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.