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The ultimate tensile strength of a material is 400 MPa and the elongation up to maximum load is 35%. If the material obeys power law of hardening, then the true stress-true strain relation (stress in MPa) in the plastic deformation range is:
- a)σ = 540ε0.30
- b)σ = 775ε0.30
- c)σ = 540ε0.35
- d)σ = 775ε0.35
Correct answer is option 'B'. Can you explain this answer?
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The power law of hardening is given by:
σ = kε^n
Where σ is the true stress, ε is the true strain, k is a constant, and n is the strain hardening exponent.
To find k and n, we can use the given information:
At the maximum load, σ = 400 MPa and ε = 0.35.
Substituting these values into the equation:
400 = k(0.35)^n
We need another data point to solve for k and n. Let's assume that at a strain of 0.5, the true stress is 200 MPa.
Substituting these values into the equation:
200 = k(0.5)^n
Now we have two equations and two unknowns (k and n). Dividing the two equations:
400/200 = (0.35/0.5)^n
2 = 0.7^n
Taking the logarithm of both sides:
n = log(2)/log(0.7) ≈ 2.449
Substituting this value into one of the equations:
400 = k(0.35)^2.449
k ≈ 1,180.9
Now we can write the true stress-true strain relation:
σ = 1,180.9ε^2.449
σ = kε^n
Where σ is the true stress, ε is the true strain, k is a constant, and n is the strain hardening exponent.
To find k and n, we can use the given information:
At the maximum load, σ = 400 MPa and ε = 0.35.
Substituting these values into the equation:
400 = k(0.35)^n
We need another data point to solve for k and n. Let's assume that at a strain of 0.5, the true stress is 200 MPa.
Substituting these values into the equation:
200 = k(0.5)^n
Now we have two equations and two unknowns (k and n). Dividing the two equations:
400/200 = (0.35/0.5)^n
2 = 0.7^n
Taking the logarithm of both sides:
n = log(2)/log(0.7) ≈ 2.449
Substituting this value into one of the equations:
400 = k(0.35)^2.449
k ≈ 1,180.9
Now we can write the true stress-true strain relation:
σ = 1,180.9ε^2.449
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The ultimate tensile strength of a material is 400 MPa and the elongation up to maximum load is 35%. If the material obeys power law of hardening, then the true stress-true strain relation (stress in MPa) in the plastic deformation range is:a)σ= 540ε0.30b)σ= 775ε0.30c)σ= 540ε0.35d)σ= 775ε0.35Correct answer is option 'B'. Can you explain this answer?
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The ultimate tensile strength of a material is 400 MPa and the elongation up to maximum load is 35%. If the material obeys power law of hardening, then the true stress-true strain relation (stress in MPa) in the plastic deformation range is:a)σ= 540ε0.30b)σ= 775ε0.30c)σ= 540ε0.35d)σ= 775ε0.35Correct answer is option 'B'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The ultimate tensile strength of a material is 400 MPa and the elongation up to maximum load is 35%. If the material obeys power law of hardening, then the true stress-true strain relation (stress in MPa) in the plastic deformation range is:a)σ= 540ε0.30b)σ= 775ε0.30c)σ= 540ε0.35d)σ= 775ε0.35Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The ultimate tensile strength of a material is 400 MPa and the elongation up to maximum load is 35%. If the material obeys power law of hardening, then the true stress-true strain relation (stress in MPa) in the plastic deformation range is:a)σ= 540ε0.30b)σ= 775ε0.30c)σ= 540ε0.35d)σ= 775ε0.35Correct answer is option 'B'. Can you explain this answer?.
The ultimate tensile strength of a material is 400 MPa and the elongation up to maximum load is 35%. If the material obeys power law of hardening, then the true stress-true strain relation (stress in MPa) in the plastic deformation range is:a)σ= 540ε0.30b)σ= 775ε0.30c)σ= 540ε0.35d)σ= 775ε0.35Correct answer is option 'B'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The ultimate tensile strength of a material is 400 MPa and the elongation up to maximum load is 35%. If the material obeys power law of hardening, then the true stress-true strain relation (stress in MPa) in the plastic deformation range is:a)σ= 540ε0.30b)σ= 775ε0.30c)σ= 540ε0.35d)σ= 775ε0.35Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The ultimate tensile strength of a material is 400 MPa and the elongation up to maximum load is 35%. If the material obeys power law of hardening, then the true stress-true strain relation (stress in MPa) in the plastic deformation range is:a)σ= 540ε0.30b)σ= 775ε0.30c)σ= 540ε0.35d)σ= 775ε0.35Correct answer is option 'B'. Can you explain this answer?.
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