BIZOMAT MAKEOS · Materials
Thermal Stress and Movement in Plastic–Metal Assemblies
What stress builds up in a plastic part restrained by metal when the temperature changes, and how much do they move relative to each other?
Thermal stress in a plastics part fully restrained by a metal part, σ = (α_m − α_p) E_p ΔT, and the relative movement between unrestrained plastic and metal parts, from their expansion coefficients, the plastic’s modulus at temperature (or an apparent creep modulus from a creep curve) and the temperature change.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Expansion coefficient of the metal | µm/m·K | Linear expansion coefficient of the metal part. |
| Expansion coefficient of the plastic | µm/m·K | Linear expansion coefficient of the plastic part. |
| Plastic modulus | choice | Use the modulus at temperature, or derive an apparent modulus from a creep curve for long-held loads. |
| Tensile modulus of the plastic | MPa | Tensile modulus of the plastic at the temperature involved. |
| Stress on the creep curve | MPa | Stress level read on the creep curve. |
| Strain on the creep curve at the time of interest | % | Strain at that stress after the time of interest. |
| Temperature change | K | Temperature change from assembly (negative for cooling). |
| Length between fixings | mm | Length between fixing points (or a hole diameter). |
| Allowable stress for the plastic | MPa | Allowable stress for the plastic in tension or compression. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Expansion coefficient of the metal
- What it is
- The linear coefficient of thermal expansion of the metal part the plastic is fixed to: how much it grows per metre of length for each kelvin of temperature rise.
- Units and format
- Enter a number in µm/m·K: micrometres per metre per kelvin. The form accepts 0 µm/m·K to 100 µm/m·K. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 11.7 µm/m·K as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Take it from the material data sheet; it is in micrometres per metre per kelvin, the same as 10⁻⁶ per kelvin.
What this means: Expansion coefficient of the plastic
- What it is
- The linear coefficient of thermal expansion of the plastic part over the temperature range involved, from the material supplier.
- Units and format
- Enter a number in µm/m·K: micrometres per metre per kelvin. The form accepts 0 µm/m·K to 500 µm/m·K. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 80 µm/m·K as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The stress and relative movement grow with the difference between the two coefficients.
- Get it right
- Filled and reinforced plastics expand differently along and across the flow direction; use the value for the direction of the length.
What this means: Plastic modulus
- What it is
- Which stiffness of the plastic to use: its tensile modulus at the temperature, or an apparent modulus from a creep curve for a temperature change that lasts.
- Units and format
- Choose one of 2 options from the list: Modulus at the temperature; Apparent (creep) modulus from a creep curve.
- Example
- The form opens with “Modulus at the temperature” selected as a worked example. Choose the option that matches your case.
- Get it right
- Use the creep option for long-held temperature changes, since plastics relax under sustained stress.
What this means: Tensile modulus of the plastic
- What it is
- The tensile modulus of the plastic at the temperature involved, from the material supplier’s data. Used when the modulus option is selected.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 100000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2000 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The thermal stress is directly proportional to the modulus.
- Get it right
- Plastics’ modulus falls as temperature rises; use the value at the service temperature. Ignored with the creep option.
What this means: Stress on the creep curve
- What it is
- A stress level read from the plastic’s creep curve, paired with the strain at the time of interest, to work out an apparent creep modulus. Used only with the creep option.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 1000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The apparent modulus, and so the stress, are proportional to it.
- Get it right
- Read stress and strain from the same curve, at the service temperature and loading time.
What this means: Strain on the creep curve at the time of intere…
- What it is
- The strain shown on the creep curve at the chosen stress after the time of interest, used to work out the apparent creep modulus. Used only with the creep option.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0.001% to 50%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger creep strain lowers the apparent modulus and so the stress.
- Get it right
- Type the strain as a percentage, so 1 means 1 % strain, not 0.01.
What this means: Temperature change
- What it is
- The change in temperature from the temperature at which the parts were assembled to the service temperature being checked.
- Units and format
- Enter a number in K: kelvin (a difference of 1 K equals 1 °C). The form accepts -300 K to 300 K. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40 K as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Stress and relative movement are both directly proportional to the temperature change.
- Get it right
- Use a negative value for cooling. A change in kelvin equals the same change in °C.
What this means: Length between fixings
- What it is
- The length between the points where the plastic is fixed to the metal, or a hole diameter, over which the relative movement is worked out.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Relative movement is directly proportional to the length.
- Get it right
- It affects only the movement; the fully restrained stress does not depend on length.
What this means: Allowable stress for the plastic
- What it is
- The allowable stress for the plastic in tension or compression at the service conditions, compared with the size of the thermal stress.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 1000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Take it from the material supplier or your design standard for the temperature and duration; it does not change the stress itself.
Method and formulas
- Fully restrained plastic: σ = (α_m − α_p) E_p ΔT (handbook formula 29).
- Unrestrained: relative movement ΔL_rel = (α_p − α_m) L ΔT (formula 30).
- Apparent creep modulus E_app = σ ÷ ε_c from the creep curve.
- Example: a plastic part restrained by steel over a 40 K rise carries about 5.464 MPa; unrestrained it moves 0.2732 mm relative to the metal over 100 mm.
Limitations
- Full restraint is an upper bound; fixings that slip or flex relieve stress.
- Plastics relax under sustained stress; the creep modulus gives the longer-term value.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a plastic housing screwed or bonded to a metal frame
- Size slots or clearances for a plastic cover on metal
- Estimate long-term stress using creep modulus
Who it is for
- Design engineers
- Product engineers
- Materials engineers
What you get
- Thermal stress in the restrained plastic
- Relative movement if unrestrained
- Apparent modulus used
Interpreting the result
- Cooling usually puts the plastic in tension, which is the cracking risk; allow slotted holes or flexible fixings.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 578–580. Topic reference; no source tables or recommended settings are reproduced.
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