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Consider a material with the stress-strain diagram shown where the yield point is 400 MPa (similar to a generic metal, but approximated to make the calculations easier). The material is stressed to 900 MPa. What is the change in the modulus of resilience? σ (MPa) 1200- 800- 400- a more realistic curve 0.10 0.20 0.30 0.40

Consider a material with the stress-strain diagram shown where the yield point is 400 MPa (similar to a generic metal, but approximated to make the calculations easier). The material is stressed to 900 MPa. What is the change in the modulus of resilience? σ (MPa) 1200- 800- 400- a more realistic curve 0.10 0.20 0.30 0.40

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Answer should be in MPa

**Text:** "Consider a material with the stress-strain diagram shown where the yield point is 400 MPa (similar to a generic metal, but approximated to make the calculations easier). The material is stressed to 900 MPa. What is the change in the modulus of resilience?" **Graph/Diagram Explanation:** - **Axes:** - The vertical axis represents stress (\( \sigma \)) in megapascals (MPa), ranging from 0 to 1200 MPa. - The horizontal axis represents strain (\( \varepsilon \)), ranging from 0 to 0.40. - **Curve:** - The graph shows a blue curve labeled "a more realistic curve." - The curve starts at the origin and increases linearly until reaching the yield point at 400 MPa. - Beyond the yield point, the curve continues to rise non-linearly and peaks around 1200 MPa at a strain of approximately 0.30. - After the peak, the curve slopes downward slightly, indicating material behavior beyond the ultimate tensile strength. This diagram is a typical stress-strain curve used to analyze the mechanical properties of materials, illustrating elastic and plastic deformation regions.
Transcribed Image Text:**Text:** "Consider a material with the stress-strain diagram shown where the yield point is 400 MPa (similar to a generic metal, but approximated to make the calculations easier). The material is stressed to 900 MPa. What is the change in the modulus of resilience?" **Graph/Diagram Explanation:** - **Axes:** - The vertical axis represents stress (\( \sigma \)) in megapascals (MPa), ranging from 0 to 1200 MPa. - The horizontal axis represents strain (\( \varepsilon \)), ranging from 0 to 0.40. - **Curve:** - The graph shows a blue curve labeled "a more realistic curve." - The curve starts at the origin and increases linearly until reaching the yield point at 400 MPa. - Beyond the yield point, the curve continues to rise non-linearly and peaks around 1200 MPa at a strain of approximately 0.30. - After the peak, the curve slopes downward slightly, indicating material behavior beyond the ultimate tensile strength. This diagram is a typical stress-strain curve used to analyze the mechanical properties of materials, illustrating elastic and plastic deformation regions.
Expert Solution
Step 1: Determine the given data

Given : 

  • Yield stress sigma subscript y space equals space 400 space M P a (initial)
  • Material stressed upto sigma subscript f space equals space 900 space M P a (final)


To find : 

  • Change in modulus of resilience 
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