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Which of the following theory over estimates the elastic strength of ductile material?

Which of the following theory over estimates the elastic strength of ductile material? Correct Answer Maximum principal strain theory

Concept:

Maximum principal strain theory(St. Venant theory):

  • According to this theory, yielding will occur when the maximum principal strain just exceeds the strain at the tensile yield point in either simple tension or compression.
  • This theory overestimates the behavior of ductile material.
  • The theory does not fit well with the experimental results except for brittle materials biaxial tension.

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Maximum principal stress theory(Rankine Theory):

  • A material fails by fracturing when the largest principal stress exceeds the ultimate strength in a simple tension test.
  • The crack will start at the most highly stressed point in a brittle material when the largest Principal stress at that point reaches ultimate strength.
  • This theory of yielding has a very poor agreement with experiment. However, the theory has been used successfully for brittle materials.
  • It is used to describe the fracture of brittle materials such as cast iron.

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Strain Energy Theory (Haigh’s Theory):

  • This theory is based on the assumption that strains are recoverable up to the elastic limit.
  • The energy absorbed by the material at failure up to this point is a single-valued function independent of the stress system causing it.
  • The strain energy per unit volume causing failure is equal to the strain energy at the elastic limit in simple tension.

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Shear Strain Energy Theory​(Von-Misses Theory):

  • It is also known as the Maximum Energy of Distortion theory.
  • The Von-Mises criterion considers the diameters of all three Mohr’s circles as contributing to the characterization of yield onset in isotropic materials. 
  • This theory provides the best agreement between experiment and theory and, along with the Tresca theory, is very widely used.

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