Muriel Palengat

Olivier Guiraud

Christophe Millet

Grégory Chagnon

Denis Favier

C Millet Minitubes

Tube Drawing Process Modelling By A Finite Element Analysis

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

Introduction

Thin-walled tubes are manufactured with the tube drawing process, reducing progressively inner and outer diameters together with wall thickness. In most cases, industries develop empirically their production. As it induces many experiments, this method costs a lot of time and energy. Numerical simulation would be an alternative solution which would require firstly to characterize the material with simple mechanical tests available for tube geometries; then numerical simulation would allow to test the feasibility of drawing passes and to give an optimized range of production. This would reduce the number of experimental tests and then the cost of development. Such an approach is explored in this paper for hollow sinking drawing of stainless steel tubes.

Few works exist on tube drawing process but different studies have already been realized to optimize tools' geometries [START_REF] Um | An upper bound solution of tube drawing[END_REF] and observe stresses and strains with several drawing processes [START_REF] Neves | Numerical and experimental analysis of tube drawing with fixed plug[END_REF][START_REF] Yoshida | Mandrel drawing and plug drawing of shape-memory-alloy fine tubes used in catheters and stents[END_REF][START_REF] Yoshida | Drawing of Ni-Ti SMA fine tubes used in medical tests[END_REF]. Karnezis and Farrugia [START_REF] Karnezis | Study of cold tube drawing by finite-element modelling[END_REF] developed an optimization procedure based on the Cockcroft-Latham workability failure criterion. None of these works justify the value of their friction coefficient. Lazzarato et al. [START_REF] Lazzarato | Identification of Coulomb's friction coefficient in real contact conditions applied to a wire drawing process[END_REF] carried out an inverse analysis on the basis of mechanical tests. They performed a new upsetting sliding test recreating the wire drawing process conditions in order to identify the Coulomb's friction coefficient.

The aim of the present study is to model tube drawing with a thermomechanical finite element (FE) analysis. This paper focuses on cold drawing without inner plug (hollow sinking) of stainless steel 316LVM (ASTM F138) tubes of small diameters (typically of the order of 1 to 6 mm).

First, hollow sinking tests are performed on draw-benches with several sensors, i.e. load cells, thermocouples and pyrometer. Drawing forces and inner and outer temperatures are measured during the drawing process for tube of initial different diameters and thicknesses.

Subsequently, a thermomechanical model is used. Accurate modeling results imply to have a deep knowledge of parameters that affect the process as tools and tubes geometries and of materials behaviour. The main difficulties are due to large deformations and complex contact conditions which must be well characterized and which involve numerical convergence problems.

In a first part, drawing experiments performed on drawbenches are described, the second part details the modelling hypotheses including constitutive equations to describe the materials mechanical behaviour. In a third part, experimental measurements and results predicted by the FE model are compared and discussed.

Drawing Experiments

Tube drawings were realized on a testing bench, presented in Fig. 1 with a stainless steel (316LVM). A simulation of this process is realized further and compared with these experimental data.

Hollow Sinking:

Measurements were done during hollow sinking tests. The process is presented in Fig. 2. A tube is introduced in a die which has a diameter smaller than the tube outer diameter. The drawing speed is 14.3 m/min. A load cell takes place on the drawing device to record the drawing force. Moreover, two thermal sensors are used. A thermocouple, placed inside the tube records the evolution of the temperature of a point on the inner surface of the tube during the process. A pyrometer is placed after the die exit, and records the time evolution of the temperature at a spatial point distant of 8 cm from the die exit. The time-drawing force curve (Fig. 3) is composed of three parts. In a first stage, the tube enters in the die and the drawing force increases quickly. During the second stage, the drawing process reaches a steady state where the force is practically constant. In the third stage, the drawing force decreases when the tube exits the die. In the following, we will consider only the steady state. Besides the tube extremities are not used for industrial applications as they do not have the same material and geometrical properties. In fact, they are only used to fix the tube.

Figure 3: Variation of the experimental drawing force

Drawing forces during the steady state and final dimensions were recorded and are summarized in table 2.

Table 2: Experimental measurements for hollow sinking after drawing.

Case

Numerical Simulation

Hypothesis:

As geometries and loading conditions are axially symmetric, an axisymmetric model is used. The steady-state condition is the dominating phase in tube drawing. Then, only the steady state and a part of the total tube length are considered in a first approach.

Tube cold drawing implies large plastic deformation. Inelastic phenomena and friction generate heat. In a first approach it is assumed that the materials behaviours are temperature independent. Thus the material model does not take into account temperature. In the range of temperature variation, the material properties do not vary more than 1%.

Besides, during drawing, strain rates are of the order of 10 to 100 s -1 . However, the tests are at room temperature T (300K), and the melting point Tf of the studied alloys are higher than 1500 K; with regard to the ratio T/Tf lower than 0.2, it is assumed that the materials behaviours are considered as insensitive to strain rates in a first approach.

Lubricants affect the drawing but lubrication is supposed homogeneous and constant during the process. Thus variations in lubrication are not taken into account and only a constant Coulomb coefficient is used to model friction.

Finally, as the time of drawing is relatively short, the model is considered adiabatic and the conduction at the tube-die contact is supposed to be negligible.

Then, an elastoplastic constitutive equation is applied to model the materials behaviour. In order to characterize the plastic behaviour, simple tests are performed.

Physical Modelling:

Material Behaviour

The studied material, a stainless steel (316LVM), has a large ductility and can be cold formed. Only tensile tests are available for thin-wall tubes. They are easy to realize, but they are not sufficient to understand the material behaviour during drawing. Indeed tensile tests permit to observe only one strain direction and are not sufficient to correctly define the hardening law.

These tests lead up to apply in a first approach an elastoplastic constitutive equation with an isotropic hardening law. The elastic behaviour is described by Young's modulus and Poisson's ratio. The true strain-true stress curve describes the plastic behaviour (Fig. 4).

Thermal properties are listed in table 3. They are valid for temperatures ranging between 20°C and 100°C. Friction coefficient is equal to 0.1, proposed by Lazzarato et al. [START_REF] Lazzarato | Identification of Coulomb's friction coefficient in real contact conditions applied to a wire drawing process[END_REF].

Heat generated by friction is equally shared between the tube and the die.

Table 3: Thermal properties

Material 316LVM WC Thermal conductivity (W.m -1 .K -1 )
15 100 Density (Kg.m -3 ) 7800 3520 Specific heat (N.m.kg -1 .K -1 ) 500 500 Inelastic heat fraction 0.9 ø

Tools Behaviour

Dies are in tungstene carbide (WC). They are assumed to deform elastically because of their high elastic limit. Moreover no plastic deformation has ever been observed on tools after a drawing. Their elastic properties are listed in table 4.

Friction

The friction coefficient depends on a lot of parameters (materials, lubricants, surfaces…) and it is difficult to determine it. In metal forming, the Coulomb model accounts for the effects of friction. A shear stress limit could have been applied if there were large normal stresses. This model does not take into account the fluctuation of lubrication. The Coulomb coefficient has been chosen in the literature [START_REF] Lazzarato | Identification of Coulomb's friction coefficient in real contact conditions applied to a wire drawing process[END_REF].

Numerical Modelling:

Load

Boundary conditions are shown in Fig. 5. They are the same as in experiments. Dies are fixed. Tube is drawn with a constant speed. In fact the speed has no influence here, as the model is quasi-static and the friction and material behaviour are rate independent (cf. § Hypotheses).

Temperature of the system die/tube is initially fixed at room temperature. Thermal flow on external surfaces of the system is null, as the system is considered adiabatic.

Meshing

Triangular elements are very versatile and convenient to mesh complex shapes. However, quadrilateral elements are able to provide an accurate solution at less cost. Quadrilateral elements have a better convergence than triangles but are less accurate if they are initially distorted (Abaqus 2006). In our case they are appropriate to mesh all instances except the dies. Consequently, tubes and plugs are meshed with 8-node axisymmetric thermally coupled quadrilateral, biquadratic in displacement and bilinear in temperature (CAX8T).

Comparison Drawing Experiments -Simulation

Observations of the simulation results Qualitatively, the same behaviours as in experimental process are noticed. First, in sinking, the tube peels off from the die, the centripetal flow continues a bit. The detachment is viewed in Fig 6 . It implies that sunken tube diameters are slightly lower than die diameters. The detachment is of the order of some hundredths of a millimetre. Moreover, two compression points on the die can also be seen in Fig. 6. They take place where the tube changes direction and creates stress in the die. Damages are also observed here on real dies on which wear rings are generated during drawing process. Figure 8 shows a wear ring on a wire drawing diamond die. Then Fig. 9 illustrates the distribution of temperature in the tube and the die. The temperature strongly increases on the outer surface of the tube because of the heat generated by friction. In the rest of the tube, the increase is lower and is due to the inelastic heat generation. Far from the die exit (it cannot be seen in this figure) temperature homogenizes in the thickness. Besides it can be noted that the die temperature is very high (> 1000 °C). Finally, in hollow sinking, the tube is not constrained inside, so the thickness increases to make the reduction of diameters easier.

Thermomechanical Modelling

As shown in Fig 7, there is a good agreement between experiment and simulation. Indeed, the numerical and experimental drawing force necessary to pull the tube through the die are quite similar for the steady state studied. To date, even if some experimental values miss, a first approach could be carried out with available data presented in table 4. For each drawing, initial tube diameters are reported. The inner and outer temperatures as well as drawing forces are obtained in the simulations. Then the data predicted by the FE model and the experimental measurements are confronted and the results are conclusive. Indeed it appears that the maximum difference between the experimental and numerical drawing forces is lower than 7%. For inner temperatures, relative error between model and tests is 13%. To finish, relative error for outer temperatures is lower than 1.2%. These results are encouraging for the continuance of the coupled thermomechanical studies. Moreover model can be improved afterwards.

Conclusions

First, forces and thermal data are observed and results were encouraging. Modelling allows to assess lots of phenomena and to be interested in data, difficult to observe experimentally.

An elastoplastic constitutive equation with an isotropic hardening is applied with a Coulomb's friction coefficient of 0.1. Hollow sinking FE model is in good agreement with experimental measurements. However, some inaccuracies appear. It may be due to the determination of the materials plasticity model. The stressstrain curves obtained by tensile tests are limited and do not account entirely for the materials behaviour. Indeed during the drawing, the material undergoes two strains: a longitudinal tension and a radial compression. Then, a better experimental test must be used. An adapted test would be a tensile test with radial compression at the same time but its realization is difficult. An equivalent of these two strains is the shearing. It seems to be easier to realize and is currently done to define better the material behaviour. Moreover, as cycling tests are not available in tensile tests, cyclic shear tests will allow to determine the hardening type. Indeed elastic springback will be observed and the influence of kinematic hardening will be quantified. Improving the determination of the hardening type will improve the prediction of the final dimensions of the final tube.

In the first approach of this paper, three parameters appear to be very important for the modelling. The first, friction coefficient is the most important; it has a great influence on the drawing force, but also on external temperature of tube and die. The second is the inelastic heat fraction. This coefficient has an influence on the temperature generated by the plastic deformation of material during drawing. Finally, the third is the heat distributed to tube fraction. This coefficient makes it possible to distribute the heat generated by friction to various surfaces in contact.

For this study two hypotheses were assumed. First, losses due to convection after die are supposed to be negligible. Studies are in progress in order to check this assumption. Secondly, contact conduction between die and tube is also considered negligible. Indeed, the time of drawing is too short and thus the time of contact between die and tube is very small (< 1s). However, it is necessary to conform these hypotheses because the difference of temperature between die and tube is large and external temperature of the tube at the end of the process is higher than the one at the beginning. Experimental data go in this way.

Figure 1 :

 1 Figure 1: Drawbench.

Figure 2 :

 2 Figure 2: Hollow sinking In the first test the outer and inner diameters of the tube before drawing are equal to 6.64 mm and 5.8 mm, respectively. Two other tests were carried out with different tube diameters (8.15 x7 mm 2 and 4.06x3.5 mm 2 ). Tungsten carbide conical dies were used. Details of experiments data (initial tube and die geometries) are listed in table 1.

  .

Figure 4 :

 4 Figure 4: Stress-strain curve of the 316LVM cycling test.

Figure 5 :

 5 Figure 5: Boundary conditions of the drawing process model.

Figure 6 :

 6 Figure 6: Observations of a finite element simulation of a hollow sinking tube process.

Figure 7

 7 Figure7presents the time evolution of the drawing force during a hollow sinking simulation. It can be observed that, after a rapid increase at the beginning, the drawing force stays constant during the process. The drawing force is recorded during the steady state.

Figure 7 :

 7 Figure 7: Evolution of the drawing force according to time for a hollow sinking test.

Figure 8 :

 8 Figure 8: Drawing ring on a die (ESTEVES-DWD).

Figure 9 :

 9 Figure 9: Observations of temperature during the hollow sinking process.

Table 1 :

 1 Experimental measurements for hollow sinking before drawing.

	Case	Initial Tube (Φext×Φint) mm	Die Angle	Die Diameter mm	Die bearing mm
	1	8.1×7.0	25	6.7	17%
	2	6.6×5.8	25	5.2	17%
	3	5.2×4.5	25	4.1	17%

Table 4 :

 4 Elastic properties of the tube and tools materials.

	Material	316LVM WC
	Young's modulus (GPa)	210	650
	Poisson's coefficient	0.3	0.2

Table 5 :

 5 Numerical and experimental results.

		Φext×Φint	Text	Tint	Drawing
		mm	(°C)	(°C)	Force(N)
	Experimental	6.6×5.8			2870
	Numerical	6.5×5.3			2677
	Experimental	5.2×4.5	117	60	1806
	Numerical	5.1×4.2	118	68	1885
	Experimental	4.1×3.5	102
	Numerical	4.0×3.2	101


INTRODUCTION

Owing to their good biocompatibility properties, silicone rubbers are being increasingly used in biomedical applications. Unfortunately, experimental studies aimed at analysing and modelling the mechanical behaviour of such materials are quite scarce [START_REF] Podnos | FEA analysis of silicone MCP implant[END_REF][START_REF] Loew | Simulation of reiterated mechanical load of silicone rubber[END_REF][START_REF] Goulbourne | Electro-elastomers: Large deformation analysis of silicone membranes[END_REF]. This is a lack for the development of structural applications involving silicone rubber parts. Within that context, and towards a better understanding of the mechanics of silicone rubbers, we have processed plates using an unfilled silicone rubber formulation (section 2). The plates have then been deformed using homogeneous tensile and pure shear deformation tests. During the tests the local strain field on the surface of deformed samples was obtained using a visible CCD camera and a Digital Image Correlation technique (section 3). Experimental results are given in section 4 and prove that Mullins effects, hysteresis as well as strain rate sensitivity are weak. This permits to model the mechanical behaviour of the studied silicone with hyperelastic formalism. Three hyperelastic models are fitted with the experiments, i.e. [START_REF] Mooney | A theory of large elastic deformation[END_REF], [START_REF] Gent | A new constitutive relation for rubber[END_REF] as well as [START_REF] Haines | Strain energy density functions for rubber like materials[END_REF] models. Lastly, in order to test the capability of the above constitutive schemes to model the deformation of complex structures, (i) a plate silicone sample containing holes is deformed in tension, (ii) Finite Element simulation of this experiment is performed with the three fitted hyperelastic models, and (iii) a comparison of resulting experimental and numerical local strain fields is achieved (section 5).

MECHANICAL TESTING PROCEDURE

The chosen silicone rubber is a unfilled formulation produced by Rhodia (RTV 141). Thin plates with an approximate thickness of 2 mm and in-plane dimensions 180100 mm² were produced using the following processing route: (i) mixing the two liquid components with a 1/10 ratio (ii) filling the rectangular mould with the liquid mixture, (iii) putting the mould with the uncured mixture under vacuum for 10 min in order to eliminate undesirable entrapped bubbles, (iv) putting the mould inside a oven at 70°C for 150 min to cure the silicone. Thereafter, the upper faces of the plates were coated with a random pattern made of small speckles (red silicone). Lastly, specimens were cut from the plates using specially designed hollow punches. Notice that a particular attention was paid to respect such a procedure, in order to obtain specimens with reproducible mechanical properties. Also notice that the quality of the coated pattern is decisive to gain a good estimation of the local strain field (see next section).

MECHANICAL TESTING PROCEDURE

All the tested samples were deformed using an universal mechanical tensile testing machine (MTS ABSTRACT: In this contribution, the mechanical behaviour of an unfilled silicone rubber was analysed. Firstly, tensile and pure shear tests were carried out on silicone plates. During the tests, full-field measurements of the strain on the surface of deformed samples were obtained using a Digital Image Correlation technique. Results show that Mullins effects, hysteresis as well as strain rate sensitivity can be considered as negligible. Consequently, three hyperelastic models were fitted with the experimental data (Mooney, Gent and Haines & Wilson models). Secondly, a plate silicone sample containing holes was deformed in tension. In parallel, Finite Element simulation of this experiment was performed with the fitted hyperelastic models. The comparison of experimental and numerical results emphasizes the importance of the choice of the hyperelastic modelling in the simulation of strain fields. For example, this could be fundamental for crack tip analysis. 4M), using both an axial load cell of 125 daN and specially designed autoblocking grips (Fig. 1). During the tests, the deformation of samples and their superimposed pattern was recorded using a CCD camera (JAI, 1280×1024 pixels, 25Hz, see figure 1). Using the Digital Image Correlation Software 7D [START_REF] Vacher | Apport des techniques de corrélation d'images en mécanique : Analyse de déformations et numérisations 3D[END_REF], it was then possible to determine the local strain field on the surface of the deformed samples.

In order to analyse the mechanical behaviour of the silicone, samples were subjected to two types of homogeneous loadings and one heterogeneous one:  Simple tensile tests were performed on bone samples having an initial gauge length l0 of 60 mm and a gauge cross section S0 of 122 mm² (Fig. 2(a)).  Pure shear strain state was approached by performing plane strain tensile tests (Fig. 2(b)). The height l0 as well as the width b0 of samples were 6 mm and 70 mm, respectively.  A tensile test was also performed on a plate (height l0  80 mm, width b0  70 mm) containing five holes (Fig. 3). The central hole has a diameter of 24 mm, whereas the four other hole's diameter was set to 19 mm. Notice that the positions of the centres have not been positioned to produce a regular arrangement, so that the plate does not have any symmetry.

For the two homogeneous tests, monotonic as well as cyclic loadings were performed at constant elongation rate 0 / l l  ranging from 2 10 -4 s -1 to 10 -1 s -1 ( l being the current gauge length). The analysis of the local displacement field deduced from 7D also proved that the strain state in the gauge zones could fairly be considered as homogeneous. Moreover, the plate with holes was subjected to a monotonic loading at a constant crosshead velocity l  =2 10 -4 mm s -1 . For this test, strong strain heterogeneities were recorded.

HOMOGENEOUS TEST

Tests and results

Experiments were designed to evaluate different physical aspects of rubber materials. First, a cyclic tensile test has been performed. Two cycles are realized at six increasing stress levels (cf. timing diagram of figure 4) at 0.008 s -1 elongation rate. This test was designed to evaluate the Mullins effect and hysteretic behaviour of the silicone.

The curves of figure 4 show a perfect non linear elastic behaviour without Mullins effect or hysteretic behaviour since all loading and unloading curves are superimposed. Furthermore, the strain rate sensitivity of this silicone has been studied through a two cycles test at different strain rates: 2 10 -4 s -1 and 10 -1 s -1 . A single specimen has been subjected to two cycles, one at each strain rate. Figure 5 shows no noticeable difference between the cycles so that we can assume the behaviour does not depend on the strain rate within the considered range.

Last, a relaxation test has been performed to test the time dependency of the silicone rubber in a different way. The global force was measured on the bounds of a simple tensile specimen when blocking the elongation at 1.8 for 14 hours. During that time, the stress diminished by 3% (Fig. 6). Consequently it is concluded that the RTV 141 behaviour presents a non-linear elasticity with very few time dependence and without Mullins effect.

Identification

Considering the results given in the previous paragraph, a hyperelastic model seems perfectly adapted to represent the silicone's behaviour. Three energy densities have been chosen: Mooney (1940), [START_REF] Haines | Strain energy density functions for rubber like materials[END_REF] and [START_REF] Gent | A new constitutive relation for rubber[END_REF]. They depend on the first and second invariants of the right Cauchy-Green tensor. Constitutive equations of the energy densities are presented in table 1. These models have been chosen because they are representative, but not exhaustive, of hyperelastic models. Mooney model is the most used in rubber industrial development. Haines and Wilson is a high order of [START_REF] Rivlin | Large elastic deformations of isotropic materials-VII Experiments on the deformation rubber[END_REF] series whereas Gent model is representative of non-Gaussian hyperelastic laws [START_REF] Boyce | Direct comparison of the Gent and the Arruda-Boyce constitutive models of rubber elasticity[END_REF].

The energy density parameters have been fitted on experimental data from tensile and pure shear tests. The values of the parameters are presented in table 2.

HETEROGENEOUS TESTS

To validate the models fitted on uniaxial data, a test with heterogeneous strain fields has been used.

Experimental results

Figure 9 shows a representation of the major principal logarithmic strain field at an current force of 36N, i.e. below the failure of the plate. When increasing the force, a failure occurred between the central hole and the lower right hole. The deformation at a force of 40N, i.e. after the failure, is presented in figure 10.

Some voids are visible in figure 9a owing to local correlation problems in relation with too large speckles in the pattern.

Numerical predictions

The numerical simulations of the above experiment were performed with the finite element code ABAQUS. The material coefficients used are those presented in table 2. The Gent model needs an Umat subroutine while Mooney and Haines & Wilson models are already implemented in ABAQUS. For numerical convenience, the material's models were defined hardly compressible; elements quadratic in displacement and linear pressure were used (C4D20H, see figure 11).

The finite element model geometry was designed using the dimensions of the experimental plate data. It is a 3D model. Furthermore, the holes positions are not symmetric thereby the model could not be reduced.

The lower side of the model is fixed and the upper face has a rigid body vertical displacement and the global force is applied on this face. These boundary conditions are designed to fit the experiment conditions.

Comparison

This part presents results of the experiments and numerical simulations processed in such way that it is possible to compare the data. Three horizontal paths are used: one passing through the upper holes, one through the central hole and one through the lower holes (Fig. 11).

Both states at 36 N and 40N are considered. The test at 36 N has rather moderate strains while the test at 40 N, after partial breakage, induces higher strains.

Below failure

The strain fields considered here have been obtained experimentally through 7D correlation software and numerically with ABAQUS. For the 36N loading, the maximum principal elongation has been plotted along the upper and central paths described previously. The results are respectively presented in figures 12 and 13.

Results show a good agreement between simulations and experiment for the central path (Fig. 12) but the strain remains at a moderate level. But for large deformation on the upper path (Fig. 13) Mooney constitutive equation gives strains too high especially where the elongation is high. It gives an error up to 40% of deformation whereas Gent and Haines & Wilson remain in good accordance with the experimental measurements.

Above failure

In that situation the geometry of the numerical models had to be modified to take into account the breakage. When applying a force of 40N, the differences between simulations and experiment are increased: the partial failure induced higher strain levels in the healthy parts of the plate.

Figure 14 shows a comparison between the photograph of the specimen and the shape predicted by the simulations. In the images, the black outlines are the FE models contour lines.

Once again, the model using Mooney constitutive equation predicts too large deformations while Gent and particularly Haines & Wilson are better.

The curves describing the major elongation are presented in figure 15 for the upper path, in figure 16 for the central path and in figure 17 for the lower path.

Mooney model gives good results for moderate strain while Gent and Haines & Wilson still well fit to the experimental data at large strains. Indeed Mooney model cannot describe the strain hardening of the material and becomes too soft for large deformations thus inducing important errors (120% on the right side of lower path, Fig. 17).

In this case, Gent is a little too soft but still has moderate errors i.e. 20% at the same place. Haines & Wilson gives very good results for every path and at all levels.

CONCLUSION

This paper first gives hints on how to model an unfilled silicone rubber but it also tests constitutive equations in a heterogeneous strain case. In particular, the study developed here shows the local errors made when using an inadequate model. The use of Mooney model for a material presenting an important strain hardening can lead to large overestimations of deformations for a given load. The use of the local strain field given by finite element analysis must be very carefully considered. This strain field is often used for crack tip analysis but errors can be very important. This emphasizes the uniaxial fit quality importance and the knowledge of the modelling limits.

Figure 4 .

 4 Figure 4. Cyclic tensile test: (a) timing diagram of the load applied

Figures 7 Figure 5 .Figure 7 .

 757 Figures 7 and 8 present respectively a comparison between simulations using the hyperelastic energy densities and experimental data for tensile and pure shear tests. Results given here show that the Mooney model can only describe the silicone rubber at low strains because it is unable to represent the strain hardening of the material. On the contrary, Gent and Haines & Wilson models have good results for the whole curves. Nevertheless, Haines and Wilson model is more difficult to fit because of the number of parameters.

Figure 9 .Figure 8 .

 98 Figure 9. (a) Major principal logarithmic strain in the plate with holes submitted to 36N; (b) deformation of the pattern (a) (b)

  Figure 11. FE mesh and paths from which the strain data is extracted

Figure 16 .Figure

 16 Figure 16. Experimental and simulated elongations along the central path at 40N

Figure

  Figure 17. Experimental and simulated elongations along the lower path at 40N

Table 1 .

 1 Hyperelastic energy density constitutive equations

Table 2 .

 2 Values of the hyperelastic energy parameters

ACKNOWLEDGEMENTS

L. Meunier thanks the Région Rhône-Alpes (France) for its financial support.


M Palengat

G Chagnon

C Millet

D Favier

Tube Drawing Process Modelling By A Finite Element Analysis

Keywords: Tube drawing, finite element analysis, elastoplasticity, experimental results. PACS:

Drawing process is used in manufacturing thin-walled tubes, while reducing progressively their wall thickness and their inner and outer diameters. In this paper a stainless steel 3161 VM and a cobalt alloy 1605 are studied with two drawing processes, hollow sinking and plug drawing. This study gets into different issues including elastoplastic behaviour, contacts, friction and numerical convergence. Experimental drawings are realized on a testing bench where forces and dimensional data are recorded. In a first approach, tensile tests lead up to apply an elastoplastic constitutive equation with an isotropic hardening law. In simulations, an axisymetric steady-state model, with numeric stabilization if needed, is used. Numerical results are compared with experimental results. Finally, in spite of some defaults, this study shows that finite element modelling is able to foresee accurately the behaviour of a tube during a drawing process. A better understanding and modelling of the mechanical behaviour of materials will improve the FEM simulation results.

INTRODUCTION

Thin-walled tubes are manufactured with the tube drawing process, reducing progressively inner and outer diameters together with wall thickness. In most cases, industries develop empirically their production. As it induces many experiments, this method costs a lot of time and energy. Numerical simulation is an alternative solution that we explore in this paper. A first step is to characterize the material with simple mechanical tests available for tube geometries; then numerical simulation will allow to test the feasibility of drawing passes and to give an optimized range of production. This will reduce the number of experimental tests and then the cost of development.

Few works exist on tube drawing process but different studies have already been realized to optimize tools' geometries [1] and observe stresses and strains with several drawing processes [2,3,4]. Kamezis and Farrugia [5] developed an optimization procedure based on the Cockcroft-1atham workability failure criterion.

The aim of the present study is to model tube drawing with a finite element (FE) analysis. Two drawing processes, hollow sinking and fixed plug drawing are studied with a stainless steel (3161) and a cobalt-based alloy (1605). Accurate modeling results imply to have a deep knowledge of parameters that affect the process as tools and tubes geometries and of materials behaviour. The main difficulties are due to large deformations and complex contact conditions which must be well characterized and which involve numerical convergence problems. In a first part, drawing experiments performed on drawbenches are described, the second part detail the modelling hypotheses including constitutive equations to describe the materials mechanical behaviour. In a third part, experimental measurements and results predicted by the FE model are compared and discussed.

DRAWING EXPERIMENTS

Tube drawings were realized on a testing bench (Figure 1) with two materials: a stainless steel (3161 VM) and a cobalt-based alloy (1605). First hollow sinking will be introduced and second the drawing process with fixed plug. The simulation of these processes will be realized further and compared with these data.

--==-FIGURE 1. Drawbench.

Hollow Sinking

A first series of measurements has been done on hollow sinking tests. The process is presented in Figure 2. A tube is introduced in a die which has a diameter smaller than the tube outer diameter. Two diamond conical dies with a half angle of 25 ° or 14° respectively have been used. The drawing speed is 2m/min. A load cell takes place on the drawing device to record the drawing force. For the 316LVM alloy, three tests have been realized with different die diameters. The initial tube inner and outer diameters were 2.00 mm and 2.37 mm, respectively. For the L605 alloy, these diameters were 1.81 mm and 2.06 mm, respectively. Details of experiments data (initial tube and die geometries) are listed in table 1.

Load cell '\. I 1ll =I !ij Tube '5 '5 j .!! 0 FIGURE 2. Hollow sinking
The shape of the time-drawing force curve is composed of three parts. When the tube enters in the die, the drawing force increases quickly and reaches a steady state where the force is practically constant. Finally, the drawing force decreases when the tube exits the die. In the following, we will consider only the steady state. Besides the tube extremities are not used for industrial applications as they do not have the same material and geometrical properties. In fact, they are only used to fix the tube. Drawing forces during the steady state and final dimensions were recorded and are summarized in table 1. Each test has been performed twice and results have been identical, accurate to within O.Olmm. Drawing With Fixed Plug Drawings with fixed plug, illustrated in Figure 3, have been performed. The process is similar to hollow sinking except that a fixed plug is inserted inside the tube to impose the final inner diameter. The plug is hold by a metal rod on which a load cell records the force applied on the plug. A diamond conical die with a half angle of 25 ° and a tungsten carbide plug with a half angle of 1 o have been used. One fixed plug drawing experiment has been performed for each of the two materials. In both cases, the same initial tubes as for hollow sinking have been used. For each test, initial and final dimensions, tools geometries, drawing forces and also forces applied on plug have been recorded and summed up in the table 2.

NUMERICAL SIMULATION Hypothesis

As geometries and loading conditions are axially symmetric, an axisymmetric model is used. The steady -state condition is the dominating phase in tube drawing. Then, only the steady state and a part of the total tube's length are considered in a first approach. Tube drawing provides large deformation and then plasticity. Inelastic phenomena and friction generate heat but in a first approach it is assumed that the materials' behaviours are temperature independent. Thus the model does not take into account temperature. Besides, during drawing, strain rates are of the order of 10 to 100 s-1 However, the tests are at room temperature T (300K), and the melting point Tf of the studied alloys are higher than 1500 K; with regard to the ratio T/Tf lower than 0.2, it is assumed that strain rates have little effects and the materials behaviours are considered as insensitive to strain rates in a first approach. Finally, lubricants affect the drawing but lubrication is supposed homogeneous and constant during the process. Thus variations in lubrication are not taken into account and only a friction coefficient will be used to model friction. Then, an elastoplastic constitutive equation is applied to model the materials behaviour, thus it is important to characterize this plastic behaviour. In this way, simple tests are performed.

Physical modelling

Materials Behaviour

The two studied materials (a stainless steel (3161 VM) and a cobalt alloy (1605)) have a large ductility and can be cold formed. Only tensile tests are available for thin-wall tubes. They are easy to realize, but they are not sufficient to understand the material behaviour during drawing. Indeed tensile tests permit to observe only one strain direction and are not sufficient to correctly define the hardening law. Thus, cycling tensile tests have been realized for each material and the stress-strain curves are reported in the figures 4 and 5. They have been performed to observe the elastic springback during unloading: tension up to 700 MPa, reducing stress down to zero followed by a tension until breaking point.

An almost perfectly linear elastic springback is obtained during unloading and the reloading curve is very close to the unloading one. These tests lead up to apply in a first approach an elastoplastic constitutive equation with an isotropic hardening law. The elastic behaviour is described by Young's modulus and Poisson's ratio. The true strain-true stress curve describes the plastic behaviour.

Tools Behaviour

Dies are in diamond (PCD) and plugs are in tungsten carbide (WC). They were assumed to deform elastically because of their high elastic limit. Moreover no plastic deformation has ever been observed on tools after a drawing. Their elastic properties are listed in table 3.

Friction

The friction coefficient depends on a lot of parameters (materials, lubricants, surfaces ... ) and it is difficult to determine it. In metal forming, the Coulomb model accounts for the effects of friction. A shear stress limit could have been applied if there are large normal stresses. This model does not take into account the fluctuation of lubrication. The Coulomb coefficient will be fit with the first simulation as it can be seen in the next paragraph.

Numerical Modelling

Load

Boundary conditions are shown in figure 6. They are the same as in experiments. Dies and plugs are fixed. Tube is drawn with a constant speed. In fact the speed has no influence here, as the model is quasistatic (cf. paragraph Hypotheses).

Meshing

Triangular elements are very versatile and convenient to mesh complex shapes. However, quadrilateral elements are able to provide an accurate solution at less cost. Quadrilateral elements have a better convergence than triangles but are less accurate if they are initially distorted (Abaqus 2006). In our case they are appropriate to mesh all instances except the dies. The use of quadratic elements does not modify results. Consequently, tubes and plugs are meshed with 4-node axisymmetric continuum elements (CAX4). In order to fit well with geometry, dies are meshed mainly with the same elements but also with some triangular elements (CAX3). Quadratic elements were tested but their use does not improve the accuracy of the results.

Friction

A drawing process has been simulated with different friction coefficients and the numerical drawing forces are noted. It shows a linear dependence of the drawing force on the friction coefficient. Then, the 3161 VM hollow sinkings have been used in order to define the friction coefficient. For each drawing, two simulations -one with a friction coefficient equal to zero and one equal to 0.25 -are realized to determine the Coulomb coefficient -drawing force curve (Figure 7). Then, the most appropriate coefficient, for which the numerical force is equal to the experimental force, is determined to be equal to 0.17. This coefficient value will be used for all the following simulations. Besides, since the observed normal stresses are not too large, no shear stress limit is applied.

Convergence

These calculations involve nonlinearities due to large deformations and contacts, which make convergence complex. It can be necessary that an automatic stabilization for static problems should be employed to ease convergence for calculations. Here it is used only for fixed plug drawing calculations. The stabilization parameter, i.e. the damping factor, is problem-dependent and must be fitted so that the viscous energy dissipated by stabilization keeps negligible in comparison with the strain energy in the model. Then, checks of the results and the trimming of the damping factor are needed to trust these simulations.

COMPARISON DRAWING EXPERIMENTS-SIMULATION Observations

Qualitatively, the same behaviours as in experimental process are noticed. First, in sinking, the tube peels off from the die, the centripetal flow continues a bit. The detachment is viewed in figure 8. It implies that sunken tube diameters are slightly lower than die diameters. The detachment is of the order of some hundredths of a millimetre (table 1 ).

Figure 9 presents the time evolution of the drawing force during a hollow sinking simulation. The three parts of the drawing are observed: an increase of the drawing force , a steady state and a decrease. In Figure 9, the simulated tube length is only 10 mm so the steady state is short. The drawing force is noted during the steady state. Moreover, two compression points on the die can also be seen in figure 9. They take place where the tube changes direction and creates stress in the die. Damages are also observed here on real dies on which wear rings are generated during drawing process (Figure 10). Finally, in hollow sinking, the tube is not constrained inside, so the thickness increases to make the reduction of diameters easier.

Compression points

,j B :~":.~•;:9~

Hardening law

Isotropic hardening has been chosen to describe the material behaviour but the tensile tests are not sufficient to be sure of the hardening law. That's why other hardening models are tested to observe the difference between the results. Three hardening models are applied: isotropic, linear kinematic and non linear kinematic hardening. In each case, three die diameters are tested and tube dimensions (<Dextx<Dint) are noted and compared with experimental measurements in the table 4. It can be noted that the hardening model has a great influence on the final geometries. For kinematic hardening, linear or not, the elastic springback is very important

Comparative Statement

Hollow Sinking 1605 tube drawing has been modelled with the same parameters as 3161 VM. An isotropic hardening and a 0.17 friction coefficient has been applied. Like in experiments, inner and outer initial diameters are respectively 1.81 x2.06 mm. All the results are listed in table 5. For each drawing, die geometry is noted. The outer and inner diameters as well as the drawing forces are obtained in the simulation. Then the data predicted by the FE model and the experimental measurements are confronted and the error is noted in percentage. The estimated geometries show good correlation with the experimental measurements. The average error on the geometries for 1605 hollow sinking is about 2.8%. With an average error of 4.8%, the drawing force obtained is also in good agreement with reality, which indicates that the chosen Coulomb coefficient is also pertinent for the contact 1605-PCD.

Drawing With Fixed Plug

Two drawings with fixed plug have been modelled, one with 3161 VM and one with 1605. The friction coefficient is taken again equal to 0.17. Stabilization is used for these calculations. Several calculations have been realized to fit the damping factor. The most appropriate values for this factor are equal to 0.05 and 0.1 for 3161 VM and 1605, respectively. These values permit calculations to converge while viscous forces stay negligible in comparison with the other forces. Dimensions and forces have been compared with experiments. The numerical and the experimental forces as well as the error between them are listed in the table 6. On the one hand, drawn tube diameters are equal to tools diameters in modelling and in experiments so the dimensional accuracy is good. The detachment phenomenon is not present because of the plug. The forces applied on the die are also correct. On the other hand drawing force is overestimated in the model. The overestimation of the drawing force is nearly 17%. This may be due to the numerical stabilization used in these calculations or to the friction coefficient with tungsten carbide.

CONCLUSIONS

Until now, only dimensions and forces data are observed and the results are encouraging. An elastoplastic constitutive equation with an isotropic hardening is applied with a Coulomb friction coefficient of 0.17. Hollow sinking FE model is in good agreement with experimental measurements. Dimensions predicted by the FE model are also good for fixed plug drawing as well, but the predicted forces are overestimated. It may be due to the determination of the materials plasticity model. The stress-strain curves obtained by tensile tests are limited and do not account entirely for the materials behaviour. Indeed during the drawing, the material undergoes two strains: a longitudinal tension and a radial compression. In drawing with plug, the radial compression is large, that's why the forces predicted by the FE model are less accurate than in hollow sinking. Then, a better experimental test must be used. An adapted test would be a tensile test with radial compression at the same time but its realization is difficult. An equivalent of these two strains is the shearing. It seems to be easier to realize and is at the planning stage to define better the material behaviour. Besides, for the contacts with tungsten carbide, the same coefficient (0.17) has been chosen as for PCD. However, several coefficients for the contact tube-plug have been tested and their influence on the drawing force has not been significant. Finally numerical stabilization is also a source of mistakes. It induces overestimated results. Indeed, it causes an increase of the stresses and consequently of the forces. Even if the energy dissipated by the stabilization is checked to be insignificant, drawing forces predicted by the FE model with plug are too large and far from the average error of hollow sinking model. Thus the overestimation due to stabilization must be quantified to ensure it can be used.

FIGURE 3 .

 3 FIGURE 3. Drawing with fixed plug.

316LVM -cycling tensileFIGURE 4 .FIGURE 5 .

 45 FIGURE 4. Stress-strain curve of the 3161 VM cycling test.

FIGURE 6 .

 6 FIGURE 6. Boundary conditions of the drawing process model.

FIGURE 7 .

 7 FIGURE 7. Influence of the Coulomb coefficient on the drawing force for a hollow sinking .

TABLE 1 .

 1 Exrerimental measurements for hollow sinking.

	Initial Tube (<l>extx<I>int) Angle Die mm	Die Diameter (<l>extx<I>int) Final Tube mm mm	Drawing Force daN
			316LVM
	2.37 x2.00	25 °	1,50	l.47 x 1.07	50
	2.37 x2.00	25 °	1.73	1.70x1.30	40
	2.37 x2.00	25 °	2.04	1.98 x 1.60	25
			L605
	2.06 x 1.81	25 °	1.45	l.46 x i.l8	37
	2.06 x 1.81	25 °	1.50	1.49x 1.21	32
	2.06 x 1.81	25 °	1.60	1.59x 1.31	26
	2.06 x 1.81	14°	1.58	1.59x 1.32	29

TABLE 2 .

 2 Exrerimental measurements for drawing with fixed r1ug.

	Material	Initial Tube (<l>extx<I>int) mm	Die Diameter mm	Plug Diameter Mm	Final Tube (<l>extx<I>int) mm	Drawing Force daN	Plug Force daN
	316LVM	2.37 x2.00	1,80	1.50	1.79 x 1.51	62	12
	L605	2.06 x 1.81	1.60	1.50	1.60 x 1.49	47	12

TABLE 3 .

 3 Elastic properties ofthe tube and tools materials.

	Materials	Young Modulus GPa	Poisson Coefficient
	316LVM	210	0.3
	1605	210	0.3
	PCD	950	0.2
	WC	650	0.2

TABLE 4 .

 4 Influence of hardening model on the final tube geometry after a hollow sinking test.

	••03 +2 . 0Be+03
	+1. 830 e+03
	+1.6 47e+03
	+1. 464e• 03
	+1. 28 1e+03
	+1. 098e+03
	+9. 150e+02
	+7 . 320e+02
	• S.490e.,.02
	+3 . 660e+02
	+l.B30e+02
	+2 .933-e-03

~ 400 ~~~NWWW~~~~~~~~MT.~~ z -B 3oo .... FIGURE 10. Drawing ring on a die (ESTEVES-DWD).

TABLE 5 .

 5 Comparison between the results predicted by the FE model and the experience measurements for L605 hollow •nk It appears that the isotropic hardening leads to the results which are the closest from experimental values. So it seems to confirm the choice of an isotropic hardening.

	SI	m g.
		Die	Die		Outer Diameter			Inner diameter		Drawing Force
	Angle	Diameter		(mm)			(mm)		(daN)
			(mm)	Model	Experiment Error Model Experiment Error Model Experiment Error
		25 °	1.45	1.400	1.455	3.8%	1.127	1.181	4.6%	36	37	1.4%
		25 °	1.50	1.452	1.488	2.4%	1.180	1.208	2.3%	33	32	3.1%
		25 °	1.60	1.550	1.586	2.3%	1.280	1.312	2.4%	28	26	7.7%
		14°	1.58	1.556	1.586	1.9%	1.288	1.322	2.6%	31	29	6.9%
	TABLE 6. Comparison between the results predicted by the FE model and the experience measurements for drawing with
	fixed plug
	Material		Model	Drawing Force (daN) Experiment	Error	Model	Plug force ( daN) Experiment	Error
	316LVM		700	625		12%	120		120	0%
	L605		580	470		23%	105		lOO	5%


Ségolène Vandevelde

Adelphine Bonneau

Jacques Élie Brochier

Christophe Petit

Ludovic Slimak

Fuliginochronology: a new way of studying fire events chronicles in archaeological sites. Example of the Grotte Mandrin during glacial period

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

The Grotte Mandrin (France) is a rock shelter located in the middle Rhône Valley, on the left bank of the River. Explored since 1990, its filling is divided into 10 stratigraphic units splittable into 13 archaeological levels. The lower part of the sequence (layers J to G) is attributed to classic Mousterian occupations, while the upper part of the stratigraphy documents late Middle Palaeolithic occupations (levels F to B2) and early Upper Palaeolithic occupations (level B1). At the very top lays a Neolithic level (layer A), recording multiple human cremation events. Soot traces, testifying of control of fire by our ancestors, are witnesses of past human activities. They can sometimes be noticed on the walls and/or vaults of caves and rock shelters and also within calcareous concretions (ex: stalagmites). They prove to be a particularly suitable material for very high temporal resolution archaeology.

At Grotte Mandrin site, wall fragments discovered in the archaeological levels of the shelter are covered with thin (infra-centimetric) black-bluish deposits. These traces result from combustions in the rock shelter during prehistoric times. This soot deposited on the vault is covered and preserved by thin calcareous crusts. Microscopic observation of these concretions shows a kind of "layer cake" in which carbonates blackened by soot and "clean" carbonates are intermingled.

.on soot layer

For analysis, the blackened wall fragments are either polished or thin sections are prepared. They are then observed under microscope in order to reveal the succession of multiple very thin soot films appearing as a single deposit to the naked eye. Position of each film is then recorded from photographs by using DataWald software, usually employed in dendrochronology (study of tree rings).

Collection of these data allows the representation of the succession of soot films in the form of "barcodes". To each sample corresponds its own barcode.

Multiple samples with their unique barcodes are then matched in order to build the entire soot films sequence for each archaeological unit. This graphical representation traces the human occupations' chronicle in the shelter (each soot deposit on the photograph = 1 line on the barcode = 1 occupation at least: two too close occupations will only leave a single black deposit). Occupations can then be counted and their succession rhythm can be studied.

At the Grotte Mandrin, occupations chronicles from archaeological levels F (underlying) and E (overlying) were traced from the wall fragments covered with fuliginous speleothems collected in the filling. Occupations of layer E are attributed to the Neronian: a Middle to Upper Palaeolithic transitional group dated around -50 ky BP. The lithic industries of the Neronian show a very high technicity and, in the state of knowledge, seem to share no technical feature with the rhodanian Quina type Mousterian that precedes it (attributed to Neanderthals, layer F).

Due to the progressive crumble of the walls and vault, some fragments that have fallen in the E archaeological layer may have recorded occupations corresponding to human installations in layer F. The reverse is impossible since wall fragments found in F have already fallen to the ground before arrival of the next group. They can no longer record the new soot deposits left by occupations of layer E. This explains the partial overlap between the occupations' chronicles of layers F and E presented here.

The same situation is observed for layers C&B: occupations' chronicles overlap. Layer B is a sedimentary unit that records three archaeological levels: B1, located at the top of the sedimentary layer, is attributed to Protoaurignacian (generally associated with H. sapiens) and is dated around 42 ky cal. BP. B2 lies directly under level B1 and is separated from B3 by a thin sterile Fuliginochronology allows definition of Minimum Number of Occupations (MNO) per archaeological layer. It also gives an idea of time:

1/ The resolution and precision of the method has made possible the demonstration of rapid succession (few seasons or years) of two different cultural groups in the Grotte Mandrin territory: around 50 ky BP (between Neanderthal's Quina Mousterian and the Neronian) and around 42 ky cal. BP (between the last regional Neanderthalians of Post-Neronian II and the Protoaurignacian, Early Upper Palaeolithic group). We can therefore rethink the Middle to Upper Palaeolithic transition thanks to the unmatched temporal resolution obtained here.

2/ Rhythms of human occupations in a site can also be recorded, at annual scale. In this case, different dynamics of occupation are seen when looking at the position of soot films in DCL/WPL doublets: occupancy dynamics are differing between the different archaeological levels (and cultural groups). It is here noteworthy that Neronian and Protoaurignacian groups succeed very quickly to local Mousterian groups that preceded them. This short time can be evaluated to few years or seasons and must be in any case inferior to a human life generation, meaning that these different cultures are contemporary, at a human scale, on a same territory. The succession rhythm of soot films depends on both the rate of occupation and the climatic conditions (influencing calcite growth). The DCL / WPL alternating in concretions is a seasonal signal related to hydric conditions. These doublets are annual at the Grotte Mandrin, since they alternate on the same scale as the variations in Sr concentration (trace element varying on an annual scale). The annual character of these doublets makes it possible to index the occupations' chronicles on an annual calendar. It thus allows the study of site's occupancy dynamics by past societies.

Mapping of raw data in barcode diagrams

DataWald software ©GLConception

This pioneer method is called Fuliginochronology, from Latin fuliginosus, fuligo: soot, fuliginous. In the particular case of an archaeological site like a rock shelter or a cave, these fuliginous calcite deposits are a record of past human occupations, which can be enumerated (Vandevelde et al. 2017;2018;Vandevelde et Dupuis 2017): Minimum Number of Occupations (MNO) per layer can be defined.

FuliginochronologyCONTEXT

  : a new way of studying fire events chronicles in archaeological sites. Example of the Grotte Mandrin during glacial period Ségolène VANDEVELDEa*, Adelphine BONNEAUb, Jacques É. BROCHIERc, Christophe PETITa, Ludovic SLIMAKd a Université Paris 1 -Panthon-Sorbonne, UMR7041 ArScAn -équipe Archéologies environnementales; b RLAHA, School of Archaeology, University of Oxford; c CNRS, UMR7269 LAMPEA; d CNRS, UMR5608 TRACES; * Fellow of the L'Oréal-UNESCO For Women in Science program 2018

  Moreover, during glacial period, fire use by Neanderthal is common on this site. It is not scarcer during colder periods (layer F or C) or more common during more temperate times (layer D). Theses elements confirm that Neanderthals were able to make fire (unlike Dibble et al. (2018)'s statement).

  two assemblages (+layer C) are assigned to the Post-Neronian II (late group of Mousterian tradition). One again, synthetic sequences overlap.

•

  Dibble, H.L., Sandgathe, D., Goldberg, P., MacPherron, S., Aldeias, V., 2018. Were Western European Neanderthals Able to Make Fire? Journal of Paleolithic Archaeology 1(1):54-79. • Vandevelde, S., Brochier, J.É., Petit, C., Slimak, L., 2017. Establishment of occupation chronicles in Grotte Mandrin using sooted concretions: Rethinking the Middle to Upper Paleolithic transition. Journal of Human Evolution 112: 70-78. • Vandevelde, S., Brochier, J.É., Desachy, B., Petit, C., Slimak, L., 2018. Sooted concretions: A new micro-chronological tool for high temporal resolution archaeology. Quaternary International 474(B): 103-118. • Vandevelde, S., Dupuis, C., 2017. Voyage au bout de la suie. Chroniques des occupations humaines à la Grotte Mandrin, in : Cleyet-Merle, J-J., Shunkov, M.V., Le troisième Homme, Préhistoire de l'Altaï, exhibition, Musée National de Préhistoire, Les Eyzies-de-Tayac, video.


Manuel Jobert and Sandrine Sorlin's collection of articles started off as a tribute to Geoffrey Leech, who was among the first to connect irony and banter in his 1983 Principles of Pragmatics and later in his 2014 Pragmatics of Politeness. But as Jobert and Sorlin make it clear in their introduction, the book soon took off in another direction, as not every researcher in the field considers it helpful to analyze both notions conjointly. The Pragmatics of Irony and Banter then mainly tackles the issue of irony, while three articles (and the introduction) address the issue of banter, either for its own sake or in conjunction with irony. The collection of articles, published in the John Benjamins' "Linguistic Approaches to Literature" series, is not, however, just another book on irony, as its focus is not so much on how irony (or banter) is processed, but rather on its (their) discursive function(s).

The Pragmatics of Irony and Banter is divided into two parts entitled "Theoretical and empirical revisiting of irony (and banter)" and "Irony and banter from 17 th and 19 th century literature to contemporary discourse." Interestingly, Jobert and Sorlin's introduction is both an introduction to the volume as a whole (in the sense that it ends with the required summary of the contents) and the first article of the first part in its own right (in that it "revisits" the literature on irony and banter). Relying on Partington's 2007 and Dynel's 2014 articles, Jobert and Sorlin show how an ironical statement does not merely imply the opposite of its propositional content (which is the classical definition of the trope), but invites its addressees to "reverse the apparent (good or understated) evaluation" involved in the propositional content while winning them over (5). Logically enough, they then emphasize how irony is characterized in the literature by an inherent polyphony, which [START_REF] Sperber | Irony and the use-mention distinction[END_REF]Wilson (1981, 1992) analyze in terms of echoic mention, [START_REF] Ducrot | Les Échelles argumentatives[END_REF]Ducrot ( , 2010) ) and [START_REF] Kerbrat-Orrechioni | L'ironie comme trope[END_REF] in terms of dual argumentative paths, and [START_REF] Kumon-Nakamura | How about another piece of pie: The allusional pretense theory of discourse irony[END_REF] in terms of allusion. Some researchers disagree, though, on the fact that the echo or its variations are central to irony: [START_REF] Clark | On the pretense theory of irony[END_REF] highlight the role of pretense (the utterer just pretending to say what s/he is saying); [START_REF] Attardo | Irony as relevant inappropriateness[END_REF] adds another maxim to Grice's four maxims of conversation to account for irony, "Be appropriate," as he feels that irony derives from contextually relevant, but inappropriate utterances. Simpson's 2011 unifying definition goes back to the central idea of paradox and explains how there can be a gap between what is said and what is meant, or between what is known and a discursive context (8). Jobert and Sorlin finally mention Dews et al.'s 2007 focus on the pragmatic function of irony, that is to say saving face and being funny (8). This shift to pragmatics and politeness theory makes it possible for them to direct their attention towards banter, which paradoxically relies on the idea of (superficially) attacking faces while (actually) saving faces, and promoting camaraderie (Leech 2014) and/or in-group membership [START_REF] Holmes | Politeness, power and provocation: How humor functions in the workplace[END_REF]. Banter has been much less studied than irony (probably in part because it is supposed to be a typically English trait-and thus is not as widespread as irony), and its definition is not self-evident: interaction and reciprocity seem to be a crucial element of banter [START_REF] Labov | Language in the Inner City. Studies in the Black Vernacular[END_REF][START_REF] Lang | No aggression, only teasing: The pragmatics of teasing and banter[END_REF], as well as mock impoliteness [START_REF] Leech | Principles of Pragmatics[END_REF](Leech , 2014)). Chapters 6, 8 and 10, which examine how banter operates and is used in specific contexts, are consequently a welcome addition to the study of banter.

In chapter 2, entitled "Irony in a theory of textual meaning," Lesley Jeffries's ambition is to make sense of the various usages of the term irony for different phenomena (verbal irony, situational irony and even dramatic irony). She posits, like [START_REF] Simpson | That's not ironic, that's just stupid!' Towards an eclectic account of the discourse of irony[END_REF] and others, that incongruity lies at the core of the concept of irony, and that irony does not result from clashes at the basic linguistic level (which only produce puns and ambiguity) but from clashes occurring between different points of her analytical framework, "textual meaning," i.e., between text and text, text and interpersonal meaning, text and situation, etc. She illustrates her typological model with examples collected from diverse literary works, the web and the literature on irony, and distinguishes irony from sarcasm, paradox and hypocrisy.

Chapter 3 deconstructs, as the title indicates, "the myth of positively evaluative irony." Marta Dynel starts with the well-documented premise that irony implies some form of evaluation (as well as "overt untruthfulness," 43), and convincingly argues that it does not imply all kinds of evaluation though. While some authors assert that there can be what Dynel calls positively evaluative irony ("a negative expression implicating a positive intended meaning," 43) alongside negatively evaluative irony ("a positive expression implicating a negative intended meaning," 43), she contends that methodological problems such as inadequate choices of examples (which were often fabricated) led authors to reach the wrong conclusion that there is such a thing as positively evaluative irony. Such utterances are, rather, instances of humorous teasing (47). Dynel further explains that the only case when negative expressions can be said to convey positive evaluations and be interpreted as ironic is when there is actually a central implicit negative evaluation concerning a prior utterance (51). The exclamation "How clumsy!" can be interpreted as conveying an implicit compliment if and only if the interlocutor first said s/he was clumsy in the first place-the exclamation being, in effect, a negative evaluation of that comment, more than a positive evaluation of the person in question. Even if Dynel does not say so in so many words, her demonstration ultimately implies that banter (which is dressed in negative words, but is meant to convey a positive evaluation or at least comradeship) cannot be interpreted as being ironic-but "just" humorous.

In chapter 4, Olivier Simonin identifies three types of verbal irony. A thorough review of the literature enables him to distinguish, first, what is called oppositional or contrastive irony (a type of irony which relies on the idea that there is a gap between the actual state of affairs and the desired state of affairs-the two not necessarily being polar opposites) from echoic / impersonation irony (which relies on both pretense theory and echoic mention theory). After discussing in depth [START_REF] Leech | Principles of Pragmatics[END_REF]2014 pragmatic analyses of irony (and his definition of irony as mock politeness), Simonin then claims that instead of considering that irony can be defined solely as mock politeness, irony-as-mock-politeness or polirudeness should be considered to be a third type of irony.

Chapter 5 by Dan McIntyre examines Louw's 1993 claim that "deviation from conventionalised semantic prosodies can be indicative of irony" (81). Unlike Louw, McIntyre uses the concept of semantic prosody to refer to the discourse function of a unit of meaning, that is to say the reasons why units of meaning are conventionally used, and semantic preference to refer to collocational patterns. He then argues how analyzing high-frequency collocates and their conventional discursive functions can help determine whether an utterance can be interpreted as ironic or not-any disruption of the prevailing semantic prosodies suggesting that the utterer may be ironic. Of course, other factors can help identify ironical clashes of expectations, as McIntyre's study of a sketch from Beyond the Fringe demonstrates.

Part II starts with two articles on irony and/or banter and how they (re)structure the places ascribed to, and relationships between, characters, narrator, author and reader in 17 th and 19 th century literature (Congreve's plays and Thackeray's novels). In chapter 6, Natalie Mandon explains how the term "banter" was used in the 17 th century-in the sense of (sometimes ironically) "causing offense"-and then examines the relationship between skilled ("bantering") and unskilled ("bantered") speakers in Congreve's plays. In chapter 7, Jacqueline Fromonot identifies the speaker's strategy in creating irony (which he directs at himself or others, whether directly or indirectly) and the hearer's reception of these ironical utterances. She stresses the risks of misinterpreting or overlooking irony and, as a result, the importance of guiding the reader and flagging irony.

In chapter 8, Linda Pillière addresses the question of banter in the television show Pointless (BBC, 2009). Relying on Lecercle's ALTER model, she compellingly studies the verbal interactions of several episodes to reveal how the various speakers use banter (each in turn) to attribute specific places to their interlocutors, and enhance their own or their interlocutors' self-image in the process.

In the following chapter, Jan Chovanec makes a qualitative analysis of ironic first-order comments to Czech online newspaper articles about the Austrian government's 2015 decision to build a fence to secure the country's borders against the influx of migrants. He conclusively shows how such comments target the proponents of the official discourse and ultimately aim at building group solidarity, while seemingly denigrating the in-group.

The final chapter of the book, by Sandrine Sorlin, analyzes the promotional video for the 2014 Monty Python Live (Mostly) show, in which banter and irony are given pride of place. She identifies the several functions of the ironic statements of the video (some of which are expressed on a bantering mode), including mocking previous or potential critiques aimed at Mick Jagger himself or Monty Python, hence fostering solidarity with the troupe and enhancing their self-image.

The readers of The Pragmatics of Irony and Banter will appreciate editors Jobert and Sorlin's discrete but welcome interventions, and namely their efforts to show the many potential connections between the various chapters (as they aptly insert references to other chapters when they feel the reader would benefit from reading them conjointly). The fact that various theoretical angles and discursive contexts are represented makes for a very engaging collected volume, which provides much food for thought and will, no doubt, trigger further research in the field of irony, sarcasm, banter and humor.

  The Pragmatics of Irony and Banter Edited by Manuel JOBERT and Sandrine SORLIN John Benjamins Publishing Company, 2018. Hardcover. vi + 221 pages. ISBN 9789027264237 -95 € -DOI: 10.1075/lal.30

	Review by Virginie Iché
	Université Paul Valéry Montpellier 3 -EMMA EA741


B T Yang

G Meng

P Y Xu

X T Tan

Z Q Feng

D H Yang

MAGNETOSTRICTIVE BLOCKED-FORCE CLAMPING MECHANISM FOR SECURE AND HEAVY-LOAD INCHWORM MOTION

The capability of inchworm motor for long-displacement, heavy-load and precise positioning is greatly conditioned by the effectiveness of the clamping mechanism. A need exists in the art for clamping mechanism capable of delivering precise and heavy load motion. This paper presents a novel giant magnetostriction material (GMM) application to the development of such mechanism. GMM is advantageous over other smart materials in this particular aspect by its remarkable magnetostriction and especially the huge blocked stress. It can, e.g., display around 4000N at moderate magnetization with a φ25×100mm GMM rod. Most desirably, such large force could be used as clamping force in inchworm movement. However, the force can only be generated under blocked state, which is generally hard to reach, especially in a moving regime.

Addressing this problem, the research utilizes GMM rod's capacity to both positively stretch and negatively contract under permanent-magnet-biased condition and presents a specially designed clamping mechanism, a permanent-magnetbiased actuator fastened in a rigid guideway. Being applied reverse magnetic field, the formerly stretched actuator may contract to a suitable size to be put into the rigid guideway. Then, removal of the field will theoretically result in the restoration of the actuator. Practically, stretching of the actuator is blocked by the rigid guideway. This forms the so-called Preblocked-clamping-on state, where no-power fastening behavior exists. Moreover, the blocked force is adjustable. When being applied the same-direction field as the permanent one, the blocked force becomes greater (Blocked-clamping-on state). When being applied adequate reverse field, the blocked force is diminished with the shrinking of the actuator, till the actuator released from the rails (Blocked-clamping-off state). This process realizes the utilization of blocked force in clamping action, thus provides resolution for secure and heavy load inchworm motion. A clamping mechanism prototype (Size:φ32×130mm, with a φ10×100mm GMM rod) has been realized. The design and working process of the setup is presented. Through experiments, the prototype can be facilely manipulated by square-instant and sinusoid-continuing current and it can agilely perform to meet the proposed blocked force the proposed clamping principle.

INTRODUCTION

Research into smart-material actuator rather than linear motor has long been the major focus, such as the work in precise positioning over micron-level span, in active vibration control, etc.. Precisely delivering and accumulating the superhigh precise deformation of solid-state smart material is a critical research task to challenge the usual belief that smart materials displacement is too small to adapt in long stroke driving application. The feasibility of applying inchworm moving principle to build a linear motor by steps accumulation to generate an infinite distance has attracted those who aim to change the small span driving actuator into a precise long distance driving motor. Combined with the development of smart materials and the inchworm moving principle, different prototypes of liner motors have been developed in the last decade. Amongst them, the capacity of motor on either large output force or precision positioning or both have been attempted to achieve by some novel and outstanding driving technologies [START_REF] Joshi | Compact magnetostrictive actuators and linear motors[END_REF][2][START_REF] Cusin | Compact and precise positioner based on the Inchworm principle[END_REF][START_REF] Yang | Magnetostrictive mini actuator for long-stroke positioning with nanometer resolution[END_REF]. Though researchers have recognized the importance of the clamping mechanism in implementing quality inchworm movement, they have so far emphasized more on its linear driving part and the solution to the inherent problems such as hysteresis [START_REF] Calkins | An energy-based hysteresis model for magnetostrictive transducers[END_REF], Joule heat [START_REF] Yamamoto | Application of giant magnetostrictive materials to positioning actuators[END_REF], etc.. In fact, we have realized that without an adequate clamping mechanism it is not possible to achieve a smart-material inchworm motor with high precise positioning even if the above-mentioned problems were well resolved. The clamping mechanism more directly affects the motor both on the positioning precision and on the thrust capacity.

CLAMPING MECHANISM OF LINEAR INCHWORM MOTOR

A typical structure of a linear inchworm motor can be illustrated as an H-shaped structure, as shown in Fig. 1. The motor is most necessarily constructed by Part A and C (the Clamping mechanism), Part B (the driving mechanism for doing displacement), and Part D (the guide-way). The motor can move as Part A, B and C are excited in sequence and alternately to do clamping-on or clamping-off actions by A and C against D, and stretching-on or stretching-off by B, see [START_REF] Yang | Magnetostrictive mini actuator for long-stroke positioning with nanometer resolution[END_REF] for the detailed description.

Fig. 1. Schematic of a typical inch-worm linear motor

Clamping mechanism A and C are placed into the guideway D to generate deformation for clamping in the vertical direction, while the driving part B is configured to produce displacement in the horizontal direction. The rigid guide-way D is used for both guiding the moving to be linear and providing clamping force (friction) as it squeezes the top and bottom ends of A or C. According to [START_REF] Calkins | An energy-based hysteresis model for magnetostrictive transducers[END_REF][START_REF] Engdahl | Handbook of giant magnetostrictive materials[END_REF], giant magnetostrictive material (GMM) has almost all the properties that are required for a clamping application, as listed in Table 1. [START_REF] Kim | Magnetostrictive self-moving cell linear motor[END_REF] present a self-moving cell mechanism that can execute both driving and clamping actions during an inchworm movement. Park et al [START_REF] Park | Design and testing of a mesoscale actuator device (MAD)[END_REF] report another clamping method that is rather unique, in which for generating large clamping force, micro-ridges fabricated through MEMS technology is used. There are respective advantages in both clamping mechanisms. The Cell-clamping mechanism can produce large clamping force by the ring elastic deformation against the walls of a guide-way which makes the cell move without slippage and with linearly guided movement. The Microridge-clamping mechanism can also produce large clamping force due to the enhanced friction by the meshed micro-ridges, which also makes the system move with high step-moving repeatability.

A and C: clamping mechanism B: driving mechanism D: rigid guide way A C B D Nevertheless, we realize that there is still room for improvement on the clamping mechanism. Some limitations mainly related to the above two clamping mechanism types exist in such aspects as that: the cell-clamping one's maximum clamping force is most likely limited by the initial configuration, and the clamping force is unable to adjust any larger during work, and the Microridge-clamping one's step is confined by the size of the microridge, the larger the microridge is, the less the resolution becomes.

Aiming to improve the current smart-material clamping technology, a novel giant magnetostrictive clamping mechanism has been proposed in this paper. This clamping mechanism can on the one hand render remarkable and adjustable clamping force as a result of fully demonstrating the GMM property in high stress, on the other hand realize a preclamping regime enabling a no-power clamping ability that is necessarily important for fastening the mechanism body when needed to work at certain slantwise position and on the poweroff occasion.

THE PRINCIPLE OF THE NEW MAGNETOSTRICTIVE CLAMPING MECHANISM

Magnetostriction can be described generally as deformation of body in response to a change in its magnetization and characterized by an even function of the magnetic field [START_REF] Engdahl | Handbook of giant magnetostrictive materials[END_REF], which implies that magnetostriction is proportional to strength H of the applied magnetic fields, and the magnetostriction is independent of the sign of the applied longitudinal magnetization as well. In addition, another fundamental effect to realize the new magnetostrictive clamping principle is that a GMM rod can perform both expansion and contraction by magnetizing it in sequence with two magnetic fields, H 1 and H 2 as illustrated in Fig. 2, both having a magnetic field but with different strength and in opposite directions. This is basically how elongation and contraction are achieved with a GMM rod. Precisely thanks to this effect, the clamping-on or clamping-off actions are realized. Therefore, the principle of the new GMM clamping mechanism is established.

Fig. 2. Illustration to the magnetostrictive expansion and contraction

Accordingly, a clamping mechanism as shown in Fig. 3 has been realized. It is pre-biased by two permanent magnet barrels for field H 1 , and is excited by a solenoid for H 2 . Through controlling the exciting field H 2 , an entire clamping process can be performed, which is illustrated in Fig. 4. M and G indicate the clamping mechanism and the rigid guide-way, respectively; and M, for mimicking its motion when following an inchworm motor walk, is illustrated to go through G from the left side to the right side by such 6 procedures as: 1) M permanent-biased by the magnet barrels for an initial stretch, 2) contracting M by exciting opposite field to the permanent one, meanwhile M cutting in G, 3) making M be in pre-clamping or clamping-on state by cutting off the exciting field, since at this moment, within the rigid guide-way, M tends to recover its initial state and thereby be squeezed in the rigid guide-way (the guide-way width is lesser than the length of the clamping mechanism being stretched in initial state), 4) applying and adjusting the exciting field again, the squeezed extent for M, i.e. the clamping force adjusted, 5) stopping adjustment, M returning to the pre-clamping state, finally 6) contracting M by applying the field opposite to the permanent field till the squeeze loosed, getting M out of G, ceasing excitation, M going back to 1) the initial state. By far, an entire clamping process has been performed. M G H 1 +H 2 Fig. 5 shows the experiment result for testing the expansion and contraction capacity of the prototype with a size of φ 32×130 mm, driven by a φ10×100 mm GMM rod. The prototype is excited with a 670-turns and 1mm thread diameter solenoid and pre-biased by two barrel permanent magnet (NdFeB). Meanwhile, there is a 7 MPa prestress, which is settled according to our previous study [START_REF] Yang | Magnetostrictive mini actuator for long-stroke positioning with nanometer resolution[END_REF], applied on the rod through Belleville springs. A Keyence LK-G30 Laser sensor is used to measure the net displacement.

Moment

M G

Plot in Fig. 5 displays the prototype deformation varied with the scanning magnetic fields from -53.6 to 53.6 kA/m. According to the result, the maximum contraction -53 μm under -13.4 kA/m (-2A current) electromagnetic fields and the maximum stretch 48 μm under 53.6 kA/m (8A current) fields, so that the total 101 μm variable displacement, without any external load, were reached. This displacement capacity of the clamping mechanism is supposedly enough to meet the requirement for completing the proposed clamping principle. And we have further completed another experiment in order to verify each clamping action of the new clamping principle that is illustrated in Fig. 4. The experiment setup is shown in Fig. 6, in which a leading-screw pressing jig and a press sensor are employed. The sensor is sandwiched between the downsideend of the leading-screw and a rigid aluminum bar which is against the upside-end of the standing clamping-mechanism on an aluminum base. By this setup the clamping mechanism can be demonstrated to do the proposed clamping actions in a guide-way that is constructed by the aluminum bar and the aluminum base. In order to simulate the clamping process and demonstrate the related clamping functions, two structured series magnetic fields (i.e. two series currents) have been applied to the prototype, meanwhile both the clamping force and the clamping displacement have been measured through the displacing sensor and the press sensor. It should be noted that though the constructed guide-way by the current setup can offer convenience to measure the clamping change in distance, but can by no means keep completely rigid for measuring the real clamping force, because the employed strain-gauge presssensor itself can deliver withdrawing displacement, when against the clamping force. Nevertheless, we have artificially made the guide-way to be as rigid as possible by applying constraining presses up to 700 N through the leading-screw press jig. The test results are presented in Fig. 7, wherein the variation procedures in clamping displacement are numbered precisely according to the 6 procedures of an entire clamping process as those shown in Fig. 4. Figure 4 is presented again together with Fig. 7 for the convenient reference. In Fig. 7(a), the exciting fields are generated by a series of square currents only, while in Fig. 7(b) the magnetic fields are generated by another series of currents that comprise square currents and a half-sine current. Moreover, during the test, different press: 100 N, 370 N and 700 N for constraining the guide-way was putting on, respectively.

The result, first of all, shows that the new clamping mechanism can be facilely manipulated by instant current (square current) or continuing current (half-sine current) signals and it can agilely perform every action to meet the proposed clamping principle satisfactorily. Secondly, it shows that the more constrain applied on the guide-way, the larger clamping force generated. To be specific, under the current test setup, maximum 1050 N (that is the measuring range of the employed press sensor) clamping force can be obtained when the displacement reaching maximum to around 73 μm under 700 N constrain force, with the clamping adjusting procedure (4) being performed either by the square currents or by the half-sine current. Supposedly, the clamping force potential of this prototype may be distinctively improved if the guide-way provides complete rigidness, to reach up to 1800 N according to Kellogg in literature [START_REF] Kellogg | Blocked-force Characteristics of Terfenol-D Transducers[END_REF]. In addition to the improvement in clamping force, the pre-clamping force of the mechanism may also be greatly improved upon desirably rigid guide-way. With reference to Fig. 5, for the maximum negative displacement -53 μm, the clamping mechanism prototype may generate up to 626 N (according to Kellogg and calculated by the equation (3), young's modulus 15GPa at 6.9MPa [START_REF] Kellogg | Blocked-force Characteristics of Terfenol-D Transducers[END_REF]) pre-clamping force. This force is sufficient to hold the clamping mechanism tightly.

Finally, for another attempt to obtain the ideal blockedclamping force, a new setup, shown in Fig. 8, has been further constructed. The new guideway comprises of two brass rails specially fastened by a hydropress bench-clamp. Supposedly, this new setup may avoid the degradation in clamping force due to the insufficient rigidity like that in the previous setup as shown in Fig. 6.

This time the maximum clamping force is deduced indirectly by the thrust i.e. the friction between the ends of the clamping mechanism and the two rails of the guide-way.

On the one hand, the press-sensor, with its both ends pushed against the leading-screw jig (the same one as used in the previous setup) and the side of the clamping mechanism, has detected the thrust of up to 244N. On the other hand, the friction-factor between the brass rail and steel end of the blocked-clamping mechanism is selected with 0.08 ~ 0.1, according to the handbook of mechanical design [11]. Thus, the maximum clamping force capacity of the designed clamping mechanism is able to reach 1220N ~ 1525N. Fig. 8 A new setup for detecting the clamping force capacity Unfortunately, the theoretically maximum 1800N, according to [START_REF] Kellogg | Blocked-force Characteristics of Terfenol-D Transducers[END_REF], has not yet be obtained even under this new setup, since expending displacements up to around 20 μm of the brass guideway is yet detected as the clamping mechanism performs blocked-clamping actions. This result has stressed us that a mono-case guideway with very sufficient rigidity should be necessarily equipped in the coming motor research. It will take a most necessary role for demonstrating the mechanism's ideal clamping capacity, and the outstanding loading behaviour of the designed motor.

CONCLUSIONS

GMM has been well known especially for its capability of generating significant driving force with super-high energy density. In applications, this outstanding property, however, has not yet been adequately implemented. This paper has presented a new clamping principle that may contribute to inchworm-like linear motor executing great loading capacity, infinite long but very precise displacement, superior stable motion with no backlash and no tilt, and position holding by its peculiar nopower latching behaviour. This paper has verified that the novel clamping principle acts very well through a prototype The prototype with a size of φ32×130 mm, driven by a φ10×100 mm GMM rod has been tested. The clamping force can be adjusted to reach up to 1050 N. And the maximum clamping and pre-clamping force can achieve around 1800 N and 626 N respectively, when served a fully rigid guide-way. The pre-clamping force proves strong enough to hold the clamping mechanism, so the future motor based on this technology may remain its position firmly even on no-power supply occasion. A new constructed rigid brass guideway that is fastened by a hydropress bench clamp is further employed, for attempting to obtain the maximum clamping force of up to 1525N, which is near the theoretically maximum blocked clamping force, 1800N.

Fig. 3 .

 3 Fig. 3. The structure of the clamping mechanism and the prototype photo

Fig. 4 .Fig. 5 .

 45 Fig. 4. Illustration to the principle of the magneto-elastic clamping mechanism EXPERIMENTAL VERIFICATION TO THE CLAMPING PRINCIPLE

Fig. 6 .Fig. 7 .

 67 Fig. 6. Experiment setup for the test of the clamping principle

  bench clamp Brass rail of the guide-way Motion [2] Kim J. W., Kim J. D. and Choi S. B., 2002, "A hybrid inchworm linear motor", Mechatronics 12 pp.525-542 completing each procedure of the proposed clamping process.

Table 1 .

 1 GMM Properties in clamping application potentials

				Potentials for
	Properties	Parameters	clamping
				application
				Large and high-
	Giant and solid-state	1500 ~ 2400	precision
	magnetostriction	(ppm)	deformation	for
				clamping action
	Remarkable compressive strength	700 (MPa)	Attaining remarkable press
	Instant time	response	<1μs	Wideband clamping frequency and no clamping delay