# Thermal shock

Thermal shock is a type of rapidly transient mechanical load. By definition, it is a mechanical load caused by a rapid change of temperature of a certain point. It can be also extended to the case of a thermal gradient, which makes different parts of an object expand by different amounts. This differential expansion can be more directly understood in terms of strain, than in terms of stress, as it is shown in the following. At some point, this stress can exceed the tensile 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.

Failure due to thermal shock can be prevented by;

1. Reducing the thermal gradient seen by the object, by changing its temperature more slowly or increasing the material's thermal conductivity
2. Reducing the material's coefficient of thermal expansion
3. Increasing its strength
4. Introducing built-in compressive stress, as for example in tempered glass
5. Decreasing its Young's modulus
6. Increasing its toughness, by crack tip blunting (i.e., plasticity or phase transformation) or crack deflection

## Effect on materials

Borosilicate glass 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 (mostly in the lithium aluminosilicate (LAS) system[1]) 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.

Among the best thermomechanical materials, there are alumina, zirconia, tungsten alloys, silicon nitride, silicon carbide, boron carbide, and some stainless steels.

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 thermal shock, the impulse excitation technique proved 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 thermal shock cycles and this way the deterioration in physical properties can be mapped out.

## Fundamental parameters

### Temperature parameter

From a simple dimensional analysis one could state that the capability of a material to sustain thermal shock depends primarily on elongation strength (directly proportional), and on its thermal expansion coefficient (inversely proportional). The first and simplest merit index for the thermal shock resistenace of materials is the temperature parameter for thermal shocks. It is defined as the simple ratio [2] (called with θ only by us, in this page):

${\displaystyle \theta ={\frac {\epsilon }{\alpha }}\,}$

where:

• ${\displaystyle \epsilon }$ is a material characteristic strain resistance: typically the ultimate strain.
• ${\displaystyle \alpha }$ is the thermal expansion coefficient

This parameter actually has the physical dimension of a temperature (in fact, it is proportional to the temperature jump): in the International System of Units it is normally measured in kelvin.

A first comparison of different materials from the thermal shock resistance point of view can be simply performed by comparing the different values of this parameter for each material. The designer should only state which strain is relevant for his case: for example, if it is more appropriate to consider the yield (strain) or the rupture (strain). However, this relation completely neglects the heat tranfer problem: it is valid when surface heat transfer of the material is very high[2].

### Heat parameter

The fundamental equation holds when the heat transfer is ideal: it works well when the Biot number is high.

Then, in case of poor heat transfer (when the Biot number is low), one should also consider the material thermal conductivity:

${\displaystyle Q=k\,\theta }$

This second parameter is derived from the first, and it is more complex: it represents a thermal power per unit length (international units: W/m).

## Brittle materials

In case of brittle materials, one considers the ultimate elongation. If this parameter is not directly available, the ultimate elongation for brittle materials can be estimated as the ratio between the ultimate strength and the Young modulus:

${\displaystyle \epsilon _{u}={\frac {\sigma _{u}}{E}}\,}$

where:

• ${\displaystyle \sigma _{u}}$ is the ultimate strength
• ${\displaystyle E}$ is the Young's modulus

Therefore, the temperature and heat parameters in this case are:

${\displaystyle \theta _{0}={\frac {\sigma _{u}}{E\alpha }}\,}$
${\displaystyle Q_{0}={\frac {k\sigma _{u}}{E\alpha }}\,}$

Which are commonly used as the reference merit indexes for the thermal shock resistance of brittle materials.

If failure is caused by a dominant crack, one should considerin turn express the effective strength in terms of the brittle strength intensity factor. For example, in case of an infinite plate, with uniform uniaxial stress:

${\displaystyle \sigma ={\frac {K_{Ic}}{\sqrt {\pi H}}}}$

where:

• ${\displaystyle K_{Ic}}$ is the strength intensity factor
• ${\displaystyle \pi =3,14...}$ is the mathematical constant
• ${\displaystyle H}$ is the half of the crack length

In this case, the temperature jump becomes[2]:

${\displaystyle \Delta T=A{\frac {K_{Ic}}{E\alpha {\sqrt {\pi H}}}}\,}$

Depending on the load case, the appropriate elastic modulus to be considered could not be the simple Young modulus, but another one. Here, one should consider one further variable: the further corresponding conventional variable is the Poisson ratio. For example, in some cases the elastic modulus can be[3]:

${\displaystyle R={\frac {E}{1-\nu }}}$

## Temperature jump

The maximum temperature jump sustainable by the solid, corresponding to the case of perfect heat transfer is [2]:

${\displaystyle \Delta T_{max}=A\theta }$

where:

• A is a nondimensional parameter depending on shock type (hot or cold) and on geometry.
• θ is the temperature shock parameter

Some values of the constant per plates are [2]:

• A ≈ 1 for cold shock in plates
• A ≈ 3.2 for hot shock in plates

while the effective temperature jump in a real case of heat exchange depends primarily also on the Biot number:

${\displaystyle \Delta T={\frac {1}{\mathrm {Bi} }}\Delta T_{max}}$

In fact, implicitly one is considering the case of the material (with its geometry and thermal conductivity k) as surrounded by a fluid (with its heat tranfer coefficient h).

## Testing

Thermal shock testing exposes products to alternating low and high temperatures to accelerate failures caused by temperature cycles or thermal shocks during normal use. The transition between temperature extremes occurs very rapidly, greater than 15 °C per minute.

Equipment with single or multiple chambers is typically used to perform thermal shock testing. When using single chamber thermal shock equipment, the products remain in one chamber and the chamber air temperature is rapidly cooled and heated. Some equipment uses separate hot and cold chambers with an elevator mechanism that transports the products between two or more chambers.

Glass containers can be sensitive to sudden changes in temperature. One method of testing involves rapid movement from cold to hot water baths, and back.[4]

## Examples of thermal shock failure

• Hard rocks containing ore veins such as quartzite were formerly broken down using fire-setting, which involved heating the rock face with a wood fire, then quenching with water to induce crack growth. It is described by Diodorus Siculus in Egyptian gold mines, Pliny the Elder, and Georg Agricola.
• 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. The outer layer expands as it warms, while the interior remains largely unchanged. This rapid change in volume between different layers creates stresses in the ice that build until the force exceeds the strength of the ice, and a crack forms, sometimes with enough force to shoot ice shards out of the container.
• Incandescent bulbs that have been running for a while have a very hot surface. Splashing cold water on them can cause the glass to shatter due to thermal shock, and the bulb to implode.
• An antique cast iron cookstove is a simple iron box on legs, with a cast iron top. A wood or coal fire is built inside the box and food is cooked on the top outer surface of the box, like a griddle. If a fire is built too hot, and then the stove is cooled by pouring water on the top surface, it will crack due to thermal shock.
• 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. Similarly, the strong gradient of temperature (due to the dousing of a fire with water) is believed to cause the breakage of the third Tsar Bell.
• Thermal shock is a primary contributor to head gasket failure in internal combustion engines.