Advances of physics-based precision modeling and simulation for manufacturing processes

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Adv.Manuf.(2013)1：75-81D0I 10.1007/s40436-013-0005-6Advances of physics-based precision modeling and simulationfor manufacturing processesGang W angYi-Ming RongReceived：17 September 2012/Accepted：5 November 2012/Published online：14 M arch 2013### Shanghai University and Springer-Verlag Berlin Heidelberg 2013Abstract The development of manufacturing processconcems precision，comprehensiveness，aglleness，higheficiency and low cost.The numerical simulation hasbecome an important method for process design and opti-mization.Physics-based modeling was proposed to pro-mote simulations with a high accuracy.In this paper，threecases，on material properties，precise boundary conditions，and micro-scale physical models，have been discussed todemonstrate how physics-based modeling can improvemanufacturing simulation.By using this method.manu。

facturing process can be modeled precisely an d optimizedfor getting better performance。

Keywords M aterial properties-Multiscale analysisPhysics-based modeling·M anufacturing process1 IntroductionThe development of manufacturing process has a tendencyof precision，comprehensiveness，agileness，high eficiencyand low cost.The numerical simulation technology hasbecome an important method for process design and opti-mization since 1 980s.Especially in the past decade，theadvancements in computer technology and high end inin situ experimental facilities have been driving modelingG.W an g ·Y.-M .RongDepartment of Precision Instruments and M echanologyTsinghua University，Beijing 100084，Peoples Republic of ChinaY.-M.Rong(区])Department of Mechanical Engineering，W orcester PolytechnicInstitute，W orcester，M A 01609-2280，USAe-mail：yrong###tsinghua.edu.cnfor manufacturing processes to be fl new frontier ofresearch。

The precise models with process simulation for micro-structure evolution，grain growth in microscale，interactionof multiphysics，highly eficient algorithms，advancedmeshing strategy， and integration of manufacturingequipment control，have been employed in real applica-tions.Physics-based modeling was proposed to promotesimulations，in both scientific and engineering fields，withhigh accuracies.Its framework is shown in Fig.1，wherephysical model， material model，process design， andfacility model are the pillars for investigating manufac-turing processes.Most processes， such as machining，casting，forging，grinding，heat treating，can be simulatedwith them.As a result，the performance of manufacturedparts and facilities，the energy consumption，and environ-ment emission are predicted to evaluate their outcomes。

In this paper，some new progress of research in materialproperties，precise boundary conditions，and refined phys-ical model will be discussed，thus presenting validity of theaforementioned modeling technique。

2 Dynamic mechanical properties of metalfor precision machining processMaterial properties，e.g.，thermal，mechanical，magneticproperties and phase transformation，are the basic data formanufacturing modeling， and accurate，complete，andreliable material data enable simulations to be close to thereality。

Dynamic mechanical property of metal describes therelationship between stress and strain.This property varieswith temperature and strain rate.Furtherm ore，notable sizeeffect on mechanical properties can be observed in the垒SpringerPrecision modeling and simulation1，(a)800gm1.200l，000c 800童6040020001，(b)400gmFig.3 Shear stress-shear strain curves for different deformed dimensionsl，000900砖800皇7060050040001，000900800童70o6005004001，2001.000矗 800600400200Ol 000900800皇706005004002 4 6 8 l0VCo)50 gm0 0.4 0.8 1.2 1，6 2.0 0.0 0.4 0.8 1.2 1.6 2.0， y(b)7×10。s (c)1.5x 10 s-Fig.4 Shear stress-shear strain curves for diferent flow sfess sizesthe experiments also demonstrate that the mechanicalproperties of the material，in the folowing two aspects，areinfluenced by the shear band width。

(i1 Flow stress size eflfect：the flow stress gives theinternal deformation of the material from the macrorespect.As is shown in Fig.4，as the shear bandwidth decreases.material shear stress-shear straincurve gradualy improves。

(ii) Failure strain size effect：in Fig.5。the failure strainsfor different specimens decrease as the strain rateincreases.Failure strain of the material alSO has thesize effect phenomenon。

2.2 Regression of material constitutive modelMaterial constitutive model iS that the flow stress of thematerial is a function of strain，strain rate，temperature，andother macroscopic thermodynamic parameters that produceheat.This model is the prerequisite for the metal plasticnumerical analysis.Johnson-Cook fJC)constitutive modelwas proposed in 1 983 by Johnson and Cook7，and is used todescribe mechanical behavior of a material with large defor-mation under high temperature and high strain rate conditions。

Because of its simplicity，and easy to use.it is widely used inthe industry.The original expression of the JC model isT(AB7 )(1Cln9 )(1-T )where T is shearing stress， shear strain rate，T tempera-ture，and dimensionless shear strain rate。

According to the experimental data obtained from threedifferent specimens，the modified JC constitutive modelexpressions，for shear band width of 800，400，and 50 gm，are as follows-(561.9246.07'341)(11.75e-3 o.14361n L%)-(658.35375.173582)(12.06e-5 0.59451n L )64321O0 1 2y/(10 SFig.5 Failure strain versus strain rate curves4垒SpringerO O 2 6 ，-S y O ) a4 ( 0 O 78 G. W ang，Y.-M .Rong(79.45138.017287)(11.75e-6，0.63571nL )3 M ultiphase model on interfacial heat transferfor water quenchingProcess control and parameters in manufacturing are cor-responding to boundary conditions in simulation.Theprecise description for boundary conditions determines theaccuracy of modeling。

The cooling method is a key factor affecting certainmaterial properties in heat treating processes.The heattransfer between workpiece and medium plays an importantrole in modeling physics.Traditionally empirical functions8-101 regressed from experimenta1 data are used asboundary conditions.It uses a simple number or curves，likeHTC，thus greatly simplifying the phenomena appearanceduring the process.The researchers[1 1-14have integratedCFD theory with process analysis and tried to do a com-prehensive modeling with workpiece and quenchant beingregarded as a whole.It goes smoothly for gas quenchingbecause of its feature of a single phase flow.However itturns out a totally different result for water quenching。

Water quenching is an unstable physica1 process withcomplex phase change of vaporization and happening fastwithin seconds.High cooling rate，large temperature gra-dient，two-phase interaction，conjugate heat transfer bringphase change and fluid-solidthe di佑culties into the mod-eling work.To overcome these dificulties，researchershave developed a water-vapor two-phase model[1 5]that isbased on Eulerian-Eulerian multiphase flow theory。

3.1 Model for water quenchingThe heat transfer in solidheat conduction equation百5ph ( r，) ，workpiece is governed by usingwhere P is density， thermal conductivity，h enthalpy，t time，T temperature，and S source term。

W al1 boiling starts when the wall temperature achieves ahigh value to initiate the activation of wal nucleation sites。

A model is used by Kurul and Podowski f161 for formu-lating wall boiling.With it，only a few parameters，e.g.，wal1 nucleation site density，bubble departure diameter，bubble detachment frequency.have to be given.The liquidwater is set as continuous fluid，and the water vaDor asdispersed phase。

The inhomogeneous particle model for interfacialtransfer between continuous water and dispersed vaDor垒Springerparticles has been chosen[1 71.For interphase momentumtransfer，the Schiller Naumann model[1 8is chosen basedon assumption that the interaction between bubbles isneglected.The drag coefficient for flow past sphericalparticles，Ca，is shown asCd (1015Re0.687)for interphase mass transfer，the mass flux can be derivedfrom heat balance as， qwqv (8)where qw and qv are the heat flux from interface to waterphase and vapor respectively，and Hv and HW are theenthalpy taken into the water and vapor due to the phasechange。

For interphase heat transfer.Ranz Marshal1 model iSused to define the heat resistance on continuous phase，water，and Zero Resistance model for vapor side。

A case study has been done with an aluminum cylindersample of 10 mm in diameter and 19 mm in length.Thecylindrical sample is placed at the center of the fluiddomajn。

3.2 Results and discussionThe simulation result is shown in the folowing figures。

Figure 6 shows the sample temperature history.Even inthis small part with a good therm al conductivity.the tem-perature difference between the hotest and coolest pointsreaches around 40。C with Biot number of the samplebeing only 0.067.The curve for the lowest temperature isfluctuant in the first 3 s.Considering that the lowest tern-perature points exist on the solid surface，it means theextremely unstable heat transfer of vaporization。

The temperature of sample and water domain changeswith time and space.The distribution at the moment oft equal to1 s is shown in Fig.7.The water temperature inmost region is below 100。C except a thin 1ayer sur-rounding the sample with a high temperature and highvolume fraction of vapor。

The transient HTC along the sample profile is dis-played in Fig.8.The curves in and BC region fluc-tuate，which may be caused by floating movement ofvapor bubbles.At the beginning，like t equal to 0.2 s，theHTC varies very fast from top c)to bottom fG 1.Aftera short period less than 0.3 s，it becomes much morestable and uniform。

Figure 9 shows HTC curve calculated using lumpedheat capacity method based on the highest temperaturecurve of sample.The HTC is low at high temperature stage，because the accumulation of a large amount of smallPrecision modeling and simulation 79Time/sFig.6 Simulated temperature history of sampleWater temperature/K708.0667.0626.0585.0544.1503.1462.1421.1380.1339.1298.1Fig.7 Temperature distribution in water at t 1 S30，000， 25，00020，00015，000≥10，000墨 5.00000 00l 0.006 0.0I1 0.0l6 0.O2l 0.026Distance/mFig.8 Calculated HTC distribution along the profile of samplebubbles separates solid and liquid，and blocks the fierceheat transfer.At middle temperature stage，HTC reachesthe highest value due to bubble boiling.Afterwards，theconvection dominates with a steady heat transfer.Theproblem is that the oeak value of calculated HTC seemslower than the experimenta1 data，and the further workneeds to be done to build more precise mode1。

2，500，2，000 1，500争芭l，000篁 5oOOTemperature/CFig.9 Calculated HTC curve dependent on sample temperatureFig.10 M esoscopic cutting process4 Discrete model for precision machining processin mesoscopic scaleModeling for man ufacturing processes，which is based onthe understanding of physical mechanism of new method-ologies，has been developed from macro-scale to micro。

Researchers need to investigate the fundamentals inmaterial behavior，microstructure evolution，and integratedmultiphysics，as well as the assumptions thought to beplausible。

Traditionally the workpiece during macro-cutting can beregarded as a continuum.The metal machining processsqueezes the workpiece with a certain depth and speed ofcutting，and elastoplastic deformation occurs along theprimary shear zone.At the same time，the slide betweenchip and workpiece generates the secondary shear zonewith high temperature an d high pressure.The strong.ther-mal interaction during the cutting process generates surfaceresidual stress as well as micro-cracks，affecting theintegrity of the workpiece surface。

From mesoscopic point of view，a workpiece is com-posed of a distribution of randomly orientated grains.Thecuting process(see Fig.10)breaks down the grains andgrain boundaries of the workpiece，and makes the chip andworkpiece become separation at the tool edge。

Different machining accuracy requires different physicalanalysis model，and traditional modeling is based on theassumption that material is a continuous medium.In the垒Springerp/aI君叠。(1旨Precision modeling and simulationthe reference plastic strain rate，and A，B，C，m，n material parameters。

For a specific material，with the given parameters，asshown in Table 1.the material constitutive model isestablished。

Another important aspect is the failure mode1.Since thedeformation of the plastic material is caused by the dislo-cations shearing.the failure model can be use of shearfailure parameters，and elastic modulus，Poissons ratio，density，thermal conductivity，specific heat capacity，etc。

The simulation and experimental results of differentcutting depths and chip shapes are shown in Fig.1 3，inwhich the chip shapes are similar to each other，thus ver-if，/ing the accuracy of the finite element mode1。

5 ConclusionsNumerical modeling，as a newly developed technique forprocess analysis，has gained a great achievement in bothacademic research and industrial applications in manufac-turing field.Physics-based modeling can enhance the accu-racy of simulation by providing precise material properties，boundary conditions，and physical models.Furthermore，bytaking advantages of the advanced equipment for testing，observing， and designing the certain characteristics ofmaterials and processes，models for manufacturing will beimproved significantly and applied to industrial processesmore widely。

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