GATE ME 2019 Set 1 — Question 44
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Manufacturing Processes → Forming → Plastic Deformation & Yield Criteria
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Question
A plane-strain compression (forging) of a block is shown in the figure. The strain in the -direction is zero. The yield strength () in uniaxial tension/compression of the material of the block is and it follows the Tresca (maximum shear stress) criterion. Assume that the entire block has started yielding. At a point where (compressive) and , the stress component is
Correct answer
(A) 340 MPa (compressive)
Solution
In plane strain forging, . For an isotropic material undergoing plastic deformation, the Poisson's ratio , which leads to the stress in the -direction being the average of the other two principal stresses: . This makes the intermediate principal stress. The Tresca criterion states that yielding occurs when the maximum shear stress reaches half the yield strength, or . Given (compressive). In a compression process like forging, the vertical stress is also compressive and typically larger in magnitude than the lateral stress . Thus, let and . Applying the Tresca criterion: . Therefore, (compressive).
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