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    • It is quite common for full scale

    2018-11-03

    It is quite common for full-scale penetration events to involve significant quantities of target material at strain rates of 103 or 104 per second. At 1/10 scale, the comparable regions will be at 104–105 per second. For many materials of interest, an order of magnitude change in strain rate in this region may make a significant difference in the stress–strain curve. Baker et al. [5] refer to “constitutive similarity” and describe the use of dissimilar materials to achieve constitutive similarity in different scales. Although we will not undertake a complete assessment of similarity methods, note that if materials in two scales are “constitutively similar”, matching a single value such as yield strength, ultimate tensile strength, or some other measure of strength, perhaps even a hardness value will suffice to ensure similar performance in both scales. This research shows that defining the Effective Flow Stress (EFS) for each case will enable satisfactory correlation between scales and varying materials, even if those materials are not constitutively similar. The significant change introduced in this research is to replace the characteristic yield or ultimate strength of the target with the Effective Flow Stress (EFS) of the target. Why is the change necessary? As previously stated, the target resistance is not a simple material property. It is related to the effective flow stress, which the authors consider to be a pseudo property. It is the effective flow stress in the target, based on the projectile diameter, the penetration rate, and the stress–strain relationship of the target material at the relevant strains, strain rates, and temperature, that defines the target\'s resistance to penetration. The flow stress changes throughout the penetration process, but it crf hormone is only a weak function of the projectile diameter and the penetration rate. For a given projectile and target pair, particularly for long (L/D > 4) projectiles, a single value of EFS not only works well for a single penetration, but it also works well over a relatively wide variation in impact velocities. One could easily be skeptical of such a statement. But, is it any more bold than claiming that the target yield strength or ultimate tensile stress is the value that works for all projectile diameters, projectile materials, and impact velocities, i.e. strain rates? What evidence exists to support the idea that EFS should be relatively constant? In testing by one of the authors (JR) at Southwest Research Institute, a number of targets were sectioned after being impacted by long-rod penetrators as shown in Fig. 2. There are a couple of things to note in the figure. First, the crater diameter remains relatively constant. Second, but what is not obvious in the picture, but could be seen after polishing the specimen, is that the extent of affected material beyond the crater was a relatively constant diameter. It is the material between the crater and the limit of the plastic flow that is primarily responsible for the resistance offered by the target. Even as the crater narrows near the end of the penetration, the extent of the plastically flowed material is relatively constant. Farrand [16] states, “Long rod penetrators are primarily consumed in the steady-state phase of penetration. This phase of penetration is where the projectile erodes at a constant rate producing a constant channel diameter”. The process is seen over a range of impact velocities (for example, 1000–2000 m/s in the analysis below). That view is supported by the WAPEN analytical model and can also be seen in hydrocodes or experimentally. Fig. 3 is a simulation of one of the experiments used in this research. It shows effective plastic strain (EPS) contours. It is clear that, in the numerical simulation, as the projectile penetrates and erodes, the crater diameter remains almost constant. Limiting the discussion to semi-infinite penetration, what happens as we change target and projectile materials? We will explore this question in more detail later in this paper, but action potential should be understood that the effective flow stress is a function of the dynamic stress–strain relationship of the target material at the relevant strain rate and temperature. For many ordnance velocity impacts, the temperature can be considered room temperature and the strain rate will generally be in the range of 103–105 per second. The EFS is a function of the crater radius and the crater radius will be influenced by the projectile properties. However, we are generally only interested in a relatively small set of materials. Most often we are concerned with materials such as tungsten alloys, steels, aluminums, copper, and depleted uranium penetrators. We find that many of these materials behave in a similar manner. However, uranium penetrators tend to produce a smaller crater diameter, resulting in a lower effective flow stress and deeper penetration as compared to a tungsten penetrator of comparable density, dimensions, and velocity.