Theories of failure

theories of failure when to consider

1. Theories of failure Presented by Onkar A. Powar

2. Failing factors Stress: 1. Principal or Normal 2. Shear Strain: 1.Principal Energy: 1.Maximum Strain Energy 2. Shear Strain Energy

3. Failure criteria’s Maximum principal stress theory Maximum shear stress theory Maximum principal strain theory Maximum strain energy theory Maximum distortion energy theory

4. Maximum principal stress theory (Rankine theory) Suitable for brittle materials Mohr circle plot should be within area shown bellow • Let σ 1, σ 2, σ 3 are the principal stresses at the critical point in component due to applied loading , and let σ 1 > σ 2 > σ 3 Then failure occurs when 𝜎 1 ≥ 𝑆𝑦𝑡 𝑜𝑟 𝜎1 ≥ 𝑆𝑢𝑡

5. Maximum shear stress theory ( Guest – Tresca ) Suitable for ductile materials

6. Maximum principal strain theory   (Saint - venant   ) Not recommended This Theory assumes that failure occurs when the maximum strain for a complex state of stress system becomes equals to the strain at yield point in the tensile test for the three dimensional complex state of stress system.

7. Maximum / total strain energy theory (Haigh) Good for ductile materials The theory assumes that the failure occurs when the total strain energy for a complex state of stress system is equal to that at the yield point a tensile test.

8. Maximum distortion energy (SHEAR STRAIN) theory (Von – Mises & Hencky ) Highly recommended This theory states that the failure occurs when the maximum shear strain energy component for the complex state of stress system is equal to that at the yield point in the tensile test.

9. Comparison x