Modeling Recrystallization for 3D Multi-pass Forming Processes

7/27/2019 Modeling Recrystallization for 3D Multi-pass Forming Processes

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Modeling recrystallization for 3D multi-pass forming processes

Mihaela Teodorescu1, a, Patrice Lasne2,b and Roland Logé3,c

1Numerical Simulation Department, ASCOMETAL CREAS, BP 70045, Hagondange, 57301 Cedex,France

2TRANSVALOR, Parc de Haute Technologie – Sophia Antipolis, 694, Av du Dr Maurice Donat,06255 Mougins, Cedex, France

3Center for Materials Forming (CEMEF), UMR CNRS 7635, Ecole des Mines de Paris, BP 207,06904 Sophia Antipolis Cedex, France

[email protected],[email protected], [email protected]

Keywords: dynamic recrystallization, meta-dynamic recrystallization, static recrystallization, multi-pass, forming, finite element.

Abstract. The present work concerns the simulation of metallurgical evolutions in 3D multi-pass

forming processes. In this context, the analyzed problem is twofold. One point refers to the

management of the microstructure evolution during each pass or each inter-pass period and the

other point concerns the management of the multi-pass aspects (different grain categories, data

structure). In this framework, a model is developed and deals with both aspects. The model

considers the microstructure as a composite made of a given (discretized) number of phases which

have their own specific properties. The grain size distribution and the recrystallized volume fraction

distribution of the different phases evolve continuously during a pass or inter-pass period. With this

approach it is possible to deal with the heterogeneity of the microstructure and its evolution in

multi-pass conditions. Both dynamic and static recrystallization phenomena are taken into account,

with typical Avrami-type equations. The present model is implemented in the Finite Element codeFORGE2005®. 3D numerical simulation results for a multi-pass process are presented.

Introduction

In the past years, microstructure analysis has continuously advanced, different models being

developed in order to simulate microstructure evolution during hot forming processes. First, semi-

empirical models based on Avrami laws have been adopted [1, 2, 3] to describe static and meta-

dynamic recrystallization phenomena. Then, new approaches based on dislocation densities were

considered [4, 5, 6]. Investigations were also carried out on the multi-pass microstructure evolution

modeling. In this framework, two different types of models were reported. The classical ones

suppose that, at the beginning of each pass, the structure is always homogenous [3, 7]. Thisassumption simplifies the mathematical considerations but is far from the reality. The second ones

take into account the heterogeneous feature of the microstructure [2, 3, 4, 7]. Most of this research

concerns the hot rolling processes.

Our work is focused on the modeling of 3D microstructure evolution for multi-pass forming

processes. The model developed and presented herein deals with the heterogeneity of the

microstructure. This model is implemented into the finite element code FORGE2005®. First

numerical results, predicting the recrystallized fraction evolution, will be presented.

Model presentation

In this context, the present model deals with the following aspects:- the microstructure evolution during a pass or an inter-pass period (dynamic, meta-

dynamic or static recrystallization),

- the multi-passes aspects management.



One pass modeling: isothermal and steady state conditions. Avrami type equations are used

to describe the recrystallized volume fraction. In the dynamic case, Eq. 1 is used:

⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎟⎟ ⎠

⎞

⎜⎜⎝

⎛

−

−

−−=

DRX n

c

c

DRX X ε ε

ε ε

5.02lnexp1 (1)

where XDRX is the dynamically recristallized volume fraction, ε is the cumulated equivalent strain,

cε is the critical equivalent strain, defined by Eq. 2:

⎟ ⎠

⎞⎜⎝

⎛ =

T d A

m

c

111

01 exp...β

ε ε α & (2)

where ε & is the equivalent strain rate, and T is the temperature. In Eq. 1 5.0ε is the equivalent strain

leading to XDRX = 0.5, and is defined by Eq. 3:

⎟

⎠

⎞⎜

⎝

⎛ =

T

d Am 222

025.0 exp...β

ε ε α & (3)

The recrystallized grain size evolution is related to the recrystallized volume fraction by using Eq. 4

DRX a

DRX d DRX X d d = (4)

where DRX d is the dynamically recrystallized grain size and d d is the grain size corresponding to

DRX X = 1. It is given by:

⎟ ⎠

⎞⎜⎝

⎛ =

T d Ad

m

d

333

03 exp..β

ε α & (5)

d 0 is the initial grain size and nDRX, aDRX, α1, α2, α3, β1, β2, β3, m1, m2, m3, A1, A2, and A3 are

material parameters.

For the static case, the recrystallized volume fraction is calculated as follows:

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟ ⎠

⎞⎜⎜⎝

⎛ −−=

SRX n

SRX t

t X

5.0

2lnexp1 (6)

where XSRX is the meta-dynamically or the statically recrystallized volume fraction, t0.5 is the time at

which XSRX = 0.5, defined by Eq. 7:

⎟ ⎠

⎞⎜⎝

⎛ =

T d At

m

f

n 4045.0 exp444

β ε ε

α & (7)

f

ε& is the average strain rate since the last recrystallization event.

The statically recrystallized grain size evolution is related to the recrystallized volume fraction by

Eq. 8:

SRX a

SRX sSRX X d d .= (8)

wheresd is the grain size corresponding to XSRX = 1, calculated by:

⎟ ⎠

⎞⎜⎝

⎛ =

T d Ad

m

f

n

s

505 exp555

β ε ε

α & (9)

The grain growth after completion of primary recrystallization is formulated by Eq. 10:

t

T

Ad d SRX GRW ⎟

⎠

⎞⎜

⎝

⎛ =− 6

6 exp66 β α α

(10)

with d SRX the statically recrystallized grain size reached at the end of the primary recrystallization

stage.



The material parameters nSRX, aSRX, α4, α5, α6 β4, β5, β6, m4, m5, n4, n5, A4, A5, et A6 are to be

determined.

One pass modeling: non-isothermal and unsteady state conditions. Fictitious time and

fictitious strain methods are used to deal with the non-isothermal and unsteady state conditions. The

process is considered as a sequence of isothermal increments, as shown on the left side of Fig. 1.For each isothermal step, the equations presented above are applied. The transition from one

increment to the next one is described in the following.

When temperature varies, one can consider that at the time stepit , the corresponding

temperature isiT and the transformed volume fraction

i X is calculated from the considered Avrami

laws. It corresponds to the point 1, plotted on Fig. 1 - middle. In order to calculate the transformed

volume fraction at the next step, 1+it , it is necessary to jump to the temperature 1+iT . This jump is

performed through an intermediate point, the point 2 of Fig. 1- middle side. This point corresponds

to the fictitious time it * , which represents the time necessary to achieve the transformed volume

fractioni X at the temperature 1+iT and is calculated from Eq. 6 with t0.5 at 1+iT . The same principle

is applied for the recrystallized grain size evolution.

One can transpose this principle to the dynamic conditions, as shown in Fig. 1, left side. The

fictitious equivalent strain concept replaces the fictitious time one. It is used for each case when

equivalent strain rate and/or temperature vary during the forming process.

Fig. 1: Process evolution discretization (left) / Fictitious time method (middle) / Fictitious strain

method (right)

Multi-pass aspects modeling

When multi-pass processes are envisaged, the history of the microstructure evolution has to be

taken into account. Hence, fictitious time or fictitious strain methods could be naturally used

whenever two dynamic phases or two static phases are connected to each other. The difficulty

appears when dynamic phases are connected to static phases. The phenomena being different, it is

necessary to follow the different grain categories previously formed during the process

(dynamically, meta-dynamically and statically recrystallized grain categories).

The developed finite element model is based on two types of heterogeneous models (see Fig. 2 –

left). One model is the conventional heterogeneous model (see Fig. 2 – top left) [2, 3], which takes

into account separately the different grain categories: recrystallized and unrecrystallized. This

procedure can induce an exponential data structure increasing with the increasing number of

process passes. The other model is the Anan model (see Fig. 2 – left, bottom) [4], which consists in

considering the microstructure as a composite made of a given number of small zones which havetheir own specific microstructure properties (grain sizes, recrystallized volume fraction, etc). This

kind of approach can help us to control the data structure, when coupled with a conventional

heterogeneous model and with the finite element method.



The present model combines both approaches in the following manner (see Fig. 2 - right). A fixed

number of grain categories is associated to each finite element. One category is defined by a grain

size interval. These categories are defined at the beginning of the simulation. For each category one

can consider the volume fraction of the grains belonging to the category, X j, the recrystallized

volume fraction, X jRX, the unrecrystallized volume fraction, X j

NRX and the average strain cumulated

from the last recrystallization event, jε . This data structure evolves during the process simulationand is updated at each transition from one phase (dynamic or static) to the next one. When

recrystallization occurs, dynamically or statically, this approach considers that the corresponding

strain is updated to 0. For the unrecrystallized grains of each category, the average strain is

unchanged, after a static phase, and is incremented by the applied value j

ε ∆ , for a dynamic phase

(as shown in Fig. 2 - right). The recrystallized volume fraction obtained in the category j isSRX or DRX

j j

RX

j X X X .= with a grain sizeSRX or DRX d . The unrecrystallized volume fraction is calculated

as )1.( SRX or DRX

j j

NRX

j X X X −= with a grain size of 3 1.SRX or DRX j X d − . Based on these obtained

grain sizes, the updating of the grain categories is performed at the transition from one phase

(dynamic or static) to the next one.

Fig. 2: Heterogeneous models (left) / Present model (right)

The model is implemented in the finite element code FORGE2005® and can deal with any kind of

multi-pass process.

Results and discussion

The model was applided to a classical austenitic stainless steel. Torsion and compression tests were

performed at different temperatures, between 900°C and 1100°C, for different initial grain sizes and

for different strains and strain rates. Simple dynamic and static tests, as well as combined

isothermal and non-isothermal dynamic and static tests were performed (about 50 tests overall), in

order to identify the model parameters and to analyze the parameters influences on the

recrystallized grain size and the recrystallized volume fraction evolution. Two examples of torsion

tests are presented in Fig. 3.



Fig. 3: Examples of torsion tests results

The main remarks can be summarized as follows:

- Increasing temperature leads to an increase of the recrystallized volume fraction and of the

recrystallized grain size, in both dynamic and static cases.

- Increasing the strain in the dynamic phase induces, in the subsequent static stage, an increaseof the recrystallized volume fraction and of the recrystallized grain size.

- A strain rate effect is also noted. For the dynamic case, the recrystallized volume fraction

and the recrystallized grain size increase with strain rate. For the static phase following a

dynamic phase, the influence is mainly related to the nuclei density.

- The initial grain size decrease favorably affects the nucleation, in dynamic as well as in static

case. Indeed, for the dynamic case, the initial grain size effect is noted only on the

recrystallized volume fraction rise. In contrast, for the static case, the initial grain size

reduction induces a recrystallized grain size decrease and a recrystallized volume fraction

increase.

Numerical simulation results

The developed model is implemented within the software FORGE2005®. First numerical results

are presented below. The forming process is sketched in Fig. 4 – left side.

Fig. 4: Simulation FORGE2005®: forming process scheme (left) / final recrystallized volume

fraction distribution (right)



The simulation results allow us to see the microstructure evolution tendencies. Comparisons

between simulation and experimental results show good agreement, as shown in the Fig 4 (right

side) for the recrystallized volume fraction. However, less precision (about 25%) can be obtained

for the regions where remeshing is often used during the process simulation. The remeshing aspects

are currently treated in order to improve these results.

Conclusions

This paper presents some theoretical aspects concerning the dynamic, meta-dynamic and static

microstructure evolution models and manners to deal with the multi-pass forming processes. A

model is developed for the analysis of 3D multi-pass forming processes. During forging and rolling

processes, for example, the microstructure varies with both deformation and thermal history. The

heterogeneity of the microstructure is taken into account. The model consists in describing the

microstructure as a composite made of a given number of small zones which have their own

specific grain sizes or recrystallized volume fraction. The present model is implemented in the FEM

code FORGE2005®. First numerical examples concerning the recrystallized volume fraction aregiven.

Further work is concentrated on the optimization of the couple "thermal-mechanical process" –

"grade" in order to control the homogeneity of the final microstructure and hence the final material

properties. Characterization of ASCOMETAL materials will be done in order to validate the model

for rolling cases. In this way simulation will become an appropriate tool to answer and control

production questions. Moreover, the heterogeneous microstructure obtained after a gear or shaft

forming (grain size distribution for example) could be considered as an initial structure for the heat

treatment simulation. This could be interesting when dealing with the prediction of distortion.

Acknowledgements

The authors gratefully thank the project SIMULFORGE and all the members of the GE1 group for

their contribution to the experimental work.

References

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Modeling Recrystallization for 3D Multi-pass Forming Processes

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