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: highcharts 12.6.0 | JavaScript 22.23.2
// Quality: 91/100 | Created: 2026-09-02
const t = window.ANYPLOT_TOKENS;
// --- Data (in-memory, deterministic) ----------------------------------------
// Fixed-seed LCG — the browser has no seeded RNG.
function lcg(seed) {
let state = seed;
return function () {
state = (state * 1664525 + 1013904223) % 4294967296;
return state / 4294967296;
};
}
const rand = lcg(42);
// Basquin's law for a steel alloy: stress = Sf' * (2N)^b
const FATIGUE_STRENGTH_COEFF = 1250; // Sf', MPa
const FATIGUE_STRENGTH_EXP = -0.095; // b
const ULTIMATE_STRENGTH = 620; // MPa
const YIELD_STRENGTH = 415; // MPa
const ENDURANCE_LIMIT = 180; // MPa — asymptote for infinite life
const RUNOUT_CYCLES = 2e7; // test termination — specimens beyond this are "runouts"
function cyclesForStress(stress) {
return 0.5 * Math.pow(stress / FATIGUE_STRENGTH_COEFF, 1 / FATIGUE_STRENGTH_EXP);
}
function stressForCycles(cycles) {
return Math.max(FATIGUE_STRENGTH_COEFF * Math.pow(2 * cycles, FATIGUE_STRENGTH_EXP), ENDURANCE_LIMIT);
}
// Test specimens at 11 stress levels, 5 specimens each (steel coupon fatigue tests).
// The top two levels (480, 450 MPa) sit above yield strength, giving the
// low-cycle/plastic region alongside the high-cycle/elastic and infinite-life ones.
const stressLevels = [480, 450, 380, 340, 305, 275, 250, 225, 205, 190, 180];
const specimensPerLevel = 5;
const testData = [];
stressLevels.forEach((stress) => {
const meanCycles = cyclesForStress(stress);
for (let i = 0; i < specimensPerLevel; i++) {
const scatterFactor = 0.6 + rand() * 0.8; // specimen-to-specimen scatter
const cycles = Math.min(Math.round(meanCycles * scatterFactor), RUNOUT_CYCLES);
testData.push([cycles, stress]);
}
});
// Basquin fit curve, floored at the endurance limit
const fitCurve = [];
const fitPoints = 60;
for (let i = 0; i <= fitPoints; i++) {
const logN = 3 + (i / fitPoints) * (Math.log10(RUNOUT_CYCLES) - 3);
const cycles = Math.pow(10, logN);
fitCurve.push([cycles, stressForCycles(cycles)]);
}
function formatCycles(value) {
if (value >= 1e6) return `${value / 1e6}M`;
if (value >= 1e3) return `${value / 1e3}k`;
return `${value}`;
}
// --- Chart -------------------------------------------------------------------
Highcharts.chart("container", {
chart: {
type: "scatter",
backgroundColor: "transparent",
animation: false,
style: { fontFamily: "inherit" },
},
credits: { enabled: false },
colors: t.palette,
title: {
text: "sn-curve-basic · javascript · highcharts · anyplot.ai",
style: { color: t.ink, fontSize: "22px", fontWeight: "600" },
},
xAxis: {
type: "logarithmic",
title: { text: "Cycles to Failure (N)", style: { color: t.inkSoft, fontSize: "16px" } },
lineColor: t.inkSoft,
tickColor: t.inkSoft,
gridLineColor: t.grid,
gridLineWidth: 1,
labels: {
style: { color: t.inkSoft, fontSize: "14px" },
formatter: function () {
return formatCycles(this.value);
},
},
min: 1e3,
max: RUNOUT_CYCLES,
},
yAxis: {
type: "logarithmic",
title: { text: "Stress Amplitude (MPa)", style: { color: t.inkSoft, fontSize: "16px" } },
lineColor: t.inkSoft,
tickColor: t.inkSoft,
gridLineColor: t.grid,
labels: { style: { color: t.inkSoft, fontSize: "14px" } },
min: 150,
max: 700,
startOnTick: false,
endOnTick: false,
plotLines: [
{
value: ULTIMATE_STRENGTH,
color: t.ink,
dashStyle: "Solid",
width: 1.5,
zIndex: 5,
label: {
text: `Ultimate Strength (${ULTIMATE_STRENGTH} MPa)`,
align: "right",
x: -10,
y: -6,
style: { color: t.inkSoft, fontSize: "13px" },
},
},
{
value: YIELD_STRENGTH,
color: t.ink,
dashStyle: "Dash",
width: 1.5,
zIndex: 5,
label: {
text: `Yield Strength (${YIELD_STRENGTH} MPa)`,
align: "right",
x: -10,
y: -6,
style: { color: t.inkSoft, fontSize: "13px" },
},
},
{
value: ENDURANCE_LIMIT,
color: t.ink,
dashStyle: "ShortDot",
width: 1.5,
zIndex: 5,
label: {
text: `Endurance Limit (${ENDURANCE_LIMIT} MPa)`,
align: "right",
x: -10,
y: -6,
style: { color: t.inkSoft, fontSize: "13px" },
},
},
],
},
legend: {
itemStyle: { color: t.inkSoft, fontSize: "14px" },
itemHoverStyle: { color: t.ink },
},
tooltip: { enabled: false },
plotOptions: {
series: { animation: false },
scatter: { marker: { radius: 5, fillColor: t.palette[0], lineColor: t.pageBg, lineWidth: 1.5 } },
line: { marker: { enabled: false }, lineWidth: 2.5 },
},
series: [
{
name: "Fatigue Test Data",
type: "scatter",
data: testData,
color: t.palette[0],
},
{
name: "Basquin Fit (S = Sf'·(2N)^b)",
type: "line",
data: fitCurve,
color: t.palette[1],
},
],
});
Runnable source as JSON, for any HTTP client: https://api.anyplot.ai/specs/sn-curve-basic/highcharts/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": "highcharts",
"page": "https://anyplot.ai/sn-curve-basic/javascript/highcharts",
"hub": "https://anyplot.ai/sn-curve-basic",
"code_json": "https://api.anyplot.ai/specs/sn-curve-basic/highcharts/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/highcharts/plot-light.png",
"render_dark_png": "https://storage.googleapis.com/anyplot-images/plots/sn-curve-basic/javascript/highcharts/plot-dark.png",
"interactive_light_html": "https://storage.googleapis.com/anyplot-images/plots/sn-curve-basic/javascript/highcharts/plot-light.html",
"interactive_dark_html": "https://storage.googleapis.com/anyplot-images/plots/sn-curve-basic/javascript/highcharts/plot-dark.html",
"quality_score": 91.0,
"license": "MIT",
"guide": "https://anyplot.ai/llms.txt"
}Part of S-N Curve (Wöhler Curve) on anyplot.ai.