A steel sheet with inhomogeneity factor of f0 = 0.995 is deforming in balanced biaxial tension with σ1a and σ2a as principal stresses in the uniform region ‘A’. What is the major principal stress σ1b in the groove ‘B’ at a small effective plastic strain of 0.05 if the material follows σ̅σ̅= 600 (0.004 +ε̅ε̅ )0.2 MPa hardening model. Find the value in MPa.
Question
A steel sheet with inhomogeneity factor of f0 = 0.995 is deforming in balanced biaxial tension with σ1a and σ2a as principal stresses in the uniform region ‘A’. What is the major principal stress σ1b in the groove ‘B’ at a small effective plastic strain of 0.05 if the material follows σ̅σ̅= 600 (0.004 +ε̅ε̅ )0.2 MPa hardening model. Find the value in MPa.
Solution
The problem involves the use of the hardening model equation and the inhomogeneity factor. Here are the steps to solve it:
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First, we need to understand the given information. The inhomogeneity factor f0 is 0.995, the effective plastic strain is 0.05, and the hardening model is given by σ̅σ̅= 600 (0.004 +ε̅ε̅ )^0.2 MPa.
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The hardening model equation is used to calculate the flow stress in the uniform region 'A'. Substituting the given effective plastic strain into the equation, we get:
σ̅σ̅= 600 (0.004 + 0.05)^0.2 = 600 * 0.054^0.2 = 600 * 0.277 = 166.2 MPa
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The principal stresses σ1a and σ2a in the uniform region 'A' are equal to the flow stress, so σ1a = σ2a = 166.2 MPa.
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The major principal stress σ1b in the groove 'B' is related to the principal stress in the uniform region 'A' by the inhomogeneity factor f0. So, σ1b = f0 * σ1a = 0.995 * 166.2 = 165.45 MPa.
So, the major principal stress σ1b in the groove 'B' is 165.45 MPa.
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