力-熱耦合作用下不同鋪層角度CFRP銑削損傷規律分析

Abstract：The wideapplicationof carbon fiber reinforced plastic（CFRP）components in modernaerospace manufacturing field puts high demandsonthe manufacturingprocess.Especially，the temperatureincrease duringcontinuousmilling processecomes akeyfactoraffecting the performanceofcomposites，andthehigh millng temperature induces avarietyof processngdefects.Thispaper obtained the temperature variation data during theendmilling process of CFRP laminates throughexperiments.Afterdata fiting，thedata were transformed intoafunction of heatfluxdensityvarying with time.In th finiteelement analysis，a double-elipsoid moving heat source model was introduced，ndamoving heat sourcesubroutine waswritenbasedonthetime-varying functionofheatfluxdensityto more accuratelydescribethethermal efects during the millng processand simulatethechangesinthetemperaturefieldduringmilling.The Hashin failurecriterion isadoptedasthe basisoffiberandmatrix failure，andthesimulationresultsofthetemperaturefieldareinput intothethermal -forcecoupling simulation modelas the predefined fieldconditions for solvingandanalyzing by meansof sequentialthermal -force coupling，soas to establishathermal-forcecoupling simulationandanalysis modelfor miling processingof CFRP endfaces.Themodel simulationresultscan provideabasis forexploring thedamageevolution lawof CFRPmaterial under theinfluence of temperature.

Keywords：CFRP；milling；finite element analysis；moving heat source；thermo-mechanical coupling

1 Introduction

Carbon Fiber Reinforced Plastic（CFRP）stands out among various materials due to its exceptional specific strength，specific stiffness，hardness，heat resistance，and corrosion resistance，exhibiting high commercial and technical value[1]. With the application of CFRP materials，continuous milling during the manufacturing of components is inevitable[2].Due to the anisotropy and non - uniformity of CFRP materials，surface damage and other defects are prone to occur during milling，severely affecting the mechanical properties and service life of the components[3].Orthogonal cutting finite element models show that cutting speed influences the deformation extent of the fiber fracture region [4]．Theheat generatedbyfriction，plasticdeformation，and other factors during milling affects the physical properties of the material. Finite element simulation results by Han et al. indicate that CFRP exhibits a tendency for low- temperature embrittlement and high -temperature thermal softening effects[5]．Considering only mechanical or thermal factors alone is insufficient to fully describe the complex behavior of composite materials during cuting. Cheng et al. used a damage - based fracture approach to obtain the failure modes of fibers，matrix，and interfaces [6]．Isbilir et al. employed finite element models to predict various damage morphologies within and between layers [7]. Currently， there is a lack of force -heat coupling modeling for multi -tooth intermittent cutting of carbon fiber composite materials at the macro scale.

Therefore，thispaper constructsa finite element analysis model for the dynamic change of temperature field during CFRP end milling，adopts a sequential thermo - mechanical coupling analysis strategy，and further establishes a force -heat coupling simulation model for CFRP end milling. It explores the damage evolution law of CFRP materials underthe influenceof temperature at different fiber layup angles， providing strong numerical simulation support for subsequent experimental verification.

2 CFRP end face milling experiment and temperature field modeling

2.1 CFRP milling experiment

Figure 1 shows the CFRP milling experimental system.Thematerialusedisacarbon fiberlaminatemade from KH1301 prepreg （ 200mm×100mm×6mm ）， and the tool geometry parameters are listed in Table 1. Milling is performed at a spindle speed of 8000r/min ， a feed rate of 600mm/min ，and a cutting depth of 2.0 mm，with temperature measurements taken using a FLIR E54 infrared thermal imaging camera.

Fig.1Schematic diagram of the milling experimental system Table1 Tool geometric parameters

2.2 CFRP milling temperature field model

During CFRP end milling，heat is generated from the shear deformation between the tool and fibers，as well as friction on the tool’s flank face.Due to anisotropicthermalconductivity，heatdistributesina gradient，with the highest temperature zone located at the intersection of the main and secondary cutting edges. A double - elipsoid heat source model[8] is used to simulate and analyze the temperature changes during milling. The double-ellipsoid heat source model is shown in Figure 2.

Fig.2Double -ellipsoid heat source model

The double - ellipsoid heat source comprises two semi-ellipsoidalshapes，frontandback，whichcanbe expressed by the formula：

In the formula： are the shape parameters of the double -ellipsoid heat source； Q isthe power of the heat source; f₁ and f₂ are the heat distribution functions of the front and back ellipsoids，respec tively，and the sum of f₁ and f₂ is ² .based on the temperature -time dataset obtained from end milling experiments，the expression for theboundaryheat flux density q is derived through nonlinear fitting.

Usefinite element software toestablish a carbon fiber composite laminate with dimensions of 200mm× 100mm×6mm and 0^°/90^° ply orientation. The material parameters[9]are as shown in Table 2，and the modelingof the carbon fiber composite and the layering configurationare depicted in Figure 3.The mesh element type used is DC3D8，with a transient heat transfer analysis step applied，and the load is imposed asbody heat flux.By fitting the temperature data obtained from milling experiments and combining it with a heat source model，a time -varying continuous function for heat flux density distribution was established， completing the Vumatsubroutine.

Table2 Model material parameters

Fig.3Carbonfibercompositematerial modelingand delamination

3 CFRP milling force - thermal coupling simulation model

Thispaper uses the Hashin failure criterion to judgewhetherthematerialisdamagedandfailedunder complex stress conditions.the expression of the threedimensional Hashin failure criterion is as follows：

Fibertensile failure （ ε₁₁?0 ）：

Fibercompression failure （ ε_?11lt;0 ）：

Matrix tensile failure（ ε₂₂+ε₃₃?0 ）：

Matrix compression failure （ε₂₂+ε₃₃lt;0 ）：

YehDelamination failure（ ε_?33?0 ）：

R_i represents the failure factors for five types of failure modes，respectively. When R_i?1 ，damage beginsto accumulate，and the stiffnessof the carbon fiber composite material gradually decreases. The damage variables are ：

where f and represent fiberand matrix，respectively；the subscript“ Φ_tΨ^′′ and“ c ”indicate tension and compression，respectively；the subscript“ ld ”denotes interlaminar delamination.the control factor isset to1， and the damage variable d_i is expressed as a function of time t：

d_i^t=max（d_i^τ，0）（τ?t;i=ft，fc，mt，mc，ld），

When constructing the milling force - thermal coupling model，continuous shell elements were used for the material，maintaining consistent ply orientationwith the temperature field model. Material properties vary with temperature，and tool wear is neglected， treating the milling cutteras a rigid body.The meshis divided as shown in Figure 4，and the temperature field results are coupled into the model for simulation calculations.

Fig.4Coupled model meshing

4 Results and discussion

The results of the force - thermal coupling simulationare shown inFigure5.Figure5（a）shows anin creasing trend in CFRP milling temperature，with a maximum of 278.9 C occurring at the milling center. Asthe tool moves，thetemperatureinthemachined area decreases，a phenomenon caused by friction and cuttingforces，which aligns with actual observationsand validates the model’s reliability. Figures 5（b）and （c）reveal compression damage in both fibers and matrix，with less damage on the bottom surface than on the sides，and side damage intensifying with rising temperatures.

By comparing Figures 6（a）and 7（b），it can be observed that the compression damage of CFRP fibersinboth 0^° and 90^o layups increaseswith the rise in milling temperature，with the 90^° layup exhibiting a larger damage range and more severe damage extent. Thisis due to the significant differences in mechanical and thermal conductivity properties of CFRP in different layup directions. The 90^° layup is more susceptible to shear stress，leading to interlaminar separation and compression damage，and heat tends to accumulate more easily，exacerbating the damage.

Fig.5 Coupled Simulation Results

Fig.6Fiber compression damage in different layup directions

Figure 7 shows that the matrix compression damage is severe in different layup directions，and the damage spreads significantly with increasing temperature and tool movement. The reason is that as the temperature approaches the glass transition temperature of the matrix，the material softens and its compressive strength decreases. The heat introducedby the tool causesdamage in new areas. The coupled thermo - mechanical effects lead to continuous spread and exacerbation of the matrix damage.

Fig.7Different layup directions of matrix compression damage

5 Conclusion

This paper establishes a finite element model for CFRP milling，simulating temperature-induced damage and analyzing the evolution of damage in different layups. The conclusions are as follows：

（1）The milling temperature increases，withthe highest temperature along the path and a droplet - shaped temperature gradient around it. The variation pattern is consistent with actual machining，confirming thereliability of the simulation.

（2）Fiber damage in both 0^° and 90^o layups worsens with increasing temperature，with more severe damage in the 90^° layup.

（3）Matrix damage in both 0^° and 90^° layups spreads with rising temperature，with the coupled thermal -mechanical effects leading to increased damage.

References

[1]XING LY，LI YF，CHENXB.The role and status of advanced composite materials in the development of aviation equipment[J].Acta MateriaeCompositaeSinica，2022，39 （9）：4179-4186.

[2]ISTVáNDP，NORBERTG，CSONGORP，et al.A critical review of the drilling of CFRP composites：Burr formation，characterisation and challenges[J].Composites Part B-Engineering，2O21，223： 17.

[3]LIU Y，PAN ZT， ZHOU HG，et al. Research progress and prospects of drilling heat in fiber-reinforced compositematerials[J].Acta Materiae Compositae Sinica，2023，40（8）：4416-4439.

[4]SU Y.Effect of the cutting speed on the cutting mechanism in machiningCFRP[J]. Composite Structures，2019，220：662-676.

[5]HANL，ZHANG JJ，LIU Y，et al.Finite element investigation on pretreatment temperature-dependent orthogonal cutting of unidirectional CFRP[J]. Composite Structures，2021，278：16.

[6] CHENG H，GAO J，KAFKA L O，et al. A micro - scale cutting model for UD CFRP composites with thermo-mechanical coupling [J].Composites Science and Technology，2017，153：18-31.

[7]ISBILIRO，GHASSEMIEHE.Finite element analysis of drilling of carbon fiber reinforced composites [J]．Applied Composite Materials，2012，19 （3-4）：637-656.

[8]LI HG，SONG XD.Effects of different heat source models on the welding temperature field of Q345medium-thick plate[J].Hot Working Technology，2017，46（23）：205-209.

[9]SAGARK，SUHASINI G，REDOUANE Z. Coupled thermo- mechanical modeling of drilling of multi-directional polymer matrix compositelaminates[J].CompositesPartA-AppliedScience And Manufacturing，2022，156：14.