Study On Constitutive Relationship Of Metal At High Temperature And High Pressure

The constitutive relationship of solids in high-pressure and high-temperature conditions is a specific equation which is necessary for the research of chemical detonation, high-energy ion or laser beam, and high velocity impact. Some shortcomings in Steinberg and his colleagues'work [J. Appl. Phys.,51(1980) 1498; J. Appl. Phys.,65(1989) 1528] on high-pressure constitutive relationship were discussed, according to some viewpoints from Chen et al [Chin. J. High Pres. Phys, 19 (2005) 193] and Peng [Ph.D.Thesis(Mianyang, CAEP)(2006)], and then a new constitutive model was presented. The main conclusions are as following:(1) A new constitutive model for closed packed crystal material was presented based on the analysis on researches of Burakovsky et al [Phys. Rev.,B71(2005)184118], Nadal et al [J.Appl.Phys.,93(2003)2472], and Yu et al [Chin.Phys. Lett.,17(2008) 64] on Steinberg's constitutive model. The new functions are Here G and Y are shear modulus and yield strength, respectively,βand n are work hardening coefficients,εP is plastic strain, To is the reference temperature, usually taken as room temperature. The values of G(P,T0), ((?)G/(?0T)p,β, n andεP can be obtained from experiments or calculations.The merits of this model are:——Compared with the methods of Steinberg et al, Nadal et al, and Yu et al, the total function, rather than the first order approximate, was applied in describing the relationship between G and P.——Although the first order approximate function was still applied to describe the change of G with T in the new functions, ((?)G/(?)T)P was used instead of ((?)G/(?)T)0, in the light of Ab initio calculation results presented by Xiang et al [Phys. Rev. B70 (2004) 174102]. (2) Taken aluminum as an example, the constitutive functions are Following issues supports the validation of these functions:——The G(P,T) function which was deduced from the Ab initio calculation results presented by Sin'ko et al [J.Phys.:Condens. Matter,4(2002) 6989] and Xiang et al has an explicit physical foundation. It is also supported by the sound velocity measurement along Hugoniot and shear modulus calculations along isentropic (with Birch- Murnaghan equation which is based on finite strain theory).——Although the physical conception of the new Y(P,T) function is still followed Steinberg's work, the constitutive form is different because the G(P,T) has a different form. And the calculation with this model is in good agreement with shock experiment results (according to Asay and Chhabildas's isotropy hardening model). Specially, the hypothesis of G(P,T)/Y(P,T)≈cons. is validated by experimental results at high pressures (for LY12 alloy, the threshold is Pc>30GPa). While under low pressures, G(P,T)lY*P,T)≈cons. is suggested (here Y*=Y/[1+β(εP+εPi)]n). In fact, this hypothesis is also the original intention of Steinberg's work.——Experimental measured velocity profiles of sample-window interface in shock/release, shock/reshock/release, shock/reshock, and shock/ release/reshock experiments on LY12 alloy were analyzed to verify the G(P,T) and Y(P,T) functions. The experimental results are in good agreement with the constitutive model. Thus the validation of the new functions is thoroughly confirmed.(3) In experiment technique field, the assembly sample method suggested by Asay et al [SAND-85-2009] was utilized, with which the puzzle that there are no reloading experiment data beyond 20GPa for aluminum was solved (～70GPa shock stress experiment data are reached in our experiments.). This is a new approach to measure yield strength accurately at higher pressures.Finally, though the constitutive model presented in this paper is based on explicit physical foundation with less approximate, it is worth pointing out that more experiments on different metals are needed to confirm its universality. Even for LY12 alloy, it is needed more experimental data or calculation results to deduce precise parameters of the model. For this purpose, it is important to develop or optimize present experimental and calculation methods. So it is necessary to develop; the laser-ultrasonic technique and static high-pressure yield strength measurements under high-temperature and high-pressure.