2.1 Strength model and newly-measured parameters
We performed tensile tests on each of the three manufactured Fe-Ni ingots. The Johnson and Cook (JC) strength model is defined as (Johnson and Cook, 1983),
\(Y\ =\ (A+B\epsilon^{N})(1\ +\ C\ \ln\ \dot{\epsilon}\ )[1-(\frac{T-T_{\text{ref}}}{T_{m\ }-\ T_{\text{ref}}})^{M}]\ \ \ \ \ \ \ \ \ \ \)Equ. 1
where Y is yield strength, T is temperature, ε is the equivalent plastic strain, \(\dot{\epsilon}\) is the strain rate (set to be 1 at the reference state in iSALE), A is the yield strength at the reference state, B, C, M and N are material constants, \(T_{m}\) is the melt temperature and \(T_{\text{ref}}\) is the reference temperature. We stress that the implementation of the JC strength model, as implemented in iSALE, neglects a temperature dependence for cases where the reference temperature of the material is greater than the surface temperature of the target. This effectively reduces the above equation to the following:
\(Y\ =\ (A+B\epsilon^{N})(1\ +\ C\ \ln\ \dot{\epsilon})\ \ \ \ \ \ \ \ \ \)Equ. 2
To produce simulations where cooled target temperature dependence is properly accounted for within the strength model, we measured and implemented JC strength constants at 77 K (that is, lower than the cooled target temperatures). We performed tensile tests on the three ingots, I-90 (a), I-90 (b) and I-94 (b) at 77 K to determine the thermal constant, M. The other constants (A, B, C and N) were determined by compression tests. The Poisson ratio, elastic modulus and strength of each ingot were also measured. We derived the necessary parameters for aluminum (Al 6061-T6) by scaling the known parameters from room temperature to 77 K using the cryogenic data of Al6061-T6 from the Cryogenic Materials Data Handbook. Results of the strength tests are shown in Figure 1. Finally, we determined the input parameters for the Gibeon targets from strength versus temperature data in Gordon et al. (1970) to fit the thermal constant, M. We used the same strain-rate constant as the ingot I-94 (b) as it matches well with data from Gordon et al. (1970). We find that the Gibeon meteorite material is extremely ductile with an equivalent strain to failure of 180%. Table 3 outlines in detail the constants.