An S-N curve (also known as a Wöhler curve) visualizes the relationship between alternating stress amplitude and the number of cycles to failure for a material under fatigue loading. Both axes typically use logarithmic scales, with stress on the y-axis and cycle count on the x-axis. This plot is fundamental for predicting material fatigue life and identifying key material properties such as ultimate strength, yield strength, and endurance limit.
""" anyplot.ai
sn-curve-basic: S-N Curve (Wöhler Curve)
Library: plotnine 0.15.4 | Python 3.13.13
Quality: 91/100 | Updated: 2026-05-20
"""
import os
import numpy as np
import pandas as pd
from plotnine import (
aes,
annotate,
element_blank,
element_line,
element_rect,
element_text,
geom_hline,
geom_line,
geom_point,
geom_ribbon,
geom_rug,
ggplot,
labs,
scale_shape_manual,
scale_x_log10,
scale_y_log10,
theme,
theme_minimal,
)
THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
ELEVATED_BG = "#FFFDF6" if THEME == "light" else "#242420"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_SOFT = "#4A4A44" if THEME == "light" else "#B8B7B0"
IMPRINT = ["#009E73", "#C475FD", "#4467A3", "#BD8233", "#AE3030", "#2ABCCD", "#954477"]
# Data - S-N curve for steel specimen fatigue testing
np.random.seed(42)
# Material properties (MPa)
ultimate_strength = 550
yield_strength = 350
endurance_limit = 250
# Using Basquin equation: S = A * N^b
A = 1200
b = -0.12
sigma_logN = 0.3 # Log-normal scatter in cycles
stress_levels = np.array([500, 450, 400, 375, 350, 325, 300, 280, 270, 260, 255])
cycles = []
stress = []
point_type = []
for s in stress_levels:
n_expected = (s / A) ** (1 / b)
n_tests = np.random.randint(3, 6)
scatter = np.random.lognormal(0, sigma_logN, n_tests)
n_values = n_expected * scatter
cycles.extend(n_values)
stress.extend([s] * n_tests)
point_type.extend(["failure"] * n_tests)
# Runout data points (did not fail) — marked with distinct marker shape
runout_cycles = [1e7, 2e7, 5e7]
runout_stress = [endurance_limit - 10, endurance_limit - 5, endurance_limit + 5]
cycles.extend(runout_cycles)
stress.extend(runout_stress)
point_type.extend(["runout"] * 3)
df = pd.DataFrame({"cycles": cycles, "stress": stress, "type": point_type})
# Basquin fit line with ±2σ scatter band (converts log-N scatter to stress bounds)
fit_cycles = np.logspace(2, 7, 100)
fit_stress = A * fit_cycles**b
fit_stress_upper = fit_stress * np.exp(2 * sigma_logN * abs(b))
fit_stress_lower = fit_stress * np.exp(-2 * sigma_logN * abs(b))
df_fit = pd.DataFrame(
{"cycles": fit_cycles, "stress": fit_stress, "stress_upper": fit_stress_upper, "stress_lower": fit_stress_lower}
)
anyplot_theme = theme(
figure_size=(8, 4.5),
plot_background=element_rect(fill=PAGE_BG, color=PAGE_BG),
panel_background=element_rect(fill=PAGE_BG),
panel_grid_major=element_line(color=INK, size=0.3, alpha=0.10),
panel_grid_minor=element_line(color=INK, size=0.2, alpha=0.05),
panel_border=element_blank(),
axis_line_x=element_line(color=INK_SOFT, size=0.8),
axis_line_y=element_line(color=INK_SOFT, size=0.8),
axis_title=element_text(color=INK, size=10),
axis_text=element_text(color=INK_SOFT, size=8),
plot_title=element_text(color=INK, size=12, weight="bold"),
legend_background=element_rect(fill=ELEVATED_BG, color=None),
legend_text=element_text(color=INK_SOFT, size=8),
legend_title=element_text(color=INK, size=9),
plot_margin=0.05,
)
plot = (
ggplot()
# ±2σ scatter band via geom_ribbon — idiomatic plotnine uncertainty visualization
+ geom_ribbon(df_fit, aes(x="cycles", ymin="stress_lower", ymax="stress_upper"), fill=IMPRINT[0], alpha=0.12)
# Basquin fit line
+ geom_line(df_fit, aes(x="cycles", y="stress"), color=IMPRINT[0], size=1.2, alpha=0.85)
# Data points — shape mapped to type for runout vs failure distinction
+ geom_point(df, aes(x="cycles", y="stress", shape="type"), color=IMPRINT[0], size=4.2, alpha=0.80)
# geom_rug exposes marginal data density along both axes — distinctive plotnine feature
+ geom_rug(df, aes(x="cycles", y="stress"), color=IMPRINT[0], alpha=0.35, size=0.5)
# Reference lines with Okabe-Ito colors; endurance limit slightly thicker as focal point
+ geom_hline(yintercept=ultimate_strength, linetype="dashed", color=IMPRINT[1], size=0.9, alpha=0.85)
+ geom_hline(yintercept=yield_strength, linetype="dashed", color=IMPRINT[2], size=0.9, alpha=0.85)
+ geom_hline(yintercept=endurance_limit, linetype="dashed", color=IMPRINT[3], size=1.2, alpha=0.90)
+ annotate(
"text",
x=1e3,
y=ultimate_strength + 20,
label="Ultimate Strength (550 MPa)",
size=10,
color=IMPRINT[1],
ha="left",
)
+ annotate(
"text", x=2e5, y=yield_strength + 20, label="Yield Strength (350 MPa)", size=10, color=IMPRINT[2], ha="left"
)
+ annotate(
"text", x=1e3, y=endurance_limit - 25, label="Endurance Limit (250 MPa)", size=10, color=IMPRINT[3], ha="left"
)
# Logarithmic scales
+ scale_x_log10()
+ scale_y_log10()
# Shape scale distinguishes runout (triangle) from failure (circle)
+ scale_shape_manual(values={"failure": "o", "runout": "^"}, name="Test Result")
# Labels
+ labs(
x="Number of Cycles to Failure (N)",
y="Stress Amplitude (MPa)",
title="sn-curve-basic · python · plotnine · anyplot.ai",
)
+ theme_minimal()
+ anyplot_theme
)
plot.save(f"plot-{THEME}.png", dpi=400, width=8, height=4.5, units="in")
Part of S-N Curve (Wöhler Curve) on anyplot.ai.