Thermal Properties of Materials

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Content :

Thermal Properties of Materials

This workbook contains information defining the effect of temperature on some physical and mechanical properties of materials used in the engineering industry. Using this tool the following tasks can be solved:

  1. Calculation of linear coefficient of thermal expansion and component extension.
  2. Extension of a group of components arranged in a linear chain.
  3. Calculation of modulus of elasticity.

The calculations use procedures, algorithms and data from various standards and specialized literature.
List of standards: EN 1561, EN 1563, EN 16079, EN 1753, EN 10088-1, EN 10095, EN 10269, EN 10302

Note: The primary source of information about a specific material should always be the supplier of the material, or possibly other verified and trusted material databases. The task of this tool is not to determine the exact material parameters. Calculated values can never replace data provided by material tests. The purpose of this document is to offer the user a qualified estimate of the expected values of material parameters when accurate data for a specific material is not available.
Warning: The calculated results are for indicative purposes only and cannot replace data obtained through accurate measurement of the particular material. 

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Control, structure and syntax of calculations.

Information on the syntax and control of the calculation can be found in the document "Control, structure and syntax of calculations".

A. Linear coefficient of thermal expansion.

This section focuses on the issue of thermal expansion of engineering materials. Paragraph [1] is for informative purposes only. Paragraph [2] is used to calculate the relevant material parameters depending on the selected temperature.

 

When a body is heated or cooled, its dimensions change. For bodies with one predominant dimension, this phenomena is referred to as thermal longitudinal expansion. The dependence of the elongation based on the type of material is expressed by the coefficient of longitudinal thermal expansion. In general, this physical phenomenon of material is defined by the following relation:

where:
L0 ... initial length of the body
D
L ... change in length
D
T ... change in temperature 

However, this factor or coefficient does not have a constant value as it changes with the increasing temperature. The mathematical description of the curve of the thermal expansion coefficient based on temperature is a rather complex function. To achieve sufficiently accurate calculation of longitudinal expansion over a wider temperature range, it is usually necessary to use a quadratic or cubic computational relationship where the longitudinal expansion is described by two or more factors. For example, the quadratic relationship to calculate elongation is described by the following formula:

where:
a1,a2 ... coefficient of thermal expansion
L ... initial length
D
T ... change in temperature 

However, even when using these complex relationships, a sufficiently accurate calculation covering the entire operating temperature range may not be guaranteed.

 

In "real life" engineering, the elongation of components is usually calculated using "linear" coefficients of thermal expansion. These linear coefficients are defined for a material which is heated starting with a precisely given initial temperature T0 until the final temperature T is reached. The thermal elongation of the component within the given temperature range may be determined using a linear relationship:

where:
a ... linear coefficient of thermal expansion for heating starting with temperature T0 up to temperature T
L ... initial length
D
T ... change in temperature T-T0 

It is obvious that in order to achieve more accurate calculations of longitudinal expansion over a wider temperature range, it will be necessary to know more values of the linear expansion coefficient for the given material. In material databases or material sheets, it is usually possible to find one or more values of the coefficient for different temperature intervals "T0-T" for the given material. The purpose of this calculation is to find the approximate value of the linear coefficient of thermal expansion for any combination of start and end temperatures "T0-T".

Typical course of linear coefficient of thermal expansion. [1]

The picture shows the usual curve of the coefficient of thermal expansion for individual material groups based on the relevant the temperature. Use the selection list to switch between individual groups.

Note: The curves shown correspond with the temperature change (heating) – starting with the initial temperature of 20°C (68°F).
Warning: For a particular material selected from the group, the actual curve may be slightly different. 

Calculation of linear coefficient of thermal expansion and component extension. [2]

This paragraph is intended for the actual calculation of the linear coefficient of thermal expansion and for longitudinal elongation of the component.

First select the system of calculation units [2.1] and the corresponding material group [2.3]. After defining one known value of the coefficient in lines [2.5 - 2.8], a curve of the linear coefficient of thermal expansion is displayed in the diagram based on the given temperature range. The results of the calculation for the required temperature change [2.10, 2.11] are given in lines [2.12, 2.16].

Note: The calculation of the coefficient of thermal expansion is performed using an empirical model, which is based on the usual behavior of materials belonging to the given material group. Therefore, the results for some materials selected from the group achieved through the theoretical calculation may differ from the actual results and shall be regarded as approximate values.
Warning: The calculated results are for indicative purposes only and cannot replace data obtained through accurate measurement of the particular material. 

2.1 Calculation units.

Select the desired set of calculation units in the list. When the units are switched, all values are immediately recalculated.

2.2 Material.

In this section, you define the required parameters of your material.

Hint: After pressing the "<--" button, the corresponding parameters of the material selected from the list [2.13] will be transferred into the calculation. 

2.3 Material group.

In the selection list, choose the material group corresponding with your material.

2.4 Typical values of thermal expansion coefficient.

This line specifies the range of usual values of the linear coefficient of thermal expansion for various materials selected from the given material group [2.3]. This coefficient is defined for a material heating process starting at 20° and ending at 100°C (68-212°F).

2.5 - 2.7 Known value of thermal expansion coefficient.

Enter one known value of the linear coefficient of thermal expansion in line [2.5] for material heating starting at temperature "T0" [2.6] until the temperature "T" [2.7] is reached.

Note: Values displayed in red in the input fields [2.6, 2.7] indicate that the typical melting point for the selected material group has probably been exceeded.

2.8 Linear coefficient of thermal expansion.

After defining all known material parameters [2.2], the system displays a curve of the linear coefficient of thermal expansion for the given material based on the given temperature range. The displayed curve corresponds with the temperature change (heating) starting at the initial temperature "T0" until the indicated temperature is reached. Select the initial or starting temperature from the list at the bottom right of the graph.

Note 1: The hatched part of the curve in the graph only shows the estimate of the expected curve of the coefficient. This is a range of temperature for which it was not possible to compile a more accurate empirical model demonstrating the behavior of materials due to insufficient data or due to significant deviation in data. 

As for the material defined above, the basic value of the linear coefficient of thermal expansion for a heating process starting at 20° and ending at 100°C (68-212°F), is calculated on line [2.9].

In line [2.12] the actual calculation of the linear coefficient of thermal expansion for the material heating process starting with the initial temperature "TI" [2.10] and ending at "TE" [2.11] is performed.

Note 2: The blue results of the calculation indicate a possible increase in the calculation inaccuracy for the given temperature range with regards to the assumed curve (hatched part of the graph).
Note 3: Values displayed in red indicate that the melting point typical for the selected material group has probably been exceeded.
Warning: The calculated results are for indicative purposes only and cannot replace data obtained through accurate measurement of the particular material. 

2.13 Indicative table of values.

The table shows informative values of the linear coefficient of thermal expansion for the selected materials. 

Explanation of parameters:
a ... linear coefficient of thermal expansion [10-6/°C, 10-6/°F]
DT ... change in temperature (heating) of the material for which the thermal expansion coefficient is defined [°C, °F]

Note: The values in the table are shown in units selected in line [2.1].

2.14 Component extension depending on temperature change.

In this part, the thermal elongation of a specific component made of the above-defined material is calculated for the temperature change described in lines [2.10, 2.11].

Note 1: The blue results of the calculation indicate a possible increase in the calculation inaccuracy for the given temperature range with regards to the assumed curve (see paragraph [2.8]).
Note 2: Values displayed in red indicate that the melting point typical for the selected material group has probably been exceeded.
Hint: The theoretical curve of the extension of the component over the given temperature range is shown in the relevant graphs. 

Extension of a group of components arranged in a linear chain. [3]

This paragraph is used to examine the mutual thermal expansion of a group of components made of different materials. The components must be arranged in a linear dimensional chain. The calculation allows you to compare the thermal extension of individual components or to compare two groups of components.

Calculation procedure:

1. Enter operating temperatures in line [3.1]

2. If the two groups of components which are being compared are not heated evenly, select the check box on line [3.2] and enter a different final temperature for the components belonging to group "B”

3. Define the parameters of the dimension chain in Table [3.3]

    Column 1 - use the list to select the comparison group to which the component belongs

    Column 3 - enter the length of the component

    Column 4 - use the list to select the material group corresponding with the material of the component

    Column 5 - enter the basic value of the linear coefficient of thermal expansion for heating from 20° to 100°C (68-212°F)

    Column 6 - if you know the exact value of the coefficient of thermal expansion for the operating temperature change (e.g. from the material sheet), uncheck the check box and enter the value manually

4. The last two columns of the table show the calculated thermal extension of the individual components

5. The total extension of both comparison groups, including a graphical comparison, is available in Section [3.4]

Hint 1: If several different components made of the same material are used in the dimensional chain, define them in the Table [3.3] as one component with the total overall length of all components.
Hint 2: If a component is made of a material that does not match any of the material groups offered in column 4 of the table, select the last "Other” item from the list. Then manually enter the corresponding value of the coefficient of thermal expansion in the 6th column of the table.

B. Young's modulus.

This section focuses on the influence of the temperature on the modulus of elasticity of engineering materials. Paragraph [4] is for informative purposes only. Paragraph [5] is used to calculate the relevant modulus of elasticity depending on the selected temperature.

The data given here relates to the modulus of tensile elasticity. To determine the modulus of shear, it is possible to use the following conversion formula:

where:
E ... modulus of tensile elasticity
m
... Poisson's ratio

Note: The Poisson's ratio for metallic materials usually increases slightly with the increasing temperature. The decrease in the shear modulus will thus be slightly steeper.

Typical course of Young's modulus. [4]

The picture shows the usual curves of the modulus of elasticity for individual groups of materials depending on the temperature. Use the selection list to switch between individual groups.

Warning: For a particular material selected from the group, the actual curve may be slightly different. 

Calculation of modulus of elasticity. [5]

This paragraph is intended to calculate the actual tensile modulus of elasticity.

First select the system of calculation units [5.1] and the corresponding material group [5.3]. After defining one known value of the modulus of elasticity in the lines [5.5, 5.6], a curve of the modulus of elasticity as the function of temperature is displayed in the graph for the given material. The resulting calculated value of the modulus of elasticity for the required temperature [5.9] is given in line [5.10].

Note: The calculation of the modulus of elasticity is performed using an empirical model which is based on the usual behavior of materials belonging to the given material group. Therefore, the results for some materials selected from the group achieved through the theoretical calculation may differ from the actual results and shall be regarded as approximate values.
Warning: The calculated results are for indicative purposes only and cannot replace data obtained through accurate measurement of the particular material. 

5.1 Calculation units.

Select the desired set of calculation units in the list. When the units are switched, all values are immediately recalculated.

5.2 Material.

In this section, you define the required parameters of your material.

Hint: After pressing the "<--" button, the corresponding parameters of the material selected from the list [5.14] will be transferred into the calculation. As for materials with a modulus of elasticity included in the list as a range of values, the mean value from this range will be used in the calculation.

5.3 Material group.

In the selection list, choose the material group corresponding with your material.

5.4 Typical values of Young's modulus.

This line shows the range of usual modulus of elasticity for different materials from the given material group [5.3] at a temperature of 20°C (68°F).

5.5 - 5.6 Known value of Young's modulus.

Enter one known value of the modulus of elasticity at temperature "T" [5.6] in line [5.5].

Note: Values displayed in red in the input field [5.6] indicate that the typical melting point for the selected material group has probably been exceeded.

5.7 Modulus of elasticity in tension.

After defining all material parameters in Section [5.2], a theoretical curve of the modulus of elasticity for the given material is displayed as the function of the temperature.  

Note 1: The hatched part of the curve in the graph only shows an estimate of the expected modulus of elasticity. This is a range of temperature for which it was not possible to compile a more accurate empirical model demonstrating the behavior of materials due to insufficient data or due to significant deviation in data. 

Line [5.8] calculates the basic value of the modulus of elasticity at a temperature of 20°C (68°F) and for the material defined above.

In line [5.10], the value of the modulus of elasticity is calculated for the required final temperature "TE" [5.9].

Note 2: The blue results of the calculation indicate a possible increase in the calculation inaccuracy for the given temperature range with regards to the assumed curve (hatched part of the graph).
Note 3: Values displayed in red indicate that the melting point typical for the selected material group has probably been exceeded.
Warning: The calculated results are for indicative purposes only and cannot replace data obtained through accurate measurement of the particular material. 

5.11 Modulus of elasticity in shear.

In this section, you may determine the corresponding value of the modulus of elasticity in shear for the above calculated value of the tensile modulus.

Note 1: The blue results of the calculation indicate a possible increase in the calculation inaccuracy for the given temperature range with regards to the assumed curve (see paragraph [5.7]).
Note 2: Values displayed in red indicate that the melting point typical for the selected material group has probably been exceeded.
Warning: The Poisson's ratio does not have a constant value as it depends on the temperature. For metallic materials, it usually increases slightly with the increasing temperature.

5.14 Indicative table of values.

The table shows informative values of the tensile modulus of elasticity for the selected materials.

Explanation of parameters:
E ... Young's modulus [GPa, 103 ksi]
T ... material temperature for which the specified modulus of elasticity is defined [°C, °F]

Note: The values in the table are shown in units selected in line [5.1].

Setting calculations, change the language.

Information on setting of calculation parameters and setting of the language can be found in the document "Setting calculations, change the language".

Workbook modifications (calculation).

General information on how to modify and extend calculation workbooks is mentioned in the document "Workbook (calculation) modifications". 

List of standards, literature list:

EN 1561
Founding - Grey cast irons
Gießereiwesen - Gusseisen mit Lamellengraphit
Fonderie - Fontes ŕ graphite lamellaire
Slévárenství - Litiny s lupínkovým grafitem

EN 1563
Founding - Spheroidal graphite cast irons
Gießereiwesen - Gußeisen mit Kugelgraphit
Fonderie - Fonte ŕ graphite sphéroďdal
Slévárenství - Litina s kuličkovým grafitem

EN 16079
Founding - Compacted (vermicular) graphite cast irons
Gießereiwesen - Gusseisen mit Vermiculargraphit
Fonderie - Fontes ŕ graphite vermiculaire (compacté)
Slévárenství - Litina s vermikulárním (kompaktním) grafitem

EN 1753
Magnesium and magnesium alloys - Magnesium alloy ingots and castings
Magnesium und Magnesiumlegierungen - Blockmetalle und Gussstücke aus Magnesiumlegierungen
Magnésium et alliages de magnésium - Lingots et pičces moulées en alliages de magnésium
Hořčík a slitiny hořčíku - Ingoty a odlitky ze slitin hořčíku

EN 10088-1
Stainless steels - Part 1: List of stainless steels
Nichtrostende Stähle - Teil 1: Verzeichnis der nichtrostenden Stähle
Aciers inoxydables - Partie 1 : liste des aciers inoxydables
Korozivzdorné oceli - Část 1: Přehled korozivzdorných ocelí

EN 10095
Heat resisting steels and nickel alloys
Hitzebeständige Stähle und Nickellegierungen
Aciers et alliages de nickel réfractaires
Oceli a niklové slitiny žáruvzdorné

EN 10269
Steels and nickel alloys for fasteners with specified elevated and/or low temperature properties
Stähle und Nickellegierungen für Befestigungselemente für den Einsatz bei erhöhten und/oder tiefen Temperaturen
Aciers et alliages de nickel pour éléments de fixation utilisés ŕ température élevée et/ou basse température
Oceli a niklové slitiny na upevňovací prvky pro použití při zvýšených a/nebo nízkých teplotách

EN 10302
Creep resisting steels, nickel and cobalt alloys
Warmfeste Stähle, Nickel- und Cobaltlegierungen
Aciers et alliage ŕ base de nickel et de cobalt résistant au fluage
Žáropevné oceli, niklové a kobaltové slitiny

 

ASM Handbook Volume 1: Properties and Selection: Irons, Steels, and High-Performance Alloys
ASM International, 1990

Metals Handbook Desk Edition, 2nd Edition
ASM International, 1998

ASM Ready Reference: Thermal Properties of Metals
ASM International, 2002

Materials Science and Engineering Handbook, Third Edition
CRC Press LLC, 2001

Smithells Light Metals Handbook
Butterworth-Heinemann, 1998

CRC Materials Science and Engineering Handbook, 4th Edition
CRC Press, 2015

Military Handbook - MIL-HDBK-5H: Metallic Materials and Elements for Aerospace Vehicle Structures
U.S. Department of Defense, 1998

Deutsches Kupferinstitut Berufsverband e.V,
Technische Broschüren und Datenblätter

Special Metals Corporation
High Performance Alloys Literature