How do engineers predict when solid materials will fail?

Material failure theory is an interdisciplinary field combining materials science and solid mechanics to predict under what conditions solid materials will break or yield under external loads. It relies on mathematical failure criteria expressed as functions in stress or strain space to separate failed states from unfailed ones. Depending on conditions like temperature or stress state, materials typically fail in either a brittle or ductile manner.

What we know

• Material failure theory attempts to predict the conditions under which solid materials fail under external loads. [2]
• The failure of a material is generally classified into brittle failure or ductile failure. [2]
• Failure criteria are mathematically expressed as functions in stress or strain space that separate failed from unfailed states. [2]
• The Mohr-Coulomb theory describes the response of brittle materials like concrete or rubble piles to shear and normal stress. [3]
• The Goodman relation quantifies the interaction of mean and alternating stresses on the fatigue life of a material. [5]

Still open

• A precise physical definition of a failed state is not easily quantified, leading to several working definitions in the engineering community.

Where to go next

• a case in pointWhat is the Mohr-Coulomb theory?
• how it workedHow does the Tsai-Hill criterion handle composite materials?
• what followedHow does the Goodman relation measure fatigue life?
• the bigger pictureHow does materials science study solid mechanics?
• compared withWhat distinguishes brittle failure from ductile yield?
• an unexpected connectionHow do rubble piles and concrete share mathematical failure models?The Mohr-Coulomb theory applies its mathematical model to both engineered structures like concrete and loose aggregate materials like rubble piles.

Sources

• [1]material failure theory (Wikidata Q6142056) · CC0 1.0
• [2]Material failure theory · CC BY-SA 4.0
• [3]Mohr–Coulomb theory · CC BY-SA 4.0
• [4]Tsai-Hill failure criterion · CC BY-SA 4.0
• [5]Goodman relation · CC BY-SA 4.0