Failure Theories for Ductile Materials

Ductile materials have ${ϵ}_f\ge 0.05$, such that the material has a minimum fracture strain of 0.05. Fracture strain is the strain at which a material ultimately fails or breaks.

Furthermore, we have $S_{yt}=S_{yc}=S_y$, where these are the compressive and tensile yield strengths of the material. This simplification is often done for ductile materials, but we can use Coulomb-Mohr Theory if it isn’t true.

Applicable failure theories to determine yield criteria:

• Maximum Shear Stress Theory
  • Quick, easy, conservative
  • Useful for design purposes
• Distortion Energy Theory
  • Not as conservative, need to consider the $n$ value carefully
  • Useful when we want to learn why a part failed
• Coulomb-Mohr Theory
  • Useful when yield strengths are unequal in tension and compression
  • Magnesium alloys and gray cast irons