The stress-strain diagram for a steel alloy having an
original diameter of $0.5$ in. and a gage length of $2$ in. is given
in the figure. Determine approximately the modulus of
resilience and the modulus of toughness for the material.

Question

Quizlet Admin · Accepted Answer

The test element has dimensions $d = 0.5$ in and $L = 2$ in. It is necessary to determine modulus of resilience and the modulus of toughness.

From the diagram we read the necessary values for solving the task:

Determination modulus of resilience:

$$
\begin{align*}
(u_{r})_{approx}&=\dfrac{1}{2}\cdot \sigma_{r}\cdot \varepsilon_{r}\&=\dfrac{1}{2}\cdot40\cdot10^3\cdot0.001\(u_{r})_{approx}&=20\dfrac{ \text{ lb in}}{\text{ in}^3}
\end{align*}
$$

Determination modulus of toughness us:

$$
\begin{align*}
(u_{t})_{approx}&=45\cdot10\cdot0.04\(u_{t})_{approx}&=18\dfrac{ \text{ kip in}}{\text{ in}^3}
\end{align*}
$$

The solution is:

{$\boxed{(u_{r})_{approx}=20\dfrac{ \text{ lb in}}{\text{ in}^3}}$}

{$\boxed{(u_{t})_{approx}=18\dfrac{ \text{ kip in}}{\text{ in}^3}}$}

The stress-strain diagram for a steel alloy having an original diameter of $0.5$ in. and a gage length of $2$ in. is given in the figure. Determine approximately the modulus of resilience and the modulus of toughness for the material.

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The stress-strain diagram for a steel alloy having an original diameter of 0.50.50.5 in. and a gage length of 222 in. is given in the figure. Determine approximately the modulus of resilience and the modulus of toughness for the material.

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Recommended textbook solutions

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Related questions

The stress-strain diagram for a steel alloy having an original diameter of $0.5$ in. and a gage length of $2$ in. is given in the figure. Determine approximately the modulus of resilience and the modulus of toughness for the material.