# 应力-应变曲线

${\displaystyle \mathrm {\sigma } ={\tfrac {F}{A_{0}}}}$
${\displaystyle \mathrm {\epsilon } ={\tfrac {L-L_{0}}{L_{0}}}={\tfrac {\Delta L}{L_{0}}}}$

## 真實應力和應變之間的關係

${\displaystyle \mathrm {\sigma _{t}} ={\tfrac {F}{A}}}$
${\displaystyle \mathrm {\epsilon _{t}} =\int {\tfrac {\delta L}{L}}}$

${\displaystyle \mathrm {\sigma _{t}} ={\tfrac {F}{A}}={\tfrac {F}{A_{0}}}*{\tfrac {A_{0}}{A}}={\tfrac {F}{A_{0}}}*{\tfrac {L}{L_{0}}}=\sigma (1+\epsilon )}$

${\displaystyle \mathrm {\delta \epsilon _{t}} ={\tfrac {\delta L}{L}}}$

${\displaystyle \mathrm {\epsilon _{t}} =ln({\tfrac {L}{L_{0}}})=ln(1+\epsilon )}$

${\displaystyle \mathrm {\delta {\textit {F}}} =0=\sigma _{t}\delta A+A\delta \sigma _{t}}$

${\displaystyle \mathrm {-{\tfrac {\delta A}{A}}} =\mathrm {\tfrac {\delta \sigma _{t}}{\sigma _{t}}} }$

${\displaystyle \mathrm {\sigma _{t}} ={\tfrac {F}{A_{neck}}}}$
${\displaystyle \mathrm {\epsilon _{t}} =ln({\tfrac {A_{0}}{A_{neck}}})}$

${\displaystyle \mathrm {\sigma _{t}} =K(\epsilon _{t})^{n}}$

## 影響因子

${\displaystyle \mathrm {\sigma _{t}} =K({\dot {\epsilon }}_{T})^{m}}$

## 參考來源

1. ^ Luebkeman, C., & Peting, D. (2012, 04 28).
2. ^ Courtney, Thomas. Mechanical behavior of materials. Waveland Press, Inc. 2005: 6–13.
3. ^ Beer, F, Johnston, R, Dewolf, J, & Mazurek, D. (2009). Mechanics of materials. New York: McGraw-Hill companies. P 51.
4. ^ Beer, F, Johnston, R, Dewolf, J, & Mazurek, D. (2009). Mechanics of materials. New York: McGraw-Hill companies. P 58.
5. ^ Mechanical Properties of Materials. （原始内容存档于2019-05-04）.
6. ^ Beer, F, Johnston, R, Dewolf, J, & Mazurek, D. (2009). Mechanics of materials. New York: McGraw-Hill companies. P 59.