# Determining the microstructure of steel after welding in modern computer software

How can the microstructure of steel after welding be determined in modern computer software?

I am aware that there are 'classic' methods of predicting microstructures like Schaeffler, DeLong or WRC constitutional diagrams. What I am wondering about is: which algorithms are used in programs based on finite element method (FEM) computing (i.e. ESI Group software, particularly SYSWELD)

What I want to find out in particular:

1. How does a FEM model made of austenite differ from the one that is made of ferrite?

2. Is a FEM model enough to determine the microstructure of a material, that is represented by that model? If not, what else do you need to examine transformations of microstructure during the welding process?

• Are you talking about performing a FEA model that discretizes down to the crystalline structure? 'Cause that's pretty intense. Mar 22, 2016 at 12:48
• @grfrazee Well, it came across my mind, but it would be madness. That would not improve precision very much, and I don't even want to think about time, that such an analysis would take. What I meant is, there are programs that let you to model, let's say a pipe. You can 'tell' that program that it is made mainly of austenite. Than, in that program you can virtually heat-treat that pipe. The output of program things like deformation etc. It also, somehow, outputs the new microstructure (like ferrite) of that pipe. How was that solved? (that' s what I meant by asking this question ;) ) Mar 23, 2016 at 8:05

Summary:

1) The answer to this question is difficult. You would need to know how austenite and ferrite behave in relation to what you are doing to them. You would also need to know their compositions, temperature field, etc. The results here could vary significantly depending on the specific parameters and how they change with time and with each other.

2) Yes and no. You can get a statistical model of each FEM element at a macro scale to determine the statistical nature of the microstructure such as grain size, particle density, etc. Or you can model what happens at a microscale when welding to determine what the microstructure might look like under a microscope. To do either requires a lot of detailed thermodynamic data about all of the components present and their phases, as discussed below.

# More Specifically...

My approach to the problem would be to use statistical modeling to determine grain size, particle size and distribution, etc. The data would come from phase diagram data based on known compositions, together with assumed kinetic governing equations. The actual thermal and compositional kinetics are governed at a bulk scale by well known PDE models, but certain features such as size and distribution are determined by microscale kinetics. What phases appear and the order in which they appear are governed by the phase diagrams. We can generally assume that bulk kinetics provides an input into the microscale kinetic and thermodynamic relationships, but that the reverse is largely irrelevant. The microstructural data in turn provides an input into structure-property relationships.

A complete model would tie all of these together more-or-less in that order, and would look something like:

• Use the bulk scale kinetics to get the temperature and composition profiles for each element.
• Use the temperature and composition profiles to generate statistical microstructural data for each element.
• Use the statistical microstructural data to determine properties.

The algorithms for common software are generally proprietary, so I can't say for sure, but I believe any package such as SYSWELD or MAGMA uses something along these lines. SYSWELD may even use the Schaeffler, DeLong, and WRC diagrams as part of its thermodynamic modeling. It depends to what degree they are making assumptions about the thermodynamic data and how much effort they've put into that part of their model.

# Microstructural FEM

FEM may be used to model microstructural behavior at a microscale, such as mechanical and thermal behavior. Generally this is done by capturing a microstructural image representation, either by microscope (optical or SEM) for 2D or by computed x-ray tomography (CT) for 3D, and converting the representation into an FEM by identifying or segmenting different phases and their interfaces, and assigning appropriate (often anisotropic) material properties to each phase and each phase-pair interface.

To do all this, you need to be able to accurately segment phases, interfaces, and crystallographic orientation, which may take some expensive equipment and characterization work. Alternately, a phase field model may be used to attempt prediction of the microstructural morphology, and then relevant data captured from the phase field model. There are limitations in using a phase field model this way, which are discussed in the next section.

There is a tool on nanoHUB.org which does microstructural FEM for 2D images called OOF2. To use the tool you would need to create an account, and it is generally intended for educational purposes, but should give a general idea how a microstructural FEA might work in the 2D case. You might need to upload your own microstructure image, it's been awhile since I've used it and I've forgotten the details.

The results of microstructural FEM are useful for determining how textured microstructures might behave. They are also useful for determining how microstructure can be linked to fatigue properties by identifying stress concentrations in the microstructure and how the microstructure might play a role in crack and void initiation.

# Phase Field Models

To model phase transformation kinetics at a microscale, generally phase field models (Wikipedia) are used. The models involve a number of moving parts, so to speak, but are sometimes faster and usually more robust for capturing moving interfaces than with traditional FEM models.

The primary concept is that, for a field of elements containing two phases, the phase discrimintation of the entire field may be modeled with a scalar value varying from 0 to 1. If the value of an element is (very close to) 0 it is one phase, and (very close to) 1 the other phase. If it has an intermediate value it is part of an interface between the phases. Thus rather than a sharp interface as would be required with an FEM, the interface is modeled by assuming it is diffuse.

Phase field models typically also track composition, temperature and free energy, and have a collection of governing equations which must be solved at each time step to determine the evolution of the next step. To use a phase field model thus requires knowledge of temperature dependent free energy curves and temperature dependent diffusion rates, both thermal and compositional, among other things.

It is possible to model diverse microstructural evolution phenomena with phase field models, including:

and certainly much more is possible, if challenging.

I am unaware of any professional phase field modeling packages, as there are drawbacks limiting their usefulness outside academia and early-stage research. One limitation is that, depending on the model, the specific variables may not have a clear relationship with physical values that can be experimentally determined. Thus, sometimes the model parameters need to be adjusted systematically until the results "look right." Additionally, getting useful information out of the model is another issue due to the same discrepancies between model parameter values and physical values. It is also possible to produce non-physical results quite easily without careful tailoring of governing equations to the specific model. Validation is another issue as performing the experiments is at best an expensive and time consuming process, and at worst virtually impossible depending on the specific parameters involved. Research is of course focused on reducing these issues, but because phase field models are relatively new (~10 years old at the earliest) there is much work yet to be done.

Generally phase field models are mostly useful for drawing a pretty picture of what a microstructure might look like without performing expensive experimentation and microscopic examination. They are also useful for creating animations of microstructural evolution. In the future their use may expand to predicting features such as statistical modeling and capturing data for FEM, but the limitations above restrict those uses.

# Statistical Thermodynamic Models

Generally, at a useful level, most engineers deal with bulk properties. After all, most engineers are designing products at a visible, macroscopic scale. As a result, the specifics of a tiny fraction of the microstructure isn't particularly useful directly to how the product might behave at a macroscopic level. Instead, we want to determine how the product behaves as a bulk.

To model the bulk microstructural evolution and final properties of a material is usually done with a CALPHAD (Calculation of Phase Diagrams, Wikipedia) program. Microstructural CALPHAD models don't generate pretty pictures like in the previous two sections, but instead generate a statistical representation of certain classes of microstructure by generating a grain size or particle size and density distribution based on thermodynamic, kinetic, compositional, and temperature data.

Such a model can be used in conjunction with a process FEM to determine local microstructural distributions for each finite element. Thermocalc does thermodynamical statistical modeling and is a CALPHAD program. MAGMA casting process simulation software combines statistical thermodynamic modeling with FEM in some of their alloy packages. A MAGMA user might then be able to predict some statistical data throughout the bulk of their product, and then generate scalar fields representing mechanical properties which vary over the product. It appears SYSWELD does the same thing for heat treatment and the welding process, probably by the general method described here.

# References

nanoHub.org - A site with many computational tools and educational resources focused on nano-scale. Some information and tools are related to larger scale modeling, especially OOF2 (Object Oriented Finite Element Analysis, 2D) and VKML (Virtual Kinetics of Materials Laboratory) tools.

solidification.org - A site with a number of neat movies of solidification processes, both experimental and phase field simulation.

I do not endorse any linked sites or softwares, the links are only intended for referential and educational purposes.

• Wow. I knew the answer would be complicated, but this is something else! Mar 23, 2016 at 11:51