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From the plot of yield strength versus (grain diameter)-1/2 for a 70 Cu-30 Zn cartridge brass, shown in Animated Figure 7.15 do the following: (a) Determine the value of the constant of Equation 7.7. MPa (b) Determine the value of the constant ky of Equation 7.7. i MPa-(mm)¹/2 (c) Predict the yield strength of this alloy when the average grain diameter is 9.0 × 10-³ mm. i MPa

From the plot of yield strength versus (grain diameter)-1/2 for a 70 Cu-30 Zn cartridge brass, shown in Animated Figure 7.15 do the following: (a) Determine the value of the constant of Equation 7.7. MPa (b) Determine the value of the constant ky of Equation 7.7. i MPa-(mm)¹/2 (c) Predict the yield strength of this alloy when the average grain diameter is 9.0 × 10-³ mm. i MPa

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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From the plot of yield strength versus (grain diameter)\(^{-1/2}\) for a 70 Cu-30 Zn cartridge brass, shown in Animated Figure 7.15, do the following: (a) Determine the value of the constant \(\sigma_0\) of Equation 7.7. [Input Box] MPa (b) Determine the value of the constant \(k_y\) of Equation 7.7. [Input Box] MPa-(mm)\(^{1/2}\) (c) Predict the yield strength of this alloy when the average grain diameter is \(9.0 \times 10^{-3}\) mm. [Input Box] MPa
Transcribed Image Text:From the plot of yield strength versus (grain diameter)\(^{-1/2}\) for a 70 Cu-30 Zn cartridge brass, shown in Animated Figure 7.15, do the following: (a) Determine the value of the constant \(\sigma_0\) of Equation 7.7. [Input Box] MPa (b) Determine the value of the constant \(k_y\) of Equation 7.7. [Input Box] MPa-(mm)\(^{1/2}\) (c) Predict the yield strength of this alloy when the average grain diameter is \(9.0 \times 10^{-3}\) mm. [Input Box] MPa
The image shows a graph illustrating the relationship between the grain size (d) of a material and its yield strength. **Graph Details:** - **X-Axis:** Represents the inverse square root of the grain size, \( d^{-1/2} \), measured in mm\(^{-1/2}\). The scale ranges from 0 to 16. - **Y-Axis (Left):** Represents the yield strength in megapascals (MPa), ranging from 0 to 200 MPa. - **Y-Axis (Right):** Represents the yield strength in kilopounds per square inch (ksi), ranging from 0 to 30 ksi. The graph plots a straight line from the origin (0,0) to a point at approximately \( d^{-1/2} = 16 \) and 200 MPa (or 30 ksi), suggesting a direct relationship between smaller grain sizes (increased \( d^{-1/2} \)) and higher yield strength. **Box Details:** A text box in the upper right corner of the image contains the following information: - \( d = 0 \) - \( d^{-1/2} = 0 \) - Yield strength = 0 (MPa) - Yield strength = 0 (ksi) This indicates that when the grain size is zero, the yield strength is also zero, which is a hypothetical representation as actual grain size cannot be zero. This graph demonstrates the Hall-Petch relationship, where reducing the grain size of a metallic material increases its yield strength.
Transcribed Image Text:The image shows a graph illustrating the relationship between the grain size (d) of a material and its yield strength. **Graph Details:** - **X-Axis:** Represents the inverse square root of the grain size, \( d^{-1/2} \), measured in mm\(^{-1/2}\). The scale ranges from 0 to 16. - **Y-Axis (Left):** Represents the yield strength in megapascals (MPa), ranging from 0 to 200 MPa. - **Y-Axis (Right):** Represents the yield strength in kilopounds per square inch (ksi), ranging from 0 to 30 ksi. The graph plots a straight line from the origin (0,0) to a point at approximately \( d^{-1/2} = 16 \) and 200 MPa (or 30 ksi), suggesting a direct relationship between smaller grain sizes (increased \( d^{-1/2} \)) and higher yield strength. **Box Details:** A text box in the upper right corner of the image contains the following information: - \( d = 0 \) - \( d^{-1/2} = 0 \) - Yield strength = 0 (MPa) - Yield strength = 0 (ksi) This indicates that when the grain size is zero, the yield strength is also zero, which is a hypothetical representation as actual grain size cannot be zero. This graph demonstrates the Hall-Petch relationship, where reducing the grain size of a metallic material increases its yield strength.
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