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Chapter 8: Problem 16

A fatigue test was conducted in which the mean stress was 70 MPa (10,000 psi), and the stress amplitude was \(210 \mathrm{MPa}(30,000\) psi). (a) Compute the maximum and minimum stress levels. (b) Compute the stress ratio. (c) Compute the magnitude of the stress range.

Short Answer

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Question: Determine the maximum and minimum stress levels, the stress ratio, and the magnitude of the stress range for a material subjected to a mean stress of 70 MPa and a stress amplitude of 210 MPa. Answer: The maximum stress level is 280 MPa, the minimum stress level is -140 MPa, the stress ratio is -0.5, and the stress range is 420 MPa.

Step by step solution

01

Compute the maximum and minimum stress levels

To compute the maximum stress level, use the formula \(\sigma_{max} = \sigma_{m} + \sigma_{a}\). \(\sigma_{max} = 70 \,\text{MPa} + 210 \,\text{MPa} = 280 \,\text{MPa}\) To compute the minimum stress level, use the formula \(\sigma_{min} = \sigma_{m} - \sigma_{a}\). \(\sigma_{min} = 70 \,\text{MPa} - 210 \,\text{MPa} = -140 \,\text{MPa}\) So the maximum stress level is 280 MPa and the minimum stress level is -140 MPa.
02

Compute the stress ratio

To compute the stress ratio (R), use the formula \(R = \frac{\sigma_{min}}{\sigma_{max}}\). \(R = \frac{-140 \,\text{MPa}}{280 \,\text{MPa}} = -0.5\) So the stress ratio is -0.5.
03

Compute the stress range

To compute the stress range (\(\Delta \sigma\)), use the formula \(\Delta \sigma = 2 \cdot \sigma_{a}\). \(\Delta \sigma = 2 \cdot 210 \,\text{MPa} = 420 \,\text{MPa}\) So the stress range is 420 MPa.

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Most popular questions from this chapter

List four measures that may be taken to increase the resistance to fatigue of a metal alloy.

A cylindrical component constructed from an S-590 alloy (Figure 8.31) has a diameter of \(14.5 \mathrm{~mm}\) (0.57 in.). Determine the maximum load that may be applied for it to survive \(10 \mathrm{~h}\) at \(925^{\circ} \mathrm{C}\left(1700^{\circ} \mathrm{F}\right)\).

A structural component is fabricated from an alloy that has a plane-strain fracture toughness of \(62 \mathrm{MPa} \sqrt{\mathrm{m}}\). It has been determined that this component fails at a stress of \(250 \mathrm{MPa}\) when the maximum length of a surface crack is \(1.6 \mathrm{~mm}\). What is the maximum allowable surface crack length (in mm) without fracture for this same component exposed to a stress of \(250 \mathrm{MPa}\) and made from another alloy with a plane-strain fracture toughness of \(51 \mathrm{MPa} \sqrt{\mathrm{m}}\) ?

The fatigue data for a brass alloy are given as follows: $$ \begin{array}{cc} \hline \text { Stress Amplitude (MPa) } & \text { Cycles to Failure } \\ \hline 170 & 3.7 \times 10^{4} \\ \hline 148 & 1.0 \times 10^{5} \\ \hline 130 & 3.0 \times 10^{5} \\ \hline 114 & 1.0 \times 10^{6} \\ \hline 92 & 1.0 \times 10^{7} \\ \hline 80 & 1.0 \times 10^{8} \\ \hline 74 & 1.0 \times 10^{9} \\ \hline \end{array} $$ (a) Make an \(S-N\) plot (stress amplitude versus logarithm of cycles to failure) using these data. (b) Determine the fatigue strength at \(4 \times 10^{6}\) cycles. (c) Determine the fatigue life for \(120 \mathrm{MPa}\).

A specimen of a 4340 steel alloy with a plane strain fracture toughness of \(54.8 \mathrm{MPa} \sqrt{\mathrm{m}}(50 \mathrm{ksi} \sqrt{\mathrm{in}}\).) is exposed to a stress of \(1030 \mathrm{MPa}\) (150,000 psi). Will this specimen experience fracture if the largest surface crack is \(0.5 \mathrm{~mm}\) (0.02 in.) long? Why or why not? Assume that the parameter \(Y\) has a value of \(1.0 .\)
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