1.Introduction

Friction based welding processes such as friction welding and friction stir welding are widely used for joining similar and dissimilar metals.These welds are not subjected to melting and solidification[1-4]compared to conventional fusion based processes.Many problems such as hot cracking,porosity,inclusion,and dilution which are characteristic features of fusion welding are absent in the friction based welding processes.In both fusion[5]and solid-state welding[6]methods,exposure to high temperature results in heterogeneous microstructure across the weldment.In fusion welding,parameters in fluencing the microstructure are thermal related such as thermal gradient and cooling rate.However,in solid state welds,the microstructural changes across the weldment are in fluenced not only by temperature but pressure too.For example,the weldment of fusion welded sample consists of solidified columnar grains followed by coarse grain heat affected zone(CGHAZ), fine grain heat affected zone(FGHAZ),inter-critical heat affected zone(ICHAZ),and unaffected zone of base metal[7].In contrast,the friction stir and friction welded weldment consists of a weld interface of very fine grain structure followed by thermomechanically heat affected zone(TMHAZ)[1-3,8].The width of re fined grain zone in friction stir welding is relativelylarger while it is smaller in a friction weld.The formation of the re fined grain structure at the weld interface or stir zone is attributed to dynamic recrystallization(DRX)phenomena due to high strain rate and temperature involvement.In these methods,friction between two metals generates heat and combination of applied pressure and rotational speed generates high strain rate in the system.Therefore,microstructural evolution in friction based methods is dictated by different strain rates and temperatures exposures across the weldment.However,prediction of these parameters by experimental route is very complicated,especially strain rates and temperatures.For friction stir welding,various modeling approaches were taken to predict the thermal pro files,metal flow behavior,strain rates[9-12]and microstructural evolution[13-15]across the weldment.As for friction welds,not much attention is paid to modeling area except few numerical studies[16].In view of the limited understanding of microstructural aspects of friction based welds through theoretical understanding,this work was taken up.It is aimed to predict the strain rates,temperatures,and microstructural evolution during friction welding through microstructuralmodeling routeusing theoreticalaspectsofdynamic recrystallization.

For modeling of DRX,several methods have been adopted such as Monte Carlo[17],phase field[18],and cellular automata[19,20]methods.Among these,cellular automata method gained much attention for microstructural modeling of DRX due to its discrete temporal evolution of space and time.Thus,cellular automata method is adopted in the present work.First part of the work is focused on DRX modeling and its validation with the experimental data of super alloy Inconel 718 during hot compression[21]taken from literature and second part is focused on using the validated model to predict the strain rates,temperatures,induced strain,and microstructural evolution during friction welding of Inconel 718 carried out in the present study by our group.

Inconel alloys are widely used for military aircraft applications to withstand a combination of high temperature,hot gas corrosion and high strength.Inconel 718 is an established alloy for commercial and military aircraft airframe and engine components.The outcome of this study would help enhance the understanding of microstructure evolution and mechanical response of Inconel 718 super alloy during friction welding as well as during any hot deformation process.Prior prediction/knowledge of these results would be useful for controlling the final microstructure and deciding the post processing treatment conditions forachieving the final property of a material.

2.Background

2.1.Cellular automata method

Cellular automata[15]is an algorithm where space of interest is divided into finite number of grids called as ‘cells’.The state of a cell is governed by its local neighborhood and the transformation rule.There are two types of neighborhood which can be used for simulation of recrystallization i.e.,von Neumann's and Moore's neighborhood.In von Neumann's only nearest neighbors are considered whereas Moore's consider both nearest and secondary neighbors.The state of any cell at time step(t+Δt)using von Neumann's neighboring rule can be expressed as

whererepresents the value of variables ξat site(i,j)at time t.Function f is the transformation rule which determines the evolution of the site(i,j)along with time,and it can be set according to the characteristics of the system of interest.

2.2.Theoretical model&simulation procedure for DRX

Dynamic recrystallization(DRX)is commonly observed in metals when subjected to high temperature deformation.Mostly low to medium stacking fault energy system show this kind of behavior such as copper and nickel based alloys.DRX is known to occur when dislocation density of the system reaches to some critical value which,in turn,depends on high temperature deformation parameters such as strain rate and temperature[22].The final microstructure of DRX depends on two important phenomena;nucleation and growth.Bothnucleation andgrowthareclosely related to dislocation density.

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whereθ0is the hardening rate and can be determined from the slope of experimental flow curve at particular temperature.The recovery parameter k2and hardening constant(k1)[22]are related with each other as follows

For this work,2D square lattice was employed.Four state variables were allocated to each of the cells;(i)grain number represents different grains,(ii)grain color represents orientation and boundary energy of the grain,(iii)dislocation density variable and(iv)distance variable which controls the grain growth.Von Neumann's neighborhood was used to simulate the grain growth.

For the evolution of dislocation density Estrin and Mecking law[23]was used.Based on this law,the dependence of dislocation density with strain can be expressed as

where k1is the constant that represents hardening and k2is the recovery parameter.The constant k1is independent of strain rate and only depends on temperature whereas recovery parameter k2 is a function of both strain rate and temperature.The high temperature flow stress at the macroscopic level can be calculated using following expression which is related to the dislocation density[24,25].

某化工企业100万t/a合成气制乙二醇，一期工程60万t/a乙二醇项目需要对2股废气、2股有机废液进行洗涤、焚烧及无害化处理。焚烧产生的烟气热量优先过热来自气化副产的120～150t/h、9.8MPa高压饱和蒸汽至520～540℃，其余热量用于产生3.8MPa饱和蒸汽。可供焚烧的燃料气源有天然气和PSA装置的解吸气，PSA解析气含体积分数24%的CH4，气源受生产负荷影响，存在压力和流量波动。工艺要求正常工况下优先使用PSA解析气，PSA解析气气量不足时，再补充天然气。

whereαis the dislocation interaction term(typically ranges from 0.5 to 1.0 for most of the metals),G is the shear modulus of the material,b is the burgers vector,andis the mean dislocation density,given by

where n is the total number of cells andρiis the dislocation density of ith cell.k1is related with the hardening rate[22]and expressed as

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whereσsis the steady state stress.The recovery parameter k2can be determined after calculating the value of k1andσs.The steady state stress[26]is calculated according to the following equation

where A，α，and n are the material constants.Z is the Zener Holloman parameter which is a function of strain rate and temperature and given by following equation

By keeping the temperature at 1473 K,simulations were run at 246 s-1and 389 s-1for 1200 and 1800 RPM,respectively.Grain size of 3.35 and 2.75μm was achieved at 246 s-1and 389 s-1strain rates,respectively as shown in Fig.11(a)and(c).The results matched almost closely with the experimental result,suggesting the temperature achieved during friction welding is almost identical for all the three rotational speeds.Identical temperature for all the rotational speed implying that once the material is plastically deformed,they achieve the steady stage temperature during frictionwelding.This type of phenomena is also observedin friction stir welding process which shows that for continuous generation of heat,a dynamic balance is required between contact stress and material yield shear stress[2,33].Similarly,the strain rates were also predicted for center location.In this case also,strain rates almost similar to analytical strain rates matched the grain size for both 1200 and 1800 RPM welds at 1323 K as shown in Fig.11(b)and(d).Identical temperature at all the RPM con firming the achievement of steady stage temperature during friction welding once it is plastically deformed.Temperatures of 1323 K(0.78Tm)and 1473 K(0.89Tm)are achieved at center and edge of the weld,respectively with 150 K difference from center to edge.

where is the strain rate,T is the temperature in Kelvin and R is the gas constant.In the beginning of the deformation,evolution of dislocation with strain was calculated using equation(2).Once the dislocation of the deforming matrix crosses the critical value of the dislocation,new nuclei will form at the grain boundary.The value of the critical dislocation density can be calculated using following expression derived by Roberts and Ahlblom[27].

where C is the nucleation constant and m is the exponent which is set to 1 in this study.For a specific hot deformation condition,if the percentage of DRX and grain size is known,nucleation rate can be calculated using equation(12)[22].

whereγiis the grain boundary energy,M is the grain boundary mobility,l is the dislocation mean free path andτis the dislocation line energy and can be calculated from the following expression[24].

where γmand θmare the grain boundary energy and mean misorientation angle,respectively.γi= γmwhen misorientation angle ′θ′is higher than 15°.

根据土层情况，本工程地下壁板桩拟采用泥浆护壁抓槽机成槽，跳仓法施工，水下灌注混凝土，具体施工顺序详见图2。

whereη is the percentage of DRX,ε is the true strain and r is the mean radius of recrystallized grain.Once the nuclei are generated at the grain boundary or any defected area that cell is considered as recrystallized cell.The dislocation density of that cell is set to zero or annealed state dislocation density which raises the difference in dislocation densities between deformed and recrystallized cells.The difference in dislocation densities generates a force for the nuclei to grow.The velocity of the grain follows the following equation[20,22].

whereΔf is the driving force per unit area and M is the grain boundary mobility which can be calculated as follows

where M0is the constant and Qbis the boundary diffusion activation energy.The driving force is a function of dislocation density difference and grain boundary energy,expressed as[20,22].

whereγiis the grain boundary energy which is a function of grain boundary misorientation(θ).It can be calculated from Read--Shockley equation[20,22].

枢纽锚固是在对外客运枢纽布局的基础上，充分发挥城市交通网络的功能，如道路、轨道交通等。在对外客运枢纽设计中，发挥锚固区域交通网络的作用，如高速公路、干线公路、城际公路、铁路以及公路客运班线等。因此，城市综合客运枢纽的锚固能够为人民群众出行的便捷性提供保障。

In the present study,nucleation rate is calculated based on following equation which is function of both strain rate and temperature[22].

The initial microstructure was created by populating fixed number of nuclei in a matrix and allowed them to grow until it impinges with each other.The orientation of the grains was selected randomly and ranges from 1 to 180°.Fig.1 represents the initial microstructure created as described above.The matrix consists of 250×250 cells.Each cell in real dimension is equivalent to 1μm.Periodic boundary conditions were used for this simulation.Time stepΔt is calculated as ,where d is the diameter of critical radius and vmaxis the maximum velocity.Table 1 shows the constants used for this simulation.All the constant values were calculated using experimental data from Chen et al.work[21].

3.Material and methods

The chemical composition(wt%)of Inconel alloy 718 rod(16.5 mm diameter)that was used for frictionwelding is as follows:51.6%Ni,18.2%Cr,5.1%Nb,3.28%Mo,1.06%Ti,0.56%Al,0.33%V,0.09%Mn,0.01%S,0.004%C,0.003%B and 19.793%Fe.The microstructure of as received Inconel 718 is shown in Fig.2.Microstructure consists of equiaxed grains and annealing twins with an average grain size of 29μm.Rotary friction welding machine was used to develop friction welds.Following welding parameters were used:Friction Pressure:300 MPa,Upset Pressure:600 MPa,Burnoff length:4 mm,and Rotational Speeds of 1200,1500,and 1800 RPM.

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4.Results&discussion

4.1.Model validation

The experimental results mentioned in this section to compare with our simulated results are referred from literature[21].A typical flow curve during high temperature deformation consists of three stages:work hardening,softening and steady state stage.In work hardening stage,the accumulation of dislocation is very high due to weak recovery leading to accelerated increase in the flowstress.Once the dislocation reaches a critical value,dynamic recrystallization takes place resulting in dislocation annihilation which reduces the flow stress of the material(softening stage).In the steady stage region,dynamic balance reaches between dislocation accumulation(work hardening)and dislocation annihilation.Fig.3(a)represents the simulated and experimental flow curves[21]at constant temperature(1253 K)with different strain rates(1,0.1,0.01,and 0.001s-1).Similarly,Fig.3(b)shows the simulated and experimental flow curves[21]at constant strain rate(1 s-1)with different temperatures(1193,1223,1253,1283,and 1313 K).

Increasing trend in flow stress was observed at high strain rates and low deformation temperature which can be attributed to(1)higher rate of dislocation accumulation and(2)low rate of recrystallization.At higher strain rate,the rate of dislocation accumulation is fast which leads to high amount of work hardening into the system.Further,the deformation time is short as compared to lower strain rates thus reduces the growth of new recrystallized grains.On the other hand,at high temperature,the mobility of growinggrainis faster which annihilates the dislocations generated by work hardening thus reducing the flow stress of the system.Simulated results are found to agree well with the experimental results as shown in Fig.3(a)and(b).All the simulated peak stress values are quite comparable with the experimental peak stress values.

Small deviation has been observed at later stages of the deformation after 0.5%of true strain.This deviation is observed when it is deformed at high strain rates or at lower temperatures.It is found that adiabatic heating also plays a role in softening of material apart from dynamic recrystallization when deformed under high strain rates and lower temperatures as reported by Weis et al.,[28].It has been reported that adiabatic heating increased the temperature of the system by 333 K when deformed at 1223 K and a strain rate of 1 s-1.In the present model, flow curves were simulated using constant temperature,therefore,it can be concluded that deviation from experimental flow curves in later stages of deformation is due to increased temperature(ΔT)in the system due to adiabatic heating.Apart from flow curve,the model is also validated with reported grain size.Fig.4 shows the simulated microstructures at different temperatures(a)1223 K(b)1253 K and(c)1283 K while keeping the strain rate constant(0.001s-1).Fig.5 shows the simulated microstructures at different strain rates(a)0.1 s-1(b)0.01s-1and(c)0.001s-1keeping the deformation temperature(1313 K)constant.The simulated microstructure agreed well with the experimental results reported by X.M.Chen et al.[21]as listed in Table 2.In micrograph,each color represents the orientation of a grain.The results indicate the closeness of experimental and simulated results.Further,this validated model is used to predict the strain rates and temperatures exposures in friction welds and covered in following section.

英的心扑通扑通地跳动着，感觉坐也不是，站也不是。她像一摊软泥一样倒在了病榻，一动不动，再也起不来了。潮湿而陈旧的床陪伴了英一辈子，依然氤氲着她和丈夫年轻气盛时的情意绵绵，而更多的是残留着她几十年独守空房的无奈和痛楚。从豆蔻年华到耄耋之年，这里见证了英简单的幸福和无限的悲痛，见证了四个孩子呱呱落地，又将见证她悲凉而去的全过程。

7）在本项目成功举办了“以标准化信息化为抓手，以创精品工程为目标，全面提升中国十七冶集团工程建设管理水平，打造中冶管廊第一品牌”为主题的管廊工程观摩交流会，得到了一致好评，起到了较好的示范和引领作用；

儿童安全教育是当前教育界非常关注的话题，也是保障儿童能够健康快乐成长的基础和前提，尤其是在儿童安全事故发生后，人们对于儿童安全教育的重视程度越来越高。这就需要真正发挥小学道德与法治课程的作用，帮助学生树立基本的安全意识。道德与法治课程涉及的内容较多，需要教师能够不断创新教学模式，提升课堂教学的有效性，增强学生的道德与法治观念，为学生的健康成长奠定基础。但是，在当前道德与法治教学中依旧存在很多问题，限制了课程价值的发挥。因此，教育者必须不断探索有效教学的策略，提升课堂教学质量。

4.2.Prediction of strain rate and temperature in friction welds using grain size

To study the grain evolution,strain rates,and temperature exposures in friction welds of Inconel 718,three welds were generated at different rotational speeds i.e.,1200,1500,and 1800 RPM.Fig.6 show the cross-sectional view of a typical friction weld developed at 1500 RPM.The welded region has shape like lens(marked with red color in Fig.6)which is mostly composed of very fine equiaxed grains and can be differentiated in the picture by the white region.The formation of re fined grains in the welded region is due to involvement of very high strain rates and temperature.Grain re finement phenomena due to involvement of high strain rates and temperatures are commonly known as dynamic recrystallization[29,30].Fig.7 shows the EBSD map from center and edge location of friction weld sample welded at 1500 RPM.Fig.7(a)and(b)corresponds to edge and center location of the weld,respectively.It can be seen from Fig.7 that the grain size at both location of the weld went through significant size reduction as compared to their base counterpart.For example,the average grain size at the center and edge of a welded sample was found to be 1.4 and 3.1μm,respectively.Although,they showed significant size reduction compared with base material,they also show different grain sizes compared with each other.The difference in grain sizes at these two regions could be attributed to different strain rate and temperature exposure.Fig.8 shows the temperature pro file captured by IR camera on the outer surface of the IN 718 rod during friction welding performed using 1500 RPM.The maximum temperature recorded by IR camera was found to be 1473 K.By assuming similar temperatures at both center and edge of the weld for a particular rotation speed,the only parameter which creates the difference in grain size will be strain rate.Afterward,the validated model is used to predict the strain rate experienced during welding.For that,the temperature was kept constant equal to recorded one(1473 K)and strain rates were varied till the grain size matched with the experimental values.

At strain rate of 294 s-1,the simulated grain size which is 2.97μm(Fig.9(a)matched veryclose tothe value(3.1μm)obtained from experiment as shown in Fig.7(a).Similarly,by assuming that the temperature experienced at the contact zone is similar though out the radial direction,a strain rate of 1850 s-1is obtained which matched the experimental grain size values which is 1.4μm(Fig.7(b)).The predicted strain rate at the center of weld is higher than the edge of the weld which is not feasible because radial velocity always increases towards periphery.O.T.Midling and O.Grong[16]showed effective strain rate(radial,axial,and rotational)increases with radial position,means periphery attain higher effective strain rate compared to the center of a rod during friction welding of aluminum alloys which is contradictory to our finding.This suggests that not only the strain rate but temperature is also different at the center of weld compared with edge.To predict the temperature variation,analytical approach is taken to first identify the strain rate during welding as adopted by Chang et al.[31,32],for friction stir welding.The material flow strain rate(˙ε)during friction welding can be derived by the torsion type deformation as

where Rmis the average material flow rate which is about half of the rotational speed,reand Leare the radius and depth of recrystallized zone.The depth of recrystallized zone is taken as thickness of material which went through dynamic recrystallization.For a given rotational speed,Rmis constant which is 12.5 rps for 1500 RPM.At edge,reis equivalent to radius of the rod(8.25 mm,half of rod diameter)and 0.1 mm for center.The depth of recrystallized zone is measured using optical micrograph,2200μm and 350μm is obtained for edge and center location,respectively and marked in Fig.6.By plugging these values,a strain rate of 294 s-1and 22 s-1 are obtained for edge and center location,respectively.The calculated strain rate for edge location also matched perfectly well with the predicted strain rate.Further,the calculated strain rate from the analytical model is used to predict the correct temperature from the simulation.Keeping the strain rate equal to calculated from analytical model,grain size of 1.4μm equivalent to experimental(Fig.7(b))is achieved at a temperature of 1323 K as shown in Fig.9(b).The difference of 150 K is noticed from edge to center of the weld which also satisfy the general agreement that frictional heat is more if the surface area is large.

To con firm the feasibility of this model,simulation was also carried out to predict the strain rates for friction welds generated with 1200 and 1800 RPM.Fig.10 represents the EBSD maps of friction welds generated with 1200 and 1800 RPM.For both center and edge locations,similar trends in grain size were observed for samples with 1200 and 1800 RPM as was observed for 1500 RPM.The average value of grain size at different locations is listed in Table 3.Depth of recrystallization and hardness value corresponding to that location is also listed inTable 3.It can be seen from Fig.10 and Table 3 that central portion of friction welds went through higher amount of grain re finement as compared to edge in all the cases and validated by their corresponding hardness values.

Variation in grain size with respect to rotational speed is very small.For example,at the edge of the weld,the average grain size for 1200 RPM sample is 3.2μm whereas for 1800 RPM sample,it is 2.9μm.The difference in grain size is very small but show signi ficant difference in strain rates as listed in Table 3.The calculated strain rate,based on equation(17),does not incorporate the temperature affect,therefore simulation was also run to check the strain rates for 1200 and 1800 RPM.

习近平总书记在十九大报告中指出，实施健康中国战略，人文关怀与心理疏导的实施使患者有了更多的自觉性，乐观的面对疾病，早期接受治疗，早期康复，推动健康中国的目标的实现。随着社会的发展，在护患长期的接触中，护患关系的不和谐也浮出水面[4]。人文关怀与心理疏导的实施有利于护患关系的缓解即是一段人际关系的缓和，促进和谐护患关系的构建，推动和谐社会的构建，减少护患纠纷与护患冲突，利于缓解护患关系紧张的现状。

4.3.Strain map

Using all the predicted strain rates and temperatures for the welds generated at three rotational speeds(1200,1500,and 1800 RPM),strain maps were plotted after the final deformation as shown in Fig.12.Fig.12(a),(b),and 12(c)corresponds to the edge location of a weld generated at 1200,1500,and 1800 RPM,respectively.In a same way,Fig.12(d),(e),and 12(f)corresponds to the center location of a weld generated at 1200,1500,and 1800 RPM,respectively.It can be observed from the overall results that at high temperature,the amount of strain accumulation is less compared to low temperature.For example,at 1473 K,the strain accumulation is 5%as comparted to 50%at 1323 K.The maximum intensity corresponds to those grains which are mostly nonrecrystallized grains and present in very less quantity.Another observation is that at low temperature and low strain rate,the distribution of lowstrained grains(Fig.12(d))is highercompared to material deformed at high strain rate(Fig.12(f)).On the other hand,at high temperature(1473 K),the strain distribution is almost uniform for all the strain rates.Overall the strain distribution map could be important data to figure out the correct temperature and time for the heat treatment process.The output of this data could be used as the input data for heat treatment grain growth model.It can be concluded that using this model localized strain rates,temperature,and induced strain in the microstructure can be calculated if one of parametersuch as temperatureand strain rate is known.In other way,a process map can be developed which will be used to get the strain rates and temperatures a material went through during any hot deformation process,if the resultant grain size is already known from the experiment.

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5.Conclusions

Cellular automata based microstructure model has been developed to simulate microstructural evolution of Inconel 718 during hot deformation.Flow curves and grain sizes obtained from experiments and simulations were found to be quite comparable.Following are the key findings from this work:

1.In simulated flow curves,small deviation in later stages of deformation was observed which was attributed to adiabatic heating of material due to plastic deformation.

2.Larger grain size was observed at low strain rates and high temperatures attributed to more deformation time and higher grain mobility.

3.The strain rates predicted from simulation for both center and edge location of the weld were found to be increasing with increasing rotational speed.

So L3=950×I3+475+475-200=950×I3+750,L4=Ls-A1-220-200-(950×I3+750)=Ls-A1-950×I3-1 170

4.Temperature difference of 150 K from center to edge of the welds was observed from the simulation result.

5.The simulated results showed that temperature tend to reach at steady state(0.78 Tm:center and 0.89 Tm:edge)for all the RPMs.

6.Higher amount of strain accumulation was noticed at low deformation temperature as compared to high deformation temperature.

7.Uniform strain distribution is observed at higher temperature for all the rotational speeds.

Acknowledgement

The authors would like to acknowledge Dr.Sekhar Rakurty and Dr.Deepankar Pal for their valuable suggestions in developing this model.

References

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