Phase Transformation
Depending on the settings at the physics interface level and the space dimension where the physics interface is used, the phase transformation node will contain different sections.
Phase Transformation
The phase transformation defines how one phase forms (the destination phase) at the expense of another (the source phase). Select Source phase ξs and Destination phase ξd from the list of defined phases. Select a Phase transformation model — Leblond–Devaux, Johnson–Mehl–Avrami–Kolmogorov, Kirkaldy–Venugopalan, simplified, Microstructure based, Koistinen–Marburger, Hyperbolic rate, or User defined.
Leblond–Devaux
Select a Formulation — Time and equilibrium, General coefficients, TTT diagram data, or Parameterized TTT diagram.
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For Time and equilibrium, select an Equilibrium phase fraction from the list. For User defined, specify an expression for . Specify a Time constant τs → d.
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For General coefficients, specify the expressions for Ks → d and Ls → d. For TTT diagram data, select an Equilibrium phase fraction from the list. For User defined, specify an expression for . Specify the Relative phase fraction X1, and the Transformation time t1.
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For Parameterized TTT diagram, select an Equilibrium phase fraction from the list. For User defined, specify an expression for . Specify the Relative phase fraction X1. In the TTT Curve 1 section, specify the transformation times tL, tN, and tU corresponding to points on the lower part, the “nose”, and the upper part of the TTT curve at the relative phase fraction X1. Specify the corresponding transformation temperatures TL, TN, and TU, and the TTT curve shape parameters qNL and qNU.
If applicable, select Define temperature limits, and select the Lower temperature limit Tl and the Upper temperature limit Tu from the respective lists. For the User defined options, specify, respectively, expressions for Tl and Tu.
The Equilibrium phase fraction, Lower temperature limit, and Upper temperature limit lists used by phase transformation nodes are populated by values calculated by the Steel Composition node.
Johnson–Mehl–Avrami–Kolmogorov
Select a Formulation — Time, equilibrium and exponent, TTT diagram data, TTT diagram data, fixed exponent, Parameterized TTT diagram, or Parameterized TTT diagram, fixed exponent.
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For Time, equilibrium and exponent, select an Equilibrium phase fraction from the list. For User defined, specify an expression for . Specify the Time constant τs → d, and the Avrami exponent ns → d.
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For TTT diagram data, select an Equilibrium phase fraction from the list. For User defined, specify an expression for . Specify the Relative phase fraction X1, the Transformation time t1, the Relative phase fraction X2, and the Transformation time t2.
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For TTT diagram data, fixed exponent, select an Equilibrium phase fraction from the list. For User defined, specify an expression for . Specify the Avrami exponent ns → d, the Relative phase fraction X1, and the Transformation time t1.
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For Parameterized TTT diagram, select an Equilibrium phase fraction from the list. For User defined, specify an expression for . Specify the Relative phase fraction X1, and the Relative phase fraction X2. In the TTT Curve 1 section, specify the transformation times tL, tN, and tU corresponding to points on the lower part, the “nose”, and the upper part of the TTT curve at the Relative phase fraction X1. Specify the corresponding transformation temperatures TL, TN, and TU, and the TTT curve shape parameters qNL and qNU. In the TTT Curve 2 section, specify the parameters for the TTT curve at the Relative phase fraction X2.
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For Parameterized TTT diagram, fixed exponent, select an Equilibrium phase fraction from the list. For User defined, specify an expression for . Specify the Avrami exponent ns → d, and the Relative phase fraction X1. In the TTT Curve 1 section, specify the transformation times tL, tN, and tU corresponding to points on the lower part, the “nose”, and the upper part of the TTT curve at the Relative phase fraction X1. Specify the corresponding transformation temperatures TL, TN, and TU, and the TTT curve shape parameters qNL and qNU.
If the rate term in the phase transformation model is to account for a nonzero initial phase fraction of the source phase, select Include effect of initial phase fraction. If applicable, select Define temperature limits, and select the Lower temperature limit Tl and the Upper temperature limit Tu from the respective lists. For the User defined options, specify, respectively, expressions for Tl and Tu.
Kirkaldy–Venugopalan, simplified
Select a Formulation — Rate coefficient, TTT diagram data, or Parameterized TTT diagram.
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For Rate coefficient, select an Equilibrium phase fraction from the list. For User defined, specify an expression for . Specify the Reference rate .
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For TTT diagram data, select an Equilibrium phase fraction from the list. For User defined, specify an expression for . Specify the Relative phase fraction X1, and the Transformation time t1.
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For Parameterized TTT diagram, select an Equilibrium phase fraction from the list. For User defined, specify an expression for . Specify the Relative phase fraction X1. In the TTT Curve 1 section, specify the transformation times tL, tN, and tU corresponding to points on the lower part, the “nose”, and the upper part of the TTT curve at the relative phase fraction X1. Specify the corresponding transformation temperatures TL, TN, and TU, and the TTT curve shape parameters qNL and qNU.
The rate term can be modified from its original form. If applicable, select Include retardation term, and specify the Retardation coefficient Cr. If applicable, select Define temperature limits, and select the Lower temperature limit Tl and the Upper temperature limit Tu from the respective lists. For the User defined options, specify, respectively, expressions for Tl and Tu.
Microstructure based
Select an Equilibrium phase fraction from the list. For User defined, specify an expression for . Select a Phase transformation function f from the list. For User defined, specify an expression for f. Select a Rate exponent a from the list. Select an Undercooling exponent m from the list. Select the Lower temperature limit Tl and the Upper temperature limit Tu from the respective lists.
The rate term can be modified from its original form. If applicable, select Include retardation term, and select a Retardation coefficient Cr from the list. For User defined, specify an expression for Cr.
Koistinen–Marburger
Select a Formulation — Koistinen–Marburger coefficient or Martensite finish temperature.
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For Koistinen–Marburger coefficient, specify the Martensite start temperature Ms and, if applicable, select Stress-dependent start temperature. Specify the Koistinen–Marburger coefficient β.
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For Martensite finish temperature, specify the Martensite start temperature Ms and, if applicable, select Stress-dependent start temperature. Specify the Martensite finish temperature M90.
If Stress-dependent start temperature has been selected, you have to specify how stresses affect the Martensite start temperature Ms.
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For the 0D space dimension, specify expression for the pressure p and the effective stress σe directly. Then specify the coefficients a1 and a2.
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For other space dimensions, you can select the pressure p and the effective stress σe from their respective lists. For the User defined options, specify expressions for these quantities directly. Then specify the coefficients a1 and a2.
If Incomplete transformation has been selected, specify the Minimum retained source phase fraction .
Hyperbolic rate
Specify the Hyperbolic rate constant Ps → d and select an Equilibrium phase fraction from the list. For User defined, specify an expression for . If applicable, select Define temperature limits, and select the Lower temperature limit Tl and the Upper temperature limit Tu from the respective lists. For the User defined options, specify, respectively, expressions for Tl and Tu.
Linear
Specify the Lower temperature limit Tl and the Upper temperature limit Tu from the respective lists. For the User defined options, specify, respectively, expressions for Tl and Tu.
Oddy–McDill–Karlsson
Specify the Eutectoid austenite fraction from the list. For User defined, specify an expression for . Under the Time parameter section, specify q1 and q2, and then specify the Avrami exponent ns → d. Specify the Lower temperature limit Tl and the Upper temperature limit Tu from the respective lists. For the User defined options, specify, respectively, expressions for Tl and Tu.
User defined
Specify the Phase transformation contribution As → d. The expression defines the rate at which the destination phase forms, at the expense of the source phase.
If applicable, select Define temperature limits, and select the Lower temperature limit Tl and the Upper temperature limit Tu from the respective lists. For the User defined options, specify, respectively, expressions for Tl and Tu.
Phase Transformation Latent Heat
This section is active if you have selected Enable phase transformation latent heat at the physics interface level. You can specify the latent heat ΔHs → d that is released during the phase transformation.
Phase Transformation Strain
The Transformation-induced plasticity checkbox is available if you have selected Enable transformation-induced plasticity at the physics interface level. In case of transformation-induced plasticity, select Transformation-induced-plasticity parameter — Thermal strain based or User defined. The Thermal strain based option is available if Enable phase plasticity and Enable thermal strains have been selected at the physics interface level. For User defined, enter a value or an expression for the transformation-induced-plasticity parameter directly. Select the Saturation function Φ — Abrassart, Desalos, Leblond, Tanaka, or User defined. For User defined, enter an expression for the derivative of the saturation function.
The Plastic recovery for destination phase checkbox is available if the Enable thermal strains has been selected at the physics interface level. If you have selected Plastic recovery for destination phase, you can specify the Plastic memory coefficient Θs → d. The default value is zero, which means that no plastic straining in the source phase will be carried over to the destination phase.
If you have selected Parameterized TTT Diagram or Parameterized TTT Diagram, Fixed Exponent, you can visualize the TTT curve corresponding to the entered parameters in the TTT curve 1 or TTT Curve 2 sections.
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Make a preview plot by selecting TTT curve preview.
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Generate a plot by selecting Create TTT curve plot.
Advanced
Numerical smoothing can be applied at temperatures that correspond to a sudden activation or deactivation of the phase transformation. If you select Advanced Physics Options, the Advanced section is used to assign smoothing:
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Transformation temperature smoothing, ΔT, in case you have used Define temperature limits.
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Martensite start temperature smoothing, ΔMs, in the case of the Koistinen–Marburger phase transformation model.
The smoothing parameters ΔT and ΔMs each defines a temperature span across which the phase transformation rate term is smoothly ramped. In the limit of a zero smoothing parameter value, the ramping reduces to a Heaviside step function.