Strain rate behaviour of multi-phase and complex-phase steels for automotive applications

Abstract. A combined study on the mechanical behaviour of multi-phase 800 high yield strength steel (MP800HY) and complex-phase 800 steel (CP800) is carried out under tensile loads in the strain rate range from 0.001 s−1 to 750 s−1. Quasistatic (0.001 s−1) tests are performed on electromechanical machine, whereas, medium (5 s−1 and 25 s−1) and high strain rate (250 s−1, 500 s−1 and 750 s−1) experiments are conducted on hydro-pneumatic machine (HPM) and modified Hopkinson bar (MHB) setup respectively. The thermal softening behaviors of the materials are investigated at quasi-static condition and the materials’ m-parameters of the existing Johnson-Cook model are imposed in authors’ previous work. Thereafter, the predicted flow stress by Johnson-Cook model has been compared with the experimental results.


Introduction
The requirement of lightweight and high strength materials in the automobile industry has motivated researchers to use different advanced high strength steels.Study of the mechanical behaviours of such materials at different loading rates is needed to design the auto-body structures for the maximum possible dissipation of crash energy.The advanced high strength steels can attain very high strengths while retaining moderate ductility, which makes them ideal for dissipating energy during an automotive crash [1][2][3][4].Their inherent high strength allows structural components to be thinner, making the vehicle lighter and more fuel efficient.Multi-phase 800 High Yield strength steel (MP800HY) and complex-phase 800 steel (CP800) are two potential materials in the range of advanced high strength steels.These steels have good combination of strength and formability.These are used in automobile industries for high yield strength values especially in crash relevant parts such as side impact protection and bumpers, and also in structural parts including reinforcements or cross members.Singh et al. [5,6] studied the mechanical behavior of these steels at strain rates 0.001 s −1 to 750 s −1 under tensile loads.The authors' previous work is extended here to study the thermal softening behavior of the materials at quasi-static condition (0.001 s −1 ).The material m-parameter of the existing Johnson-Cook model has been imposed in the previous work and the predicted flow stresses by this model are compared with the experimental results at different strain rates.Thereafter, the overall mechanical characteristics are compared.
Quasi-static tests are performed on electromechanical machine at room temperature (20 • C) as well as high temperature (200 • C) to understand the high temperature effect in the deformation of the materials.The medium (5 s −1 and 25 s −1 ) and high strain rates (250 s −1 , 500 s −1 and 750 s −1 ) experiments are conducted on hydro-pneumatic machine (HPM) and modified Hopkinson bar (MHB) setup respectively.The descriptions of the used experimental techniques are discussed in authors' previous work [5,6].

Materials and specimen design
The investigated materials, MP800HY and CP800 are obtained from FIAT research centre, Turin, Italy whose chemical composition in wt.% is given in Ref. [5,6].The microstructure of MP800HY consists of mainly ferrite matrix and granular bainite, whereas, the microstructure of CP800 contains small amounts of martensite, retained austenite and pearlite within the ferrite -bainite matrix where, Nital (HNO 3 + CH 3 OH) is used as the etching reagent.The fractographs of the materials tested at room temperature (20 • C) in quasi-static, medium and high strain rates are presented in Fig. 1.Fractographs of MP800HY is coarser, whereas, CP800 has smooth fracture.The cup like depressions (dimples) shows ductile fracture of the materials.The dimple increases and becomes deeper with increasing strain rate.These pictures are taken by SEM at the magnification of 2500x.Flat sheet specimens [1,2] of the materials have gauge length 10 mm, width 4 mm and, thickness 3 mm and 0.97 mm for MP800HY and CP800 respectively, are cut by electro discharging machine from the sheet materials following the direction of the lamination.The thin sheet metal specimen is inserted in the specimen holders by glue; subsequently, a steel dowel is used to prevent slippage.Both specimen and supports are threaded jointly for 8 mm for effective gripping with the bars.

Results and discussion
The experimental data of various experiments are investigated for the materials MP800HY and CP800 under tensile loads.The stress-strain curves of different strain rates at room temperature are compared and the measured experimental results are presented in [5,6].Here, the quasi-static tests at high temperature (200 • C) are done in electromechanical machine (Fig. 2).The stressstrain curves (Figs. 3 and 4  699 MPa.Thus, the flow stresses of both the materials decreases at 200 • C. The variation of dynamic increase factor (DIF) with the obtained strain rate for yield stress and ultimate tensile strength are compared in Fig. 5.In case of MP800HY, DIF of U.T.S. slightly increases with increasing strain rate compared to that for Y.S., whereas, in case of CP800, DIF of U.T.S. decreases significantly with increasing strain rate at high strain rates in comparison to Y.S.
The Fig. 6 shows that reduction in area is more in MP800HY compared to CP800 at each strain rate.As the area under the stress-strain curve decreases at high temperature, the fracture energy and toughness of the materials will decrease.The elongation in the materials decreases, therefore, the ductility will decrease at the high temperature (200 • C).

Material model
Material model incarnates dynamic response of the material due to thermo-mechanical parameters and is the important basis for numerical simulation in metal plastic deformation process.
In order to have confidence in the results of such simulations, an accurate material model is required.Here, the material parameters of existing Johnson-Cook model are determined based on the experimental results and thereafter, the experimental flow stress is fitted with the predicted result.J-C model is purely empirical and is widely used model.These days, it is already in-built in most of the simulation software.This model can reproduce  several important material responses observed in impact and penetration of metals.
The Johnson-Cook model is expressed [7] as Where, ε is the equivalent plastic strain, ε is the strain rate, ε * = ε/ ε0 is the dimensionless plastic strain rate for ε0 = 0.001 s −1 T * = T − T ROOM T MELT − T ROOM T * is the homologous temperature, A is the true yield stress, B and n represent the effects of strain hardening, C is the strain rate sensitivity constant, m is the thermal softening parameter.