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: makie 0.21.9 | Julia 1.11.9
# Quality: 91/100 | Created: 2026-09-02
using CairoMakie
using Colors
using Random
using Statistics
Random.seed!(42)
# --- Theme tokens -----------------------------------------------------------
const THEME = get(ENV, "ANYPLOT_THEME", "light")
const PAGE_BG = THEME == "light" ? colorant"#FAF8F1" : colorant"#1A1A17"
const INK = THEME == "light" ? colorant"#1A1A17" : colorant"#F0EFE8"
const INK_SOFT = THEME == "light" ? colorant"#4A4A44" : colorant"#B8B7B0"
const IMPRINT_PALETTE = [
colorant"#009E73", colorant"#C475FD", colorant"#4467A3", colorant"#BD8233",
colorant"#AE3030", colorant"#2ABCCD", colorant"#954477", colorant"#99B314",
]
# --- Data: fatigue test coupons across 8 stress levels, 4 specimens each ---
stress_levels = [550.0, 500.0, 450.0, 400.0, 350.0, 300.0, 275.0, 260.0]
specimens_per_level = 4
sigma_f_prime = 900.0 # Basquin fatigue strength coefficient (MPa)
basquin_b = -0.09 # Basquin fatigue strength exponent
stress = Float64[]
cycles = Float64[]
for s in stress_levels
mean_n = 0.5 * (s / sigma_f_prime)^(1 / basquin_b)
for _ in 1:specimens_per_level
n_i = mean_n * 10^(0.09 * randn())
push!(stress, s)
push!(cycles, n_i)
end
end
# Basquin power-law fit (least squares in log-log space)
log_n = log10.(cycles)
log_s = log10.(stress)
slope = sum((log_n .- mean(log_n)) .* (log_s .- mean(log_s))) / sum((log_n .- mean(log_n)) .^ 2)
intercept = mean(log_s) - slope * mean(log_n)
fit_cycles = exp10.(range(log10(50.0), log10(1.5e6); length = 200))
fit_stress = exp10.(intercept .+ slope .* log10.(fit_cycles))
ultimate_strength = 600.0
yield_strength = 450.0
endurance_limit = 250.0
# Fatigue-region boundaries: low-cycle/high-cycle split at the conventional
# 10^3-cycle mark; high-cycle/infinite-life split at the cycle count where the
# Basquin fit crosses the endurance limit.
xlim_lo, xlim_hi = 50.0, 1.5e6
low_cycle_boundary = 1.0e3
infinite_life_boundary = clamp(
exp10((log10(endurance_limit) - intercept) / slope),
low_cycle_boundary * 1.5,
xlim_hi * 0.98,
)
# --- Plot --------------------------------------------------------------------
fig = Figure(
size = (1600, 900),
fontsize = 14,
backgroundcolor = PAGE_BG,
)
ax = Axis(
fig[1, 1];
title = "sn-curve-basic · julia · makie · anyplot.ai",
titlesize = 20,
titlecolor = INK,
xlabel = "Cycles to Failure, N",
ylabel = "Stress Amplitude (MPa)",
xlabelsize = 14,
ylabelsize = 14,
xlabelcolor = INK,
ylabelcolor = INK,
xticklabelsize = 12,
yticklabelsize = 12,
xticklabelcolor = INK_SOFT,
yticklabelcolor = INK_SOFT,
xtickcolor = INK_SOFT,
ytickcolor = INK_SOFT,
xscale = log10,
yscale = log10,
yticks = [200, 250, 300, 400, 500, 600, 700],
ytickformat = ys -> string.(round.(Int, ys)),
backgroundcolor = PAGE_BG,
topspinevisible = false,
rightspinevisible = false,
leftspinecolor = INK_SOFT,
bottomspinecolor = INK_SOFT,
xgridcolor = RGBAf(INK.r, INK.g, INK.b, 0.15),
ygridcolor = RGBAf(INK.r, INK.g, INK.b, 0.15),
xminorgridvisible = false,
yminorgridvisible = false,
)
xlims!(ax, xlim_lo, xlim_hi)
ylims!(ax, 200.0, 700.0)
# Fatigue-region demarcation: subtle dotted separators + bottom-edge labels,
# called out per the spec's low-cycle / high-cycle / infinite-life regions.
vlines!(ax, [low_cycle_boundary, infinite_life_boundary];
color = RGBAf(INK_SOFT.r, INK_SOFT.g, INK_SOFT.b, 0.4),
linestyle = :dot, linewidth = 1.5)
region_label_y = 207.0
mid_low = exp10(0.5 * (log10(xlim_lo) + log10(low_cycle_boundary)))
mid_high = exp10(0.5 * (log10(low_cycle_boundary) + log10(infinite_life_boundary)))
mid_inf = exp10(0.5 * (log10(infinite_life_boundary) + log10(xlim_hi)))
text!(ax, mid_low, region_label_y; text = "Low-Cycle", fontsize = 11,
color = INK_SOFT, align = (:center, :bottom))
text!(ax, mid_high, region_label_y; text = "High-Cycle", fontsize = 11,
color = INK_SOFT, align = (:center, :bottom))
text!(ax, mid_inf, region_label_y; text = "Infinite Life", fontsize = 11,
color = INK_SOFT, align = (:center, :bottom))
hlines!(ax, [ultimate_strength]; color = IMPRINT_PALETTE[2], linestyle = :dash,
linewidth = 2.5, label = "Ultimate Strength")
hlines!(ax, [yield_strength]; color = IMPRINT_PALETTE[3], linestyle = :dash,
linewidth = 2.5, label = "Yield Strength")
hlines!(ax, [endurance_limit]; color = IMPRINT_PALETTE[4], linestyle = :dash,
linewidth = 2.5, label = "Endurance Limit")
lines!(ax, fit_cycles, fit_stress; color = INK_SOFT, linewidth = 3,
label = "Basquin fit")
scatter!(ax, cycles, stress; color = IMPRINT_PALETTE[1], markersize = 16,
strokewidth = 1.5, strokecolor = PAGE_BG, label = "Test specimens")
# Annotate where the Basquin fit crosses the endurance limit — the point
# beyond which infinite fatigue life is predicted.
n_label = infinite_life_boundary >= 1e6 ?
string(round(infinite_life_boundary / 1e6; digits = 2), "M") :
string(round(Int, infinite_life_boundary / 1e3), "k")
text!(ax, infinite_life_boundary * 0.97, endurance_limit * 1.1;
text = "fit crosses endurance limit\nN ≈ $(n_label)",
fontsize = 11, color = INK_SOFT, align = (:right, :bottom))
axislegend(ax; position = :rt, labelcolor = INK_SOFT, framevisible = false,
labelsize = 12)
# --- Save --------------------------------------------------------------------
save("plot-$(THEME).png", fig; px_per_unit = 2)
Runnable source as JSON, for any HTTP client: https://api.anyplot.ai/specs/sn-curve-basic/makie/code. Any spec id and library id listed in llms-full.txt fit the same URL shape; every URL below is complete and callable.
{
"spec_id": "sn-curve-basic",
"language": "julia",
"library": "makie",
"page": "https://anyplot.ai/sn-curve-basic/julia/makie",
"hub": "https://anyplot.ai/sn-curve-basic",
"code_json": "https://api.anyplot.ai/specs/sn-curve-basic/makie/code",
"spec_json": "https://api.anyplot.ai/specs/sn-curve-basic",
"render_light_png": "https://storage.googleapis.com/anyplot-images/plots/sn-curve-basic/julia/makie/plot-light.png",
"render_dark_png": "https://storage.googleapis.com/anyplot-images/plots/sn-curve-basic/julia/makie/plot-dark.png",
"quality_score": 91.0,
"license": "MIT",
"guide": "https://anyplot.ai/llms.txt"
}Part of S-N Curve (Wöhler Curve) on anyplot.ai.