Influences of Residual Stress Induced by Cutting on Subsequent ScratchUsing Smooth Particle Hydrodynamic (SPH)

Hongwei Zhao1,+, Peng Zhang1, Hongda Liu1, Chuang Liu1, Da Tong1,Lin Zhang1, Luquan Ren2, Xiaolong Dong1 and Shanshan Liang1

1College of Mechanical Science and Engineering, Jilin University, Changchun 130025, China2Key Laboratory of Bionic Engineering Ministry of Education, Jilin University, Changchun 130025, China

A smooth particle hydrodynamic (SPH)-based scratch model was proposed to study the influences of residual stress induced by the firstcutting on subsequent scratch. In this paper, comparisons were made between the results of only scratching the specimen and those of subsequentscratching the specimen after cutting under different scratch depths. Chip formation, scratching forces and residual stress in scratching-inducedsubsurface were recorded on oxygen-free high-conductivity copper (OFHC) during the simulations. Simulation results indicated that the firstcutting produced work hardening in the subsurface of the specimen and the increased hardness led to a thinner and more curled chip. Meanwhile,the minimum chip thickness also decreased because of residual stress induced by cutting. Moreover, it also resulted in high resistance during thesubsequent scratch so that the scratched surface presented flat. However, the material on both the sides of the groove bulged in Scratch model.Therefore, scratch after cutting is beneficial to obtain scratched surface with high quality. [doi:10.2320/matertrans.M2014078]

(Received March 3, 2014; Accepted May 9, 2014; Published August 1, 2014)

Keywords: smooth particle hydrodynamic (SPH), micro-scratch, residual stress, work hardening

1. Introduction

The service quality of a mechanical component such asits fatigue life, tribological properties, and distortion aresignificantly affected by the surface integrity of the sub-surface generated by the machining process.1­3) Residualstress is a major part of the mechanical state whichdetermines surface integrity.4,5) Residual stress is consid-erable important in metal machining because they can affectmachining condition and creep or cracking. As opticaldevices have put forward higher requirements for high-quality surfaces and micro-machining process is complex, theinfluence of residual stress on micro-machining process isworth studying.

Nowadays, many studies have been carried out toinvestigate the surface integrity of the machined layer.6­9)

Liu et al. experimentally investigated mechanical residualstress in a machined surface.10) The results showed that foundthat the length of the shear plane in chip formation correlatedwith subsurface deformation and residual stress formation.Khabeery et al. studied the effects of cutting speed, feedrate and depth of cut on residual stress distribution in themachined surface region using an electrolytic etching-deflection technique.11) It’s found that the residual stresswas low tensile at the machined surface and it increased withan increase in depth beneath the surface, then decreased witha further increase in depth, eventually became vanishinglysmall.

In addition to the experimental studies on machining,simulations of metal machining have been widely used forperforming stress analysis.12­14) Most of the machiningnumerical simulations are carried out by finite elementmethods (FEM). However, it may suffer from excessivemesh distortion, which may cause the simulation of firstscratch to stop. To overcome this problem, the SPH method isused.

Limido et al. simulated high speed cutting using the SPHmethod and compared the results of the SPH model withexperimental data.15) They found that the SPH model wasable to predict continuous and shear localized chips and allthe steps of its formation. Moreover, the simulation of cuttingusing the SPH method was discussed by Espinosa.16) Resultsshowed that the simulation data reached an agreement withthe experimental data. Villumsen et al. performed a 3Dorthogonal cutting simulation of Al 6082-T6 alloy using theSPH method.17) It’s found that the cutting force wasunderestimated by 8.4% and the thrust force was under-estimated by 12% when compared with the simulated forcefrom experiments.

Compared with the achievements in studies of scratchmechanism and machining factors on residual stress, fewliteratures have studied the influence of residual stressesinduced by cutting on mechanism of sequential micro-scratching. It is of great significance for getting qualifiedsurface quality in finish machining. Thus, in this paper, amesh-less method called smooth particle hydrodynamic(SPH), is used to study the effects of residual stresses onsequential scratch.

2. MD Simulation

2.1 SPH methodSPH is a mesh-free numerical method based on Lagrangian

method, where a set of particles is used to represent acontinuum. Hydro-dynamical parameters such as pressure,velocity, and density may then be tracked at these finiteparticles. Therefore, the specimen can be discretized with acloud of nodes using this method. The nodal connectivity isdefined by a circular domain called support domain where theneighboring nodes contribute to the field value approxima-tion according to equation.

2.2 Simulation modelThe SPH model consists of two parts, an SPH specimen+Corresponding author, E-mail: hwzhao@jlu.edu.cn

Materials Transactions, Vol. 55, No. 9 (2014) pp. 1440 to 1444©2014 The Japan Institute of Metals and Materials

and a diamond tool (FEM elements), as shown in Fig. 1.Oxygen-free high-conductivity copper (OFHC) is chosen asthe specimen, assuming that it is homogenous and isotropic.The size of the specimen is 1.4 µm © 1µm © 0.9 µm in X, Yand Z directions, respectively. The whole 6 degrees offreedom of specimen’s bottom side and right side are fixed.The specimen’s front side and back side are fixed throughdefining two symmetry planes. In order to reduce computa-tional time and memory requirements, the cutting andscratching speed are set at 100m/s along X direction.Considering the accuracy of simulation, the diameter of theSPH particle is set to 20 nm.

The scratching tip used in the current model has aconfiguration of cone shape with a tip angle of 30 degrees,and the radius of the edge is 100 nm. The cutting tool rakeangle ¡ = 20°, the cutting tool clearance angle ¢ = 7°, andthe cutting tool edge radius is 200 nm. Due to the evidentlyhigher hardness of diamond than oxygen-free high-conduc-tivity copper, the scratching tip and cutting tool are bothtreated as a rigid body.

To study the effect of residual stress on mechanismof micro-scratch, two scratch models are founded withSPH in the framework of LS-DYNA hydrodynamicsoftware.

Figure 2 shows the simulation procedure of two scratchtests. For convenience, the simulation models shown inFigs. 2(a) and 2(b) are named “Cut-scratch model” and“Scratch model”, respectively. In Cut-scratch model, at firstthe cutting tool cuts the specimen along X direction, then thescratch tip scratches the specimen. In Scratch model, thescratch tip scratches the specimen directly.

The Johnson and Cook constitutive model is used todescribe the flow stress of material by considering strain,strain rate and temperature.18) In this paper, it is expressed asfollows:

· ¼ ½Aþ Bð¾pÞn� 1þ C ln_¾p

_¾o

� �� �1� T � Troom

Tmelt � Troom

� �m� �

ð1ÞThe material parameters are given in Table 1.19)

3. Simulation Results and Discussion

3.1 Analysis of stress distribution during cuttingIn order to investigate the residual stress induced by

cutting, a particle in the subsurface is selected. The particle’sstress variations during cutting process are shown in Fig. 3.As the cutting tool approaches the particle, the lattice distortsand dislocations take place under the cutting force. Therefore,the particle’s stresses along X and Y direction are bothcompressive stress. With the cutting tool leaving the particle,the compressive stress on the particle releases. Becauseof irreversible plastic work consumption, the particle stillpresents small compressive stress.

Fig. 1 Micro-scratch model: (a) schematic diagram, (b) micro-scratchmodel in LS-DYNA, (c) subsequent micro-scratch after cutting model inLS-DYNA.

Fig. 2 (a1)­(a2) Schematic of Scratch model, (b1)­(b2) Schematic of Cut-scratch model.

Table 1 Material parameters of OFHC.

Parameter Value

Elastic modulus (GPa) 124

Shear modulus (GPa) 47.7

Poisson’s ratio 0.34

A (initial yield stress in MPa) 90

B (hardening modulus in MPa) 292

N (work hardening exponent) 0.31

C (strain rate dependency coefficient in MPa) 0.025

m (thermal softening coefficient) 1.09

Fig. 3 The variation of particle’s stress along X and Y direction duringcutting process.

Influences of Residual Stress Induced by Cutting on Subsequent Scratch Using Smooth Particle Hydrodynamic (SPH) 1441

3.2 Chip formationThe local top and cross-section views of the specimen’s

surface in Cut-scratch model and Scratch model underdifferent scratch depths are shown in Fig. 4. In oursimulations, the scratch depths are 50, 100 and 150 nm,respectively. From the front views, it can be seen clearly thatthe maximum stress areas center the groove in Scratch model,but in Cut-scratch model the maximum stress areas not onlycenter the groove but also distribute in the subsurface of thespecimen. Meanwhile, the maximum stress areas that centerthe groove in Scratch model are larger than those in Cut-scratch model. Moreover, compared with Scratch model, thescratching chip from Cut-scratch model curls more severely.From the back views, the material on both sides of the groovebulges in Scratch model, especially when at the scratch depthof 150 nm. However, the corresponding surface presents flatin Cut-scratch model. The reason is likely that the first cuttingproduces work hardening in the subsurface of the specimen.It is consistent with the previous conclusion.20) Therefore,because of high resistance from the hardened surface in Cut-scratch model, the material flows towards both sides in thesubsurface. However, the material bulges from surface due tothe extrusion force suffered from the scratch tip in Scratchmodel. The effect of increased hardness on subsurface of thespecimen also leads to the maximum stress areas movetowards both sides.

Figure 5 shows the chip formation process of Cut-scratchmodel and Scratch model under different scratch depths.From Fig. 5, the Von Mises stress distribution around thescratch tip varies greatly from Cut-scratch model to Scratchmodel. In Scratch model, the maximum stress area growsin the shear plane and extends to the free surface of thespecimen. It is consistent with conventional cutting mechan-ism.21,22) However, in Cut-scratch model, the maximumstress area partly extends to the free surface of specimenalong the shear plane, and partly extends along the scratchingdirection under the subsurface of the specimen. In addition, asmall amount of scratching chip forms in Cut-scratch model,while there forms no scratching chip in Scratch model underthe scratch depth of 50 nm. So the residual stress can decreaseminimum chip thickness. It’s also found that the real negative

shear angle of Cut-scratch model becomes larger. Under thestronger extrusion of the scratch tip, the material gathers andflows through the scratch tip’s edge so that chips form. Insuch a case, chips of Cut-scratch model are thinner and easierto curl.

3.3 Residual strain and stressThe equivalent plastic strain in the two simulations is

shown in Fig. 6. The equivalent plastic strain on themachined surface goes down from 0.4 to 0.25. Thus thedegree of strain hardening near the machined surface fromScratch model is larger than that from Cut-scratch model.From Fig. 6, the equivalent plastic strain from Scratch modelfirst approaches to zero. Therefore, the affected layer isdeeper in Cut-scratch model. It is the result of workhardening.

3.4 Scratching forceThe variations of scratching force Ft and thrust force Fn in

two simulations at scratch depth of 100 nm are shown inFig. 7. Compared with the scratch without cutting, in thescratch after cutting, the scratching force becomes smaller.The surface residual stress presents compressive stress alongscratching direction after cutting, and the compressive stresscontributes to the material’s shear deformation during thesubsequent scratch. Therefore, the material removal in thesubsequent scratch requires smaller scratching force. Follow-ing the same law, the thrust force in the scratch after cuttingrequires smaller thrust force. The frictional coefficient ® canbe readily calculated from the scratching force Ft as well asthe thrust force Fn during scratch.23)

® ¼ Ft=Fn ð2ÞThe calculated result of ® is 0.986 in Scratch model, but

0.885 in Cut-scratch model. Affected by residual compres-sive stress, the frictional coefficient in Cut-scratch becomeslower.

4. Conclusion

Using the SPH method, the influences of residual stress

Fig. 4 Local top and cross-section views of scratched surface with scratch depths equaling to 50, 100 and 150 nm, respectively:(a1)­(a3) scratching the specimen’s surface without cutting, (b1)­(b3) scratching the specimen’s surface after cutting.

H. Zhao et al.1442

induced by the first cutting on subsequent scratch wereinvestigated. The following conclusions can be drawn:(1) The first cutting produces work hardening in the

subsurface of the specimen and this phenomenonresults in a thinner and more curled chip, anddecreasing minimum chip thickness.

(2) Due to high resistance from the hardened surface, thescratched surface presents flat after scratch. However, inthe scratch without cutting, the material on both sides ofthe groove bulges from surface.

(3) Compared with the scratch without cutting, in thescratch after cutting, the scratching force, the thrustforce and the frictional coefficient all become smaller.

Acknowledgement

This research is funded by the National Natural ScienceFoundation of China (Grant No. 50905073, 51275198),Special Projects for Development of National MajorScientific Instruments and Equipments (Grant No.2012YQ030075), National Hi-tech Research and Develop-ment Program of China (863 Program) (Grant

Fig. 6 Comparison of equivalent plastic strains along depth direction intwo simulations.

Fig. 5 Section views of residual Von Mises stress distribution during scratching process with scratch depths equaling to 50, 100 and150 nm, respectively: (a1)­(a3) scratching the specimen’s surface without cutting, (b1)­(b3) scratching the specimen’s surface aftercutting.

Fig. 7 Comparison of cutting force and thrust force during scratchingprocess in two simulations at scratch depth of 100 nm.

Influences of Residual Stress Induced by Cutting on Subsequent Scratch Using Smooth Particle Hydrodynamic (SPH) 1443

No. 2012AA041206), and Key Projects of Science andTechnology Development Plan of Jilin Province (GrantNo. 20110307), Program for New Century Excellent Talentsin University of Ministry of Education of China (NCET-12-0238), Research Fund for the Docoral Program of HigherEducation of China (20130061110026).

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