Elastic and plastic behaviour — common mistakes

Remember the distinction: 'limit of proportionality' is where Hooke's Law stops being true (graph curves), while 'elastic limit' is where plastic deformation starts (won't return to original shape).

Stiffness (quantified by Young Modulus) is a material's resistance to elastic deformation; how much force is needed to produce a small extension. Strength refers to the material's ability to withstand a large force without fracturing. A material can be stiff but not strong (e.g., cast iron is stiff but brittle, so not strong against bending).

Strain is the ratio of two lengths (extension/original length). Since both numerator and denominator have the same unit (e.g., metres), they cancel out, leaving strain as a pure number without any units.

Generally, increasing temperature tends to make materials less stiff (lower Young Modulus) and more ductile (more prone to plastic deformation before fracturing). This is because higher thermal energy allows atoms to move more easily within the material's structure.

A force-extension graph depends on the specific dimensions of the object being tested (its length and area). A stress-strain graph is independent of dimensions and describes the fundamental properties of the material itself. The gradient of the linear part of a stress-strain graph is the Young Modulus, a material constant.