Material Testing and Chip Formation Simulation for ... - Science Direct

Available online at www.sciencedirect.com

ScienceDirect Procedia CIRP 58 (2017) 181 – 186

16th CIRP Conference on Modelling of Machining Operations

Material testing and chip formation simulation for different heat treated workpieces of 51CrV4 steel A. Zabela*, T. Röddera, M. Tiffea a

Institute of Machining Technology, TU Dortmund University, Baroper Straße 303, 44227 Dortmund, Germany

* Corresponding author. Tel.: +49-231-755-2708; fax: +49-755-5141. E-mail address: [email protected]

Abstract The heat treatment has a major impact on the mechanical properties of steel alloys and therefore on the condition of a machining processes. In this paper, the low alloy steel 51CrV4 with different heat treatments is investigated in terms of its mechanical properties under high dynamic conditions using a Split Hopkinson Pressure Bar (SHPB) and by means of orthogonal cutting tests. The latter provide a detailed insight in the ongoing processes during chip formation by analyzing the present microstructure of the generated chips. Furthermore, the obtained data from the SHPB tests is used as an input for material models applied for the simulation of chip formation with the Finite-Element-Method. The results reveal fundamental differences in the chip formation mechanisms between the differently heat treated workpiece materials. 2017The The Authors. Published by Elsevier B.V. ©©2017 Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license Peer-review under responsibility of the scientific committee of The 16th CIRP Conference on Modelling of Machining Operations, in the (http://creativecommons.org/licenses/by-nc-nd/4.0/). Conference Chairs J.C. Outeiro and Prof. Poulachon. person of the Peer-review under responsibility of theProf. scientifi c committee of The 16thG. CIRP Conference on Modelling of Machining Operations Keywords: Machining; Split Hopkinson Pressure Bar (SHPB); Chip formation simulation; Finite-Element-Method (FEM)

1. Introduction Since Finite-Element simulations of chip formation do not just end in itself but can be used for prediction of component states like residual stresses and fatigue strength proper input data is needed. One major prerequisite for such predictions is the correct calculation of process forces, temperatures and consequently also the chip’s shapes. The material behaviour, in terms of flow stress models depending on the plastic deformation, the deformation rate and the temperature is crucial for the quality of the simulation results. In cutting these factors reach very high values and have to be properly addressed by the parameters of the applied flow stress models. The Johnson-Cook model is well established for the simulation of machining operations and is used by many researchers [1-3]. In addition to the original formulation several modifications were developed, e.g. to include the hardness [4, 5], recrystallization [6] or a stress state effect on the flow stress [7]. In order to identify adequate model parameters material characterization tests have to be carried out, but in contrast to other manufacturing processes like forming, where comparatively low strain rates and small temperature gradients

are present such experiments and the measurement are very difficult. In order to capture the relevant effects at conditions at least close to those in cutting, the Split Hopkinson Pressure Bar is commonly applied [8, 9]. In this investigation the low alloy steel 51CrV4 with two different heat treatments is analyzed in a Split Hopkinson Pressure Bar test. The obtained data is used for fitting of constitutive flow stress model parameters which are applied in finite element simulations of chip formation. 2. SHPB design and material testing For material characterization and the determination of constitutive material model parameters for cutting simulations a Split Hopkinson Pressure Bar was designed and installed at the Institute of Machining Technology of TU Dortmund University. The setup can be seen in Fig. 1. The SHPB has an overall length of 8 m including the tube, the incident bar and the transmission bar as well as devices like a compressed air vessel and a momentum trap to slow down the moving transmission bar. The air is released by a magnetic valve and accelerates the projectile in the tube. The projectile, the

2212-8271 © 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of The 16th CIRP Conference on Modelling of Machining Operations doi:10.1016/j.procir.2017.03.218

182

A. Zabel et al. / Procedia CIRP 58 (2017) 181 – 186

incident bar and the transmission bar are made of AISI H11 steel with a diameter of dbar = 14 mm. The length of the two bars is lbar = 1.5 m which yields in a length-to-diameter-ratio of lbar/dbar > 100 ensuring the assumption of a one-dimensional propagation of elastic waves within the bar. In order to test materials like high strength steels or nickel- and titanium-based alloys, ceramik plates are adapted at the interfaces where the metarial sample is located to prevent plastic deformation of the two bars. The ceramic plates have a diameter of dcera = 15.85 mm to match the mechanical impedance J of the bars which can be calculated as J = ρcA, whereas ρ is the density, c is the sonic velocity and A is the cross section. Sleeves made of polyethylene with a high impact strength are used to hold the ceramic plates in place. Furthermore, the SHPB is equipped with an induction heating furnace. A high frequency converter with a power of P = 2 kW is attached to a double coil inductor which surrounds the sample and the caremic plates. The heating of the sample is PID-controlled and the current sample temperature is measured by an infrared pyrometer in order set certain testing temperatures. All in all, sample temperatures up to Tspec = 750°C can be achieved with this setup. The measurement of the elastic wave in the incident and the transmission bar is carried out by using strain gauges which are arranged in a bridge circuit. The signal is captured with a sample frequency of fS = 1 MHz by the transient recorder HBM GEN3i.

Fig. 1: SHPB setup with induction heating

For this investigation material samples of low alloy steel 51CrV4 in a ferritic-perlitic state with a hardness of 250 HV and in a martensitic state with a hardness of 650 HV are used. The achievable strain-rates are directly influenced by the dimension of the sample. Therefore, a cylindrical shape of the size Ø3 mm x 3 mm is chosen. With this configuration maximum strains of φ ≈ 0.4 can be achieved. In order to provide good contact conditions and to reduce notch effects, the samples are ground at their interface surfaces, leading to an elaborate preparation of the samples and need for an intelligent

design of experiments to reduce the overall effort. Therefore, a latin hypercube experimental design is setup, including a total number of experiments of twelve, where the temperature Tspec and the pressure p are varried in the parameter ranges of Tspec = [20, 170 - 750]°C and p = [1 - 3.5] bar. The results from the experiments are later used for the fitting of constitutive material model parameters based on statistical methods. Due to the variation of the parameters on multiple levels also nonlinear influences of parameters and their interactions can be captured by the application of DACE-modeling [10]. Therefore, the adjusted temperature, the measured strain and the strain-rate are used as input parameters and the measured flow stress is included as the objective. Eventually, a functional relationship between the parameters and the flow stress is obtained. 3. Modelling of flow stress and fitting of constitutive model parameters The obtained models describing the flow stress of the ferritic-pearlitic and the martensitic steel are illustrated in Fig. 2 for a strain of φ = 0.2 as functions of strain-rate and temperature. It can be seen, that the achieved strain-rates are ߮ሶ ≈ 8000 1/s for the softer material and ߮ሶ ≈ 6500 1/s for the harder material. This difference of the latter can be explained by the higher strength of the material resulting in a higher resistance against deformation. Both response surfaces reveal a decrease of the flow stress with rising temperatures due to thermal activation. The softer material shows a decrease of the flow stress from σy ≈ 1600 MPa at room temperature to σy ≈ 900 MPa at T = 600 - 800 °C, where a plateau can be detected. The decrease of flow stress is even stronger for the harder material. The flow stress declines from σy ≈ 3100 MPa at room temperature to σy ≈ 1100 MPa at T = 750°C. The influence of the strain-rate is rather small, but more pronounced in case of the softer material. Increasing the strainrate leads to higher flow stresses because the faster movements of dislocations need a higher driving force in terms of stress fields. Although, the strain-rate does not show a high influence in the observed interval, the flow stress reveals a big difference to quasi-static compression tests at a strain-rate of ߮ሶ ≈ 0.0006 1/s where the corresponding flow stresses at room temperature are σy = 1100 MPa (250 HV) and σy = 2700 MPa (650 HV).

183

A. Zabel et al. / Procedia CIRP 58 (2017) 181 – 186

illustrated space in Fig. 2 as well as the extrapolation. It can be seen, that due to the formulation used, the flow stress decreases to zero at the chosen melting temperature of Tm = 1500°C. Furthermore, the gradient of the flow stress is high in the high temperature regime for the 250 HV steel while the harder material reveals a high gradient in the low temperature regime. In both cases the impact of the stain-rate can be considered as being low. Table 1. Johnson-Cook flow stress model parameters for 51CrV4 steel Parameter

Material testing

250 HV

650 HV

A

Compression test

666 MPa

1914 MPa

B

Compression test

662 MPa

2438 MPa

n

Compression test

0.269

0.436

C

SHPB test

0.0228

0.0102

m

SHPB test

1.1468

0.6491

߮Ͳሶ

-

0.0006 1/s

0.0006 1/s

Tr

-

20°C

20°C

Tm

-

1500°C

1500°C

Fig. 2: DACE-models of the flow stress for 51CrV4

The temperature and strain-rate ranges of the measured flow stresses in the figure shown above are not sufficient to be used in a Finite-Element based chip formation simulation directly. An extrapolation beyond the observed ranges is required for both parameters. This can be obtained by the usage of well established flow stress models like the Johnson-Cook-model (JC-model) [11]. In this model the influences of the strain φ, strain-rate ߮ሶ and temperature T are modeled separately and the formula reads

Vy



§ § M · · § § T  Tr A  B ˜ M ˜ ¨¨1  C ˜ ln ¨¨ ¸¸ ¸¸ ˜ ¨1  ¨¨ © M0 ¹ ¹ ¨© © Tm  Tr © n



· ¸¸ ¹

m

· ¸ (1) ¸ ¹

The first term describes the work hardening due to plastic deformation. The second and the third term represent the viscous hardening due to increasing deformation rates and the thermal softening, respectively. The influence of the strain-rate is referred to the reference strain-rate ߮଴ሶ while the influence of the temperature is described in the space between the reference temperature Tr and the melting temperature of the material Tm. The parameters A, B, n, C and m are material dependent and need to be fitted to the measured data. Due to the separately described influences of strain, strain-rate and temperature it is sufficient to identify the model parameters in a sequential way. In this investigation the parameters of the work hardening term A, B and n are fitted to conventional compression tests at a strain-rate of ߮଴ሶ = 0.0006 1/s. Afterwards, the parameters C and m are fitted to the measured flow stresses from the SHPBtests. The obtained parameters of the flow stress model are summarized in Table 1. This process enables the calculation of flow stresses for higher strain-rates and temperatures as those used in the SHPB tests. The calculated flow stresses are illustrated in Fig. 3. This figure further shows the area that is used for the parameter fitting which corresponds to the

Fig. 3: JC-flow stress for 51CrV4 over strain-rate and temperature

4. Simulation of chip formation The obtained flow stress models are used for twodimensional Finite-Element simulations of chip formation under consideration of a plane strain deformation and thermomechanical coupling. The engagement situation and the process condition are shown in Fig. 4. With respect to the machining of hardened steel, a chamfered cutting wedge is chosen for both materials. The cutting speed and the uncut chip thickness are set to vc = 180 m/min or h = 0.17 mm, respectively. The material behavior was considered as elastoplastic and the contact condition between the workpiece and the tool is implemented by applying a Coulomb-friction model

184

A. Zabel et al. / Procedia CIRP 58 (2017) 181 – 186

with µ = 0.1. The cutting wedge is a non-deformable rigid body. Simulations are carried out by three different software packages. The first software is DEFORM-2D V11.1 by SFTC, which is widely used for chip formation simulation due to a good accessibility of simulation parameters. Furthermore, it involves an automatic remeshing routine that is necessary because of a high distortion of the Finite-Element mesh during the simulation. Here, bi-linear brick elements with a size of ~6.8 µm in the primary shear zone are used. The second software is AdvantEdge (AE) V 7.3 by Third Waves Systems, which is also a special purpose software for the simulation of machining processes. The modeling of processes is quickly feasible but the manipulation of simulation parameters is more limited than in DEFORM. The general purpose FE-software Abaqus/CAE V 6.14 by Dassault Systems is applied as the third system, offering implicit and explicit solving procedures for Finite-Element problems. The built-in remeshing capabilities are not sufficient for chip formation simulations, therefore different remeshing and data mapping algorithms were implemented. Furthermore, the complete infrastructure for handling the time steps of a chip formation simulation are programmed using the Python API of Abaqus. The used remeshing procedure is based on a superconvergent node patch recovery method by Zienkiewicz and Zhu [12, 13]. The elements used here are bi-linear bricks with a size of ~20 µm. Due to continuous remeshing in all three simulation systems no separation criteria for the chip formation is needed.

Fig. 4: Process setup for the FE-simulation

5. Experimental investigation of chip formation In order to validate the simulations, orthogonal cutting experiments were carried out. Therefore, a fundamental chip formation machine was designed and realized at the Institute of Machining Technology (Fig. 5). The machine provides three axes which can be used for cutting and feed motion simultaneously. The horizontal table in x-direction offers a maximum stroke of 900 mm. The acceleration of the linear direct drives with 30 m/s² is high enough to reach a maximum speed of 180 m/min. A cross table in the y-z-plane can be moved with a maximum speed of 15 m/min over a length of 200 mm in y-direction and 95 mm in z-direction. Therefore, the horizontal table realizes the cutting motion and the cross table positioning of the tool.

Fig. 5: Fundamental chip formation machine

For the orthogonal cutting experiments, workpieces from the same stock material batches as used for the SHPB tests in section 2 and 3 are applied. The workpieces provide a length of cut of lc = 24 mm and a width of the undeformed chip of bexp = 2.4 mm. A turning insert of the designation TNGA 110308 with a low CBN-content and a ceramic binder is chosen. The cutting edge micro geometry and angles correspond to the cutting wedge of the simulation in section 4. The process forces are measured with a dynamometer of the type 9257B by Kistler. 6. Comparison of experimental and simulation results The resulting process forces for all simulation systems are compared to the measured forces in Fig. 6. The measured process forces for 650 HV are higher than those for 250 HV. This can be explained by the higher strength and higher resistance against deformation of the harder material. Nevertheless, the cutting forces are overestimated in each simulation. In case of the harder material the deviation is even higher. When comparing the cutting forces for both materials it can be noticed that the highest deviations are obtained by DEFORM while Abaqus provides the lowest differences. The difference of the simulated normal forces and the measured ones are smaller in general. Moreover, the normal forces are underestimated for 250 HV by Abaqus while they are in good agreement for DEFORM. It can be assumed that the flow stress model might be insufficient due to overestimated cutting forces and concurrently underrated or matching normal forces. In correlation to the cutting forces the deviations are higher for the harder material. This indicates the calculation of exaggerated flow stresses by the JC-model used.

185

A. Zabel et al. / Procedia CIRP 58 (2017) 181 – 186

dislocations in the material during deformation the plasticity term is replaced by an approach from Hockett and Sherby [15]:

Vy

m § § M · · § § T  Tr · ·¸ ¸¸ V HS ˜ ¨¨1  C ˜ ln ¨¨ ¸¸ ¸¸ ˜ ¨1  ¨¨ © M0 ¹ ¹ ¨© © Tm  Tr ¹ ¸¹ ©

(2)

with

V HS

Fig. 6: Simulated and measured process forces

The simulated chip formation and the experimentally obtained chip for 650 HV are illustrated in Fig. 7. The simulations result in a continuous chip formation while the real chip is distinctly segmented with white layers in the chip root and on the bottom side. The high material strength of the hardened steel leads to thermal softening and material damaging causing a periodic formation of chip segments as it is investigated by Barry and Byrne [14]. In contrast, the temperature is the only factor which is responsible for flow stress softening in the FE-models. The occurring temperatures are obviously too low to decrease the flow stress significantly, although temperatures of T ≈ 1000 °C are reached with all three simulation systems. The temperature distribution is similar for the different simulation systems. In case of 250 HV continuous chip formation occurs in the simulations and in the experiment as well.

V  V f

f

 k f 0 ˜ e dM

e



(3)

The parameters are fitted the same way as previously described (Table 1). Simulations with the modified JC-flow stress model are carried out with DEFORM only. In addition, the normalized Cockroft and Latham damage criterion (nCL) is used in the simulation for 650 HV. The Cockroft and Latham criterion was used by Umbrello et al. for simulation of hard machining of AISI H13 tool steel and showed reasonable results in terms of process forces and chip segmentation [4]. The process forces are illustrated in Fig. 8. For the continuous chip formation of the 250 HV steel the modification of the JC-flow stress (JC-mod) reveals a good agreement between the simulation and the experiment. Both force components deviate less than 10 % from the measured values. In case of the harder material the simulation without damage modelling overestimates the process forces for both components. Here, the illustrated values represent the mean process forces. Nevertheless, the deviation is reduced by the modification of the extended flow stress model. Furthermore a good agreement is achieved for both force components by application of the damage model.

Fig. 8: Simulated (DEFORM) mechanical load with modified JC-flow stress model and additional damage criterion

Fig. 7: Temperature plots of the simulated chip formation and microstructure of experimentally obtained chip for 650 HV

Regarding the deviations of the simulated process forces and the chip shapes a modification of the original JC-flow stress model was implemented. With respect to the saturation of

In Fig. 9 the resulting chip formation is shown. It can be seen that both chips do not exhibit a homogeneous thickness. In fact, the chip formation resembles a periodic gliding of segments. Therefore, the resulting process forces have to be averaged over a sequence of segments in order to be compared to the measurement as it is shown in Fig. 8. When comparing the simulations with and without the nCL it can be noticed that the usage of the nCL leads to a more distinct segmentation of the chip. The segment has a longer and thinner shape than the

186

A. Zabel et al. / Procedia CIRP 58 (2017) 181 – 186

chip of the JC-mod simulation. The maximum temperatures are similar but the gradient of the chip thickness is bigger for the simulation with nCL. Finally, a good overall agreement of the simulated and the experimentally obtained chips in shape and in size can be stated.

Fig. 9: Temperature plots of the simulated chip formation with a modified flow stress model and the additional nCL-damage criterion

7. Conclusion and Outlook In this investigation, samples of a low alloy steel with two different heat treatments were characterized by SHPB tests at different temperatures. The measured data was used to fit flow stress model parameters. The parametrized models served as an input for chip formation simulations with three different FiniteElement simulation systems. The application of the wellestablished Johnson-Cook model revealed an overestimation of the process forces and deviations of the chip form in comparison to measured results. A modification of the plasticity term leads to an improved prediction of the process forces and an additional damage criterion generates simulated segmented chips as they can be observed in real cutting tests. The presented study showed reasonable simulation results although a simple coulomb friction with µ = 0.1 was used. By combining the experimentally obtained cutting and normal force with the assumption of a tool-chip contact exclusively in the chamfer area (cf. length bf in Fig. 4) friction coefficients of µ 250HV, exp = 0.039 and µ 650HV, exp = 0.097 can be analytically estimated. This indicates that the used friction model might be adequate for the chip formation considered here. Nevertheless, the frictional conditions also depend on the temperature and the sliding velocity. In order to consider these influences in future

simulations experimental test should be carried out as proposed by Puls et al. [16]. References [1] Umbrello D, M’Saoubi R, Outeiro J. The influence of Johnson-Cook material constants on finite elemente simulations of machining of AISI 316L steel. International Journal of Machine Tools and Manufacture 2007; 47:3-4; 462-470 [2] Mabrouki T, Courbon C, Zhang Y, Rech J, Nélias D, Asad M, Hamdi H, Belhadi S, Salvatore F. Some insights on the modelling of chip formation and its morphology during metal cutting operations. Comptes Rendus Mecanique 2016; 344; 335-354 [3] Zanger F. Segmentspanbildung, Werkzeugverschleiß, Randschichtzustand und Bauteileigenschaften: Numerische Analysen zur Optimierung des Zerspanungsprozesses am Beispiel von Ti-6Al-4V. Dissertation Karlsruhe; 2013 [4] Umbrello D, Rizzuti S, Outeiro JC, Shivpuri R, M´Saoubi R. Hardnessbased flow stress for numerical simulation of hard machining AISIH13 tool steel. Journal of Materials Processing Technology 2008; 199; 64-73 [5] Umbrello D, Hua J, Shivpuri R. Hardness-based flow stress and fracture models for numerical simulation of hard machining AISI52100 bearing steel. Materials Science and Engineering A 2004; 374; 90-100 [6] Karpat Y. Temperature dependent flow softening of titanium alloy Ti6Al4V: An investigation using finite element simulation of machining. Journal of Materials Processing Technology 2011; 211; 737-749 [7] Buchkremer S, Wu B, Lung D, Münstermann S, Klocke, F, Bleck, W. FEsimulation of machining processes with a new material model. Journal of Materials Processing Technology 2014; 214; 599-611 [8] Lee WS, Lin CF, Plastic deformation and fracture behaviour of Ti–6Al–4V alloy loaded with high strain rate under various temperatures. Materials Science and Engineering 1998; A241; 48-59 [9] Whitenton E. The NIST Kolsky Bar Data Processing System. In: Proceedings of the 2005 SEM Annual Conference and Exposition, Portland, OR, USA; 2005 [10] Sacks J, Welch WJ, Mitchell TJ, Wynn HP. Design and Analysis of Computer Experiments. Statistical Science 1989;4:4, 409-435 [11] Johnson GR, Cook WH. A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. In: Proc. 7th Int. Symp. On Ballistics, Hague, Netherlands, April 1983; 541-547. [12] Zienkiewicz OC, Zhu JZ. The superconvergent patch recovery and a posteriori error estimates part 1: the recovery technique. International Journal for Numerical Methods in Engineering 1992; 33; 1331-1364 [13] Zienkiewicz OC, Zhu JZ. The superconvergent patch recovery and a posteriori error estimates part 2: error estimates. International Journal for Numerical Methods in Engineering 1992; 33; 1365-1382 [14] Barry J, Byrne G. The Mechanisms of Chip Formation in Machining Hardened Steels. Journal of Manufacturing Science and Engineering 2002; 124:3; 528-535 [15] Hockett JH, Sherby OD. Large strain deformation of polychrystalline metals at low homologous temperatures. Journal of the Mechanics and Physics of Solids 1975; 23:2, 87-98 [16] Puls H, Klocke F, Lung D. Experimental investigation on friction undermetal cutting conditions. Wear 2014; 310; 63-71