Final answer:
The gradient of a stress-strain graph represents the material's elastic modulus within the linear limit before the limit of proportionality.
Step-by-step explanation:
The gradient of a stress-strain graph, also known as the slope, represents the material's elastic modulus within the linear limit before the limit of proportionality. The elastic modulus is a measure of a material's stiffness and resistance to deformation. It indicates how much stress is needed to produce a given amount of strain.
For stress values within the linear limit, the stress-strain relationship is described by Hooke's law, which states that stress is directly proportional to strain. The proportionality constant in this relationship is the elastic modulus.
As an example, consider a stress-strain graph of a ductile metal. The gradient of the graph at low stress values represents the elastic modulus of the metal. If the slope of the graph is steeper, it means the material is stiffer and requires more stress to cause strain.