Clarisse Faugier

Sébastien Igonet

Damien Cornut

Romain Besson

Grégory Durand
email: gregory.durand@univ-avignon.fr

Anass Jawhari
email: ajawhari@calixar.com

Lactobionamide-based fluorinated detergent for functional and structural stabilization of membrane proteins

Keywords: detergent, surfactant, membrane proteins, solubilization, stabilization, lactobionamide, fluorinated detergent, Adenosine receptor, BmrA, AcrB

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Membrane proteins (MPs) make up between 20 and 30% of the total eukaryotic proteome [START_REF] Wallin | Genome-wide analysis of integral membrane proteins from eubacterial, archaean, and eukaryotic organisms[END_REF]. They are composed of integral membrane proteins which are embedded in the hydrophobic region of the lipid bilayer, as they span across the membrane once (single-pass), or multiple times (multi-pass), and extrinsic or peripheral membrane proteins that weakly associate with the hydrophilic surfaces of the lipid bilayer or intrinsic membrane proteins [START_REF] Yeagle | The membranes of cells[END_REF]. Membrane proteins are the gatekeepers of the cell and are therefore essential for its function. They are capable of regulating the flow of molecules and information across the plasma and internal membranes of organelles such as mitochondria, endoplasmic reticulum, golgi and nuclei [START_REF] Sadowski | Sub-cellular localization of membrane proteins[END_REF]. They are involved in regulating a large panel of important cellular processes such as cell adhesion, energy transduction, signaling, cell recognition and transport. Membrane proteins (MPs) can therefore function as receptors (e.g G protein-coupled receptors or GPCRs), transporters, channels or anchoring proteins. Because of the importance of those functions, MPs are of high interest for fundamental research and pharmaceutical purposes since more than 60% of therapeutic targets are MPs [START_REF] Overington | How many drug targets are there?[END_REF]. Understanding the structure function relationship is key to developing effective drugs against unmet medical needs. In order to gain a true understanding of the molecular basis of membrane protein functions, they must be isolated by physically disrupting the membrane. This is often done using detergents or other non-polar solvents.

Unfortunately, MPs are often unstable outside of their membrane environment.

Several attempts have been made to improve MP stability by changing the native amino acid sequence through protein mutagenesis, truncation and engineering [START_REF] Scott | Stabilizing membrane proteins through protein engineering[END_REF].

MPs have also been stabilized using classical antibodies or nanobodies [START_REF] Kobilka | G protein coupled receptor structure and activation[END_REF]. These methods are very helpful for structural investigations of MPs, but they require significant efforts of engineering and/or generation of relevant antibodies. In addition, there is an important risk in altering the native conformation of the protein target. An emerging alternative consists of maintaining the native sequence of MPs and looking for suitable solubilization conditions that ensure the conservation of the functional and structural integrity [START_REF] Desuzinges Mandon | Novel systematic detergent screening method for membrane proteins solubilization[END_REF][START_REF] Hardy | The yin and yang of solubilization and stabilization for wild-type and full-length membrane protein[END_REF]. Solubilization reagents are available in a range of strengths form harsh anionic detergents such as SDS and Sarkosyl, to mild zwitterionic, Fos-Cholines (FC) and CHAPS detergents, to weaker non-ionic n-Dodecyl β-D-maltoside (DDM) and octyl glucoside (OG) detergent [START_REF] Reynolds | Binding of dodecyl sulfate to proteins at high binding ratios. Possible implications for the state of proteins in biological membranes[END_REF][START_REF] Li | Monomeric state and ligand binding of recombinant GABA transporter from Escherichia coli[END_REF][START_REF] Cladera | Liposome solubilization and membrane protein reconstitution using Chaps and Chapso[END_REF][START_REF] De La Maza | Solubilizing effects caused by the nonionic surfactant dodecylmaltoside in phosphatidylcholine liposomes[END_REF][START_REF] Radominska-Pyrek | Solubilization of microsomal phosphoethanolaminetransferase by octyl glucoside[END_REF]. Detergent common features consisting on a hydrophobic acyl tail and a hydrophilic head group allow them to remove the lipids surrounding the membrane protein. So far one of the most popular detergents used for MP structural and functional studies is n-Dodecyl β-D-maltoside (DDM). While it has generally good solubilization properties, the stability of MPs is often compromised and requires the use of additional stabilizing reagents such as cholesteryl hemisuccinate [START_REF] Thompson | GPCR stabilization using the bicelle-like architecture of mixed sterol-detergent micelles[END_REF]. This has motivated a number of recent efforts to develop new polymers [START_REF] Knowles | Membrane proteins solubilized intact in lipid containing nanoparticles bounded by styrene maleic acid copolymer[END_REF][START_REF] Sharma | Non-ionic amphiphilic homopolymers: synthesis, solution properties, and biochemical validation[END_REF][START_REF] Oluwole | Solubilization of Membrane Proteins into Functional Lipid-Bilayer Nanodiscs Using a Diisobutylene/Maleic Acid Copolymer[END_REF] and mild detergents with enhanced stabilization properties such as MNG (Maltose-Neopentyl Glycol), GNG (Glucose-Neopentyl Glycol) [START_REF] Chae | Tandem Facial Amphiphiles for Membrane Protein Stabilization[END_REF][START_REF] Chae | Glucose-Neopentyl Glycol (GNG) amphiphiles for membrane protein study[END_REF][START_REF] Chae | Maltose-neopentyl glycol (MNG) amphiphiles for solubilization, stabilization and crystallization of membrane proteins[END_REF] and calixarene-based detergents [START_REF] Hardy | The yin and yang of solubilization and stabilization for wild-type and full-length membrane protein[END_REF][START_REF] Matar-Merheb | Structuring Detergents for Extracting and Stabilizing Functional Membrane Proteins[END_REF].

Fluorinated surfactants (FSs) are known to be less destabilising towards MPs because they hardly compete with protein-protein and protein-lipid/hydrophobic cofactor interactions and various reports have shown the superiority of FSs over hydrogenated detergents in stabilizing MPs [START_REF] Breyton | Hemifluorinated surfactants: a non-dissociating environment for handling membrane proteins in aqueous solutions?[END_REF][START_REF] Talbot | Hydrogenated and fluorinated surfactants derived from Tris(hydroxymethyl)-acrylamidomethane allow the purification of a highly active yeast F1-F0 ATP-synthase with an enhanced stability[END_REF]. Indeed, the fluorinated chains of FSs exhibit the peculiar property of being both hydrophobic and lipophilic due to the weak van der Waals interactions between fluorocarbons and hydrocarbons, thereby preserving native interactions while avoiding delipidation. Moreover, fluorinated chains are bulkier than hydrogenated chains and thus protrude less easily between protein transmembrane helices. Other biochemical applications of FSs such as in vitro synthesis [START_REF] Park | Fluorinated and hemifluorinated surfactants as alternatives to detergents for membrane protein cell-free synthesis[END_REF], inserting MPs into preformed membranes [START_REF] Posokhov | FCS Study of the Thermodynamics of Membrane Protein Insertion into the Lipid Bilayer Chaperoned by Fluorinated Surfactants[END_REF] or MPs refolding [START_REF] Frotscher | A Fluorinated Detergent for Membrane-Protein Applications[END_REF] have been successfully reported making FSs promising tools for MPs stabilization.

Recently, Keller and colleagues showed that the fluorinated analogue of DDM called F6OM was able to partition into lipid membranes and to solubilise them almost as efficiently as its hydrogenated counterpart [START_REF] Frotscher | A Fluorinated Detergent for Membrane-Protein Applications[END_REF]. On the contrary a phosphocholine derivative called F6OPC failed to show any detergency. More recently we could show that Diglucose fluorinated derivatives exhibited detergency in terms of both, lipidvesicle solubilization as well as membrane protein extraction [START_REF] Boussambe | Fluorinated diglucose detergents for membraneprotein extraction[END_REF]. To explore that further, we report herein the evaluation of a lactobionamide-based fluorinated detergent named FLAC6 for the functional and structural stabilization of MPs. The evaluation was performed using three different full length and wild type membrane proteins, namely adenosine receptor A2AR, AcrB and BmrA belonging to 3 classes of MPs (GPCR, pump and transporter) which were expressed in two cell types, insect cells (Sf9) and bacteria (E.coli). The theoretical molecular weights of A2AR, AcrB and BmrA are ~45, ~113 and ~65 kDa, respectively (with a migration on SDS-PAGE at 42, 100 and 72 kDa; respectively). Their quaternary structure may correspond to monomers, trimers and dimers for A2AR, AcrB and BmrA, respectively. The solubilization, purification, thermostability, behavior in solution as well as functionality were all evaluated for the three MPs prepared using FLAC6 or a reference detergent, pointing out promising features of this detergent for MP fundamental studies and drug discovery.

MATERIAL & METHODS

Expression and Membrane preparation

Full-length and wild-type human A2AR was cloned into a pOET1 transfer plasmid in frame with a N-terminal hemagglutinin signal sequence, Strep-tag II and 8xHis tag.

The baculovirus was produced according to the manufacturer's protocol (flashback ULTRA™ system, Oxford Expression Technologies). Sf9 insect cells were infected with recombinant baculovirus and grown at 28 °C for 64 hours in an orbital shaker as described [START_REF] Igonet | Enabling STD-NMR fragment screening using stabilized native GPCR: A case study of adenosine receptor[END_REF]. Cell pellets were collected, washed in Hepes buffer pH 7.4, 200 mM NaCl, 1X protease inhibitor cocktail (Sigma) and then stored at -80°C until use.

BmrA was over-expressed in E.coli as previously described [START_REF] Desuzinges Mandon | Novel systematic detergent screening method for membrane proteins solubilization[END_REF][START_REF] Ravaud | The ABC transporter BmrA from Bacillus subtilis is a functional dimer when in a detergent-solubilized state[END_REF]. AcrB was also produced in E.coli as previously reported [START_REF] Eicher | Transport of drugs by the multidrug transporter AcrB involves an access and a deep binding pocket that are separated by a switch-loop[END_REF][START_REF] Pos | Purification, crystallization and preliminary diffraction studies of AcrB, an inner-membrane multi-drug efflux protein[END_REF]. Frozen cell pellets were thawed, resuspended in Hepes buffer (A2AR), PBS buffer (AcrB) or TBS buffer (BmrA) pH 7.4, 200 mM NaCl, 1X protease inhibitor cocktail. Cell lysis was performed on ice using a BeadBeater homogenizer with 0.1mm diameter glass beads. Membrane fractionation was then carried out at 4°C by sequential centrifugations. For both insect or E.Coli cells, two centrifugations were performed: 4000g for 15min and 100000g for 45min. Membrane pellets were washed twice in buffer containing high salt (1M NaCl) to remove membrane associated proteins only for A2AR. Membrane enriched pellets were resuspended in Hepes, PBS or TBS buffer pH 7.4, 200 mM NaCl, 1X protease inhibitor cocktail and glycerol 20%, quantified using the Pierce Micro BCA Protein Assay Kit (Thermo Scientific) and then flash-frozen and stored at -80°C until use.

Membrane protein solubilization

Membrane were incubated for 2h at 4°C at a final total protein concentration of 5mg/ml in 50mM Hepes buffer pH 7.4, 200 mM NaCl (A2AR), or 50 mM Tris pH8, 100 mM NaCl (BmrA) or 50mM Phosphate buffer pH8, 150mM NaCl (AcrB) 1X protease inhibitor cocktail, and with 10-fold the critical micelle concentration (CMC) of detergent FLAC6 (CALIXAR), DDM (Carl Roth Int) or SDS. The synthesis FLAC6 will be described in another manuscript. The extraction with SDS served as a "positive" control. After solubilization, samples were centrifuged at 100000g for 45min at 4°C and an aliquot of the pellet and the supernatant from each solubilization condition were analyzed by SDS-PAGE and/ or western-blot.

SDS-PAGE and Western-blot

A2AR samples were denatured with 5x Laemmli buffer and incubated at RT for 20 min prior to analysis without heating to avoid the formation of aggregates. Proteins were separated by SDS-PAGE on a 4-15% acrylamide gel (4-15% Mini-PROTEAN® TGX Stain-Free™ Gel, Bio-Rad) and subsequently immobilized by electro-transfer to a PVDF membrane. The immunodetection of A2AR with an anti-A2AR monoclonal antibody HRP (7F6-G5-A2, Santa cruz Biotechnology), and of BmrA with an anti-His HRP antibody (Sigma), were performed by using the SNAP i.d. system (Millipore). A SDS-PAGE stain free gel was used to analyze the fractions of AcrB.

Thermostability assay

Membranes of A2AR, AcrB or BmrA (4mg/ml total protein) were solubilized under different conditions (see solubilization method above) for 2 hours at 4°C. Solubilized fractions were obtained after ultracentrifugation (100,000g) for 1h at 4°C. The solubilized fraction serves to make 50μl aliquots to be submitted to one temperature each as part of a gradient of temperature ranging from 25 to 85°C using PCR thermal cycler (PeqSTAR 2x gradient, Peqlab). Samples were subsequently centrifuged 40min (at 20000g) and supernatants were analyzed by SDS-PAGE and western-blot using an anti-A2AR antibody (7F6-G5-A2) and an anti-His antibody. The relative intensity of the target protein at each temperature was quantified by Western-blot using the Image Lab software 4.1 from Bio-rad. Each condition was performed in duplicate. The intensity was plotted as a function of the temperature, normalized and fit to the Boltzmann equation with the least square method using the Solver Adds-in of the Excel software. This method was previously described [START_REF] Igonet | Enabling STD-NMR fragment screening using stabilized native GPCR: A case study of adenosine receptor[END_REF][START_REF] Hardy | Stabilization of Human Multidrug Resistance Protein 4 (MRP4/ABCC4) Using Novel Solubilization Agents[END_REF].

Clear Native-PAGE (CN-PAGE) and Western-blot

Non-denaturated proteins were separated by native-PAGE on a 4-15% acrylamide gel (4-15% Mini-PROTEAN ® TGX Stain-Free™ Gel, Bio-Rad) using 25 mM imidazole as anode buffer and 7.5 mM imidazole, 0.05% deoxycholate, 0.01% DDM as cathode buffer. Clear Native PAGE gels were migrated for 90min at 200V and 4°C. Proteins were then immobilized by electro-transfer to a PVDF membrane. The immunodetection of A2AR, AcrB or BmrA was performed using the SNAP i.d. system (Millipore) with an anti-A2AR (7F6-G5-A2) and an anti-His antibodies (AcrB and BmrA).

His-tag affinity chromatography

The soluble protein fractions were loaded onto a TALON column equilibrated with 50mM Hepes buffer pH 7.

Size exclusion chromatography

Affinity purified A2AR, AcrB or BmrA were concentrated using Centriprep contractors with a 50K cut-off and loaded to a superdex 200 Increase 5/150 GL(GE-Healthcare) at 0.1 ml/min. The running buffer was 50mM Hepes buffer pH 7.4, 200mM NaCl (A2AR), 50 mM Tris pH8, 100 mM NaCl (BmrA) or 50mM Phosphate buffer pH8, 150mM NaCl (AcrB), all in presence of 1CMC of DDM.

Functional assays

To assess the functionality of A2AR, radioligand binding assays were performed at 4°C in triplicate using 96 well plates. Protein at a final concentration of 24 µg/ml (1µg -50µL per well) was incubated at 4°C in the presence of 3.6µM 3 H-CGS21680 (0.6µM final, 10µL per well) (Perkin-Elmer) +/-1mM of cold ligand (0.17mM final) in binding buffer (50mM Tris-HCl pH 7.4, 10mM MgCl2, 0.5mM EDTA) or CGS21680. After 2h of incubation, 60µL of 0,1% γ-globulin (prepared in wash buffer) and 120µl of 25% PEG6000 (prepared in wash buffer) were added per well, mixed and further incubated for 15mins at RT. Samples were then filtered using PEIpre-coated GF/B plates (Perkin-Elmer). After 4 washes with ice-cold wash buffer (50mM Tris-HCl pH 7.4), 25µl of scintillation reagent was added per well, and the samples were incubated for 1 hour. CPM detection was performed using the Microbeta2 equipment (Perkin Elmer), applying 5 min counting per well.

To test the functionality of AcrB, fluorescent polarization binding assays using rhodamine G6 as previously described [START_REF] Su | Ligand-transporter interaction in the AcrB multidrug efflux pump determined by fluorescence polarization assay[END_REF] were performed. Therefore, the polarization values of Rhodamine 6G (ranging from 4µM to 1mM) in the presence or absence of AcrB were measured using 530nm and 560nm as excitation and emission wavelengths, respectively. ATPase assays were used to assess BmrA activity as previously reported [START_REF] Matar-Merheb | Structuring Detergents for Extracting and Stabilizing Functional Membrane Proteins[END_REF].

RESULTS & DISCUSSION

Solubilization using FLAC6

Figure 1 displays the chemical structure of FLAC6. This molecule consists of a lactobionamide polar head group attached through an amide bond to a C9 alkyl tail, containing six perfluorinated terminal carbon atoms. Two structurally related lactobionamide-based fluorinated surfactants showed improved stabilizing properties for the fragile b6f complex when compared to DDM [START_REF] Lebaupain | Lactobionamide surfactants with hydrogenated, perfluorinated or hemifluorinated tails: physical-chemical and biochemical characterization[END_REF]. However, their ability to both solubilize and stabilize MPs has not previously been reported. We conducted a comparative study of this newly developed FLAC6 versus DDM and have evaluated their ability to solubilize and stabilize of wild type and full-length membrane proteins.

We chose three full length and unmutated targets for which DDM has already been used for solubilization and purification. GPCR, pump channel and transporter proteins, namely adenosine receptor A2AR, AcrB and BmrA, respectively [START_REF] Ravaud | The ABC transporter BmrA from Bacillus subtilis is a functional dimer when in a detergent-solubilized state[END_REF][START_REF] Pos | Purification, crystallization and preliminary diffraction studies of AcrB, an inner-membrane multi-drug efflux protein[END_REF][START_REF] Lebon | Agonist-bound adenosine A2A receptor structures reveal common features of GPCR activation[END_REF].

The three targets were expressed in two different expression systems E.coli and insect cells, which provide a sufficient diversity in terms of lipid composition of the biological membrane as well as the nature of MPs. For each MP, solubilization trials were carried out using FLAC6 and SDS being a "positive" control for solubilization.

Figure 2 shows that SDS allowed an almost total solubilization of all three membrane proteins A2AR, AcrB and BmrA. This was expected given that this detergent is extremely harsh. Moreover, better solubilization was obtained with FLAC6 when compared to DDM (Figure 2, compare lanes corresponding to soluble and pellet fractions for each condition). This clearly demonstrates that the novel fluorinated detergent FLAC6 exhibits efficient and broad solubilization properties of membrane proteins belonging to different families and expressed in different expression systems (bacterial and insect cells).

Purification of membrane proteins using FLAC6

To evaluate the impact of this novel solubilizing agent on membrane protein purification, his-tag affinity purifications were performed for A2AR, AcrB and BmrA solubilized in FLAC6. Figure 3 shows that the majority of solubilized BmrA could bind to the Talon affinity column. All solubilized AcrB bound to the column and eluted from the resin. The efficiency of binding of A2AR was difficult to evaluate due to the non-specific signal of the antibody used for western blot. SDS-PAGE stain free gels showed the specificity of the purification (Figure 3A, 3B and 3C for A2AR, AcrB and BmrA, respectively). Side by side gel panels representing the three purified proteins displayed in Figure 3D, show a high degree of purity for all preparations (>95%), except of a degradation product observed for A2AR, which is consistent with a previous report [START_REF] Igonet | Enabling STD-NMR fragment screening using stabilized native GPCR: A case study of adenosine receptor[END_REF]. This clearly demonstrates that FLAC6 efficiently solubilizes the three proteins A2AR, AcrB and BmrA and thereby allows an efficient purification.

Functionality of membrane proteins produced using FLAC6

The next step was to verify whether MP preparations were still functional. We therefore analyzed the function of each solubilized and purified membrane protein.

For each of them, we compared FLAC6 to the most stabilizing conditions previously reported (DDM/CHS for A2AR and DDM for BmrA and AcrB) [START_REF] Dauvergne | Glycosylated Amphiphilic Calixarene-Based Detergent for Functional Stabilization of Native Membrane Proteins[END_REF] and named, reference conditions. Figure 4A depicts significant differences between radioligand binding of 3 H-CGS-21680 to A2AR produced in DDM/CHS (reference) and the FLAC6 condition. This difference may be due to the presence of inactive A2AR or to a possible interference of FLAC6 with binding. To address this, we replaced FLAC6 by DDM/CHS after solubilization and purification during the final steps of the purification. Interestingly, ligand binding activity could be recovered suggesting that the protein produced in FLAC6 was functional and that FLAC6 may displace the binding of 3 H-CGS-21680 to A2AR. Similar type of interference was observed with a calixarene-based detergent and melatonin (data not shown). However, we cannot exclude that FLAC6 unfolds A2AR and that we recover the activity in a reversible manner after buffer exchange.

The ATPase activity of BmrA prepared in FLAC6 was 2.5 higher when compared to the reference condition DDM (Figure 4B). Similarly, an increase of ligand binding activity (3-fold) was observed for AcrB in FLAC6 instead of DDM (Kd of 9.46µM vs 27.99µM, respectively) (Figure 4C). Thus, FLAC6 based solubilizations and purifications allow to maintain and improve ligand binding activities of AcrB and A2AR as well as the ATPase activity of BmrA.

Behavior in solution of membrane proteins produced using FLAC6

To ensure the absence of aggregates in our membrane protein preparations, we evaluated their behavior in solution using Native PAGE Western blot analysis (Figures 5A, 5C and5E). Whereas small traces of aggregates were observed in the gel loading wells, the majority of A2AR, AcrB or BmrA were non-aggregated and could therefore migrate into the gel. To confirm these results, we applied analytical size exclusion chromatography (SEC) on affinity purified proteins solubilized and purified using FLAC6. Figures 5B,5D and 5F show that most of the proteins displayed similar and typical non-aggregated protein profiles, with the proteins eluting after the void volume, which is consistent with the Native-PAGE result. Thus, Native PAGE and SEC confirmed that AcrB, BmrA and A2AR were aggregates free when FLAC6 was used for the solubilization and the purification.

Thermostability of solubilized membrane proteins

The ability of FLAC6 to stabilize A2AR, AcrB and BmrA was further assessed using a previously established western blot-based thermal shift assay [START_REF] Igonet | Enabling STD-NMR fragment screening using stabilized native GPCR: A case study of adenosine receptor[END_REF]. This assay relies on the assumption that unstable heated proteins are prone to aggregate and therefore after ultracentrifugation and western blot the band intensity corresponding to the protein will decay proportionally to its instability. By measuring the amount of MPs that remains soluble at increasing temperatures the denaturing point (Tm), corresponding to 50% of soluble proteins, can be estimated. A2AR solubilized using DDM displays a Tm of 36.4 °C (Figure 6A andtable 6D), which is in good agreement with what has been previously reported using the same method [START_REF] Igonet | Enabling STD-NMR fragment screening using stabilized native GPCR: A case study of adenosine receptor[END_REF][START_REF] Ashok | Defining thermostability of membrane proteins by western blotting[END_REF].

Replacing DDM by FLAC6 at the solubilization step resulted in a Tm of 43.5 °C. A similar thermostability improvement was also observed for AcrB which gained 8.6°C in presence of FLAC6 in comparison to DDM (Figure 6B and6D). The same tendency but significantly amplified was noticed for BmrA which was over-stabilized to a Tm of 58.6°C when FLAC6 was used instead of 36°C for the DDM condition (~23 °C improvement). This suggests that this novel fluorinated detergent maintains the structural and functional integrities of MPs by increasing their thermostability.

Recently, we reported the development of a series of glucose-based surfactants with a fluorinated chain [START_REF] Boussambe | Fluorinated diglucose detergents for membraneprotein extraction[END_REF]. These surfactants had the ability to solubilize lipid vesicles and extract a broad range of proteins from E.Coli. However, none of the three proteins studied in this work could be efficiently extracted (Data not shown). Interestingly, we demonstrated herein that FLAC6 was efficient on solubilization, functional stabilization and thermo-stabilization. The superiority of FLAC6 may arise from two parameters. On the one hand, the sugar-based lactobionamide polar head group brings good water solubility of the detergent which is packed in a rather compact volume due to the linear arrangement of the two sugar moieties compared to the bulky branched arrangement of the Diglu series [START_REF] Boussambe | Fluorinated diglucose detergents for membraneprotein extraction[END_REF][START_REF] Guillet | Hydrogenated Diglucose Detergents for Membrane-Protein Extraction and Stabilization[END_REF]. Therefore, the lactobionamide polar head group can be considered as a close analog to the maltoside polar head group with a slightly more aggressive character as previously demonstrated with the hydrogenated analog H12-Lac [START_REF] Lebaupain | Lactobionamide surfactants with hydrogenated, perfluorinated or hemifluorinated tails: physical-chemical and biochemical characterization[END_REF]. On the other hand, the 9-carbon alkyl chain adds sufficient hydrophobicity and mild detergency due to the 6 perfluorinated carbon atoms. Other Lactobionamide-based fluorinated detergents were also studied in the stabilization of the fragile cytochrome b6f complex and showed a stabilization of the dimeric form while DDM resulted in the dissociation of inactive monomers [START_REF] Lebaupain | Lactobionamide surfactants with hydrogenated, perfluorinated or hemifluorinated tails: physical-chemical and biochemical characterization[END_REF]. This work highlights the advantage of FLAC6 in both solubilizing and stabilizing functional and non-aggregated MPs similar to what was observed with stabilizing lipids or ligands. This novel fluorinated lactobionamide-based detergent is therefore of high interest for enabling structure-function studies and drug discovery of challenging unstable MP targets of high medical relevance.

CONCLUSION

Here we report the use of a fluorinated detergent FLAC6 which consists of a lactobionamide polar head group attached through an amide bond to a C9 alkyl tail, with six perfluorinated terminal carbon atoms. This detergent shows a great potential for remarkable membrane protein solubilization and stabilization. We first demonstrate that FLAC6 was efficient in solubilizing three different membrane proteins of very different structure and function (GPCR, pump channel and transporter namely A2AR, AcrB and BmrA, respectively). Then, solubilized MPs could successfully be affinity purified to high purity, resulting in pure, homogenous, aggregate-free and functional preparations. Finally, striking overstabilization features were observed with improvements of the Tm of native A2AR, AcrB and BmrA by 7, ~9 and ~23 °C, respectively when FLAC6 was used instead of the reference detergent. This work demonstrates that FLAC6 is an efficient tool to maintain structural and functional integrities of different classes of MPs which represents the main prerequisite for their functional and structural investigations. Taken together, these findings support the relevance of this new fluorinated detergent as promising solubilizing and stabilizing agent, representing therefore an efficient and valuable addition to the growing membrane protein toolbox. A2AR was either solubilized and purified using DDM/CHS (labelled "DDM/CHS"), FLAC6 (labelled "FLAC6") or solubilized with FLAC6 and then further purified with DDM/CHS (labelled "FLAC6+DDM/CHS"). Purified A2AR was assessed for its functionality in a radioligand binding assay using 3 The thermostability was measured by the percent of soluble membrane proteins present after applying a heating range from 25 to 75°C, as previously reported [START_REF] Igonet | Enabling STD-NMR fragment screening using stabilized native GPCR: A case study of adenosine receptor[END_REF][START_REF] Ashok | Defining thermostability of membrane proteins by western blotting[END_REF]. A-Thermostability curves of A2AR solubilized with DDM or FLAC6. B-Thermostability curves of AcrB solubilized with DDM or FLAC6. C-Thermostability curves of BmrA solubilized with DDM or FLAC6 The Tm was calculated as the temperature at which 50% of the protein remained soluble. Dose (temperature) vs normalised response curve fitted for all graphs. Table D summarizes the mean and the variation between FLAC6, and reference conditions duplicates for each membrane protein (A2AR, AcrB and BmrA).

  4, 200 mM NaCl (A2AR), 50 mM Tris pH8, 100 mM NaCl (BmrA) or 50mM Phosphate buffer pH8, 150mM NaCl (AcrB), 2CMC of DDM or FLAC6. After a 2h incubation at 4°C, the resin was washed with 12 Column Volumes (CV) of Wash Buffer containing Hepes, phosphate or Tris buffer, 2CMC of DDM or FLAC6 and 20mM Imidazole. Target proteins were eluted with 4 CV of washing buffer with 150mM Imidazole. Samples of each fraction T, S, FT, W and E (corresponding to Total, Solubilized, Flow through, Wash and Elution, respectively) were analyzed by SDS-PAGE and/ or western-blot.

FIGURES LEGENDFigure 1 -

 1 FIGURES LEGEND

Figure 2 -

 2 Figure 2-Membrane proteins Solubilization using FLAC6.

Figure 3 -

 3 Figure 3-Membrane protein purification using FLAC6.

Figure 4 -

 4 Figure 4-Evaluation of the functionality of AcrB, BmrA and A2AR after solubilization and purification using FLAC6.

  H-CGS-21680 (A). Total (protein sample), non-specific (detergent buffer) and specific signals (total -non-specific) are indicated. BmrA purified in DDM or in FLAC6 were functionally evaluated by an ATPase activity assay (B). Ligand binding assay using Rhodamine G fluorescence polarization for the evaluation of the activity of FLAC6 or DDM based solubilization & purification of AcrB (C).

Figure 5 -

 5 Figure 5-Behavior in solution of purified membrane proteins.

Figure 6 -

 6 Figure 6-Thermostability of A2AR, AcrB and BmrA.

  Figure 1

ACKNOWLEDGMENTS

This work was supported by the Agence National de la Recherche (ANR) through LabCom Chem2staB (ANR14-LAB7-0002-01). We thank the CALIXAR team, Elodie DESUZINGES MANDON for helpful discussion and Emmanuel DEJEAN for continuous support. We acknowledge the financial support of the European Regional Development Fund, the French Government, the "Région Provence Alpes Côte d'Azur", the "Département de Vaucluse" and the "Communauté d'agglomération Grand Avignon" for access to the NMR platform (CPER 3A).

AUTHORS CONTRIBUTION

CF, SI & RB performed the expression, solubilization, purification, thermal-shift and functional assays. GD designed FLAC6 and DC synthetized and characterized it. DC and GD designed and synthetized the FLAC6 compound. AJ designed the experiments and managed the project. AJ wrote the paper with the help of SI and GD.

CONFLICT OF INTEREST

The detergent reported in this study, FLAC6 is commercially available at calixar.com


Yasmine Charfeddine
email: yasmine.charfeddine29@gmail.com

Sawsen Youssef
email: sawsen.youssef@gmail.com

Salem Sghaier
email: salemsghaier@yahoo.fr

Jalila Sghaier
email: jalila.sghaier@enim.rnu.tn

Hédi Hamdi
email: hedi.hamdi@enise.fr

Study of the simultaneous Grinding/Ball-burnishing of AISI 4140 based on finite element simulations and experiments

Keywords: Thermo-mechanical process, Grinding, Ball-burnishing, 3D FEM Simulations, Combined process, Hybrid process, Simultaneous grinding/ball-burnishing

In the manufacturing field, a growing interest is being held to the environment, to sustainability and more precisely saving energy and time. Combining thermomechanical with pure mechanical processes is an eco-friendly and profitable technique. In this paper, it is proposed to combine grinding and ball-burnishing processes. Further from reducing time, energy and cost of the manufacturing operations, this original combination is imagined to take benefit from thermomechanical history occurring while grinding to optimise ballburnishing process in order to enhance the workpiece surface integrity. In this paper, the impact of this newly developed process on the surface and subsurface behaviour is studied through experiments and 3D FEM simulations. It is shown that performing simultaneously grinding and ball-burnishing processes leads to a thick surface layer up to several millimetres with compressive residual stresses state. This is an interesting result to increase sustainability of metallic workpieces by enhancing wear resistance, fatigue strength and fatigue lifetime.

Introduction

Grinding process is generally the final operation in the machining process procedure as well as it is often considered as a finishing operation offering high dimensional precision, geometrical shaping accuracy and good surface roughness [1,2]. Nevertheless, this abrasive process can introduce some material deteriorations like microcracks formed at the surface and below the ground zone [3,4] and also burning marks that can appear when reaching high grinding temperature values [5][6][7][8]. Some other studies have shown that grinding can lead to scratched and tore surface [9] probably caused by free abrasive grains, pulled off the grinding wheel, in the grinding interface [10][11][12] or very high workpiece speeds [9]. Moreover, grinding of hardened steel leads to tensile residual stress results at the surface and even beneath it [13,14] that are known to be bad for fatigue resistance [15][16][17][18][19]. Burnishing process is often launched after grinding to fix workpiece deteriorations caused by this thermomechanical abrasive process [20,21].

Burnishing is a purely mechanical process capable of improving surface roughness by pushing into the valleys the microscopic peaks left by the cutting tool on metals by applying a pressure through a burnishing ball or roller. The surface obtained after burnishing has a mirror like finish and is smoother [22][23][24][START_REF] Charfeddine | Grinding temperature field prediction by meshless finite block method with double infinite element[END_REF] and harder [26][START_REF] Charfeddine | Austenite-martensite phase transformation of biomedical Nitinol by ball burnishing[END_REF][28][29][30]. Fatigue resistance of mechanical components exposed to cyclic loads is enhanced too [31][32][33][34][35], thanks to the Yasmine Charfeddine et al.

appearance of compressive residual stresses [36,37]. These compressive residual stress results [38] reduce drastically the tensile stress values responsible for the emergence of the cracks and their propagation which enhances fatigue strength. Further, the plastic deformation [39] imposed by the pressure leads to strain hardening which has an impact on the workpiece microstructure [40,41] by refining the material grains beneath the surface [42].

Combining simultaneously grinding with ball-burnishing is a newly developed technique. It consists in grinding and burnishing performing together by placing the burnishing tool on the grinding machine and taking advantages of thermo-mechanical history of the workpiece initiated by the temperature changes occurring while grinding [43,44]. This hybrid manufacturing process ensures obtaining a better surface quality and durability while reducing manufacturing energy and time if compared to grinding and burnishing acting separately.

REGAL (French abbreviation of the combined Grinding Ball-burnishing process) is a promising process since it can enhance surface integrity like the combined turning/burnishing process in terms of surface roughness [45,46], hardness [45,47] and compressive residual stresses obtained on the top surface and subsurface [48]. Such surface integrity improvement increases wear resistance and fatigue life of workpiece. One of the main advantages of this simultaneous grinding/ball-burnishing process is the increase of the affected depth by compressive residual stresses compared to ordinary burnishing process.

The aim of this paper is to present an exploratory research study of the effectiveness of the newly developed technique combining grinding with ball-burnishing process. Researches are carried out by both experimentations and 3D FEM simulations using ABAQUS™/Standard.

Materials and experimental set-up

Materials

The workpiece material considered is the AISI 4140 and its chemical composition and thermo-mechanical behavior properties are resumed subsequently in Table 1 andTable 2. The burnishing ball is made of ceramic and is considered rigid for the rest of the study since its hardness is equal to 75HRC which is more important than the workpiece hardness, equal to 46HRC.

Experimental set-up

The grinding machine used in this study is the ERNAULT-SOMUA FU-500 plane grinder and the burnishing tool used is a hydrostatic Ecoroll HG13 ball-burnishing tool. To Yasmine Charfeddine et al. make possible the combined grinding and ball-burnishing processes simultaneously, the ball burnishing tool is clamped to the grinding machine head using an aluminum fixing plate (Figure 1). This plate replaces the actual cover of the grinding machine head and it is designed and manufactured to suit the grinding machine used in this study.

The fixing plate is placed on the grinding machine using its two existing nuts and the two clamps on both sides of the grinding machine to guarantee the stiffness of the fixing system on the grinder head. Moreover, the ball-burnishing tool Ecoroll HG13 is placed in the center of the aluminum plate and fastened to it using two U clamps and four nuts and bolts (Figure 1(b)). To ensure grinding and burnishing simultaneously, the ball-burnishing tool is placed vertically in a plane parallel to the grinding wheel disk plane (Figure 1(b)). Further, centers of the contact areas of the grinding wheel and the burnishing ball with the workpiece are in a plane orthogonal to the manufactured workpiece surface containing the wheel center (Figure 1(b)). The "following system" existing in Ecoroll ball burnishing tools guarantees the ball to be always in contact with the ground workpiece.

The performance of grinding and burnishing simultaneously occur when the workpiece is placed under the grinding wheel and the ball-burnishing tool at the same time. The workpiece is then moved forwards and backwards according to a precise cross feed f and at workpiece speed V w . The grinding machine table is equipped with a KISTLER 9257A force dynamometer to register the resulting forces. The abrasive tool is a type 1 CBN Wendt Boart grinding wheel 250-10-3-B126-RXJ75-76.2. The main dimensions are 250 mm in diameter (D ), 10 mm in width (b) and 3 mm CBN layer. The burnishing tool used is a hydrostatic Ecoroll HG13 with a ceramic 13 mm diameter burnishing ball controlled using an Ecoroll hydraulic pump supplier (Figure 1(a)). The workpieces are extracted and manufactured from an AISI 4140 bar. The dimensions are 15 mm in width, 50 mm in length and a height of 50 mm.

Process conditions

The combined grinding/ball-burnishing process conditions are conducted for a workpiece speed of 250 mm.s -1 . The other grinding process conditions considered in this study are shown in Table 3 and the other ball-burnishing process conditions are cited in Table 4. P is the set hydraulic pressure supplied by the Ecoroll pump (Figure 1(a)).

3. Modelling and simulation

Modelling of grinding process

Grinding normal and tangential mechanical forces values are very low and the grinding cutting speeds are very high as compared to other material removing processes such as turning, milling and so on. Nevertheless, grinding power is high due to high grinding speed and it is assumed that all this power is converted as heat [2,6,49]. A fraction of this heat energy goes into the workpiece and involves thermomechanical phenomena because of the loading type, and the strain resulting from the thermal expansion. The rest of energy is dissipated trough out grinding micro-chips and environment.

The grinding process is modeled as a moving heat source representing the action of the abrasive wheel on the workpiece surface (Figure 2). To quantify the input power, it is assumed that all the grinding power is sooner or later converted as heat in the manufacturing area [2,6,49]. Between 65% and 85% of the generated thermal power enter into the workpiece as heat [49][50][51][52][53]. Furthermore, many researchers demonstrated that the heat flux distribution in the grinding area is linearly arranged [43,54]. It is then said that the heat flux is modelled by a triangular moving heat flux [55] along the specimen's surface (Figure 2). In this paper the linear heat flux density is computed using Equation 1 as a function of the contact length (Equation 2), the thermal power entering into the workpiece, the active grinding wheel width b, and the curvilinear abscissa Y [43]. The thermal power (Equation 3) is as well depending on the grinding tangential force , the grinding wheel velocity Vs and the fraction ε of the total energy generated that really goes into the workpiece. In this paper, ε is taken equal to 75% [49]. Yasmine Charfeddine et al.

q w (Y)= 2.P w b.l c 2 .Y; Y∈[0,l c ] (1)
The contact between the grinding wheel and the workpiece (Figure 2) is defined by an arc circle. The length of this arc is defined as the grinding contact length lc (Equation 2). l c = a p .D s (2)

The thermal power Pw (Equation 3) entering the workpiece is the fraction ε of the total mechanical power generated in the grinding interface. Total mechanical power is the dot product of the grinding force vector by the speed vector that is finally equal to the product of the tangential force component Ft and the peripheral grinding wheel speed Vs.

P w =ℰ.F t .V s (3)
The grinding tangential force can be modeled as a function of the equivalent chip thickness ℎ considered for the contact surface between the grinding wheel and the workpiece (Equation 4) [43].

F t =20.b. h eq 0.615 (4)
Where:

h eq = a p . V w V s (5)
With Equations 1 to 5, it is possible to compute grinding heat flux density that goes into the workpiece (Table 5) for different workpiece speed values and according to the grinding conditions cited in Table 3.

Table 5. Data used to calculate the heat flux densities for different workpiece speed values. The heat flux trajectory for numerical simulations of the grinding process are represented in Figure 3. The cross-feed f (Figure 3) is imposed by the ball-burnishing process.

V w [mm.s -1 ]

Ball-burnishing process modelling approaches

The burnishing process can be modelled using two different manners. The first approach consists in using the burnishing force when using the hydrostatic Ecoroll system used in this study (Figure 4(a)). The ball-burnishing force is calculated from the hydraulic pressure P (Figure 4(b)) that is assumed applied on the upper half sphere of the burnishing ball, Equation 6. The other approach consists in applying to the ball the involved vertical displacement δ (Figure 4(a)) resulting from the burnishing force.

F b =П R ball 2 P (6) Where: R !"## is the burnishing ball radius. In the case of the second approach, many research papers, modelled the ball-burnishing process using a burnishing ball controlled by a vertical displacement corresponding to the indentation depth δ (Figure 4(a)) [56,57] calculated thanks to Hertz theory of contact considered between two elastic solids (Figure 5). The Hertz theory of contact is only valid in the elastic domain whereas burnishing process reaches the plastic domain. For this reason, to study the relevance of using Hertz theory of contact, the calculated value of the vertical displacement δ is compared to the numerical one obtained after indentation taking into account the work hardening.

The computed ball-burnishing force using Equation 6 is different from the real force applied on the 13 mm burnishing ball found experimentally for a set hydraulic pressure P of 30 MPa. This experimental ball-burnishing force measured by a KISTLER 9257A force dynamometer is 25% lower than the calculated force. This can be due to the pressure loss occurring in the gap between the ball and the burnishing tool socket (Figure 4(b)). Then, a new relationship between the calculated and experimental ball-burnishing force is expressed in Equation 7and is in accordance with literature results [58].

F b, exp = 3 4 F b (7)
The indentation numerical simulation is then launched using the experimental ballburnishing force of 2986 N found using Equation 7. The indentation simulation using the experimental burnishing force permits to compare not only the penetration depth δ but also other contact parameters given by Hertz theory of contact. Yasmine Charfeddine et al. From Hertz elastic theory between a rigid sphere and a half-space (Figure 5) it is also possible to estimate the contact characteristics between the burnishing ball and the workpiece. One of them is the maximum contact pressure P0 (Equation 8) between the burnishing ball and the workpiece when ball-burnishing force Fb is applied. Another one is the contact area and the last one is the indentation distance δ of the ball in the part calculated using Equation 9. The circular contact area diameter 2a is calculated using Equation 10, knowing that E * (Equation 11) is the effective modulus, and R is the effective radius (Equation 12).

P 0 = 3 F b 2 П a 2 (8) δ= a 2 R ball (9) 2a= 2 * 3 F b R 4E * + 1 3 (10) E * = , 1-υ workpiece 2 E workpiece + 1-υ ball 2 E ball - -1 (11) 1 R = , 1 R workpiece + 1 R ball - (12)
The contact material properties of the workpiece and the burnishing ball used in this study are cited in Table 6. Yasmine Charfeddine et al. 6(a) is equal to 0.029 mm and is 15% lower than the calculated value using Hertz theory of contact that is equal to 0.034 mm. In addition, the contact area diameter 2a found numerically in Figure 6(b) is equal to the calculated Hertzian value given in Table 8 and equal to 0.95 mm. In the other hand, Hertz theory of contact maximizes the contact pressure results P 0 equal to 6359 MPa calculated using Equation 8 as it is equal to 2456 MPa for the numerical simulations of indentation in Figure 7(a) and Figure 7(b). This difference can be explained by the fact that Hertz theory of contact is only valid in the elastic contact hypothesis and does not take into consideration the plastic deformation occurring.

From this comparative study, it is clear that the determination of the penetration depth δ by Hertz theory of contact is a poor approximation to simulate the burnishing process since it is overestimated by 15%. Using such penetration depth δ in burnishing process simulations involve an overestimation of the residual stress results obtained by burnishing.

To avoid further singularities related to the use of Hertz elastic theory of contact, the numerical simulations of the ball-burnishing process in this work are conducted using the experimental ball-burnishing force F b, exp instead of using the depth of penetration calculated using Hertz theory of elastic contact.

Adopted approach for modelling ball-burnishing process

In the previous section, it has been demonstrated that using Hertz elastic theory of contact is not adequate for the burnishing process since it does not take into account the work hardening occurring while burnishing. The best way to model burnishing process is either to launch an indentation study using the experimental burnishing force and taking into consideration plasticity and then simulate the burnishing process using the value of the vertical displacement found numerically or directly simulate the burnishing process using the experimental burnishing force. In this study, the burnishing simulation adopted is using an applied experimental burnishing force to avoid supplementary time by using two simulations instead of one.

The ball-burnishing process is modeled by a rigid ball rolling on the workpiece surface at the workpiece velocity Vw and on which an experimental burnishing force Fb,exp is applied at its center (Figure 8). Yasmine Charfeddine et al.

Modelling of combined grinding/ball-burnishing process

The combined grinding/ball-burnishing process model consists in placing the burnishing ball next to the triangular heat flux. The burnishing ball and the heat flux move forwards and backwards along a predefined path and at the same speed equal to the workpiece speed Vw (Figure 3 and Figure 9). The 3D model of combined grinding/ball-burnishing is considered thanks to the software ABAQUS™/Standard. The implicit method of calculation is then chosen to simulate especially material spring back in order to obtain the simulated residual stress.

Only a part of the experimental specimen with the dimensions of 40x10x5 mm 3 (Figure 9) was considered in the numerical simulation in order to optimize the geometrical model and to reduce simulations time. The workpiece is considered deformable with a Johnson-Cook elasto-plastic constitutive law and is fixed at its bottom.

The Johnson-cook parameters used in this study for the AISI 4140 are in Table 9. Grinding is modeled by a moving heat flux along the workpiece surface following a stepcross path (Figure 3). The shape distribution of the heat flux is considered triangular in the grinding working interface where the initial workpiece temperature is 20°C and the convective heat exchange coefficient is equal to 10 5 W.m -².K -1 . Whereas, the ball-burnishing process is modeled by a rigid ball free to rotate along the workpiece surface with an imposed vertical force (along Z direction) applied to its center (Figure 9) and calculated using Equation 7. The value of the ball-burnishing force applied to the burnishing ball considered for the ball-burnishing conditions presented in Table 4 equal to 2986 N is validated thanks to the normal experimental force obtained in the stabilized zone (Figure 10(b)). Yasmine Charfeddine et al.

The simulation of the ball-burnishing process is composed of three steps: indentation, rolling and disengagement. The ball-burnishing boundary conditions vary according to the actual step used along the study and are summarized in Table 10.

Table 10. Boundary conditions of the burnishing ball. In order to estimate the right numerical coulomb friction coefficient proper to the ballburnishing process, finite element residual stress results obtained for different friction coefficient are compared to the experimental residual stress results. The dynamic friction force F t is composed of an adhesive force F t,a and a force related to the plastic deformation F t,d given by the Equation 13[60].

Step

F t =F t,a +F t,d =(µ a +µ d )F n ( 13
)
Where: µ a is the adhesive friction coefficient and µ d is the deformation friction coefficient.

The ABAQUS software permits introducing the Coulomb friction coefficient proper to purely friction. The Coulomb friction law becomes a poor approximation since there is an adhesive friction that needs to be considered. The friction coefficient obtained experimentally μ /0 includes the adhesive μ 1 and deformation friction coefficient μ 2 expressed in Equation 14. Therefore, from the numerical simulation it is possible to guess the adhesive coefficient by inserting the right coulomb friction value. To determine the adhesive coefficient, the coulomb friction coefficient is changed until obtaining similar experimental and numerical residual stress curves.

μ /0 =

3 4 3 5 =(μ 1 + μ 2 ) (14)
Considering the experimental ball-burnishing force results given in Figure 10(a) and Figure 10(b), the calculated force ratio between the tangential ball-burnishing force Ft and the normal ball-burnishing force Fn mean values is equal to 0.06 which is the experimental value of the friction coefficient calculated in the stabilized zone.

Combined grinding/ball-burnishing is a thermo-mechanical study so the mesh considered is type C3D8T. A refined mesh is adopted for a part of the workpiece (3x10x5 mm 3 ) which is the interest zone presented in Figure 11. This precision of the mesh was chosen to see clearly the impact of this newly developed technique beneath the workpiece surface and reduce the calculation time by not considering a refined mesh for the total workpiece.

A study of mesh convergence of the workpiece was launched where different mesh sizes were considered (Figure 11). The choice of the adequate workpiece mesh was adopted based on two criteria. First criterion is that the mesh size along X-axis has to be lower than the cross feed f (1 mm) and the mesh size according to Y-axis has to be lower than the contact length between the workpiece and the grinding wheel lc (3.5 mm) and at the same time lower than the contact area diameter between the burnishing ball and the workpiece 2a (0.95 mm). The second criterion is the report CPU time (Table 11). The mesh strategy adopted in Figure 11(a) does not obey to the first criterion and the mesh strategy adopted in Figure 11(b) gave results with a lack of precision if compared to results obtained for the mesh strategy in Figure 11(c) and Figure 11(d). Further, no noticeable changes in the output data are registered between the mesh strategy in Figure 11(c) and Figure 11(d) except time CPU that is higher (Table 11).

Since the precision of the results given by workpiece mesh in Figure 11(c) and Figure 11(d) are close, the adopted mesh in this study is the one illustrated the in Figure 11(c) with a total of 26,962 elements and 30,058 nodes (Figure 12). This chosen mesh strategy permits to gain in simulation time and ensures convergence of the model.

Figure 12. Adopted workpiece mesh.

Results

Simultaneous combined grinding/ball-burnishing consists in burnishing a pre-heated surface by the grinding process. The effect of grinding temperature results is studied numerically for different workpiece speeds V 8 and cross feed values f (Figure 13 and Figure 14). The purpose behind this study is to maximize temperature results reached at the surface and beneath it while burnishing. The temperature results according to the depth of the workpiece are studied to optimize the grinding temperatures and choose the adequate grinding parameters to consider in the combined grinding/ball-burnishing process. Yasmine Charfeddine et al. The highest temperature result at the workpiece surface is obtained for V w =500 mm.9 :; and is equal to 565°C and the lowest equal to 295°C is obtained for V w =100 mm.9 :; shown (Figure 13). The temperature of the workpiece surface increases when the workpiece speed increases. The more the workpiece speed increases, the more the heat flux density values increase, the more the temperature obtained at the surface are high.

Regardless of the cross-feed variations, the same heat flux densities ae obtained since the cutting parameters (ap,Vw,Vs) and the contact length lc didn't change. When the cross-feed increases, the contact surface Sc=f.lc increases which leads to higher thermal power entering the workpiece which explains obtaining higher temperature results. As the surface of contact between the heat flux and the workpiece is the greatest for a cross-feed f=1 mm, the maximum temperature of about 470°C is then reached at the top surface (Figure 14). Yasmine Charfeddine et al.

Figure 14. Effect of the cross feed on the numerical grinding temperature results along the workpiece depth for V w =250 . 9 -1 and q w (Y)=42.74. = >. :? . The grinding heat flux affects not only the workpiece surface, but heat generated also diffuses in the workpiece core, and leads to high temperature gradients up to different workpiece depths (Figure 13 and Figure 14). The temperature values reach 150°C at a depth of 0.4 mm of the workpiece for a cross-feed of 1 mm and V w =250 mm.s -1 (Figure 14).

For the following numerical and experimental study of the combined grinding/ballburnishing process, the experiments are launched at a workpiece speed of V w =250 mm.s -1 and a cross feed of f=1 mm where high temperature values are reached while grinding.

After grinding, tensile residual stress are obtained in the grinding direction S22 and perpendicular to grinding direction S11 (Figure 15). These tensile residual stress results are known to be bad for the workpiece lifetime, wear and corrosion resistance since they are responsible for the emergence and propagation of fatigue cracks [61]. Yasmine Charfeddine et al.

Figure 15. Numerical grinding residual stress results along the workpiece depth for a cross feed of f= 1 mm, V w =250 mm.s -1 and q 8 (Y) = 42.74 = >. :? .

The modelling approach adopted for the ball-burnishing process has an impact on the residual stress obtained. As mentioned earlier in the modelling of ball-burnishing process section 3.2, two ways of modelling the ball-burnishing process are possible either applying a vertical displacement δ=0.034 mm calculated using Hertz theory of contact or applying the experimental value of the ball-burnishing force F b, exp =2986 N to the burnishing ball (Table 8). When comparing numerical residual stress obtained for those two types of modelling it is clear that there is a significant difference. The residual stress results are more compressive in the burnishing direction S22 for the imposed δ compared to the residual stress results obtained for an imposed ball-burnishing force (Figure 16). These compressive residual stress results in the burnishing direction S22 reach a value of -257 MPa at the surface and a maximum compressive value of -578 MPa at a 0.3 mm depth whereas the maximum value of the compressive residual stress result obtained when a ball-burnishing force is applied are equal to -147 MPa obtained at the top surface (Figure 16). Residual stress computed in the perpendicular to burnishing direction S11 are more compressive at the surface equal to -693 MPa when applying a ball-burnishing force, as they are equal to -412 MPa when imposing a vertical displacement to the burnishing ball (Figure 17). Moreover, the compressive residual stress layer reaches a more important depth equal to 0.65 mm when imposing a vertical displacement δ than when applying a ball-burnishing force with an affected depth of 0.5 mm (Figure 16). This can be explained by the fact that the indentation depth δ considered as vertical displacement calculated with Hertz theory of contact equal to 0.034 mm is higher than the indentation depth found numerically when imposing a ball-burnishing force equal to 0.029 mm (Figure 6(a)). Thus, higher indentation depth leads to higher compressive residual stress results at a more important workpiece depth. Yasmine Charfeddine et al. Residual stress results obtained experimentally for the combined grinding/ballburnishing process are compared to the numerical results obtained for both modelling approaches used to model the ball-burnishing process (Figure 18 and Figure 19). Residual stress results are more compressive at the top surface when numerical vertical displacement is adopted. These residual stresses can reach a value of -863 MPa in the perpendicular to grinding and burnishing direction S11 (Figure 18) and -311 MPa in the grinding and burnishing direction S22 (Figure 19). But residual stress profile at the top surface and beneath it for S11 and S22 when applying a ball-burnishing force are closer to the experimental results of the combined grinding/ball-burnishing. This led to the use of the imposed ballburnishing force for the numerical simulation of ball-burnishing in the combined grinding/ball-burnishing process. Yasmine Charfeddine et al. S22 (in the burnishing and grinding direction) using an applied vertical displacement δ=0.034 mm and a numerical ball-burnishing force F b, exp =2986 N and µ=0.06.

Different Coulomb friction coefficient values of μ=0.03, 0.04, 0.05 and 0.06 where considered in the numerical simulation of the REGAL process using an imposed experimental ball-burnishing force applied to the burnishing ball modelling approach.

Residual stress results obtained numerically in the grinding and burnishing direction (S22) and perpendicular to them (S11) are compressive and in agreement qualitatively with the experimental curve obtained for the same operating conditions (Figure 20 and Figure 21). Furthermore, the same affected depth by the combined grinding/ball-burnishing equal to 2.7 mm is obtained numerically and experimentally (Figure 20 and Figure 21). Maximum compressive residual stress results are obtained at the surface and decrease gradually beneath it according to the perpendicular direction to grinding and burnishing S11 (Figure 20). Whereas in the grinding and burnishing direction S22, the compressive residual stress results increase gradually in the subsurface until reaching a certain depth equal to 0.35 mm (Figure 21).

Residual stress profiles obtained numerically for several friction coefficients are perfectly superimposed on each other in the direction that is perpendicular to burnishing S11 (Figure 20). Residual stress profiles in the grinding and burnishing direction S22 are slightly different for the four different friction coefficients and only for the first 0.75 mm depth of the specimen (Figure 21). These curves deviations are compared to experimental residual stress profiles (Figure 20 and Figure 21). At the surface, the residual stress results in the burnishing direction S22 for the friction coefficient values of 0.04, 0.05 and 0.06 are equal to -197 MPa. However, for a friction coefficient of 0.03, the residual stress value at the surface is equal to the experimental value of -218 MPa. Knowing that the force ratio between the tangential force Ft and the normal force Fn (Figure 10) is equal to 0.06. The approximation of the adhesive coefficient is then possible using Equation 14. Thanks to the adequacy between the experimental and numerical curve obtained for a friction coefficient of 0.03, the adhesive coefficient is then equal to 0.03. In order to analyze the effect of the newly developed technique involving grinding and ball-burnishing acting simultaneously, the residual stress results obtained by FE simulations are compared to those obtained numerically for grinding and ball-burnishing acting separately (Figure 22 and Figure 23). From these figures, it is seen that combining grinding with burnishing converts the tensile residual stresses obtained after grinding into compressive ones. These tensile residual stress results are equal to 161 MPa in the grinding direction S22 (Figure 23) and 62 MPa for the perpendicular to grinding direction S11 (Figure 22). The compressive residual stresses in perpendicular to grinding and burnishing direction S11 obtained at the surface reach values up to -693 MPa (Figure 22) for both REGAL and ballburnishing process. On the other hand, REGAL process increases the compressive residual stresses results in the grinding and burnishing direction S22 if compared to the stress results obtained after the ball-burnishing process acting separately. Indeed, the compressive residual stress results at the surface increased from-147 MPa for the conventional ball-burnishing to -218 MPa for the combined grinding/ball-burnishing process (Figure 23). This can be interpreted by the fact that more mechanical working is induced when combing grinding with ball-burnishing process. Knowing that two mechanical loadings are involved in REGAL process one related to the thermo-mechanical loading relative to the grinding wheel and the other to the force applied to the burnishing ball.

The affected depth by the compressive residual stress results is more important for the combined process reaching 2.7 mm as it is only 0.5 mm for the regular ball-burnishing process (Figure 22 and Figure 23). This can be explained by the fact that in REGAL process, it seems that grinding temperature may activate for a sufficient duration a decrease of the mechanical behavior optimizing the ball-burnishing process leading to a deeper affected surface layer. The association of high temperature with high burnishing pressure leads to more mechanical working, which enhances compressive residual stress results at a more affected depth.

Figure 23. Numerical residual stress results S22 (in the grinding/ball-burnishing direction) along the workpiece depth obtained for grinding (G), burnishing (B) and combined grinding/ball-burnishing (GB). Yasmine Charfeddine et al.

To see the impact of the burnishing pressures on the residual stress state and the compressive affected depth by the combined grinding/ball-burnishing process, five different supply pressures were considered in the numerical study: 10 MPa, 22.5 MPa, 30 MPa, 32.5 MPa and 35 MPa (Figure 24 and Figure 25). At the surface, the maximum compressive residual stress results are obtained for the maximum pressure of 35 MPa (Figure 24 and Figure 25) reaching a value of -934 MPa for S11 and -310 MPa for S22. Higher pressure values generate more compressive residual stress at the surface and beneath it and a more important compressive affected layer depth as reflected for the residual stress results S11 (Figure 24). This would be the results of the increase in the burnishing ball penetration depth related to the increase of the ball-burnishing force applied to the rolling burnishing ball.

Tensile residual stress results in the burnishing direction S22 equal to 36 MPa are obtained for a pressure of 10 MPa (Figure 25). This can be explained by the fact that this pressure might not be sufficient to convert the grinding tensile residual stress results into compressive ones.

The affected depth by the combined grinding/ball-burnishing process is the same for the pressure values of 22.5 MPa, 30 MPa, 32.5 MPa and 35 MPa equal to 2.7 mm but this depth is equal to 1.75 mm for a pressure of 10 MPa (Figure 24 and Figure 25). According to these numerical results, the more the pressure increases, the more the affected depth increases but not infinitely since it is stabilized at 2.7 mm for a pressure of 22.5 MPa. in the grinding/ball-burnishing direction along the workpiece depth.

Higher burnishing pressures lead to more compressive residual stress results at the surface and reach a more important affected layer. This can be explained according to Revankar et al. [62] that the increase of the ball-burnishing force applied to the burnishing ball leads to an increase in the amount of plastic deformations involved and enhance the hardness of the workpiece at an important workpiece depth.

Indeed, the temperature change under the ground surface and the plastic deformation occurring with ball-burnishing acting simultaneously increase the depth of the plastically deformed layer. The more the burnished depth increase the more the strain hardening increase. Since while ball-burnishing, the material is deformed at a constant volume and the surface deformation leads to its hardening which affects its subsurface by the same material strain hardening circle.

The study of the effect of the pressure on the residual stress results leads to knowing that there is a certain threshold value of the pressure. Starting from this pressure value, the affected workpiece depth by the combined grinding/ball-burnishing process does not increase and is stable for the current process manufacturing conditions to 2.7 mm.

Further, simultaneous grinding/ball-burnishing is a time effective process if compared to thermochemical surface treatments such as nitriding that is a time-consuming process and where the compressive residual stresses reach a depth of 0.1 mm for 36 hours of treatment process [63].

Conclusions

In this present work, the thermal aspect of the grinding process was studied for different workpiece speeds and cross feed values to optimize its thermal effect on the combined grinding/ball-burnishing process. The ball-burnishing modelling approach based on applying an experimental ball-burnishing force to the burnishing ball is adopted in this study since the modelling approach using a vertical displacement based on Hertz theory of contact is not adequate because it over estimates the indentation depth and further the residual stresses values and profile. This ball-burnishing model chosen in this work was validated numerically and experimentally. Furthermore, the numerical study of the combined grinding/ball-burnishing process was conducted for different friction coefficient values and compared to the experimental study for validation.

In addition, the comparison between combined grinding/ball-burnishing process with the grinding and ball-burnishing processes acting separately permits to see the advantages of the newly developed technique summarized as follows:

• Tensile residual stress obtained after grinding process became compressive thanks to combining grinding/ball-burnishing process acting simultaneously. • Compressive residual stress results after combined grinding/ball-burnishing process are obtained in both directions and at a more important affected depth than the ballburnishing process acting separately. • Combined grinding/ball-burnishing affects a more important workpiece depth (2.7 mm) exceeding the depth obtained by thermo-chemical surface treatments. • The increase of the burnishing pressure increases the compressive residual stress results and ensures obtaining a deeper compressive layer. The affected depth is stable at a certain pressure threshold value.

A thick layer of the compressive residual stress with small gradient are obtained when grinding and ball-burnishing processes are exerted simultaneously. This might improve workpiece resistance to environmental and mechanical external solicitations like severe rolling contact or slip contact. Future study will focus on investigating the impact of the burnishing pressure, the workpiece speed and the step over on the surface integrity of the simultaneously ground/burnished workpiece.

  Figure 1. (a) Combined grinding/ball-burnishing setup; (b) SOLIDWORKS CAD front and side views of the burnishing tool assembly.

Figure 2 .

 2 Figure 2.Triangular heat flux distribution.

Figure 3 .

 3 Figure 3. 3D model of step-cross grinding process.

Figure 4 .

 4 Figure 4. Ball-burnishing model for (a) an applied ball-burnishing force F b or an applied vertical displacement δ; (b) Illustration of the burnishing ball and ball retainer.

Figure 5 .

 5 Figure 5. Illustration of Hertz elastic theory of contact.

Figure 6 .

 6 Figure 6. Numerical results of indentation using F b, exp : (a) Indentation depth δ; (b) circular contact area diameter between the burnishing ball and the workpiece.

Figure 8 .

 8 Figure 8. Ball-burnishing model.

Figure 9 .

 9 Figure 9. Combined grinding/ball-burnishing model.

Figure 10 .

 10 Figure 10. (a) Experimental ball-burnishing tangential force results; (b) Experimental ball-burnishing normal force results.

Figure 11 .

 11 Figure 11. Different workpiece mesh: (a) coarse mesh; (b) normal mesh; (c) optimal mesh; (d) very fine mesh.

Figure

  Figure11(a)1 day

Finer

  Figure11(c)1 week

Figure 13 .

 13 Figure13. Effect of the workpiece speed on the numerical grinding temperature results along the workpiece depth for a cross feed of f=0.25 mm.

Figure 16 .

 16 Figure16. Numerical ball-burnishing residual stress results in the burnishing direction S22 along the workpiece depth for an applied vertical displacement δ=0.034 mm and a numerical ball-burnishing force F b, exp =2986 N for µ=0.06.

Figure 17 .

 17 Figure 17. Numerical ball-burnishing residual stress results perpendicular to burnishing direction S11 along the workpiece depth for an applied vertical displacement δ=0.034 mm and a numerical ball-burnishing force F b, exp =2986 N for µ=0.06.

Figure 18 .

 18 Figure 18. Comparison between experimental and numerical REGAL residual stress resultsS11 (perpendicular to burnishing and grinding direction) using an applied vertical displacement δ=0.034 mm and a numerical ball-burnishing force F b, exp =2986 N and µ=0.06.

Figure 19 .

 19 Figure 19. Comparison between experimental and numerical REGAL residual stress resultsS22 (in the burnishing and grinding direction) using an applied vertical displacement δ=0.034 mm and a numerical ball-burnishing force F b, exp =2986 N and µ=0.06.

Figure 20 .

 20 Figure 20. Comparison between numerical and experimental REGAL residual stress results S11 (perpendicular to the grinding/ball-burnishing direction) along the workpice depth for different friction coefficient values, a cross feed of f=1 mm, V w =250 mm.s -1 and F b, exp =2986 N.

Figure 21 .

 21 Figure 21. Comparison between experimental and numerical REGAL residual stress results S22 (in the grinding/ball-burnishing direction) along the workpiece depth for different friction coefficient values, a cross feed of f=1 mm, V w =250 mm.s -1 and F b, exp =2986 N.

Figure 24 .

 24 Figure24. Impact of the burnishing pressure (P) on the numerical residual stress results S11 perpendicular to grinding/ball-burnishing direction along the workpiece depth.

Figure 25 .

 25 Figure25. Impact of the burnishing pressure (P) on the numerical residual stress results S22 in the grinding/ball-burnishing direction along the workpiece depth.

Table 1 .

 1 Chemical compositions of AISI 4140.

	Components	C	Si	Mn	P	S	Cr	Mo
	Percent (%)	0.41	0.39	0.72	0.025	0.035	1.12	0.27

Table 2 .

 2 AISI 4140 thermo-mechanical properties.

	Young modulus [MPa]	210,000
	Poisson's ratio υ	0.3
	Density [Kg.m -3 ]	7800
	Thermal conductivity [mW.mm -1 .K -1 ]	46
	Specific heat [mJ.t -1 .K -1 ]	477,000,000
	Heat change coefficient [W.m -².K -1 ]	10 5

Table 3 .

 3 Grinding conditions.

	Peripheral wheel speed	[m.s -1 ]	37.5
	Depth of cut	a p [µm]	50
	Workpiece speed	V w [mm.s -1 ]	250

Table 4 .

 4 Ball-burnishing conditions.

	Burnishing ball diameter	d b [mm]	13
	Pressure	P [MPa]	30
	Workpiece speed Cross feed	V w [mm.s -1 ] f [ ]	250

2.P w b.l c 2 [W.mm -3 ] 100

		24.3
	200	37.26
	250	42.74
	300	47.81
	400	57.1
	500	65.46
	Yasmine Charfeddine et al.

Table 6 .

 6 Mechanical and geometric properties related to Hertzian contact calculation. The calculated Hertzian parameters for a pressure value of 30 MPa are presented in Table7.

	E workpiece	E ball	υ workpiece υ ball	E *	R workpiece	R ball	R
	[MPa]	[MPa]			[MPa]	[mm]	[mm]	[mm]
	210,000	315,000	0.3	0.26 137,111	∞	6.5	6.5

Table 7 .

 7 Calculated Hertzian parameters for an applied hydraulic pressure of 30 MPa.

	P [MPa]	F b [N]	2a [mm]	P 0 [MPa]	δ [mm]
	30	3,982	1.04	6,999	0.042
	The maximum indentation depth δ obtained numerically in Figure

Table 8 .

 8 Calculated Hertzian parameters versus numerical results after indentation for an applied ball-burnishing force of 2986 N.

		F b, exp [N]	δ [mm]	2a [mm]	P 0 [MPa]
	Hertz theory	2,986	0.034	0.95	6,359
	FEM Analysis	2,986	0.029	0.95	2,456

Table 9 .

 9 Johnson-cook parameters for the AISI 4140[59]. A is the yield stress (MPa), B the hardening modulus (MPa), n is the work hardening exponent and m the thermal softening coefficient.

	A[MPa]	B[MPa]	n	m
	595	580	0.133	1.03
	Where:

Table 11 .

 11 Mesh strategy versus CPU time.

	Mesh strategy	Illustration	CPU time
	Coarse mesh size in the
	interest zone

Acknowledgments:

The authors are grateful to the Program "Investissements d'Avenir"labelled by the French Government and operated by the National Research Agency (ANR)for financial support to the LabEx MANUTECH-SISE of Université de Lyon (France).

Graphical abstract

Yasmine Charfeddine

Main results Combined process Grinding/Ball-Burnishing