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Pol Grasland-Mongrain edited Let_s_describe_the_phenomenon__.tex
over 8 years ago
Commit id: 3f097c58770d157c4edd80ddfa5e0fb872ce349d
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Substituting the experimental parameters ($\gamma^{-1} \approx$ 40 $\mu$m$^{-1}$, $S$ = 20 mm$^{2}$, $E$ = 0.2 J, $\rho \approx$ 1000 kg.m$^{-3}$, $C \approx$ 4180 J.kg$^{-1}$.K$^{-1}$) lead to a maximum increase of temperature of 15 K.
This local increase of temperature can lead a local dilatation of the medium occurs. We suppose that the medium is homogeneous and isotropic, and as the depth of absorption
(about 40 $\mu$m) is small compared to the beam
diameter, diameter (5 mm), we adopt a 1D model. The stress $\sigma_{zz}$ is the sum between the axial strain component and the thermal expansion component \cite{scruby1990laser}:
\begin{equation}
\sigma_{zz} = (\lambda + 2 \mu) \frac{\partial u_z}{\partial z} - 3(\lambda + \frac{2}{3}\mu) \frac{\alpha E}{\rho C S \zeta}
\label{eq:stressThermo}