Toughness is a term that relates to both strength and ductility. The fracture toughness, for example, is defined as the total area under the stress-strain curve to fracture, . This area, called the modulus of toughness, is the strain energy per unit volume required to cause the material to fracture. A similar term, but defined within the elastic limit of the material, is called the modulus of resilience, where ǫy is the strain at yield. If the stress-strain is linear to σ = Sy , then it can be shown that . For the material in Prob. 2–9: (a) Determine the modulus of resilience, and (b) Estimate the modulus of toughness, assuming that the last data point corresponds to fracture.