Quantify expansion mismatch, stress, and interface reliability. Compare bonded materials across temperature swings with confidence.
Use the responsive grid below: 3 columns on large screens, 2 on tablets, and 1 on mobile.
This chart compares strain, differential expansion, stress utilization, and the warping indicator from the current case.
| Case | Pair | ΔT (°C) | CTE Gap (ppm/°C) | Length (mm) | Estimated Stress (MPa) | Screening Note |
|---|---|---|---|---|---|---|
| 1 | Aluminum / FR-4 | 100 | 9.6 | 100 | 13.40 | Moderate expansion difference in bonded electronics. |
| 2 | Copper / Ceramic | 180 | 10.5 | 60 | 28.75 | High interface stress during thermal cycling. |
| 3 | Steel / Polymer | 65 | 38.0 | 250 | 21.10 | Watch distortion in long constrained assemblies. |
| 4 | Silicon / Solder | 120 | 21.4 | 20 | 17.95 | Relevant for package and board-level reliability. |
CTE mismatch strain: ε = (α₁ − α₂) × ΔT
Differential expansion: ΔL = L × ε
Biaxial modulus: M = E / (1 − ν)
Bonded pair equivalent stress: σ = ε / (1/M₁ + 1/M₂)
Single constrained stress: σ = M × ε
Stress utilization: Utilization = |σ| / allowable × 100
These equations provide a practical engineering screening model for layered or bonded materials under thermal excursion. They are intended for early design comparison, not detailed finite element validation.
CTE mismatch is the difference in thermal expansion rate between bonded materials. During heating or cooling, that difference creates restrained strain at the interface. A 10 ppm/°C gap across a 100°C excursion produces about 0.10% free mismatch strain. In laminates, packages, housings, and bonded plates, that strain can drive cracking, fatigue, seal leakage, and dimensional instability.
Thermal excursion usually dominates early screening. A pair that is safe over 25°C to 55°C may become risky during reflow, sterilization, autoclave exposure, or outdoor cycling. Because mismatch strain scales with delta T, doubling the temperature range nearly doubles free strain, differential growth, and estimated constrained stress. That makes service, storage, and process temperatures equally important in design reviews.
Two material pairs can show the same mismatch strain but very different stress levels. Stiffer materials resist deformation and therefore develop higher interface loading when bonded. The calculator uses biaxial modulus, E divided by 1 minus Poisson ratio, to represent this effect. Ceramic-metal combinations often stress interfaces more severely than polymer-metal combinations under the same thermal profile.
Differential expansion increases with part length, so long assemblies can accumulate meaningful offset even when local strain looks modest. Thickness balance also matters. If one layer is much thicker or stiffer, bending becomes uneven and warpage increases. That is why the tool reports a warping indicator, helping engineers compare flatness risk in boards, covers, rails, bonded panels, and sensor stacks.
Estimated stress becomes more useful when compared with an allowable design limit. Low utilization suggests comfortable margin, moderate values indicate closer review, and results near the limit justify redesign. Engineers may respond by shortening spans, selecting closer CTE matches, adding compliant layers, reducing process temperature, or changing joint geometry. This approach turns raw calculations into practical design action.
This calculator is intended for concept ranking, supplier comparison, and preliminary reliability assessment. It helps identify whether one pairing is clearly better for a defined temperature profile. Final approval should still consider creep, nonlinear behavior, anisotropy, moisture, cure shrinkage, local geometry, and cycle count. Used properly, the tool reduces risk early and improves the quality of later simulation work.
It is the difference in thermal expansion rate between two materials. When bonded parts heat or cool together, that difference creates strain, stress, and possible warpage.
Biaxial modulus better represents constrained in-plane loading for bonded layers. It converts mismatch strain into a practical screening stress for interfaces and laminates.
No. It is an early engineering estimate. Final certification should include detailed analysis, material test data, geometry effects, and real operating cycles.
Use a design limit from your material data, adhesive supplier, joint specification, or internal reliability standard. Apply margin for uncertainty and service conditions.
Yes. Run several cases with the same geometry and temperature range. Compare mismatch strain, stress utilization, differential expansion, and warping indicator.
A softer layer can reduce stress transfer, but it may increase creep, long-term movement, or local deformation. Use the tool as screening, then validate physically.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.