(a) Compare the fatigue limits for polystyrene (Figure 15.11) and the cast iron for which fatigue data are given in Problem 8.20. (b) Compare the fatigue strengths at \(10^{6} \mathrm{cy}\) cles for poly(ethylene terephthalate) (PET, Figure 15.11) and red brass (Figure 8.34).

First, we need to refer to Figure 15.11 to find the fatigue limit of polystyrene. From the graph, we find that the fatigue limit of polystyrene is approximately \(5 \mathrm{MPa}\) (estimate the value using the graph). Next, we must refer to the data in Problem 8.20 to find the fatigue limit of cast iron. According to the given data, the fatigue limit of cast iron is approximately \(190 \mathrm{MPa}\). Now, we can compare these two values. The fatigue limit for polystyrene is \(5 \mathrm{MPa}\), and the fatigue limit for cast iron is \(190 \mathrm{MPa}\). Clearly, cast iron has a higher fatigue limit than polystyrene.

First, we need to refer to Figure 15.11 to find the fatigue strength at \(10^6\) cycles for PET. From the graph, we estimate that the fatigue strength of PET at \(10^6\) cycles is approximately \(60 \mathrm{MPa}\) (estimate the value using the graph). Next, we must refer to Figure 8.34 to find the fatigue strength at \(10^6\) cycles for red brass. According to the graph, the fatigue strength of red brass at \(10^6\) cycles is approximately \(140 \mathrm{MPa}\). Now, we can compare these two values. The fatigue strength for PET at \(10^6\) cycles is \(60 \mathrm{MPa}\), and the fatigue strength for red brass at \(10^6\) cycles is \(140 \mathrm{MPa}\). Clearly, red brass has a higher fatigue strength at \(10^6\) cycles than PET.