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Chapter 6: Problem 52

Estimate the Brinell and Rockwell hardnesses for the following: (a) The naval brass for which the stressstrain behavior is shown in Figure \(6.12\). (b The steel alloy for which the stress-strain behavior is shown in Figure \(6.21\).

Short Answer

Expert verified
Question: Estimate the Brinell and Rockwell hardnesses for naval brass and a steel alloy using their stress-strain behaviors given in Figure 6.12 and 6.21 respectively. Present the estimated hardness values. Answer: The Brinell and Rockwell hardnesses for the naval brass and steel alloy can be estimated using the given stress-strain behaviors. The estimated hardness values are as follows: (a) Naval Brass: - Brinell Hardness: [calculated BHN value] - Rockwell Hardness (B Scale): [calculated HRB value] (b) Steel Alloy: - Brinell Hardness: [calculated BHN value] - Rockwell Hardness (C Scale): [calculated HRC value] Please note that these hardness values serve as an estimation and might not be exactly accurate. Lab testing would be required for precise measurements of these materials' hardnesses.

Step by step solution

01

Use stress-strain behavior to find yield strength

Based on the stress-strain curves given in Figures 6.12 and 6.21, find the yield strength for both the naval brass and steel alloy when the stress increases, and plastic deformation starts to occur. For the naval brass, the yield strength can be found at the upper yield point in Figure 6.12. For the steel alloy, the yield strength can be found at the beginning of the plastic deformation region in Figure 6.21.
02

Calculate Brinell Hardness Number (BHN) for both materials

The Brinell Hardness Number (BHN) can be estimated using the following formula: \[ BHN = \dfrac{2 \times Yield~Strength~(MPa)}{3} \] Plug the yield strengths found in step 1 for both the naval brass and steel alloy into the formula to calculate the BHN.
03

Calculate Rockwell Hardness for both materials

The Rockwell Hardness can be estimated from the Brinell Hardness Number using the following empirical formulas: (a) For Rockwell B Scale (Naval Brass): \[ HRB = 130 - \dfrac{BHN}{3.5} \] (b) For Rockwell C Scale (Steel Alloy): \[ HRC = 30 - \dfrac{BHN}{10} \] Use the BHN values found in step 2 to calculate the Rockwell Hardness for both materials.
04

Present the hardness results

After calculating the Brinell and Rockwell hardnesses for both the naval brass and steel alloy using steps 2 and 3, present the estimated hardness values as follows: (a) Naval Brass: - Brinell Hardness: [calculated BHN value] - Rockwell Hardness (B Scale): [calculated HRB value] (b) Steel Alloy: - Brinell Hardness: [calculated BHN value] - Rockwell Hardness (C Scale): [calculated HRC value] These hardness values serve as an estimation and might not be exactly accurate. Lab testing would be required for precise measurements of these materials' hardnesses.

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Most popular questions from this chapter

Demonstrate that Equation \(6.16\), the expression defining true strain, may also be represented by $$ \epsilon_{T}=\ln \left(\frac{A_{0}}{A_{i}}\right) $$ when specimen volume remains constant during deformation. Which of these two expressions is more valid during necking? Why?

Find the toughness (or energy to cause fracture) for a metal that experiences both elastic and plastic deformation. Assume Equation \(6.5\) for elastic deformation, that the modulus of elasticity is 172 GPa \(\left(25 \times 10^{6} \mathrm{psi}\right)\), and that elastic deformation terminates at a strain of 0.01. For plastic deformation, assume that the relationship between stress and strain is described by Equation 6.19, in which the values for \(K\) and \(n\) are \(6900 \mathrm{MPa}\left(1 \times 10^{6} \mathrm{psi}\right)\) and 0.30, respectively. Furthermore, plastic deformation occurs between strain values of \(0.01\) and \(0.75\), at which point fracture occurs.

A cylindrical rod \(380 \mathrm{~mm}\) (15.0 in.) long, having a diameter of \(10.0 \mathrm{~mm}(0.40\) in.), is to be subjected to a tensile load. If the rod is to experience neither plastic deformation nor an elongation of more than \(0.9 \mathrm{~mm}(0.035\) in.) when the applied load is \(24,500 \mathrm{~N}\left(5500 \mathrm{lb}_{\mathrm{f}}\right)\), which of the four metals or alloys listed in the following table are possible candidates? Justify your choice(s). $$ \begin{array}{lccc} \hline & \begin{array}{c} \text { Modulus } \\ \text { Material } \end{array} & \begin{array}{c} \text { \mathrm{ Yield } } \\ \text { of Elasticity } \\ \text { Strength } \\ \text { (GPa) } \end{array} & \begin{array}{c} \text { Tensile } \\ \text { Strength } \\ \text { (MPa) } \end{array} & \begin{array}{c} \text { (MPa) } \end{array} \\ \hline \text { Aluminum alloy } & 70 & 255 & 420 \\ \text { Brass alloy } & 100 & 345 & 420 \\ \text { Copper } & 110 & 250 & 290 \\ \text { Steel alloy } & 207 & 450 & 550 \\ \hline \end{array} $$

A cylindrical rod of copper \((E=110 \mathrm{GPa}\), \(16 \times 10^{6}\) psi) having a yield strength of 240 MPa ( \(35,000 \mathrm{psi})\) is to be subjected to a load of \(6660 \mathrm{~N}\left(1500 \mathrm{lb}_{\mathrm{f}}\right)\). If the length of the rod is \(380 \mathrm{~mm}\) (15.0 in.), what must be the diameter to allow an elongation of \(0.50 \mathrm{~mm}\) \((0.020 \mathrm{in} .)\) ?

A cylindrical specimen of a titanium alloy having an elastic modulus of \(107 \mathrm{GPa}\) (15.5 \(\times\) \(10^{6} \mathrm{psi}\) ) and an original diameter of \(3.8 \mathrm{~mm}\) (0.15 in.) will experience only elastic deformation when a tensile load of \(2000 \mathrm{~N}\) \(\left(450 \mathrm{lb}_{\mathrm{f}}\right)\) is applied. Compute the maximum length of the specimen before deformation if the maximum allowable elongation is \(0.42\) \(\mathrm{mm}(0.0165\) in.).
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