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+ | ====== Primary precipitates ====== | ||
+ | |||
+ | ===== Compatibility ===== | ||
+ | |||
+ | MatCalc version: 5.44 - ... \\ | ||
+ | Author: E. Kozeschnik \\ | ||
+ | Created: 2011-11-14 \\ | ||
+ | Revisions: | ||
+ | |||
+ | ===== Objectives ===== | ||
+ | |||
+ | In this document, some strategies are discussed on how to treat //primary precipitation// | ||
+ | |||
+ | |||
+ | ===== Related documents ===== | ||
+ | |||
+ | - [[techpapers: | ||
+ | - [[examples: | ||
+ | - [[examples: | ||
+ | |||
+ | |||
+ | ====== Main document ======= | ||
+ | |||
+ | |||
+ | Primary precipitates nucleate and grow in the residual liquid pockets before final solidification. They are usually significantly larger compared to secondary and tertiary precipitates. Due to their large size,((The radius of primary precipitates is commonly in the order of micrometers)) primary precipitates occur in the microstructure commonly widely spaced and they do not contribute to precipitation strengthening. Primary precipitates are usually visible in optical light microscopy investigation. They might be potential nucleation sites for fatigue cracks under dynamic loading conditions. | ||
+ | |||
+ | Although primary precipitates are commonly not involved in the evolution of precipitation reactions after solidification due to their large size, they can potentially influence the chemical composition of the matrix (precipitation domain) by reducing the amount of available elements for precipitation after solidification. Consequently, | ||
+ | |||
+ | The basic idea of the present treatment of primary precipitates is to introduce the primary precipitates by some method discussed below and keep them as part of the precipitation simulation, however, without nucleation of new particles of this type throughout the regular heat treatment. Thereby, the primary precipitates are fully involved in the precipitation process. They maintain mass conservation by binding the solute elements from the precipitation process in the residual liquid pockets. And it is also possible, though not likely, that they dissolve again and release the solute atoms into the matrix again. | ||
+ | |||
+ | ====== Estimation of amount and size of primary precipitates ====== | ||
+ | |||
+ | Primary precipitates are formed in the liquid state. The //MatCalc// precipitation models are not designed for liquid phase precipitation since its growth models have been developed for diffusion in the solid state. Convection and particle collisions in the liquid state are not accounted for. However, in order to take primary precipitation into account in the simulations, | ||
+ | |||
+ | The most straightforward means to determine (or estimate) the amount of primary precipitation is the application of the Scheil-Gulliver model. It is described in some detail in the technical paper [[techpapers: | ||
+ | |||
+ | ====== Introduce size distribution of primary precipitates ====== | ||
+ | |||
+ | The size distribution, | ||
+ | |||
+ | |||
+ | ===== Size distributions defined from parent phase ===== | ||
+ | |||
+ | Starting from version 5.61, MatCalc allows to create size distribution for the precipitate phase. It follows a simple routine in which the required input values are: | ||
+ | |||
+ | * Phase fraction of the phase | ||
+ | * Values for minimal, mean and maximal radius for the precipitate | ||
+ | * Size distribution function | ||
+ | |||
+ | This feature can be accessed in ‘Phase status’ window. Select the relevant precipitate, | ||
+ | |||
+ | {{ : | ||
+ | |||
+ | On the left side of this window, a table is available which will contain the number density, radius and composition (in term of site fractions) data for each class of the phase. On the bottom right side, the distribution function for the size precipitates can be chosen and the data for the size range can be entered. | ||
+ | |||
+ | {{ : | ||
+ | |||
+ | It must be noted that for the phase fraction, the value relevant for the parent phase of the precipitate (which is usually the equilibrium or the solidified phase) is taken. If needed, the phase fraction value can be modified by selecting the parent phase, switching to the ‘General’ tab, clicking on the ‘Set amount’ button and typing the value in the appearing window. | ||
+ | |||
+ | {{ : | ||
+ | |||
+ | Starting from the Scheil-Gulliver analysis, the size distribution of the primary precipitate can be created simply by selecting the solidified phase (the one with ‘_S’-suffix) and creating a precipitate phase out of it. This procedure is demonstrated in [[examples: | ||
+ | |||
+ | |||
+ | ===== Manually defined size distributions ===== | ||
+ | |||
+ | When attempting to enter size distributions manually, please consider the following note. | ||
+ | |||
+ | <box 90% round blue | // | ||
+ | It is //not// recommended that size distribution and composition of // | ||
+ | Upon that, it is even more difficult to define the chemical composition of each of the size classes properly, which means, in such a way that the chemical potentials of all elements are consistent. | ||
+ | </ | ||
+ | |||
+ | One major exception to this consideration is the special case of strictly stoichiometric precipitates. For instance, the Fe< | ||
+ | |||
+ | After generation of the size distribution in some pre-processing, | ||
+ | |||
+ | {{ : | ||
+ | |||
+ | It is most convenient to copy and paste the values into // | ||
+ | |||
+ | ===== Size distributions from virtual pre-treatment ===== | ||
+ | |||
+ | For complex precipitates, | ||
+ | |||
+ | These pre-treatments are commonly performed in the following steps: | ||
+ | |||
+ | * Set up the precipitation system, create precipitate phases and precipitation domains. | ||
+ | * Create an additional precipitation domain for the pre-treatment. | ||
+ | * Create an additional precipitate population for the primary precipitate. Use the ' | ||
+ | * Select the ' | ||
+ | * Design the pre-treatment such that after executing the pre-treatment, | ||
+ | |||
+ | The last step in this recipe is the most important one, and there are several strategies on how to design this virtual pre-treatment most efficiently in terms of computational effort. Minimum simulation time for pre-treatments can be achieved, if time-consuming coarsening regimes are avoided, as well as long continuous cooling segments, where nucleation of precipitates can also make the computation times longer than necessary. A simple methodology for designing efficient pre-treatments is as follows: | ||
+ | |||
+ | * In a preliminary step, perform a // | ||
+ | * Remember the amount (phase fractions) of your primary precipitates as well as their approximate chemical composition. This is also elaborated and discussed in the example E20. | ||
+ | * Set up an // | ||
+ | * Set up your full precipitation system as described above for the //**virtual pre-treatment**// | ||
+ | * Create a ' | ||
+ | |||
+ | In principle, the segments of the virtual pre-treatment and all temperatures, | ||
+ | |||
+ | |||
+ | ==== Design of a computationally efficient virtual pre-treatment ==== | ||
+ | |||
+ | The two main achievements of a successful pre-treatment are to produce an initial distribution of (primary) precipitates that have the desired values for | ||
+ | |||
+ | * phase fraction and | ||
+ | * mean precipitate radius. | ||
+ | |||
+ | The //phase fraction// of primary precipitates is commonly obtained from the preliminary equilibrium calculation as described above. The //mean radius// is commonly observed from light optical or electron microscopy. Its value is usually in the order of a few µm. | ||
+ | |||
+ | In the virtual pre-treatment, | ||
+ | |||
+ | * For only a few seconds, run the pre-treatment at an isothermal temperature $T_\text{nucl, | ||
+ | * For adjustment of the desired number density, first of all adjust the nucleation sites of the primary precipitates in the nucleation tab of the phase status dialog. By this procedure, you modify the constant $N_0$ of the nucleation rate expression by several orders of magnitude. Often, 'grain boundary corners' | ||
+ | * At heating rates in the order of 100 K/s, move to the temperature $T_\text{grow, | ||
+ | |||
+ | The following screen shot displays a typical pre-treatment for primary TiN precipitation in micro-alloyed steel. | ||
+ | |||
+ | {{ : | ||
+ | |||
+ | The end time of the virtual pre-treatment $t_\text{end, | ||
+ | |||
+ | The actual distribution of your primary precipitates can be inspected in the precipitate distribution - histogram plot. In the early stages, directly after reaching the phase fraction maximum, the distribution is often rather small. If you want to start your simulation with a wider initial distribution, | ||
+ | |||
+ | ===== Transfer results / size distribution ===== | ||
+ | |||
+ | Once you have generated a size distribution of your primary precipitate(s) in the virtual treatment, you have two options to carry on. | ||
+ | |||
+ | * Save the size distribution into a calc state. Use this state as a starting condition for further precipitation simulation. | ||
+ | * Export the size distribution into a file. Read the distribution file and import it into any independent further computation. | ||
+ | |||
+ | Both ways are demonstrated in the example P20 ([[examples: | ||