Final answer:
The area under a stress-strain graph signifies the energy absorbed per unit volume, known as material toughness, calculated by integrating stress-strain up to fracture.
Step-by-step explanation:
The area under a stress-strain graph represents the energy per unit volume that is absorbed by the material until fracture. This is also known as the toughness of the material. To calculate this area, one may use the integration of the stress-strain curve, typically up to the point of fracture. For the linear portion of the graph, the area under the curve (which is a triangle) can be computed using the formula Area = 1/2 × stress × strain. But for the non-linear portion, numerical integration methods are generally used since the relationship between stress and strain is not a simple straight line.
The stress is defined as the ratio of force to area (σ = F/A), measured in N/m², and strain is the ratio of the change in length to the original length (a unitless quantity). When materials are subjected to tensile stress, it causes tensile strain, which can be seen as fractional elongation. Each material has its own characteristic stress-strain diagram illustrating the relationship between stress and strain and these curves are vital for understanding material properties.