Thermal shock

# Thermal shock

Discussion

Encyclopedia
Thermal shock is the name given to cracking as a result of rapid temperature change. Glass
Glass
Glass is an amorphous solid material. Glasses are typically brittle and optically transparent.The most familiar type of glass, used for centuries in windows and drinking vessels, is soda-lime glass, composed of about 75% silica plus Na2O, CaO, and several minor additives...

and ceramic
Ceramic
A ceramic is an inorganic, nonmetallic solid prepared by the action of heat and subsequent cooling. Ceramic materials may have a crystalline or partly crystalline structure, or may be amorphous...

objects are particularly vulnerable to this form of failure
Structural failure
Structural failure refers to loss of the load-carrying capacity of a component or member within a structure or of the structure itself. Structural failure is initiated when the material is stressed to its strength limit, thus causing fracture or excessive deformations...

, due to their low toughness
Toughness
In materials science and metallurgy, toughness is the ability of a material to absorb energy and plastically deform without fracturing; Material toughness is defined as the amount of energy per volume that a material can absorb before rupturing...

, low thermal conductivity
Thermal conductivity
In physics, thermal conductivity, k, is the property of a material's ability to conduct heat. It appears primarily in Fourier's Law for heat conduction....

, and high thermal expansion coefficients. However, they are used in many high temperature applications due to their high melting point
Melting point
The melting point of a solid is the temperature at which it changes state from solid to liquid. At the melting point the solid and liquid phase exist in equilibrium. The melting point of a substance depends on pressure and is usually specified at standard atmospheric pressure...

.

Thermal shock occurs when a thermal gradient
In vector calculus, the gradient of a scalar field is a vector field that points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change....

causes different parts of an object to expand by different amounts. This differential expansion can be understood in terms of stress
Stress (physics)
In continuum mechanics, stress is a measure of the internal forces acting within a deformable body. Quantitatively, it is a measure of the average force per unit area of a surface within the body on which internal forces act. These internal forces are a reaction to external forces applied on the body...

or of strain
Strain (materials science)
In continuum mechanics, the infinitesimal strain theory, sometimes called small deformation theory, small displacement theory, or small displacement-gradient theory, deals with infinitesimal deformations of a continuum body...

, equivalently. At some point, this stress overcomes the strength
Tensile strength
Ultimate tensile strength , often shortened to tensile strength or ultimate strength, is the maximum stress that a material can withstand while being stretched or pulled before necking, which is when the specimen's cross-section starts to significantly contract...

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. Decreasing its Young's modulus
Young's modulus
Young's modulus is a measure of the stiffness of an elastic material and is a quantity used to characterize materials. It is defined as the ratio of the uniaxial stress over the uniaxial strain in the range of stress in which Hooke's Law holds. In solid mechanics, the slope of the stress-strain...

5. Increasing its toughness
Toughness
In materials science and metallurgy, toughness is the ability of a material to absorb energy and plastically deform without fracturing; Material toughness is defined as the amount of energy per volume that a material can absorb before rupturing...

, by
1. crack tip blunting, i.e., plasticity
Plasticity (physics)
In physics and materials science, plasticity describes the deformation of a material undergoing non-reversible changes of shape in response to applied forces. For example, a solid piece of metal being bent or pounded into a new shape displays plasticity as permanent changes occur within the...

or phase transformation
2. crack deflection

## Effect on materials

Borosilicate glass
Borosilicate glass
Borosilicate glass is a type of glass with the main glass-forming constituents silica and boron oxide. Borosilicate glasses are known for having very low coefficients of thermal expansion , making them resistant to thermal shock, more so than any other common 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
Fused quartz
Fused quartz and fused silica are types of glass containing primarily silica in amorphous form. They are manufactured using several different processes...

outperforms it in both these respects. Some glass-ceramic
Glass-ceramic
Glass-ceramics are polycrystalline material produced through controlled crystallization of base glass. Glass-ceramic materials share many properties with both glasses and ceramics...

materials (mostly in LAS system) 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
Reinforced carbon-carbon
Carbon fibre-reinforced carbon is a composite material consisting of carbon fibre reinforcement in a matrix of graphite. It was developed for the nose cones of intercontinental ballistic missiles, and is most widely known as the material for the nose cone and wing leading edges of the Space Shuttle...

is extremely resistant to thermal shock, due to graphite
Graphite
The mineral graphite is one of the allotropes of carbon. It was named by Abraham Gottlob Werner in 1789 from the Ancient Greek γράφω , "to draw/write", for its use in pencils, where it is commonly called lead . Unlike diamond , graphite is an electrical conductor, a semimetal...

's extremely high thermal conductivity and low expansion coefficient, the high strength of carbon fiber
Carbon fiber
Carbon fiber, alternatively graphite fiber, carbon graphite or CF, is a material consisting of fibers about 5–10 μm in diameter and composed mostly of carbon atoms. The carbon atoms are bonded together in crystals that are more or less aligned parallel to the long axis of the fiber...

, and a reasonable ability to deflect cracks within the structure.

To measure thermal shock the impulse excitation technique
Impulse excitation technique
-Practical:The impulse excitation technique is a nondestructive test method that uses natural frequency, dimensions and mass of a test-piece to determine Young's modulus, Shear modulus, Poisson's ratio and damping coefficient....

proved to be a useful tool. It can be used to measure Young's modulus
Young's modulus
Young's modulus is a measure of the stiffness of an elastic material and is a quantity used to characterize materials. It is defined as the ratio of the uniaxial stress over the uniaxial strain in the range of stress in which Hooke's Law holds. In solid mechanics, the slope of the stress-strain...

, Shear modulus, Poisson's ratio
Poisson's ratio
Poisson's ratio , named after Siméon Poisson, is the ratio, when a sample object is stretched, of the contraction or transverse strain , to the extension or axial strain ....

and damping
Damping
In physics, damping is any effect that tends to reduce the amplitude of oscillations in an oscillatory system, particularly the harmonic oscillator.In mechanics, friction is one such damping effect...

coefficient in a non destructive way. The same test-piece can be measured after different thermal shock cycles and this way the detoriation in physical properties can be mapped out.

## Relative robustness of materials

The robustness of a material
Material
Material is anything made of matter, constituted of one or more substances. Wood, cement, hydrogen, air and water are all examples of materials. Sometimes the term "material" is used more narrowly to refer to substances or components with certain physical properties that are used as inputs to...

to thermal shock is characterized with the thermal shock parameter:,

where
• is thermal conductivity,
• is maximal tension the material can resist,
• is the thermal expansion coefficient
• is the Young's modulus
Young's modulus
Young's modulus is a measure of the stiffness of an elastic material and is a quantity used to characterize materials. It is defined as the ratio of the uniaxial stress over the uniaxial strain in the range of stress in which Hooke's Law holds. In solid mechanics, the slope of the stress-strain...

, and
• is the Poisson ratio.

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

The laser
Laser
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of photons. The term "laser" originated as an acronym for Light Amplification by Stimulated Emission of Radiation...

gain medium generates heat. This heat is drained through the heat sink
Heat sink
A heat sink is a term for a component or assembly that transfers heat generated within a solid material to a fluid medium, such as air or a liquid. Examples of heat sinks are the heat exchangers used in refrigeration and air conditioning systems and the radiator in a car...

. The transfer of heat occurs at certain temperature gradient
A temperature gradient is a physical quantity that describes in which direction and at what rate the temperature changes the most rapidly around a particular location. The temperature gradient is a dimensional quantity expressed in units of degrees per unit length...

.
The non-uniform thermal expansion
Thermal expansion
Thermal expansion is the tendency of matter to change in volume in response to a change in temperature.When a substance is heated, its particles begin moving more and thus usually maintain a greater average separation. Materials which contract with increasing temperature are rare; this effect is...

of a bulk material causes the stress
Stress (physics)
In continuum mechanics, stress is a measure of the internal forces acting within a deformable body. Quantitatively, it is a measure of the average force per unit area of a surface within the body on which internal forces act. These internal forces are a reaction to external forces applied on the body...

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.
(see above)

Roughly, at the efficient operation of laser, the power of heat generated in the gain medium is proportional to the output power of the laser, and the coefficient of proportionality can be interpreted as heat generation parameter; then, The heat generation parameter is basically determined by the quantum defect
Quantum defect
The term quantum defect is ambiguous. Various meanings are discussed below. Characteristic is that the defect deals with the loss on the smallest energy scale of light: that of the quantum.-Quantum defect in laser science:...

of the laser action, and one can estimate , where and 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
where is thickness of the layer and 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 of temperature, at which the medium still can efficiently lase, is also important property of the laser material.
This overheating limits the maximal power with estimate

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

where

and the loss  determine the limit of power scaling
Power scaling
Power scaling of a laser is increasing its output power without changing the geometry, shape, or principle of operation. Power scalability is considered an important advantage in a laser design....

of the disk laser
Disk laser
A disk laser or active mirror is a type of solid-state laser characterized by a heat sink and laser output that are realized on opposite sides of a thin layer of active gain medium...

s
.
Roughly, the maximal power at the optimised sizes and , is of order of
.
This estimate is very sensitive to the loss .
However, the same expression can be interpreted as a robust estimate of the upper bound of the loss required for the desirable output power :
All the disk lasers reported 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 related 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
Power scaling
Power scaling of a laser is increasing its output power without changing the geometry, shape, or principle of operation. Power scalability is considered an important advantage in a laser design....

.

## Examples of thermal shock failure

• Hard rocks containing ore veins such as quartzite
Quartzite
Quartzite is a hard metamorphic rock which was originally sandstone. Sandstone is converted into quartzite through heating and pressure usually related to tectonic compression within orogenic belts. Pure quartzite is usually white to gray, though quartzites often occur in various shades of pink...

were formerly broken down using fire-setting
Fire-setting
Fire-setting is a method of mining used since prehistoric times up to the Middle Ages. Fires were set against a rock face to heat the stone, which was then doused with water...

, which involved heating the rock face with a wood fire, then quenching with water to induce crack growth. It is described by Diodorus Siculus
Diodorus Siculus
Diodorus Siculus was a Greek historian who flourished between 60 and 30 BC. According to Diodorus' own work, he was born at Agyrium in Sicily . With one exception, antiquity affords no further information about Diodorus' life and doings beyond what is to be found in his own work, Bibliotheca...

in Egyptian gold mines, Pliny the Elder
Pliny the Elder
Gaius Plinius Secundus , better known as Pliny the Elder, was a Roman author, naturalist, and natural philosopher, as well as naval and army commander of the early Roman Empire, and personal friend of the emperor Vespasian...

and Georg Agricola
Georg Agricola
Georgius Agricola was a German scholar and scientist. Known as "the father of mineralogy", he was born at Glauchau in Saxony. His real name was Georg Pawer; Agricola is the Latinised version of his name, Pawer meaning "farmer"...

.
• 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. As ice has a larger volume than the water that created it, the outer layer shrinks as it warms and begins to melt, whilst 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.
• 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 basically a iron box on legs, that has a cast iron top. One builds a wood or coal 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
United Airlines Flight 585
United Airlines Flight 585 was a scheduled domestic passenger airline flight from the now-decommissioned Stapleton International Airport in Denver to Colorado Springs Municipal Airport in Colorado Springs, Colorado....

, USAir Flight 427
USAir Flight 427
US Air Flight 427 was a scheduled flight from Chicago's O'Hare International Airport to Pittsburgh, with a final destination of West Palm Beach, Florida...

and Eastwind Airlines Flight 517
Eastwind Airlines Flight 517
Eastwind Airlines Flight 517 was a scheduled flight from Trenton-Mercer Airport in Trenton, New Jersey to Richmond International Airport in Richmond, Virginia. The crew lost rudder control but successfully landed on June 9, 1996. No casualties occurred and one flight attendant suffered only minor...

). 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
Bellfounding
Bellfounding is the casting of bells in a foundry for use in churches, clocks, and public buildings. A practitioner of the craft is called a bellmaker or bellfounder. The process in Europe dates to the 4th or 5th century. In early times, when a town produced a bell it was a momentous occasion in...

of the Liberty Bell
Liberty Bell
The Liberty Bell is an iconic symbol of American Independence, located in Philadelphia, Pennsylvania. Formerly placed in the steeple of the Pennsylvania State House , the bell was commissioned from the London firm of Lester and Pack in 1752, and was cast with the lettering "Proclaim LIBERTY...

, 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 fire) is believed to cause the crash of the Tsar Bell.