High Rate Characterization of Three DP980 Steels

Advanced high strength steels (AHSS) are used extensively in the automotive industry in the ongoing effort to reduce vehicle weight. Their increased strength allows for the reduction of sheet thickness, and thus a reduction in mass, while offering formability and cost advantages when compared to other metal alloys typically considered for lightweight applications. DP980 steels are AHSS being considered for structural energy absorbing components; however, there is a lack of published information on their high rate behaviour. This paper presents the results of an experimental program that characterized three production DP980 steels from three different manufacturers at strain rates of 0.001, 1, 10, 100 and 1,000 s. An electro-mechanical frame was used for the quasi-static tests, the 1, 10, and 100 s tests were carried out using a fast hydraulic apparatus and the 1,000 s experiments were carried out using a tensile split Hopkinson bar. The quasi-static hardening response at strains higher than the uniform elongation of about 7% was obtained by using a shear test, thus avoiding the use of inverse modelling techniques. The results indicate that the DP980 steels are moderately rate sensitive, with one of the materials showing higher sensitivity than the others. One of the materials exhibited a yield point phenomenon that appears to affect the behaviour of the material at 100 and 1,000 s, however, the reasons for this behaviour remain an open question. The data was fit to modified Johnson-Cook and Cowper-Symonds model to account for rate sensitivity. The results presented in this paper provide a tool for modelling the dynamic behaviour of DP980 steels.


Introduction
Minimizing vehicle weight is a crucial part of modern vehicle design. The reduction of fuel consumption and associated emissions is the primary driver for minimizing vehicle weight. More recently, increased crashworthiness requirements, have increased the drive to reduce the weight of structural components. One way of reducing vehicle weight is by replacing energy absorbing components made from conventional steels with components made from advanced high strength steels (AHSS). Their increased strength allows for the reduction of sheet thickness, and thus a reduction in mass, without compromising safety, while offering formability and cost advantages when compared to other metal alloys typically considered for lightweight applications.
A significant challenge faced by engineers and researchers considering the use of AHSS is the lack of published high rate constitutive data for use in computer aided engineering (CAE). To add to the difficulties, AHSS that are produced by different manufactures can have differences in properties that should be accounted for in CAE predictions. This work aims to provide this data for DP980, a dual phase steel with a nominal ultimate tensile strength (UTS) of 980 MPa. To explore the differences between the products of different manufacturers, a blind testing program of three production DP980 steels from three different manufacturers was performed at rates of 0.001, 1, 10, 100 and 1,000 s -1 . This paper presents the experimental procedures and results of these tests, together with the fitting of the data to the Johnson-Cook (JC) [1] and Cowper-Symonds (CS) [2] models. To ensure the constitutive data is suitable for vehicle crash applications, the quasi-static hardening curves are obtained experimentally to strains of 50% using both tensile and shear tests using the methodology recently proposed by Rahmaan et al. [3].

Experimental Methods and Procedures
The standard JIS specimen geometry shown in Fig, 1-a was used for the 0.001 s -1 experiments and the miniature dog-bone (MDB) specimen geometry shown in Fig. 1-b were used for the 1 to 1,000 s -1 experiments. The MDB geometry was developed at the University of Waterloo (UW) and has been shown to produce the same results as standard geometries up to UTS [4]. A comparison between the JIS and MDB results obtained in this work EPJ Web of Conferences 183, 02060 (2018) https://doi.org/10.1051/epjconf/201818302060 DYMAT 2018 will be shown in the Results and Discussion section. The mini-shear specimen geometry developed by Piers et al. [5] (Fig 1-c) was used for the shear experiments. The shear specimens were fabricated at -56° to the TD so that the principal stress direction was aligned with the TD and consistent with the tensile tests. The shear experiments were performed to obtain tensile constitutive response beyond UTS, following the procedure outlined in [3], the tensile-to-shear stress ratio is computed at the plastic work corresponding to the UTS. Assuming that shear anisotropy does not evolve beyond the UTS work level, this stress ratio is then used to convert the shear stress to an equivalent tensile stress. It is then straightforward to decompose the plastic work into an equivalent strain.
The 0.001 s -1 tensile and shear experiments utilized an MTS Criterion 45 electro-mechanical testing machine as shown in Fig. 2. All three specimens were used. The JIS specimens were secured using hydraulic grips. A 100 kN load cell was used to measure the load. The MDB specimens were tested using a 10 kN load cell and specialized grips. The specimens were tested to failure. Specimen strains were measured using in situ three dimensional (3D) Digital Image Correlation (DIC), as described below.   Fig. 3. The apparatus has a 13.3 kN hydraulic actuator with 101.6 mm stroke. The apparatus functions by accelerating the engagement sleeve to a constant velocity which then contacts the engagement piston at the bottom of the stroke as shown in the schematic in Fig. 3. A capacity is used to achieve a maximum stroke rate of 1400 mm/s. A Kistler 9500A4 ±30 kN piezoelectric load cell, which is located directly above the upper grip assembly, measured the load during the test.   Specimen deformation was directly measured using stereoscopic DIC in the MTS and 2D DIC in the HISR. Each specimen was first painted white and then painted with a randomized black speckle pattern. The tests were recorded and then the images were analysed using DIC software by Correlated Solutions. For the MTS tests, two Point Grey Gazelle cameras were used, recording at a frame rate of 1 frame per second (fps). For the HISR tests, a Photron SA5 high speed camera was used to capture the images at a rate of 2,000, 15,000 and 70,000 fps for the 1, 10 and 100 s -1 tests, respectively. A virtual strain gauge length of 0.3 mm was used throughout. During the tests, the Correlated Solutions DIC data acquisition system was used to capture the force data from the load cell for each recorded image. After postprocessing was completed, a user defined virtual extensometer was used to determine the engineering strain. The strain fields in the mini-shear specimens were analysed using the detailed procedures described in [3].
The stress-strain response of the Hopkinson bar specimens was determined using the standard analysis following [6].

Experimental Results
The materials were first tested at 0.001 s -1 using the JIS samples to determine the baseline low-rate properties. The results are presented in Fig. 5, where it can be seen that the materials exhibited similar, yet distinct behaviours. Material 1 had the highest UTS, Material 2 had the most distinct behaviour due to the presence of yield point phenomenon, and Material 3 had a UTS similar to Material 2, but with the yield behaviour of Material 1. Given that the intermediate and high rate tests were performed with the MDB specimen, a comparison was made between data obtained from the JIS samples and data obtained with MDB specimens tested at 0.001 s -1 . Fig. 6 shows this comparison for Material 2 and it can be seen that the MDB results are essentially equal to the JIS results, at least up to the onset of necking. The comparisons for the other two materials were similar, but are not shown for brevity. Material 2 was chosen for presentation because it had the most complex behaviour. The engineering stress-strain data for Material 2 at 1, 10, 100 and 1,000 s -1 are shown in Figs. 7 to 10, together with an average curve, to show the data and the repeatability of the tests. The data for Materials 1 and 3 is of similar repeatability; however, the 100 and 1,000 s -1 data for Material 2 showed some oscillations that were not present in Materials 1 and 3. The oscillations observed in the Material 2 results are attributed to the yield point phenomenon observed, but a complete investigation of their cause was beyond the scope of this work. The full data set for Materials 1 and 3 is not shown for brevity.     The shear and true tensile stress as a function of plastic work is shown for a nominal von Mises equivalent strain rate of 0.001 s -1 is presented in Fig. 11 for Material 1. The tensile work is computed until the UTS whereas the work in shear is computed until the peak load is reached. The clear advantage of the shear test is that it does not experience localization and is valid to large strain levels. The shear-extrapolated data is show below. A plot showing the strain rate sensitivity of all three materials is shown in Fig. 12, which shows the true stress at 6% true strain for each strain rate tested. Each data point is the average of five repeat tests. All three materials showed moderate strain rate sensitivity, with Material 3 showing a slightly higher sensitivity.

Constitutive Fits
The experimental data was fit to the following constitutive equation, where ( ) is a scaling function for strain rate dependence that was used to examine the rate sensitivity in the constitutive response by fitting the single parameter form Johnson-Cook (JC) rate sensitivity [1] given by, and to the Cowper-Symonds (CS) model [2] given by; where p ε& = effective plastic strain and The model constants fit to the data are shown in Table 1. The resulting constitutive fits for each DP980 material at 0.001 s -1 are shown in Fig. 13 along with the simple Holloman law (Eq. 2) calibrated to 50% strain. This data includes both the tensile and shear data at this rate, showing the extrapolation to large strains enabled by the shear specimen. This calibration was then combined with either the JC (Eq. 3) and CS (Eq. 4) scaling factors to account for rate sensitivity.    The CS predictions are compared to the measured data for Materials 1-3 in Figs. 15-20. In general, the fit quality was deemed superior using the CS rate sensitivity term. The greatest discrepancy between the model and the experiments occurred for Material 2 due to the presence of the yield point phenomenon, as can be seen in Fig. 17.

Conclusions
The high rate constitutive behaviour of three commercial DP980 steels was determined by testing the materials at 0.001, 1, 10, 100 and 1,000 s -1 . All materials showed moderate strain rate sensitivity. Although generally similar, noticeable differences were observed, namely the presence of yield point phenomena in Material 2. Material 3 seem to have a slightly higher strain rate sensitivity. The data was fit to the JC and CS rate sensitivity terms, with the latter being able to reproduce the experimental data somewhat more accurately. The data and models presented in this paper provide a useful tool for modelling the dynamic behaviour of DP980 steels.