BI6727 Supplier br Material modeling This research attempts

Material modeling This research attempts to relate the penetration performance back to the material properties of the projectile and target. But, what properties are important? Assuming that one is working in an impact regime where thermal effects can be ignored, the primary requirement is to define the mechanical relationship between stress and strain. In Johnson and Cook\'s original paper presenting their constitutive model [8], they explain that their motivation was to develop a computationally-efficient method to estimate the von Mises flow stress that could be calibrated with a relatively small number of laboratory tests. Per Graff [17], “The function of constitutive equations is to relate states of deformation with states of traction.” Graff provides a brief review of the methods for evaluating elastic material response that were developed by Green and Cauchy. Graff points out that Green\'s method is based on the assumption of small strains, and that the relationship must be derivable from an internal BI6727 Supplier function. He notes that the Cauchy method starts with the assumption of a direct relationship between stress and strain. With various assumptions, we find that elastic constants such as Young\'s modulus, bulk modulus, and Poisson\'s ratio can be defined. For all of the theory, the problem eventually comes down to running experiments or tests to determine the values of the various elastic constants and how many constants will suffice to describe the material. The maximum would appear to be 81 constants, but symmetry can reduce that number to 36 and perhaps down to 21 or even down to 2. Recall that this is the situation for elastic behavior. Many research efforts strive to develop strength models that capture this complex behavior. There are theoretically-based approaches as well as strictly empirical approaches. One of the most widely used material models for dealing with very dynamic events such as penetration mechanics is the Johnson–Cook (JC) strength model. The appeal of this model is that it does a reasonably good job for many problems and it is computationally efficient to implement. It has proven to be an extremely important model, but it is not perfect. Per Meyers [18], the well-known Zerilli-Armstrong (ZA) [19] model is physically based on dislocation motion brought on by thermal activation. The research leading to the ZA model showed that significant strain rate response differences occur for face centered cubic (FCC) as compared to body centered cubic (BCC) metals. Meyers states that, as compared to Taylor Anvil experiments, “The Zerilli-Armstrong model shows a better correlation with the results for a BCC metal (Fe).” Zerilli–Armstrong and Johnson–Cook models can provide essentially the same results for FCC materials. Banerjee [20] compares the empirical JC parameters with another more physical model known as the Mechanical Threshold Stress model. For this discussion, we shall limit ourselves to the more common JC model. The JC model is defined aswhere A, B, C, m, and n are constants, is the plastic strain, is the ratio of the strain rate to a reference strain rate, and is a non-dimensional, or homologous temperature given bywhere is the temperature at which the constant A is determined and is the melting temperature of the material. The JC parameters can be obtained from “torsion tests over a wide range of strain rates, static tensile tests, dynamic Hopkinson bar tensile tests, and Hopkinson bar tests at elevated temperatures” [8]. Being an empirical model, capillary bed would seem that a set of experiments such as the ones listed above, devised to produce the data needed to define the constants, would produce unequivocal values. Unfortunately, such is not the case. First, the constant A is handled differently by different researchers. Some take A to represent the 0.2% offset yield. Others assume that A is nothing more than a regression parameter and allow it to be set on the best overall fit with the other parameters. Still others take a value that would be more consistent with the first instance of yield, well below the 0.2% offset. The problem with using these various methods is that a single set of laboratory tests to characterize a material can be interpreted to give a wide range of JC parameters. Thus, one must be very careful in selecting the parameters to use for a specific problem. If A has a physical meaning associated with it, it may be possible to estimate the JC parameters for a slightly different heat treatment of an alloy from which the original parameters were evaluated. If A is strictly a regression parameter, no such adjustment should be attempted. Still, it would seem reasonable to expect consistent estimates of the parameters from a set of data. This is not the case.