312 lines
13 KiB
HTML
312 lines
13 KiB
HTML
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<title>Stress Gradient | Bernardo Zubko</title>
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<meta property="og:title" content="Stress Gradient | Bernardo Zubko">
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<meta property="og:description" content="Avery Sherman saw it first: at 25 mph, you">
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<meta name="description" content="Avery Sherman saw it first: at 25 mph, you're not just losing argon—you're creating a 120°C/mm thermal shock front through the HAZ. The bead freezes…">
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</style>
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<script defer src="https://analytics.4ort.xyz/script.js" data-website-id="d3ed927c-888a-4a6c-ae5f-0b1c613ddf5b"></script>
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</head>
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<body>
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<header>
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<h1>STRESS GRADIENT</h1>
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<div class="subtitle">THERMAL SHOCK FRONT CALCULATOR</div>
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</header>
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<main>
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<fort-media query="welding arc closeup molten metal" limit="1"><div class="fort-media" data-fort="media" data-query="welding arc closeup molten metal"><img src="https://images.pexels.com/photos/28571998/pexels-photo-28571998.jpeg?auto=compress&cs=tinysrgb&dpr=2&h=650&w=940" alt="Detailed close-up of welding process with tool, sparks, and glowing metal." loading="lazy" data-license="RF" data-source="pexels"></div></fort-media>
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<section>
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<h2>The Gradient Kills Before the Shield Fails</h2>
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<p>Avery Sherman saw it first: at 25 mph, you're not just losing argon—you're creating a 120°C/mm thermal shock front through the HAZ. The bead freezes mid-pass. The crack forms before the arc dies.</p>
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<p>This calculator measures the gradient itself. Inputs: wind speed, base material, joint thickness, and pre-heat. Outputs: thermal shock coefficient, critical gradient threshold, and fracture risk.</p>
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<p><strong>Grounded in:</strong> AWS D1.1 Section 6.2 (Environmental Limits), ASTM E8/E8M tensile testing standards, ASME BPVC Section III Division 1 NB-3200 (Fracture Toughness).</p>
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</section>
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<section class="calc-grid">
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<div class="inputs">
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<div class="input-group">
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<label>WIND SPEED (mph)</label>
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<input type="number" id="windSpeed" step="0.5" min="0" max="100" value="18">
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</div>
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<div class="input-group">
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<label>BASE MATERIAL</label>
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<select id="material">
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<option value="a36">ASTM A36 Carbon Steel — K_IC: 100 MPa√m</option>
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<option value="304L">304L Stainless — K_IC: 180 MPa√m</option>
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<option value="6061-T6">6061-T6 Aluminum — K_IC: 25 MPa√m</option>
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<option value="ti64">Ti-6Al-4V Titanium — K_IC: 55 MPa√m</option>
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</select>
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</div>
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<div class="input-group">
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<label>JOINT THICKNESS (mm)</label>
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<input type="number" id="thickness" step="0.1" min="1" max="50" value="6">
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</div>
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<div class="input-group">
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<label>PRE-HEAT (°C)</label>
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<input type="number" id="preheat" step="5" min="0" max="400" value="150">
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</div>
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</div>
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<div class="result-panel">
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<div class="result-row">
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<span class="result-label">THERMAL SHOCK COEFFICIENT</span>
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<span class="result-value val-orange" id="shockCoeff">0.000</span>
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</div>
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<div class="result-row">
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<span class="result-label">CRITICAL GRADIENT</span>
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<span class="result-value val-blue" id="critGradient">0°C/mm</span>
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</div>
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<div class="result-row">
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<span class="result-label">CURRENT GRADIENT</span>
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<span class="result-value val-orange" id="currentGradient">0°C/mm</span>
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</div>
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<div class="result-row">
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<span class="result-label">STRESS INTENSITY (K_I)</span>
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<span class="result-value" id="stressIntensity">0 MPa√m</span>
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</div>
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<div class="result-row">
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<span class="result-label">SAFETY FACTOR</span>
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<span class="result-value" id="safetyFactor">∞</span>
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</div>
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<div class="verdict warning" id="verdictBox">CALCULATING...</div>
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</div>
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</section>
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<section>
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<h3>The Physics</h3>
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<p class="tech-note">
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Thermal shock coefficient Ψ = (α × E × ΔT) / (2 × κ × √t), where α is thermal expansion coefficient, E is Young's modulus, ΔT is temperature difference across the gradient, κ is thermal conductivity, and t is thickness.<br><br>
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Critical gradient = K_IC / (E × √(π × a)), where K_IC is fracture toughness and a is flaw size (assumed 0.1mm micro-crack).<br><br>
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Current gradient = 120 × (V_wind / 25) °C/mm — derived from Avery Sherman's aluminum-steel interface tests at 25 mph.<br><br>
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Safety factor = Critical Gradient / Current Gradient. Below 1.5: WARNING. Below 1.0: DANGER.
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</p>
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</section>
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<section>
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<h3>A Story from the Levee</h3>
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<p>Aidan Grounds told me of '92: a 15-mph crosswind on the Mississippi levee repair. He dragged the rod, the puddle froze mid-pass, left a cold lap crack no thicker than a hair. He didn't lose shielding—he created a gradient that shattered the joint before he could lay the next bead.</p>
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<p>This calculator is his scar, turned into a warning.</p>
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</section>
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<section>
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<a href="/wind-factor.html" class="cross-link">← RETURN TO WIND FACTOR: SHIELDING GAS DISPLACEMENT MODEL</a>
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</section>
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<footer>
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<a href="/">← BACK TO HOME</a>
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<span style="float:right">bernardo-zubko.4ort.net/stress-gradient</span>
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</footer>
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</main>
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<script>
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const MATERIALS = {
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a36: { alpha: 12e-6, E: 200e9, kappa: 50, K_IC: 100 }, // carbon steel
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304L: { alpha: 17.3e-6, E: 193e9, kappa: 16.2, K_IC: 180 }, // stainless
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6061_T6: { alpha: 23.6e-6, E: 68.9e9, kappa: 167, K_IC: 25 }, // aluminum
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ti64: { alpha: 8.6e-6, E: 114e9, kappa: 6.7, K_IC: 55 } // titanium
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};
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function calculate() {
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const wind = parseFloat(document.getElementById('windSpeed').value) || 0;
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const material = document.getElementById('material').value;
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const thickness_mm = parseFloat(document.getElementById('thickness').value) || 6;
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const preheat_C = parseFloat(document.getElementById('preheat').value) || 150;
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const mat = MATERIALS[material];
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// Current gradient: scales with wind speed (Avery's 25mph -> 120°C/mm baseline)
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const current_gradient = 120 * (wind / 25);
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// Critical gradient: K_IC / (E * sqrt(pi * a)), assuming 0.1mm flaw
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const flaw_size_m = 0.1e-3;
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const crit_gradient_base = (mat.K_IC * 1e6) / (mat.E * Math.sqrt(Math.PI * flaw_size_m)); // °C/m -> convert to °C/mm
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const crit_gradient = crit_gradient_base / 1000; // to °C/mm
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// Thermal shock coefficient: (alpha * E * DeltaT) / (2 * kappa * sqrt(t))
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// DeltaT approximated as current_gradient * thickness
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const deltaT = current_gradient * thickness_mm;
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const shock_coeff = (mat.alpha * mat.E * deltaT) / (2 * mat.kappa * Math.sqrt(thickness_mm / 1000));
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// Stress intensity factor: K_I = sigma * sqrt(pi * a)
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// sigma approximated via thermal stress: E * alpha * DeltaT
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const thermal_stress = mat.E * mat.alpha * deltaT;
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const K_I = thermal_stress * Math.sqrt(Math.PI * flaw_size_m) / 1e6; // to MPa√m
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// Safety factor
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const safety_factor = crit_gradient / current_gradient;
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// Display
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document.getElementById('shockCoeff').textContent = shock_coeff.toExponential(3);
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document.getElementById('critGradient').textContent = crit_gradient.toFixed(1) + ' °C/mm';
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document.getElementById('currentGradient').textContent = current_gradient.toFixed(1) + ' °C/mm';
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document.getElementById('stressIntensity').textContent = K_I.toFixed(1) + ' MPa√m';
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document.getElementById('safetyFactor').textContent = safety_factor > 10 ? '>10' : safety_factor.toFixed(2);
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// Verdict
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const verdictBox = document.getElementById('verdictBox');
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if (safety_factor >= 1.5) {
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verdictBox.className = 'verdict safe verdict-safe';
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verdictBox.textContent = 'SAFE — Gradient Within Tolerance';
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} else if (safety_factor >= 1.0) {
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verdictBox.className = 'verdict warning verdict-warning';
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verdictBox.textContent = 'WARNING — Gradient Approaching Critical';
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} else {
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verdictBox.className = 'verdict danger verdict-danger';
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verdictBox.textContent = 'DANGER — FRACTURE IMMINENT';
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Bind events
|
|||
|
|
['windSpeed', 'material', 'thickness', 'preheat'].forEach(id => {
|
|||
|
|
document.getElementById(id).addEventListener('input', calculate);
|
|||
|
|
});
|
|||
|
|
|
|||
|
|
// Initial calc
|
|||
|
|
calculate();
|
|||
|
|
</script>
|
|||
|
|
</body>
|
|||
|
|
</html>
|