Deformation Stability of GH4033 Superalloy in the Hot Continuous Rolling Process Based on Dynamic Material Model and Finite Element Model

WANG Panpan ,XI Taotao ,SUI Fengli＊ ,YANG Lianjin

(1.School of Metallurgical Engineering,Anhui University of Technology,Ma’anshan 243002,China;2.Jiangsu Shenyuan Group Co.,Ltd.,Taizhou 225722,China)

Abstract: The flow stress behavior of GH4033 superalloy was determined by the hot compression tests at the temperatures of 1 223-1 473 K and the total strains of 0.6 with the strain rates of 0.001-30.0 s-1 by using cylindrical samples.The processing maps based on the dynamic material model (DMM) combined with the corresponding microstructure observations indicate the reasonable processing domain locating at the strain rates of 0.1-1.0 s-1 and the deformation temperature of 1 273-1 423 K.Meanwhile,the numerical simulation based on finite element model (FEM) described the variation of the effective strain,effective strain rate and the temperature for the core node,and unveiled the influence of the hot rolling parameters considering the initial temperature (T0) range of 1 223-1 473 K and the first-stand biting velocity (v0) range of 0.15-0.35 m·s-1.Furthermore,the deformation stability of GH4033 superalloy in the round rod hot continuous rolling (HCR)process is described and analyzed by coupling the three-dimensional (3-D) processing map,and the spatial trajectory lines were determined by the numerically simulated temperatures,the strains and the strain rates.Finally,the results show that the hot deformation stability of GH4033 can be achieved by the rolling process parameters located at T0=1 423 K and v0=0.25 m·s-1.Additionally,the practical HCR processes as T0=1 423 K and v0=0.15,0.25,0.35 m·s-1 were operated to verify the influence of the hot rolling parameters on the hot deformation stability by the microstructure observation of the final products.

Key words: GH4033 superalloy;dynamic material model;finite element model;hot continuous rolling;hot deformation stability

1 Introduction

Nickel-based superalloys have been developed for specialized applications,mainly serving as turbine blades and disks in aero-engines.The requirements have driven the development of nickel-based superalloys to exhibit more excellent properties.Furrer and Fechtreported that nickel-based superalloys have been used in harsh environments such as high operating temperatures and high-stress levels,then pointed out that and the process design is a considerable factor to optimize the mechanical properties.Also,Wan

et

al

found that the main application of nickel-based superalloys is high-temperature components due to their excellent mechanical properties and long-time structural stability under harsh environments.For example,GH4033 superalloy is a typical nickel-based superalloy widely used in manufacturing engine turbine blades,aerospace vehicles,and high-temperature components mainly.Although the hot continuous rolling (HCR) is the preferred production of this superalloy to achieve higher productivity and better mechanical properties,the application fields-working under higher operating temperatures and higher stress levels pose a tremendous challenge for materials producing to meet the required properties,especially GH4033 superalloy of narrow deformation parameter ranges,large deformation resistance,and complicated microstructure evolution during the hot deformation process.In addition,Wen

et al

proposed that the mechanical properties of the materials are determined by the microstructure which is sensitive to the hot deformation parameters such as temperatures,strains and strain rates.Many previous researches have been carried out on nickel-based superalloy GH4033 over the past decades.Chen

et al

found the high-temperature properties and the microstructural change of this superalloy were closely related to the hot deformation process.Finally,they provided a reliable reference for the microstructural evolution controlling during the hot rolling deformation process.After that,Tong

et al

found that the service time of the turbine blade made of GH4033 superalloy is associated with the working parameters such as working temperature,stress and time,especially the complicated microstructure during microstructural evolution.They further demonstrated that studying the microstructural evolution would provide guidance for studying the hot deformation stability of the GH4033 superalloy.Furthermore,Ma

et al

investigated the microstructural characteristics and mechanical properties of the GH4033 superalloy through the flow stress behavior combining the effects of work hardening,dynamic strain aging and dynamic recrystallization (DRX).The focus of these studies was to investigate the microstructural characteristics of GH4033 superalloy and the corresponding relationships between microstructure characteristics and mechanical properties but never paid much attention to conduct specific experiments on how to control the microstructure evolution during the hot deformation process to reach the excellent mechanical properties and long-time structural stability under their working condition.What’s worse,the corresponding relationships of GH4033 between the hot deformation stability and specific hot processing parameters were not obtained in these previous studies.On the other hand,Pakdel

et al

concluded that the hot deformation stability is significantly determined by microstructural evolution,which is related to the HCR processing parameters such as temperature (

T

),strain (

ε

) and strain rate.He

et al

did the hot compression tests to investigate a new type of nickel-based superalloy deformation behavior.Zhou

et al

stated that the flow behaviors are fairly complex because the work hardening and softening mechanisms significantly influence the deformation behaviors,and these mechanisms are sensitive to the processing parameters.Given these,Prasad

et al

first proposed the processing map method widely employed to optimize hot deformation parameters for many metals and alloys.Therefore,to further investigate the microstructure evolution of GH4033 superalloy during hot deformation,processing maps based on the data of the hot compression tests were conducted at the temperatures of 1 223-1 473 K and the total strains of 0.6 with strain rates of 0.001-30.0 s.Besides,the observation of the corresponding microstructure was employed to investigate the instability and stability domains and optimize the processing parameters for the HCR process.Generally,microstructures observation is regarded as a necessary supplement of the processing maps to analyze the influence of the hot deformation parameters.Zhong

et al

observed the corresponding microstructure evolution of the typical domains located at the processing map and concluded that the optimal processing parameters were located at the domains where the corresponding microstructure evolution promotes the DRX.Thus,hot deformation stability and mechanical properties can be enhanced by DRX.

The former part of the present study is to determine the optimal processing parameters to ensure the excellent microstructure of the material.However,the multi-pass HCR process accompanying the variation of many parameters leaves a challenge for researchers to design a perfect hot rolling process to reach the hot deformation stability.Besides,the flow stress calculation is the critical factor for the rolling force determination and parameter optimization in the HCR process.

In order to fully consider all these influence factors,the finite element model (FEM) was established to simulate the multi-pass rolling process.In addition,the construction of mathematical models,the deformation resistance model and softening fraction model,affects the dynamic flow behaviors and provides feasibility for the subsequent numerical simulation.Sui

et al

demonstrated that numerical simulation is regarded as an economical and efficient way to be widely applied in industrial production,which has achieved numerous successful examples in the past decades.Galantucci and Tricaricoopportunely conducted a FEM to simulate hot deformation behaviors at a single pass,which was considered a good approach to studying the hot rolling process.Nevertheless,multi-pass rolling is a continuous process,and there is limited research to conduct numerical simulation considering the multi-pass HCR process.In this paper,multi-pass numerical simulation was realized successfully by invoking the mathematical models of the experiment data into the FE software and transferring the calculation results of the former pass to be the initial conditions ofthe folloingpass.Besides,Rout

et al

provedthat the numerical simulationbased on the FEM can accurately predict the variation of the temperatures (

T

),strains (

ε

) and strain rates () of the workpiece under different hot rolling conditions.Early works gave good examples of describing the multipass HCR process by FEM.Sui

et al

demonstrated that hot deformation stability during the HCR process is affected by the hot rolling parameters and the material itself.Liu

et al

built the 3-D processing maps considering strain to analyze metal workability by integrating FEM and the 3-D processing maps.Consequently,we built the simulated rolling parameters of the multi-pass rolling process into spatial trajectory lines and invoked all the lines into the 3-D processing maps to intuitively show the relationship between the multi-pass rolling parameter and the processing domain.This coupling analysis is a holistic analysis that integrates dynamic and static scopes,contributing to acquiring the optimal HCR process parameters to reach the hot deformation stability.Meaningfully,the HCR processing parameters set have been verified by the practical production.In this way,the research in this paper not only fills the research gap in designing the HCR process parameters to ensure hot deformation stability for GH4033 superalloy reaching wider applications but also provides a theoretical reference and practical guidance for the subsequent HCR process parameter setting and deformation stability of GH4033 superalloy.

2 Experimental

The research samples in this study were GH4033 superalloy round rods with a diameter of 8 mm and length of 12 mm,and the chemical composition of GH4033 superalloy employed in this investigation is shown in Table 1.Single-pass and double-pass hot compression tests (Fig.1) were carried out on a Gleeble-3 500 hot simulation machine at different deformed conditions.The total strain level under all deformed conditions was 0.6.The single-pass hot compression tests were carried out at 1 223 to 1 473 K with an interval of 323 K and six strain rates from 0.001 to 30.0 s,and the graphite sheets and tantalum tablets were set between the sample and the interface to order to minimize the effect of the friction.Firstly,the samples were heated to the deformation temperature(

T

) at a 323 K·srate and soaked for 120 seconds to reach the deformed conditions and eliminate hot gradients.Secondly,the samples were compressed to the true strain (

ε

) of 0.6 at different strain rates () of 0.001,0.01,0.1,1.0,10.0 and 30.0 s.Finally,the compressed samples were immediately cooled by water to room temperature for retaining the deformed microstructure at high temperatures.Different from the single-pass hot compression tests,the per strain for double-pass was 0.3 (

ε

=0.3) and 0.3 (

ε

=0.3),and the interrupted holding time between passes is 5,10 and 15 s,respectively.The experiment requirements of the double-pass tests were similar to the single-pass tests.

Furthermore,the compressed samples were sectioned uniformly parallel to the hot compressing direction.Then the uncovered surfaces were treated with grinding,mechanical polishing and chemical corroding (corrosion agent:4 vol% alcohol nitrate).

3 Results and discussion

3.1 Single and double-pass flow behavior

Fig.1 Schematic diagrams of hot compression tests:(a) single-pass;(b) double-pass

The typical flow stress curves of the single-pass hot compression tests are displayed in Fig.2,which shows that the flow stress starts to ascend gently with a decrease in temperature or increase in strain rate.In addition,a work hardening stage can be observed before the samples deformed to a peak strain at all deformation temperatures and strain rates.Gao

et al

found that competition happens between the workhardening effect and dynamic-softening behavior according to the curves.The flow stress increases dramatically to a peak value (

σ

) during the initial work hardening stage of deformation,which indicates that the work-hardening effect can be compensated entirely by dynamic softening at this moment.Subsequently,as strain increases,the flow stress curves decrease and the occurrence of dynamic softening is gradually apparent during the hot deformation process.Finally,the flow stress curves reach a steady state,a dynamic equilibrium,achieved by the work hardening and dynamic softening.Correspondingly,Wan

et al

described the standard features of the flow stress curves,which are affected by the onset of DRX behavior.

The typical flow stress curves of the double-pass hot compression tests are displayed in Fig.3.The flow stress curves in the second pass apparently decrease with an increase of temperature and decrease of strain rate,which are sensitive to hot deformation parameters.Furthermore,the second pass flow stress curves are more pronounced with the holding time,resulting from the dynamic softening behavior affected by DRX decreasing dislocation density remarkably.

3.2 Mathematical models for flow behavior

According to the flow stress curves of the single and double-pass compression tests,the flow behavior and the softening behavior should be considered in the flow stress calculation during the HCR process.Based on the characteristics of the single-pass flow behaviors,the deformation resistance model is related to

T

,

ε

andwhich can be calculated as Eq.(1),and the correlation coefficient of the calculated values and the experimental values is 98.69%:

Fig.2 Flow stress curves of the single-pass hot compression tests

Fig.3 Flow stress curves of the double-pass hot compression tests

During the shorter interval time between passes,the meta-dynamic recrystallization is the primary softening mechanism for nickel-based superalloys as the critical strain (

ε

) for the dynamic recrystallization is attained in the former hot rolling process,which can be expressed as Eqs.(2) and (3):where

Z

is the Zenner-Hollomon parameter,

Q

is the activation energy calculated by hot deformation parameters (368 940 J·mol),

R

is the gas constant(8.314 5 J·mol).

Typically,the kinetics of meta-dynamic recrystallization of GH4033 superalloy during the pass intervals follows the Avrami equation.The softening fraction models due to the meta-dynamic recrystallization can be calculated by Eqs.(4) and(5) based on the characteristics of the double-pass flow behaviors and the correlation coefficient of the calculated values and the experimental values is 96.13%:

where

X

is the softening fraction，

t

is the holding time between passes (s)，

t

is the time required for the dynamic recrystallization fraction to reach 50% (s),

T

is the soaking temperature (K).Based on the mathematical models above,the flow stress of the alloy can be calculated by adjusting the strain (

ε

) in Eq.(1) according to Eqs.(6) and (7):

whereare the accumulated strain in the rolling process with the number

i

and (

i

-1) considering the deformation in the former rolling passes,

ε

is the strain only caused by the deformation in the currentrolling pass with the number

i

,is the accumulated strain before the deformation of the rolling pass with the number

i

,and

X

is the softening rate calculated by Eqs.(6) and (7) at the interval of the rolling passes with the numbers

i

and

i

-1.As the

ε

in Eq.(1) is replaced with the in Eq.(6),the flow stress of this alloy for the HCR process can be calculated.

3.3 Processing map analysis

Prasad and Seshacharyuluregarded the processing maps based on the dynamic material model(DMM) as significant tools for optimizing the hot rolling parameters and controlling microstructures.The workpiece in the process of hot deformation is equal to a closed power dissipation system,and the total input power (

P

) containing two sections,which can be expressed as:

where the

G

and

J

contents refer to the dissipated power of plastic deformation and the dissipated power of microstructure evolution,respectively.The power dissipation efficiency

η

is introduced to reflect the power dissipation capacity of the material,which can be expressed as Eq.(9):

where

J

is the maximum dissipated power of plastic deformation,

m

is the strain rate sensitivity.The value of

m

can be obtained from Eq.(10):

According to the Prasad instability criterion,which identifies the flow instability domains,the instability parameter

ξ

can be expressed as Eq.(11):

where the value of

ξ

flows instability parameter,which essentially describes the flow instability based on the deformed temperature and strain rate at a fixed strain,and the negative value of

ξ

indicates that flow instability occurs.

The construction of the processing map is the combination of the power dissipation map and the flow instability map.Fig.4 presents the processing map of GH4033 superalloy at the strain of 0.6.The shadow areas in the processing map are the instability domains and the white is the safe machining domains.It can be observed that the two instability domains emerge at the deformation condition of high strain rates.The power dissipation efficiency and instability domains in the processing map essentially represent the microstructural evolution under the hot deformation conditions.Generally,the microstructural observation is often regarded as a necessary supplementary for the processing map to identify the processing parameters and determine the optimal hot deformation conditions.Therefore,the microstructure of the compressed samples at different deformation conditions,including safe domains and instability domains has been observed to check the predictability of the processing map.

Fig.4 Processing map of GH4033 superalloy at the strain of 0.6

Fig.5 Metallographic structure of the superalloy under different deformation conditions

Fig.5 shows the corresponding microstructure of the four characteristic regions (A,B,C and D) in Fig.4 orderly.It can be seen from Fig.5(a) that the grains on the shear zone deformed under the action of the principal shear stress at the temperature of 1 223 K and the high strain rate of 30 s,and the angle between the deformation direction and the shear band direction is 45 degrees;Fig.5(b) shows the coarse grains emerge and reduce the grain boundary area at the temperature of 1 473 K and the high strain rate of 30 s,which is easy to crack during the hot rolling conditions.Obviously,domain A and B should be avoided during processing because the grains after compression is uneven and mechanical instability occurs in the structure,which reduces the processing properties of the alloy.Fig.5 (c) shows microstructure undergoes partial dynamic recrystallization (PDRX) at the temperature of 1 373 K and the strain rate of 0.01 s,where the grains size is large and various.Fig.5(d)shows the microstructure undergoes full dynamic recrystallization at the temperature of 1 273 K and the strain rate of 1.0 s,and the grain structure is uniform and fine.By contrast,it is evident that the grains sizes of domain C are bigger than those of domain D,but the power dissipation efficiency of domain C is lower than that of domain D,which illustrates the growth of the grains has consumed energy provided from the power dissipation efficiency.In addition,Ke

et al

proposed that dynamic recrystallization is a beneficial deformation mechanism for the reconstruction of deformed structures,especially the uniform and fine DRX grains.The above analysis based on the combination of the processing map and the microstructure observation provides guidance for determining the hot deformation conditions.The domain D is an extremely stable and suitable hot processing domain,where uniform fine DRX grains can be achieved to ensure the desired mechanical properties.Sun

et al

conducted a similar work and confirmed that the higher power dissipation efficiency (0.36-0.41) can provide more energy to support the internal microstructure change of the alloy.Therefore,the reasonable processing range of the alloy is at the strain rate of 0.1-1.0 sand temperature of 1 273-1 473 K.

3.4 FE simulation and analysis

3.4.1 Establishment and validation of FEM

Serajzadeh and Tricaricosuccessfully used the rigid plasticity FE method to predict temperature,strain and strain rate distributions during the hot rolling process.They also verified the accuracy of the modeling results and finally concluded that the approach of numerical simulation may be extended to simulate other steady-state deforming processes.Therefore,the rigid plasticity FE method should be considered in the present study to build a model to control the microstructure of the products,which are substantially affected by the processing parameters.Sui

et al

selected the core node (

n

) of the cross-section of the workpiece,and the previous mathematical models are invoked to the FE software for accurately simulating the twelve-pass rolling process.In this program,the FEM for the 12-pass HCR process is shown in Fig.6.The original billet with the square cross-section of 80 × 80 mm has meshed with 900 elements and the final product with a diameter of 25 mm.The initial temperature of the billet (

T

) was set as 1 273-1 473 K,the first-stand biting velocity (

v

) was set as 0.15,0.25,and 0.35 m·s,and the corresponding rolling velocity (

v

) of each pass is shown in Table 2.

Fig.6 FEM for 12-pass hot rolling of GH4033 round rod

Fig.7 Comparison between the simulated and the measured values of the maximal rolling force

Fig.7 shows the comparison of the maximal rolling force between the simulated and measured values to verify the validity of the simulation process at

T

=1 423 K and

v

=0.25 m·s,and it can be seen that the simulated results from the FE method are approximate to the measured results in the practical HCR process.Therefore,in the following study,the 3-D FEM is used to simulate temperature,the effective strain and the effective strain rate fields during the HCR process.The related simulation can provide an essential reference and optimization to design the HCR process parameters in a steel factory.

3.4.2 Multiple field distribution

Fig.8 shows effective strains of

n

in the whole rolling process at

T

=1 423 K and

v

=0.25 m·s.It can be seen that the values of the effective strain between passes have a significant downward trend even close to zero,which implies that

n

has undergone the softening behavior but has not been completely softened between the passes in the rolling process.

Fig.8 Effective strains of nc in the rolling process

Fig.9 Effective strain rates of nc in the rolling process

Fig.9 shows effective strain rates of

n

in the whole rolling process at

T

=1 423 K and

v

=0.25 m·s.It can be seen that the effective rate continuously increases until it reaches a maximum value of 9.88 sat the 8th pass,which shows the increase is mainly due to the accelerated rolling velocity.In addition,the effective strain rate gradually decreases in the 9th-12th pass due to the stable rolling stage,which illustrates that the smaller deformation contributes to achieving the higher rolling accuracy required in the later stages of rolling.Fig.10 exhibits the temperature rainbow map of the temperature changing at the end of the first and second pass of the cross-section of the workpiece at

T

=1 423 K and

v

=0.25 m·s.It can be seen from Fig.10 that the outer temperature is the lowest,the temperature gradually decreases from the inside to the outside,and the phenomena that the temperature inside the cross-section is higher and the temperature difference is obviously smaller depending on the effects of heat transfer and hot convective.The effect of hot convection of workpiece is not good,and the heat transfer is the main form,the contact area between the outside surface and the roll is larger,the influence of heat transfer is very strong so that the temperature of the outside decreases more than that of the inside and high-temperature areas only exist in the

n

.

Table 2 Rolling velocity at each pass corresponding to

Fig.11 shows the temperature variation of

n

during the hot rolling process,which shows that the variations of the initial temperatures have little influence on the temperatures of

n

during the rolling process,but the rolling velocity exerts obvious influence on the temperatures of

n

.The phenomena can be attributed to two main reasons:the faster rolling velocity allows less rolling time to dissipate heat and the faster rolling velocity promotes the more generation of plastic deformation heat.

3.5 Coupling analysis based on DMM and FEM for rolling optimization

It is a fundamental principle of the HCR process through controlling the hot rolling parameters to obtain the required and stable microstructure of the alloy after processing to ensure that the alloy obtains excellent processing properties.However,the study of DMM or FEM alone cannot provide a reference for selecting optimal rolling process parameters.Therefore,the coupled analysis of the DMM and FEM is a perfect combination of the static and dynamic scopes of analysis to optimize the rolling process parameters.Furthermore,the relationship between the hot rolling parameters and microstructure is described by combining the constructed spatial trajectory of temperature-strain-strain rate based on the FEM analysis and the reasonable processing domain based on the three-dimensional processing map.Combined with the discussion in section 3.3,the optimal processing temperature and strain rate were further chosen at 1 423 K and 0.1-1.0 srespectively,which are in the domain of the peak dissipation value,and the highest power dissipation efficiency can provide more energy to support the internal microstructure change of the alloy.Subsequently,the spatial trajectory processing maps at the chosen

T

=1423 K and

v

=0.15,0.25 and 0.35 m·scan be well described in Figs.12-14,respectively.Obviously,it can be seen that the spatial trajectory lines at

v

=0.25 m·sare all located in the optimal processing domains,

i e

,the fully dynamic recrystallization domains.However,some of the spatial trajectory lines at 0.15 or 0.35 m·sare located in the partial dynamic recyclization domains and even the instability domains.

Fig.10 Temperature field distribution of the cross-section

Fig.11 Temperature variation of nc in the rolling process

Based on the above analysis,it can be concluded that the optimal parameters are at

T

=1423 K and

v

=0.25 m·s,which is the absolutely stable domain as shown in Figs.12-14.The stable domain is suitable for setting HCR process parameters and reaching deformation stability.

3.6 Verification by the practical HCR processes

Fig.12 Spatial trajectory line of nc when T0=1 423 K and v0=0.15 m·s-1 (a:1-6 pass,b:7-12 pass)

In order to verify the accuracy of the coupling analysis results,the actual HCR processes were carried out on the GH4033 superalloy round bar.The original billet is the square one with a cross-section of 80 mm × 80 mm and the final product is the round rod with a diameter of 25 mm.The

T

was set as 1 423 K and

v

was set as 0.15,0.25 and 0.35 m·s.And the microstructure observations for the core of the finish products were displayed in Fig.15.The low rolling velocity provides more time for the grains to grow and the relative coarse grains can be seen in Fig.15(a).It is displayed in Fig.15 (c) that the recrystallized grains coexist with the unrecrystallized grains since the HCR process has not undergone fully dynamic recrystallization.The abnormal mixed microstructure will be prone to cracking during further deformation and even service.The dynamically recrystallized grains with uniform and fine grain sizes are shown in Fig.15(b) since the deformation of the workpiece is under a stable state during the HCR process.In comparison,the results of the practical rolling process are completely consistent with the results of the coupling analysis.It is further concluded that the hot deformation stability of GH4033 superalloy round rods can be well achieved

T

=1423 K and

v

=0.15 m·s.

Fig.13 Spatial trajectory line of nc when T0=1 423 K and v0=0.25 m·s-1 (a:1-6 pass,b:7-12 pass)

Fig.14 Spatial trajectory line of nc when T0=1 423 K and v0=0.35 m·s-1 (a:1-6 pass,b:7-12 pass)

Fig.15 Metallographic structure of the core of the GH4033 superalloy round rods for different v0:(a) 0.15 m·s-1,(b)0.25 m·s-1,(c) 0.35 m·s-1

4 Conclusions

The flow behavior of GH4033 superalloy was evaluated through hot compression tests at the temperatures of 1 223-1 473 K and the total strains of 0.6 with strain rates of 0.001-30.0 s.Based on the characteristics of the flow behaviors,mathematical models were constructed for constructing the FEM to simulate the HCR process,and the processing maps based on DMM were constructed to identify the microstructure to ensure stable processable domains.The coupling analysis based on DMM and FEM was well described by 3-D processing maps combining the spatial trajectory lines of temperature-strain-strain rate.And the results of the practical rolling process and the coupling analysis were completely consistent.The following conclusions were drawn:

a) The flow behavior of GH4033 superalloy was significantly sensitive to the deformation parameters,and the mathematical models are as follows:

b) The processing map initially determined the processable domain locating at the strain rate of 0.1-10 sand the temperature range of 1 273-1 423 K.

c) The practical results have confirmed the results of the coupling analysis that the deformation stability of GH4033 superalloy round rod in the HCR process can be achieved by setting the rolling process parameters at

T

=1 423 K and

v

=0.25 m·s.