Forming Limit Strain Calculator<\/title>\n <style>\n :root {\n --bg: #f3f6f8;\n --surface: #ffffff;\n --surface-2: #f8fafc;\n --text: #13212b;\n --muted: #5d6b76;\n --line: #d7e0e6;\n --accent: #176b7a;\n --safe: #1c7c43;\n --caution: #b46a0a;\n --risk: #b3261e;\n --radius: 12px;\n --shadow: 0 10px 24px rgba(15, 24, 32, 0.06);\n }\n\n .fld-calculator, .fld-calculator * { box-sizing: border-box; }\n .fld-calculator {\n font-family: ui-sans-serif, system-ui, -apple-system, BlinkMacSystemFont, \"Segoe UI\", sans-serif;\n background: linear-gradient(180deg, #f8fafc 0%, var(--bg) 100%);\n color: var(--text);\n margin: 0;\n padding: 22px 0 28px;\n }\n\n .fld-calculator .wrap {\n width: min(1320px, calc(100% - 24px));\n margin: 0 auto;\n }\n\n .fld-calculator .panel {\n background: var(--surface);\n border: 1px solid var(--line);\n border-radius: var(--radius);\n box-shadow: var(--shadow);\n overflow: hidden;\n }\n\n .fld-calculator .panel + .panel { margin-top: 14px; }\n\n .fld-calculator .panel-head {\n padding: 14px 16px;\n border-bottom: 1px solid var(--line);\n background: linear-gradient(180deg, #fff, var(--surface-2));\n font-weight: 700;\n }\n\n .fld-calculator .panel-body { padding: 16px; }\n\n .fld-calculator .grid {\n display: grid;\n grid-template-columns: repeat(3, minmax(0, 1fr));\n gap: 12px;\n }\n\n .fld-calculator .field {\n display: grid;\n gap: 6px;\n }\n\n .fld-calculator .full { grid-column: 1 \/ -1; }\n\n .fld-calculator label {\n font-size: 0.9rem;\n font-weight: 600;\n }\n\n .fld-calculator input, .fld-calculator select {\n width: 100%;\n border: 1px solid var(--line);\n border-radius: 10px;\n background: #fff;\n color: var(--text);\n font: inherit;\n padding: 10px 12px;\n outline: none;\n }\n\n .fld-calculator input:focus, .fld-calculator select:focus {\n border-color: rgba(23, 107, 122, 0.45);\n box-shadow: 0 0 0 3px rgba(23, 107, 122, 0.1);\n }\n\n .fld-calculator details {\n border: 1px solid var(--line);\n border-radius: 10px;\n background: #fff;\n overflow: hidden;\n margin-top: 12px;\n }\n\n .fld-calculator summary {\n list-style: none;\n cursor: pointer;\n padding: 12px 14px;\n font-weight: 700;\n background: linear-gradient(180deg, #fff, var(--surface-2));\n }\n\n .fld-calculator summary::-webkit-details-marker { display: none; }\n\n .fld-calculator .details-body { padding: 14px; border-top: 1px solid var(--line); }\n\n .fld-calculator .buttons {\n display: flex;\n gap: 10px;\n margin-top: 14px;\n flex-wrap: wrap;\n justify-content: center;\n }\n\n .fld-calculator button {\n border: 1px solid var(--line);\n background: #fff;\n border-radius: 10px;\n padding: 10px 14px;\n font: inherit;\n cursor: pointer;\n }\n\n .fld-calculator button.primary {\n background: rgb(37, 99, 235);\n color: #fff;\n border-color: rgba(0, 0, 0, 0.05);\n font-weight: 700;\n min-width: 240px;\n padding: 12px 26px;\n }\n\n .fld-calculator .results[hidden] { display: none !important; }\n\n .fld-calculator .metrics {\n display: grid;\n grid-template-columns: repeat(3, minmax(0, 1fr));\n gap: 10px;\n }\n\n .fld-calculator .metric {\n border: 1px solid var(--line);\n border-radius: 10px;\n padding: 12px;\n background: #fff;\n min-height: 86px;\n }\n\n .fld-calculator .metric .label {\n color: var(--muted);\n font-size: 0.84rem;\n font-weight: 600;\n margin-bottom: 6px;\n }\n\n .fld-calculator .metric .value {\n font-size: 1.15rem;\n font-weight: 800;\n line-height: 1.15;\n word-break: break-word;\n }\n\n .fld-calculator .metric .sub {\n color: var(--muted);\n font-size: 0.84rem;\n margin-top: 6px;\n }\n\n .fld-calculator .value.safe { color: var(--safe); }\n .fld-calculator .value.caution { color: var(--caution); }\n .fld-calculator .value.risk { color: var(--risk); }\n\n .fld-calculator .message {\n margin-top: 12px;\n border: 1px solid var(--line);\n border-radius: 10px;\n background: #fff;\n padding: 12px;\n }\n\n .fld-calculator .message.warning {\n border-color: rgba(180, 106, 10, 0.3);\n background: rgba(180, 106, 10, 0.07);\n }\n\n .fld-calculator .message.error {\n border-color: rgba(179, 38, 30, 0.3);\n background: rgba(179, 38, 30, 0.07);\n }\n\n .fld-calculator .list {\n margin: 0;\n padding-left: 18px;\n }\n\n @media (max-width: 960px) {\n .fld-calculator .grid, .fld-calculator .metrics { grid-template-columns: 1fr; }\n }\n <\/style>\n<\/head>\n<body>\n <div class=\"fld-calculator\">\n <div class=\"wrap\">\n <section class=\"panel\">\n <div class=\"panel-head\">Inputs<\/div>\n <div class=\"panel-body\">\n <div class=\"grid\" id=\"inputGrid\">\n <div class=\"field full\">\n <label for=\"presetSearch\">Material preset<\/label>\n <input id=\"presetSearch\" list=\"presetList\" placeholder=\"Search preset\">\n <datalist id=\"presetList\"><\/datalist>\n <\/div>\n <div class=\"field\">\n <label for=\"materialType\">Material type<\/label>\n <select id=\"materialType\"><\/select>\n <\/div>\n <div class=\"field\">\n <label for=\"materialGrade\">Material grade<\/label>\n <input id=\"materialGrade\" type=\"text\">\n <\/div>\n <div class=\"field\">\n <label for=\"unitThickness\">Thickness unit<\/label>\n <select id=\"unitThickness\">\n <option value=\"mm\">mm<\/option>\n <option value=\"in\">inch<\/option>\n <\/select>\n <\/div>\n <div class=\"field\">\n <label for=\"sheetThickness\">Sheet thickness t<\/label>\n <input id=\"sheetThickness\" type=\"number\" step=\"any\" min=\"0\">\n <\/div>\n <div class=\"field\">\n <label for=\"unitStrength\">Strength unit<\/label>\n <select id=\"unitStrength\">\n <option value=\"MPa\">MPa<\/option>\n <option value=\"psi\">psi<\/option>\n <option value=\"ksi\">ksi<\/option>\n <\/select>\n <\/div>\n <div class=\"field\">\n <label for=\"yieldStrength\">Yield strength<\/label>\n <input id=\"yieldStrength\" type=\"number\" step=\"any\" min=\"0\">\n <\/div>\n <div class=\"field\">\n <label for=\"utsStrength\">Ultimate tensile strength<\/label>\n <input id=\"utsStrength\" type=\"number\" step=\"any\" min=\"0\">\n <\/div>\n <div class=\"field\">\n <label for=\"strainInputType\">Strain input type<\/label>\n <select id=\"strainInputType\">\n <option value=\"true\">True strain<\/option>\n <option value=\"engineering\">Engineering strain<\/option>\n <\/select>\n <\/div>\n <div class=\"field\">\n <label for=\"strainDisplayType\">Display strain as<\/label>\n <select id=\"strainDisplayType\">\n <option value=\"true\">Decimal true strain<\/option>\n <option value=\"percent\">True strain percent<\/option>\n <option value=\"engineering\">Engineering strain<\/option>\n <\/select>\n <\/div>\n <div class=\"field\">\n <label for=\"actualMajor\">Actual major strain e1<\/label>\n <input id=\"actualMajor\" type=\"number\" step=\"any\">\n <\/div>\n <div class=\"field\">\n <label for=\"actualMinor\">Actual minor strain e2<\/label>\n <input id=\"actualMinor\" type=\"number\" step=\"any\">\n <\/div>\n <div class=\"field\">\n <label for=\"strainPath\">Strain path<\/label>\n <select id=\"strainPath\">\n <option>Uniaxial tension<\/option>\n <option>Plane strain<\/option>\n <option>Biaxial stretching<\/option>\n <option>Drawing<\/option>\n <option selected>Custom major\/minor strain<\/option>\n <\/select>\n <\/div>\n <div class=\"field\">\n <label for=\"nValue\">Strain hardening exponent n<\/label>\n <input id=\"nValue\" type=\"number\" step=\"any\" min=\"0\">\n <\/div>\n <div class=\"field\">\n <label for=\"rValue\">Average plastic strain ratio r-bar<\/label>\n <input id=\"rValue\" type=\"number\" step=\"any\" min=\"0\">\n <\/div>\n <div class=\"field\">\n <label for=\"elongation\">Total elongation A80<\/label>\n <input id=\"elongation\" type=\"number\" step=\"any\" min=\"0\">\n <\/div>\n <div class=\"field\">\n <label for=\"uniformElongation\">Uniform elongation<\/label>\n <input id=\"uniformElongation\" type=\"number\" step=\"any\" min=\"0\">\n <\/div>\n <\/div>\n\n <details open>\n <summary>Advanced Settings<\/summary>\n <div class=\"details-body\">\n <div class=\"grid\">\n <div class=\"field\">\n <label for=\"fldMode\">FLD0 model<\/label>\n <select id=\"fldMode\">\n <option value=\"advanced\">Empirical FLD0<\/option>\n <option value=\"simple\">Simplified FLD0<\/option>\n <\/select>\n <\/div>\n <div class=\"field\">\n <label for=\"curveMode\">Primary curve source<\/label>\n <select id=\"curveMode\">\n <option value=\"estimated\">Estimated piecewise curve<\/option>\n <option value=\"measured\">Measured polynomial fit<\/option>\n <\/select>\n <\/div>\n <div class=\"field\">\n <label for=\"chartSpan\">Chart span<\/label>\n <select id=\"chartSpan\">\n <option value=\"auto\">Auto<\/option>\n <option value=\"tight\">Tight<\/option>\n <option value=\"wide\">Wide<\/option>\n <\/select>\n <\/div>\n <div class=\"field\">\n <label for=\"coefA\">A \/ C0<\/label>\n <input id=\"coefA\" type=\"number\" step=\"any\">\n <\/div>\n <div class=\"field\">\n <label for=\"coefB\">B \/ C1<\/label>\n <input id=\"coefB\" type=\"number\" step=\"any\">\n <\/div>\n <div class=\"field\">\n <label for=\"coefC\">C \/ C2<\/label>\n <input id=\"coefC\" type=\"number\" step=\"any\">\n <\/div>\n <div class=\"field\">\n <label for=\"coefD\">C3<\/label>\n <input id=\"coefD\" type=\"number\" step=\"any\">\n <\/div>\n <div class=\"field\">\n <label for=\"coefE\">C4<\/label>\n <input id=\"coefE\" type=\"number\" step=\"any\">\n <\/div>\n <div class=\"field\">\n <label for=\"simpleC\">Simple C<\/label>\n <input id=\"simpleC\" type=\"number\" step=\"any\">\n <\/div>\n <div class=\"field\">\n <label for=\"leftSlope\">Left slope KL<\/label>\n <input id=\"leftSlope\" type=\"number\" step=\"any\">\n <\/div>\n <div class=\"field\">\n <label for=\"rightSlope\">Right slope KR<\/label>\n <input id=\"rightSlope\" type=\"number\" step=\"any\">\n <\/div>\n <div class=\"field\">\n <label for=\"thicknessRef\">Thickness reference tref<\/label>\n <input id=\"thicknessRef\" type=\"number\" step=\"any\">\n <\/div>\n <div class=\"field\">\n <label for=\"thicknessExp\">Thickness exponent m<\/label>\n <input id=\"thicknessExp\" type=\"number\" step=\"any\">\n <\/div>\n <div class=\"field\">\n <label for=\"nRef\">n reference<\/label>\n <input id=\"nRef\" type=\"number\" step=\"any\">\n <\/div>\n <div class=\"field\">\n <label for=\"nSensitivity\">n sensitivity<\/label>\n <input id=\"nSensitivity\" type=\"number\" step=\"any\">\n <\/div>\n <div class=\"field\">\n <label for=\"rRef\">r-bar reference<\/label>\n <input id=\"rRef\" type=\"number\" step=\"any\">\n <\/div>\n <div class=\"field\">\n <label for=\"rSensitivity\">r-bar sensitivity<\/label>\n <input id=\"rSensitivity\" type=\"number\" step=\"any\">\n <\/div>\n <div class=\"field\">\n <label for=\"safeThreshold\">Safe threshold (%)<\/label>\n <input id=\"safeThreshold\" type=\"number\" step=\"any\">\n <\/div>\n <div class=\"field\">\n <label for=\"cautionThreshold\">Caution threshold (%)<\/label>\n <input id=\"cautionThreshold\" type=\"number\" step=\"any\">\n <\/div>\n <\/div>\n <\/div>\n <\/details>\n\n <div class=\"buttons\">\n <button class=\"primary\" id=\"calculateBtn\" type=\"button\">Calculate<\/button>\n <\/div>\n <\/div>\n <\/section>\n\n <section class=\"panel results\" id=\"results\" hidden>\n <div class=\"panel-head\">Calculation Results<\/div>\n <div class=\"panel-body\">\n <div class=\"metrics\" id=\"metrics\"><\/div>\n <div id=\"messages\"><\/div>\n <\/div>\n <\/section>\n <\/div>\n <\/div>\n\n <script>\n const presets = {\n \"Low Carbon Steel\": { type: \"Steel\", grade: \"Low Carbon Steel\", thickness: 1.2, yield: 210, uts: 340, n: 0.2, r: 1.5, a80: 28, ue: 16 },\n \"Dual Phase Steel\": { type: \"Steel\", grade: \"DP590\", thickness: 1.0, yield: 410, uts: 620, n: 0.14, r: 0.9, a80: 18, ue: 11 },\n \"High Strength Low Alloy Steel\": { type: \"Steel\", grade: \"HSLA 340\", thickness: 1.2, yield: 300, uts: 430, n: 0.16, r: 1.1, a80: 20, ue: 12 },\n \"Stainless Steel\": { type: \"Stainless Steel\", grade: \"304\", thickness: 0.9, yield: 230, uts: 580, n: 0.45, r: 1.0, a80: 45, ue: 26 },\n \"Aluminum 5xxx\": { type: \"Aluminum Alloy\", grade: \"5052-H32\", thickness: 1.5, yield: 190, uts: 240, n: 0.2, r: 0.8, a80: 14, ue: 10 },\n \"Aluminum 6xxx\": { type: \"Aluminum Alloy\", grade: \"6061-T6\", thickness: 1.6, yield: 275, uts: 310, n: 0.12, r: 0.6, a80: 12, ue: 8 },\n \"Deep Drawing Steel\": { type: \"Steel\", grade: \"DDQ\", thickness: 0.8, yield: 180, uts: 320, n: 0.22, r: 1.8, a80: 33, ue: 18 },\n \"Custom Material\": { type: \"Custom\", grade: \"Custom\", thickness: 1.2, yield: 210, uts: 340, n: 0.2, r: 1.2, a80: 25, ue: 15 }\n };\n\n const defaults = {\n presetSearch: \"Low Carbon Steel\",\n materialType: \"Steel\",\n materialGrade: \"Low Carbon Steel\",\n unitThickness: \"mm\",\n sheetThickness: 1.2,\n unitStrength: \"MPa\",\n yieldStrength: 210,\n utsStrength: 340,\n strainInputType: \"true\",\n strainDisplayType: \"true\",\n actualMajor: 0.22,\n actualMinor: -0.05,\n strainPath: \"Custom major\/minor strain\",\n nValue: 0.2,\n rValue: 1.5,\n elongation: 28,\n uniformElongation: 16,\n fldMode: \"advanced\",\n curveMode: \"estimated\",\n chartSpan: \"auto\",\n coefA: 0.32,\n coefB: 1.75,\n coefC: 0.015,\n coefD: 0.045,\n coefE: 0.006,\n simpleC: 0.08,\n leftSlope: 0.58,\n rightSlope: 0.42,\n thicknessRef: 1.0,\n thicknessExp: 0.12,\n nRef: 0.18,\n nSensitivity: 0.9,\n rRef: 1.2,\n rSensitivity: 0.08,\n safeThreshold: 80,\n cautionThreshold: 100\n };\n\n const state = { ...defaults };\n const ids = [\n \"presetSearch\",\"materialType\",\"materialGrade\",\"unitThickness\",\"sheetThickness\",\"unitStrength\",\"yieldStrength\",\"utsStrength\",\n \"strainInputType\",\"strainDisplayType\",\"actualMajor\",\"actualMinor\",\"strainPath\",\"nValue\",\"rValue\",\"elongation\",\"uniformElongation\",\n \"fldMode\",\"curveMode\",\"chartSpan\",\"coefA\",\"coefB\",\"coefC\",\"coefD\",\"coefE\",\"simpleC\",\"leftSlope\",\"rightSlope\",\"thicknessRef\",\n \"thicknessExp\",\"nRef\",\"nSensitivity\",\"rRef\",\"rSensitivity\",\"safeThreshold\",\"cautionThreshold\"\n ];\n const el = Object.fromEntries(ids.map(id => [id, document.getElementById(id)]));\n const calculateBtn = document.getElementById(\"calculateBtn\");\n const results = document.getElementById(\"results\");\n const metrics = document.getElementById(\"metrics\");\n const messages = document.getElementById(\"messages\");\n\n function readNumber(value, fallback = NaN) {\n const n = Number(value);\n return Number.isFinite(n) ? n : fallback;\n }\n\n function toMPa(value) {\n const n = readNumber(value);\n if (!Number.isFinite(n)) return NaN;\n if (state.unitStrength === \"psi\") return n \/ 145.0377;\n if (state.unitStrength === \"ksi\") return n * 6.894757;\n return n;\n }\n\n function toMM(value) {\n const n = readNumber(value);\n if (!Number.isFinite(n)) return NaN;\n return state.unitThickness === \"in\" ? n * 25.4 : n;\n }\n\n function parseStrain(value) {\n const n = readNumber(value);\n if (!Number.isFinite(n)) return NaN;\n if (state.strainInputType === \"engineering\") {\n if (n <= -1) return NaN;\n return Math.log(1 + n);\n }\n return n;\n }\n\n function formatNumber(value, digits = 4) {\n if (!Number.isFinite(value)) return \"n\/a\";\n return value.toFixed(digits).replace(\/\\.?0+$\/, \"\");\n }\n\n function formatStrain(value) {\n if (!Number.isFinite(value)) return \"n\/a\";\n if (state.strainDisplayType === \"percent\") return `${formatNumber(value * 100, 2)}%`;\n if (state.strainDisplayType === \"engineering\") return `${formatNumber(Math.exp(value) - 1, 4)}`;\n return formatNumber(value, 4);\n }\n\n function syncStateFromInputs() {\n ids.forEach(id => {\n state[id] = el[id].type === \"number\" ? readNumber(el[id].value, defaults[id]) : el[id].value;\n });\n }\n\n function syncInputsFromState() {\n ids.forEach(id => {\n el[id].value = state[id];\n });\n }\n\n function applyPreset(name) {\n const preset = presets[name];\n if (!preset) return;\n state.presetSearch = name;\n state.materialType = preset.type;\n state.materialGrade = preset.grade;\n state.sheetThickness = preset.thickness;\n state.yieldStrength = preset.yield;\n state.utsStrength = preset.uts;\n state.nValue = preset.n;\n state.rValue = preset.r;\n state.elongation = preset.a80;\n state.uniformElongation = preset.ue;\n syncInputsFromState();\n }\n\n function currentModel() {\n const t = toMM(state.sheetThickness);\n const n = readNumber(state.nValue);\n const r = readNumber(state.rValue);\n const a80 = readNumber(state.elongation);\n const baseAdvanced = readNumber(state.coefA) + readNumber(state.coefB) * n + readNumber(state.coefC) * t + readNumber(state.coefD) * r + readNumber(state.coefE) * a80;\n const baseSimple = readNumber(state.coefA) + readNumber(state.coefB) * n + readNumber(state.simpleC) * t;\n const base = state.fldMode === \"simple\" ? baseSimple : baseAdvanced;\n const thicknessFactor = Math.pow(Math.max(0.0001, t) \/ Math.max(0.0001, readNumber(state.thicknessRef, 1)), readNumber(state.thicknessExp));\n const nFactor = 1 + readNumber(state.nSensitivity) * (n - readNumber(state.nRef));\n const rFactor = 1 + readNumber(state.rSensitivity) * (r - readNumber(state.rRef));\n return { base, thicknessFactor, nFactor, rFactor, fld0: base * thicknessFactor * nFactor * rFactor };\n }\n\n function limitAtMinor(minor, fld0) {\n return minor < 0 ? fld0 + readNumber(state.leftSlope) * Math.abs(minor) : fld0 + readNumber(state.rightSlope) * minor;\n }\n\n function metric(label, value, sub, cls = \"\") {\n return `\n <div class=\"metric\">\n <div class=\"label\">${label}<\/div>\n <div class=\"value ${cls}\">${value}<\/div>\n <div class=\"sub\">${sub}<\/div>\n <\/div>\n `;\n }\n\n function calculate() {\n syncStateFromInputs();\n applyPreset(state.presetSearch);\n\n const warnings = [];\n const errors = [];\n const major = parseStrain(state.actualMajor);\n const minor = parseStrain(state.actualMinor);\n const yieldMPa = toMPa(state.yieldStrength);\n const utsMPa = toMPa(state.utsStrength);\n const thicknessMM = toMM(state.sheetThickness);\n\n if (!(thicknessMM > 0)) errors.push(\"Sheet thickness must be greater than zero.\");\n if (!(readNumber(state.nValue) > 0)) warnings.push(\"n-value should be greater than zero when used.\");\n if (!(yieldMPa > 0)) warnings.push(\"Yield strength should be positive.\");\n if (!(utsMPa > 0)) warnings.push(\"Ultimate tensile strength should be positive.\");\n if (!Number.isFinite(major) || !Number.isFinite(minor)) errors.push(\"Actual strain inputs must be valid numbers.\");\n\n const model = currentModel();\n const limit = limitAtMinor(minor, model.fld0);\n const margin = limit - major;\n const utilization = limit !== 0 ? (major \/ limit) * 100 : NaN;\n const normalizedMargin = limit !== 0 ? ((limit - major) \/ limit) * 100 : NaN;\n const ratio = major !== 0 ? minor \/ major : NaN;\n const equivalent = Number.isFinite(major) && Number.isFinite(minor)\n ? Math.sqrt((2 \/ 3) * (major * major + major * minor + minor * minor))\n : NaN;\n const risk = !Number.isFinite(utilization)\n ? \"Unknown\"\n : utilization < readNumber(state.safeThreshold)\n ? \"Safe\"\n : utilization < readNumber(state.cautionThreshold)\n ? \"Caution\"\n : \"High Risk\";\n\n results.hidden = false;\n metrics.innerHTML = [\n metric(\"Estimated FLD0\", formatStrain(model.fld0), `Base ${formatNumber(model.base, 4)} | t factor ${formatNumber(model.thicknessFactor, 3)} | n factor ${formatNumber(model.nFactor, 3)} | r factor ${formatNumber(model.rFactor, 3)}`),\n metric(\"Actual major strain\", formatStrain(major), `Input type: ${state.strainInputType}`),\n metric(\"Actual minor strain\", formatStrain(minor), `Strain path: ${state.strainPath}`),\n metric(\"Limit major strain\", formatStrain(limit), `Curve source: ${state.curveMode}`),\n metric(\"Strain path ratio beta\", Number.isFinite(ratio) ? formatNumber(ratio, 4) : \"n\/a\", \"beta = e2 \/ e1\"),\n metric(\"FLD utilization\", Number.isFinite(utilization) ? `${formatNumber(utilization, 1)}%` : \"n\/a\", `Safe threshold ${formatNumber(readNumber(state.safeThreshold), 0)}%`),\n metric(\"Strain margin\", formatStrain(margin), \"Margin = limit - actual major\"),\n metric(\"Normalized margin\", Number.isFinite(normalizedMargin) ? `${formatNumber(normalizedMargin, 1)}%` : \"n\/a\", \"Relative distance to the limit\"),\n metric(\"Equivalent strain\", formatStrain(equivalent), \"Auxiliary metric\"),\n metric(\"Forming risk\", risk, \"Safe \/ Caution \/ High Risk\", risk === \"Safe\" ? \"safe\" : risk === \"Caution\" ? \"caution\" : risk === \"High Risk\" ? \"risk\" : \"\")\n ].join(\"\");\n\n const messagesHtml = [];\n if (errors.length) {\n messagesHtml.push(`<div class=\"message error\"><strong>Input error<\/strong><ul class=\"list\">${errors.map(x => `<li>${x}<\/li>`).join(\"\")}<\/ul><\/div>`);\n }\n if (warnings.length) {\n messagesHtml.push(`<div class=\"message warning\"><strong>Warnings<\/strong><ul class=\"list\">${warnings.map(x => `<li>${x}<\/li>`).join(\"\")}<\/ul><\/div>`);\n }\n messages.innerHTML = messagesHtml.join(\"\");\n }\n\n function init() {\n Object.keys(presets).forEach(name => {\n document.getElementById(\"presetList\").insertAdjacentHTML(\"beforeend\", `<option value=\"${name}\"><\/option>`);\n });\n\n el.materialType.innerHTML = [\"Steel\", \"Stainless Steel\", \"Aluminum Alloy\", \"Copper Alloy\", \"Titanium\", \"Custom\"]\n .map(v => `<option value=\"${v}\">${v}<\/option>`).join(\"\");\n\n syncInputsFromState();\n\n el.presetSearch.addEventListener(\"change\", () => applyPreset(el.presetSearch.value));\n el.presetSearch.addEventListener(\"input\", () => applyPreset(el.presetSearch.value));\n calculateBtn.addEventListener(\"click\", calculate);\n }\n\n init();\n <\/script>\n<\/body>\n<\/html>\n","protected":false},"excerpt":{"rendered":"<p>The Forming Limit Strain Calculator is a practical engineering tool designed to estimate sheet metal forming limits using major strain, minor strain, material thickness, strain-hardening…<\/p>","protected":false},"author":2,"featured_media":24831,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"pmpro_default_level":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[8647],"tags":[8693,8695,2396,8694],"class_list":["post-24830","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-materials-science-and-properties","tag-fld-calculator","tag-forming-limit","tag-sheet-metal","tag-strain-analysis","pmpro-has-access"],"acf":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/www.mechstream.com\/wp-content\/uploads\/2026\/09\/Forming-Limit-Strain-Calculator.png","_links":{"self":[{"href":"https:\/\/www.mechstream.com\/pt\/wp-json\/wp\/v2\/posts\/24830","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mechstream.com\/pt\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.mechstream.com\/pt\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.mechstream.com\/pt\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mechstream.com\/pt\/wp-json\/wp\/v2\/comments?post=24830"}],"version-history":[{"count":2,"href":"https:\/\/www.mechstream.com\/pt\/wp-json\/wp\/v2\/posts\/24830\/revisions"}],"predecessor-version":[{"id":24833,"href":"https:\/\/www.mechstream.com\/pt\/wp-json\/wp\/v2\/posts\/24830\/revisions\/24833"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mechstream.com\/pt\/wp-json\/wp\/v2\/media\/24831"}],"wp:attachment":[{"href":"https:\/\/www.mechstream.com\/pt\/wp-json\/wp\/v2\/media?parent=24830"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.mechstream.com\/pt\/wp-json\/wp\/v2\/categories?post=24830"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.mechstream.com\/pt\/wp-json\/wp\/v2\/tags?post=24830"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}

{"id":24830,"date":"2026-09-07T05:56:08","date_gmt":"2026-09-07T05:56:08","guid":{"rendered":"https:\/\/www.mechstream.com\/?p=24830"},"modified":"2026-09-07T06:00:18","modified_gmt":"2026-09-07T06:00:18","slug":"forming-limit-strain-calculator","status":"publish","type":"post","link":"https:\/\/www.mechstream.com\/pt\/forming-limit-strain-calculator\/","title":{"rendered":"Forming Limit Strain Calculator"},"content":{"rendered":"\n

The Forming Limit Strain Calculator<\/strong> is a practical engineering tool designed to estimate sheet metal forming limits using major strain, minor strain, material thickness, strain-hardening behavior, and other material properties. It helps engineers evaluate forming safety, strain margin, FLD utilization, and the risk of localized necking during stamping, deep drawing, and stretch forming. The Forming Limit Strain Calculator is useful for sheet metal process planning, material comparison, forming analysis, and preliminary manufacturing optimization.<\/p>\n\n\n\n\n\n\n \n \n Forming Limit Strain Calculator<\/title>\n <style>\n :root {\n --bg: #f3f6f8;\n --surface: #ffffff;\n --surface-2: #f8fafc;\n --text: #13212b;\n --muted: #5d6b76;\n --line: #d7e0e6;\n --accent: #176b7a;\n --safe: #1c7c43;\n --caution: #b46a0a;\n --risk: #b3261e;\n --radius: 12px;\n --shadow: 0 10px 24px rgba(15, 24, 32, 0.06);\n }\n\n .fld-calculator, .fld-calculator * { box-sizing: border-box; }\n .fld-calculator {\n font-family: ui-sans-serif, system-ui, -apple-system, BlinkMacSystemFont, \"Segoe UI\", sans-serif;\n background: linear-gradient(180deg, #f8fafc 0%, var(--bg) 100%);\n color: var(--text);\n margin: 0;\n padding: 22px 0 28px;\n }\n\n .fld-calculator .wrap {\n width: min(1320px, calc(100% - 24px));\n margin: 0 auto;\n }\n\n .fld-calculator .panel {\n background: var(--surface);\n border: 1px solid var(--line);\n border-radius: var(--radius);\n box-shadow: var(--shadow);\n overflow: hidden;\n }\n\n .fld-calculator .panel + .panel { margin-top: 14px; }\n\n .fld-calculator .panel-head {\n padding: 14px 16px;\n border-bottom: 1px solid var(--line);\n background: linear-gradient(180deg, #fff, var(--surface-2));\n font-weight: 700;\n }\n\n .fld-calculator .panel-body { padding: 16px; }\n\n .fld-calculator .grid {\n display: grid;\n grid-template-columns: repeat(3, minmax(0, 1fr));\n gap: 12px;\n }\n\n .fld-calculator .field {\n display: grid;\n gap: 6px;\n }\n\n .fld-calculator .full { grid-column: 1 \/ -1; }\n\n .fld-calculator label {\n font-size: 0.9rem;\n font-weight: 600;\n }\n\n .fld-calculator input, .fld-calculator select {\n width: 100%;\n border: 1px solid var(--line);\n border-radius: 10px;\n background: #fff;\n color: var(--text);\n font: inherit;\n padding: 10px 12px;\n outline: none;\n }\n\n .fld-calculator input:focus, .fld-calculator select:focus {\n border-color: rgba(23, 107, 122, 0.45);\n box-shadow: 0 0 0 3px rgba(23, 107, 122, 0.1);\n }\n\n .fld-calculator details {\n border: 1px solid var(--line);\n border-radius: 10px;\n background: #fff;\n overflow: hidden;\n margin-top: 12px;\n }\n\n .fld-calculator summary {\n list-style: none;\n cursor: pointer;\n padding: 12px 14px;\n font-weight: 700;\n background: linear-gradient(180deg, #fff, var(--surface-2));\n }\n\n .fld-calculator summary::-webkit-details-marker { display: none; }\n\n .fld-calculator .details-body { padding: 14px; border-top: 1px solid var(--line); }\n\n .fld-calculator .buttons {\n display: flex;\n gap: 10px;\n margin-top: 14px;\n flex-wrap: wrap;\n justify-content: center;\n }\n\n .fld-calculator button {\n border: 1px solid var(--line);\n background: #fff;\n border-radius: 10px;\n padding: 10px 14px;\n font: inherit;\n cursor: pointer;\n }\n\n .fld-calculator button.primary {\n background: rgb(37, 99, 235);\n color: #fff;\n border-color: rgba(0, 0, 0, 0.05);\n font-weight: 700;\n min-width: 240px;\n padding: 12px 26px;\n }\n\n .fld-calculator .results[hidden] { display: none !important; }\n\n .fld-calculator .metrics {\n display: grid;\n grid-template-columns: repeat(3, minmax(0, 1fr));\n gap: 10px;\n }\n\n .fld-calculator .metric {\n border: 1px solid var(--line);\n border-radius: 10px;\n padding: 12px;\n background: #fff;\n min-height: 86px;\n }\n\n .fld-calculator .metric .label {\n color: var(--muted);\n font-size: 0.84rem;\n font-weight: 600;\n margin-bottom: 6px;\n }\n\n .fld-calculator .metric .value {\n font-size: 1.15rem;\n font-weight: 800;\n line-height: 1.15;\n word-break: break-word;\n }\n\n .fld-calculator .metric .sub {\n color: var(--muted);\n font-size: 0.84rem;\n margin-top: 6px;\n }\n\n .fld-calculator .value.safe { color: var(--safe); }\n .fld-calculator .value.caution { color: var(--caution); }\n .fld-calculator .value.risk { color: var(--risk); }\n\n .fld-calculator .message {\n margin-top: 12px;\n border: 1px solid var(--line);\n border-radius: 10px;\n background: #fff;\n padding: 12px;\n }\n\n .fld-calculator .message.warning {\n border-color: rgba(180, 106, 10, 0.3);\n background: rgba(180, 106, 10, 0.07);\n }\n\n .fld-calculator .message.error {\n border-color: rgba(179, 38, 30, 0.3);\n background: rgba(179, 38, 30, 0.07);\n }\n\n .fld-calculator .list {\n margin: 0;\n padding-left: 18px;\n }\n\n @media (max-width: 960px) {\n .fld-calculator .grid, .fld-calculator .metrics { grid-template-columns: 1fr; }\n }\n <\/style>\n<\/head>\n<body>\n <div class=\"fld-calculator\">\n <div class=\"wrap\">\n <section class=\"panel\">\n <div class=\"panel-head\">Inputs<\/div>\n <div class=\"panel-body\">\n <div class=\"grid\" id=\"inputGrid\">\n <div class=\"field full\">\n <label for=\"presetSearch\">Material preset<\/label>\n <input id=\"presetSearch\" list=\"presetList\" placeholder=\"Search preset\">\n <datalist id=\"presetList\"><\/datalist>\n <\/div>\n <div class=\"field\">\n <label for=\"materialType\">Material type<\/label>\n <select id=\"materialType\"><\/select>\n <\/div>\n <div class=\"field\">\n <label for=\"materialGrade\">Material grade<\/label>\n <input id=\"materialGrade\" type=\"text\">\n <\/div>\n <div class=\"field\">\n <label for=\"unitThickness\">Thickness unit<\/label>\n <select id=\"unitThickness\">\n <option value=\"mm\">mm<\/option>\n <option value=\"in\">inch<\/option>\n <\/select>\n <\/div>\n <div class=\"field\">\n <label for=\"sheetThickness\">Sheet thickness t<\/label>\n <input id=\"sheetThickness\" type=\"number\" step=\"any\" min=\"0\">\n <\/div>\n <div class=\"field\">\n <label for=\"unitStrength\">Strength unit<\/label>\n <select id=\"unitStrength\">\n <option value=\"MPa\">MPa<\/option>\n <option value=\"psi\">psi<\/option>\n <option value=\"ksi\">ksi<\/option>\n <\/select>\n <\/div>\n <div class=\"field\">\n <label for=\"yieldStrength\">Yield strength<\/label>\n <input id=\"yieldStrength\" type=\"number\" step=\"any\" min=\"0\">\n <\/div>\n <div class=\"field\">\n <label for=\"utsStrength\">Ultimate tensile strength<\/label>\n <input id=\"utsStrength\" type=\"number\" step=\"any\" min=\"0\">\n <\/div>\n <div class=\"field\">\n <label for=\"strainInputType\">Strain input type<\/label>\n <select id=\"strainInputType\">\n <option value=\"true\">True strain<\/option>\n <option value=\"engineering\">Engineering strain<\/option>\n <\/select>\n <\/div>\n <div class=\"field\">\n <label for=\"strainDisplayType\">Display strain as<\/label>\n <select id=\"strainDisplayType\">\n <option value=\"true\">Decimal true strain<\/option>\n <option value=\"percent\">True strain percent<\/option>\n <option value=\"engineering\">Engineering strain<\/option>\n <\/select>\n <\/div>\n <div class=\"field\">\n <label for=\"actualMajor\">Actual major strain e1<\/label>\n <input id=\"actualMajor\" type=\"number\" step=\"any\">\n <\/div>\n <div class=\"field\">\n <label for=\"actualMinor\">Actual minor strain e2<\/label>\n <input id=\"actualMinor\" type=\"number\" step=\"any\">\n <\/div>\n <div class=\"field\">\n <label for=\"strainPath\">Strain path<\/label>\n <select id=\"strainPath\">\n <option>Uniaxial tension<\/option>\n <option>Plane strain<\/option>\n <option>Biaxial stretching<\/option>\n <option>Drawing<\/option>\n <option selected>Custom major\/minor strain<\/option>\n <\/select>\n <\/div>\n <div class=\"field\">\n <label for=\"nValue\">Strain hardening exponent n<\/label>\n <input id=\"nValue\" type=\"number\" step=\"any\" min=\"0\">\n <\/div>\n <div class=\"field\">\n <label for=\"rValue\">Average plastic strain ratio r-bar<\/label>\n <input id=\"rValue\" type=\"number\" step=\"any\" min=\"0\">\n <\/div>\n <div class=\"field\">\n <label for=\"elongation\">Total elongation A80<\/label>\n <input id=\"elongation\" type=\"number\" step=\"any\" min=\"0\">\n <\/div>\n <div class=\"field\">\n <label for=\"uniformElongation\">Uniform elongation<\/label>\n <input id=\"uniformElongation\" type=\"number\" step=\"any\" min=\"0\">\n <\/div>\n <\/div>\n\n <details open>\n <summary>Advanced Settings<\/summary>\n <div class=\"details-body\">\n <div class=\"grid\">\n <div class=\"field\">\n <label for=\"fldMode\">FLD0 model<\/label>\n <select id=\"fldMode\">\n <option value=\"advanced\">Empirical FLD0<\/option>\n <option value=\"simple\">Simplified FLD0<\/option>\n <\/select>\n <\/div>\n <div class=\"field\">\n <label for=\"curveMode\">Primary curve source<\/label>\n <select id=\"curveMode\">\n <option value=\"estimated\">Estimated piecewise curve<\/option>\n <option value=\"measured\">Measured polynomial fit<\/option>\n <\/select>\n <\/div>\n <div class=\"field\">\n <label for=\"chartSpan\">Chart span<\/label>\n <select id=\"chartSpan\">\n <option value=\"auto\">Auto<\/option>\n <option value=\"tight\">Tight<\/option>\n <option value=\"wide\">Wide<\/option>\n <\/select>\n <\/div>\n <div class=\"field\">\n <label for=\"coefA\">A \/ C0<\/label>\n <input id=\"coefA\" type=\"number\" step=\"any\">\n <\/div>\n <div class=\"field\">\n <label for=\"coefB\">B \/ C1<\/label>\n <input id=\"coefB\" type=\"number\" step=\"any\">\n <\/div>\n <div class=\"field\">\n <label for=\"coefC\">C \/ C2<\/label>\n <input id=\"coefC\" type=\"number\" step=\"any\">\n <\/div>\n <div class=\"field\">\n <label for=\"coefD\">C3<\/label>\n <input id=\"coefD\" type=\"number\" step=\"any\">\n <\/div>\n <div class=\"field\">\n <label for=\"coefE\">C4<\/label>\n <input id=\"coefE\" type=\"number\" step=\"any\">\n <\/div>\n <div class=\"field\">\n <label for=\"simpleC\">Simple C<\/label>\n <input id=\"simpleC\" type=\"number\" step=\"any\">\n <\/div>\n <div class=\"field\">\n <label for=\"leftSlope\">Left slope KL<\/label>\n <input id=\"leftSlope\" type=\"number\" step=\"any\">\n <\/div>\n <div class=\"field\">\n <label for=\"rightSlope\">Right slope KR<\/label>\n <input id=\"rightSlope\" type=\"number\" step=\"any\">\n <\/div>\n <div class=\"field\">\n <label for=\"thicknessRef\">Thickness reference tref<\/label>\n <input id=\"thicknessRef\" type=\"number\" step=\"any\">\n <\/div>\n <div class=\"field\">\n <label for=\"thicknessExp\">Thickness exponent m<\/label>\n <input id=\"thicknessExp\" type=\"number\" step=\"any\">\n <\/div>\n <div class=\"field\">\n <label for=\"nRef\">n reference<\/label>\n <input id=\"nRef\" type=\"number\" step=\"any\">\n <\/div>\n <div class=\"field\">\n <label for=\"nSensitivity\">n sensitivity<\/label>\n <input id=\"nSensitivity\" type=\"number\" step=\"any\">\n <\/div>\n <div class=\"field\">\n <label for=\"rRef\">r-bar reference<\/label>\n <input id=\"rRef\" type=\"number\" step=\"any\">\n <\/div>\n <div class=\"field\">\n <label for=\"rSensitivity\">r-bar sensitivity<\/label>\n <input id=\"rSensitivity\" type=\"number\" step=\"any\">\n <\/div>\n <div class=\"field\">\n <label for=\"safeThreshold\">Safe threshold (%)<\/label>\n <input id=\"safeThreshold\" type=\"number\" step=\"any\">\n <\/div>\n <div class=\"field\">\n <label for=\"cautionThreshold\">Caution threshold (%)<\/label>\n <input id=\"cautionThreshold\" type=\"number\" step=\"any\">\n <\/div>\n <\/div>\n <\/div>\n <\/details>\n\n <div class=\"buttons\">\n <button class=\"primary\" id=\"calculateBtn\" type=\"button\">Calculate<\/button>\n <\/div>\n <\/div>\n <\/section>\n\n <section class=\"panel results\" id=\"results\" hidden>\n <div class=\"panel-head\">Calculation Results<\/div>\n <div class=\"panel-body\">\n <div class=\"metrics\" id=\"metrics\"><\/div>\n <div id=\"messages\"><\/div>\n <\/div>\n <\/section>\n <\/div>\n <\/div>\n\n <script>\n const presets = {\n \"Low Carbon Steel\": { type: \"Steel\", grade: \"Low Carbon Steel\", thickness: 1.2, yield: 210, uts: 340, n: 0.2, r: 1.5, a80: 28, ue: 16 },\n \"Dual Phase Steel\": { type: \"Steel\", grade: \"DP590\", thickness: 1.0, yield: 410, uts: 620, n: 0.14, r: 0.9, a80: 18, ue: 11 },\n \"High Strength Low Alloy Steel\": { type: \"Steel\", grade: \"HSLA 340\", thickness: 1.2, yield: 300, uts: 430, n: 0.16, r: 1.1, a80: 20, ue: 12 },\n \"Stainless Steel\": { type: \"Stainless Steel\", grade: \"304\", thickness: 0.9, yield: 230, uts: 580, n: 0.45, r: 1.0, a80: 45, ue: 26 },\n \"Aluminum 5xxx\": { type: \"Aluminum Alloy\", grade: \"5052-H32\", thickness: 1.5, yield: 190, uts: 240, n: 0.2, r: 0.8, a80: 14, ue: 10 },\n \"Aluminum 6xxx\": { type: \"Aluminum Alloy\", grade: \"6061-T6\", thickness: 1.6, yield: 275, uts: 310, n: 0.12, r: 0.6, a80: 12, ue: 8 },\n \"Deep Drawing Steel\": { type: \"Steel\", grade: \"DDQ\", thickness: 0.8, yield: 180, uts: 320, n: 0.22, r: 1.8, a80: 33, ue: 18 },\n \"Custom Material\": { type: \"Custom\", grade: \"Custom\", thickness: 1.2, yield: 210, uts: 340, n: 0.2, r: 1.2, a80: 25, ue: 15 }\n };\n\n const defaults = {\n presetSearch: \"Low Carbon Steel\",\n materialType: \"Steel\",\n materialGrade: \"Low Carbon Steel\",\n unitThickness: \"mm\",\n sheetThickness: 1.2,\n unitStrength: \"MPa\",\n yieldStrength: 210,\n utsStrength: 340,\n strainInputType: \"true\",\n strainDisplayType: \"true\",\n actualMajor: 0.22,\n actualMinor: -0.05,\n strainPath: \"Custom major\/minor strain\",\n nValue: 0.2,\n rValue: 1.5,\n elongation: 28,\n uniformElongation: 16,\n fldMode: \"advanced\",\n curveMode: \"estimated\",\n chartSpan: \"auto\",\n coefA: 0.32,\n coefB: 1.75,\n coefC: 0.015,\n coefD: 0.045,\n coefE: 0.006,\n simpleC: 0.08,\n leftSlope: 0.58,\n rightSlope: 0.42,\n thicknessRef: 1.0,\n thicknessExp: 0.12,\n nRef: 0.18,\n nSensitivity: 0.9,\n rRef: 1.2,\n rSensitivity: 0.08,\n safeThreshold: 80,\n cautionThreshold: 100\n };\n\n const state = { ...defaults };\n const ids = [\n \"presetSearch\",\"materialType\",\"materialGrade\",\"unitThickness\",\"sheetThickness\",\"unitStrength\",\"yieldStrength\",\"utsStrength\",\n \"strainInputType\",\"strainDisplayType\",\"actualMajor\",\"actualMinor\",\"strainPath\",\"nValue\",\"rValue\",\"elongation\",\"uniformElongation\",\n \"fldMode\",\"curveMode\",\"chartSpan\",\"coefA\",\"coefB\",\"coefC\",\"coefD\",\"coefE\",\"simpleC\",\"leftSlope\",\"rightSlope\",\"thicknessRef\",\n \"thicknessExp\",\"nRef\",\"nSensitivity\",\"rRef\",\"rSensitivity\",\"safeThreshold\",\"cautionThreshold\"\n ];\n const el = Object.fromEntries(ids.map(id => [id, document.getElementById(id)]));\n const calculateBtn = document.getElementById(\"calculateBtn\");\n const results = document.getElementById(\"results\");\n const metrics = document.getElementById(\"metrics\");\n const messages = document.getElementById(\"messages\");\n\n function readNumber(value, fallback = NaN) {\n const n = Number(value);\n return Number.isFinite(n) ? n : fallback;\n }\n\n function toMPa(value) {\n const n = readNumber(value);\n if (!Number.isFinite(n)) return NaN;\n if (state.unitStrength === \"psi\") return n \/ 145.0377;\n if (state.unitStrength === \"ksi\") return n * 6.894757;\n return n;\n }\n\n function toMM(value) {\n const n = readNumber(value);\n if (!Number.isFinite(n)) return NaN;\n return state.unitThickness === \"in\" ? n * 25.4 : n;\n }\n\n function parseStrain(value) {\n const n = readNumber(value);\n if (!Number.isFinite(n)) return NaN;\n if (state.strainInputType === \"engineering\") {\n if (n <= -1) return NaN;\n return Math.log(1 + n);\n }\n return n;\n }\n\n function formatNumber(value, digits = 4) {\n if (!Number.isFinite(value)) return \"n\/a\";\n return value.toFixed(digits).replace(\/\\.?0+$\/, \"\");\n }\n\n function formatStrain(value) {\n if (!Number.isFinite(value)) return \"n\/a\";\n if (state.strainDisplayType === \"percent\") return `${formatNumber(value * 100, 2)}%`;\n if (state.strainDisplayType === \"engineering\") return `${formatNumber(Math.exp(value) - 1, 4)}`;\n return formatNumber(value, 4);\n }\n\n function syncStateFromInputs() {\n ids.forEach(id => {\n state[id] = el[id].type === \"number\" ? readNumber(el[id].value, defaults[id]) : el[id].value;\n });\n }\n\n function syncInputsFromState() {\n ids.forEach(id => {\n el[id].value = state[id];\n });\n }\n\n function applyPreset(name) {\n const preset = presets[name];\n if (!preset) return;\n state.presetSearch = name;\n state.materialType = preset.type;\n state.materialGrade = preset.grade;\n state.sheetThickness = preset.thickness;\n state.yieldStrength = preset.yield;\n state.utsStrength = preset.uts;\n state.nValue = preset.n;\n state.rValue = preset.r;\n state.elongation = preset.a80;\n state.uniformElongation = preset.ue;\n syncInputsFromState();\n }\n\n function currentModel() {\n const t = toMM(state.sheetThickness);\n const n = readNumber(state.nValue);\n const r = readNumber(state.rValue);\n const a80 = readNumber(state.elongation);\n const baseAdvanced = readNumber(state.coefA) + readNumber(state.coefB) * n + readNumber(state.coefC) * t + readNumber(state.coefD) * r + readNumber(state.coefE) * a80;\n const baseSimple = readNumber(state.coefA) + readNumber(state.coefB) * n + readNumber(state.simpleC) * t;\n const base = state.fldMode === \"simple\" ? baseSimple : baseAdvanced;\n const thicknessFactor = Math.pow(Math.max(0.0001, t) \/ Math.max(0.0001, readNumber(state.thicknessRef, 1)), readNumber(state.thicknessExp));\n const nFactor = 1 + readNumber(state.nSensitivity) * (n - readNumber(state.nRef));\n const rFactor = 1 + readNumber(state.rSensitivity) * (r - readNumber(state.rRef));\n return { base, thicknessFactor, nFactor, rFactor, fld0: base * thicknessFactor * nFactor * rFactor };\n }\n\n function limitAtMinor(minor, fld0) {\n return minor < 0 ? fld0 + readNumber(state.leftSlope) * Math.abs(minor) : fld0 + readNumber(state.rightSlope) * minor;\n }\n\n function metric(label, value, sub, cls = \"\") {\n return `\n <div class=\"metric\">\n <div class=\"label\">${label}<\/div>\n <div class=\"value ${cls}\">${value}<\/div>\n <div class=\"sub\">${sub}<\/div>\n <\/div>\n `;\n }\n\n function calculate() {\n syncStateFromInputs();\n applyPreset(state.presetSearch);\n\n const warnings = [];\n const errors = [];\n const major = parseStrain(state.actualMajor);\n const minor = parseStrain(state.actualMinor);\n const yieldMPa = toMPa(state.yieldStrength);\n const utsMPa = toMPa(state.utsStrength);\n const thicknessMM = toMM(state.sheetThickness);\n\n if (!(thicknessMM > 0)) errors.push(\"Sheet thickness must be greater than zero.\");\n if (!(readNumber(state.nValue) > 0)) warnings.push(\"n-value should be greater than zero when used.\");\n if (!(yieldMPa > 0)) warnings.push(\"Yield strength should be positive.\");\n if (!(utsMPa > 0)) warnings.push(\"Ultimate tensile strength should be positive.\");\n if (!Number.isFinite(major) || !Number.isFinite(minor)) errors.push(\"Actual strain inputs must be valid numbers.\");\n\n const model = currentModel();\n const limit = limitAtMinor(minor, model.fld0);\n const margin = limit - major;\n const utilization = limit !== 0 ? (major \/ limit) * 100 : NaN;\n const normalizedMargin = limit !== 0 ? ((limit - major) \/ limit) * 100 : NaN;\n const ratio = major !== 0 ? minor \/ major : NaN;\n const equivalent = Number.isFinite(major) && Number.isFinite(minor)\n ? Math.sqrt((2 \/ 3) * (major * major + major * minor + minor * minor))\n : NaN;\n const risk = !Number.isFinite(utilization)\n ? \"Unknown\"\n : utilization < readNumber(state.safeThreshold)\n ? \"Safe\"\n : utilization < readNumber(state.cautionThreshold)\n ? \"Caution\"\n : \"High Risk\";\n\n results.hidden = false;\n metrics.innerHTML = [\n metric(\"Estimated FLD0\", formatStrain(model.fld0), `Base ${formatNumber(model.base, 4)} | t factor ${formatNumber(model.thicknessFactor, 3)} | n factor ${formatNumber(model.nFactor, 3)} | r factor ${formatNumber(model.rFactor, 3)}`),\n metric(\"Actual major strain\", formatStrain(major), `Input type: ${state.strainInputType}`),\n metric(\"Actual minor strain\", formatStrain(minor), `Strain path: ${state.strainPath}`),\n metric(\"Limit major strain\", formatStrain(limit), `Curve source: ${state.curveMode}`),\n metric(\"Strain path ratio beta\", Number.isFinite(ratio) ? formatNumber(ratio, 4) : \"n\/a\", \"beta = e2 \/ e1\"),\n metric(\"FLD utilization\", Number.isFinite(utilization) ? `${formatNumber(utilization, 1)}%` : \"n\/a\", `Safe threshold ${formatNumber(readNumber(state.safeThreshold), 0)}%`),\n metric(\"Strain margin\", formatStrain(margin), \"Margin = limit - actual major\"),\n metric(\"Normalized margin\", Number.isFinite(normalizedMargin) ? `${formatNumber(normalizedMargin, 1)}%` : \"n\/a\", \"Relative distance to the limit\"),\n metric(\"Equivalent strain\", formatStrain(equivalent), \"Auxiliary metric\"),\n metric(\"Forming risk\", risk, \"Safe \/ Caution \/ High Risk\", risk === \"Safe\" ? \"safe\" : risk === \"Caution\" ? \"caution\" : risk === \"High Risk\" ? \"risk\" : \"\")\n ].join(\"\");\n\n const messagesHtml = [];\n if (errors.length) {\n messagesHtml.push(`<div class=\"message error\"><strong>Input error<\/strong><ul class=\"list\">${errors.map(x => `<li>${x}<\/li>`).join(\"\")}<\/ul><\/div>`);\n }\n if (warnings.length) {\n messagesHtml.push(`<div class=\"message warning\"><strong>Warnings<\/strong><ul class=\"list\">${warnings.map(x => `<li>${x}<\/li>`).join(\"\")}<\/ul><\/div>`);\n }\n messages.innerHTML = messagesHtml.join(\"\");\n }\n\n function init() {\n Object.keys(presets).forEach(name => {\n document.getElementById(\"presetList\").insertAdjacentHTML(\"beforeend\", `<option value=\"${name}\"><\/option>`);\n });\n\n el.materialType.innerHTML = [\"Steel\", \"Stainless Steel\", \"Aluminum Alloy\", \"Copper Alloy\", \"Titanium\", \"Custom\"]\n .map(v => `<option value=\"${v}\">${v}<\/option>`).join(\"\");\n\n syncInputsFromState();\n\n el.presetSearch.addEventListener(\"change\", () => applyPreset(el.presetSearch.value));\n el.presetSearch.addEventListener(\"input\", () => applyPreset(el.presetSearch.value));\n calculateBtn.addEventListener(\"click\", calculate);\n }\n\n init();\n <\/script>\n<\/body>\n<\/html>\n","protected":false},"excerpt":{"rendered":"<p>The Forming Limit Strain Calculator is a practical engineering tool designed to estimate sheet metal forming limits using major strain, minor strain, material thickness, strain-hardening…<\/p>","protected":false},"author":2,"featured_media":24831,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"pmpro_default_level":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[8647],"tags":[8693,8695,2396,8694],"class_list":["post-24830","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-materials-science-and-properties","tag-fld-calculator","tag-forming-limit","tag-sheet-metal","tag-strain-analysis","pmpro-has-access"],"acf":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/www.mechstream.com\/wp-content\/uploads\/2026\/09\/Forming-Limit-Strain-Calculator.png","_links":{"self":[{"href":"https:\/\/www.mechstream.com\/pt\/wp-json\/wp\/v2\/posts\/24830","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mechstream.com\/pt\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.mechstream.com\/pt\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.mechstream.com\/pt\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mechstream.com\/pt\/wp-json\/wp\/v2\/comments?post=24830"}],"version-history":[{"count":2,"href":"https:\/\/www.mechstream.com\/pt\/wp-json\/wp\/v2\/posts\/24830\/revisions"}],"predecessor-version":[{"id":24833,"href":"https:\/\/www.mechstream.com\/pt\/wp-json\/wp\/v2\/posts\/24830\/revisions\/24833"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mechstream.com\/pt\/wp-json\/wp\/v2\/media\/24831"}],"wp:attachment":[{"href":"https:\/\/www.mechstream.com\/pt\/wp-json\/wp\/v2\/media?parent=24830"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.mechstream.com\/pt\/wp-json\/wp\/v2\/categories?post=24830"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.mechstream.com\/pt\/wp-json\/wp\/v2\/tags?post=24830"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}