MECHANICAL ANISOTROPY OF COLD-ROLLED ST-37 STEEL PLATE UNDER HIGH STRAIN RATES LOADINGS

Cold rolling process in metal could increase its strength and hardness, but also induces mechanical anisotropy. This is caused by unresolved plastic strain and microstructural changes caused by plastic deformation exerted by pair of rolls at a relatively low temperature. This research aims to provide understandings on anisotropic and strain rate sensitive behaviour of St-37 mild steel. The microstructure of rolled and unrolled St-37 plate were observed in 3 directions relative to the rolling direction. The cylindrical specimens were then prepared from rolled plate with 33.3% reduction in the orientation of 0o, 45o, and 90o relative to the rolling direction. Specimens were also prepared from unrolled plate as comparison in the same directions. These specimens were then tested in compression loading, first in quasi-static condition, and then by using Split-Hopkinson Pressure Bar (SHPB) at the strain rate of 1200 s-1. The experimental results in the form of stress-strain curves are used to obtain the parameters of Simplified Johnson-Cook viscoplastic model. The anisotropy of yield strength in rolled specimens could be seen on both quasi-static and high strain rate condition, where the highest strength found on the specimens perpendicular to the rolling direction. In addition, the effect of cold rolling to the strain rate sensitivity of the material were also captured successfully in this study, where specimens from rolled plate show less strain rate sensitivity compared to the unrolled specimens.


INTRODUCTION
Cold rolling is a process where a plate of metal is being plastically deformed to reduce its thickness, which carried out below the recrystallization temperature of the metal. Typically, cold rolling is performed at room temperature. This causes the metal plate possess higher strength and hardness after the rolling process due to untreated strain hardening [1]. However, cold rolling could also induce preferred crystallographic orientation and mechanical fibering, i.e., reorientation structural discontinuity such as grain boundary and second-phase constituents due to directional plastic deformation. These could lead to mechanical anisotropy of the plate, i.e., difference in mechanical properties according to its loading direction, such as on its yield strength, ultimate tensile strength, and ductility [2][3][4][5].
Hence, it is necessary to test the cold rolling product in various directions of loading to obtain more complete mechanical properties of the material.
St-37 steel is a grade of mild steel which has been used in various engineering applications [6][7][8]. One of its common usages is in the impact energy absorber structure (crash box) of vehicles. This structure is a type of thin-walled structure designed to absorb kinetic energy during impact through a plastic deformation mechanism. In this case, a cold-rolled St-37 material is widely used in the fabrication of this structure [9][10][11][12][13]. In relation to impact loading, it is known that St-37 is a strain rate sensitive material [14][15][16], where mechanical properties of St-37 subjected to high strain rate loading could be different from those subjected to the medium or quasi-static loading. In term of yield strength, the material will experience higher yield strength following the increase of strain rates value. Strain rate sensitivity of a material depends on how dislocations of material move at various strain rates [17].
Furthermore, numerical simulation is widely used in the design process of an impact energy absorber structure [9], [12], [18][19][20]. The understanding of material behaviour is an important key to obtain realistic numerical simulation results. Accuracy in choosing material model and defining its parameters will greatly determine success in predicting the behavior of the designed structure. Many researchers have developed material models capable to capture the strain rate sensitive behavior of metals with very satisfying results [21][22][23][24]. Simplified Johnson-Cook model is one of the material models that could give good prediction in the viscoplastic behaviour of metals with relatively easy physical understanding [25], [26]. The accuracy of this model depends on the accuracy of the inputted material parameter. In this case, testing the mechanical behaviour, especially the anisotropic and strain rate sensitive behaviour of St-37 material will help to define good material parameters which could lead to accurate numerical simulation results.
Comprehensive understandings in the anisotropic and strain rate sensitive behaviour of St-37 are really important to obtain an optimum design of energy-absorbing structures. This study aims to observe the effect of anisotropy due to the cold-rolling process on the high strain rate mechanical properties of St-37. Series of experimental works, starting from metallography, quasi-static compression test, and high strain rate test are performed. A Split Hopkinson Pressure Bar (SHPB) is used as the technique to obtain the mechanical properties of St-37 in high strain rate condition. Curve fittings are performed to the experimental results of St-37 specimen in three anisotropic orientations to obtain the material parameters of Simplified Johnson-Cook model. This study will contribute to enrich the understanding in the behaviour of anisotropic St-37 material in high strain rates condition. Besides, the Simplified Johnson-Cook material parameters will be useful to build more realistic numerical simulations in the prediction of structure made of cold-rolled St-37 material.

Specimen Preparations
This study used specimens prepared from St-37 steel plate, where a portion of this plate was cold rolled with thickness reduction of 33%. A cylindrical shaped specimen is used in both quasi-static and SHPB test, with a detailed geometrical information shown in Figure 1. For SHPB specimens, the dimension is selected to fulfill the test validity standard of the SHPB, where the specimen's length-to-diameter ratio is 1 and specimen-to-bar diameter ratio must be between 0.5 to 0.8 [27]. For each unrolled and rolled plate, specimens with the orientation of 0 0 (RD), 45 0 (TD), and 90 0 (TD) relative to the rolling direction were made in order to capture the anisotropy effect of each plate. The orientation of the specimens relative to the rolling direction of the plate is shown in Figure 2.    Table 1 shows the designation of specimens used in this study. The two first letters indicate the direction of the specimens, where RD, DD, and TD stand for Rolling Direction, Diagonal Direction, and Transverse Direction, respectively. The third letter depicts the rolling condition of the specimen, where U stands for Unrolled condition and R for Rolled condition. Lastly, the last letter indicates the loading condition during testing, where S stands for Quasi-Static loading and D for Dynamic/high strain rate loading.
Furthermore, specimens for metallography were also prepared. The specimens were basically cut into rectangular shape, where their upper surface should be parallel with its base to ensure the microstructure observation is perpendicular to its upper surface. The observed (upper) surface was then grinded and polished prior to further processing for microstructure observation. The observation direction is further explained in the next section.

Metallography
The microstructure of both unrolled and rolled plates were observed using metallography in order to detect the effect of rolling to the microstructure of the cold-rolled St-37 specimen. The microstructure observation was conducted using a Nikon Epiphot microscope using 200X magnification. Both plates were observed from 3 principal directions relative to its rolling direction, i.e., its rolling direction, transverse direction (perpendicular to its rolling direction), and planar direction (perpendicular to the plate surface).

Figure 3. Direction of metallography observation relative to the plate rolling direction
Before the observation, the observed surface was etched using nital solution to ensure the grain boundaries were visible when observed. As mentioned before, the observation should be ensured perpendicular with the observed surface. Hence, proper support at the observation table should be maintained. Microstructures from beforementioned directions from both unrolled and rolled plates were then compared to understand the effect of cold rolling to the microstructure of the plate, which could affect the mechanical properties of the plate.

Quasi-Static Compression Testing
The quasi-static compression tests were conducted to obtain the yield strength value of the specimen on the directions of 0 0 , 45 0 , and 90 0 relative to its rolling direction. These data will be used in the curve fitting process to construct the Simplified Johnson-Cook model parameters as the parameter A. The testing followed ASTM -E09 standard with the compression rate of 3 mm/min. A HUNGTA -5021 testing machine with the maximum capacity of 18 tons were used in this compression test. The scheme of the quasi-static testing is shown in the Figure 4.

High Strain Rate Test using Split Hopkinson Pressure Bar (SHPB)
The Split Hopkinson Pressure Bar (SHPB) is one of typical test used to measure the behaviour of material under high strain rate loadings (500 -10 4 s -1 ). The main objective of this testing is to obtain a stress vs strain curve of a material loaded with a high strain rate compression loading based on a one-dimensional wave theory. The SHPB consists of a striker bar, incident bar, and transmitter bar. The three bars should be made from the same material and diameter. The specimen is sandwiched between the incident and transmitter bars [28], [29]. All of the bars and the specimen are in the shape of cylinders, and are arranged in one axis as shown in Figure 5.  [17] To obtain the mechanical properties of the specimen, a compressive, axial loading is generated by striking the striker bar to the end of the incident bar by using a high-pressure gas. The loading then transmitted as a compressive strain pulse propagating along the incident bar. When reaching the other end, the pulse will be partially reflected as tensile strain pulse, which will be recorded by the strain gauge when the reflection reached the middle of the incident bar. Meanwhile, the remaining compression pulse will be transmitted to the specimen and deforms it before transmitted to the transmitter bar. This transmitted pulse then will also be recorded by the strain gauge when reaching the middle of the transmitter bar [30]. Typical pulses produced by SHPB testing are shown in Figure 6. From the recorded reflected and transmitted pulse, the strain rate (), strain ( ), and stress ( ) experienced by the specimen could be calculated [31]. The strain rate is calculated from the reflected pulse data by the following equation.
where Cb, Ls, and εR(t) are the speed of sound inside the bar material, length of the specimen, and reflected strain pulse. To obtain the overall strain of the specimen throughout the loading, the strain rate then will be integrated with the respect of time.
Meanwhile, the stress of the specimen throughout the loading is calculated from the transmitted pulse using this equation where E is the Young modulus of the bar, A is cross-sectional area of the bar, As is crosssectional area of the speciment, and εT(t) is the transmitted strain pulse. The strain and stress data then constructed from the calculation then used to plot the stress vs strain curve. The typical strain rate vs time, strain vs time, stress vs time, and stress vs strain curve are shown in Figure 7. To ensure the validity of the experiment, the loading should be made to remain onedimensional. Hence, sufficient supporting for bar systems is needed beside keeping the bars are physically straight. Moreover, the bars material needs to be stronger than the specimen material so it remains in linear elastic condition during the loading [28], [32].
The SHPB used in this study is developed in the Lightweight Structure Laboratory, Bandung Institute of Technology. This SHPB uses round bars made of AISI 4340 steel as bar system, where the diameter of the stainless steel bars were 10 mm [33]. AISI 4340 steel has the density (ρ) of 7850 kg/m 3 , Young modulus (E) of 205 GPa, wave velocity (CB) of 5110.25 m/s, and yield strength (σy) of 710 MPa. The density and modulus elasticity of the bar, which in turn also affect the wave velocity, determine how the strain wave will propagate along the bar, and the yield strength of the bar should be ensured higher than the yield strength of the specimens to keep the bar from deforming during testings. The length of the incident and transmitted bars were 1000 mm, and the striker bar length were 300 mm. The specimen diameter (Ds) and length (Ls) of 5 mm were chosen to reduce the frictional, and also the axial and radial inertia effect on the specimen. By using a relatively small specimen, the stress homogeneity of the specimen is ensured, and the specimen could be deformed in proper strain rate and strain [28]. Tests conducted on 5 mm specimens using the gas pressure for striker bar ranged from 85-100 psi could produce the strain rate around 1200 s -1 for both unrolled and rolled specimens. The set-up of this testing is shown in Figure 8 a. To record the pulses, strain gages were attached on the middle of each incident bar and transmitter bar (Figure 8 (b)). Both strain gages were connected to a data acquisition system with the sampling rate of 100 kHz before the pulses obtained were processed using Eq. 1, 2, and 3 to produce the strain rate, strain, and stress data of the specimens.

Curve Fitting Process
The curve fitting is performed to obtain the material parameters of Simplified Johnson-Cook model. The plastic portion of the stress vs strain curves were then taken in the form of effective plastic strain (EPS) curve. These EPS curves were then fitted to Simplified Johnson-Cook material model (Equation 4) to obtain the material parameters A, B, n, and C, where A indicates the yield strength of the material under quasi-static loading, both B and n represent the strain hardening of the material, and C depicts the strain rate sensitivity of the material, i.e., the hardening of the material due to an elevated strain rate. As opposed to regular Johnson-Cook material model, in Simplified Johnson-Cook model the temperature effect on the material behaviour is neglected [25].

= [ + ][1 + lṅ̇0]
The curve fitting process was done on experimental data using the generalize reduced gradient (GRG) method which is available as an add-on Solver in Microsoft Excel, which in turn could generate the material parameters [14]. An example of a curve fitting result compared to its respective experimental plot is shown in Figure 9.  Figure 10 shows the metallography results of cold-rolled St-37 specimens. It could be seen that the grains are relatively uniform in term of shape, whether observed from its rolling direction, transverse direction, and planar direction. The different result could be seen in Figure 11, where for rolled steel, there are grain elongations along its rolling direction, which is a characteristic of a rolled plate microstructure. This kind of microstructure, along with several other factors, could induce mechanical anisotropy on steel plate. This is due to the strength of metal and its ability to plastically deform are determined by how easy its dislocations move along the crystal lattice. The dislocation movement along the lattice could be hindered by the grain boundary. This movement hindrance could cause accumulation and multiplication of dislocation, hence increasing the strength and reducing the ability to plastically deform in that direction. With the grain boundary elongation along the rolling direction, the dislocation path perpendicular to rolling direction is shorter than the path parallel to the rolling direction. This cause dislocation movement perpendicular to the rolling direction is harder to move, which increase its strength compared to dislocation parallel to the rolling direction [34].    The result of SHPB testing in terms of strain rate vs time and stress vs strain are shown in Figure 12, where curve for unrolled and rolled specimens are shown in solid and dashed lines, respectively. From Figure 12 (a), it could be seen that the strain rate experienced by all of the specimens are averaged around 1200 s -1 . As mentioned beforehand, strain data were obtained by integrating the strain rate data with respect to time. Later, the strain data obtained were then combined with stress data to construct the stress vs strain data. These stress vs strain curves were then transformed into stress vs effective plastic strain (EPS) curve in order to only describe the plastic region. Curve fitting according to Simplified Johnson-Cook material model were then conducted to obtain the Simplified Johnson-Cook material parameters, namely A, B, n, and C. The experimental results (shown in scatters) alongside their curve fitting results are shown in Figure 13.   Table 3 shows the detailed information of Simplified Johnson-Cook parameters obtained from the curve fitting process. It could be seen that there are increase in yield strength compared to its static yield strength (A) for both unrolled and rolled specimens. This increase in yield strength is due to the nature of St-37 steel itself, where St-37 steel is a strain rate sensitive material. There are also differences in yield strength of rolled specimens in the three directions, where the values for RDRD, DDRD, and TDRD are 707 MPa, 740 MPa, and 810 MPa, respectively. The lowest yield strength value showed by RDRD specimen and the highest value showed by TDRD, where the yield strength of DDRD specimen fall between the former two specimens. While there are increase in these yield strength values, the trend is still the same compared to the yield strength obtained from the quasi-static testing (A), where there are increase of yield strength after the specimens are rolled. Both unrolled and rolled specimens have the highest yield strength at their transverse direction, and exhibit the lowest yield strength on their rolling directions. In terms of the yield strength difference between orientations, the anisotropy of rolled plate is also more pronounced on SHPB testing.

SHPB Testing Result
In simplified Johnson-Cook model, B and n parameters indicate the strain hardening behaviour of the material. These parameters obtained from the testing show no specific trends for both unrolled and rolled specimens. On the other hand, parameter C indicates the strain rate sensitivity, where higher value of C means more pronounced effect of strain rate to the strength of the material. It could be seen that the value of C become minuscule for all of the orientations of rolled plate (0.001, compared to 0.028, 0.022, and 0.036 for RDUD, DDUD, and TDUD, respectively). Thus, it could be said that in this experiment, rolled specimens are less strain rate sensitive than unrolled specimens.

CONCLUSIONS
A comprehensive study of the high-strain rate behaviour of cold-rolled St-37 plates has been performed. The testing showed that cold rolling process could induce anisotropy to the specimen, where specimen 90 0 relative to its rolling direction (TDRD) shows the highest strength and specimen 0 0 relative to its rolling direction (RDRD) shows the lowest strength. The elongated microstructure of the rolled plate supported this result since non-equiaxial microstructure could induce anisotropy of the metal. In addition, the cold rolled specimens exhibit less strain rate sensitivity, as shown by their lower value of C compared to their unrolled counterparts.