1.3. Plastic behavior

There are materials whose strain does not vanish upon removal of the applied load. This is in contrast with elastic materials that we have learnt till now - elastic materials come back to their original shape upon removal of the applied load.

Plastic behavior refers to the characteristic of certain materials that do not return to their original shape after the load causing deformation is removed. Unlike elastic materials, which can regain their shape, plastic materials will retain some deformation permanently. This means that even when the load is taken away, there will still be some strain present in the material.

Imagine a piece of clay. If you press it and then release your hands, it retains the shape of your fingers. This is similar to how plastic materials behave, while a rubber band, when stretched and then released, goes back to its original form, showcasing elastic behavior.

Consider a steel bar on which a uniformly distributed load σ is applied at both its ends. We have shown the applied stress σ vs. the longitudinal strain ϵ curve in Figure 6.

When a steel bar is subjected to a uniform load, we can plot the relationship between the applied stress (the force per unit area) and the resulting strain (the deformation experienced by the material). The graph typically starts linear, indicating a straightforward relationship where strain increases proportionally with stress. However, as more load is applied, the curve begins to bend, indicating a change in how the material responds to the stress, leading eventually to yielding and then breaking.

Think about stretching a rubber band. Initially, when you apply a small force, it stretches easily (linear behavior), but if you stretch it too much, it may reach a point where it won’t return to its original shape at all – this represents yielding in the stress-strain curve.

As we keep increasing the load, there comes a point where the body yields, i.e., the beam elongates a lot even with very small increment in the applied load. The regime between the yield point and the breaking point is called the plastic regime.

The transition from elastic behavior to plastic behavior is characterized by the yield point, where the material begins to deform plastically. In this context, 'yielding' means that if you keep applying more load, the strain increases significantly with little additional stress. This stage is crucial because it indicates the limits of what the material can withstand before it permanently deforms.

This is akin to trying to bend a piece of metal like a spoon. Initially, it can bend back to its original shape when you apply pressure, but beyond a certain point, it will bend permanently. This moment, where further increases in pressure yield substantial bending without much added force, is similar to the yield point in plastic behavior.

If we decrease the applied load in this regime, the original curve is not traced back as shown in the figure. Hence, when the stress becomes zero, the body retains some strain. This strain is called plastic strain (ϵp).

Once a material has yielded and goes through the plastic regime, even if we remove the applied load, it will not return to its initial shape. The deformation it retains after the load is removed is referred to as plastic strain. This is important from a design perspective because it indicates that the material has been altered permanently and may no longer function as intended if the strain is excessive.

Consider a piece of modeling clay. If you mold it into a shape and then remove it from the pressure, it holds that shape permanently. This permanent change in shape parallels how plastic strain works in materials: once the load is removed, it doesn't go back.

The yielding behavior is common in other materials too which give them ductile property. We also have brittle materials like glass. They have a different stress-strain relationship.

Ductile materials are those that can undergo significant plastic deformation before breaking, while brittle materials fail with little or no plastic deformation. The stress-strain curve for ductile materials exhibits yielding behavior leading to plastic strain, while for brittle materials, it rises linearly until fracture without the yielding phase. This indicates essential differences in how materials behave under stress and impacts how they can be used in applications.

Think of a piece of soft metal like a copper wire, which bends and stretches without breaking (ductile). In contrast, a thin, fragile piece of glass, when stress is applied, will crack suddenly without bending (brittle). This highlights the significant difference in behavior between ductile and brittle materials.

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