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Ignoring the small elastic region, the true stress versus true strain relationship for a
metal is given by σ=400ϵ
0.3 MPa. Determine the engineering ultimate tensile strength of
material?
metal is given by σ=400ϵ
0.3 MPa. Determine the engineering ultimate tensile strength of
material?
Most Upvoted Answer
Ignoring the small elastic region, the true stress versus true strain ...
Engineering Ultimate Tensile Strength Calculation
1. Given:
- True stress versus true strain relationship: σ = 400ϵ^0.3 MPa
2. Explanation:
- The true stress-strain relationship provided is in the form of σ = 400ϵ^0.3 MPa. This relationship represents the behavior of the material in the plastic region, excluding the small elastic region.
3. Conversion to Engineering Stress-Strain:
- To determine the engineering ultimate tensile strength, we need to convert the true stress to engineering stress. The relationship between true stress and true strain is given by σ = Kε^n, where K is the strength coefficient and n is the strain-hardening exponent.
- In engineering stress-strain, σ_e = σ(1+ε) where ε is the engineering strain. So, we have σ_e = 400(1+ε)^0.3 MPa.
4. Engineering Ultimate Tensile Strength Calculation:
- The engineering ultimate tensile strength is obtained at the point of fracture, where ε = ε_f and σ_e = σ_u.
- Therefore, at fracture, σ_u = 400(1+ε_f)^0.3 MPa.
5. Conclusion:
- The engineering ultimate tensile strength of the material can be calculated using the relationship obtained from the true stress versus true strain data provided. This conversion helps in determining the behavior of the material in the plastic region, which is important for engineering applications.
1. Given:
- True stress versus true strain relationship: σ = 400ϵ^0.3 MPa
2. Explanation:
- The true stress-strain relationship provided is in the form of σ = 400ϵ^0.3 MPa. This relationship represents the behavior of the material in the plastic region, excluding the small elastic region.
3. Conversion to Engineering Stress-Strain:
- To determine the engineering ultimate tensile strength, we need to convert the true stress to engineering stress. The relationship between true stress and true strain is given by σ = Kε^n, where K is the strength coefficient and n is the strain-hardening exponent.
- In engineering stress-strain, σ_e = σ(1+ε) where ε is the engineering strain. So, we have σ_e = 400(1+ε)^0.3 MPa.
4. Engineering Ultimate Tensile Strength Calculation:
- The engineering ultimate tensile strength is obtained at the point of fracture, where ε = ε_f and σ_e = σ_u.
- Therefore, at fracture, σ_u = 400(1+ε_f)^0.3 MPa.
5. Conclusion:
- The engineering ultimate tensile strength of the material can be calculated using the relationship obtained from the true stress versus true strain data provided. This conversion helps in determining the behavior of the material in the plastic region, which is important for engineering applications.
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Ignoring the small elastic region, the true stress versus true strain relationship for a metal is given by σ=400ϵ 0.3 MPa. Determine the engineering ultimate tensile strength of material?
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Ignoring the small elastic region, the true stress versus true strain relationship for a metal is given by σ=400ϵ 0.3 MPa. Determine the engineering ultimate tensile strength of material? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Ignoring the small elastic region, the true stress versus true strain relationship for a metal is given by σ=400ϵ 0.3 MPa. Determine the engineering ultimate tensile strength of material? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ignoring the small elastic region, the true stress versus true strain relationship for a metal is given by σ=400ϵ 0.3 MPa. Determine the engineering ultimate tensile strength of material?.
Ignoring the small elastic region, the true stress versus true strain relationship for a metal is given by σ=400ϵ 0.3 MPa. Determine the engineering ultimate tensile strength of material? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Ignoring the small elastic region, the true stress versus true strain relationship for a metal is given by σ=400ϵ 0.3 MPa. Determine the engineering ultimate tensile strength of material? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ignoring the small elastic region, the true stress versus true strain relationship for a metal is given by σ=400ϵ 0.3 MPa. Determine the engineering ultimate tensile strength of material?.
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