An engineering stress-strain curve visualizes the relationship between applied stress (MPa) and resulting strain (dimensionless) in a material under uniaxial tensile loading. The curve reveals distinct mechanical behavior regions — elastic deformation, yielding, strain hardening, and necking — culminating in fracture. It is the foundational plot for characterizing material mechanical properties and comparing material performance.
// anyplot.ai
// line-stress-strain: Engineering Stress-Strain Curve
// Library: highcharts 12.6.0 | JavaScript 22.23.2
// Quality: 89/100 | Created: 2026-08-24
const t = window.ANYPLOT_TOKENS;
// --- Data: Aluminum 6061-T6 tensile test (Ramberg-Osgood elastic-plastic model) --
const E = 69000; // Young's modulus, MPa
const sigmaY = 276; // 0.2% offset yield strength, MPa
const sigmaUTS = 310; // ultimate tensile strength, MPa
const sigmaFracture = 235; // fracture stress, MPa
const roExponent = 25; // Ramberg-Osgood hardening exponent
const curve = [];
const hardeningSteps = 220;
for (let i = 0; i <= hardeningSteps; i++) {
const sigma = (sigmaUTS * i) / hardeningSteps;
const strain = sigma / E + 0.002 * Math.pow(sigma / sigmaY, roExponent);
curve.push([strain, sigma]);
}
const strainAtUTS = curve[curve.length - 1][0];
const strainAtFracture = 0.11;
const neckingSteps = 80;
for (let i = 1; i <= neckingSteps; i++) {
const frac = i / neckingSteps;
const strain = strainAtUTS + frac * (strainAtFracture - strainAtUTS);
const stress = sigmaUTS - (sigmaUTS - sigmaFracture) * Math.pow(frac, 1.6);
curve.push([strain, stress]);
}
// 0.2% offset method: yield point is where the curve meets the offset line
const strainAtYield = sigmaY / E + 0.002;
const elasticModulusLine = [
[0, 0],
[strainAtYield, sigmaY],
];
const offsetLine = [
[0.002, 0],
[strainAtYield + 0.0015, E * (strainAtYield + 0.0015 - 0.002)],
];
// x-axis min pulled slightly negative so the origin-anchored elastic-modulus
// and offset construction lines get breathing room from the left edge.
const xAxisMin = -strainAtFracture * 0.03;
const criticalPoints = [
{
x: strainAtYield,
y: sigmaY,
name: "Yield (0.2% offset)",
color: t.ink,
dataLabels: { align: "left", x: 20, y: -14 },
},
{
x: strainAtUTS,
y: sigmaUTS,
name: "UTS",
color: t.ink,
dataLabels: { align: "center", x: 0, y: -16 },
},
{
x: strainAtFracture,
y: sigmaFracture,
name: "Fracture",
color: t.palette[4],
dataLabels: { align: "right", x: -10, y: -10 },
},
];
// --- Title (scaled to the mandated + descriptive prefix length) ------------
const titleText = "Al 6061-T6 tensile test · line-stress-strain · javascript · highcharts · anyplot.ai";
const titleLen = titleText.length;
const titleFontSize = Math.max(14, Math.round(22 * (titleLen > 67 ? 67 / titleLen : 1)));
// --- Chart -------------------------------------------------------------------
Highcharts.chart("container", {
chart: {
type: "line",
backgroundColor: "transparent",
animation: false,
style: { fontFamily: "inherit" },
},
credits: { enabled: false },
colors: t.palette,
title: {
text: titleText,
style: { color: t.ink, fontSize: `${titleFontSize}px`, fontWeight: "600" },
},
xAxis: {
title: { text: "Engineering strain (mm/mm)", style: { color: t.inkSoft, fontSize: "16px" } },
min: xAxisMin,
max: strainAtFracture * 1.05,
lineColor: t.inkSoft,
tickColor: t.inkSoft,
gridLineWidth: 0,
labels: { style: { color: t.inkSoft, fontSize: "14px" } },
plotBands: [
{ from: xAxisMin, to: strainAtYield, color: Highcharts.color(t.palette[0]).setOpacity(0.05).get(), label: { text: "Elastic", align: "center", verticalAlign: "top", y: 30, style: { color: t.inkMuted, fontSize: "13px", fontStyle: "italic" } } },
{ from: strainAtYield, to: strainAtUTS, color: "transparent", label: { text: "Plastic (strain hardening)", align: "center", verticalAlign: "top", y: 30, style: { color: t.inkMuted, fontSize: "13px", fontStyle: "italic" } } },
{ from: strainAtUTS, to: strainAtFracture, color: Highcharts.color(t.palette[0]).setOpacity(0.05).get(), label: { text: "Necking", align: "center", verticalAlign: "top", y: 30, style: { color: t.inkMuted, fontSize: "13px", fontStyle: "italic" } } },
],
plotLines: [
{ value: strainAtYield, color: t.grid, width: 1, dashStyle: "Dot", zIndex: 0 },
{ value: strainAtUTS, color: t.grid, width: 1, dashStyle: "Dot", zIndex: 0 },
],
},
yAxis: {
title: { text: "Engineering stress (MPa)", style: { color: t.inkSoft, fontSize: "16px" } },
min: 0,
lineColor: t.inkSoft,
tickColor: t.inkSoft,
gridLineColor: t.grid,
labels: { style: { color: t.inkSoft, fontSize: "14px" } },
},
legend: {
align: "center",
verticalAlign: "bottom",
itemStyle: { color: t.inkSoft, fontSize: "14px" },
itemHoverStyle: { color: t.ink },
},
tooltip: {
headerFormat: "",
pointFormat: "strain {point.x:.3f} · stress {point.y:.0f} MPa",
},
plotOptions: {
series: { animation: false },
line: { marker: { enabled: false } },
},
series: [
{
name: "Al 6061-T6 stress-strain",
type: "line",
data: curve,
color: t.palette[0],
lineWidth: 3.5,
zIndex: 3,
},
{
name: "Elastic modulus (E ≈ 69 GPa)",
type: "line",
data: elasticModulusLine,
color: t.ink,
lineWidth: 1.5,
dashStyle: "Dash",
enableMouseTracking: false,
zIndex: 1,
},
{
name: "0.2% offset (yield method)",
type: "line",
data: offsetLine,
color: t.palette[1],
lineWidth: 1.5,
dashStyle: "LongDash",
enableMouseTracking: false,
zIndex: 1,
},
{
name: "Critical points",
type: "scatter",
data: criticalPoints,
color: t.ink,
marker: { enabled: true, radius: 6, lineWidth: 1.5, lineColor: t.pageBg },
dataLabels: {
enabled: true,
formatter() {
return `${this.point.name}: ${Math.round(this.y)} MPa`;
},
style: { color: t.ink, fontSize: "13px", fontWeight: "500", textOutline: "none" },
verticalAlign: "bottom",
y: -12,
},
zIndex: 4,
},
],
});
Part of Engineering Stress-Strain Curve on anyplot.ai.