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A spur gear model showing phase fractions of austenite in blue and martensite in red.

Simulate Metallurgical Phase Transformations with the Metal Processing Module

Phase Transformations in Mechanical Components

When a material like steel undergoes heating or cooling from an elevated temperature, metallurgical phase transformations may occur. These transformations are sometimes deliberate, as part of the heat treatment of a mechanical component, or introduced inadvertently, as with welding. The metallurgical phases that are present in a component will affect its mechanical and thermal properties, and by optimizing the phase composition, you can improve the performance of a component. The Metal Processing Module, an add-on to the COMSOL Multiphysics® software, can be used to simulate metallurgical phase transformations in 3D, 2D, and 2D axisymmetric bodies.

What You Can Model with the Metal Processing Module

The Metal Processing Module provides a comprehensive set of tools for simulating manufacturing processes like steel quenching, welding, and additive manufacturing. These tools are packaged into physics interfaces, which automatically set up and solve the equations specific to the manufacturing process that you are modeling.

Steel Quenching

Steel quenching is a heat treatment process in which steel parts, heated to a fully austenitic state, are quenched. Being a multiphysics process, steel quenching involves a combination of austenite decomposition, heat transfer, and structural analysis. With the Steel Quenching multiphysics interface in the Metal Processing Module, several features are added automatically to facilitate the model setup. The interface prompts you to enter settings for the austenite, ferrite, pearlite, bainite, and martensite phases as well as the phase transformations from austenite to each of the others. Multiphysics couplings are also set up to account for the effects of latent heat and phase transformation strains.

Additionally, material properties for structural analysis can be temperature dependent and the plastic dissipation can act as a heat source in the heat transfer analysis. After running the analysis, you can examine phase compositions as well as the influence of cooling rate on the final distortions and residual stresses during quenching of a component. With these results, you gain insight into the efficacy of a certain quenchant and how the physical geometry of a component affects the attainable phase composition in its interior.

A spur gear model with a section cut out to show the inside and residual stresses shown in red. Spur gear after quenching


The process of carburization involves heating a steel component and exposing it to a carbon-rich environment, such as carbon monoxide. Diffusion of carbon from the surrounding environment occurs through the boundary and into the material by means of a time-dependent diffusion process. The flexibility of the software makes it straightforward to model related heat treatment processes like carburization, where you may modify your phase transformation model data to depend on the calculated carbon content. Running carburization analyses helps ensure that the process is carried out correctly; carburization followed by quenching can produce compressive stresses at the surface of a component, which is beneficial from a fatigue standpoint.
The COMSOL Multiphysics UI, when using the Metal Processing Module, showing the Carburization study settings and a steel gear model in the Graphics window. Carburization and quenching study of a steel gear

Transformation-Induced Plasticity (TRIP)

In general, phase transformations occur while the material is subjected to a mechanical stress, resulting in transformation-induced plasticity (TRIP). An inelastic straining of the material results from stresses that are below the yield stress and would not cause plastic flow in a classical plasticity sense. The Metal Processing Module can be used to analyze the TRIP effect, for example, in the transformation from austenite to martensite.

Diffusive and Displacive Phase Transformations

For diffusion-controlled phase transformations, such as when austenite decomposes into ferrite, two types of phase transformation models are provided: Leblond–Devaux and Johnson–Mehl–Avrami–Kolmogorov (JMAK). For modeling displacive (diffusionless) martensitic phase transformations, the Koistinen–Marburger model is available. These phase transformation models are available through the generalized Metal Phase Transformation interface that lets you define an arbitrary number of phases and phase transformations.

Additionally, it is possible to define your own phase transformation models to use in a simulation, and experimental calibration may be necessary for a given phase transformation. It is also possible to compute common phase transformation diagrams to facilitate calibration against experimental data, such as continuous cooling transformation (CCT) and time temperature transformation (TTT) diagrams.

A 1D plot of phase fractions over time with separate lines for austenite, ferrite, pearlite, bainite, and martensite. Phase fractions over time
The COMSOL Multiphysics UI for the Metal Processing Module showing CCT and TTT diagrams to the right of the Model Builder. CCT and TTT diagrams in COMSOL Multiphysics

Structural Analysis

Stresses and strains are computed using the effective material properties of the compound material, which are generally temperature and phase-composition dependent. The elastoplastic behavior of the compound material is averaged across the individual phases. In the case where one phase is significantly harder than the others, a nonlinear weighting scheme can be used to model the effective initial yield stress of the compound material. There is a plastic recovery option for ensuring that phases appear gradually and devoid of prior plastic straining. The volume reference temperature and thermal expansion coefficient are used to compute a thermal strain tensor in each phase. The thermal strain tensors of the phases are averaged into a thermal strain of the compound material. For more advanced structural analyses, the Metal Processing Module can be combined with the Structural Mechanics Module.

Three models of a steel billet showing martensite phase fraction, plastic strain, and axial stress. Structural analysis of a steel billet after 10 minutes of quenching

Thermal Analysis

The Metal Processing Module is equipped to model heat transport by using the full heat equation in the analysis. Additionally, the thermal conductivity, density, and specific heat capacity can be temperature dependent, and can even depend on the current phase composition. For example, the thermal conductivity of austenite is different from that of ferrite, and as the phase fractions evolve, so will the thermal conductivity of the compound material. For more advanced heat transfer analyses, the Metal Processing Module can be combined with the Heat Transfer Module.

Induction Hardening

If you add the AC/DC Module, you can perform induction hardening simulations, where you use the calculated temperature field from an induction heating simulation as the input to a quenching simulation.

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