Precipitation Calculator Plot Renderer

Select whether the diagram’s legend displays On or Off.

Set the state variable you want plotted along the X-axis and the Y-axis. The available variables in the list are based on how your system is set up.

Below are additional details related to the axis variable chosen.

• Separate Multimodal PSD: If you select Mean radius, Number density, Volume fraction, Size distribution, Number density distribution, or Normalized number density distribution then the Separate multimodal PSD checkbox is available. For variables with time for the X-axis, the number of Points used to sample the results can be modified. The Inflection neighbors and Smoothing iterations are used to identify individual particle populations. See Separate Multimodal PSD below for more detail.
• 3D → 2D: For a spherical morphology, and if you select Mean radius, Number density, Volume fraction, Size distribution, Number density distribution, or Normalized number density distribution as an axis variable, you can also select the 3D → 2D checkbox to convert the 3D property to the corresponding 2D property considering the resulting 2D size distribution obtained from sectioning a 3D spherical dispersion. See 3D to 2D Conversion below for more detail.
• Yield Strength: If you select this as an axis variable there are additional settings. See Yield Strength below for more detail.

If you choose Yield strength as an Axis variable, you can further define the model. Click to expand the drop down list to the right of the Axis variable, then select any or all of the checkboxes listed below to plot the respective contributing elements to the yield strength.

Click Configuration Panel toggle between the settings options and to further fine-tune the model. These options are described for the Yield Strength Property Model: Simplified Mode Settings and Yield Strength Property Model: Advanced Mode Settings. The greyed out sections (e.g. the Matrix, Precipitate phases, and Grain size) are defined on the Precipitation Calculator and cannot be changed.

To see these settings after clicking Configuration Panel, you need to expand the Plot Renderer Configuration window to the right. Either detach the window to resize, or hover with the mouse until you see the double arrow, then click and drag to expand the window.

• Total yield strength
• Intrinsic strength
• Solid solution strengthening
• Solid solution strengthening FCC
• Solid solution strengthening BCC
• Solid solution strengthening HCP
• Grain boundary strengthening
• Total precipitation strengthening
• Precipitation strengthening per phase
• Constant strength addition

The P_01: Isothermal Precipitation of Al3Sc example demonstrates the use of this Yield Strength Model.

This setting is available if you select Mean radius, Number density, Volume fraction, or Size distribution as the Axis Variable.

When the Separate multimodal PSD checkbox is selected on a Plot Renderer activity for the Precipitation Calculator, the size distribution is evaluated at the given time steps and results for individual particle populations are identified and presented. These are separated and used to calculate the specified property.

P_06: Precipitation of γ’ in Ni Superalloys - Non-isothermal

Points

This field is available when the Separate multimodal PSD checkbox is selected. It is not available with the Size distribution variable.

Since the evaluation of multimodality at each time step is costly, you can specify how many evaluation Points to use. The points are geometrically distributed over the time scale where nucleated particles are found. The default is 40 points.

Inflection Neighbors

This field is available when the Separate multimodal PSD checkbox is selected.

Enter the Inflection neighbors, which are the number of neighboring points with consistent gradient direction to identify inflection points. The default is 6. As a guide, too low a number is sensitive to noise and too high a number can fail to detect particle populations.

Smoothing Iterations

This field is available when the Separate multimodal PSD checkbox is selected.

Enter the number of Smoothing iterations performed to reveal significant particle populations. The default is 500. As a guide, too small a number can fail to remove noise, and too high a number can remove the particle populations of interest.

When the Precipitate Phase Morphology is set to Sphere on the Precipitation Calculator, the following options are available when certain axis variables are also selected.

Select the 3D → 2D checkbox if you want to make a direct comparison between the predicted three-dimensional (3D) radius of the precipitates and the two-dimensional (2D) data obtained from a cross-section taken through the dispersion.

The stereological conversion is described in the theory for spherical particles. See Stereology.

These variables can be converted to 2D:

• Mean radius: The average circular radius of cross sections of particles obtained by taking a section through the dispersion, assuming spherical precipitates.
• Number density The number concentration of precipitates found on a 1 m² cross-section through the microstructure.
• Volume fraction The area fraction of precipitates found on a cross-section taken through the microstructure.
• Size distribution: The number density of particle cross sections that have a radius varying within a given size class in a unit area.
• Number density distribution: The number of particle cross sections that have a radius varying within a given size class in a unit area.
• Normalized number density distribution: The probability of finding particle cross sections with a cross sectional radius varying within the size class. The radius is normalized by the volumetric mean of the dispersion.

Select the type of axis scale: Linear, Logarithmic, Logarithmic 10, or Inverse.

Specify the range along the axis to show in the plot. In the fields, enter the minimum and maximum values of the axis variable. You can also determine the step size between the tick marks along each axis.

Select the Automatic scaling checkbox to allow the program to set the limits.

Choose a Unit: Seconds, Hours, or Days.

Use the Add an axis and Remove this axis buttons to add additional X- and/or Y-axes to a plot or to merge plots (to overlay one plot with another in the same diagram). When merging plots, you define this variable as the Z-axis.

• Mean radius: Spherical radius of average volume of all particles for a specific phase and nucleation type, regardless of their actual shapes. If the matrix phase is selected, it outputs the average grain radius.
• Critical radius: Spherical radius of critical nuclei for a specific phase and nucleation type. If the matrix phase is selected, it outputs critical grain radius.
• Yield strength: To use the Yield Strength Property Model to calculate yield stress. For more information see About the Yield Strength Property Model.
• Matrix composition: Instantaneous compositions of the matrix phase.
• Precipitate composition: To track the instantaneous composition of precipitate particles. In particular, it is useful to distinguish different composition sets of the same phase (for example, FCC_A1#2 and FCC_A1#3). Further choose Solutes or All.
• Number density: Instantaneous number of particles per unit volume for a specific phase and nucleation type. If the matrix phase is selected, it outputs instantaneous number of grains per unit volume.
• Size distribution: Number of particles, or grains if the matrix phase is selected, varying with their sizes per unit volume per unit length, for a specific phase and nucleation type, at a specific time.
• Number density distribution: Retrieve the number density (number of particles per unit volume) of precipitates, or grains if the matrix phase is selected, distributed in different particle sizes.
• Normalized Number density distribution: Retrieve the number density (number of particles per unit volume) of precipitates, or grains if the matrix phase is selected, normalized by total number of particles or grains per unit volume, distributed in different particle sizes normalized by average size.
• Volume fraction: Instantaneous volume fraction for a specific phase and nucleation type.
• Nucleation rate: Instantaneous number of nuclei per unit volume per unit time for a specific phase and nucleation type.
• Normalized driving force: Instantaneous nucleation driving force per unit mole of elements for a specific phase and nucleation type. It is normalized with RT and therefore, dimensionless.
• Temperature
• Mean cubic factor: Average cubic factor of cuboid particles. Available only when cuboid is selected as the Morphology.

The following settings area available as indicated when Needle, Plate, or Cuboid are selected as the Morphology in the Precipitate Phase section on the Precipitation Calculator.

• Cubic factor distribution: Variation of cubic factor with particle size at a specific time. Available with a cuboid morphology.
• Mean aspect ratio: Average aspect ratio of non-spherical particles. Available with a needle or plate morphology. Note that this is always larger than 1, where 1 = a sphere.
• Mean particle length: Diameter of non-spherical particles along the longer axis. Available with a needle or plate morphology.
• Aspect ratio distribution: Variation of aspect ratio with particle size at a specific time. Available with a needle or plate morphology.

This field is available when Size distribution or Number density distribution is selected as the Y-axes variable. Enter one or a series of numbers in the field, separated by a space.

P_09: Precipitation of Al-Sc AL3SC with Assumption of Sphere and Cuboid Morphologies

If you open the example P_09, then change the Time settings on the PSD Plot Renderer to be 100.0 1000.0 1.0E7:

When you click Perform the series of times are plotted: