the energy which is introduced in the material before fracture during a tensile test (i.e., the material resistance in energy temrs) is the area under the stress-strain curve.
However, if you are working in fracture mechanics, please, take into account that there is no a simple relation between such area and fracture resistance in the presence of cracks or notches. To my knowledge, the Strain Energy Density Approach (SED, linear-elastic) is the most comprehensive model to assess fracture conditions by using the area below the stress-strain curve. This being said, it also requires defining a control volume (where the SED must be measured) which depends on the material fracture thougness (among other material properties).