# How to Use Sensitivity Calculations to Evaluate the Effect of Composition Variation on Critical Phase Transformation Temperatures

In order to establish suitable processing windows for alloys, it is important to know their critical phase transformation temperatures such as: liquidus and solidus, A1, A3 and Martensite Start temperatures for steels, gamma prime / double prime solvus temperatures for Ni-Superalloys, beta-transus temperatures for Ti-based alloys, and so on. However, these values can be sensitive to differences in the heat-to-heat chemistries, resulting in wide variations, even over the allowable specification range of an alloy.

For existing alloys, process engineers will often look up these temperatures in handbooks or data sheets. However, these values rarely account for variations attributable to chemistry differences. Additionally, it can be difficult to capture the sensitivity experimentally without many costly and time consuming experiments.

One of the strengths of computational thermodynamics is the ability to quantify the variation of properties as a function of temperature or chemistry and predict the sensitivity associated with these variations. Such calculations can be easily made using the Uncertainty Calculation type in the Property Model Calculator in Thermo-Calc and the results visualized as a histogram or normal probability plot. Three such examples are illustrated below for alloy 718, Ti-6Al-4V, and a 4140 steel.

It should also be noted that similar calculations can be made to establish upper and lower temperatures to avoid certain deleterious phases, such as TCP phases, or to predict the volume fraction of certain phases at a specific operating temperature.

## Alloy 718

Understanding the melting temperature in Ni-base alloys is critical for casting, welding, and additive processes. The melting temperatures can be very sensitive to small variations in chemical composition. Understanding the minimum possible equilibrium solidus temperature, for example, can help set limits on homogenization and solution heat treatments, so that incipient melting is avoided. Here the Uncertainty Calculation is used to show the variation in solidus temperature calculated for 1000 compositions that fall within the alloy 718 specification range. As can be seen in Figure 1, as much as a 60°C variation is predicted over the allowed chemistry range. Similar diagrams can be calculated for other properties, such as γ′ solvus temperature or volume fraction of eutectic.

## Ti-6Al-4V

Many Titanium alloys respond well to heat treatments, through which the microstructure can be manipulated to optimize properties for a particular application. For example, some microstructures are better for high temperature creep, and some are better for fatigue strength. This is primarily achieved by controlling the nature and amount of α and β phases in the microstructure.

At high temperatures, titanium alloys are primarily β phase. At the β-transus temperature, α phase becomes stable and can start to form. The β-transus temperature can change as a function of alloy chemistry. Knowing the range of β transus temperatures that can occur across the entire alloy specification can help set maximum and minimum process control allowables and prevent part rework or scrapping. Figure 2 shows the calculated variation in the β transus temperature for 1000 chemistries within the Ti-6Al-4V alloy specification which are in broad agreement with typically reported values in the literature of 995°C – 1000°C +/- 14°C.

## 410 Stainless Steel

In martensitic stainless steels, such as 410, the martensite start temperature (Ms) can be very sensitive to the exact alloy chemistry. Ms can be predicted using the Steel Model Library in Thermo-Calc as a function of alloy chemistry.

In Figure 3 below, the calculated Ms temperature variation across the 410 stainless steel composition specification is shown and is found to be in good agreement with an experimentally determined value of 672K by Stone (Thesis: Ohio State University, 2017) for a commercial heat.

## Setting up Sensitivity Calculations in Thermo-Calc

Setting up these kinds of sensitivity calculations in Thermo-Calc is easy to do with the Property Model Calculator. You can watch a video tutorial here to see an example:

Whether you’re an experienced user or simply curious about Thermo-Calc, we’d be happy to show you over a web call how to set up a sensitivity calculation that could help you in your work. Schedule a free consultation today!

## About the Property Model Calculator in Thermo-Calc

The Property Model Calculator within Thermo-Calc offers predictive models for material properties based on their chemical composition and temperature and is included with all Thermo-Calc installations. This article is part of a series of blog posts that take a deeper dive into the different calculation types included in the Property Model Calculator and how they can be applied to materials design, process optimization, and ICME frameworks.