Constitutive equation for hardened SKD11 steel at high temperature and high strain rate using the SHPB technique

Abstract

In this present work, dynamic tests have been performed on hardened SKD11 steel (62 Rockwell C hardness) specimens by means of a high temperature split Hopkinson pressure bar (SHPB) test system. Effects of temperature as well as those of strain and strain rate for the hardened steel are taken into account by using two ellipsoidal radiant heating reflectors with two halogen lamps and magnetic valve. The result obtained at high stain rates were compared with those at low strain rates under the different temperature. It was seen that the flow stress curves are found to include a work hardening region and a work softening region and the mechanical behavior of the hardened steel is highly sensitive to both the strain rate and the temperature. To determine the true flow stress-true strain、temperature relationship, specimens are tested from room temperature to 1073K at a strain rate form 0.01 s -1 to 104 s -1 : The parameters for a Johnson-Cook constitutive equation and a modified Johnson-Cook constitutive equation are determined from the test results by fitting the data from both quasi-static compression and high temperature-dynamic compression tests. The modified Johnson-Cook constitutive equation is more suitable for expressing the dynamic behavior of the hardened SKD11 steel above the vicinity of the recrystallization temperature. Keyword: constitutive model, high temperature, high strain rate, flow stress, hardened SKD11 steel IntroductionMaterial properties generally differ between dynamic and quasi-static states. The dynamic mechanical properties of a material are known to be dependent on the strain, strain-rate, and temperature [1]. Hardened SKD11mould steel (Pre-hardened 40 Rockwell C hardness, 40 HRC) is an important class of industry engineering materials due to its excellent combination of strength, good resistance to thermal softening, high toughness and high hardness as well as high wear-resistance [2]. However, it is not widely used because the deformation behaviors of this material at temperature and high strain rate are unknown. In particular, it is regarded as difficult to machine because of its high strength, high hardness and big brittle in the high-speed machining [3][4]. Moreover, the high strength and hardness inhibits material plastic deformation producing larger cutting forces and higher temperature at the cutting edge and generating for higher cutting speed a rapid chipping at the cutting edge which leads to catastrophic failure [5]. Many investigators have studies the mechanism and machinability including tool wear, residual stresses, cutting force and vibration on high speed milling process [6][7][8][9][10]. But the mechanical behavior of materials subjected to high temperature and high strain rates is of great interest in a wide range of engineering applications as well as in fundamental studies of material behavior. In some of these applications such as high-strength and high wearable structures, characterizing and modeling the high strain rate response of the hardened steel are necessary f...

Modeling and simulation of the high-speed milling of hardened steel SKD11 (62 HRC) based on SHPB technology

“…The modified J-C constitutive equation is where T c is the recrystallization temperature, (s f ) rec and (s f ) def are respectively the flow stress before and after the recrystallization temperature, and k is related to the coefficient of the strain-rate effect of the workpiece material after heat treatment. Material constants and other properties given in the literature [12] are listed in Table 4. Fig.…”

“…This means that the conventional empirical J-C model does not well reflect the flow stress of materials in the high-speed cutting of SKD11. The conventional empirical J-C model therefore needs to be modified according to the negative strain rate effect and temperature effect; the detailed procedure of modifying the J-C constitutive model has been described in the literature [12]. The modified J-C constitutive equation is where T c is the recrystallization temperature, (s f ) rec and (s f ) def are respectively the flow stress before and after the recrystallization temperature, and k is related to the coefficient of the strain-rate effect of the workpiece material after heat treatment.…”

“…In previous work [12], SHPB technology under high temperatures (20-800°C) and a high strain rate (0.01-10 4 s À 1 ) was used to obtain the dynamic mechanical behaviors of SKD11 hardened steel. The relationships of the flow stress, strain, and strain rate are shown in Fig.…”

“…According to the analysis of the dynamic mechanical behaviors of SKD11 hardened steel at a high strain rate (0.01-10 5 s À 1 ) and high temperature (20-800°C), Tang [12] found that flow stress decreases with an increase in strain rate at temperatures of 20-300°C and dynamic recrystallization occurs in materials when the temperature exceeds the recrystallization temperature. This means that the conventional empirical J-C constitutive equation no longer fits the flow stress of SKD11 hardened steel in highspeed cutting, and the J-C constitutive equation should be modified.…”

“…Comparison of flow stress between experiment data and the J-C constitutive equation[12] Empirical J-C constitutive equation fitting: (a) ε1 5 Â 10 3 s À 1 , (b) ε1 1 Â 10 4 s À 1 . Modified J-C constitutive equation fitting: (c) ε1 5 Â 10 3 s À 1 , (d) ε1 1 Â 10 4 s À 1 .…”