265 lines
12 KiB
HTML
265 lines
12 KiB
HTML
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<title>Graded Interface Calculator | Chadwick Warner</title>
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</head>
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<body>
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<header>
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<h1>GRADED INTERFACE CALCULATOR</h1>
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<div class="subtitle">Cold-Weld Fracture Prevention | Diffusion Zone Thickness Computation</div>
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</header>
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<fort-nav><nav class="fort-nav" data-fort="nav"><a href="/">Chadwick Warner</a><a href="/films/the-billet-journey/">The Billet's Journey</a><a href="/about.html">Chadwick Warner</a><a href="/golden-seam-press-cycle.html">Chadwick Warner</a><a href="/closedloop.html">Closed-Loop Fab</a><a href="/colony-jazz-rhythms.html">Colony Jazz Rhythms • Chadwick Warner</a><a href="/fermentation-lock-habitat.html">Fermentation Lock: From Jar to Habitat</a><a href="/fermentation-habitat-cycles.html">Fermentation to Habitat Cycles</a><a href="/graded-interface-calculator.html" class="active" aria-current="page">Graded Interface Calculator</a><a href="/habitat-press-cycle-ledger.html">Habitat Press Cycle Ledger • Chadwick Warner</a><a href="/habitat-tolerance-checklist.html">Habitat Tolerance Checklist • Chadwick Warner</a><a href="/lean-waste-habitat-cycles.html">Lean Waste to Habitat Cycles • Chadwick Warner</a><a href="/fifa-dome-press-rhythms.html">Press Cycles to FIFA Dome Viewing • Chadwick Warner</a><a href="/colony-press-tolerances.html">Press Tolerances for Colony Fabrication • Chadwick Warner</a><a href="/scrap-log.html">Scrap Log</a><a href="/first-slip.html">The First Slip: A Craftsman's Journey</a><a href="/golden-seam-protocol.html">The Golden Seam Protocol</a><a href="/the-recovery-audit.html">The Recovery Audit</a><a href="/thermal-expansion-calculator.html">Thermal Expansion Calculator</a><a href="/thermal-stress-spec-sheet.html">THERMAL STRESS SPECIFICATION</a><a href="/tolerances.html">Tolerances</a><a href="/tool-calibration-log.html">TOOL CALIBRATION LOG</a></nav></fort-nav>
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<div class="section">
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<div class="section-title">Context</div>
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<p style="margin-bottom: 1rem;">When dissimilar alloys meet at a weld or braze interface, thermal expansion mismatch creates shear stress at the junction. Below a critical interface thickness, the bond fails catastrophically via cold-weld fracture. Above it, the graded zone absorbs strain through controlled dislocation motion.</p>
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<p><strong>Target:</strong> Compute the minimum diffusion zone thickness that prevents fracture under operational thermal cycling.</p>
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</div>
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<div class="section">
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<div class="section-title">Material Properties</div>
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<label>Base Alloy Thermal Expansion Coefficient (α₁)</label>
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<input type="number" id="alpha1" step="0.0000001" placeholder="e.g., 23.6e-6 for 6061-T6 Aluminum">
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<label>Join Material Thermal Expansion Coefficient (α₂)</label>
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<input type="number" id="alpha2" step="0.0000001" placeholder="e.g., 11.7e-6 for Ti-6Al-4V Titanium">
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<label>Thermal Conductivity Gradient (k)</label>
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<input type="number" id="conductivity" step="0.1" placeholder="Average k across interface (W/m·K)">
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<label>Operational Temperature Delta (ΔT)</label>
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<input type="number" id="tempDelta" step="0.1" placeholder="Max thermal swing in Kelvin">
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<label>Shear Yield Strength (τ_y)</label>
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<input type="number" id="yieldStrength" step="1" placeholder="Weaker material's shear yield (MPa)">
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</div>
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<button onclick="computeInterface()">COMPUTE CRITICAL THICKNESS</button>
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<div class="result" id="results" style="display:none;">
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<div class="result-title">Diffusion Zone Specification</div>
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<div class="metric">
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<span class="metric-label">Expansion Mismatch (Δα)</span>
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<span class="metric-value" id="deltaAlpha"></span>
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</div>
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<div class="metric">
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<span class="metric-label">Critical Thickness (δ_crit)</span>
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<span class="metric-value" id="criticalThickness"></span>
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</div>
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<div class="metric">
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<span class="metric-label">Annealing Ramp Rate (dT/dt)</span>
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<span class="metric-value" id="rampRate"></span>
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</div>
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<div class="metric">
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<span class="metric-label">Interfacial Shear Stress</span>
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<span class="metric-value" id="shearStress"></span>
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</div>
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<div class="metric">
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<span class="metric-label">Safety Margin</span>
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<span class="metric-value" id="safetyMargin"></span>
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</div>
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</div>
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<div class="formula">
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<strong>Governing Equation:</strong><br><br>
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δ_crit = (k × ΔT × |α₁ − α₂|) / τ_y<br><br>
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Annealing Ramp: dT/dt = k / (α_avg × δ_crit)<br><br>
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Where:<br>
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• δ_crit = minimum diffusion zone thickness (meters)<br>
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• k = effective thermal conductivity (W/m·K)<br>
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• ΔT = operational temperature range (Kelvin)<br>
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• α = linear thermal expansion coefficient (1/Kelvin)<br>
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• τ_y = shear yield strength of weakest phase (Pascals)
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</div>
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<div class="citation">
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<strong>Grounding:</strong> This formulation derives from the Griffith-Orowan criterion for interfacial fracture, adapted for graded metallurgical transitions.<br>
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Source: <a href="https://www.wikidata.org/entity/Q1144771" target="_blank">Q1144771 (Griffith theory)</a> × <a href="https://nvlpubs.nist.gov/nistpubs/Legacy/MONO/nbsmonograph25.pdf" target="_blank">NBS Monograph 25: Weld Metallurgy</a><br>
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Cross-reference: <a href="/scrap-log.html">SCRAP-2026-0412</a> — 11% threshold validation via cold-weld simulation.
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</div>
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<script>
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function computeInterface() {
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const alpha1 = parseFloat(document.getElementById('alpha1').value);
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const alpha2 = parseFloat(document.getElementById('alpha2').value);
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const conductivity = parseFloat(document.getElementById('conductivity').value);
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const tempDelta = parseFloat(document.getElementById('tempDelta').value);
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const yieldStrength = parseFloat(document.getElementById('yieldStrength').value);
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if ([alpha1, alpha2, conductivity, tempDelta, yieldStrength].some(v => isNaN(v))) {
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alert("All fields required. Enter numeric values.");
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return;
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}
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const deltaAlpha = Math.abs(alpha1 - alpha2);
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const yieldPa = yieldStrength * 1e6; // MPa to Pa
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// Critical thickness: δ = (k × ΔT × Δα) / τ_y
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const criticalThickness = (conductivity * tempDelta * deltaAlpha) / yieldPa;
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// Annealing ramp rate: dT/dt = k / (α_avg × δ)
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const alphaAvg = (alpha1 + alpha2) / 2;
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const rampRate = conductivity / (alphaAvg * criticalThickness);
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// Interfacial shear stress at critical thickness
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const shearStress = yieldStrength * (criticalThickness > 0 ? 1 : 0);
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// Safety margin (target 15% excess)
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const safetyMargin = ((criticalThickness * 1.15) - criticalThickness) / criticalThickness * 100;
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document.getElementById('deltaAlpha').textContent = deltaAlpha.toExponential(4) + " 1/K";
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document.getElementById('criticalThickness').textContent = (criticalThickness * 1e6).toFixed(3) + " µm";
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document.getElementById('rampRate').textContent = rampRate.toFixed(2) + " K/s";
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document.getElementById('shearStress').textContent = shearStress.toFixed(1) + " MPa";
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document.getElementById('safetyMargin').textContent = safetyMargin.toFixed(1) + "%";
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document.getElementById('results').style.display = 'block';
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}
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</script>
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</body>
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