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: chartjs 4.4.7 | JavaScript 22.23.2
// Quality: 88/100 | Created: 2026-09-02
const t = window.ANYPLOT_TOKENS;
// --- Data (in-memory, deterministic) ----------------------------------------
// Fatigue test results for a steel alloy: stress amplitude (MPa) vs. cycles to
// failure (N). Basquin's equation: sigma_a = A * N^b, plus scatter typical of
// multiple coupon specimens tested at the same stress level.
function lcg(seed) {
let state = seed;
return () => {
state = (state * 1664525 + 1013904223) % 4294967296;
return state / 4294967296;
};
}
const rand = lcg(42);
const basquinA = 950; // MPa, fatigue strength coefficient
const basquinB = -0.11; // fatigue strength exponent
const stressLevels = [520, 480, 440, 400, 360, 320, 290, 260, 240, 220];
const specimensPerLevel = 4;
const testPoints = [];
stressLevels.forEach((stress) => {
const meanLogN = Math.log10(stress / basquinA) / basquinB;
for (let i = 0; i < specimensPerLevel; i++) {
const scatter = (rand() - 0.5) * 0.42; // log10(N) scatter band
const logN = meanLogN + scatter;
testPoints.push({ x: Math.pow(10, logN), y: stress });
}
});
const fitCycles = [1e3, 1e7];
const fitLine = fitCycles.map((n) => ({ x: n, y: basquinA * Math.pow(n, basquinB) }));
const ultimateStrength = 780; // MPa
const yieldStrength = 620; // MPa
const enduranceLimit = 230; // MPa
const enduranceStart = 1e6; // cycles beyond which the endurance limit applies
// --- Mount -------------------------------------------------------------------
const canvas = document.createElement("canvas");
document.getElementById("container").appendChild(canvas);
// --- Chart ---------------------------------------------------------------------
new Chart(canvas, {
type: "scatter",
data: {
datasets: [
{
label: "Test specimens",
data: testPoints,
backgroundColor: t.palette[0],
borderColor: t.pageBg,
borderWidth: 1,
pointRadius: 6,
pointHoverRadius: 6,
showLine: false,
order: 1,
},
{
label: "Basquin fit",
data: fitLine,
type: "line",
borderColor: t.palette[1],
backgroundColor: t.palette[1],
borderWidth: 3,
pointRadius: 0,
tension: 0,
order: 2,
},
{
label: "Ultimate strength (780 MPa)",
data: [
{ x: 1e3, y: ultimateStrength },
{ x: 1e7, y: ultimateStrength },
],
type: "line",
borderColor: t.palette[2],
backgroundColor: t.palette[2],
borderWidth: 2,
borderDash: [12, 4, 2, 4],
pointRadius: 0,
tension: 0,
order: 3,
},
{
label: "Yield strength (620 MPa)",
data: [
{ x: 1e3, y: yieldStrength },
{ x: 1e7, y: yieldStrength },
],
type: "line",
borderColor: t.palette[3],
backgroundColor: t.palette[3],
borderWidth: 2,
borderDash: [10, 6],
pointRadius: 0,
tension: 0,
order: 4,
},
{
label: "Endurance limit (230 MPa)",
data: [
{ x: enduranceStart, y: enduranceLimit },
{ x: 1e7, y: enduranceLimit },
],
type: "line",
borderColor: t.palette[5],
backgroundColor: t.palette[5],
borderWidth: 2,
borderDash: [3, 5],
pointRadius: 0,
tension: 0,
order: 5,
},
],
},
options: {
responsive: true,
maintainAspectRatio: false,
animation: false,
plugins: {
title: {
display: true,
text: "sn-curve-basic · javascript · chartjs · anyplot.ai",
color: t.ink,
font: { size: 22, weight: "500" },
padding: { bottom: 20 },
},
legend: {
position: "top",
align: "end",
labels: { color: t.inkSoft, font: { size: 14 }, boxWidth: 24, usePointStyle: true },
},
},
scales: {
x: {
type: "logarithmic",
min: 1e3,
max: 1e7,
title: { display: true, text: "Cycles to Failure (N)", color: t.ink, font: { size: 16 } },
ticks: {
color: t.inkSoft,
font: { size: 14 },
callback: (value) => {
const log10 = Math.log10(value);
return Number.isInteger(log10) ? `10^${log10}` : null;
},
},
grid: { color: t.grid },
},
y: {
type: "logarithmic",
min: 150,
max: 850,
title: { display: true, text: "Stress Amplitude (MPa)", color: t.ink, font: { size: 16 } },
ticks: {
color: t.inkSoft,
font: { size: 14 },
callback: (value) => {
if ([150, 200, 300, 400, 500, 600, 700, 800].includes(value)) return value;
return null;
},
},
grid: { color: t.grid },
},
},
},
});
Runnable source as JSON, for any HTTP client: https://api.anyplot.ai/specs/sn-curve-basic/chartjs/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": "javascript",
"library": "chartjs",
"page": "https://anyplot.ai/sn-curve-basic/javascript/chartjs",
"hub": "https://anyplot.ai/sn-curve-basic",
"code_json": "https://api.anyplot.ai/specs/sn-curve-basic/chartjs/code",
"spec_json": "https://api.anyplot.ai/specs/sn-curve-basic",
"render_light_png": "https://storage.googleapis.com/anyplot-images/plots/sn-curve-basic/javascript/chartjs/plot-light.png",
"render_dark_png": "https://storage.googleapis.com/anyplot-images/plots/sn-curve-basic/javascript/chartjs/plot-dark.png",
"interactive_light_html": "https://storage.googleapis.com/anyplot-images/plots/sn-curve-basic/javascript/chartjs/plot-light.html",
"interactive_dark_html": "https://storage.googleapis.com/anyplot-images/plots/sn-curve-basic/javascript/chartjs/plot-dark.html",
"quality_score": 88.0,
"license": "MIT",
"guide": "https://anyplot.ai/llms.txt"
}Part of S-N Curve (Wöhler Curve) on anyplot.ai.