Thermal stress analysis for parts that heat and cool
Predict the stress and distortion that temperature puts into your design, from uneven heating, restrained expansion and mismatched materials, and find the changes that let it move without cracking, warping or loosening.
Temperature change makes materials expand or contract. When that movement is free, there is no stress. When it is restrained by fixings, by a stiffer neighbour, by a cooler region of the same part or by a bonded material with a different expansion coefficient, stress builds. It can be large: a steel bar fully restrained against a 100 K rise sees σ = EαΔT ≈ 200 GPa × 12 × 10⁻⁶ /K × 100 K = 240 MPa, with no external load at all.
More about thermal stress analysis
Thermal stress analysis takes the temperature field, either specified or predicted by a thermal or conjugate heat transfer study, and applies it to the structure. That gives the expansion stress, the distortion, and the change in clearances, preloads and contact pressures as the product heats up. Transient studies follow fast heating or cooling, where steep gradients near a surface can produce a higher stress early on than the part ever sees once temperatures settle. Stiffness and expansion are taken at temperature, and stresses are judged against the material’s strength at the temperature where they occur.
F-CAD®’s design engineers run these thermo-structural studies, and the answers lead to practical choices: slotted holes or flexures to release expansion, better-matched materials, revised bond lines or a different heating arrangement. Whichever is chosen feeds straight into the detailed design and drawings of the part, and on into production.
Typical parts: aluminium housings on steel frames, heated platens and tooling, exhaust and process pipework, windows and lenses in metal mounts, power module baseplates, and brazed or bonded assemblies.
What a thermal stress study answers
Will it crack or yield as it heats up?
Peak thermal stress at the critical temperature condition, against the material’s strength at that temperature.
How much will it distort?
Warping and bowing from uneven heating or through-thickness gradients, for parts where flatness or alignment matters.
What happens where materials meet?
Stress at joints between materials that expand differently, such as aluminium on steel, glass in a metal frame or a ceramic on a metal base.
Will the bolts and seals hold?
The change in bolt preload, gasket pressure and clearance as parts expand, at the hottest and coldest conditions.
Is warm-up or steady running worse?
Stress through a heating or cooling transient, showing whether the peak comes during start-up, a quench or at full temperature.
Will repeated cycles cause damage?
The stress range per thermal cycle, ready for a fatigue assessment of parts that heat and cool many times.
What we analyse
Temperature fields
Steady-state and transient temperatures from conduction, convection and radiation, or applied directly from your measured data.
Thermal expansion stress
Stress from restrained expansion and from temperature gradients within a part.
Mismatched materials
Joints between materials with different expansion coefficients, including bonded, bolted, brazed and press-fitted assemblies.
Thermal distortion
Bowing, warping and the change in flatness, alignment and clearance at temperature.
Thermal transients
Rapid heating, quenching and start-up, where surface-to-core gradients drive the highest stress.
Thermal cycling
Stress range per cycle for parts that repeatedly heat and cool, as the basis for a thermal fatigue assessment.
Combined thermal and mechanical loads
Temperature applied together with pressure, preload and mechanical loads, as the product sees them in service.
Before you start
What to send us
- CAD of the parts and their fixings or joints
- Temperatures, or the heat loads and cooling needed to predict them
- Heating and cooling rates for transient cases
- Materials, with properties over the working temperature range
- Mechanical loads and preloads acting at the same time
- Limits on stress, distortion, flatness or clearance
Which material combinations cause the most trouble?
Large differences in expansion across a long joint. Aluminium expands by about 23 × 10⁻⁶ /K and steel by about 12 × 10⁻⁶ /K, so a 500 mm aluminium part bolted to steel moves about 0.55 mm relative to it over a 100 K rise.
Do we need a thermal simulation first?
Only if the temperature field is not already known. Measured temperatures or a specified gradient may be enough; where the heat flow is complex, a thermal or conjugate heat transfer study comes first.
Why does stress peak during warm-up?
Fast heating raises the surface temperature before the core can follow, so the hot surface is held back by cooler material beneath it. As temperatures even out, that gradient and its stress fall away.
Is a hot part weaker?
Usually. Yield strength and stiffness fall with temperature, markedly so for aluminium alloys and polymers, which is why stresses are compared with the strength at the temperature where they occur.
Send us the part that warps or cracks
