Acquaintance with Plasticity in high-strain cases
This post is a continuation of the Getting Started with Abaqus series
Many metals have approximate linear elastic behavior at low strain magnitudes, and the stiffness of the material, known as its Young's modulus or elastic modulus, is constant.
Figure 1. Stress-strain behavior for a linear elastic material, such as steel, at small strains.
Figure 2. Stress-strain behavior for a linear elastic material at higher strains.
👉At higher stress and strain magnitudes, metals begin to have nonlinear, inelastic behavior which is referred to as plasticity.
➡️A material's switch from elastic behavior (where it returns to its original shape) to plastic behavior (where it deforms permanently) happens at a specific point on its stress-strain curve called the yield point. This point tells us the stress at which plastic deformation begins. In most metals, the initial yield stress is considerably small, around 0.05 to 0.1% of the material's stiffness (elastic modulus).
👉When metals are stretched, they initially experience temporary changes in shape called elastic strains. These changes disappear completely when the stress is removed, like a rubber band returning to its original size. However, once the stress surpasses a certain limit (yield stress), the metal suffers permanent deformations called plastic strains. These permanent changes remain even after the stress is gone, for example: a bent paperclip holding its new shape. Both types of strains (elastic and plastic) contribute to the overall deformation of the metal after the yield point.
👉Metals lose their resistance to bending (stiffness) significantly when they reach their yield point (as shown in Figure 2). However, a metal (ductile) that has yielded will regain its original stiffness once the pressure is removed (Figure 2). Interestingly, the permanent deformation of the metal often makes it harder to yield again under future stress this phenomenon known as work hardening.
👉 When metals deform permanently (as the plastic model), they tend to maintain their volume almost entirely. Simulating this behavior in elastic-plastic situations significantly limits the types of elements that can be used effectively.
👉When a metal stretches under tension, it might develop a localized area of extreme thinning called necking (illustrated in Figure 2). This happens despite the stress measured (force per original area) being lower than the metal's true strength. This behavior arises from the test setup, the inherent differences between tension and compression, and the way we measure stress and strain. For instance, compressing the same material won't cause necking because the sample doesn't thin under those forces.
In a nutshell:
🔖A good model describing metal plasticity should account for these differences in behavior regardless of the sample shape or applied load. To achieve this, the standard definitions of stress and strain (using the subscript for original undeformed values) need to be replaced with measures that consider the actual change in area during deformation.
