| Scenario | Method | Example inputs | Typical output |
|---|---|---|---|
| Thin film on wafer | Stoney | Es 130 GPa, νs 0.28, ts 0.5 mm, tf 1 µm, R0 ∞, R 20 m | Stress in hundreds of MPa |
| Cooling after deposition | Thermal mismatch | E 200 GPa, ν 0.30, αf 12 ppm/K, αs 3 ppm/K, ΔT −200°C | Often compressive if αf>αs and cooling |
| XRD sin²ψ scan | XRD slope | E 210 GPa, ν 0.30, slope 800 microstrain per sin²ψ | Order of 100 MPa |
| Locked-in elastic strain | Strain-based | E 210 GPa, ν 0.30, εx 600 µε, εy 0 µε | σx ≈ 130 MPa (uniaxial) |
- Pick the method matching your measurement setup.
- Enter elastic constants, thicknesses, and measured values.
- Press Calculate to view results above the form.
- Check the sign label for tension or compression.
- Download CSV or PDF for a quick report.
- Review the formula section for assumptions and limits.
1) What is residual stress?
Residual stress is stress locked into a material after processing, without external loads. It may come from thermal gradients, plastic deformation, phase changes, or constrained shrinkage.
2) What does a negative result mean?
A negative value indicates compressive stress under the calculator’s sign convention. Compressive surface stress can improve fatigue resistance but may cause buckling in thin films.
3) When should I use the Stoney method?
Use it for thin films on much thicker substrates when you can measure curvature or radius before and after deposition. It’s common for wafer-based thin films.
4) How accurate is the thermal mismatch estimate?
It’s a first-order estimate assuming a biaxially constrained film and uniform temperature change. Real stress may differ due to creep, cracking, plasticity, or partial constraint.
5) Why does XRD need a slope versus sin²ψ?
The sin²ψ method linearizes how lattice spacing changes with tilt angle under stress. The fitted slope relates directly to stress through elastic constants for the chosen reflection.
6) What if my XRD fit has low R²?
Low R² suggests nonlinearity, poor d0, texture effects, or measurement noise. Try more angles, confirm peak fitting, and ensure you’re in the linear elastic regime.
7) Can I use strain-based mode for plastic strain?
This mode assumes elastic strain. If plastic strain contributes, the stress cannot be obtained by Hooke’s law alone. You may need unloading measurements or method-specific standards.
8) Which unit system should I use?
Choose MPa for most engineering metals and films. Use GPa for very stiff materials or large stresses. Keep inputs consistent and use the unit selectors for thickness and modulus.