# Thermal stress (mechanics)

Thermal stresses , more precisely thermally induced mechanical stresses , arise through temperature changes in connection with the thermal expansion coefficients of the materials or also material combinations . There are mechanical tensions that arise without the influence of external forces.

A distinction is made between permanent , latent and temporary thermal stresses. The latter lead to the material parameter resistance to thermal shock .

## Permanent thermal stress

Permanent thermal stresses only arise in material pairings if their production temperature was different from the temperature in use and if the thermal expansion coefficients of the two materials differ.

Examples are glazes, enamels , different materials welded together, materials welded with different filler materials and soldered connections (also and especially glass solder ).

Permanent thermal stress cannot be eliminated by tempering. They can contribute to an increase or decrease in strength. Strength increases in brittle materials when the surface comes under compressive stress when it cools down, for example due to a glaze with a lower thermal expansion coefficient.

## Latent thermal stresses

Latent stresses arise in the homogeneous material when it cools down quickly. They remain in place with temperature equalization after a treatment with an inhomogeneous temperature distribution beyond the plasticity limit has taken place. This can also involve the cooling of a casting progressing from the outside inwards.

Examples are furthermore the (too) rapid cooling after the manufacture of glass products, the manufacture of toughened safety glass or also the hardening of steel by quenching.

Latent compressive stresses on the surface of many, especially brittle materials lead to an increase in flexural strength. They can be generated by cooling down the hot, still ductile workpiece.

Latent thermal stresses can be eliminated by heating. One example is the tempering of steel after hardening.

## Thermal shock resistance

Temporary thermal stresses arise from inhomogeneous temperature distribution in a material or workpiece. If they only lead to elastic deformation, they disappear when the temperature equals. However, if they exceed the strength of the material, changes can result, up to and including breakage. Materials are therefore characterized by their resistance to temperature changes or shock. There are compressive, tensile and shear stresses. Usually the tensile stresses are the failure-relevant quantity.

Under thermal shock refers to the fast, shock-like change in temperature at the material or workpiece . This leads to mechanical stresses between the outer and inner part of the material, since the heat is transferred or dissipated to or from the surface faster than to the interior.

### Simplified calculation model

The workpiece is at a constant temperature T. When the ambient temperature changes, the outer part of the model also experiences a temperature change towards T 1 (T 1 not equal to T). Since the outer part now has a different temperature, it changes its volume through thermal expansion . The core, however, still has the same temperature T, so its volume has also remained constant. So-called thermal stresses develop between the jacket and core. This can be estimated with the following equation:

${\ displaystyle \ sigma _ {\ mathrm {therm}} \; = {\ frac {E \ cdot \ alpha} {1- \ nu}} \ \ cdot (T _ {\ mathrm {1}} -T)}$

in which

σ therm ... thermal stress in the component [MPa]
E ... modulus of elasticity [MPa]
α ... (linear) thermal expansion [/ K]
ν ... Poisson's ratio [-]
(T 1 -T) ... temperature difference [K]

### Damage Mechanisms

If a critical, internal tension is exceeded, the material is damaged. Depending on the material, this can lead to different cases of damage due to different mechanisms: In the case of metals , there are structural changes (e.g. breakdown of pearlite structures or formation of martensites in stainless steels) up to the formation of hot cracks that can destroy the workpiece. In the case of ceramics , cracks usually occur in the interior due to the high tendency to brittle fracture, which can quickly lead to failure. Plastics show both mechanisms, but with significantly lower temperature differences.

### Parameters

In practice one tries to find criteria according to which one can decide which material is suitable for a certain application . Depending on the application, different parameters are therefore defined:

#### First thermal shock parameter R s

For infinitely large heat transfer applies:

${\ displaystyle R _ {\ mathrm {s}} \; = \ sigma _ {\ mathrm {crit}} \ cdot {\ frac {1- \ nu} {E \ cdot \ alpha}} \}$

in which

σ crit ... strength of the material [MPa], e.g. B. from the 4-point bending test .

In reality, however, there is no such thing as an "infinitely large" heat transfer, application examples are most likely the quenching of a hot workpiece in water or oil, or the introduction of cold workpieces into a melt .

#### Second thermal shock parameter R s '

with constant heat transfer, the thermal shock parameter is expanded:

${\ displaystyle R '_ {\ mathrm {s}} \; = \ lambda \ cdot \ sigma _ {\ mathrm {crit}} \ cdot {\ frac {1- \ nu} {E \ cdot \ alpha}} \ }$

in which

λ ... thermal conductivity [W / (m K)]

The thermal shock does not immediately lead to complete failure of the workpiece. Cracks inside weaken the workpiece, so that its strength decreases.

#### Third thermal shock parameter R s "

If there is a constant heating or cooling rate on the surface of the workpiece, the following is extended:

${\ displaystyle R '' _ {\ mathrm {s}} \; = \ lambda \ cdot \ sigma _ {\ mathrm {crit}} \ cdot {\ frac {1- \ nu} {E \ cdot \ alpha \ cdot \ rho \ cdot c _ {\ mathrm {p}}}} \}$

in which

ρ ... density of the material [kg / m³]
c p ... specific heat capacity [J / (kg K)]

### Typical values ​​for R s

Because the heat transfer in reality also depends on the component geometry, the values ​​shown give a first impression of the thermal shock resistance of the material:

The glass ceramic used for hobs is particularly resistant to temperature changes.