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FIGURE 4-1 A schematic illustration of the stress-strain curves for two idealized solids. The material corresponding to (a) exhibits ideal plasticity, in which there is no deformation until a critical stress (the yield point) is exceeded, at which point the material continues to deform at a constant rate until the stress is removed. The instant the stress falls below the critical value, such a material will stop deforming—that is, it exhibits no recovery. In contrast, linear elastic–ideal plastic material deforms elastically as the stress is applied before the plastic yield point. As before, the material deforms irreversibly when the yield point is exceeded. But in this case, upon removal of the stress, the elastic portion of the deformation is recovered as illustrated in (b). Real materials always exhibit some degree of elastic recovery. SOURCE: Fung and Tong, 2001, Copyright 2001, World Scientific Publishing Co.

A contour gauge is a device familiar to craftsmen. It consists of a linear array of steel pins held parallel by a light clamping force. A typical device is illustrated in Figure 4-2. The pins are held in place with friction and therefore do not move until the application of stress. The relative motion in this case is caused by moving onto a shaped surface, but the principal is the same as in the armor test. In the latter case, the relative motion is the same, but it is the back face of the armor that moves into the backing material. If the backing material exhibited ideal plasticity, the resultant cavity would be a record of the maximum deflection of the BFD of the armor system, but this is manifestly not the case.

As illustrated in Figure 4-1b, the deformation of real materials differs in important ways from ideal plasticity. The first distinction is that all real materials have a finite elastic modulus. The consequence of this is that the material deforms reversibly prior to the onset of yielding and will exhibit elastic recovery when the load is removed. In the context of armor testing, this means that the cavity that remains in the backing material after the armor system has been struck by the projectile will be smaller than the maximum BFD.



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