Laser Keyhole Welding Depth Calculator
Industrial Laser Processing: Predict deep-penetration weld depth ($h$), aspect ratio, Péclet number ($Pe$), and conduction-to-keyhole transition threshold.
Laser Beam & Material Parameters
Weld Depth & Keyhole Physics
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Mechanics of Deep Penetration Keyhole Laser Welding
High-brightness fiber and disk lasers focus multi-kilowatt optical power into spot diameters under $200\ \mu\text{m}$, creating peak irradiances exceeding $10^7\ \text{W/cm}^2$ for high-speed automotive and aerospace joining.
1. Conduction to Keyhole Transition Threshold
The transition occurs when laser irradiance delivers enough energy density to boil metal within the interaction transit time:
I_threshold ≈ (T_boil · k · √π) / (2 · A · √(α · τ_interaction)) ≈ 1.0 - 1.5 × 10⁶ W/cm²
2. Penetration Scaling Law
In the keyhole regime, weld penetration depth $h$ scales with laser power $P$ and inversely with the square root of welding speed $v$ and spot diameter $d_f$:
h ≈ C · η_abs · [ P_kW / √(v_m/min · d_spot_mm) ]
where $\eta_{\text{abs}} \approx 80\%\text{--}90\%$ due to multiple Fresnel internal reflections trapping photons within the vaporized keyhole cavity.
Frequently Asked Questions
What is the physical difference between conduction mode and keyhole mode laser welding?
At lower laser power densities ($I < 10^6\ \text{W/cm}^2$), heat conducts into the workpiece purely by thermal diffusion from the surface, creating shallow, wide weld pools with aspect ratios ($h/w$) of $0.5$ to $1.0$. Above the vaporization threshold ($I > 1.5 \times 10^6\ \text{W/cm}^2$), metal boils instantly; recoil pressure from escaping vapor excavates a narrow deep channel (the "keyhole") that traps the beam via multiple internal reflections, producing deep welds with aspect ratios exceeding $5:1$ to $10:1$.
Why does welding copper with near-IR fiber lasers (1070 nm) suffer from spatter and instability?
Solid copper reflects over $95\%$ of near-infrared light ($1070\text{ nm}$). Consequently, immense laser power is required just to initiate melting. However, once a keyhole forms, absorption jumps violently from $4\%$ to $>80\%$, causing extreme over-boiling and catastrophic liquid droplet expulsion (spatter). Switching to green ($515\text{ nm}$) or blue ($450\text{ nm}$) lasers provides $40\%\text{--}60\%$ cold absorption, yielding spatter-free, stable copper welds.
What role does the Péclet Number (Pe) play in laser welding thermodynamics?
The thermal Péclet number $Pe = \frac{v \cdot d_f}{2\alpha}$ compares the rate of heat advection due to workpiece travel speed ($v$) against thermal conduction into the material ($\alpha$). At high Péclet numbers ($Pe > 2$), the weld pool is elongated and heat conducts primarily 2D transverse to the seam, enabling narrow heat-affected zones (HAZ) and minimal thermal distortion.