What physical property is related to the "maximum stress that can be applied before failure"?

The physical property that relates to the "maximum stress that can be applied before failure" is tensile strength. Tensile strength is defined as the maximum amount of tensile (stretching) stress that a material can withstand before failure. This means it is the highest point on the stress-strain curve of the material, representing the ultimate resistance to being pulled apart.

In contrast, while shear strength pertains to how much force a material can withstand before it fails in shear, compressive strength relates to the maximum amount of compressive load a material can handle before failing. Elasticity refers to the ability of a material to return to its original shape after the stress is removed, but does not directly define how much stress a material can take before failing. Therefore, tensile strength is the most relevant measure in this context.