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: echarts 6.1.0 | JavaScript 22.23.2
// Quality: 89/100 | Created: 2026-09-02
const t = window.ANYPLOT_TOKENS;
// --- Data (in-memory, deterministic) ----------------------------------------
// Fatigue test data for a quenched-and-tempered 4340 steel coupon, fit with a
// Basquin power law: stress = fitA * cycles^fitB.
function lcg(seed) {
let state = seed;
return () => {
state = (state * 1103515245 + 12345) % 2147483648;
return state / 2147483648;
};
}
const rand = lcg(42);
const ultimateStrength = 745; // MPa
const yieldStrength = 650; // MPa — ~0.87 of ultimate, typical for Q&T 4340 steel
const enduranceLimit = 260; // MPa
const fitA = 1450; // MPa — Basquin intercept
const fitB = -0.11; // Basquin exponent
// Nominal stress levels tested, multiple specimens per level (scatter in
// cycles-to-failure at fixed stress is the realistic fatigue-test outcome).
const stressLevels = [620, 560, 500, 450, 410, 375, 345, 320, 300, 280, 265];
const specimensPerLevel = 4;
const testPoints = [];
stressLevels.forEach((stress) => {
const meanCycles = Math.pow(stress / fitA, 1 / fitB);
for (let i = 0; i < specimensPerLevel; i++) {
// Spread specimens deterministically around the mean so same-stress
// clusters stay visually distinct instead of overlapping into one blob.
const jitter = (i - (specimensPerLevel - 1) / 2) * 0.24;
const scatterFactor = 1 + jitter + (rand() - 0.5) * 0.08;
testPoints.push([meanCycles * scatterFactor, stress]);
}
});
// Basquin fit curve, drawn from the low-cycle data down to the endurance limit.
const cyclesAtEndurance = Math.pow(enduranceLimit / fitA, 1 / fitB);
const logNStart = 3;
const logNEnd = Math.log10(cyclesAtEndurance);
const fitSteps = 60;
const fitCurve = [];
for (let i = 0; i <= fitSteps; i++) {
const logN = logNStart + (i / fitSteps) * (logNEnd - logNStart);
const cycles = Math.pow(10, logN);
fitCurve.push([cycles, fitA * Math.pow(cycles, fitB)]);
}
// --- Helpers -----------------------------------------------------------------
const SUPERSCRIPTS = { 0: "⁰", 1: "¹", 2: "²", 3: "³", 4: "⁴", 5: "⁵", 6: "⁶", 7: "⁷", 8: "⁸", 9: "⁹" };
function formatDecadeTick(value) {
const exponent = Math.log10(value);
if (Math.abs(exponent - Math.round(exponent)) > 1e-6) return "";
const digits = String(Math.round(exponent)).split("");
return "10" + digits.map((d) => SUPERSCRIPTS[d] ?? d).join("");
}
// --- Init ---------------------------------------------------------------------
const chart = echarts.init(document.getElementById("container"));
// --- Option ---------------------------------------------------------------------
chart.setOption({
animation: false,
color: t.palette,
backgroundColor: "transparent",
title: {
text: "sn-curve-basic · javascript · echarts · anyplot.ai",
left: "center",
top: 36,
textStyle: { color: t.ink, fontSize: 24, fontWeight: 600 },
},
legend: {
data: ["Test specimens", "Basquin fit"],
top: 96,
left: "center",
itemWidth: 22,
itemHeight: 12,
textStyle: { color: t.inkSoft, fontSize: 16 },
},
tooltip: {
trigger: "item",
backgroundColor: t.elevatedBg,
borderColor: t.grid,
textStyle: { color: t.ink },
valueFormatter: (value) => Math.round(value).toLocaleString(),
},
grid: { left: 140, right: 90, top: 180, bottom: 120 },
xAxis: {
type: "log",
min: 1e3,
max: 1e7,
name: "Cycles to Failure (N)",
nameLocation: "middle",
nameGap: 50,
nameTextStyle: { color: t.ink, fontSize: 16 },
axisLabel: { color: t.inkSoft, fontSize: 14, formatter: formatDecadeTick },
axisLine: { lineStyle: { color: t.inkSoft } },
axisTick: { show: false },
splitLine: { show: true, lineStyle: { color: t.grid } },
},
yAxis: {
type: "log",
min: 200,
max: 900,
name: "Stress Amplitude (MPa)",
nameLocation: "middle",
nameGap: 80,
nameRotate: 90,
nameTextStyle: { color: t.ink, fontSize: 16 },
axisLabel: { color: t.inkSoft, fontSize: 14 },
axisLine: { lineStyle: { color: t.inkSoft } },
axisTick: { show: false },
splitLine: { show: true, lineStyle: { color: t.grid } },
},
series: [
{
name: "Test specimens",
type: "scatter",
data: testPoints,
symbolSize: 13,
itemStyle: { color: t.palette[0], opacity: 0.85 },
},
{
name: "Basquin fit",
type: "line",
data: fitCurve,
showSymbol: false,
lineStyle: { color: t.palette[1], width: 3 },
itemStyle: { color: t.palette[1] },
markArea: {
silent: true,
itemStyle: { color: t.ink, opacity: 0.06 },
label: { show: true, position: "insideTopLeft", color: t.inkSoft, fontSize: 13, fontStyle: "italic" },
data: [[{ yAxis: 200, name: "Infinite life region" }, { yAxis: enduranceLimit }]],
},
markLine: {
silent: true,
symbol: "none",
label: { color: t.ink, fontSize: 14, position: "insideEndTop" },
lineStyle: { color: t.ink, width: 1.5 },
data: [
{
yAxis: ultimateStrength,
lineStyle: { type: "solid" },
label: { formatter: "Ultimate Strength · {c} MPa" },
},
{
yAxis: yieldStrength,
lineStyle: { type: "dashed" },
label: { formatter: "Yield Strength · {c} MPa" },
},
{
yAxis: enduranceLimit,
lineStyle: { type: "dotted" },
label: { formatter: "Endurance Limit · {c} MPa", position: "insideEndBottom" },
},
],
},
},
],
});
Runnable source as JSON, for any HTTP client: https://api.anyplot.ai/specs/sn-curve-basic/echarts/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": "echarts",
"page": "https://anyplot.ai/sn-curve-basic/javascript/echarts",
"hub": "https://anyplot.ai/sn-curve-basic",
"code_json": "https://api.anyplot.ai/specs/sn-curve-basic/echarts/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/echarts/plot-light.png",
"render_dark_png": "https://storage.googleapis.com/anyplot-images/plots/sn-curve-basic/javascript/echarts/plot-dark.png",
"interactive_light_html": "https://storage.googleapis.com/anyplot-images/plots/sn-curve-basic/javascript/echarts/plot-light.html",
"interactive_dark_html": "https://storage.googleapis.com/anyplot-images/plots/sn-curve-basic/javascript/echarts/plot-dark.html",
"quality_score": 89.0,
"license": "MIT",
"guide": "https://anyplot.ai/llms.txt"
}Part of S-N Curve (Wöhler Curve) on anyplot.ai.