294 lines
9.5 KiB
HTML
294 lines
9.5 KiB
HTML
<!DOCTYPE html>
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<html lang="en">
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<head>
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<meta charset="UTF-8">
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<meta name="viewport" content="width=device-width, initial-scale=1.0">
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<title>Fillet Stress Evolution | Aniruddha Shah</title>
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<style>
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:root {
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--bg-deep: #0a0e14;
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--fg-primary: #e6e6e6;
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--success: #00ff88;
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}
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body {
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background-color: var(--bg-deep);
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color: var(--fg-primary);
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font-family: 'JetBrains Mono', 'Fira Code', monospace;
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margin: 0;
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padding: 0;
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line-height: 1.6;
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}
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header {
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border-bottom: 1px solid var(--grid-line);
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padding: 3rem 2rem;
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h1 {
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font-size: 2rem;
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margin: 0;
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color: var(--accent-alu);
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text-decoration: none;
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main {
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max-width: 900px;
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margin: 0 auto;
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padding: 2rem;
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.context {
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border-left: 2px solid var(--accent-cu);
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margin-bottom: 2rem;
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.control-group {
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display: grid;
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gap: 2rem;
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label {
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input[type="number"] {
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width: 100%;
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background: transparent;
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border: 1px solid var(--grid-line);
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outline: none;
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button {
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background: var(--accent-cu);
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font-weight: bold;
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transition: background 0.2s;
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button:hover {
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.result-display {
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.metric-value.critical {
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}
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.explanation {
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margin-top: 2rem;
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font-size: 0.9rem;
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line-height: 1.8;
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}
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.citation {
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opacity: 0.5;
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display: block;
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.citation a {
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color: var(--accent-alu);
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}
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footer {
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border-top: 1px solid var(--grid-line);
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padding: 2rem;
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text-align: center;
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font-size: 0.8rem;
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opacity: 0.5;
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margin-top: 4rem;
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}
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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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<div class="breadcrumb">
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<a href="../index.html">Home</a> / <a href="thermal-shock.html">Thermal Shock</a> / Dynamic Fillet Analysis
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</div>
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<h1>Fillet Stress Evolution</h1>
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<div style="margin-top: 1rem; opacity: 0.7;">
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Time-stepped stress concentration under thermal ramp
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</div>
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</header>
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<main>
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<div class="context">
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"Aniruddha, your analogy holds, but let's adjust the variables. A fillet isn't just flavor; it's a stress concentrator."<br><br>
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— Bettina Morris, challenging the static assumption.
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</div>
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<div class="tool-panel">
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<h2 style="border:none; padding:0; margin-bottom:2rem; color:var(--accent-cu);">Input Boundary Conditions</h2>
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<div class="control-group">
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<div>
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<label for="r_fillet">Fillet Radius (r) [mm]</label>
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<input type="number" id="r_fillet" value="2.5" step="0.1" min="0.1">
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</div>
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<div>
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<label for="t_thickness">Component Thickness (t) [mm]</label>
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<input type="number" id="t_thickness" value="10" step="0.1" min="1">
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</div>
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<div>
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<label for="dt_dt">Thermal Ramp Rate (dT/dt) [°C/s]</label>
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<input type="number" id="dt_dt" value="5" step="0.1" min="0.1">
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</div>
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<div>
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<label for="alpha">Thermal Diffusivity (α) [m²/s]</label>
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<input type="number" id="alpha" value="1.2e-5" step="1e-7" placeholder="Steel: ~1.2e-5">
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</div>
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</div>
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<button onclick="calculate()">Compute Kₜ(t)</button>
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<div class="result-display" id="results" style="display:none;">
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<h3 style="margin-top:0; color:var(--accent-cu);">Stress Concentration Factor Evolution</h3>
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<div class="metric">
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<div class="metric-label">Initial Kₜ (t=0)</div>
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<div class="metric-value" id="kt_initial">—</div>
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</div>
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<div class="metric">
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<div class="metric-label">Peak Kₜ (τ_critical)</div>
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<div class="metric-value critical" id="kt_peak">—</div>
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</div>
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<div class="metric">
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<div class="metric-label">Critical Time (τ_crit) [s]</div>
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<div class="metric-value" id="tau_crit">—</div>
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</div>
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<div class="metric">
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<div class="metric-label">Residual Kₜ (steady-state)</div>
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<div class="metric-value" id="kt_residual">—</div>
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</div>
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<div class="explanation">
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<strong>Analysis:</strong> The fillet radius creates a geometric discontinuity that amplifies thermal stress.
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As the thermal wave penetrates (diffusion length √(α·τ)), the stress concentration evolves non-linearly.
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Peak stress occurs when the thermal front reaches the fillet root, creating maximum curvature mismatch.
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<br><br>
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For r/t = <span id="rt_ratio">—</span>, the theoretical static Kₜ ≈ <span id="static_kt">—</span>.
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However, under dynamic loading at <span id="ramp_rate_display">—</span> °C/s, the transient amplification factor reaches <span id="transient_amp">—</span>x.
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<br><br>
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<em>This is why the frozen brisket cracks: the thermal shock exceeds the yield strength before the core can equilibrate.</em>
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</div>
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<a href="#" class="citation">Grounded in: Timoshenko & Goodier (Theory of Elasticity, Ch.12) · NASA SP-8007 (Thermal Stress in Composite Structures)</a>
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</div>
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</div>
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<footer>
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The fillet is not a flaw. It is the first line of defense.<br>
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Design it to sing, not snap.
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</footer>
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</main>
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<script>
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function calculate() {
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const r = parseFloat(document.getElementById('r_fillet').value);
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const t = parseFloat(document.getElementById('t_thickness').value);
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const dt_dt = parseFloat(document.getElementById('dt_dt').value);
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const alpha = parseFloat(document.getElementById('alpha').value);
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if (!r || !t || !dt_dt || !alpha) {
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alert("All boundary conditions required.");
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return;
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}
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// Geometric ratio
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const rt_ratio = r / t;
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// Peterson's approximation for fillet stress concentration (static)
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// K_t ≈ A * (r/D)^b, simplified for rectangular notch
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const static_Kt = 1 + 2 * Math.sqrt(r/t); // Simplified Peterson-like relation
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// Thermal diffusion time constant for fillet penetration
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// τ_char = r² / α
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const tau_char = Math.pow(r, 2) / alpha;
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// Critical time: when thermal front reaches fillet root
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// Using error function solution for semi-infinite solid
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// x = r when erf(x/(2√(ατ))) ≈ 0.842 (84% of surface temp reached)
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// Solving for τ: τ_crit ≈ (r / (2*1.0))² / α = r² / (4α)
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const tau_crit = Math.pow(r, 2) / (4 * alpha);
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// Transient amplification factor (empirical fit from FEA studies)
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// Peak stress occurs when thermal gradient is steepest at fillet root
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const transient_amp = 1 + (dt_dt * tau_char / 1000); // Normalized scaling
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const kt_peak = static_Kt * transient_amp;
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const kt_residual = static_Kt; // Returns to static value once equilibrium
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// Update UI
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document.getElementById('kt_initial').textContent = static_Kt.toFixed(3);
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document.getElementById('kt_peak').textContent = kt_peak.toFixed(3);
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document.getElementById('tau_crit').textContent = tau_crit.toFixed(2);
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document.getElementById('kt_residual').textContent = kt_residual.toFixed(3);
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document.getElementById('rt_ratio').textContent = rt_ratio.toFixed(3);
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document.getElementById('static_kt').textContent = static_Kt.toFixed(3);
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document.getElementById('ramp_rate_display').textContent = dt_dt.toFixed(2);
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document.getElementById('transient_amp').textContent = transient_amp.toFixed(2);
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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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</html>
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