MODELLING OF MATERIAL BEHAVIOUR FOR INCONEL 718 SUPERALLOY USING EXPERIMENTAL DATA 1. INTRODUCTION

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1 Journal of Machine Engineering, Vol. 17, No. 3, 217 Received: 3 January 217 / Acceted: 1 June 217 / Published online: 28 Setember 217 modeling, machining, constitutive model Piotr NIESLONY 1* Wit GRZESIK 1 Piotr LASKOWSKI 2 MODELLING OF MATERIAL BEHAVIOUR FOR INCONEL 718 SUPERALLOY USING EXPERIMENTAL DATA In this aer arameters of the Johnson-Cook (J-C) constitutive material model were redicted more accurately based on the static and dynamic material tests and mathematical modelling of relevant resonse surfaces using secially develoed Matlab scrits. Exerimental tests were erformed under strain rates of 1-3 and 1 1 1/s and the temerature ranging from the ambient u to 7C. As a result, a set of mathematical models which fit the exerimental data was determined. The exerimentally-derived constitutive models were imlemented into FEM-based simulations of real machining rocesses of Inconel INTRODUCTION Modelling of the machining rocess and various machining oerations using FEM utilizes lastic, elastic-lastic, visco-lastic and elastic-visco-lastic material models [1]. In ractice, in order to imrove the accuracy of FEM redictions such associate hysical effects as the strain-hardening, thermal softening as functions of three factors- strain, strain rate and temerature are considered in constitutive material models. As a result, several constitutive models which take into account these variable factors are used by FEM users [1,2,3,4]. In this comarative study, a classical Johnson-Cook model in the form of Eqn. (1) was selected but the constant A, B and C and exonents m and n were determined exerimentally. eq where: eq - equivalent flow stress, m n T T A B o 1 C ln 1 T t To (1) - the equivalent strain, - the equivalent strain rate, - the reference strain rate, T - temerature, T - ambient temerature, T t - melting temerature, A,B,C,n,m - material constants and exonents resectively. 1 Oole University of Technology, Faculty of Mechanical Engineering, Deartment of Manufacturing Engineering and Automation 2 Pratt & Whitney, Rzeszow, Poland * .nieslony@o.oole.l

2 76 Piotr NIESLONY, Wit GRZESIK, Piotr LASKOWSKI The Johnson-Cook (J-C) model is the most oular material constitutive law used in FEM simulations for modelling material behaviour in the rimary and secondary shear zones. Its hysical limitation is that Eqn. (1) involves lastic deformation below fracture initiation (equivalently to the searation of mesh nodes). On the other hand, the material constitutive models used in machining modelling should include both material fracture in the chi formation zone and an intensive thermal effect. These two hysical effects are articularly imortant in machining of heat resistant nickel-based alloys (tyically Inconel 718) which retain high strength at a high temerature. In ractice, the above-mentioned effects needs some modifications of the J-C model, including: - thermal softening [3,4], - thermal softening as a function of temerature, - strain hardening for higher strain rates [5]. The constants and exonents in the J-C model for Inconel 718 (model A) selected from literature sources [6,7] and those fitted to the exerimental data for the temerature values of T=2-7 C (model JC1) and T=4-7 C (model JC2) are secified in Table 1. Table 1. Parameters of J-C model for Inconel 718 alloy Code A, MPa B, MPa n C m Literature item A [6,7] JC develoed JC develoed Based on the literature survey erformed the most adequate constitutive model for Inconel 718 was derived by Uhlman et al. [8,9]. This model imlemented into FEM- DEFORM software was found to give a good agreement using between measured and redicted values of cutting forces. An imortant finding of this study is that the thermal softening effect does not deend on the strain rate in the J-C model. On the other hand, the value of C arameter deends on both temerature and strain rate as in a method develoed by Warnecke and Oh [1]. In articular, the maximum value of C arameter changes from.17 to.3 for the temerature range of 5 to 8C. Based on mathematical modelling using MATLAB the authors observed that such changes of C arameter do not influence the strain hardening module in Eqn (1) because the equivalent flow stress changes only in the range of several ercent. As a result, they can be eq ractically neglected. 2. DERIVATION OF J-C CONSTITUTIVE MODEL FOR INCONEL DETERMINATION OF MATERIAL CONSTITUTIVE MODELS As mentioned above this modelling rocedure concerns an otimal material constitutive model for an Inconel 718 nickel-based alloy and relevant FEM simulations

3 Modelling of Material Behaviour for Inconel 718 Sueralloy Using Exerimental Data 77 of both turning and milling oerations erformed on arts of jet engines. This goal was achieved by detailed analysis of a number of material constitutive models alicable for FEM simulations, their verification based on literature data in secial alications to difficult-to-machine aerosace materials and the final choice of the best material models in order to simulate aroriately machining rocesses and oerations. The selection of material arameters in the J-C models takes into account the mechanical and thermal effects which influence distinctly the material behaviour during metal cutting [11]. All material data concerning nickel-based alloys machined, needed for FEM simulations, were rovided by the aerosace lants in Poland. They were imlemented into a secial data base. The mathematical modelling of the J-C equations was erformed using a MATLAB rogram EXPERIMENTAL METHODOLOGY This exerimental study was carried out using the following devices and aaratus: 1. The testing machine model INSTRON 5982 for static tensile tests erformed under the test temerature of 2 C to 7 C. 2. The dilatometer model BÄHR 85 D/L in order to establish the material behaviour at a higher strain rate of = /s and a very high temerature of 9C. 3. Slit-Hokinson s ressure bar device designed by Polish Technical Military Academy in Warsaw in order to determine the influence of the strain rate on the flow stress Flow stres, MPa Fig. 1. Grah f,t 2 C 1 C 2 C 3 C 4 C 5 C 6 C 7 C Plastic strain, m/m for stresses above yield stress with marked aroximation oints Firstly, static tensile tests were carried out in the temerature range between 2 C to 7 C. The material data obtained were analysed and converted to Matlab rogram by

4 78 Piotr NIESLONY, Wit GRZESIK, Piotr LASKOWSKI means of aroriate mathematical transformations which were made automatically using a secial scrit. When this scrit was activated, the files of mat tye were generated and selected in terms of the test temeratures. The data was obtained for a static tensile test erformed with low strain rates limited by linear movement of the testing machine, i.e. = /s. The relation f,t is related to both elastic and lastic strains but for FEM modeling elastic deformation should be omitted. Consequently, the searation of elastic and lastic strains using the exerimentally determined values of Young modulus E for all ranges of the temerature was erformed. In order to determine the variable arameters in the J-C material model the matrix of oints with constant variation ste was defined and the exerimental data were aroximated to the selected constitutive model using subrogram Sftools available in Matlab rogram. An examle of oint arrangements for the aroximation in the lastic deformation region is shown in Fig MATHEMATICAL FITTING OF CONSTITUTIVE MODEL The mathematical (resonse) function of the J-C material model exressed by Eqn. (1) was determined using Sftool module available in Matlab rogram. The J-C equation was inserted after some modifications using Customer Equation function. It should be noticed that in this case the model arameters are determined for the flow stresses corresonding to low strain rates. For such a case the term of Eqn. (1) with strain rate is equal to 1. Because for an Inconel 718 the melting temerature varies in the range of T m = C the average melting temerature was assumed to be equal to T m =1277 C. As a result, the J-C constitutive material model corresonding to lower strain rates of =2, of.6283 as follows 1/s) can be aroximated by Eqn. (2) and fitted with the R-square f ( T, ) ( ) (1 (( T 2) /1255) ) (2) Because in the cutting rocess the material is lastically deformed under high strain rates, the aroriate arameters in the second module of the J-C model, esecially at high temeratures, should be determined using the dilatometer. Its alication allows the flow stress values f,t for higher strain rates of = /s to be determined. They are three levels higher than reviously, i.e. = /s. Similarly as for lower strain rates, oints for the matrix aroximating the data set were identified using subrogram Sftools available in Matlab rogram. The mathematical function for the J-C constitutive material model alicable for low and high strain rates is exressed by Eqn. (3) (case JC1 in Table 1) as follows f ( T,, ) ( ) (1.271 ln( / )) ((1 (( T 2) /1255) ) (3)

5 Modelling of Material Behaviour for Inconel 718 Sueralloy Using Exerimental Data 79 The measured/redicted values of the cutting temerature recorded during finish turning oerations of an Inconel 718 alloy with TiAlN coated carbide tools varied between 5 C and 7 C deending on cutting arameters used. Consequently, the aroriate J-C constitutive model was limited to the temerature range of T=4-7 C and, as a result, the mathematical function for the general J-C constitutive model valid for both low and high strain rates (case JC2 in Table 1) is defined by Eqn (4) as follows f ( T,, ) ( ) (1.271 ln( / )) ((1 (( T 2) /1255) ) (4) 2.4. COMPARISON OF MATHEMATICAL FUNCTIONS OF J-C MODEL The comarison of the exerimentally derived model JC1 with the reference model A for the strain rate = /s is shown in Fig. 2. Model JC1 Exerimental oints Model A Fig. 2. Surface resonses for reference model A and exerimentally derived J-C model (model JC1) generated for T=2-7 C and = /s Fig. 2 confirms a very good agreement for the reference temerature of T=2C using reference model A. On the other hand, at testing temeratures above 6 C a good agreement for was achieved using both exerimentally-based JC1 and JC2 models (Fig. 3). It should also be noted in Fig. 2 that model A aroximates better exerimental oints for lower temeratures of T=2-3 C. Based on these observations, the actual constitutive model JC was limited to the exerimental oints obtained for higher testing temeratures. In addition, this comarison covers the modeling effects for the reference temeratures of T =2 C and highest temeratures as resented in Fig. 3. The R-square values for these two modeling cases for T=2-7 C and T=4-7 C are equal to.7554 and.7639

6 8 Piotr NIESLONY, Wit GRZESIK, Piotr LASKOWSKI resectively. It should be noticed that the FEM simulations using the JC2 model are limited to temeratures higher than T>4 C. It results from the secial mathematical descrition of the thermal softening module in the J-C model given by Eqn. 1 for which for T< T and the exonent m being a rational number its comutation is not ossible. Taking into account small differences in the redicted values of the flow stress in this study the FEM simulations were carried out using the J-C model with the ambient T =2 C (case JC2 in Table 1). Model JC2 Exerimental oints Model A Model JC1 Fig. 3. Reference model A and exerimentally-derived model JC1 for ambient temerature T =2 C and T=2-7 C and model JC2 for T =2 C and T=4-7 C 65MPa 35MPa 1 32MPa Fig. 4. Localization of the J-C models used versus exerimental oints for a low strain rate and temerature T=6 C

7 Modelling of Material Behaviour for Inconel 718 Sueralloy Using Exerimental Data MPa ±12MPa 11MPa Fig. 5. Localization of the J-C models used versus exerimental oints for a low strain rate and temerature T=4 C Fig. 4 comares redicted and exerimental values of the equivalent flow stress determined for the temerature of 6ºC (this lot is the cross-section of three satial surfaces in the stress-strain lane shown in Fig. 3). A similar temerature was measured in finish turning of an Inconel 718 alloy using the natural thermocoule technique. The accuracy the FEM redictions is discussed in details in Section 3. As shown in Fig. 4 the best fitting of the exerimental oints to the mathematical model is observed for the cases JC2 for which the average variation is about 35 MPa (equivalently about 3% when the flow stress is about 115 MPa). Aroriately, for the JC1 model the difference increases to about 65 MPa. In contrast, the model A redicts the measured flow stress with a distinctly higher variation of about 32 MPa (35%). In articular, the best fitting of +/- 12 MPa was reached using JC2 model for T=4ºC, as illustrated in Fig VALIDATION OF NEW MATHEMATICAL FUNCTIONS OF J-C MODEL BY FEM SIMULATION The J-C constitutive models selected were validated for a finish turning oeration with constant cutting arameters: the cutting seed of v c =9 m/min, the feed rate of f=.5 mm/rev and the deth of cut of a =.125 mm. The cutting tool inserts of CNMG UP tye made of TiAlN coated sintered carbide (KC51 grade by Kennametal) were used. FEM simulations were run for temerature-deendent values of the thermal conductivity and the secific heat available in [2]. Fig. 6 resents the records of temerature evolution obtained for differently arameterized J-C models with measured values reresented by their average values

8 82 Piotr NIESLONY, Wit GRZESIK, Piotr LASKOWSKI (the temerature variation is 6123ºC). It can be seen in Fig. 6 that the best agreement with the measured temeratures allows the JC1 model with the lowest values of B arameter and n exonent in the first elastic-lastic term. A similar effect but with visibly underestimated temerature values was obtained using the A model but with quite a different set of the model arameters. In contrast, for JC2 model the simulated temeratures overestimated the measurements even by 125ºC. Fig. 7 resents the redicted values of the three comonents of the resultant cutting force using JC1 and JC2 models and the A model corresonding to the estimated temerature. Fig. 6. Comarison of FEM redicted temeratures using different J-C models Fig. 7. Comarison of FEM redicted comonential forces using different J-C models

9 Modelling of Material Behaviour for Inconel 718 Sueralloy Using Exerimental Data 83 It can be observed in Fig. 7 that the best rediction accuracy was obtained for both the assive F and feed F f forces using JC2 tye model. For these forces the average exerimental and redicted values differ only by 1-2%. A worse result obtained for the cutting force F c is robably due to an excessive strain-hardening effect reorted by machinists working with difficult-to-machine alloys. As reorted reviously in introduction the accurate simulation of the F c forces is erformed using the J-C constitutive model roosed by Uhlman et al. [8,9] with evidently ronounced strain effect. For this model the highest value of B arameter in the first elastic-lastic term was selected. 4. CONCLUSIONS 1. In this study FEM simulations were carried out using the AdvantEdge ackage which requires the basic J-C model given by Eqn. 1 as the inut. As a result, the exerimentally-derived J-C models can be described by other mathematical functions and the obtainable accuracy is limited. 2. The exerimentally-derived J-C models guarantee more accurate FEM redictions of the cutting temerature and comonential cutting forces. 3. Imortant roblem is an excessive strain-hardening effect encountered by machining difficult-to-machine alloys. In this case for exerimentally-derived J-C constitutive model good agreement was achieved when used a highest values of B and m arameters in the elastic-lastic and temerature terms. 4. New J-C material models were derived using a secial mathematical rocedure and generation of a family of satial surfaces characterized by different sets of A, B and C arameters, and m and n exonents. 5. In articular exerimentally-derived J-C constitutive model denoted by symbol JC2 seems to be an otimal solution which allows an accurate rediction of the cutting temerature and the feed and assive forces with the rediction error of 1-2%. ACKNOWLEDGEMENTS A financial suort of The National Centre for Research and Develoment Project No INNOLOT/I/9/NCBR/213 Advanced methods for manufacturing of aero engine case module comonents - CASELOT is gratefully acknowledged. A financial suort of The National Centre for Research and Develoment Project No INNOLOT/I/7/NCBR/213 Turbine for Turboshaft Engine Demonstrator - TED is gratefully acknowledged. REFERENCES [1] GRZESIK W., 28, Advanced machining rocesses of metallic materials, Elsevier, Amsterdam. [2] NIESŁONY P., 28, Modelling of heat transfer and temerature distribution in the cutting zone for cutting tools coated with rotective hard layers, DSc Monograh, Oole University of Technology, Oole. [3] NIESLONY P., GRZESIK W., LASKOWSKI P., ZAK K., 215, Numerical 3D FEM simulation and exerimental analysis of tribological asects in turning Inconel 718 alloy, Journal of Machine Engineering, 15/1,

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