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    • Meyer and Kleponis analyze JC parameters for Rolled Homogene

    2018-11-03

    Meyer and Kleponis [21] analyze JC parameters for Rolled Homogeneous Armor (RHA). The Military Standard for RHA, known as MIL-A-12560, allows significant variation in the material properties as a function of thickness. Even within a given thickness specification, the hardness can vary by more than 10%. As Meyer notes, hardness is an indicator of several material properties. Relative to this research, such a variation in hardness might be expected to change the EFS by a comparable percentage, although there is not a simple, direct relationship between the two. To place this variation in perspective, it histone methyltransferase was found that the difference between penetration by a depleted uranium (DU) projectile and penetration by a tungsten alloy (WA) projectile of the same density can be explained with a change in the target EFS of approximately 15%. The permissible variation in hardness within the standard is significant; the difference in penetration depth is comparable to changing the penetrator from tungsten to uranium. In a report by Grubinskas [22] the hardness variation between lots of high hard steel was on the order of 10%. Thinking back to our discussion of similarity methods, it would be considered sloppy research to not understand material properties to better than 10%. Given the known variation of hardness with thickness (Table 1), imagine running a 1/10 scale test with a 0.5-inch (12.7 mm) RHA plate that happens to have a hardness value of almost 400 BHN and comparing it to a full scale 5-inch (127.0 mm) steel plate with a 250 BHN. Then consider that the subscale test will occur at strain rates that are ten times greater than the full-scale test. There is no reason to expect similarity in the results. Meyer utilizes the CTH hydrocode in his work and refers to the RHA parameters within CTH. The original fits, based on 2-inch thick RHA, are attributed to Gray. “The fits resulted in overprediction [sic] of the quasi-static yield strength.” Gray opted to fit all parameters rather than assign a physical meaning to the constant “A”. Meyer opted to set the value of “A” based on quasi-static data and then fit the remaining constants. In addition, some of the fits were based on all of the data and one set was based on using a strain of 0.20, which was the upper limit of the data. The variation in JC parameters as a function of how the data was fitted is disturbing. The six sets of parameters used by Meyer are shown in Table 2. Meyer explains the different sets: It is an interesting exercise to see how these parameters compare at strain rates of 103 and 104, a range typical of ordnance velocity penetration for typical size projectiles. To minimize the problem, assume that the temperature is equal to the reference temperature. From the Johnson–Cook equation, big bang theory can be seen that this makes the temperature factor equal to one. In addition to making the comparison simpler, Meyer explains that the non-dimensional temperature factor used in sets developed by Gray is different from that used in the other sets. Fig. 4 shows the variability in the stress–strain curves at two strain rates. To further illustrate the variability, Fig. 5 shows the predicted stress as a function of strain rate at a strain of 0.1 or 10 percent. Recall that the same strain rate data source was used for at least four of these sets of Johnson–Cook parameters and that temperature effects are neglected in the analysis. At the higher strain rate and a strain of approximately 15%, there is almost a factor of 2 between the stress as determined from Set 2 and the stress as determined from Set 6. Meyer goes on to compare CTH penetration calculations to two experiments. The results, which were reported by Meyer, are repeated in Table 3. In 2011 Schraml [25] considered how the selection of Johnson–Cook parameters affected the simulation results for tungsten alloy impacts on RHA. “The parameter space involved two sets of Johnson–Cook model parameters for RHA, two sets of Johnson–Cook parameters for the tungsten rod material, four tungsten rod length-to-diameter (L/D) ratios, and two continuum mechanics codes. Striking velocities considered in the study ranged from approximately 1000 to 2000 m/s. The study revealed that no single combination of Johnson–Cook model parameters provides superior overall prediction of penetration depth over the other possible combinations across the full range of rod L/D considered”.