Thermal shock
Load caused by rapid temperature change
Mechanical failure modes


Thermal shock is a phenomenon characterized by a rapid change in temperature that results in a transient mechanical load on an object. The load is caused by the differential expansion of different parts of the object due to the temperature change. This differential expansion can be understood in terms of strain , rather than stress . When the strain exceeds the tensile strength of the material, it can cause cracks to form and eventually lead to structural failure.
Methods to prevent thermal shock include: ^{ [1] }
 Minimizing the thermal gradient by changing the temperature gradually
 Increasing the thermal conductivity of the material
 Reducing the coefficient of thermal expansion of the material
 Increasing the strength of the material
 Introducing compressive stress in the material, such as in tempered glass
 Decreasing the Young's modulus of the material
 Increasing the toughness of the material through crack tip blunting or crack deflection, utilizing the process of plastic deformation and phase transformation
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 glassceramic materials (mostly in the lithium aluminosilicate (LAS) system ^{ [2] } ) 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 carboncarbon 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 testpiece can be measured after different thermal shock cycles and this way the deterioration in physical properties can be mapped out.
Thermal shock resistance
Thermal shock resistance measures can be used for material selection in applications subject to rapid temperature changes. A common measure of thermal shock resistance is the maximum temperature differential, $\Delta \; T\; \{\backslash displaystyle\; \backslash Delta\; T\}$ , which can be sustained by the material for a given thickness. ^{ [3] }
Strengthcontrolled thermal shock resistance
Thermal shock resistance measures can be used for material selection in applications subject to rapid temperature changes. The maximum temperature jump, $\Delta \; T\; \{\backslash displaystyle\; \backslash Delta\; T\}$ , sustainable by a material can be defined for strengthcontrolled models by: ^{ [4] } ^{ [3] }
where $\sigma \; f\; \{\backslash displaystyle\; \backslash sigma\; \_\{f\}\}$ is the failure stress (which can be yield or fracture stress ), $\alpha \; \{\backslash displaystyle\; \backslash alpha\; \}$ is the coefficient of thermal expansion, $E\; \{\backslash displaystyle\; E\}$ is the Young's modulus, and $B\; \{\backslash displaystyle\; B\}$ is a constant depending upon the part constraint, material properties, and thickness.
where $C\; \{\backslash displaystyle\; C\}$ is a system constrain constant dependent upon the Poisson's ratio, $\nu \; \{\backslash displaystyle\; \backslash nu\; \}$ , and $A\; \{\backslash displaystyle\; A\}$ is a nondimensional parameter dependent upon the Biot number , $B\; i\; \{\backslash displaystyle\; \backslash mathrm\; \{Bi\}\; \}$ .
$A\; \{\backslash displaystyle\; A\}$ may be approximated by:
where $H\; \{\backslash displaystyle\; H\}$ is the thickness, $h\; \{\backslash displaystyle\; h\}$ is the heat transfer coefficient , and $k\; \{\backslash displaystyle\; k\}$ is the thermal conductivity .
Perfect heat transfer
If perfect heat transfer ( $B\; i\; =\; \infty \; \{\backslash displaystyle\; \backslash mathrm\; \{Bi\}\; =\backslash infty\; \}$ ) is assumed, the maximum heat transfer supported by the material is: ^{ [4] } ^{ [5] }
 $A\; 1\; \approx \; 1\; \{\backslash displaystyle\; A\_\{1\}\backslash approx\; 1\}$ for cold shock in plates
 $A\; 1\; \approx \; 3.2\; \{\backslash displaystyle\; A\_\{1\}\backslash approx\; 3.2\}$ for hot shock in plates
A material index for material selection according to thermal shock resistance in the fracture stress derived perfect heat transfer case is therefore:
Poor heat transfer
For cases with poor heat transfer ( $B\; i\; <\; 1\; \{\backslash displaystyle\; \backslash mathrm\; \{Bi\}\; <1\}$ ), the maximum heat differential supported by the material is: ^{ [4] } ^{ [5] }
 $A\; 2\; \approx \; 3.2\; \{\backslash displaystyle\; A\_\{2\}\backslash approx\; 3.2\}$ for cold shock
 $A\; 2\; \approx \; 6.5\; \{\backslash displaystyle\; A\_\{2\}\backslash approx\; 6.5\}$ for hot shock
In the poor heat transfer case, a higher heat transfer coefficient is beneficial for thermal shock resistance. The material index for the poor heat transfer case is often taken as:
According to both the perfect and poor heat transfer models, larger temperature differentials can be tolerated for hot shock than for cold shock.
Fracture toughness controlled thermal shock resistance
In addition to thermal shock resistance defined by material fracture strength, models have also been defined within the fracture mechanics framework. Lu and Fleck produced criteria for thermal shock cracking based on fracture toughness controlled cracking. The models were based on thermal shock in ceramics (generally brittle materials). Assuming an infinite plate and mode I cracking, the crack was predicted to start from the edge for cold shock, but the center of the plate for hot shock. ^{ [4] } Cases were divided into perfect and poor heat transfer to further simplify the models.
Perfect heat transfer
The sustainable temperature jump decreases, with increasing convective heat transfer (and therefore larger Biot number). This is represented in the model shown below for perfect heat transfer ( $B\; i\; =\; \infty \; \{\backslash displaystyle\; \backslash mathrm\; \{Bi\}\; =\backslash infty\; \}$ ). ^{ [4] } ^{ [5] }
where $K\; I\; c\; \{\backslash displaystyle\; K\_\{Ic\}\}$ is the mode I fracture toughness , $E\; \{\backslash displaystyle\; E\}$ is the Young's modulus, $\alpha \; \{\backslash displaystyle\; \backslash alpha\; \}$ is the thermal expansion coefficient, and $H\; \{\backslash displaystyle\; H\}$ is half the thickness of the plate.
 $A\; 3\; \approx \; 4.5\; \{\backslash displaystyle\; A\_\{3\}\backslash approx\; 4.5\}$ for cold shock
 $A\; 4\; \approx \; 5.6\; \{\backslash displaystyle\; A\_\{4\}\backslash approx\; 5.6\}$ for hot shock
A material index for material selection in the fracture mechanics derived perfect heat transfer case is therefore:
Poor heat transfer
For cases with poor heat transfer, the Biot number is an important factor in the sustainable temperature jump. ^{ [4] } ^{ [5] }
Critically, for poor heat transfer cases, materials with higher thermal conductivity, k , have higher thermal shock resistance. As a result, a commonly chosen material index for thermal shock resistance in the poor heat transfer case is:
Kingery thermal shock methods
The temperature difference to initiate fracture has been described by William David Kingery to be: ^{ [6] } ^{ [7] }
where $S\; \{\backslash displaystyle\; S\}$ is a shape factor, $\sigma \; \ast \; \{\backslash displaystyle\; \backslash sigma\; ^\{*\}\}$ is the fracture stress, $k\; \{\backslash displaystyle\; k\}$ is the thermal conductivity, $E\; \{\backslash displaystyle\; E\}$ is the Young's modulus, $\alpha \; \{\backslash displaystyle\; \backslash alpha\; \}$ is the coefficient of thermal expansion, $h\; \{\backslash displaystyle\; h\}$ is the heat transfer coefficient, and $R\; \prime \; \{\backslash displaystyle\; R\text{'}\}$ is a fracture resistance parameter. The fracture resistance parameter is a common metric used to define the thermal shock tolerance of materials. ^{ [1] }
The formulas were derived for ceramic materials, and make the assumptions of a homogeneous body with material properties independent of temperature, but can be well applied to other brittle materials. ^{ [7] }
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. ^{ [8] }
Examples of thermal shock failure
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 Hard rocks containing ore veins such as quartzite were formerly broken down using firesetting , 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 . ^{ [ citation needed ] }
 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 ^{ [ by whom? ] } 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.
See also
References
 1 2 Askeland, Donald R. (January 2015). "224 Thermal Shock". The science and engineering of materials . Wright, Wendelin J. (Seventh ed.). Boston, MA. pp. 792–793. ISBN 9781305076761 . OCLC 903959750 .
 ↑ US Patent 6066585 , Scott L. Swartz, "Ceramics having negative coefficient of thermal expansion, method of making such ceramics, and parts made from such ceramics", issued 20000523, assigned to Emerson Electric Co.
 1 2 Ashby, M. F. (1999). Materials selection in mechanical design (2nd ed.). Oxford, OX: ButterworthHeinemann. ISBN 0750643579 . OCLC 49708474 .
 1 2 3 4 5 6 Soboyejo, Wole O. (2003). "12.10.2 Materials Selection for Thermal Shock Resistance". Mechanical properties of engineered materials . Marcel Dekker. ISBN 0824789008 . OCLC 300921090 .
 1 2 3 4 T. J. Lu; N. A. Fleck (1998). "The Thermal Shock Resistance of Solids" (PDF) . Acta Materialia . 46 (13): 4755–4768. Bibcode : 1998AcMat..46.4755L . doi : 10.1016/S13596454(98)00127X .
 ↑ KINGERY, W. D. (Jan 1955). "Factors Affecting Thermal Stress Resistance of Ceramic Materials". Journal of the American Ceramic Society . 38 (1): 3–15. doi : 10.1111/j.11512916.1955.tb14545.x . ISSN 00027820 .
 1 2 Soboyejo, Wole O. (2003). "12.10 Thermal Shock Response". Mechanical properties of engineered materials . Marcel Dekker. ISBN 0824789008 . OCLC 300921090 .
 ↑ ASTM C149 — Standard Test Method for Thermal Shock Resistance of Glass Containers