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: pygal 3.1.0 | Python 3.13.13
Quality: 86/100 | Updated: 2026-05-20
"""
import math
import os
import re
import sys
import numpy as np
THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_MUTED = "#6B6A63" if THEME == "light" else "#A8A79F"
IMPRINT = ("#009E73", "#C475FD", "#4467A3", "#BD8233", "#AE3030", "#2ABCCD", "#954477")
# Remove current dir from sys.path to avoid shadowing the pygal package
_cwd = sys.path[0] if sys.path[0] else "."
if _cwd in sys.path:
sys.path.remove(_cwd)
import pygal
from cairosvg import svg2png as _svg2png
from pygal.style import Style
sys.path.insert(0, _cwd)
# ── Data ──────────────────────────────────────────────────────────────────────
np.random.seed(42)
stress_levels = np.array([450, 400, 350, 300, 275, 250, 225, 210, 200, 195])
base_cycles = np.array([1e2, 5e2, 2e3, 1e4, 3e4, 1e5, 4e5, 1e6, 5e6, 1e7])
cycles_data: list[float] = []
stress_data: list[float] = []
for stress, base_n in zip(stress_levels, base_cycles, strict=True):
n_samples = np.random.randint(3, 6)
scatter = np.exp(np.random.normal(0, 0.3, n_samples))
cycles = base_n * scatter
cycles_data.extend(cycles)
stress_data.extend([stress] * n_samples)
cycles_arr = np.array(cycles_data)
stress_arr = np.array(stress_data)
# Basquin equation fit: S = A * N^b (linear in log-log space)
log_cycles = np.log10(cycles_arr)
log_stress = np.log10(stress_arr)
coeffs = np.polyfit(log_cycles, log_stress, 1)
b = coeffs[0]
A = 10 ** coeffs[1]
fit_cycles = np.logspace(2, 7, 100)
fit_stress = A * (fit_cycles**b)
# Material reference values (MPa)
ultimate_strength = 520
yield_strength = 350
endurance_limit = 190
# pygal's logarithmic=True only applies to the x-axis in XY mode.
# Log10-transform all stress (y) values for a true log-log plot,
# then map explicit y_labels back to human-readable MPa values.
_zone = lambda c: (
"Low-Cycle Fatigue" if c < 1e3 else ("High-Cycle Fatigue" if c < 1e6 else "Near Endurance Limit")
)
xy_points = [
{
"value": (float(c), math.log10(float(s))),
"label": f"{_zone(float(c))}: {float(c):.2e} cycles @ {float(s):.0f} MPa",
}
for c, s in zip(cycles_arr, stress_arr, strict=True)
]
fit_points = [
{"value": (float(c), math.log10(float(s))), "label": f"Fit: {float(c):.2e} → {float(s):.0f} MPa"}
for c, s in zip(fit_cycles, fit_stress, strict=True)
]
ult_log = math.log10(ultimate_strength)
yld_log = math.log10(yield_strength)
end_log = math.log10(endurance_limit)
# ── Style ─────────────────────────────────────────────────────────────────────
custom_style = Style(
background=PAGE_BG,
plot_background=PAGE_BG,
foreground=INK,
foreground_strong=INK,
foreground_subtle=INK_MUTED,
colors=IMPRINT,
title_font_size=66,
label_font_size=56,
major_label_font_size=44,
legend_font_size=44,
value_font_size=36,
stroke_width=3,
opacity=0.75,
opacity_hover=1.0,
)
# ── Chart ─────────────────────────────────────────────────────────────────────
chart = pygal.XY(
width=3200,
height=1800,
style=custom_style,
title="Steel Fatigue · sn-curve-basic · python · pygal · anyplot.ai",
x_title="Cycles to Failure (N)",
y_title="Stress Amplitude (MPa)",
logarithmic=True,
show_dots=True,
dots_size=12,
stroke=True,
show_x_guides=False,
show_y_guides=True,
x_label_rotation=45,
legend_at_bottom=True,
legend_box_size=44,
margin=100,
# Tighter y-range: start just below endurance limit to reduce empty bottom space
range=(math.log10(165), math.log10(600)),
value_formatter=lambda xy: f"{xy[0]:.2e} cycles, {10 ** xy[1]:.0f} MPa" if isinstance(xy, tuple) else str(xy),
)
# X-axis: major log decades
chart.x_labels = [100, 1_000, 10_000, 100_000, 1_000_000, 10_000_000]
# Y-axis: stress labels within the tightened range
y_tick_vals = [200, 250, 300, 350, 400, 450, 500, 550]
chart.y_labels = [{"value": math.log10(v), "label": str(v)} for v in y_tick_vals]
# Series: Test Data first (most prominent), then derived/reference
chart.add("Test Data", xy_points, dots_size=20, stroke=False, show_dots=True)
chart.add(
"Basquin Fit (S = A·N^b)",
fit_points,
stroke=True,
show_dots=False,
stroke_style={"width": 9, "dasharray": "20, 10"},
)
# Distinct stroke styles per reference line: solid / long-dash / short-dash
chart.add(
f"Ultimate Strength, Su = {ultimate_strength} MPa",
[(100, ult_log), (1e7, ult_log)],
stroke=True,
show_dots=False,
stroke_style={"width": 5, "opacity": 0.80},
)
chart.add(
f"Yield Strength, Sy = {yield_strength} MPa",
[(100, yld_log), (1e7, yld_log)],
stroke=True,
show_dots=False,
stroke_style={"width": 5, "dasharray": "30, 8", "opacity": 0.80},
)
# Endurance limit: thicker + shorter dashes for better visibility on light bg
chart.add(
f"Endurance Limit, Se = {endurance_limit} MPa",
[(100, end_log), (1e7, end_log)],
stroke=True,
show_dots=False,
stroke_style={"width": 12, "dasharray": "14, 5", "opacity": 0.90},
)
# ── SVG injection: fatigue region bands ───────────────────────────────────────
def _get_plot_dims(svg: str) -> tuple[float, float]:
"""Return (width, height) of plot area from the inner background rect in pygal SVG.
pygal renders <g class="plot" transform="translate(tx,ty)"> containing the inner
background <rect x=0 y=0 width=W height=H/>. Coordinates inside that group are
relative; we only need W and H to map log-scale x positions.
"""
# Find the opening tag of <g class="plot"> (exact class, not "plot overlay")
plot_tag = re.search(r'<g[^>]*\bclass="plot"[^>]*>', svg)
if plot_tag:
# Find the first <rect> after the plot group tag (that's the background rect)
rect_m = re.search(r"<rect\b[^>]+>", svg[plot_tag.end() :])
if rect_m:
attrs: dict[str, float] = {}
for attr in ("width", "height"):
am = re.search(rf'\b{attr}="([0-9.]+)"', rect_m.group(0))
if am:
attrs[attr] = float(am.group(1))
if "width" in attrs and "height" in attrs:
return attrs["width"], attrs["height"]
# Fallback for width=3200, height=1800, margin=100 with our font sizes
return 2760.0, 1290.0
def _inject_region_bands(svg: str, theme: str) -> str:
"""Inject colored fatigue-region background bands and labels into pygal SVG.
Elements are placed in the plot group's local coordinate space (origin = top-left
of the inner plot area), so no absolute pixel offset calculation is needed.
"""
pw, ph = _get_plot_dims(svg)
# X-axis: log10(100)=2 → log10(1e7)=7, five decades mapped to [0, pw]
def log_to_x(log_n: float) -> float:
return (log_n - 2.0) / 5.0 * pw
x_lcf = log_to_x(3.0) # LCF | HCF boundary at N = 1 000
x_hcf = log_to_x(6.0) # HCF | Infinite Life boundary at N = 1 000 000
# Semi-transparent fills (fill + fill-opacity for cairosvg compatibility)
if theme == "light":
region_fills = [("#CC8888", "0.10"), ("#88AA88", "0.10"), ("#8888BB", "0.10")]
div_stroke = "#6B6A63"
lbl_fill = "#6B6A63"
else:
region_fills = [("#BB5555", "0.09"), ("#55994A", "0.09"), ("#5577BB", "0.09")]
div_stroke = "#A8A79F"
lbl_fill = "#A8A79F"
# Labels near the top of the plot area (above all data points)
lbl_y = 55.0
lbl_sz = 38
parts = ['<g class="fatigue-regions">']
# Three region fills
for rx, rw, (rfill, rop) in [
(0.0, x_lcf, region_fills[0]),
(x_lcf, x_hcf - x_lcf, region_fills[1]),
(x_hcf, pw - x_hcf, region_fills[2]),
]:
parts.append(
f'<rect x="{rx:.1f}" y="0" width="{rw:.1f}" height="{ph:.1f}" '
f'fill="{rfill}" fill-opacity="{rop}" stroke="none"/>'
)
# Subtle vertical dividers at region boundaries
for xd in (x_lcf, x_hcf):
parts.append(
f'<line x1="{xd:.1f}" y1="0" x2="{xd:.1f}" y2="{ph:.1f}" '
f'stroke="{div_stroke}" stroke-width="2" stroke-dasharray="8,4" opacity="0.30"/>'
)
# Region labels centered in each band
for lx, lbl in [
(x_lcf / 2, "Low-Cycle"),
((x_lcf + x_hcf) / 2, "High-Cycle Fatigue"),
((x_hcf + pw) / 2, "Infinite Life"),
]:
parts.append(
f'<text x="{lx:.1f}" y="{lbl_y:.1f}" text-anchor="middle" '
f'fill="{lbl_fill}" font-size="{lbl_sz}" font-family="sans-serif" '
f'opacity="0.55">{lbl}</text>'
)
parts.append("</g>")
region_block = "".join(parts)
# Insert immediately after the plot background rect so bands appear above bg,
# but behind grid guides and data series.
plot_tag = re.search(r'<g[^>]*\bclass="plot"[^>]*>', svg)
if plot_tag:
after_tag = svg[plot_tag.end() :]
bg_rect = re.search(r"<rect\b[^>]+>", after_tag)
if bg_rect:
insert_pos = plot_tag.end() + bg_rect.end()
return svg[:insert_pos] + region_block + svg[insert_pos:]
# Fallback: insert just before </svg>
return svg.replace("</svg>", region_block + "</svg>")
# ── Render & save ─────────────────────────────────────────────────────────────
svg_raw = chart.render()
# Inject region bands into a copy of the SVG, then convert to PNG via cairosvg
svg_enhanced = _inject_region_bands(svg_raw.decode("utf-8"), THEME).encode("utf-8")
_svg2png(bytestring=svg_enhanced, write_to=f"plot-{THEME}.png")
# HTML export uses the original SVG (preserves full pygal interactivity)
with open(f"plot-{THEME}.html", "wb") as f:
f.write(svg_raw)
Part of S-N Curve (Wöhler Curve) on anyplot.ai.