10.4 TTT and CCT Diagrams, Constitutional Supercooling & Scheil Microsegregation

10.2 Continuous Cooling Transformation (CCT) & Solidification Microstructures

Quick Answer: Welding is fundamentally a non-equilibrium process characterized by rapid, continuous cooling rather than isothermal holds. Consequently, Continuous Cooling Transformation (CCT) diagrams—not isothermal Time-Temperature-Transformation (TTT) diagrams—must be used to predict weld metal and HAZ microstructures. In CCT diagrams, transformation noses are shifted down in temperature and to longer times. Weld pool solidification morphology transitions from planar to cellular, columnar dendritic, and equiaxed dendritic per the constitutional supercooling criterion ($G_L/R < \Delta T_0 / D_L$). Solute segregation into terminal interdendritic liquid is modeled by the Scheil equation ($C_s = k C_0 (1 - f_s)^{k-1}$), explaining why sulfur and phosphorus ($k \approx 0.05$) trigger hot cracking. For optimal low-temperature Charpy toughness, weld metals are formulated to promote intragranularly nucleated acicular ferrite (AF) over grain-boundary upper bainite. Martensite forms via diffusionless shear below the Martensite Start ($M_s$) temperature, calculated using Andrews empirical formulas.

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TTT vs. CCT Diagrams: Non-Equilibrium Weld Cooling Kinetics

In furnace heat treatment, steel components can be rapidly quenched into a salt bath and held isothermally at a fixed temperature to generate specific microstructures (such as austempering to produce lower bainite). These transformations are mapped on Time-Temperature-Transformation (TTT) or Isothermal Transformation (IT) diagrams.

In fusion welding, however, molten and heated metal undergoes continuous, non-linear cooling driven by thermal conduction into the surrounding cold base plate. The microstructural evolution during this continuous descent must be analyzed using Continuous Cooling Transformation (CCT) diagrams.

                     ISOTHERMAL (TTT) vs. CONTINUOUS COOLING (CCT)

    Temp ^                                          Temp ^
         |   Ae3                                         |   Ae3
         |  -----                                        |  -----
         |       \                                       |       \      Continuous Cooling Curves
         |        \                                      |        \    (Fast ---> Slow)
         |    +-----\--+                                 |         \    \   \   \
         |    | TTT |  |                                 |          \    \   \   \
         |    | Nose|  |                                 |     +-----\----+   \   \
         |    +-----+--+                                 |     | CCT |     \   \   \
         |              \                                |     | Nose|      \   \   \
         |               \                               |     +-----+-------+   \   \
         |  Ms -----------                               |  Ms -------------------
         +------------------------>                      +------------------------>
                    Time (log t)                                    Time (log t)

      TTT: Instantaneous quench to constant T          CCT: Temperature continuously drops;
           Holds isothermally.                              Noses shift DOWN and to the RIGHT.

The Thermodynamic & Kinetic Shift in CCT Diagrams

When comparing CCT diagrams to their parent TTT diagrams for an identical steel composition:

1. Shift to Longer Times (Rightward Displacement): During continuous cooling, steel spends finite time passing through elevated temperatures where the thermodynamic driving force (undercooling $\Delta T = T_e - T$) is small. Nucleation incubation accumulates incrementally along the cooling path. Consequently, the apparent transformation "start" and "finish" boundaries are displaced to longer times.
2. Shift to Lower Temperatures (Downward Displacement): Because cooling is continuous, transformation does not complete at the high-temperature incubation point; latent heat is released while the material drops into lower temperature regimes. The transformation noses for ferrite, pearlite, and bainite are shifted downward by $20^\circ\text{C}$ to $>50^\circ\text{C}$ relative to isothermal TTT noses.
3. Depression or Elimination of Intermediate Phases: Rapid continuous cooling curves can bypass the ferrite and pearlite transformation "noses" entirely. If the cooling rate exceeds the critical cooling velocity ($CR_{\text{crit}}$), diffusion is suppressed, and austenite transforms purely into non-equilibrium martensite.

The Cooling Parameter: $\Delta t_{8/5}$

In international welding engineering (EN ISO, IIW), cooling severity is quantified by $\Delta t_{8/5}$—the elapsed time in seconds required for the weld deposit or HAZ to cool from $800^\circ\text{C}$ to $500^\circ\text{C}$. This temperature window represents the critical kinetic corridor where austenite decomposes into ferrite, pearlite, bainite, or martensite. Fast cooling (small $\Delta t_{8/5} < 5\text{ s}$, low heat input, thick plates) yields hard martensite/bainite; slow cooling (large $\Delta t_{8/5} > 30\text{ s}$, high heat input, high preheat) yields coarse ferrite and pearlite.

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Weld Metal Solidification Dynamics & Constitutional Supercooling

Solidification in fusion welding occurs epitaxially from the partially melted grains at the fusion boundary. The solidifying interface morphology is dictated by the Constitutional Supercooling Criterion formulated by Tiller, Jackson, Rutter, and Chalmers.

                            CONSTITUTIONAL SUPERCOOLING CRITERION

      Liquidus Temp ^                             Concentration ^
                    |      Liquid                       C_L     |         Liquid
                    |    /                                      |       /--------
              T_L --+---/ Solidus                               |      / Solute Boundary
                    |  /                                C_0 ----+-----/   Layer (δ_N)
              T_S --+-/                                         |    /|
                    +------------------->                       |   / |  C_s = k*C_L
                       Distance (x)                             +------------------->
                                                                   Distance (x)

      STABLE PLANAR FRONT (High G_L / R)           DENDRITIC BREAKDOWN (Low G_L / R)
            Solid       Liquid                           Solid            Liquid
          +-------+                                    +-------+
          |       |                                    |       |   Columnar
          |       |=======> Solidification             |       |===/\==/\==> Dendrites
          |       |         Front                      |       |   \/  \/
          +-------+                                    +-------+

The Constitutional Supercooling Equation

During solidification of an alloy, solute is rejected into the liquid (for solutes with equilibrium partition coefficient $k < 1$). This creates a solute-enriched boundary layer ahead of the advancing solid interface, locally depressing the thermodynamic liquidus temperature ($T_L$). If the actual thermal gradient in the liquid ($G_L$) is shallower than the liquidus temperature gradient ($dT_L/dx$), a zone of constitutionally supercooled liquid exists ahead of the interface:

$$\frac{G_L}{R} < \frac{\Delta T_0}{D_L} = \frac{m_L C_0 (1 - k)}{k D_L}$$

where:

• $G_L = \frac{dT}{dx}$: Thermal temperature gradient in the liquid at the interface ($\text{K/mm}$ or $^\circ\text{C/cm}$).
• $R$: Solidification interface growth velocity ($\text{mm/s}$).
• $\Delta T_0 = T_{\text{liquidus}} - T_{\text{solidus}}$: Equilibrium freezing temperature range ($^\circ\text{C}$).
• $m_L$: Slope of the equilibrium liquidus line ($^\circ\text{C/wt}%$).
• $C_0$: Nominal bulk alloy solute concentration ($\text{wt}%$).
• $k = C_S / C_L$: Equilibrium partition coefficient.
• $D_L$: Diffusion coefficient of the solute in the liquid melt (typically $\sim 3 \times 10^{-5}\text{ cm}^2\text{/s}$).

Morphological Transitions Across the Weld Pool

As the ratio $G_L / R$ progressively decreases, the advancing solid-liquid interface becomes unstable, evolving through four distinct morphologies:

$$\text{Planar} \xrightarrow{\text{decreasing } G_L/R} \text{Cellular} \xrightarrow{} \text{Columnar Dendritic} \xrightarrow{} \text{Equiaxed Dendritic}$$

In a moving weld pool, the local solidification velocity $R$ and thermal gradient $G_L$ vary systematically with position along the trailing pool boundary:

$$R = v_{\text{travel}} \cdot \cos\theta$$

where $\theta$ is the angle between the welding travel direction and the normal to the solidification front.

1. At the Fusion Boundary ($\theta \approx 90^\circ$): The growth rate $R \to 0$, while the thermal gradient into the cold base metal ($G_L$) is at its absolute maximum. Therefore, $G_L / R \to \infty$. A thin layer of planar or fine cellular growth initiates epitaxially from the base-metal grains.
2. Between Fusion Boundary and Centerline: As the interface advances, $\theta$ decreases toward $0^\circ$. The growth velocity $R$ accelerates toward $v_{\text{travel}}$, while the thermal gradient $G_L$ flattens due to heat accumulation in the trailing liquid. $G_L / R$ plunges by orders of magnitude, triggering rapid breakdown into columnar dendritic morphology.
3. At the Weld Centerline ($\theta = 0^\circ$): Growth rate reaches its maximum ($R = v_{\text{travel}}$) and $G_L$ drops to its minimum. $G_L / R$ reaches its lowest value across the weld. If constitutional supercooling is sufficiently intense and heterogeneous nucleants are present, equiaxed dendrites nucleate in the liquid ahead of the advancing columnar fronts, blocking competitive columnar impingement.

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Microsegregation Dynamics & The Scheil Equation

Solidification in welds occurs too rapidly for solid-state diffusion to homogenize the growing crystals. Non-equilibrium solute redistribution is governed by the classical Scheil-Gulliver equation, derived under three fundamental metallurgical assumptions:

1. Negligible diffusion in the solid phase ($D_S \approx 0$).
2. Complete, instantaneous diffusion and convective mixing in the liquid phase ($D_L \to \infty$).
3. Local thermodynamic equilibrium maintained at the solid-liquid interface ($C_s^* = k \cdot C_L$).

                               SCHEIL SOLUTE REDISTRIBUTION

      Solute Concentration (C) ^
                               |                                    Terminal Eutectic
                               |                                      Liquid Film
                               |                                         |
                               |                                         v
                               |                                        |--|
                               |                              C_L(f_s)  |  |
                               |                                /-------+--|
                               |                               /        |  |
                               |                      C_s(f_s)/         |  |
                           C_0 +-----------------------------/----------+--|
                               |                 ..---------'           |  |
                         k*C_0 +----------------'                       |  |
                               +----------------------------------------+--+--->
                               0.0                  Solid Fraction (f_s)   1.0

The Mathematical Formulation

The solute concentration in the solid at solid fraction $f_s$ ($0 \le f_s < 1$) is given by:

$$C_s = k C_0 (1 - f_s)^{k - 1}$$

The solute concentration in the remaining liquid pool is:

$$C_L = C_0 (1 - f_s)^{k - 1}$$

Segregation of Tramp Elements and Hot Cracking

For solutes with equilibrium partition coefficients far below unity ($k \ll 1$), solute rejection is extreme:

• Sulfur in Iron: $k_S \approx 0.05$.
• Phosphorus in Iron: $k_P \approx 0.06$.
• Carbon in Iron ($\delta$-ferrite): $k_C \approx 0.19$.

As solidification proceeds toward completion ($f_s > 0.90\text{ to }0.98$), sulfur and phosphorus are rejected into the shrinking interdendritic liquid channels. When $f_s = 0.98$, the concentration of sulfur in the remaining liquid spikes by a factor of:

$$\frac{C_L}{C_0} = (1 - 0.98)^{0.05 - 1} = (0.02)^{-0.95} \approx 40.7$$

A bulk sulfur level of just $0.020\text{ wt}%$ enriches to $>0.80\text{ wt}%$ in the final liquid! This concentrated liquid forms low-melting eutectic phases (iron-iron sulfide eutectic, $\text{Fe}-\text{FeS}$, freezing at $988^\circ\text{C}$, or iron phosphide, $\text{Fe}_3\text{P}$, freezing at $1050^\circ\text{C}$).

Because pure steel solidifies at $\sim 1500^\circ\text{C}$, these low-melting liquid films wet the columnar grain boundaries over a $500^\circ\text{C}$ temperature span while the surrounding weld metal contracts thermally. When solidification shrinkage tensile strains pull across these wetted boundaries, the liquid tears apart, producing solidification hot cracks.

The Metallurgical Countermeasure: The Mn/S Ratio

To neutralize sulfur-induced hot cracking, manganese is added to structural steels. Manganese possesses a vastly higher thermodynamic affinity for sulfur than iron ($\Delta G_{\text{MnS}} \ll \Delta G_{\text{FeS}}$):

$$\text{FeS} + \text{Mn} \rightleftharpoons \text{MnS} + \text{Fe}$$

Manganese sulfide (MnS) freezes as discrete, high-melting refractory globules ($T_m \approx 1610^\circ\text{C}$) that precipitate within the liquid before terminal solidification, preventing continuous wetting of grain boundaries. AWS standards mandate a minimum $\text{Mn/S}$ ratio $\ge 25\text{ to }30$ (and ideally $>40$ in high-restraint joints) to ensure freedom from solidification cracking.

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Weld Pool Pulsation and the Origin of Weld Ripples

AWS B5.16 Clause 8.3.4 lists the origin of weld ripples as a distinct metallurgy sub-topic, and the reason is that ripples are a free, continuous record of how the weld pool actually solidified.

A weld bead does not solidify as a smoothly retreating front. The trailing edge of the pool advances in discrete pulses, and each pulse freezes a thin arc-shaped ridge on the bead surface. Three mechanisms drive the pulsation:

1. Periodic variation in arc force. Metal transfer is inherently periodic. Each droplet detachment, each short-circuit event and each current pulse in a synergic waveform momentarily depresses and then releases the pool surface.
2. Surface-tension oscillation of the pool. A molten pool behaves as a damped oscillator with a natural frequency set by its mass and surface tension, so it rings after every disturbance.
3. Latent heat release. Solidification is not continuous: the pool supercools slightly, then releases latent heat as a layer freezes, briefly halting the front before it advances again.

Ripple spacing therefore carries information:

$\text{ripple spacing} \approx \frac{\text{travel speed}}{\text{pulsation frequency}}$

The last row is the reason this topic belongs in metallurgy rather than in cosmetic inspection. Ripples map the instantaneous pool boundary, so a bead whose ripples form long, sharply pointed chevrons is telling you the pool was teardrop-shaped, that solute segregated to the centreline, and that centreline cracking risk is elevated. A rounded elliptical ripple pattern indicates a pool shape in which grains meet the centreline at a shallow angle and cracking risk is far lower.

In pulsed GTAW and pulsed GMAW the relationship becomes exact: one ripple is deposited per current pulse, so counting ripples over a measured length directly verifies the pulse frequency and travel speed actually used in production against the values recorded in the procedure.