10.5 Non-Equilibrium Transformation Products & Martensite Modeling

Non-Equilibrium Transformation Products

                               MICROSTRUCTURAL COMPARISON

       UPPER BAINITE (400-550°C)                      LOWER BAINITE (250-400°C)
    Parallel Ferrite Laths (Sheaves)             Fine Acicular Ferrite Plates
    +------------------------------+             +------------------------------+
    |        Ferrite Lath          |             |   \\\  \\\  \\\  \\\        | Fine Internal
    |==============================| Brittle     |    \\\  \\\  \\\  \\\       | Carbides at
    | Continuous Interlath Fe3C    | Carbide     |        Ferrite Plate         | 55°-60° to
    |==============================| Films       |   \\\  \\\  \\\  \\\        | Plate Axis
    |        Ferrite Lath          |             +------------------------------+
    +------------------------------+             High Toughness & High Strength
    Poor CVN Toughness (Cleavage Path)           

       ACICULAR FERRITE (AF)                         LATH MARTENSITE (<0.6% C)
    Interlocking "Basketweave"                   Diffusionless Shear Structure
    +------------------------------+             +------------------------------+
    |    /\     Intragranular      |             |  / / / / / / / / / / / / /   | Invariant
    |   /  \    Inclusion (Ti-O)   |             | / / / / / / / / / / / / /    | Plane
    |  / () \   Nucleation         |             |/ / / / / / / / / / / / /     | Dislocation
    | /  /\  \                     |             |  High Hardness, Low Toughness| Laths
    |/  /  \  \ Interlocking Laths |             +------------------------------+
    +------------------------------+             BCT Lattice; Andrews Ms Formula
    Optimum Low-Temp CVN Toughness               

1. Bainite: Upper vs. Lower Morphology

Bainite forms by a non-lamellar decomposition of austenite occurring below the pearlite range and above the martensite start temperature ($M_s$):

• Upper Bainite ($400^\circ\text{C} \text{ to } 550^\circ\text{C}$): Consists of parallel sheaves of lath ferrite. Because carbon cannot be held in solution in ferrite, it is rejected into the untransformed austenite between the laths. This enriched interstitial austenite decomposes into continuous films of cementite ($\text{Fe}_3\text{C}$) along the lath boundaries. These brittle interlath carbide films provide unobstructed, planar pathways for cleavage microcracks, resulting in disastrously low Charpy V-notch impact toughness.
• Lower Bainite ($250^\circ\text{C} \text{ to } 400^\circ\text{C}$): Forms at lower temperatures where carbon diffusion is restricted. Fine cementite precipitates internally within the ferrite plates, nucleating on dislocation arrays and aligned at a characteristic angle of approximately $55^\circ\text{ to }60^\circ$ to the longitudinal plate axis. Interlath carbide films are absent. Consequently, lower bainite exhibits an exceptional combination of high yield strength and high fracture toughness.

2. Acicular Ferrite (AF): The Optimal Weld Metal Microstructure

Acicular ferrite is widely recognized as the most desirable microstructural constituent in carbon-manganese and low-alloy steel weld metals for low-temperature toughness (e.g., offshore structures, arctic pipelines, pressure vessels):

• Morphology: A chaotic, interlocking "basketweave" arrangement of short, lenticular ferrite plates with widths between $0.5\text{ and }2.0\ \mu\text{m}$ and high dislocation densities.
• Intragranular Nucleation Mechanism: Unlike bainite and Widmanstätten ferrite, which nucleate competitively at prior austenite grain boundaries and propagate inward as parallel packets, acicular ferrite nucleates intragranularly on fine, sub-micron non-metallic inclusions distributed uniformly within the austenite grain interiors.
• Inclusion Chemistry: The most potent inclusions for AF nucleation are complex titanium-bearing oxides and carbonitrides, specifically $\text{Ti}_2\text{O}_3$, $\text{TiO}$, $\text{TiN}$, and manganese galaxite spinel ($\text{MnO}\cdot\text{Al}_2\text{O}_3$). These inclusions promote nucleation via two primary mechanisms:
  1. Low Crystallographic Lattice Misfit: Excellent epitaxy between $\text{Ti}_2\text{O}_3$ / $\text{TiO}$ (crystal plane {001}) and BCC ferrite (plane {110}), minimizing activation energy for nucleation (Baker-Nutting orientation relationship).
  2. Local Manganese Depletion Zones (MDZ): Inclusions precipitate adjacent manganese-rich phases or absorb manganese into their lattice, depleting the surrounding matrix of Mn over a distance of $0.1-0.5\ \mu\text{m}$. Because manganese is a strong austenite stabilizer, this localized Mn-depletion elevates the local $Ae_3$ transformation temperature, transforming the surrounding shell into ferrite before the bulk grain boundaries can transform.
• Toughness Mechanism: The chaotic, interlocking orientation of AF plates means that a propagating cleavage crack encounters high-angle crystallographic grain boundaries every $1-2\ \mu\text{m}$. The crack is repeatedly deflected, blunted, and forced to branch, absorbing tremendous fracture energy down to $-40^\circ\text{C}$ or $-60^\circ\text{C}$.

3. Martensite Formation Kinetics & The Andrews Equations

When cooling through the transformation range is sufficiently rapid to suppress all diffusion-controlled transformations (ferrite, pearlite, bainite), austenite transforms into martensite:

• Mechanism: Athermal, diffusionless, military shear transformation governed by the Bain strain model. FCC austenite undergoes a coordinated shuffle of iron atoms, trapping carbon interstitials within the octahedral sites along one axis, distorting the lattice into a Body-Centered Tetragonal (BCT) crystal structure.
• Substructure: In low-carbon steels ($<0.6\%\text{ C}$), martensite forms as fine laths clustered in packets with high dislocation densities ($10^{11}\text{ to }10^{12}\text{ cm}^{-2}$). Above $0.8\%\text{ C}$, martensite forms as lenticular plates containing internal transformation twins.
• Athermal Kinetics: The extent of transformation depends solely on the temperature to which the alloy is cooled below the Martensite Start ($M_s$), not on time: $$f_M = 1 - \exp\left[ -0.011 (M_s - T) \right]$$

Predicting Transformation Temperatures: The Andrews Formulas

The Martensite Start ($M_s$) and Martensite Finish ($M_f$) temperatures are dictated by chemical composition. Carbon exerts by far the strongest depressing effect. The widely recognized Andrews linear regression equations (AWS D1.1 / Welding Handbook) state:

$$M_s\ (^\circ\text{C}) = 539 - 423(\%\text{C}) - 30.4(\%\text{Mn}) - 17.7(\%\text{Ni}) - 12.1(\%\text{Cr}) - 7.5(\%\text{Mo})$$

The Martensite Finish ($M_f$) temperature, representing $\approx 99\%$ transformation to martensite, is approximately:

$$M_f\ (^\circ\text{C}) \approx M_s - 215^\circ\text{C}$$

If alloying additions drive $M_f$ below ambient room temperature ($20^\circ\text{C}$), untransformed austenite remains trapped in the microstructure as retained austenite, which may subsequently transform to untempered martensite during mechanical service, causing unexpected brittle failure.

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Comprehensive Worked Numerical Example: Microsegregation & Martensite Modeling

Problem Statement

A welding engineer is qualifying a high-strength low-alloy (HSLA) steel submerged arc weld deposit for arctic offshore service. The deposited weld metal chemical composition is determined by optical emission spectroscopy (OES):

• Carbon: $C_0 = 0.11\text{ wt}\%$
• Manganese: $\text{Mn} = 1.40\text{ wt}\%$
• Nickel: $\text{Ni} = 0.85\text{ wt}\%$
• Chromium: $\text{Cr} = 0.35\text{ wt}\%$
• Molybdenum: $\text{Mo} = 0.25\text{ wt}\%$
• Phosphorus: $P_0 = 0.018\text{ wt}\%$ (equilibrium partition coefficient $k_P = 0.06$)
• Sulfur: $S_0 = 0.010\text{ wt}\%$

Perform the following engineering evaluations:

1. Using the Scheil equation, calculate the phosphorus concentration in the liquid ($C_L$) at solid fractions of $f_s = 0.90$ and $f_s = 0.98$. Assess whether phosphide eutectic segregation poses a hot cracking threat.
2. Calculate the manganese-to-sulfur ratio ($\text{Mn/S}$) and evaluate compliance with cracking resistance criteria.
3. Calculate the Martensite Start ($M_s$) temperature using the Andrews formula.
4. Calculate the Martensite Finish ($M_f$) temperature and determine whether retained austenite will persist at a room temperature of $20^\circ\text{C}$.

Step-by-Step Solution

Step 1: Calculate Phosphorus Enrichment via Scheil Equation The Scheil equation for liquid concentration is:

$$C_L = P_0 (1 - f_s)^{k_P - 1}$$

Given $k_P = 0.06$, the exponent is $k_P - 1 = 0.06 - 1 = -0.94$.

• At $f_s = 0.90$ ($1 - f_s = 0.10$ remaining liquid): $$C_L(0.90) = 0.018\% \times (0.10)^{-0.94} = 0.018\% \times 8.7096 = 0.1568\text{ wt}\%\text{ P}$$
• At $f_s = 0.98$ ($1 - f_s = 0.02$ remaining liquid): $$C_L(0.98) = 0.018\% \times (0.02)^{-0.94} = 0.018\% \times 39.585 = 0.7125\text{ wt}\%\text{ P}$$

Engineering Evaluation: At $98\%$ solidification completion, phosphorus in the interdendritic liquid has segregated to $0.713\text{ wt}\%$, an enrichment factor of nearly $40\times$. Concentrations exceeding $0.7\%\text{ P}$ depress the local solidus below $1050^\circ\text{C}$ through $\text{Fe}_3\text{P}$ eutectic formation, creating a severe hot cracking risk if high restraint is present.

Step 2: Calculate and Evaluate Mn/S Ratio

$$\frac{\text{Mn}}{\text{S}} = \frac{1.40\text{ wt}\%}{0.010\text{ wt}\%} = 140$$

Engineering Evaluation: The $\text{Mn/S}$ ratio of $140$ significantly exceeds the mandatory threshold of $25-30$ and the recommended high-restraint threshold of $40$. All available sulfur will be tied up as high-melting MnS inclusions ($T_m = 1610^\circ\text{C}$), completely preventing $\text{FeS}$ liquid film wetting.

Step 3: Calculate Martensite Start ($M_s$) Temperature Apply the Andrews formula:

$$M_s = 539 - 423(\text{C}) - 30.4(\text{Mn}) - 17.7(\text{Ni}) - 12.1(\text{Cr}) - 7.5(\text{Mo})$$

Substitute alloy percentages:

• Carbon contribution: $423 \times 0.11 = 46.53^\circ\text{C}$
• Manganese contribution: $30.4 \times 1.40 = 42.56^\circ\text{C}$
• Nickel contribution: $17.7 \times 0.85 = 15.045^\circ\text{C}$
• Chromium contribution: $12.1 \times 0.35 = 4.235^\circ\text{C}$
• Molybdenum contribution: $7.5 \times 0.25 = 1.875^\circ\text{C}$

Total alloy depression:

$$\Delta T_{\text{alloy}} = 46.53 + 42.56 + 15.05 + 4.24 + 1.88 = 110.26^\circ\text{C}$$ $$M_s = 539 - 110.26 = 428.74^\circ\text{C} \approx 429^\circ\text{C}$$

Step 4: Calculate Martensite Finish ($M_f$) & Retained Austenite Evaluation

$$M_f \approx M_s - 215^\circ\text{C} = 428.74 - 215 = 213.74^\circ\text{C} \approx 214^\circ\text{C}$$

Engineering Evaluation: Because $M_f = 214^\circ\text{C}$ is well above ambient room temperature ($20^\circ\text{C}$), any martensitic transformation triggered by fast cooling will proceed to $100\%$ completion during cooling to room temperature. There is negligible risk of retained austenite transforming to untempered, brittle martensite in subsequent sub-zero service.

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Real-World Engineering Scenarios & Exam Pitfalls

Industrial Case: Loss of Toughness in Arctic Offshore Linepipe Welds

A pipeline contractor welding API 5L X70 submerged arc girth welds for an Arctic subsea project failed procedure qualification testing: Charpy V-notch impact toughness at $-40^\circ\text{C}$ averaged a dismal $18\text{ J}$ (specification requirement: $>60\text{ J}$). Metallographic sectioning and SEM electron backscatter diffraction (EBSD) revealed that the weld metal microstructure consisted of $75\%$ coarse upper bainite with grain-boundary ferrite, and less than $15\%$ acicular ferrite.

Root Cause Investigation: Chemical analysis revealed that the submerged arc flux-wire combination contained an excessive level of active aluminum deoxidizer ($0.045\text{ wt}\%$ Al in deposit) and insufficient titanium ($0.003\text{ wt}\%$ Ti). The strong aluminum affinity for oxygen scavenged all available weld pool dissolved oxygen, forming coarse, floatable $\text{Al}_2\text{O}_3$ inclusions that separated into the slag. This starved the weld pool of fine $\text{Ti}_2\text{O}_3$ and $\text{MnO}\cdot\text{Al}_2\text{O}_3$ spinels necessary to nucleate acicular ferrite intragranularly. Without internal nucleation sites, transformation defaulted to prior austenite grain boundaries, growing inward as continuous packets of upper bainite with cleavage-prone interlath carbides.

Corrective Engineering Action: The engineer reformulated the consumable wire-flux system to maintain deposit aluminum at $\le 0.015\%$, introduced titanium at $0.020-0.035\%$, and controlled dissolved oxygen to $250-350\text{ ppm}$. The resulting density of intragranular $\text{Ti}_2\text{O}_3$ nucleants drove the acicular ferrite fraction above $85\%$, elevating average Charpy energy at $-40^\circ\text{C}$ to $165\text{ J}$.

Common Exam Traps

Exam Trap 1: Confusing Acicular Ferrite with Upper Bainite Nucleation Sites A favorite CWEng exam question asks to distinguish acicular ferrite from bainite. Both transform in similar temperature ranges ($400-500^\circ\text{C}$) and exhibit plate-like morphologies. However, acicular ferrite nucleates intragranularly on non-metallic inclusions, whereas bainite nucleates heterogeneously on prior austenite grain boundaries. This difference in nucleation site is what gives acicular ferrite its chaotic basketweave morphology and superior impact toughness.

Exam Trap 2: Direct Translation of TTT Diagram Data to Welding Cooling Rates Candidates frequently make the mistake of using isothermal TTT diagrams to select welding travel speeds and preheats. Because continuous cooling delays transformation incubation and lowers transformation temperatures, using a TTT diagram will underestimate hardenability and lead to unconservative preheat specifications. Always use CCT diagrams for welding applications.

Exam Trap 3: The Myth of Martensite Formation Halting at $M_s$ Certification candidates often confuse $M_s$ with the complete transformation to martensite. $M_s$ marks only the start of martensite formation ($<1\%$ martensite). As the workpiece cools between $M_s$ and $M_f$, the volume fraction of martensite increases athermally. If cooling stops or the part is held between $M_s$ and $M_f$, transformation arrests, leaving untransformed austenite.