Effect of strain rate on the forming behaviour of sheet metals

https://doi.org/10.1016/j.jmatprotec.2011.03.018Get rights and content

Abstract

The strain rate dependence of plastic yield and failure properties displayed by most metals affects energies, forces and forming limits involved in high speed forming processes. This paper investigates the influence of the strain rate on the forming properties of one laboratory made and three commercial steel grades: a CMnAl TRIP steel, the ferritic structural steel S235JR, the drawing steel DC04 and the ferritic stainless steel AISI 409. First, split Hopkinson tensile bar (SHTB) experiments are carried out to assess the influence of the strain rate on the materials’ stress–strain curves. Subsequently, the obtained SHTB results, together with static tensile test results, are used to model the constitutive behaviour of the investigated steels using the phenomenological Johnson–Cook (JC) model and the Voce model, thus allowing dynamic modelling of forming processes. Finally, forming limit diagrams (FLDs) are calculated using the Marciniak–Kuczynski method. The results clearly show that the effect of the strain rate on forces and energies involved in a forming process, and the forming limits is non-negligible and strongly material dependent.

Introduction

Forming processes very often involve high rates of deformation. Electromagnetic pulse forming (magnetic pulse forming), hydroforming and explosive forming are obvious examples, however also in more conventional sheet forming techniques, such as deep drawing, roll forming and bending, locally high strain rates occur deviating from those used in static material tests. In Oliveira et al. (2005) maximum strain rates of 3500 s−1 and velocities of 250–300 m/s were predicted for the electromagnetic forming process based on numerical models.

Since the strain rate has an influence on both the plastic flow stresses and the ductility of materials, important parameters such as forming forces, energies and forming limits will be affected by the rate of deformation. Static forming limit diagrams are traditionally obtained through Marciniak or bulge tests. Experimental determination of high speed FLDs is not straightforward. Little experimental data is available and no correlations have been presented between the experimental results and those of the numerical or analytical predictive models of FLDs (Zidane et al., 2010). Recently, biaxial tests on cruciform specimens have become the most promising method to realize various strain states for assessment of FLDs (Hannon and Tiernan, 2008). These biaxial tests have several advantages: one single specimen geometry for all strain states, friction effects have no influence on the results and complex strain paths can be applied. However, much uncertainty about the interpretation of the experimental results remains. Although specimens of the cruciform type have been investigated quite extensively, no standard geometry exists for the specimen design. As biaxial machines are usually hydraulically driven, it is possible to test at intermediate strain rates. Shimamoto et al. (2003) performed tests on an aluminium alloy (A7075-T6) cruciform specimen at 1 mm/s. Recently, Zidane et al. (2010) developed a similar hydraulic machine, capable of applying a deformation speed of 2 m/s. Recently, efforts have been spent on developing dynamic bulge tests on split Hopkinson pressure bar setups. These tests, however, are in the development stage and accurate determination of FLDs from the test results still has to be developed. Grolleau et al. (2008) developed such a technique and applied it to aluminium 6111-T4 sheets. Strain rates of 500 s−1 are obtained. The newly developed testing device of Ramezani and Ripin (2010) uses a rubber-pad as pressure carrying medium. The specimen is dynamically loaded between the rubber-pad and a die which are mounted on the Hopkinson bars. The maximum strain rate achieved in the experiments performed on AA6005-T6 aluminium sheet is 215 s−1.

Especially on the forming limits, the influence of the strain rate can be diverse. Jie et al. (2009) conclude that for rate-dependent materials, a large discrepancy exists between the experimental FLD and FLD predicted using strain rate independent material properties. When the strain rate is taken into account, the studied AKDQ steel shows a higher FLD. In Lee et al. (2008) the formability of AZ31 Mg alloy is studied experimentally and numerically; the FLD of this material is found to decrease with increasing strain rate. Seth et al. (2005) show that at very high strains rates, the FLD of steels with low quasi-static ductility improves significantly while the forming limit of steels with already high quasi-static ductility does not improve.

In this paper, one laboratory and three commercial steels are studied: a CMnAl TRIP steel, the structural steel S235JR (EN 10025-2, 1.0038), the drawing steel DC04 (EN 10130, 1.0338) and the ferritic stainless steel AISI 409 (EN 10088-2, 1.4512). The steel grades are selected based on their specific dynamic behaviour. As is the case for most TRIP steels, the CMnAl TRIP steel exhibits an increase of both the yield stress and the elongation as the strain rate increases (Van Slycken et al., 2006). For AISI 409, or more generally for ferritic stainless steels, irrespective of the absolute value of the yield stress, the increase of yield stress as a function of the strain rate, is very similar to that of pure ferritic iron and low-carbon steels (Clarke et al., 2008). For DC04 a remarkable increase of strength is observed as the strain rate increases, however with a decreasing ductility (Schael and Bleck, 2001). S235 also displays a significant positive strain rate effect on the yield stress as is shown by Seifried et al. (2010). Whether the influence of the strain rate on the FLD is positive or not, is dependent on the materials’ strain rate response. As the strain rate increases, most materials present significantly higher plastic flow stresses, however much lower deformation levels (Meyers, 1994). Other materials combine an increase in flow stresses with an increase in elongation values. Exceptionally, some materials experience no strain rate sensitivity at all.

First, to determine the influence of the strain rate, high strain rate tensile experiments are performed on a split Hopkinson tensile bar setup. The specimen is loaded by waves travelling in long bars. In this way strain rates varying from 500 s−1 up to 2000 s−1 are reached. Next to the dynamic experiments, also static tensile test experiments are carried out. Both static and dynamic test results are subsequently used to model the strain rate and temperature dependent constitutive behaviour of the materials. For this purpose the widely used, phenomenological Johnson–Cook model is used (Johnson and Cook, 1983). Major advantage of this model is that with a limited number of parameters, the constitutive behaviour of a wide range of materials can be described (Liang and Khan, 1999). Moreover, the Johnson–Cook model is implemented in most commercial finite element codes. The model and material parameters, presented here, can consequently be used for numerical modelling of forming processes. Besides the Johnson–Cook model, also the classical Voce law is considered (Voce, 1955). Since no explicit strain rate and temperature dependence is included in this law for the strain rates of interest, different sets of parameters are calculated.

Finally, using the tensile stress–strain curves, forming limit diagrams are calculated at different strain rates. These diagrams can be used to predict onset of strain localization in high speed forming processes. For this purpose, the well-known Marciniak–Kuczynski (M–K) model is used (Marciniak and Kuczynski, 1967, Marciniak et al., 1973). The model assumes a material imperfection in the form of a band with smaller thickness. This small inhomogeneity in load bearing capacity can give rise to unstable strain growth in the region of the imperfection, and consequently, cause localized necking and failure. The use of the M–K technique is justified since, for the ductile materials considered here, failure will be related to sheet metal instability.

Section snippets

Investigated materials

AISI 409 is an alloy designed principally for the automotive exhaust industry, although it has been used successfully in other industrial applications as well. It combines good elevated temperature corrosion resistance with medium strength, good formability and overall cost. DC04 is an unalloyed deep-drawing steel. This steel grade is frequently used in the production of body components in the automotive industry. S235 is a structural carbon steel with a minimal guaranteed 0.2%-yield stress of

Test techniques

In order to characterize the (quasi-) static behaviour of the investigated materials, standard tensile tests are carried out using a screw driven electromechanical test bench. The tensile tests are performed according to the European standard specifications EN 10002-1:2001. A tensile specimen, with a length of the parallel section of 120 mm, is used in the tests. The tensile tests are carried out with an initial strain rate of 5.6 × 10−4 s−1 in the gage section of the specimen, which is increased

Material behaviour modelling

The experimental data described in the previous paragraphs are used to model the material behaviour. Two different frequently used constitutive models are used: the Voce law (Voce, 1955) and the Johnson–Cook model (Johnson and Cook, 1983, Liang and Khan, 1999). The Voce law describes the relation between the equivalent stress σ and equivalent plastic strain ɛp. The model contains only three parameters σ0, K and n which can easily be determined from only one experiment.σ=σ0+K(1enεF)The Voce

Prediction of FLDs by the Marciniak–Kuczynski method

The experimentally obtained stress–strain relationships at various strain rates are used to predict the metal forming limits of the studied steel grades. In order to calculate initiation of necking under the multi-axial strain conditions occurring in forming processes based on the uni-axial tensile test results, the well-known Marciniak–Kuczinski model is used (Marciniak and Kuczynski, 1967).

In the Marciniak–Kuczynski (M–K) method, it is assumed that an initial imperfection is present in the

Conclusions

The influence of the strain rate on the forming properties of three commercial steels (S235, DC04 and AISI 409) and one laboratory made CMnAl TRIP steel is studied. By performing static and high strain rate tensile experiments, the influence of the strain rate on the mechanical behaviour is assessed. The obtained stress–strain curves clearly show that distinct differences exist between the static behaviour and the dynamic behaviour. Going from static to dynamic loading rates, for all

Acknowledgement

The authors are grateful to the IWT (Agentschap voor Innovatie door Wetenschap en Technologie – Flemish government agency for Innovation by Science and Technology) for the funding of research project MAGPULS (IWT 070644) and the Interuniversity Attraction Poles Program phase 6 of the Federal Science Policy of Belgium for the funding of research project m3phys (IUAP P6/24).

References (25)

  • K.D. Clarke et al.

    Effect of strain rate on the yield stress of ferritic stainless steels

    Metall. Mater. Trans. A: Phys. Met. Mater. Sci.

    (2008)
  • A. Graf et al.

    Calculations of forming limit diagrams

    Metall. Mater. Trans. A: Phys. Met. Mater. Sci.

    (1990)
  • Cited by (0)

    View full text