Calculator Inputs
This page keeps a single stacked content flow, while the input grid expands to three columns on large screens, two on tablets, and one on phones.
Example Data Table
| Alloy system | Type | Model | Solute concentration | Size misfit | Predicted Δσ | Total yield |
|---|---|---|---|---|---|---|
| Al-Cu | Substitutional | Fleischer-style | 4.0 at% | 10.49% | 37.67 MPa | 127.67 MPa |
| Fe-Si | Substitutional | Labusch-style | 3.0 at% | 5.65% | 4.36 MPa | 224.36 MPa |
| Ni-Cr | Substitutional | Fleischer-style | 8.0 at% | 0.81% | 71.91 MPa | 251.91 MPa |
These rows are illustrative engineering examples. Actual strengthening depends on chemistry, temperature, processing route, defects, and precipitation effects.
Formula Used
1) Size misfit
ε_size = |(r_solute − r_matrix) / r_matrix|
2) Modulus misfit
ε_modulus = |(G_solute − G_matrix) / G_matrix|
3) Effective misfit
ε_eff = √(ε_size² + α·ε_modulus²)
4) Critical resolved shear increment
Δτ = k · G_matrix · ε_effp · cn
5) Yield strength increment and total yield
Δσ = M · Δτ and σ_total = σ_base + Δσ
In this calculator, p and n depend on the selected model:
- Fleischer-style: p = 1.5, n = 0.5
- Labusch-style: p = 4/3, n = 2/3
This is an empirical engineering estimate. It is useful for screening alloy changes, but it does not replace test data or a full strengthening decomposition.
How to Use This Calculator
- Enter the matrix and solute shear moduli in GPa.
- Enter the matrix and solute atomic radii in pm.
- Choose a solute concentration and select at% or wt%.
- Select Fleischer-style or Labusch-style strengthening behavior.
- Set the Taylor factor and model coefficient to match your calibration method.
- Click Calculate to show results above the form.
- Review the graph to see how strengthening changes with concentration.
- Use the CSV and PDF buttons to save the calculated report.
FAQs
1) What does solid solution strengthening measure?
It estimates how much dissolved solute atoms raise strength by distorting the lattice and resisting dislocation motion. The calculator reports the strengthening increment and the new total yield strength.
2) When should I use the Fleischer-style model?
Use it for quick screening where strengthening scales roughly with the square root of concentration. It is a practical first-pass option for many dilute alloy cases.
3) When is the Labusch-style model better?
It is often chosen when collective solute interactions matter more strongly. That can make it more suitable for some higher-concentration solid solutions or calibration studies.
4) Why include both size and modulus misfit?
Some alloy systems strengthen mainly through size mismatch, while others also show meaningful elastic mismatch. Combining both terms gives a more flexible engineering estimate.
5) Is atomic percent better than weight percent?
Atomic percent is usually more consistent with lattice-based strengthening models. Weight percent can still be useful for approximate plant-level comparisons when detailed atomic conversions are unavailable.
6) What does the Taylor factor do?
It converts the calculated shear resistance increase into a polycrystalline yield-strength increment. Different crystal structures and textures can justify different Taylor factor values.
7) Does this include precipitation or grain refinement?
No. This page isolates solid solution strengthening only. Real alloys may also gain strength from precipitation, dislocation density, phase fraction changes, and grain-size effects.
8) Can I use this for final design allowables?
Use it for estimation, comparison, and sensitivity studies. Final design values should come from validated material data, standards, and testing under the relevant processing and service conditions.