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TRIP and Transformation Plasticity in Welding

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TRIP and Transformation Plasticity in Welding

State of the art in transformation-induced plasticity models for welding and additive manufacturing FEM simulation.

Greenwood-Johnson mechanism

The foundational model (1965) describes how a polycrystalline material undergoing a phase transformation with volume change Delta-V/V yields at stresses far below the macroscopic yield stress. Individual grains transform with volumetric strain, generating internal micro-plasticity in the weaker surrounding matrix.

Classical GJ relation:

epsilon_tp = (5/4) * (Delta-V/V) * (sigma / sigma_y)

Citation: Greenwood, G.W. & Johnson, R.H. (1965). “The deformation of metals under small stresses during phase transformations.” Proc. Royal Society A, 283. Cited >1500 times.

Taleb & Sidoroff (2003) provided micromechanical re-derivation showing the GJ model underestimates TRIP strain under multiaxial loading.

Citation: Taleb, L. & Sidoroff, F. (2003). “A micromechanical modeling of the Greenwood-Johnson mechanism in transformation induced plasticity.” Int. J. Plasticity, 19(10). Cited 297 times.

Leblond model: the standard for welding FEM

The Leblond model (1989) extends Greenwood-Johnson by coupling TRIP with strain hardening and handling multi-phase transformations. Most widely implemented TRIP formulation in welding simulation software.

Formulation:

d(epsilon_tp)/dz = (3/2) * K * (d-sigma/dz) * h(sigma/sigma_y)

where z is the phase fraction, K is the transformation plasticity coefficient, and h is a saturation function.

Citations:

  • Leblond, J.B., Devaux, J. & Devaux, J.C. (1989). “Mathematical modelling of transformation plasticity in steels I: Case of ideal-plastic phases.” Int. J. Plasticity, 5(6). Cited 747 times.
  • Leblond, J.B. (1989). “Mathematical modelling of transformation plasticity in steels II: Coupling with strain hardening.” Int. J. Plasticity, 5(6). Cited 458 times.

FEM implementations

Kim, Im & Kim (2005) provided detailed FEM implementation algorithm for thermo-elastic-plastic constitutive equations with TRIP.

Citation: Kim, J., Im, S. & Kim, H.G. (2005). “Numerical implementation of a thermo-elastic-plastic constitutive equation in consideration of transformation plasticity in welding.” Int. J. Plasticity, 21(7). Cited 60 times.

Deng & Murakawa (2013) demonstrated TRIP can reduce predicted residual stresses by 30—50% in low-transformation-temperature steels.

Citation: Deng, D. & Murakawa, H. (2013). “Influence of transformation induced plasticity on simulated results of welding residual stress in low temperature transformation steel.” Computational Materials Science, 78. Cited 143 times.

Volume change and stress coupling

Phase transformations in steels produce volumetric strains:

  • Austenite to Ferrite/Pearlite: +1 to 4% volume expansion
  • Austenite to Bainite: +1 to 3%
  • Austenite to Martensite: +2 to 4.5%

Total strain decomposition in welding FEM:

epsilon_total = epsilon_elastic + epsilon_plastic + epsilon_thermal
              + epsilon_tp + epsilon_vol

where epsilon_vol is the isotropic volume change from phase transformation and epsilon_tp is the deviatoric TRIP strain.

The coupling is bidirectional: stress state affects transformation kinetics (stress-assisted nucleation, Magee mechanism for martensite), and transformation strains affect the stress field.

Key papers on volume change coupling

Zhang, Dong & Lu (2021): TRIP of AF1410 steel and its influences on welding residual stress and distortion.

Citation: Zhang, K., Dong, W. & Lu, S. (2021). “Transformation plasticity of AF1410 steel and its influences on the welding residual stress and distortion.” Materials Science and Engineering A, 819. Cited 37 times.

Chen et al. (2021) exploited TRIP to engineer compressive residual stresses in directed energy deposition.

Citation: Chen, W., Xu, L., Han, Y., Zhao, L. & Jing, H. (2021). “Control of residual stress in metal additive manufacturing by low-temperature solid-state phase transformation.” Additive Manufacturing, 47. Cited 97 times.

When TRIP matters

TRIP is significant when:

  • Material systems: Steels undergoing martensitic or bainitic transformation (especially LTT filler metals), Ti alloys with beta-to-alpha-prime transformation
  • Thermal cycles: Rapid cooling through transformation temperatures under constraint (welding, AM, quenching)
  • Stress regime: Applied or residual stress is 20—80% of yield stress during transformation

TRIP is negligible for:

  • Austenitic stainless steels (no solid-state transformation)
  • Aluminum alloys (no displacive transformation)
  • Pure metals

Implementation in FEM codes

SoftwareTRIP ModelNotes
Sysweld (ESI)Leblond (native)Purpose-built for welding
ABAQUSUMAT/UEXPANResearch UMATs available
JWRIANDeng & Murakawa in-houseResearch code, Leblond-based
Simufact WeldingLeblondCommercial, GUI-driven
COMSOLCustom PDEResearch implementations only
MOOSE/deal.IINone built-inMust implement as custom kernels

Research gaps for WAAM

Gap 1: No WAAM-specific TRIP calibration

TRIP coefficients (K in Leblond model) are calibrated for single-pass welding thermal cycles. WAAM involves repeated thermal cycling (reheating of previously deposited layers 5—50 times). The cumulative TRIP strain under cyclic transformation is uncharacterized.

Gap 2: Multi-phase TRIP under partial re-austenitization

WAAM interpass temperatures often fall between Ac1 and Ac3, producing partial austenitization. Existing Leblond formulations assume complete transformation. The TRIP behavior during incomplete, cyclic transformations is not modeled.

Gap 3: TRIP in LTT filler metals for WAAM

LTT wires produce compressive residual stress in WAAM, but no TRIP model was included in existing studies. The coupling between LTT-induced TRIP and WAAM-specific thermal histories (slow cooling rates, large heat input) is unexplored.

Gap 4: Stress-assisted transformation kinetics under WAAM constraints

The Magee mechanism (stress-assisted martensite nucleation) is calibrated for uniaxial stress. WAAM produces complex triaxial stress states that evolve during deposition. No model couples Magee kinetics with WAAM-scale FEM.

ML surrogate opportunities

  • TRIP coefficient prediction: ML models trained on experimental TRIP data (K values for different steels, cooling rates, stress states) could predict TRIP coefficients for untested alloy compositions and WAAM thermal cycles.
  • Leblond model replacement: A neural network trained on high-fidelity micromechanical simulations could replace the phenomenological Leblond model with a data-driven alternative that captures multiaxial effects the GJ model misses.
  • Cumulative TRIP under cycling: Recurrent neural networks could learn the history-dependent accumulation of TRIP strain across multiple WAAM thermal cycles.

Connection to TMM surrogate project

See TMM Surrogates. TRIP coupling is a critical component of the mechanical stage (stage 2) of the neural operator chain. The volume change from phase transformations must feed back into the stress prediction. This is one of the reasons why the mechanical GNO needs temperature history as input, not just the thermal field.

See also JMAK Phase Transformation for the metallurgical models that drive TRIP.

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