How is proof stress defined in materials science?

Proof stress is defined specifically as the stress level at which a material exhibits a specified amount of permanent (plastic) deformation. This characteristic makes it particularly useful in engineering and material science, as it provides insight into how a material will behave when subjected to stress beyond its elastic limits.

Selecting this definition emphasizes the critical point where the material's deformation transitions from elastic behavior, where it can return to its original shape after unloading, to plastic behavior, where the deformation becomes permanent. Proof stress is typically quantified at a specific strain level, often 0.2% for metals, thus offering a reliable benchmark for engineers to assess the material's strength in practical applications.

The other definitions, while related to material properties, do not capture the essence of proof stress as effectively. The maximum stress a material can endure refers to ultimate tensile strength rather than the defined yield point connected to stored energy and deformation. Similarly, recovery stress focuses on behavior after unloading, and the stress point at which a material begins to yield pertains to the onset of yielding rather than the accompanying plastic deformation criteria that proof stress measures.