纖維方向對CFRP切削過程應力狀態影響規律研究

摘要：碳纖維增強樹脂基復合材料（CFRP）作為典型的難加工材料，實際加工中產生的高切削力和高切削溫度使得刀具磨損相較于切削傳統金屬材料更為劇烈，纖維切削過程中剪切斷裂不完全，從而形成未切斷纖維、毛刺等表面缺陷。為了分析切削不同纖維角度的CFRP時的切削力及刀具磨損區域，基于三維Hashin準則，采用有限元軟件與VUMAT子程序建立了CFRP三維正交切削模型。仿真結果表明在CFRP切削過程中，各纖維方向下的高應力區域都出現在切削刃與工件接觸區域，其主要集中在與切削刃接觸的第一變形區。切削 90^°"纖維時Mi-ses應力最大，切削 0^°"纖維時的Mises應力最小。切削 0^°"和 135^°"纖維時，刀具的前刀面和后刀面容易發生磨損，切削 45^°"和 90^°"纖維時，刀具的前刀面容易發生磨損。

關鍵詞：CFRP；三維Hashin準則；纖維方向；有限元

Abstract：Carbon fiber reinforced polymer（CFRP）composites，asatypical dificult-to-machine material，exhibit high cutting forces and temperatures during actual machining，leading to more severe tol wearcompared to traditional metal materials.The shearfracture during fibercuting is incomplete，resulting insurface defects such asunclosed fibersandurrs. To analyzethecutting forces andtoolwearareas when cutting CFRPwith diffrent fiberangles，athree-dimensionalorthogonalcuting model of CFRPwasestablished using finite element softwareandthe VUMAT subroutine，basedon the three-dimensional Hashin criterion.Simulationresults show thatduringthe cutting process of CFRP，high-stressareas appearintheregion where thecuting edge contacts the workpiece foreach fiberorientation，primarilyconcentrated in he firstdeformation zone incontact withthecuttingedge.The Misesstress is highest whencuting the9O°fibersand lowest when cutting the 0^°"fibers.When cutting the 0^°"and 135^°"fibers，the tool is prone to wear on both the rake and flank faces， while when cutting the 45^°"and 90^o"fibers，the tool's rake face is more likely to experience wear.

Keywords：CFRP，three-dimensional hashin criterion，fiber orientation，finiteelement

1 Introduction

Carbon fiber reinforced polymer （CFRP） composites possess numerous advantages such as high specific strength and modulus， excellent corrosion resistance， and good fatigue resistance，and are widely used in fields like aerospace，marine，and shipbuilding ?1-2? ： Although most composite materials are processed using near-net shaping methods，milling operations are often necessary to meet the dimensional and assembly requirements of composite parts ?3-5? . CFRP， as a typical difficult - to - machine material，is usually processed by dry cutting in practical production due to its certain waterabsorption and moisture retention.However，its poor thermal conductivity leads to high cutting temperatures in the cutting zone.Consequently，the high cutting forces and temperatures experienced during machining cause more severe tool wear compared to traditional metallic materials. Excessive tool wear can result in incomplete shear fracture during fiber cutting，leading to surface defects like uncut fibers and burrs [6].

Currently，finite element simulationhasgradually emerged as a superior method for analyzing the cutting process of composite materials. Zhang [7] et al. established a three - dimensional macro orthogonal cutting simulation to analyze the failure modes of materials milled atdifferent fiberangles.The simulationrevealed that during cutting，the fibers primarily undergo shear failure and brittle fracture. Shear failure mainly propagatesalong the cuttingdirection，with 90^°"CFRP exhibitingthe largest shear failure zone and 135^°"CFRP showing the smallest. Prakash [8] et al. utilized an established three-dimensional milling model of composites to analyze the influence of feed rate and spindle speed on milling forces and chip morphology. The resultsindicated that at lower cuting speeds，delamination and fiber pull - out are the predominant failure modes.

Basedon finiteelement simulation softwareand the VUMAT subroutine，thispaper establishes a three-dimensional orthogonal cutting finite elementmodel of

CFRP，analyzes the cutting forces and tool wear areas whencutting CFRPwithdifferent fiberangles.Thisresearch provides certain reference value for process optimization and tool life during the milling of CFRP.

2 Finite element theoretical analysis of CFRP cutting

2. 1 CFRPFailureCriteria

The initiation criterion for CFRP damage adopts the three-dimensional Hashin criteria[9]，and the expressions for the four different failure modes areas follows ：

In the above equations， σ_ij（i，j=1，2，3） represents the effective stress tensor， X_C"and X_T"denote thetensile strength and axial compressive strength of the unidirectional composite laminate along the fiber direction，respectively，while Y_T"and Y_c"represent the transverse tensile strengthand transverse compressive strength，respectively. S_ij"signifies the shear strength in the""plane. α isthe shear failure coefficient，used to determine the degree of influence of shear stress on fibertensilefailure，witl"₁0?α?1 ： F is the failure criterion value for the compositematerial；when thevalue of F is equal to or greater than 1，it indicates material failure.

2.2 CFRP Damage Evolution Model

Aftercompositesmeet thefailurecriteria，continuedloading leads to a decrease in the material’ s stiffness coefficients. The reduction in stiffness coefficients iscontrolled by damage variables.When the stiffness of the material model decreases，the damage exhibitslo calization characteristics as the energy dissipated in the mesh elements reduces with refinement. At this point， the energy dissipated in an element can be expressed as [10]

In the equation， G_I"represents the fracture energy for failure mode I，U_eq^f"and ε_eq^f"are the equivalent peak stressand equivalent failure strain，respectively，and I_c"isthecharacteristic length of theelement.Thecharacteristiclengthof theelementisthecubicroot of thevolume of the solid element，and its value depends on the mesh size during meshing.

Theevolution of the damage variable for each failure mode I can be expressed as ：

mt ，mc

In the equation， d_I"represents the damage conditionof the fiberormatrixunder failure mode I .When the damagevalue of either the fiber or the matrix reaches1，it indicates that the material has completely failed，thereby reducing its load -bearing capacity. δ_I，eq^f"is the equivalent damage displacement correspondingto thefailure modeatthe final failure ofCFRP，and （24號 δ_I，eq^υ"is the equivalent displacement when CFRP just meets the failure criteria. ft ，""， m_?"，mc denote fiber tension，fiber compression，matrix tension，and matrix compression，respectively.

3 CFRP Cutting Process Finite Element Analysis

To analyze the forces acting on the cutting edge of the tool during the CFRP cutting process，a simplified model of a single cutting edge is selected for establishment.The model of the tool cutting edge and the CFRP workpieceis created in thePartmoduleof finite element simulation software. The CFRP cutting model and the layerthickness of the workpiece are shown in Figure 1. In the Property module，material parameters are assigned to the CFRP as shownin Table1.

Fig.1CFRP Cutting Model and Workpiece Layer Thickness

To analyze the stress state during the cutting process of CFRP with four fiber orientations in detail， fourdirectional CFRPcutting modelswere established. Finite element simulation was used to calculate and output the Mises stress nephograms. By selecting the stress state information of the cutting force at the same time， the tool wear location and tool wear form were analyzed through the Misesstress state of thematerial. TheMises stress state and nephograms for each fiber orientation are shown in Figure 2.

Table1CFRPMaterialParameters

Fig.2StressStates ofCFRPin VariousFiber Orientations

FromFigures2（a）to2（d），itcanbeobserved that high - stress areas appear in the region where the cuttingedgecontacts theworkpiece for each fiber orientation，primarilyconcentrated in the first deformation zone in contact with the cutting edge. This is because during the cutting process， the cutting edge's rake face exerts extrusion and friction against the chip，significantly increasing the stress in the contact area，which makes the tool prone to wear on the rake face.

In the 0^°"and 135^°"fiber orientations，both the first and third deformation zones exhibit high-stress states. In these cases，the tool is susceptible to wear on both therake and flank faces，while the surface qualityof the machined workpiece is lower，characterized by unevenness and partially uncut fibers with bending deformation.

When cutting the 45^°"and 90^o"fiber orientations， extrusion and friction between the chip and the tool's rakefacelead to high-stressstatesin the first deformation zone，making the tool’s rake face prone to wear. During the cutting process，the 45^°"fibersbend upwards to form chips under the tool's pushing action without significant friction against the flank face，resulting in minimal flank wear. The 90^o"fibers，subjected to shearing bythe tool，undergo minimal bendingdeformation with little fiber springback，thus causing minimal friction andwear on the flank face.

4 Conclusion

Based on the three-dimensional Hashin criterion， thispaper establishesa three-dimensional orthogonal cutting model of CFRP using finite element simulation software and the VUMAT subroutine，and analyzes the cutting forces and tool wear areas when cutting CFRP with different fiber angles. The conclusions are as follows ：

（1）During the cutting process of CFRP，high - stress areas appear in the region where the cutting edge contacts the workpiece for each fiber orientation，primarilyconcentrated in the first deformation zone in contact with the cutting edge.

（2）When cutting the 0^°"and 135^°"fibers，the tool isprone to wear on both the rakeand flank faces. When cutting the 45^°"and 90^°"fibers，the tool‘srake face is more likely to experience wear.

（3）The Mises stress is highest when cutting the 90^o"fibers and lowest when cutting the 0^°"fibers.

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