[IMPL] Implement S-N curve power-law model

[MartinNesladek]

ℹ️ General Information

Component Name: Power law

Component Location: material_laws/SN/

Suggested Python Name: wohler_power_law

FABER WG Relation: 2.1

Brief Description: Stress to life and life to stress calculation via the power law

Priority: 10

Technical Complexity: 2

Estimated Effort: 4

Dependencies: -

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Implementation Details

📋 Specification

A function implementing the power-law representation of an S–N curve, allowing the computation of the number of cycles ($N$) from a given stress amplitude ($\sigma_a$), and vice versa. The parameters ($C$) and ($w$) are regression constants (coefficient and exponent) obtained from fatigue testing.

Mathematical Formulation

Life from stress amplitude:

$$ \displaystyle N = \frac{C}{\sigma_{a}^{w}} $$

Stress amplitude from life:

$$ \displaystyle \sigma_{a} = \left(\frac{C}{N}\right)^{1/w} $$

$$  \displaystyle N = \frac{C}{\sigma_{a}^{w}} $$

$$  \displaystyle \sigma_{a} = \left(\frac{C}{N}\right)^{1/w} $$

Inputs

1. Power-law model regression parameters

Parameter	Symbol	Type	Description	Units	Constraints
SN_C	$C$	array of floats	power-law coefficient	$MPa^{w}$	$>0$
SN_w	$w$	array of floats	power-law exponent	-	$>0$

2. Stress / Strain values or life

Parameter	Symbol	Type	Description	Units	Range
stress_amp	$\sigma_a$	array of floats	stress amplitude	MPa	$(0; \infty)$
life	$N$	array of floats	Number of cycles	-	$(0; \infty)$

Outputs

Parameter	Type	Description	Units	Range
$N$	array of floats	Number of cycles	-	$(0; \infty)$
$\sigma_{a}$	array of floats	Stress amplitude	-	$(0; \infty)$

Expected Behavior

🔧 Implementation Guidelines

Function Signature

# Suggested function signature

Code Structure

Error Handling

✅ Validation & Testing

Test Cases

Test Case	Inputs	Expected Outputs	Notes
Example 1	$\sigma_{a} = 300 MPa; C = 2.2\cdot10^{13} MPa^{3}, w = 3$	$N = 814,814$

Validation Criteria

• Mathematical accuracy verified against literature
• Edge cases handled appropriately
• Output format matches specification

📚 References & Resources

J. Draper: Modern Metal Fatigue Analysis. EMAS Publishing, 2008

📝 Technical Notes

Performance Considerations

Edge Cases to Handle

Special Requirements