitutive models [9], [10], [11], [12], [13], [14].
In order to provide suitable coefficients for such advanced constitutive models, it is necessary to employ the non-conventional testing method. In particular, it is important to probe the material response at large strain without premature plastic flow localization and to achieve a sufficient load at reversal to effectively determine suitable coefficients for AHSS. In this sense, a conventional uniaxial tension test is not appropriate to capture the Bauschinger behavior of high strength materials because of its monotonic nature and its tendency to premature flow localization at low strain. Alternate testing methods have been reported, which include torsion-reverse torsion [15], [16], tension–compression [17] and forward–reverse simple shear tests [18]. The disadvantage of the torsion-reverse torsion test is that, for a sheet sample, it requires bending and welding prior to testing, which are likely to change the mechanical properties of the original material. In the case of in-plane tension–compression, an anti-bulking system is necessary for sheet specimens, which modifies the stress state and introduces uncertain friction effects [12], [17], [19]. Moreover, the strains attainable in the tension–compression test are limited due to either flow localization during tension or buckling during compression, phenomena which are a challenge in high strength steels. For example, the uniform elongation of DP980 steel measured in uniaxial tension is less than 5%, which is not sufficient for an accurate constitutive model identification and FE modeling [20].
The simple shear (SS) test has been designed to circumvent the disadvantages of the existing methods. In this test, the specimen preparation is simpler than in other methods and large homogenous strains can be achieved without plastic flow localization. Moreover, reverse loading is easy to control without major changes in the deformation mode. Due to these advantages, several researchers adopted this approach to characterize the anisotropic hardening behavior of metals after load reversal [21], [22], [23], [24], [25], [26], [27]. However, most of the previous studies pertaining to the SS test focused on softer materials such as mild steels [21], [23], [24], aluminum alloys [22], [25], [27] and polymers [28]. Only few investigations on the SS behavior of AHSS have been published [29], [30].
The aim of the present work is first to introduce a modification of the SS device that allows testing for AHSS, sheets for which the tensile strength ranges from 700 to 1000 MPa (or even higher). Then, this improved SS device is used to measure the forward–reverse stress–strain responses of AHSS sheets, which involve complex hardening behavior during load reversal. The measured stress–strain curves are approximated by a recently developed anisotropic hardening model, so-called HAH [31], [32], [33]. Finally, the effectiveness of the measurement method is validated by a comparison of the predicted reverse loading behavior in compression-tension (CT) and by the finite element (FE) prediction of springback.
Section snippets
Simple shear device
The simple shear (SS) test device for sheet metals consists of two rigid grips, which translate with respect to each other along the sample longitudinal direction [28], [34], [35]. A rectangular sample is firmly clamped by the two grips, one of them immobile while the other translates along the x-axis (Fig. 1). The constant width h of the deformation area is maintained during the test. In Fig. 1, L and Δx are the current length of the specimen and the relative displacement of the two grips
Constitutive models
In order to utilize the measured SS stress–strain curves in the FE simulations, an accurate constitutive model is necessary to describe the complex material responses under strain path changes. In this study, an advanced constitutive model, which consists in an anisotropic non-quadratic yield function and a distortional hardening approach, was considered. The main features of the constitutive models are briefly summarized in the following sections and additional details can be found elsewhere
Strain homogeneity in simple shear
The measured SS deformation is not homogeneous over the whole specimen surface during the test, particularly, near the ends of the shear specimen. Nevertheless, the shear stress is calculated from the SS test as the ratio of the force recorded by the load cell divided by the cross-section area along the whole specimen length. In contrast, the value of average shear strain is determined using digital image correlation (DIC) in the AOI in which the deformation field is more generally uniform.
Effect of anisotropic yield function
For the CT simulations, the yield function may not influence the predicted stress–strain response when the reference hardening curve is based on uniaxial data. However, for SS simulations, the yield function may play an important role in the predicted stress–strain response. In other words, when the reference flow curve is obtained from uniaxial or biaxial tension test, the shear stress response depends on the employed yield function.
In this study, three different yield functions were
Application to springback simulation
Finally, springback simulations were conducted using the HAH model with the two sets of coefficients based on CT and SS data (Table 6) in order to assess whether a similar deformation and springback behavior is obtained in forming simulations. The 2D draw-bending springback model proposed in the Numisheet׳93 benchmark [48] was considered in Fig. 17. All the numerical conditions such as element type, number of elements, integration scheme, boundary conditions, etc., are the same as in the
Conclusions
A simple shear (SS) test device was improved to determine the flow curves of advanced high strength steel (AHSS) sheets under monotonic and reverse loading. Three AHSS sheet samples were considered, namely, DP980, TRIP780 and TWIP980. From the measured SS flow curves with load reversals, a recently proposed distortional anisotropic hardening model, so-called HAH, was identified. Comparisons of predicted flow curves and springback results using the SS-based and CT-based constitutive coefficients
Acknowledgments
Authors appreciate the support by POSCO and by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MSIP) (No. 2012R1A5A1048294) and (No. 2014R1A2A1A11052889). FB appreciates the support of FEDER funds through the Operational Program for Competitiveness Factors - COMPETE and National Funds through the Portuguese FCT - Foundation for Science and Technology under the projects PTDC/EMS-TEC/2404/2012.
References (48)
- et al.
Simulation of springback
Int J Mech Sci
(2002) - et al.
Complex unloading behavior: nature of the deformation and its consistent constitutive representation
Int J Plast
(2011) - et al.
Study on the influence of work-hardening modeling in springback prediction
Int J Plast
(2007) - et al.
Modeling the Bauschinger effect for sheet metals, part I: theory
Int J Plast
(2002) - et al.
Modeling the Bauschinger effect for sheet metals, part II: applications
Int J Plast
(2002) - et al.
Elastic–plastic behavior of steel sheets under in-plane cyclic tension–compression at large strain
Int J Plast
(2002) - et al.
Experimental evaluation and constitutive modeling of non-proportional deformation for asymmetric steels
Int J Plast
(2011) - et al.
A model of large-strain cyclic plasticity describing the Bauschinger effect and workhardening stagnation
Int J Plast
(2002) - et al.
Backlash model for large deformation behavior of aluminum under torsional cyclic loading
Int J Plast
(1991) Work-hardening behavior of mild steel under cyclic deformation at finite strains
Acta Metall Mater
(1994)
Continuous, large strain, tension/compression testing of sheet material
Int J Plast
Effective Method for Fitting Complex Constitutive Equations
Int J Plast
Plastic anisotropy of sheet metals determined by simple shear tests
Mater Sci Eng A
Anisotropic strain hardening behavior in simple shear for cube textured aluminum alloy sheets
Int J Plast
Characterization of the strain-induced plastic anisotropy of rolled sheets by using sequences of simple shear and uniaxial tensile tests
J Mater Process Technol
Comparison of the work-hardening of metallic sheets using tensile and shear strain paths
Int J Plast
Prediction of anisotropy and hardening for metallic sheets in tension, simple shear and biaxial tension
Int J Mech Sci
Simple shear tests: experimental techniques and characterization of the plastic anisotropy of rolled sheets at large strains
J Mater Process Technol
Measurements of Bauschinger effect and transient behavior of a quenched and partitioned advanced high strength steel
Mater Sci Eng A
The mechanical stability of retained austenite in low-alloyed TRIP steel under shear loading
Mater Sci Eng A
An alternative to kinematic hardening in classical plasticity
Int J Plast
Extension of homogeneous anisotropic hardening model to cross-loading with latent effects
Int J Plast
Finite element modeling using homogeneous anisotropic hardening and application to spring-back prediction
Int J Plast
A sheet tension/compression test for elevated temperature
Int J Plast
Cited by (50)
Application of distortional plasticity framework to EDDQ and TRIP steel sheets: Prediction of latent hardening and its influence on springback
2024, European Journal of Mechanics, A/SolidsSimple shear methodology for local structure–property relationships of sheet metals: State-of-the-art and open issues
2024, Progress in Materials ScienceAn enhanced boundary lubrication friction model for sheet metal forming
2023, International Journal of Mechanical SciencesInvestigation on a novel in-line incremental die forming process for sheet metals
2023, Thin-Walled StructuresA crystal plasticity finite element analysis on the effect of prestrain on springback
2023, International Journal of Mechanical SciencesCitation Excerpt :Although the potential gradient in texture was not apparent in the inverse pole figure map as shown in Fig. 1a, the prediction accuracy on R-values by the current ΔEVPSC model significantly improved when the entire span of thickness was used for the COD calculation according to a preliminary study [54]. The mechanical behavior of the EDDQ specimen has been previously reported in [55,56]. The details on the experimental conditions are available in the mentioned studies, from which only a set of selected experimental data were used in the present work.
A VFM-based identification method for the dynamic anisotropic plasticity of sheet metals
2022, International Journal of Mechanical Sciences