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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Larson–Miller relation ： ウィキペディア英語版 Larson–Miller relation The Larson–Miller relation, also widely known as the Larson-Miller Parameter and often abbreviated LMP, is a parametric relation used to extrapolate experimental data on creep and rupture life of engineering materials. ==Background and usage== F.R. Larson and J. Miller proposed that creep rate could adequately be described by the Arrhenius type equation: :$r\; =\; A\; \backslash cdot\; e^$ Where r is the creep process rate, A is a constant, R is the universal gas constant, T is the absolute temperature, and $\backslash Delta\; H$ is the activation energy for the creep process. Taking the natural log of both sides: :$ln(r)\; =\; ln(A)\; -\; \backslash Delta\; H/(R\; \backslash cdot\; T)$ With some rearrangement: :$\backslash Delta\; H/R\; =\; T\; \backslash cdot\; (ln(A)\; -\; ln(r))$ Using the fact that creep rate is inversely proportional to time, the equation can be written as: :$\backslash Delta\; l/\backslash Delta\; t\; =\; A\text{'}\; \backslash cdot\; e^$ Taking the natural log: :$\backslash ln(\backslash Delta\; l/\backslash Delta\; t)\; =\; ln(A\text{'})\; -\; \backslash Delta\; H/(R\; \backslash cdot\; T)$ After some rearrangement the relation finally becomes: :$\backslash Delta\; H/R\; =\; T\; \backslash cdot\; (B\; +\; ln(\backslash Delta\; t))$, where B = $\backslash ln(A\text{'}/\backslash Delta\; l)$ This equation is of the same form as the Larson–Miller relation. :$LMP\; =\; T\; \backslash cdot\; (C\; +\; log(t))$ where the quantity LMP is known as the Larson-Miller parameter. Using the assumption that activation energy is independent of applied stress, the equation can be used to relate the difference in rupture life to differences in temperature for a given stress. The material constant C is typically found to be in the range of 20 to 22 for metals when time is expressed in hours and temperature in degrees Rankine. The Larson-Miller model is used for experimental tests so that results at certain temperatures and stresses can predict rupture lives of time spans that would be impractical to reproduce in the laboratory. Expanding the equation as a Taylor series makes the relationship easier to understand. Only the first terms are kept. :$\backslash Delta\; LMP\; =\; \backslash frac\; \backslash cdot\; \backslash Delta\; T\; +\; \backslash frac\; \backslash cdot\; \backslash Delta\; log(t)\; +...$ :$\backslash frac\; =\; 20\; +\; log(t)\; \backslash qquad\; \backslash qquad\; \backslash frac\; =\; T$ Changing the time, by a factor of 10, changes the logarithm by 1 and the LMP changes by an amount equal to the temperature. :$\backslash Delta\; LMP\; =\; \backslash frac\; \backslash cdot\; \backslash Delta\; log(t)\; =\; T\; \backslash cdot\; \backslash Delta\; log(t)\; =\; T\; \backslash cdot\; 1\; =\; T$ To get an equal change in LMP by changing the temperature, the temperature needs to be raised or lowered by about 5% of its absolute value. :$\backslash Delta\; LMP\; =\; T\; =\; \backslash frac\; \backslash cdot\; \backslash Delta\; T\; \backslash qquad\; \backslash Delta\; T\; =\; \backslash frac\}\; =\; \backslash frac\; \backslash approx\; \backslash frac\; =5\backslash \%\; T$ Typically a 5% increase in absolute temperature will increase the rate of creep by a factor of ten. The equation was developed during the 1950s while Miller and Larson were employed by GE performing research on turbine blade life. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Larson–Miller relation」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.