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Channel-die compression at high temperature
Materials Science and Engineering A 476 (2008) 322–332
Channel-die compression at high temperature N. Vanderesse ∗ , Ch. Desrayaud, S. Girard-Insardi, M. Darrieulat Ecole Nationale Sup´erieure des Mines de Saint-Etienne, Centre SMS, Dpt MTT, UMR CNRS 5146, 158 Cours Fauriel, 42023 Saint-Etienne Cedex 2, France Received 17 May 2006; received in revised form 26 April 2007; accepted 30 April 2007
Abstract A new high temperature channel-die compression equipment is introduced. It is designed to operate under inert atmosphere at constant strain rate. Its main characteristics are described and compared to those of a previous appliance based on different principles, and designed for tests up to 600 ◦ C [C. Maurice, J.H. Driver, Acta Metall. Mater. 41 (1993) 1653–1664]. Tests have been performed in the same conditions with both appliances. The stress–strain curves show good agreement, but the deformed samples have different shapes. This difference is explained with the help of a finite element analysis which indicates that the deformation is more homogeneous in the new appliance, where the walls are unconstrained in the vertical direction. The new equipment is currently used to investigate the microstructural evolution of beta quenched Zircaloy-4 up to 750 ◦ C. Some results regarding stress–strain relationships of Zircaloy-4 and deformation heterogeneities of lamellar microstructures are provided; they illustrate the potentialities of this equipment for the simulation of industrial processes. © 2007 Elsevier B.V. All rights reserved. Keywords: Plane strain compression; Channel-die; Zircaloy-4; Twinning
1. Introduction High temperature mechanical tests of materials are a matter of academic and industrial interest. They are used to provide rheological laws that can be implemented in finite element calculations, as well as texture and microstructure characterization which are difficult to perform in an industrial context. Stress–strain relationships are usually derived by three types of deformation tests: uniaxial compression, plane strain compression and torsion. The advantages and drawbacks of these tests have been extensively discussed [2]. To mention but a few, torsion is well suited for investigating large strains without friction effects, nevertheless the deformation path lacks relevance for the majority of industrial processes. The most frequent transformations, forging and rolling, are more realistically simulated by uniaxial and plane strain compressions (PSC), respectively. The last 10 years have seen an increasing interest in PSC, with two main variants: bi-punching and channel-die compression. In the former, a preheated sample is compressed by a punching tool. The relative simplicity of the equipment allows to test up to 1200 ◦ C, and friction is restricted to the upper and lower contact
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surfaces. Nevertheless, a major inconvenient of this technique is the lateral extension of the sample, which leads to vaguely defined plastic zone and strain state. Care should then be taken to extract the stress–strain curves from the force–displacement data [3,4]. By contrast the channel-die compression test offers the opportunity to impose plane strain in most of the sample. It consists of compressing a parallelepipedic piece blocked by two walls that inhibit lateral spreading. The sample can then extend along a single direction and possibly show two modes of shearing. The strain rate tensor has thus two free components, against four in uniaxial compression. Practically, friction is a crucial issue, as it occurs on four of the six faces of the sample. Nevertheless the use of proper lubrication makes this appliance suitable for precise rheological studies, as shown in Ref. [2]. Following an early realization in 1930 [5], Chin et al. popularized the channel-die appliance from 1966 on for the plane strain compression of materials at room temperature [6]. However, its use for hot deformation was restrained by technological difficulties. One was the need of heat-resistant alloys for the die and the punch. Another was to maintain a homogeneous, well-controlled temperature in the sample and in the compressing parts. In the 1990s, several channel-die rigs operating up to 500 or 600 ◦ C were constructed [1,7,8]. The appliance of the Mining School of Saint-Etienne (France) was documented
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Fig. 1. Punch, die and walls.
in Ref. [9]. Since then, it has been used extensively, so that it is referred to below as ‘the medium temperature channel-die’. The four parts (punch, die and two walls) are made of stainless steel. The walls are pressed against the sample by a hydraulic ram, and the channel is 7 mm wide. The quench is performed by means of a pneumatically activated finger. The energy necessary to heat the punch, die and walls is provided to each component separately by graphite resistance heating elements. The heating time of the tools up to 500 ◦ C is of the order of 15 min. The sample is placed in the channel a few minutes before the compression. A distinctive advantage of the channel-die with respect to other compression devices is that the faces of the test piece in contact with the walls remain approximately plane. This facilitates greatly the observation of the local texture by various techniques of microscopy [10,11], or the deposition of grids, allowing the quantification of the deformation at various scales [12]. The test-piece may even be cut into two parts vertically along a plane parallel to the walls: the parts remain pressed one against the other during the compression and observations at the heart of the sample become possible [8]. Nevertheless, the medium temperature device has two limitations: the upper bound of the temperature is 600 ◦ C and the rig does not work under an inert atmosphere. The latter is essential for metals reacting with oxygen at high temperature such as titanium or zirconium. Lubrication has its own limitations, too, as the Teflon TM sheets that are usually wrapped around the samples deteriorate quickly above 400 ◦ C. So an appliance based on different principles has been conceived. Its fabrication is part of a project that focuses on the deformation mechanisms of Zircaloy-4 in the high alpha field and was undertaken under two major constraints, namely reproducing rolling up to 800 ◦ C, and ensure reproducible microstructural and rheological results. The principle of the appliance is documented in the second section, followed by a comparison between tests performed with the medium and high temperature appliances on the same material. The fourth section presents a finite element simulation that accounts for the different kinematic conditions of both appliances. The last section provides rheological and microstructural results obtained on Zircaloy-4, and presents the microgrids/split samples technique as a promising example of the investigations that can be achieved with this equipment.
2. Appliance description The high temperature channel-die is made up of four components: two walls, the punch and the die (Fig. 1). The upper part (acting as the punch) and the lower one (acting as the die) have identical dimensions, so that they follow identical thermal evolutions. The two walls fit into grooves cut in the punch and the die. They can glide vertically during the test. This has a limiting effect
Fig. 2. Setting of the sample and the devices at the beginning of a test. (a) Punch, (b) die, (c) walls, (d) sample and (e) nickel wires.
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Fig. 3. Temperature evolution during the heating to 750 ◦ C.
on friction, as shown below. The usual test-pieces are 7 mm × 10 mm × 8 mm (width, height, length, i.e. constrained direction, compression direction and extension direction, respectively), the face ratio 10/8 resulting from a compromise between friction and strain gradients [13]. The grooves of the higher and lower parts are 100 m wider than the walls, so that the latter do not get stuck into the former during the test. The sample is placed between the walls, the punch and the die at the beginning of the test, and then heated. Thermal uniformity is of concern and requires symmetry with respect to the horizontal plane of the sampledevice system. Nickel wires are thus placed in the grooves below the walls to maintain them at equal distance from the higher and lower grooves’ bottoms during heating (Fig. 2). They crush as the walls go down with the deformation. Temperature is monitored by two thermocouples placed 2 mm underneath the surface of the punch and the die. The four components are made of TZM, a solid-solution hardened and particle-strengthened molybdenum based alloy. Its approximate composition is (wt.%): 0.5 Ti, 0.08 Zr, 0.02 C, balance Mo. The strengthening Ti-carbide particles dissolve around 1400 ◦ C, which makes this alloy suitable for high temperatures applications. The sample and the compressive parts are placed within a 12 cm diameter silica tube. It is enclosed by a circular lighting furnace which transmits heat by radiation. The vertical displacement of the furnace along the silica tube allows the adjustment of the temperatures measured by the thermocouples. Proceeding that way ensures that variations in the zone occupied by the sample are less than 5 ◦ C at 800 ◦ C. The heating time is set to ca 15 min (Fig. 3). It results from a compromise between the heating speed and the thermal homogeneity. The furnace can heat up to 1200 ◦ C. The rig works under a continuous flow of argon, and room is spared to take extra precautions against oxidation by means of a getter which consists of scraps of zirconium and titanium which absorb the traces of oxygen. The channel-die test rig is mounted on a servo hydraulic Schenck machine, the servo system of which was specifically developed to provide sequences of constant strain rates. It is the same machine that is already used by the medium temperature
appliance [1]. This system enables thus to reproduce accurately strain paths specific to industrial hot deformation processes such as forging, rolling . . . The real time adaptability of the electronic device permits high frequency sampling of the displacement. The strain rate value can be updated every hundredth of second through the gain of an electronic loop. The upcoming displacement value is then adjusted so as to maintain the gain at an average value: increased if the ram is too fast and decreased if too slow. This system allows the control of the displacement following aperiodic signals required to apply constant strain rates. Strain rates between 10−4 and 20 s−1 can be obtained with the two servo valves available on the system. The displacement and load ranges are, respectively, 100 mm and 100 kN. The quenching system has been designed with special care (Fig. 4(a) and (b)). A mechanical finger (c) worked out manually hits the sample (d) and projects it in less than 1 s down the silica tube. To facilitate this manipulation, the punch moves 1 mm upward right after the end of the compression. The sample falls into a small chamber which fills with cold water as soon as the argon flow is interrupted. As can be seen from Fig. 4(a) and (b), due to dimensional constraints the sample cannot be completely pushed outside the channel by the finger. The impact of the finger on the sample has to be strong enough to eject it dynamically. In practice, this is achieved for nominal deformations up to ca 0.30. Beyond this value, the axis (a) has to rotate further, which causes the arm (b) to get in contact with the walls. The latter are then ejected along with the sample, which makes the quench somewhat less significant. This limitation is likely to be extended by the use of specific lubricants that must be determined for any newly tested material. In the scope of the study presented hereafter, the quenching system fulfils its function, since moderate deformation steps are required so as to observe the initiation of the deformation mechanisms. 3. Compared tests on the medium and high temperature appliances Since the medium temperature channel-die has proved to be a reliable equipment for studying the rolling of metals, it appeared
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at 400 and 500 ◦ C at a strain rate of 0.1 s−1 . It has been seen that in the high temperature appliance, the tools and the sample are heated together, due to the necessity to confine the protective atmosphere. So were they in the medium temperature appliance, so as to guarantee an identical state for the material and the lubricant at the beginning of the test in both configurations. The heating time was of the order of 15 min in each case. This is the reason why boron nitride spray was chosen as lubricant instead of Teflon TM sheets, since they melt down when heated more than a few minutes above 400 ◦ C. The material was considered a von Mises solid with a material flow stress (or von Mises equivalent stress) σ0 . The latter varies with the equivalent strain ¯ . If h0 and h are the initial and current height of the sample, ¯ is given in the case of the plane strain compression by h0 2 (1) ¯ = √ ln h 3 while it is ¯ = ln(h0 / h) in the case of uniaxial compression. Friction was described according to the Tresca analysis by the shear stress of the form: σ0 (2) τ=m ¯√ 3
Fig. 4. Schematic functioning of the quenching system (the punch is not represented). (a) Axis, (b) arm, (c) finger and (d) sample.
interesting to compare it with the new appliance in the same conditions. Tests were performed on both appliances, using the same material, lubrication and test conditions. The samples were made of the AISI 1010 (AFNOR XC10) low carbon steel. Its composition in weight percentage can be resumed briefly as 0.08–0.13 C, 0.3–0.6 Mn, Fe balance. The tests were performed
m ¯ being the Tresca coefficient. Following Refs. [14] and [15], it was taken an m ¯ = 0.1. It is now necessary to explain how σ0 can be calculated from the measurement of the stress applied by the punch σa . The power input transmitted by the rams is the sum of ˙ P and the power of friction the plastic deformation work rate W F ˙ W . The problem is to separate them so as to obtain the equivalent flow stress σ0 of the material, supposed to be an isotropic von Mises solid. Such an analysis can be found in Ref. [13] in the case of fixed walls (medium temperature appliance). It consists of a finite element calculation backed by a variational approach, compared to an analytical solution assuming homogeneity of the deformation in the sample. Among other results, it is found that the analytical calculation provides a good estimation of σ0 , which means that the inhomogeneity of the deformation weakly affects the overall flow stress. σ0 can be derived from σa by the
Fig. 5. Comparison of the stress–strain curves of XC10 alloy tested at 400 and 500 ◦ C in the medium (disks) and high (crosses) temperature appliances at ¯˙ = 0.1 s−1 .
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Fig. 6. XC10 samples deformed to ¯ = 0.75 at 400 ◦ C, at ¯˙ = 0.1 s−1 in the medium (left) and high (right) temperature appliances.
expression: ˙ F −1 W σ0 = σa 1 + P ˙ W
(3)
˙ F /W ˙ P shows that it is The analytical formulation of the ratio W proportional to m ¯ and that it also depends on the initial aspect ratio of the sample and on ¯ . Here, this analysis has been applied to both configurations, i.e. fixed and mobile walls. In the latter case, it will be established in Section 4 that it provides a good approximation of σ0 . The stress–strain curves are given in Fig. 5. In the transient phase, up to ¯ = 0.2, the curves obtained with fixed walls are higher than the others. At higher deformation they are much the same, especially at 500 ◦ C. In both cases the sample has to adapt to the rig before the full effect of the applied force is transmitted, but it takes more time in the case of mobile walls. Nevertheless, the main matter of interest for hot deformation is the steady regime, for which the agreement is very good. However, Fig. 6 shows that the samples have different shapes. In the medium temperature apparatus, the upper face is longer than the lower one. This does not happen with the high temper-
ature apparatus: both faces have the same length, but barrelling is observed at mid-height. The following section aims at giving an explanation to this difference by means of a finite element analysis. 4. Finite element simulation: fixed and mobile walls 4.1. Strain homogeneity Besides the material, the protective atmosphere and the heating system, the principal difference between the medium and high temperature appliances resides in the mobility of the walls. Following Ref. [13], these distinct kinematic conditions have been simulated using the finite element code ABAQUS TM in its standard implicit version. In the mobile walls configuration, a vertical degree of freedom was allowed to the walls, due to the depth of the grooves. They are in fact dragged by the sample as the punch moves down. All the tools were treated like rigid bodies and the sample flow rule was assumed to fit a Norton Hoff law of the form: σ0 = k¯˙
m
(4)
Fig. 7. Repartition of the calculated frictional and plastic works in the mobile and fixed walls configurations with m ¯ = 0.1 (MW: mobile walls; FW: fixed walls; Pl: plastic work; Fr: frictional work; Total: total work). (a) m ¯ = 0.02, (b) m ¯ = 0.02, (c) m ¯ = 0.10, (d) m ¯ = 0.10, (e) m ¯ = 0.20 and (f) m ¯ = 0.20.
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k being the consistency, and m is the strain rate sensitivity. This flow rule is not temperature sensitive because tests are performed isothermally. Eight-node fully integrated brick elements were chosen to mesh the sample. The contact between the sample and the tools was treated by means of Lagrange multipliers to control the node penetration into the rigid bodies. The tangential behaviour was treated by a penalty method, and the flow stress considered for the calculation of the shear stress τ due to the friction was taken locally in each element submitted to contact. τ was limited by the value of the flow stress multiplied by the friction coefficient. For the sake of homogeneity with the rest of this article, the results are presented using m ¯ (Tresca description). In fact the ABAQUS TM code uses a Coulomb coefficient, but the correspondence between both is straightforward [13]. The calculations were performed incrementally assuming that equilibrium was achieved at the end of each increment. No dynamic effect was considered. Tresca coefficients ranging from
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0.02 to 0.2 were used. Values of k = 350 MPa and m = 0.12 were assumed. They do not refer to a particular metal but are current orders of magnitude with metallic alloys. The strain rate was ¯˙ = 0.1 s−1 . Fig. 7 has been done with m ¯ = 0.1, but the conclusions are identical for 0.02 ≤ m ¯ ≤ 0.2. It shows the total work provided by the ram and the respective contributions of the plastic deformation and the friction. The mobility of the walls has no profound impact either on their repartition or on their sum. Hence, for both rigs, the analytical formula (3) is a good approximation to estimate the material flow stress σ0 from the experimental applied stress σa . Fig. 8 exhibits the influence of the configuration (mobile or fixed walls) on the shape of the sample for various friction coefficients. As found experimentally, the shapes of the deformed samples differ significantly, except for low friction coefficients.
Fig. 8. Contours of the plastic equivalent strain at ¯ = 0.8 in the fixed walls (left) and mobile walls (right) configurations for various friction coefficients. (a), (b) m ¯ = 0.02, (c), (d) m ¯ = 0.10, (e), (f) m ¯ = 0.20. For m ¯ = 0.1, please note the similarity between the simulated and real samples presented in Fig. 6.
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the rolls. Since channel-die compression is largely regarded as a good simulation of rolling, the central part of the samples compressed with the new rig are particularly suitable for microstructural analyses linked to the processing of sheets. 5. Application to the study of Zircaloy-4 5.1. Context
Fig. 9. Distribution of the plastic equivalent strain calculated at ¯ = 0.8 in the fixed walls configuration.
In both cases, some inhomogeneity is observed in the strain distribution. The scatter of the strain throughout the sample can be visualized through the representation of the equivalent strain values computed at the centroid points of the integration elements (Figs. 9 and 10). In each case the distribution is centered on the imposed strain, the main difference being that the values are less scattered in the mobile walls configuration. Above the value 0.10, the friction coefficient has a limited impact on the spread of the deformation. The relative velocities of the sample and the walls thus affects the homogeneity of the strain, which in turn determines the shape of the sample. When the walls are free to move in the vertical direction, the strain is more homogeneous and the deformed sample has a symmetrical shape with respect to the horizontal plane at half height. These observations can be explained by considering that one of the sources of inhomogeneity is the difference of vertical velocity between the upper and the lower faces of the sample. This difference is considerably reduced with mobile walls. It is worth noting, too, that rolling is also a process symmetrical with respect the plane which runs at mid distance from
As mentioned before, the first use of the new appliance is the investigation of the deformation mechanisms of Zircaloy-4 in its beta quenched state. The rheological and microstructural characterization reported hereafter illustrate the potentiality of the appliance. The Zircaloy-4 is a zirconium alloy which finds its main use in the nuclear industry. It presents two allotropic forms: beta phase body cubic centered (bcc) at high temperature, and alpha phase hexagonal close packed (hcp) at room temperature. The alloy is biphased between 810 and 980 ◦ C. A key step of the industrial forming process consists in a quench from the beta phase field (around 1050 ◦ C), which produces the so-called Widmanst¨atten microstructure. It is entirely constituted by alpha lamellae that are more or less entangled. They are delimited by a thin layer of intermetallic precipitates that form during quenching [16]. The following transformation steps aim at globulizing the lamellae so as to obtain an equiaxed microstructure in the finished product. From the quench, all thermomechanical treatments are performed without any new phase transformation (i.e. under 810 ◦ C). The response of the microstructure to the deformation appears to be very heterogeneous: while some lamellae tend to fragment and form buckling-like patterns, others orientate themselves perpendicular to the loading direction. Several nonexclusive factors can give an explanation to this variety of behaviours: crystalline anisotropy (as investigated by Bieler and Semiatin in a Ti alloy [17]), morphological anisotropy (i.e. orientation of the lamellae relatively to the strain direction, as is the case in a wide range of stratified media [18]), correlation of the deformation between neighbouring zones of the material (as studied by Doumalin et al. in an equiaxed Zr alloy [19]). It is shown below that the study of these phenomena during rolling is made possible by the use of the high temperature appliance. 5.2. Determination of the friction coefficients
Fig. 10. Distribution of the plastic equivalent strain calculated at ¯ = 0.8 in the mobile walls configuration.
Lubrication is a major concern of the experimental procedure, since four faces of the sample are in contact with the pieces. The tools have been lubricated with graphite spray. As for the samples, several solutions have been tested: boron nitride spray, graphite spray, pre-oxidized samples, and a specific lubricant furnished by the Zircaloy-4 manufacturer CEZUS. The latter has given the best results: it remained efficient until 0.8 of von Mises deformation, and assured the ejection of the sample without difficulty. Ring compression tests have been carried out to determine the friction coefficient of Zircaloy-4 against TZM with this lubri-
N. Vanderesse et al. / Materials Science and Engineering A 476 (2008) 322–332 Table 1 Determination of the Tresca friction coefficients between TZM and industrially lubricated Zircaloy-4, under inert atmosphere from 650 to 800 ◦ C, at ¯˙ = 0.1 s−1 Temperature (◦ C)
Deformation
D
m ¯
650 700 750 775 800
0.38 0.41 0.40 0.41 0.36
0.08 0.05 0.04 0.03 0.02
0.18 0.13 0.13 0.11 0.12
cant. This method has been first proposed by Male and Cockcroft [20]. It is based on the variation of the internal diameter of a ring that has been compressed at a given strain, and the friction coefficient μ is derived from an abacus. The internal diameter variation is expressed as D =
Di1 − Di0 Di0
(5)
where Di0 and Di1 are the initial and final internal diameters. Rings of internal diameter 6.35 mm, external diameter 9.5 mm and height 19 mm were used. They respect the dimensional ratios 1:1.5:3 corresponding to the abacus established by Male and Cockcroft. The tests were performed under inert atmosphere at temperatures ranging from 650 to 800 ◦ C at a rate of 0.1 s−1 . The results are summarized in Table 1. In the range of interest (i.e. between 750 and 800 ◦ C), the values of m ¯ are of the order of 0.1. This is substantially higher than what can be achieved at lower temperatures, especially using Teflon TM sheets, but it should be recalled that the oxidation, which is very active in the case of heated zirconium even in protective atmosphere, has a detrimental influence on the friction characteristics. Using these values allowed the determination of σ0 from the experimental σa , as previously done for the XC10 alloy.
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5.3. Rheological results The rheological characteristics of Zircaloy-4 were evaluated through uniaxial and channel-die compression. The tests were carried out with the same servo-hydraulic machine, between 650 and 750 ◦ C under inert atmosphere, at a strain rate of 0.1 s−1 . The same lubricant was used, and the uniaxial compression tools (i.e. punch and die) were also made of TZM. Accordingly, the analysis of the raw data takes into account the friction coefficients determined by the ring tests. In uniaxial compression, the stress was computed following the method of Avitzur [21]. The stress–strain curves are reported in Fig. 11 with the usual definitions of ¯ for plane and uniaxial compression recalled in Section 3. Some discrepancy exists in the transient states but the steady states match closely, especially at 750 ◦ C. This confirms the rheological qualities of the high temperature channel-die. However, its main interest lies in the facilities it provides in the study of microstructures, as developed hereafter. 5.4. Microstructure Two types of tests have been carried out: • compression of one-piece samples, • compression of split samples: each half sample is 3.5 mm wide, the other dimensions being unchanged, and is pressed against another one throughout deformation. The results given here concern the second technique, which is less usual than the first one. To the best of the authors’ knowledge, it has been used on metals only twice, by Panchanadeeswaran and Doherty [8] on aluminium samples at 375 ◦ C in channel-die, and by Hernandez-Castillo et al. on steel at 900 and 950 ◦ C in bi-punching [22]. It has the strong advantage to permit observations of the same microstructural region during successive deformation steps, provided the internal surfaces do
Fig. 11. Comparison between the stress–strain curves in uniaxial and channel-die compressions for Zircaloy-4 at ¯˙ = 0.1 s−1 (circles: uniaxial compression, squares: channel-die compression).
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not alter too much. It is worth reminding that if this is an aim that can now be achieved in a non-destructive way on aluminium using a synchrotron beam [23], this is out of reach for zirconium, which is a very X-rays absorbent medium. At low temperature and with Teflon TM sheets, it is also possible to observe the sides of the sample as illustrated in Ref. [12], but in the tests discussed here, the lubricant covers the sample with a hard coating that prevents all investigation after deformation. The first example concerns twinning at high temperature in Zircaloy-4. Twinning is often mentioned at room temperature where it is complementary to pyramidal slip for the accommodation of strains along the c-axis of the hexagonal cell. At high temperature it is generally admitted that pyramidal slip overrides twinning [24]. Fig. 12(a) and (b) are micrographs of the same zone of a half sample before and after deformation (T = 750 ◦ C, ¯ = 0.05 and ¯˙ = 0.1 s−1 ). It is a so-called parallel platelets zone: the lamellae are parallel to each other and despite the layer of precipitates, they share the same crystallographic orientation. Such a group of parallel lamellae is called a colony. Three colonies can be seen—they are marked as (a), (b), (c) in Fig. 12, and each one belongs to a different ex-beta grain. The boundaries of these grains are still visible. The surface after deformation
Fig. 12. Twinning activity at 750 ◦ C in Zircaloy-4. (a) Microstructure before deformation and (b) microstructure after deformation.
appears altered by the oxidation and the contact against the other half sample. Nevertheless, rectilinear, parallel, dark marks are observed in each of the colonies. Between colonies (a) and (b), they cross the former beta grain boundary. In spite of the oxide layer, a partial determination of the orientations has been performed by EBSD. It reveals that each mark is a lenticular {1 0 1¯ 2}twin, which presents a characteristic disorientation angle of ca 85◦ around an a-axis common with the matrix. Perpendicular marks in colony (c) indicate that two twin modes have been activated. This is a direct proof of the twinning activity at high temperature occurring at the onset of plasticity. The dimensions and orientations of the colonies are undoubtedly no stranger to that fact, as it is known that the alpha grain size favors twinning [25]. The second example presents some results obtained by the microgrids technique. Microgrids have been chemically etched on split samples prior to deformation, using a diluted Kroll reagent (10% 1.2N diluted HF, 90% 5.5N HNO3 ). The choice of etching instead of sputtering fiducial grids [26,27] was driven by the severe conditions undergone by the surfaces during the tests (oxydation, contact with the other half sample’s surface, and deformation itself). The integrity of the microgrids is thus improved, at the price of a lower accuracy: the lines are 1.5–2 m wide, and the step size is about 12.5 m. The same microgrid observed after 7.5% deformation (Fig. 13) reveals that some zones have been intensively sheared between adjacent colonies. A more detailed analysis is under work. It is based on the optical phase shift caused by the deformation of the grids [28], and will allow to map the plane strains. The whole strain state cannot be tracked down by this method, however. Indeed, deformation at this scale is far from being plane, as shown in Fig. 14. In this example, relief imaging has been performed using the imaging software ANALYSIS TM . The amplitude of out-of-plane displacements is of the order of 100 m. It is also interesting to note that the surfaces are in close mechanical contact. Fig. 15 shows the internal surface of a split
Fig. 13. 2D view of a microgrid after a strain of ¯ = 0.075 (T = 750 ◦ C, ¯˙ = 0.1 s−1 ). The arrows indicate intensively sheared zones between neighbouring colonies.
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Fig. 14. 3D view of the microgrid of Fig. 13(65 m/graduation).
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microstructural and micromechanical insights into the deforming material. Special care has been devoted to the design of the rig so as to guarantee its thermal uniformity, the reduction of the effects of friction, and quenching efficiency. This issue has been solved for Zircaloy-4 up to 800 ◦ C, but should of course receive attention for any new material. The appliance is built so as to reach 1200 ◦ C, but the feasibility of such tests has yet to be proved. The design of the rig yields a more homogeneously distributed strain within the sample in comparison with the fixed walls configuration. This is clearly visible on the deformed samples, and has been reproduced through finite element simulation. The macroscopic stress and strain values measured on the same material, however, remain equivalent in both configurations. High temperature stress–strain curves have been obtained on Zircaloy-4 samples, as well as optical characterization of a same microstructural zone between successive compression steps. As a first result, the activation of lenticular twinning at 750 ◦ C has been observed. The microgrid technique has been successfully adapted to the case of split samples. Out-of-plane displacement have been put into evidence, as well as shearing zones localized between adjacent colonies. These deformation patterns are considered to be representative of the behaviour of one-piece samples, since observations show that half samples are in strong mechanical contact throughout the deformation. These possibilities make this appliance a promising means of investigating the microstructural and rheological evolutions of materials during high temperature plane strain compression. Acknowledgements The authors would like to thank Mr. Barb´eris and Mr. Barritou (CEZUS, France) for providing the Zircaloy-4 material and its lubricant, Mr. Douet (Mining School of Saint-Etienne) for conceiving the quenching bath.
Fig. 15. Printing in relief of a microgrid (T = 750 ◦ C, ¯ = 0.075, ¯˙ = 0.1 s−1 ).
sample which had no microgrid etched on it prior to deformation. Regular marks are visible: they were created by the printing in relief of the microgrid that was present on the opposite half sample. Out of plane displacements of each half sample are then closely linked. This comforts the idea according to which the local deformations at the half samples’ surfaces are representative of those occurring within a one-piece sample, which are out of reach otherwise. 6. Conclusions Up to now, channel-die compression was limited to an upper bound of 600 ◦ C due to several technological difficulties. These have been overcome to produce a new appliance which has been successfully tested up to 800 ◦ C under a protective atmosphere at constant strain rate. In addition to compression of one-piece samples aimed at rheological results, it permits the compression of split samples so as to get
References [1] C. Maurice, J.H. Driver, Acta Metall. Mater. 41 (1993) 1653–1664. [2] C. Maurice, D. Piot, H. Klocker, J. Driver, Metall. Mater. Trans. A 36A (2005) 1039–1047. [3] R.W. Evans, P.J. Scharning, Mater. Sci. Technol. 20 (2004) 431–440. [4] N.J. Silk, M.R. van der Winden, Mater. Sci. Technol. 15 (1999) 295–300. [5] V.F. Wever, W. Schmid, Z. Metallkd. 22 (1930) 133– 140. [6] G.Y. Chin, E.A. Nesbitt, A.J. Williams, Acta Metall. Mater. 14 (1966) 467–476. [7] J.M.T.G. Langdon, H.D. Merchant, M. Zaidi, in: Hot Deformation of Aluminum Alloys Metallurgical Society Conference, The Minerals, Metals and Materials Society, Detroit, 1990. [8] S. Panchanadeeswaran, R.D. Doherty, Scr. Metall. Mater. 28 (1993) 213–218. [9] B. Mor`ere, Recristallisation d’un alliage d’aluminium 7010 apr`es d´eformation a` chaud; influence sur la t´enacit´e, PhD Thesis, Institut National Polytechnique de Grenoble, 1999 (in French). [10] Y. Huang, F.J. Humphreys, Acta Mater. 48 (2000) 2017–2030. [11] N. Stanford, D. Dunne, M. Ferry, Mater. Sci. Eng. A 348 (2003) 154– 162. [12] D. Chapelle, M. Darrieulat, Mater. Sci. Eng. A 347 (2003) 32–41. [13] C. Chovet, C. Desrayaud, F. Montheillet, Int. J. Mech. Sci. 44 (2002) 343–357.
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[14] C. Desrayaud, S. Girard, J. Le Coze, F. Montheillet, Mater. Trans. 43 (2002) 135–140. [15] C. Desrayaud, S. Girard, L. Vaughan, J. Le Coze, F. Montheillet, Mat´eriaux et Techniques (2003) 70–74. [16] R.A. Holt, J. Nucl. Mater. 35 (1970) 322–334. [17] T.R. Bieler, S.L. Semiatin, Int. J. Plasticity 18 (2002) 1165–1189. [18] H. Ramberg, Geol. Rundsch. 51 (1961) 405–439. [19] P. Doumalin, M. Bornert, J. Cr´epin, M´ecanique & Industries 4 (2003) 607–617 (in French). [20] A.T. Male, M.G. Cockcroft, J.I. Met. 93 (1964) 38–46. [21] B. Avitzur, Metal Forming: Processes and Analysis, Mc Graw-Hill, NewYork, 1968.
[22] L.E. Hernandez-Castillo, J.H. Beynon, C. Pinna, S. van der Zwaag, Steel Res. Int. 76 (2005) 137–141. [23] H. Sorensen, B. Jakobsen, E. Knudsen, E. Lauridsen, S. Nielsen, H. Poulsen, S. Schmidt, G. Winther, L. Margulies, Nucl. Instrum. Meth. B 246 (2006) 232–237. [24] E. Tenckhoff, ASTM special technical publication STP 966, ASTM, 1988. [25] A. Salinas-Rodriguez, Acta Metall. Mater. 43 (1995) 485–498. [26] D.G. Attwood, P.M. Hazzledine, Metallography 9 (1976) 483–501. [27] L. Allais, M. Bornert, T. Bretheau, D. Caldemaison, Acta Metall. Mater. 42 (1994) 3865–3880. [28] F. Pierron, E. Alloba, Y. Surrel, A. Vautrin, Compos. Sci. Technol. 58 (1998) 1939–1947.
Channel-die compression at high temperature N. Vanderesse ∗ , Ch. Desrayaud, S. Girard-Insardi, M. Darrieulat Ecole Nationale Sup´erieure des Mines de Saint-Etienne, Centre SMS, Dpt MTT, UMR CNRS 5146, 158 Cours Fauriel, 42023 Saint-Etienne Cedex 2, France Received 17 May 2006; received in revised form 26 April 2007; accepted 30 April 2007
Abstract A new high temperature channel-die compression equipment is introduced. It is designed to operate under inert atmosphere at constant strain rate. Its main characteristics are described and compared to those of a previous appliance based on different principles, and designed for tests up to 600 ◦ C [C. Maurice, J.H. Driver, Acta Metall. Mater. 41 (1993) 1653–1664]. Tests have been performed in the same conditions with both appliances. The stress–strain curves show good agreement, but the deformed samples have different shapes. This difference is explained with the help of a finite element analysis which indicates that the deformation is more homogeneous in the new appliance, where the walls are unconstrained in the vertical direction. The new equipment is currently used to investigate the microstructural evolution of beta quenched Zircaloy-4 up to 750 ◦ C. Some results regarding stress–strain relationships of Zircaloy-4 and deformation heterogeneities of lamellar microstructures are provided; they illustrate the potentialities of this equipment for the simulation of industrial processes. © 2007 Elsevier B.V. All rights reserved. Keywords: Plane strain compression; Channel-die; Zircaloy-4; Twinning
1. Introduction High temperature mechanical tests of materials are a matter of academic and industrial interest. They are used to provide rheological laws that can be implemented in finite element calculations, as well as texture and microstructure characterization which are difficult to perform in an industrial context. Stress–strain relationships are usually derived by three types of deformation tests: uniaxial compression, plane strain compression and torsion. The advantages and drawbacks of these tests have been extensively discussed [2]. To mention but a few, torsion is well suited for investigating large strains without friction effects, nevertheless the deformation path lacks relevance for the majority of industrial processes. The most frequent transformations, forging and rolling, are more realistically simulated by uniaxial and plane strain compressions (PSC), respectively. The last 10 years have seen an increasing interest in PSC, with two main variants: bi-punching and channel-die compression. In the former, a preheated sample is compressed by a punching tool. The relative simplicity of the equipment allows to test up to 1200 ◦ C, and friction is restricted to the upper and lower contact
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Corresponding author. Tel.: +33 477 42 66 23; fax: +33 477 42 66 78. E-mail address: [email protected] (N. Vanderesse).
0921-5093/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2007.04.118
surfaces. Nevertheless, a major inconvenient of this technique is the lateral extension of the sample, which leads to vaguely defined plastic zone and strain state. Care should then be taken to extract the stress–strain curves from the force–displacement data [3,4]. By contrast the channel-die compression test offers the opportunity to impose plane strain in most of the sample. It consists of compressing a parallelepipedic piece blocked by two walls that inhibit lateral spreading. The sample can then extend along a single direction and possibly show two modes of shearing. The strain rate tensor has thus two free components, against four in uniaxial compression. Practically, friction is a crucial issue, as it occurs on four of the six faces of the sample. Nevertheless the use of proper lubrication makes this appliance suitable for precise rheological studies, as shown in Ref. [2]. Following an early realization in 1930 [5], Chin et al. popularized the channel-die appliance from 1966 on for the plane strain compression of materials at room temperature [6]. However, its use for hot deformation was restrained by technological difficulties. One was the need of heat-resistant alloys for the die and the punch. Another was to maintain a homogeneous, well-controlled temperature in the sample and in the compressing parts. In the 1990s, several channel-die rigs operating up to 500 or 600 ◦ C were constructed [1,7,8]. The appliance of the Mining School of Saint-Etienne (France) was documented
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Fig. 1. Punch, die and walls.
in Ref. [9]. Since then, it has been used extensively, so that it is referred to below as ‘the medium temperature channel-die’. The four parts (punch, die and two walls) are made of stainless steel. The walls are pressed against the sample by a hydraulic ram, and the channel is 7 mm wide. The quench is performed by means of a pneumatically activated finger. The energy necessary to heat the punch, die and walls is provided to each component separately by graphite resistance heating elements. The heating time of the tools up to 500 ◦ C is of the order of 15 min. The sample is placed in the channel a few minutes before the compression. A distinctive advantage of the channel-die with respect to other compression devices is that the faces of the test piece in contact with the walls remain approximately plane. This facilitates greatly the observation of the local texture by various techniques of microscopy [10,11], or the deposition of grids, allowing the quantification of the deformation at various scales [12]. The test-piece may even be cut into two parts vertically along a plane parallel to the walls: the parts remain pressed one against the other during the compression and observations at the heart of the sample become possible [8]. Nevertheless, the medium temperature device has two limitations: the upper bound of the temperature is 600 ◦ C and the rig does not work under an inert atmosphere. The latter is essential for metals reacting with oxygen at high temperature such as titanium or zirconium. Lubrication has its own limitations, too, as the Teflon TM sheets that are usually wrapped around the samples deteriorate quickly above 400 ◦ C. So an appliance based on different principles has been conceived. Its fabrication is part of a project that focuses on the deformation mechanisms of Zircaloy-4 in the high alpha field and was undertaken under two major constraints, namely reproducing rolling up to 800 ◦ C, and ensure reproducible microstructural and rheological results. The principle of the appliance is documented in the second section, followed by a comparison between tests performed with the medium and high temperature appliances on the same material. The fourth section presents a finite element simulation that accounts for the different kinematic conditions of both appliances. The last section provides rheological and microstructural results obtained on Zircaloy-4, and presents the microgrids/split samples technique as a promising example of the investigations that can be achieved with this equipment.
2. Appliance description The high temperature channel-die is made up of four components: two walls, the punch and the die (Fig. 1). The upper part (acting as the punch) and the lower one (acting as the die) have identical dimensions, so that they follow identical thermal evolutions. The two walls fit into grooves cut in the punch and the die. They can glide vertically during the test. This has a limiting effect
Fig. 2. Setting of the sample and the devices at the beginning of a test. (a) Punch, (b) die, (c) walls, (d) sample and (e) nickel wires.
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Fig. 3. Temperature evolution during the heating to 750 ◦ C.
on friction, as shown below. The usual test-pieces are 7 mm × 10 mm × 8 mm (width, height, length, i.e. constrained direction, compression direction and extension direction, respectively), the face ratio 10/8 resulting from a compromise between friction and strain gradients [13]. The grooves of the higher and lower parts are 100 m wider than the walls, so that the latter do not get stuck into the former during the test. The sample is placed between the walls, the punch and the die at the beginning of the test, and then heated. Thermal uniformity is of concern and requires symmetry with respect to the horizontal plane of the sampledevice system. Nickel wires are thus placed in the grooves below the walls to maintain them at equal distance from the higher and lower grooves’ bottoms during heating (Fig. 2). They crush as the walls go down with the deformation. Temperature is monitored by two thermocouples placed 2 mm underneath the surface of the punch and the die. The four components are made of TZM, a solid-solution hardened and particle-strengthened molybdenum based alloy. Its approximate composition is (wt.%): 0.5 Ti, 0.08 Zr, 0.02 C, balance Mo. The strengthening Ti-carbide particles dissolve around 1400 ◦ C, which makes this alloy suitable for high temperatures applications. The sample and the compressive parts are placed within a 12 cm diameter silica tube. It is enclosed by a circular lighting furnace which transmits heat by radiation. The vertical displacement of the furnace along the silica tube allows the adjustment of the temperatures measured by the thermocouples. Proceeding that way ensures that variations in the zone occupied by the sample are less than 5 ◦ C at 800 ◦ C. The heating time is set to ca 15 min (Fig. 3). It results from a compromise between the heating speed and the thermal homogeneity. The furnace can heat up to 1200 ◦ C. The rig works under a continuous flow of argon, and room is spared to take extra precautions against oxidation by means of a getter which consists of scraps of zirconium and titanium which absorb the traces of oxygen. The channel-die test rig is mounted on a servo hydraulic Schenck machine, the servo system of which was specifically developed to provide sequences of constant strain rates. It is the same machine that is already used by the medium temperature
appliance [1]. This system enables thus to reproduce accurately strain paths specific to industrial hot deformation processes such as forging, rolling . . . The real time adaptability of the electronic device permits high frequency sampling of the displacement. The strain rate value can be updated every hundredth of second through the gain of an electronic loop. The upcoming displacement value is then adjusted so as to maintain the gain at an average value: increased if the ram is too fast and decreased if too slow. This system allows the control of the displacement following aperiodic signals required to apply constant strain rates. Strain rates between 10−4 and 20 s−1 can be obtained with the two servo valves available on the system. The displacement and load ranges are, respectively, 100 mm and 100 kN. The quenching system has been designed with special care (Fig. 4(a) and (b)). A mechanical finger (c) worked out manually hits the sample (d) and projects it in less than 1 s down the silica tube. To facilitate this manipulation, the punch moves 1 mm upward right after the end of the compression. The sample falls into a small chamber which fills with cold water as soon as the argon flow is interrupted. As can be seen from Fig. 4(a) and (b), due to dimensional constraints the sample cannot be completely pushed outside the channel by the finger. The impact of the finger on the sample has to be strong enough to eject it dynamically. In practice, this is achieved for nominal deformations up to ca 0.30. Beyond this value, the axis (a) has to rotate further, which causes the arm (b) to get in contact with the walls. The latter are then ejected along with the sample, which makes the quench somewhat less significant. This limitation is likely to be extended by the use of specific lubricants that must be determined for any newly tested material. In the scope of the study presented hereafter, the quenching system fulfils its function, since moderate deformation steps are required so as to observe the initiation of the deformation mechanisms. 3. Compared tests on the medium and high temperature appliances Since the medium temperature channel-die has proved to be a reliable equipment for studying the rolling of metals, it appeared
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at 400 and 500 ◦ C at a strain rate of 0.1 s−1 . It has been seen that in the high temperature appliance, the tools and the sample are heated together, due to the necessity to confine the protective atmosphere. So were they in the medium temperature appliance, so as to guarantee an identical state for the material and the lubricant at the beginning of the test in both configurations. The heating time was of the order of 15 min in each case. This is the reason why boron nitride spray was chosen as lubricant instead of Teflon TM sheets, since they melt down when heated more than a few minutes above 400 ◦ C. The material was considered a von Mises solid with a material flow stress (or von Mises equivalent stress) σ0 . The latter varies with the equivalent strain ¯ . If h0 and h are the initial and current height of the sample, ¯ is given in the case of the plane strain compression by h0 2 (1) ¯ = √ ln h 3 while it is ¯ = ln(h0 / h) in the case of uniaxial compression. Friction was described according to the Tresca analysis by the shear stress of the form: σ0 (2) τ=m ¯√ 3
Fig. 4. Schematic functioning of the quenching system (the punch is not represented). (a) Axis, (b) arm, (c) finger and (d) sample.
interesting to compare it with the new appliance in the same conditions. Tests were performed on both appliances, using the same material, lubrication and test conditions. The samples were made of the AISI 1010 (AFNOR XC10) low carbon steel. Its composition in weight percentage can be resumed briefly as 0.08–0.13 C, 0.3–0.6 Mn, Fe balance. The tests were performed
m ¯ being the Tresca coefficient. Following Refs. [14] and [15], it was taken an m ¯ = 0.1. It is now necessary to explain how σ0 can be calculated from the measurement of the stress applied by the punch σa . The power input transmitted by the rams is the sum of ˙ P and the power of friction the plastic deformation work rate W F ˙ W . The problem is to separate them so as to obtain the equivalent flow stress σ0 of the material, supposed to be an isotropic von Mises solid. Such an analysis can be found in Ref. [13] in the case of fixed walls (medium temperature appliance). It consists of a finite element calculation backed by a variational approach, compared to an analytical solution assuming homogeneity of the deformation in the sample. Among other results, it is found that the analytical calculation provides a good estimation of σ0 , which means that the inhomogeneity of the deformation weakly affects the overall flow stress. σ0 can be derived from σa by the
Fig. 5. Comparison of the stress–strain curves of XC10 alloy tested at 400 and 500 ◦ C in the medium (disks) and high (crosses) temperature appliances at ¯˙ = 0.1 s−1 .
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Fig. 6. XC10 samples deformed to ¯ = 0.75 at 400 ◦ C, at ¯˙ = 0.1 s−1 in the medium (left) and high (right) temperature appliances.
expression: ˙ F −1 W σ0 = σa 1 + P ˙ W
(3)
˙ F /W ˙ P shows that it is The analytical formulation of the ratio W proportional to m ¯ and that it also depends on the initial aspect ratio of the sample and on ¯ . Here, this analysis has been applied to both configurations, i.e. fixed and mobile walls. In the latter case, it will be established in Section 4 that it provides a good approximation of σ0 . The stress–strain curves are given in Fig. 5. In the transient phase, up to ¯ = 0.2, the curves obtained with fixed walls are higher than the others. At higher deformation they are much the same, especially at 500 ◦ C. In both cases the sample has to adapt to the rig before the full effect of the applied force is transmitted, but it takes more time in the case of mobile walls. Nevertheless, the main matter of interest for hot deformation is the steady regime, for which the agreement is very good. However, Fig. 6 shows that the samples have different shapes. In the medium temperature apparatus, the upper face is longer than the lower one. This does not happen with the high temper-
ature apparatus: both faces have the same length, but barrelling is observed at mid-height. The following section aims at giving an explanation to this difference by means of a finite element analysis. 4. Finite element simulation: fixed and mobile walls 4.1. Strain homogeneity Besides the material, the protective atmosphere and the heating system, the principal difference between the medium and high temperature appliances resides in the mobility of the walls. Following Ref. [13], these distinct kinematic conditions have been simulated using the finite element code ABAQUS TM in its standard implicit version. In the mobile walls configuration, a vertical degree of freedom was allowed to the walls, due to the depth of the grooves. They are in fact dragged by the sample as the punch moves down. All the tools were treated like rigid bodies and the sample flow rule was assumed to fit a Norton Hoff law of the form: σ0 = k¯˙
m
(4)
Fig. 7. Repartition of the calculated frictional and plastic works in the mobile and fixed walls configurations with m ¯ = 0.1 (MW: mobile walls; FW: fixed walls; Pl: plastic work; Fr: frictional work; Total: total work). (a) m ¯ = 0.02, (b) m ¯ = 0.02, (c) m ¯ = 0.10, (d) m ¯ = 0.10, (e) m ¯ = 0.20 and (f) m ¯ = 0.20.
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k being the consistency, and m is the strain rate sensitivity. This flow rule is not temperature sensitive because tests are performed isothermally. Eight-node fully integrated brick elements were chosen to mesh the sample. The contact between the sample and the tools was treated by means of Lagrange multipliers to control the node penetration into the rigid bodies. The tangential behaviour was treated by a penalty method, and the flow stress considered for the calculation of the shear stress τ due to the friction was taken locally in each element submitted to contact. τ was limited by the value of the flow stress multiplied by the friction coefficient. For the sake of homogeneity with the rest of this article, the results are presented using m ¯ (Tresca description). In fact the ABAQUS TM code uses a Coulomb coefficient, but the correspondence between both is straightforward [13]. The calculations were performed incrementally assuming that equilibrium was achieved at the end of each increment. No dynamic effect was considered. Tresca coefficients ranging from
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0.02 to 0.2 were used. Values of k = 350 MPa and m = 0.12 were assumed. They do not refer to a particular metal but are current orders of magnitude with metallic alloys. The strain rate was ¯˙ = 0.1 s−1 . Fig. 7 has been done with m ¯ = 0.1, but the conclusions are identical for 0.02 ≤ m ¯ ≤ 0.2. It shows the total work provided by the ram and the respective contributions of the plastic deformation and the friction. The mobility of the walls has no profound impact either on their repartition or on their sum. Hence, for both rigs, the analytical formula (3) is a good approximation to estimate the material flow stress σ0 from the experimental applied stress σa . Fig. 8 exhibits the influence of the configuration (mobile or fixed walls) on the shape of the sample for various friction coefficients. As found experimentally, the shapes of the deformed samples differ significantly, except for low friction coefficients.
Fig. 8. Contours of the plastic equivalent strain at ¯ = 0.8 in the fixed walls (left) and mobile walls (right) configurations for various friction coefficients. (a), (b) m ¯ = 0.02, (c), (d) m ¯ = 0.10, (e), (f) m ¯ = 0.20. For m ¯ = 0.1, please note the similarity between the simulated and real samples presented in Fig. 6.
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the rolls. Since channel-die compression is largely regarded as a good simulation of rolling, the central part of the samples compressed with the new rig are particularly suitable for microstructural analyses linked to the processing of sheets. 5. Application to the study of Zircaloy-4 5.1. Context
Fig. 9. Distribution of the plastic equivalent strain calculated at ¯ = 0.8 in the fixed walls configuration.
In both cases, some inhomogeneity is observed in the strain distribution. The scatter of the strain throughout the sample can be visualized through the representation of the equivalent strain values computed at the centroid points of the integration elements (Figs. 9 and 10). In each case the distribution is centered on the imposed strain, the main difference being that the values are less scattered in the mobile walls configuration. Above the value 0.10, the friction coefficient has a limited impact on the spread of the deformation. The relative velocities of the sample and the walls thus affects the homogeneity of the strain, which in turn determines the shape of the sample. When the walls are free to move in the vertical direction, the strain is more homogeneous and the deformed sample has a symmetrical shape with respect to the horizontal plane at half height. These observations can be explained by considering that one of the sources of inhomogeneity is the difference of vertical velocity between the upper and the lower faces of the sample. This difference is considerably reduced with mobile walls. It is worth noting, too, that rolling is also a process symmetrical with respect the plane which runs at mid distance from
As mentioned before, the first use of the new appliance is the investigation of the deformation mechanisms of Zircaloy-4 in its beta quenched state. The rheological and microstructural characterization reported hereafter illustrate the potentiality of the appliance. The Zircaloy-4 is a zirconium alloy which finds its main use in the nuclear industry. It presents two allotropic forms: beta phase body cubic centered (bcc) at high temperature, and alpha phase hexagonal close packed (hcp) at room temperature. The alloy is biphased between 810 and 980 ◦ C. A key step of the industrial forming process consists in a quench from the beta phase field (around 1050 ◦ C), which produces the so-called Widmanst¨atten microstructure. It is entirely constituted by alpha lamellae that are more or less entangled. They are delimited by a thin layer of intermetallic precipitates that form during quenching [16]. The following transformation steps aim at globulizing the lamellae so as to obtain an equiaxed microstructure in the finished product. From the quench, all thermomechanical treatments are performed without any new phase transformation (i.e. under 810 ◦ C). The response of the microstructure to the deformation appears to be very heterogeneous: while some lamellae tend to fragment and form buckling-like patterns, others orientate themselves perpendicular to the loading direction. Several nonexclusive factors can give an explanation to this variety of behaviours: crystalline anisotropy (as investigated by Bieler and Semiatin in a Ti alloy [17]), morphological anisotropy (i.e. orientation of the lamellae relatively to the strain direction, as is the case in a wide range of stratified media [18]), correlation of the deformation between neighbouring zones of the material (as studied by Doumalin et al. in an equiaxed Zr alloy [19]). It is shown below that the study of these phenomena during rolling is made possible by the use of the high temperature appliance. 5.2. Determination of the friction coefficients
Fig. 10. Distribution of the plastic equivalent strain calculated at ¯ = 0.8 in the mobile walls configuration.
Lubrication is a major concern of the experimental procedure, since four faces of the sample are in contact with the pieces. The tools have been lubricated with graphite spray. As for the samples, several solutions have been tested: boron nitride spray, graphite spray, pre-oxidized samples, and a specific lubricant furnished by the Zircaloy-4 manufacturer CEZUS. The latter has given the best results: it remained efficient until 0.8 of von Mises deformation, and assured the ejection of the sample without difficulty. Ring compression tests have been carried out to determine the friction coefficient of Zircaloy-4 against TZM with this lubri-
N. Vanderesse et al. / Materials Science and Engineering A 476 (2008) 322–332 Table 1 Determination of the Tresca friction coefficients between TZM and industrially lubricated Zircaloy-4, under inert atmosphere from 650 to 800 ◦ C, at ¯˙ = 0.1 s−1 Temperature (◦ C)
Deformation
D
m ¯
650 700 750 775 800
0.38 0.41 0.40 0.41 0.36
0.08 0.05 0.04 0.03 0.02
0.18 0.13 0.13 0.11 0.12
cant. This method has been first proposed by Male and Cockcroft [20]. It is based on the variation of the internal diameter of a ring that has been compressed at a given strain, and the friction coefficient μ is derived from an abacus. The internal diameter variation is expressed as D =
Di1 − Di0 Di0
(5)
where Di0 and Di1 are the initial and final internal diameters. Rings of internal diameter 6.35 mm, external diameter 9.5 mm and height 19 mm were used. They respect the dimensional ratios 1:1.5:3 corresponding to the abacus established by Male and Cockcroft. The tests were performed under inert atmosphere at temperatures ranging from 650 to 800 ◦ C at a rate of 0.1 s−1 . The results are summarized in Table 1. In the range of interest (i.e. between 750 and 800 ◦ C), the values of m ¯ are of the order of 0.1. This is substantially higher than what can be achieved at lower temperatures, especially using Teflon TM sheets, but it should be recalled that the oxidation, which is very active in the case of heated zirconium even in protective atmosphere, has a detrimental influence on the friction characteristics. Using these values allowed the determination of σ0 from the experimental σa , as previously done for the XC10 alloy.
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5.3. Rheological results The rheological characteristics of Zircaloy-4 were evaluated through uniaxial and channel-die compression. The tests were carried out with the same servo-hydraulic machine, between 650 and 750 ◦ C under inert atmosphere, at a strain rate of 0.1 s−1 . The same lubricant was used, and the uniaxial compression tools (i.e. punch and die) were also made of TZM. Accordingly, the analysis of the raw data takes into account the friction coefficients determined by the ring tests. In uniaxial compression, the stress was computed following the method of Avitzur [21]. The stress–strain curves are reported in Fig. 11 with the usual definitions of ¯ for plane and uniaxial compression recalled in Section 3. Some discrepancy exists in the transient states but the steady states match closely, especially at 750 ◦ C. This confirms the rheological qualities of the high temperature channel-die. However, its main interest lies in the facilities it provides in the study of microstructures, as developed hereafter. 5.4. Microstructure Two types of tests have been carried out: • compression of one-piece samples, • compression of split samples: each half sample is 3.5 mm wide, the other dimensions being unchanged, and is pressed against another one throughout deformation. The results given here concern the second technique, which is less usual than the first one. To the best of the authors’ knowledge, it has been used on metals only twice, by Panchanadeeswaran and Doherty [8] on aluminium samples at 375 ◦ C in channel-die, and by Hernandez-Castillo et al. on steel at 900 and 950 ◦ C in bi-punching [22]. It has the strong advantage to permit observations of the same microstructural region during successive deformation steps, provided the internal surfaces do
Fig. 11. Comparison between the stress–strain curves in uniaxial and channel-die compressions for Zircaloy-4 at ¯˙ = 0.1 s−1 (circles: uniaxial compression, squares: channel-die compression).
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not alter too much. It is worth reminding that if this is an aim that can now be achieved in a non-destructive way on aluminium using a synchrotron beam [23], this is out of reach for zirconium, which is a very X-rays absorbent medium. At low temperature and with Teflon TM sheets, it is also possible to observe the sides of the sample as illustrated in Ref. [12], but in the tests discussed here, the lubricant covers the sample with a hard coating that prevents all investigation after deformation. The first example concerns twinning at high temperature in Zircaloy-4. Twinning is often mentioned at room temperature where it is complementary to pyramidal slip for the accommodation of strains along the c-axis of the hexagonal cell. At high temperature it is generally admitted that pyramidal slip overrides twinning [24]. Fig. 12(a) and (b) are micrographs of the same zone of a half sample before and after deformation (T = 750 ◦ C, ¯ = 0.05 and ¯˙ = 0.1 s−1 ). It is a so-called parallel platelets zone: the lamellae are parallel to each other and despite the layer of precipitates, they share the same crystallographic orientation. Such a group of parallel lamellae is called a colony. Three colonies can be seen—they are marked as (a), (b), (c) in Fig. 12, and each one belongs to a different ex-beta grain. The boundaries of these grains are still visible. The surface after deformation
Fig. 12. Twinning activity at 750 ◦ C in Zircaloy-4. (a) Microstructure before deformation and (b) microstructure after deformation.
appears altered by the oxidation and the contact against the other half sample. Nevertheless, rectilinear, parallel, dark marks are observed in each of the colonies. Between colonies (a) and (b), they cross the former beta grain boundary. In spite of the oxide layer, a partial determination of the orientations has been performed by EBSD. It reveals that each mark is a lenticular {1 0 1¯ 2}twin, which presents a characteristic disorientation angle of ca 85◦ around an a-axis common with the matrix. Perpendicular marks in colony (c) indicate that two twin modes have been activated. This is a direct proof of the twinning activity at high temperature occurring at the onset of plasticity. The dimensions and orientations of the colonies are undoubtedly no stranger to that fact, as it is known that the alpha grain size favors twinning [25]. The second example presents some results obtained by the microgrids technique. Microgrids have been chemically etched on split samples prior to deformation, using a diluted Kroll reagent (10% 1.2N diluted HF, 90% 5.5N HNO3 ). The choice of etching instead of sputtering fiducial grids [26,27] was driven by the severe conditions undergone by the surfaces during the tests (oxydation, contact with the other half sample’s surface, and deformation itself). The integrity of the microgrids is thus improved, at the price of a lower accuracy: the lines are 1.5–2 m wide, and the step size is about 12.5 m. The same microgrid observed after 7.5% deformation (Fig. 13) reveals that some zones have been intensively sheared between adjacent colonies. A more detailed analysis is under work. It is based on the optical phase shift caused by the deformation of the grids [28], and will allow to map the plane strains. The whole strain state cannot be tracked down by this method, however. Indeed, deformation at this scale is far from being plane, as shown in Fig. 14. In this example, relief imaging has been performed using the imaging software ANALYSIS TM . The amplitude of out-of-plane displacements is of the order of 100 m. It is also interesting to note that the surfaces are in close mechanical contact. Fig. 15 shows the internal surface of a split
Fig. 13. 2D view of a microgrid after a strain of ¯ = 0.075 (T = 750 ◦ C, ¯˙ = 0.1 s−1 ). The arrows indicate intensively sheared zones between neighbouring colonies.
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Fig. 14. 3D view of the microgrid of Fig. 13(65 m/graduation).
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microstructural and micromechanical insights into the deforming material. Special care has been devoted to the design of the rig so as to guarantee its thermal uniformity, the reduction of the effects of friction, and quenching efficiency. This issue has been solved for Zircaloy-4 up to 800 ◦ C, but should of course receive attention for any new material. The appliance is built so as to reach 1200 ◦ C, but the feasibility of such tests has yet to be proved. The design of the rig yields a more homogeneously distributed strain within the sample in comparison with the fixed walls configuration. This is clearly visible on the deformed samples, and has been reproduced through finite element simulation. The macroscopic stress and strain values measured on the same material, however, remain equivalent in both configurations. High temperature stress–strain curves have been obtained on Zircaloy-4 samples, as well as optical characterization of a same microstructural zone between successive compression steps. As a first result, the activation of lenticular twinning at 750 ◦ C has been observed. The microgrid technique has been successfully adapted to the case of split samples. Out-of-plane displacement have been put into evidence, as well as shearing zones localized between adjacent colonies. These deformation patterns are considered to be representative of the behaviour of one-piece samples, since observations show that half samples are in strong mechanical contact throughout the deformation. These possibilities make this appliance a promising means of investigating the microstructural and rheological evolutions of materials during high temperature plane strain compression. Acknowledgements The authors would like to thank Mr. Barb´eris and Mr. Barritou (CEZUS, France) for providing the Zircaloy-4 material and its lubricant, Mr. Douet (Mining School of Saint-Etienne) for conceiving the quenching bath.
Fig. 15. Printing in relief of a microgrid (T = 750 ◦ C, ¯ = 0.075, ¯˙ = 0.1 s−1 ).
sample which had no microgrid etched on it prior to deformation. Regular marks are visible: they were created by the printing in relief of the microgrid that was present on the opposite half sample. Out of plane displacements of each half sample are then closely linked. This comforts the idea according to which the local deformations at the half samples’ surfaces are representative of those occurring within a one-piece sample, which are out of reach otherwise. 6. Conclusions Up to now, channel-die compression was limited to an upper bound of 600 ◦ C due to several technological difficulties. These have been overcome to produce a new appliance which has been successfully tested up to 800 ◦ C under a protective atmosphere at constant strain rate. In addition to compression of one-piece samples aimed at rheological results, it permits the compression of split samples so as to get
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