crf hormone A brief review of the state of analytical

A brief review of the state of analytical and empirical modeling was included in Anderson and Riegel [4]. In brief, the discussion stated that Tate [10], and independently Alekseevskii [11], modified the Bernoulli equation to account for projectile strength and target resistance. It further noted that it crf hormone is often necessary to let the target resistance change with velocity [12]. The review also stated that Winter [13], after reviewing a large number of regressions and analytical models, concluded that there were insufficient data to draw definite conclusions regarding the importance of target and projectile parameters. Likewise, a study by de Rosset and D\'Amico [14] noted that projectile and target hardness or strength was not considered and “this effect would have to be included in future refinements of the model”. Herein lies one of the most significant impediments to making progress in this field. Namely, that in many cases, the basic material properties have not been sufficiently measured and documented. For example, the WAPEN model, one of the most advanced analytical penetration models available, requires an average flow stress value as an input parameter [2]. It also requires bar wave speed, the elastic, bulk, and shear moduli, and a linear Hugoniot relationship between particle velocity and shock velocity. Rarely are any of these items included with terminal ballistics data.
Similitude analysis, scaling, and constitutive behavior Similitude analysis is a powerful tool that is often ignored. Relative to penetration problems, it has long been recognized as a method that can prove helpful, but, according to Wright [15], “…it has not been possible to reduce the important nondimensional [sic] groups to two or even three.” Wright refers to prior work in which the focus was on relatively thin targets and rigid projectiles but states that the methods are applicable to thick targets as well. With regard to past efforts, he states that, “For the most part nondimensional [sic] groups have not been used, which tend to limit the applicability of each empirical formula to the specific test data from which it was derived.” He further notes that many of the empirical formulae do not include material properties. The research conducted for the Wright study is almost exclusively in non-dimensional groups and includes material properties. Wright mentions the problem of testing in different sizes if the stress–strain relationship of the material being tested has a rate dependency. For constant geometry and materials, a 1/10 scale test will occur at a strain rate ten times as great as the same test in full scale. This can be a confusing point. To help place it in perspective, consider that velocity is invariant with scale. If we conduct a full-scale test at 1 km/s we also conduct a 1/10th scale test at 1 km/s. The reason is because the distance covered is scaled by the scale factor and the time to cover that distance is also scaled by the same factor. Considering strain rate (strain per unit time), we note that strain is non-dimensional so it is not affected by the scale factor; however, time, as noted above, does scale. The strain in a small scale test must occur in a shorter period of time, increasing the strain rate. In mechanical terms, the rate of deformation is ten times as great in the smaller scale. Rate effects are seen in the Hohler–Stilp data, a subset of which is in the Appendix. The collection lists velocities, penetrations and hole diameters for 36 tests of L/D = 10 flat-nosed tungsten projectiles fired into HzB,A steel targets. Most of the tests were made with projectiles that were 58.0 mm long. For the higher velocities the length was 41.7 mm. In effect, the higher-velocity tests were made at a scale of 72% relative to the others. Strengths are greater at the smaller scale due to strain rate effects, and the penetration data reflect this trend (Fig. 1). P/L values for the shorter (smaller) projectiles are approximately 1% smaller than those of the longer (larger) ones. Similar results were seen in Hohler–Stilp data for steel projectiles impacting steel targets and in hydrocode calculations (discussed below) using the Johnson–Cook strength model, which includes an explicit strain-rate factor.