Give the information requested below.  a) On the stress-strain graph below determine the yield strength. Be sure to sketch precisely how you do this. b) Determine the value for the modulus of elasticity for this material. c) Determine the value for the modulus of resilience for this material.

Elements Of Electromagnetics
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Give the information requested below.

 a) On the stress-strain graph below determine the yield strength. Be sure to sketch precisely how you do this.

b) Determine the value for the modulus of elasticity for this material.

c) Determine the value for the modulus of resilience for this material.

d) Estimate the toughness of this material.

e) What is the ductility (%EL) of this material?

This graph is a stress-strain curve that illustrates the relationship between stress (σ) and strain (ε) for a material under tensile testing. The x-axis represents strain, ranging from 0.000 to 0.150, while the y-axis represents stress in megapascals (MPa), ranging from 0 to 450 MPa.

Key features of the graph:

1. **Initial Region**: The curve starts steeply, indicating the elastic deformation region where the material returns to its original shape when the load is removed.

2. **Elastic Limit to Ultimate Strength (TS - Tensile Strength)**: The curve peaks at this point, denoted as "TS," representing the maximum stress the material can withstand while being stretched. In this graph, the tensile strength is around 400 MPa.

3. **Necking Region and Failure (F - Fracture Point)**: After reaching the ultimate tensile strength, the curve gradually declines, showing the material undergoing plastic deformation, leading to necking and eventual fracture. The endpoint is marked as "F," where the material finally breaks.

The graph provides crucial insights into the material's mechanical properties, such as elasticity, yield strength, tensile strength, and ductility.
Transcribed Image Text:This graph is a stress-strain curve that illustrates the relationship between stress (σ) and strain (ε) for a material under tensile testing. The x-axis represents strain, ranging from 0.000 to 0.150, while the y-axis represents stress in megapascals (MPa), ranging from 0 to 450 MPa. Key features of the graph: 1. **Initial Region**: The curve starts steeply, indicating the elastic deformation region where the material returns to its original shape when the load is removed. 2. **Elastic Limit to Ultimate Strength (TS - Tensile Strength)**: The curve peaks at this point, denoted as "TS," representing the maximum stress the material can withstand while being stretched. In this graph, the tensile strength is around 400 MPa. 3. **Necking Region and Failure (F - Fracture Point)**: After reaching the ultimate tensile strength, the curve gradually declines, showing the material undergoing plastic deformation, leading to necking and eventual fracture. The endpoint is marked as "F," where the material finally breaks. The graph provides crucial insights into the material's mechanical properties, such as elasticity, yield strength, tensile strength, and ductility.
Expert Solution
Step 1

Yield strength:-  The yield strength is defined as the point at which the material starts to deform plastically.

So observe the graph where the material gets deformed and mark that point as yield strength.

In case of some Brittle materials

To find yield strength, the predetermined amount of permanent strain is set along the strain axis of the graph, to the right of the origin (zero). A straight line is drawn through Point (permanent strain) at the same slope as the initial portion of the stress-strain curve.

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