91Ó°ÊÓ

What is the magnitude of the maximum stress that exists at the tip of an internal crack having a radius of curvature of \(1.9 \times 10^{-4} \mathrm{mm}\) \(\left(7.5 \times 10^{-6} \text {in. }\right)\) and a crack length of \(3.8 \times\) \(10^{-2} \mathrm{mm}\left(1.5 \times 10^{-3} \mathrm{in.}\right)\) when a tensile stress of \(140 \mathrm{MPa}(20,000 \mathrm{psi})\) is applied?

Estimate the theoretical fracture strength of a brittle material if it is known that fracture occurs by the propagation of an elliptically shaped surface crack of length \(0.5 \mathrm{mm}(0.02 \mathrm{in.})\) and having a tip radius of curvature of \(5 \times\) \(10^{-3} \mathrm{mm}\left(2 \times 10^{-4} \mathrm{in.}\right),\) when a stress of \(1035 \mathrm{MPa}(150,000 \mathrm{psi})\) is applied.

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 \(1030 \mathrm{MPa}\) \((150,000 \mathrm{psi}) .\) Will this specimen experience fracture if it is known that the largest surface crack is \(0.5 \mathrm{mm}(0.02 \text { in. })\) long? Why or why not? Assume that the parameter \(Y\) has a value of 1.0.

Some aircraft component is fabricated from an aluminum alloy that has a plane strain fracture toughness of \(40 \mathrm{MPa} \sqrt{\mathrm{m}}(36.4 \mathrm{ksi} \sqrt{\mathrm{in} .})\) It has been determined that fracture results at a stress of \(300 \mathrm{MPa}(43,500 \mathrm{psi})\) when the maximum (or critical) internal crack length is \(4.0 \mathrm{mm}(0.16 \text { in. }) .\) For this same component and alloy, will fracture occur at a stress level of \(260 \mathrm{MPa}(38,000 \mathrm{psi})\) when the maximum internal crack length is \(6.0 \mathrm{mm}(0.24 \mathrm{in.}) ?\) Why or why not?

A large plate is fabricated from a steel alloy that has a plane strain fracture toughness of \(82.4 \mathrm{MPa} \sqrt{\mathrm{m}}(75.0 \mathrm{ksi} \sqrt{\text { in. }}) .\) If, during service use, the plate is exposed to a tensile stress of \(345 \mathrm{MPa}(50,000 \mathrm{psi})\), determine the minimum length of a surface crack that will leadd to fracture. Assume a value of 1.0 for \(Y\).

Following is tabulated data that were gathered from a series of Charpy impact tests on a ductile cast iron. $$ \begin{array}{cc} \hline \text { Temperature }\left({ }^{\circ} \boldsymbol{C}\right) & \text { Impact Energy }(\boldsymbol{J}) \\ \hline-25 & 124 \\ -50 & 123 \\ -75 & 115 \\ -85 & 100 \\ -100 & 73 \\ -110 & 52 \\ -125 & 26 \\ -150 & 9 \\ -175 & 6 \\ \hline \end{array} $$ (a) Plot the data as impact energy versus temperature. (b) Determine a ductile-to-brittle transition temperature as that temperature corresponding to the average of the maximum and minimum impact energies. (c) Determine a ductile-to-brittle transition temperature as that temperature at which the impact energy is \(80 \mathrm{~J}\).

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

Three identical fatigue specimens (denoted \(A\), B, and \(C\) ) are fabricated from a nonferrous alloy. Each is subjected to one of the maximum-minimum stress cycles listed below; the frequency is the same for all three tests.$$\begin{array}{ccc} \hline \text {Specimen} & \sigma_{\max }(M P a) & \sigma_{\min }(M P a) \\\\\hline \mathrm{A} & +450 & -150 \\\\\mathrm{B} & +300 & -300 \\\\\mathrm{C} & +500 & -200\end{array},$$ (a) Rank the fatigue lifetimes of these three specimens from the longest to the shortest. (b) Now justify this ranking using a schematic \(S-N\) plot.

Cite five factors that may lead to scatter in fatigue life data.

Briefly explain the difference between fatigue striations and beachmarks both in terms of (a) size and (b) origin.