GATE ME 2023 Set 1 — Question 57
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Engineering Materials → Structure & Properties → Mechanical Properties & Stress-Strain
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Question
Ignoring the small elastic region, the true stress () – true strain () variation of a material beyond yielding follows the equation MPa. The engineering ultimate tensile strength value of this material is ________ MPa. (Rounded off to one decimal place)
Correct answer
206 to 207
Solution
Given the true stress-true strain relationship: , where MPa and .At the point of ultimate tensile strength (where necking begins), the condition for instability in tension is:For the power law , the derivative is:Setting the derivative equal to the true stress:Thus, the true strain at the ultimate tensile strength (UTS) is .The true stress at UTS is:The relationship between engineering stress () and true stress () is given by:where is the engineering strain. Since true strain , we have . Substituting this into the stress relationship:At the ultimate tensile strength point:Performing the calculation:Rounding to one decimal place, the engineering ultimate tensile strength is 206.5 MPa.
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