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基于 SOC 职业分类
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基于 SOC 职业分类
| name | fatigue-analysis-1-s-n-curve-fundamentals |
| description | Sub-skill of fatigue-analysis: 1. S-N Curve Fundamentals. |
| version | 1.0.0 |
| category | engineering |
| type | reference |
| scripts_exempt | true |
S-N Curve Equation:
N = a / (Δσ)^m
Where:
- N = Number of cycles to failure
- Δσ = Stress range
- a = S-N curve constant
- m = Slope of S-N curve (typically 3 for steel, 3-5 for welds)
DNV S-N Curves:
import numpy as np
def get_dnv_sn_curve(
curve_class: str,
thickness: float = 25
) -> dict:
"""
Get DNV S-N curve parameters.
DNV-RP-C203 S-N curves:
- B1: High strength welds, machined
- C: Good quality welds
- D: Normal welds
- E: Rough welds
- F, F1, F3: Poor quality, notches
- G: Severe notches
- W1, W2, W3: Seawater with cathodic protection
Args:
curve_class: DNV curve classification
thickness: Plate thickness (mm) for thickness effect
Returns:
S-N curve parameters
"""
# DNV-RP-C203 Table 2-1
sn_curves = {
'B1': {'log_a1': 15.117, 'm1': 4.0, 'log_a2': 17.146, 'm2': 5.0},
'B2': {'log_a1': 14.885, 'm1': 4.0, 'log_a2': 16.856, 'm2': 5.0},
'C': {'log_a1': 12.592, 'm1': 3.0, 'log_a2': 16.320, 'm2': 5.0},
'C1': {'log_a1': 12.449, 'm1': 3.0, 'log_a2': 16.081, 'm2': 5.0},
'C2': {'log_a1': 12.301, 'm1': 3.0, 'log_a2': 15.835, 'm2': 5.0},
'D': {'log_a1': 12.164, 'm1': 3.0, 'log_a2': 15.606, 'm2': 5.0},
'E': {'log_a1': 11.972, 'm1': 3.0, 'log_a2': 15.350, 'm2': 5.0},
'F': {'log_a1': 11.699, 'm1': 3.0, 'log_a2': 14.832, 'm2': 5.0},
'F1': {'log_a1': 11.546, 'm1': 3.0, 'log_a2': 14.576, 'm2': 5.0},
'F3': {'log_a1': 11.398, 'm1': 3.0, 'log_a2': 14.330, 'm2': 5.0},
'G': {'log_a1': 11.245, 'm1': 3.0, 'log_a2': 14.080, 'm2': 5.0},
'W1': {'log_a1': 11.764, 'm1': 3.0, 'log_a2': 15.091, 'm2': 5.0},
'W2': {'log_a1': 11.533, 'm1': 3.0, 'log_a2': 14.706, 'm2': 5.0},
'W3': {'log_a1': 11.262, 'm1': 3.0, 'log_a2': 14.183, 'm2': 5.0}
}
if curve_class not in sn_curves:
raise ValueError(f"Unknown S-N curve class: {curve_class}")
params = sn_curves[curve_class]
# Convert log_a to a
a1 = 10 ** params['log_a1']
a2 = 10 ** params['log_a2']
# Thickness correction (ref thickness = 25mm)
if thickness > 25:
t_factor = (25 / thickness) ** 0.25
a1 *= t_factor ** params['m1']
a2 *= t_factor ** params['m2']
return {
'class': curve_class,
'a1': a1,
'm1': params['m1'],
'a2': a2,
'm2': params['m2'],
'thickness_mm': thickness
}
# Example: Get F3 curve for mooring chain
sn_f3 = get_dnv_sn_curve('F3', thickness=127) # 127mm chain
print(f"S-N Curve F3 (Chain):")
print(f" a1 = {sn_f3['a1']:.2e}, m1 = {sn_f3['m1']}")
print(f" a2 = {sn_f3['a2']:.2e}, m2 = {sn_f3['m2']}")
Calculate Cycles to Failure:
def calculate_cycles_to_failure(
stress_range: float,
sn_curve: dict
) -> float:
"""
Calculate cycles to failure for given stress range.
N = a / (Δσ)^m
Args:
stress_range: Stress range (MPa)
sn_curve: S-N curve parameters from get_dnv_sn_curve()
Returns:
Cycles to failure
"""
# Use first segment if stress range is high
# Switch to second segment if N > 1e7 (DNV bi-linear curve)
N1 = sn_curve['a1'] / (stress_range ** sn_curve['m1'])
if N1 <= 1e7:
return N1
else:
# Use second segment
N2 = sn_curve['a2'] / (stress_range ** sn_curve['m2'])
return N2
# Example
stress_range = 50 # MPa
N = calculate_cycles_to_failure(stress_range, sn_f3)
print(f"Stress range: {stress_range} MPa")
print(f"Cycles to failure: {N:.2e}")
print(f"Years at 1 Hz: {N / (365.25 * 24 * 3600):.2f}")