Metallurgical phase transformations

This problem contains basic test cases for one or more Abaqus elements and features.

This page discusses:

Elements tested
Features tested
Problem description
Results and discussion
Input files
References
Tables
Figures

Elements tested

DC3D8

Features tested

This section provides basic verification tests of metallurgical phase transformations.

Problem description

This verification test contains single-element heat transfer analyses with nodal temperature degree of freedom driven by predefined amplitude curves. The test is designed to qualitatively verify metallurgical phase transformations under predefined thermal histories.

Material

Two materials, titanium alloy Ti-6AL-4V and steel 5140, are tested.

Titanium alloy Ti-6AL-4V consists primary of three solid phases: a hexagonal close-packed (hcp) α-phase, a body-centred cubic (bcc) β-phase, and a martensitic α’-phase. The material is considered as fully β-phase on solidification. Three transformations can occur between those three solid phases. They can be categorized as one martensitic transformation and two diffusional transformations, as shown in Table 1. The solidus and liqudus temperatures of Ti-6AL-4V are 1604°C and 1650°C, respectively.

A simplified metallurgical model of steel 5140 is used. The material consists of five solid phases: austenite(A), bainite (B), ferrite (F), pearlite (P), and martensite (M). The material is considered as fully austenite on solidification. Eight transformations can occur between those five solid phases. They can be categorized as one martensitic and seven diffusional transformations, as shown in Table 2. The solidus and liqudus temperatures of steel 5140 are 1750°C and 1800°C, respectively.

Boundary conditions

The nodal temperature degree of freedom is driven by predefined amplitude curves.

Two different thermal histories are applied to test metallurgical phase transformations in titanium alloy Ti-6Al-4V. One thermal history contains thermal cycles ranging between 26°C and 1826°C with constant heating or cooling rates. The other thermal history is a typical thermal cycle experienced during an additive manufacturing process followed by a slow heat treatment process.

One thermal history is applied to test metallurgical phase transformations in steel 5140. The thermal history contains thermal cycles ranging between 20°C and 1826°C.

Results and discussion

The results of metallurgical phase transformations in titanium alloy Ti-6Al-4V with the two thermal cycles are shown in Figure 1 and Figure 2, respectively. Graphs show the temperature, RLS state, and phase content. The RLS indicator describes the material state as Raw (-1), Liquid (0), or Solid (1). It can be seen that the microstructure is fully β-phase on solidification. The β-phase quickly transforms to α’-phase during the rapid cooling that is typical during printing processes. The two diffusional transformations occur slowly during heating and slow cooling conditions. The results agree with the specified material definition.

The results of the metallurgical phase transformations in steel 5140 for a thermal cycle with differenced segments of constant rate are shown in Figure 3. At the slow cooling rate (1°C/s), the alloy transforms to mainly ferrite and pearlite. At the medium cooling rate (10°C/s), a small amount of bainite phase is formed. At the high cooling rate (100°C/s), the martensitic phase transformation occurs and only negligible diffusional transformations occur. The results agree with the specified material definition.

Input files

oneelem_phase_trans_ti64.inp: Single-element analysis of metallurgical phase transformations in titanium alloy Ti-6Al-4V by applying temperature cycles with constant heating and cooling rates.
oneelem_phase_trans_ti64_amprint.inp: Single-element analysis of metallurgical phase transformations in titanium alloy Ti-6Al-4V by applying typical thermal cycles of manufacturing processes.
oneelem_phase_trans_s5140.inp: Single-element analysis of metallurgical phase transformations in steel 5140 by applying temperature cycles with constant heating and cooling rate.

Input files containing definitions or data to be included in the input files listed above

ABQ_phase_trans_types.inp: Types of property tables and parameter tables used by the metallurgical phase transformation framework in Abaqus.
amp_temp_amprint.inp: Amplitude curves representing typical thermal cycles during printing and heat treatment processes.
mat_phase_trans_ti64.inp: Material definitions of titanium alloy Ti-6Al-4V.
mat_phase_trans_s5140.inp: Material definitions of steel 5140.

References

Xie, J., V. Oancea, and J. Hurtado, “Phase Transformations in Metals During Additive Manufacturing Processes,” NAFEMS World Congress, 2017.
Zhang, Q., J. Xie, Z. Gao, T. London, D. Griffiths, and V. Oancea, “A Metallurgical Phase Transformation Framework Applied to SLM Additive Manufacturing Processes,” Materials & Design, vol. 166 107618, 2019.

Tables

Table 1. Phase transformations considered in the metallurgical model of Ti-6Al-4V.
Transformation		Type	Occurring conditions
1	$β \to α'$	Martensitic	$\dot{θ}$ < –410°C/s	$θ$ < 650°C
2	$α' \to α + β$	Diffusional	$\dot{θ}$ > 0°C/s	None
3	$β \leftrightarrow α$	Diffusional	$\dot{θ}$ > –410°C/s	None

Table 2. Phase transformations considered in the metallurgical model of steel 5140.
Transformation		Type	Occurring conditions
1	$A \to F$	Diffusional	$\dot{θ}$ < 0°C/s	539°C < $θ$ < 735°C
2	$A \to P$	Diffusional	$\dot{θ}$ < 0°C/s	539°C < $θ$ < 735°C
3	$A \to B$	Diffusional	$\dot{θ}$ < 0°C/s	333°C < $θ$ < 539°C
4	$A \to M$	Martensitic	$\dot{θ}$ < 0°C/s	$θ$ < 333°C
5	$F \to A$	Diffusional	$\dot{θ}$ > 0°C/s	$θ$ > 735°C
6	$P \to A$	Diffusional	$\dot{θ}$ > 0°C/s	$θ$ > 735°C
7	$B \to A$	Diffusional	$\dot{θ}$ > 0°C/s	$θ$ > 735°C
8	$M \to A$	Diffusional	$\dot{θ}$ > 0°C/s	$θ$ > 735°C

Figures