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# Thermal shock

## Thermal shock in mechanical models

Mechanical failure modes
Buckling
Corrosion
Creep
Fatigue
Fracture
Melting
Rupture
Thermal shock
Wear
Yielding
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Thermal shock is the name given to cracking as a result of rapid temperature change. Glass and ceramic objects are particularly vulnerable to this form of failure, due to their low toughness, low thermal conductivity, and high thermal expansion coefficients. However, they are used in many high temperature applications due to their high melting point.

Thermal shock occurs when a thermal gradient causes different parts of an object to expand by different amounts. This differential expansion can be understood in terms of stress or of strain, equivalently. At some point, this stress overcomes the strength of the material, causing a crack to form. If nothing stops this crack from propagating through the material, it will cause the object's structure to fail.

Thermal shock can be prevented by:

1. Reducing the thermal gradient seen by the object, by
1. changing its temperature more slowly
2. increasing the material's thermal conductivity
2. Reducing the material's coefficient of thermal expansion
3. Increasing its strength
4. Increasing its toughness, by
1. crack tip blunting, i.e., plasticity or phase transformation
2. crack deflection

Borosilicate glass such as Pyrex is made to withstand thermal shock better than most other glass through a combination of reduced expansion coefficient and greater strength, though fused quartz outperforms it in both these respects. Some glass-ceramic materials include a controlled proportion of material with a negative expansion coefficient, so that the overall coefficient can be reduced to almost exactly zero over a reasonably wide range of temperatures.

Reinforced carbon-carbon is extremely resistant to thermal shock, due to graphite's extremely high thermal conductivity and low expansion coefficient, the high strength of carbon fiber, and a reasonable ability to deflect cracks within the structure.

To measure thermo shock the impulse excitation technique proofed to be a useful tool. It can be used to measure Young's modulus, Shear modulus, Poisson's ratio and damping coefficient in a non destructive way. The same test-piece can be measured after different thermo shock cycles and this way the detoriation in physical properties can be mapped out.

## Thermal shock parameter in the physics of solid-state lasers

The laser gain medium generates heat. This heat is drained through the heat sink. The transfer of heat occurs at certain temperature gradient. The non-uniform thermal expansion of a bulk material causes the stress and tension, which may break the device even at slow change of the temperature. (for example, continuous-wave operation). This phenomenon is also called thermal shock. The robustness of a laser material to the thermal shock is characterized with the thermal shock parameter [1]

$R_{\mathrm{T}} = \frac{k\sigma_{\mathrm{T}}(1-\nu)}{\alpha E}\,$,

where

• k is thermal conductivity,
• σT is maximal tension the material can resist,
• α is the thermal expansion coefficient
• E is the Young's modulus, and
• ν is the Poisson ratio.

Roughly, at the efficient operation of laser, the power Ph of heat generated in the gain medium is proportional to the output power Ps of the laser, and the coefficient q of proportionality can be interpreted as heat generation parameter; then, Ph = qPs. The heat generation parameter is basically determined by the quantum defect of the laser action, and one can estimate q = 1 − ωs / ωp, where ωp and ωs are frequency of the pump and that of the lasing.

Then, for the layer of the gain medium placed at the heat sink, the maximal power can be estimated as

$P_{\mathrm{s, max}} = 3 \frac{R_{\mathrm{T}}}{q} \frac{L^2}{h},\,$

where h is thickness of the layer and L is the transversal size. This estimate assumes the unilateral heat drain, as it takes place in the active mirrors. For the double-side sink, the coefficient 4 should be applied.

The estimate above is not the only parameter which determines the limit of overheating of a gain medium. The maximal raise ΔT of temperature, at which the medium still can efficiently lase, is also important propertiy of the laser material. This overheating limits the maximal power with estimate

$P_{\mathrm{s, max}} = 2 \frac {k \Delta T}{q} \frac{L^2}{h}\,$

Combination of the two estimates above of the maximal power gives the estimate

$P_{\mathrm{s, max}} = R \frac{L^2}{h}\,$

where

$R= \textrm{min} \left\{ \begin{array}{c} 3 R_{\mathrm{T}}/q\\ 2 k\Delta T/q \end{array} \right.$

is thermal loading; parameter, which is important property of the laser material. The thermal loading, saturation intensity Q and the round-trip loss β determine the limit of power scaling of the disk lasers [2]. Roughly, the maximal power at the optimised sizes L and h, is of order of $P=\frac{R^2}{Q\beta^3}$. This estimate is very sensitive to the loss β. However, the same expression can be interpreted as a robust estimate of the upper bound of the loss $~\beta~$ required for the desirable output power P:

$~\beta_{\mathrm{max}}=\left(\frac{R^2}{PQ}\right)^{\frac{1}{3}}$

All the disk lasers reported seem to work at the round-trip loss below this estimate. The thermal shock parameter and the loading depend of the temperature of the heat sink. Certain hopes are relates with a laser, operating at cryogenic temperatures. The corresponding Increase of the thermal shock parameter would allow to softer requirements for the round-trip loss of the disk laser at the power scaling.

## Examples of thermal shock failure

• Ice cubes placed in a glass of warm water crack by thermal shock as the exterior surface increases in temperature much faster than the interior surfaces. Because of thermal expansion, the outer surface stretches because it is hotter, but the inner surface is nearly the same length, and thus, the crack forms to allow for this difference.
• A Sheepherder stove is basically a steel box on legs, that has a cast iron top. One builds a wood fire inside the box and cooks on the top outer surface of the box, like a griddle. If one builds too hot a fire, and then tries to cool the stove by pouring water on the top surface, it will crack and perhaps fail by thermal shock.
• The causes of three aircraft incidents in the 1990s (United Airlines Flight 585, USAir Flight 427 and Eastwinds Flight 517). Thermal shock caused their power control unit in the tail to jam and cause rudder hardover, forcing the planes in the direction the rudder turns.
• It is widely hypothesized that following the casting of the Liberty Bell, it was allowed to cool too quickly which weakened the integrity of the bell and resulted in a large crack along the side of it the first time it was rung.
• In the sci-fi movie Alien 3, the alien is able to survive being immersed in molten lead, but when the sprinklers are activated, the cool water hitting the super hot alien exoskeleton causes it to crack and the alien dies.

## References

1. ^ W.F.Krupke; M.D. Shinn, J.E. Marion, J.A. Caird, and S.E. Stokowski (1986). "Spectroscopic, optical, and thermomechanical properties of neodymium- and chromium-doped gadolinium scandium gallium garnet". JOSAB 3 (1): 102-114.
2. ^ D. Kouznetsov; J.F. Bisson, J. Dong, and K. Ueda (2006). "Surface loss limit of the power scaling of a thin-disk laser". JOSAB 23 (6): 1074–1082. Retrieved on 2007-01-26.; [1]