Orientation dependence of Portevin Le Châtelier plastic instabilities in depth-sensing microindentation

Transcription

1 Orientation dependence of Portevin Le Châtelier plastic instabilities in depth-sensing microindentation Zs. Kovács, N.Q. Chinh, and J. Lendvai Department of General Physics, Eötvös University, Budapest, H-1518, P.O.B. 32, Budapest, Hungary (Received 7 February 2000; accepted 1 February 2001) Plastic instabilities were investigated in an Al Zn Mg Cu alloy by depth-sensing microhardness testing in Vickers geometry. The alloy investigated showed strong age hardening as a consequence of Guiner Preston zone formation at room temperature. The orientation dependence of the Portevin Le Châtelier (PLC) effect was investigated by microindentation tests in differently oriented grains. If the direction of the indentation was close to the 100 crystal axis and the diagonal of the Vickers indenter coincides with the 110 crystal direction, the PLC effect was more pronounced. Under these conditions the instabilities could be observed even after 5 h of natural aging, while the PLC effect disappeared in grains with other orientations after 2 h of aging. The orientation dependence of the indentation curves was observed up to the maximal measured imprint size (d 80 m). It is suggested that the initialization of the PLC bands takes place in the close vicinity of indenter/sample contact surface. Considering only a uniaxial compressive stress component in the sample/indenter contact planes, in the vicinity of the indenter single sliplike and multiple sliplike conditions are attained depending on the orientation of the indenter relative to the sample. Changes of the slip conditions correlate with changes in the observation regime of instability which explains the orientation dependence. I. INTRODUCTION The kind of plastic instability called the Portevin Le Châtelier (PLC) effect is caused by the negative strain rate sensitivity (SRS) of the plastic stress 1 and is mostly manifested in repeated yielding of the material. It is now widely accepted that the negative SRS in the case of PLC effect is due to the interaction of dislocations with diffusing solute atoms, the so-called dynamic strain aging (DSA), and to cooperative dislocation motion. 2,3 The PLC effect which was most widely studied on Al base alloys containing Mg atoms can be observed within a region of strain and strain rate which is bounded by critical points mainly determined by the zero SRS condition. The position of the critical points for a chosen alloy depends on the elementary strain 4 ( m bl t w. ), where m is the mobile dislocation density, b is the Burgers vector, L is the average obstacle distance, and t w is the average waiting time during the jerky motion of dislocations. The appearance of the phenomenon in a macroscopic measurement depends largely on the investigation technique: in displacement control like in tensile experiments carried out at constant cross-head velocity serrated yielding is observed, while in load control (the load is increased at constant loading rate) steps appear on the deformation curve. Load control is less widely used, although machine-independent information can be obtained in a more direct way than from displacementcontrolled measurements. 4 PLC plastic instabilities have been recently reported in dynamic microhardness tests under constant load rate control. 5,6 In the present work similar microhardness measurements were carried out in load-controlled depth-sensing indentation tests. In this type of experiment the penetration depth (h) of the indenter is measured continuously during continuous loading up to the maximum load (F max ). The alloy investigated here is an Al Zn Mg Cu alloy which is considerably strengthened upon room-temperature aging after solution heat treatment and quenching due to the formation of Guiner Preston (GP) zones. The PLC effect which can be clearly observed in the early stages of room-temperature aging is suppressed after a few hours of aging. The period of time over which the instabilities could be detected was found to be orientation dependent. A comprehensive investigation of the PLC effect observed in tensile experiments was recently published 7 for an alloy with very similar composition to that investigated here, which allows for comparison between the results of the tension and indentation tests. In depth-sensing experiments different material properties (like elastic modulus, 8 yield strength, or fracture properties) can be determined from a single indentation J. Mater. Res., Vol. 16, No. 4, Apr Materials Research Society 1171

2 measurement. Indentation experiments have the advantage of relatively simple sample preparation, and they can yield local characterization, down to the nanometer scale. However, comparison between the single crystal or polycrystal tension or compression experiments and the indentation tests is difficult. While at relatively large imprint sizes the Vickers hardness is constant, with decreasing imprint size, i.e., at small penetration depth of the indenter, the hardness increases. This has been described as an example of the deformation size effect caused by geometrically necessary dislocations 9,10 or by the strain gradient effect. 11 On the other hand, investigations of Iost and Bigot 12 have shown that the size dependence of the hardness is mainly caused by pile-up formation on the surface, which is in correlation with crystal orientation and dislocation motion. 13 This is supported by the fact that pile-up formation and orientation dependence was observed up to 3- m imprint size in Vickers hardness of tungsten which is a material with very small elastic asymmetry similarly to aluminium. 13 In the region of the nanoindentation the orientation dependence definitely appears, which is thought to be in connection with the nucleation of single dislocations taking place on the surface of the material at the contact area In contrast to this, orientation dependence in indentation measurements at larger imprint sizes (like in microindentation) is observed only in extreme cases, in materials with strong mechanical anisotropy. 17 Our measurements were done in the microindentation region, where the orientation dependence of the conventional hardness is negligible. II. EXPERIMENTAL The experiments were carried out on an Al-5.7% Zn 1.9% Mg 1.4% Cu alloy (the composition given in wt%) prepared of 99.99% purity aluminium. Samples for the indentation tests were prepared from hot extruded rods. Slabs for the indentation experiments of approximately 3-mm thickness were cut perpendicular to the axis of extrusion. The slabs were subjected to solution heat treatment (470 C, 0.5 h) and quenched into roomtemperature water. The surface of the samples was electrolytically polished. The indentation tests were made at room temperature on a depth-sensing, load-controlled, ultramicrohardness tester (Shimadzu DUH-202, Kyoto, Japan). A Vickers diamond tip was used in the investigations. During the tests the load rate (Ḟ) was kept constant. The loading rates were so selected as to obtain approximately the same total loading times for measurements with different ultimate imprint sizes. This choice was motivated by earlier results, 5,6 in which the time to reach the critical point (onset of the instability) in depth-sensing indentation was found to be nearly constant, independently of the loading rate. The orientation of the indented grains was determined from the angles of the slip lines with the help of a computer program. Orientation dependence of the plastic behavior was investigated by rotating the specimen around the indentation axis. The angles of the slip lines and rotation angle were measured by 1 accuracy. The average grain size was about 200 m. III. RESULTS AND DISCUSSION A. Effect of aging on plastic instabilities Figure 1 shows the increase of the Vickers hardness as a function of aging time at room temperature. The strong hardening is the consequence of the GP-zone formation during the natural aging. Figure 2 shows the indentation depth load curves for different aging times. The steps, indicating the PLC effect, endure up to about 2 h aging after quenching, although there is a regime at about 1700 mn on the 10-min curve where the steps are less enhanced. This kind of behavior was observed also in other zone forming alloys while it was not observed in binary Al Mg solid solution alloys. 18 As it can be seen from Figs. 1 and 2 the PLC effect disappears at an aging time (2 h) when the age hardening has just started, i.e. at this time the GP-zone formation is in its initial stage. The effect of GP-zones and precipitates on the PLC plastic instabilities was investigated by several authors. 7,19 21 The critical strain, at which the instability sets in, was observed to increase as a function of aging time. 7 This can be explained by the decrease of the solute content of the matrix with the progress of precipitation. The depletion of the solute atoms from the solid solution leads to the weakening of DSA. FIG. 1. Increase of the Vickers hardness in consequence of GP-zone formation during room-temperature aging. After about 2 h of natural aging (indicated by the vertical line) the PLC effect disappears (F max 2000 mn, Ḟ 70 mn/s) J. Mater. Res., Vol. 16, No. 4, Apr 2001

3 B. Orientation determination To investigate the orientation dependence of the PLC effect several grains of different orientations were examined by indentation. The orientation of selected grains was determined from the slip line pattern around the indents in the following way. The slip lines are the intersections of the slip planes of the crystal with the surface plane of the sample. The surface of a sample with an imprint can be seen in Fig. 3(a). The directions of the slip lines and the angles between them are indicated. In the fcc Al alloy investigated the slip planes are the {111} planes, which are visualized as a tetrahedron in Fig. 3(b). The intersection lines of the four planes of the tetrahedron and a (100) sample plane are shown on the (100) surface, where from the four lines the orientations of two pairs of lines coincide. Generally, in the case of fcc crystals, four branches of slip lines appear on the surface around the imprint. The orientation of a grain in which the imprint is placed can be calculated by means of the FIG. 2. After about 2 h of room-temperature aging, the steps indicating the PLC effect disappear. The curves correspond to 10, 73, 125, and 230 min of aging (F max 2000 mn, Ḟ 14 mn/s). relative angles of the slip lines. 22 The orientation determination by visual observations has a longstanding literature; formerly it was applied by the help of etch figures 23 and more recently by slip lines. See the work of Chang and Chen 22 for a careful review of the different cases. In Fig. 3(c) the orientation of the grain of Fig. 3(a) is indicated in a stereographical triangle. In the following the grains the surface plane of which coincides with a {hkl} plane, are referred to as hkl -oriented grains. Since the Vickers indenter has no axial symmetry to determine exactly the relative orientation of the indenter and the crystal, a further parameter describing the azimuthal orientation is necessary. In the present work the azimuthal orientation dependence was investigated only for 100 -oriented grains, and we used the angle,, between the diagonal of the indent and the 110 direction in the surface plane for the characterization of the azimuthal orientation. C. Orientation dependence As it was shown in Fig. 2, the PLC effect disappears from the indentation curves after about 2 h of aging in a randomly chosen grain. It was found, however, that at a special grain orientation the instability steps can be observed for remarkably longer times. In Fig. 4 instability steps can be clearly seen on the curve measured on a 100 -oriented grain after 3 h of aging, while, in grains the orientation of which deviates stronger from 100, the indentation curve remains smooth. In 100 -oriented grains in a narrow angle region if the azimuthal angle is close to 0 the effect of the instability could be observed even after 5 h of room-temperature aging, as it is shown in Fig. 5. The PLC instability effect can be observed for the longest aging time at the exact ( 100, 0 ) orientation. The angular regime around the 0 orientation in which the instability appears is continuously shrinking with increasing aging time. FIG. 3. (a) Typical Vickers imprint surrounded by slip lines. The angles of the slip lines are indicated. (b) Schematic picture of the tetrahedron formed by {111} slip planes in an fcc lattice indicated by dashed lines. The intersections of a (100) plane (like the surface plane perpendicular to the indentation) and the tetrahedron are lines parallel to the slip lines. (c) Orientation of the grain in (a) calculated from the slip line geometry in the stereographical map. J. Mater. Res., Vol. 16, No. 4, Apr

4 FIG. 4. The instability disappears in grains far from the 100 orientation (II) after 2 h of room-temperature aging, while it can be still observed in grains close to the 100 orientation (I). Curve I is shifted by 2 m upward (F max 2000 mn, Ḟ 14 mn/s). To examine the azimuthal orientation dependence the sample was rotated relative to the indentation axis and several measurements were made in a 100 -oriented grain of the sample. To avoid the interference of the stress and strain fields of the indents the maximum indentation depth was restricted to 2 m, correspondingly the maximal load and the loading rate were chosen as F max 100 mn and Ḟ 2.6 mn/s. In Fig. 5(a) indentation curves can be seen as a function of the azimuthal orientation in a 100 -oriented crystal grain. If the slip lines are parallel to the diagonals of the Vickers imprint ( 0 ), the instability can be definitely observed. On the other hand, if the angle between the diagonals and the slip lines increases the instability gradually disappears. The Vickers hardness (HV F/h 2 ; 0.038) for the indentations of different azimuthal angles is shown in Fig. 5(b) as a function of the indentation depth. The error bars correspond to a 20-nm error in the displacement measurements. The steps observed in the load displacement curves appear here as regular serrations. Although fluctuations in the hardness appear in all curves, the serrations apart from the 0 and 6 curves are random and rare events. D. Crystal orientation related pile-up formation The shape of the Vickers imprints generally deviates from the ideal pyramidal shape. In Fig. 6 two imprints are shown, both in a nearly 100 -oriented grain. The azimuthal orientation was 0 for Fig. 6(a) and 45 for Fig. 6(b). The 0 imprint has a cushion shape, while in the 45 case the imprint shape is like a barrel. The reason for the shape distortion can be the elastic relaxation of the material during the unloading period and/or the pile-up formation in the indenter near region on the free sample surface. 24 The pile-up formation was attributed to the high plastic to total deformation FIG. 5. Indentation curves measured in one selected grain with different azimuthal orientation angles ( ) between the diagonal of the Vickers imprint and the 100 direction. The measurements were performed after 5 h of natural aging (F max 100 mn, Ḟ 2.6 mn/s; the indentation curves are shifted by 0.4 m with respect to the curves with higher values). (b) Variation of the Vickers hardness with indentation depth. Regular serrations occur at 0, and irregular serrations appear randomly on all curves. (Error bars indicate 20-nm error in the displacement measurements. The hardness curves were shifted by 0.5 GPa compared to the curve with higher values.) ratio 24 (which in our case was 0.93) and the low strain hardening rate 24 (which is a general characteristic of aluminum alloys for large strains), and it was reproduced also in numerical simulations. 25 Since the contribution of the elastic deformation in our case is small, the observed variation in the shape of the remnant contact impression should be attributed to pile-up formation. According to the work of Stelmashenko et al. 13 the orientation and the extent of the pile-up are determined by the crystal orientation; i.e., at a given surface orientation the height of the upheavals is maximum in definite crystal directions. Consequently, changing the azimuthal orientation of the indenter results in variations of the indent shape. The same effect has been observed at smaller imprint sizes in bcc tungsten 13 where the highest upheavals formed in the 011 directions in the {100} surface plane J. Mater. Res., Vol. 16, No. 4, Apr 2001

5 FIG. 6. Irregular imprint shapes caused by surface pile-up formation at (a) 0 and (b) 45 azimuthal orientations. E. PLC instabilities in indentation experiments In a comparison of the critical parameters obtained in the tensile measurements of Thevenet et al. 7 and in the present indentation measurements, a contradiction seems to arise. The PLC steps disappear after about 2 h of aging from the indentation curves (except in the narrow region around the 100, 0 orientation) while the PLC effect was observed in a wide range of strain rate ( /s /s), for large strains in the cited tensile experiments (see Fig. 3 in Ref. 7) even after 3 h of aging, and in a more restricted range the serrations were detected even after 24 h of natural aging. To compare the results of tensile and indentation experiment the equivalent strain and strain rate in indentation have to be estimated. During indentation the strain covers a range from 0 up to high values, 26 while the strain rate under self-similar indenters (Vickers, Berkovich, etc.) can be approximated as. kḣ/h, where ḣ is the penetration velocity and k is a dimensionless constant (the value of which is k 0.09 for conical geometry, which can be used also for the present estimation). 27 This strain rate approximation for our measurements gives /s /s in the load interval mn. Consequently, it can be seen that the strain rate ranges in the two types of experiments (tensile and indentation) are strongly overlapping and the strain in particular points of the plastic zone of the indentation is equal to the attained strains in the comparative tensile tests. 7 In spite of these PLC steps can be hardly observed in indentation tests after 2 h of aging in randomly chosen grains. This contradiction can be resolved by taking into account the differences in the two kinds of measurements. The critical parameters in the paper of Thevenet et al. were determined in tension tests on polycrystalline material, while the disappearance of the PLC effect in our work is observed in selected single crystallites. A difference of the critical parameters in single crystalline and in polycrystalline material was reported in the work of Kalk et al., 28 where PLC plastic instabilities were observed under single-glide single-crystalline and multiple-glide single-crystalline or polycrystalline conditions. The results could be compared by taking into account the different elementary strain values for single-glide and multiple-glide conditions, respectively. From the comparison the critical flow stress is found to be about three times higher for single than for multiple glide in single crystals, 28 and the difference in critical strain is even higher. At the same time, the polycrystal results were found to be in agreement with those of the single-crystal multiple-glide experiments. This emphasizes the influence of glide conditions on the critical PLC parameters. This indicates that differences in the deformation process have to be taken into account e.g. for the tests carried out under different azimuthal orientations. Further, to understand the characteristics of the PLC effect in indentation experiments, the observations must be compared to results of other kinds of tests with inhomogenous stress and strain fields. E.g., in torsion tests the strain in the sample is also inhomogenous, and results indicate that the initialization of the high strain rate bands occurs on the surface of the sample, 29 where the strain is the highest. Similarly, band initialization in tension occurs mostly at the edges of the extensometers in consequence of stress concentration. This characteristic of the PLC effect resembles a nucleation process. 30 A high strain rate band has to nucleate somewhere in the sample to evolve into a macroscopic instability band. In indentation tests the strain localization is highest at the contact area; J. Mater. Res., Vol. 16, No. 4, Apr

6 consequently, this is the place where dislocation avalanches are initialized (this was observed in nanoindentations 31 as well and reproduced also in quasi-continuum simulations 32 ). Consequently, it can be assumed that although the volume susceptible to unstable deformation is not restricted to the region close to the contact area, the initialization of the PLC steps occurs in the near vicinity of the indenter. Therefore small differences in the indenter near region may result in large variations in the results, even if the indentation size is already above the few micrometer regime in which surface-related effects (size effects) influence the conventional hardness. If we assume that the PLC bands are initialized very close to the faces of the indenter and if we consider a ˆ stress tensor containing only a uniaxial pressure component (p 0 ) perpendicular to one face of the Vickers pyramid, which is an approximation near the surface plane of the indenter, the resolved shear stress ( ) can be obtained for each possible Burgers vector direction (b)as ( ˆ b)n, where n is the normal vector of the slip plane (Fig. 7). In Fig. 7(a) the different b Burgers vectors are denoted by small letters from a to f and the slip planes of different n by capital letters from A to D to which the calculated resolved shear stresses are corresponding as a function of the azimuthal orientation in Fig. 7(b). The maximal resolved shear stress for both 0 and 45 is degenerate, but while at 45 the slip plane is common [plane A, Burgers vector b (Ab) and plane A Burgers vector a (Aa); see Fig. 7(b)], leading to deformation similar to single glide, at 0 the two cases [plane A, Burgers vector b (Ab) and plane B Burgers vector a (Ba) in Fig. 7] correspond to two different slip planes, leading to multiple-glide-like deformation. So, the applied assumptions predict that conditions similar to single-crystal single-glide behavior may occur in the close vicinity of the indenter head, in spite of the fact that in the major part of the plastic zone under the indenter multiple slip conditions might exist. However, since the nucleation of PLC bands takes place at the contact area, the PLC effect enhances the influence of the contact region and this is reflected by the azimuthal orientation dependence in 100 -oriented grains even for larger indentations. Consequently, at 45, single-glide conditions prevail. The critical value of the strain for a single glide is comparatively quite high. 28 High values of the critical strain suppress the onset of PLC instabilities. Conversely, for a multiple glide, the critical strain is much lower, which allows the appearance of PLC instabilities at 0. FIG. 7. (a) Schematic picture showing four slip planes (A D) around the indenter with the six possible Burgers vectors (a f) at 0. (b) Resolved shear stress for the different Burgers vectors and slip planes as a function of the azimuthal orientation in a 100 -oriented grain around a Vickers indenter assuming a p 0 homogeneous pressure on the shaded surface plane of the Vickers pyramid. The maximal resolved stress for both 0 and 45 is degenerate; however, at 45 the slip planes coincide. IV. CONCLUSIONS Orientation dependence of the PLC plastic instabilities was investigated by depth sensing ultramicrohardness measurements in an Al Zn Mg Cu alloy, during natural aging. The indentation steps signalizing PLC instabilities were observed to disappear during the process of the GP-zone formation after 2 h; nevertheless in oriented grains at a special azimuthal orientation the nearly periodic oscillation of the dynamic hardness could be observed for considerably longer times. It is suggested that the PLC bands in indentation experiments are initialized in the indenter near surface region. Considering a uniaxial compressive stress on the contact surface, the resolved shear stresses acting on the dislocations in {111} planes were calculated and it was found that in the two extreme cases ( 0 and 45 ) of azimuthal orientation single-slip-like and multiple-slip-like conditions prevail. The changes in the slip conditions explain the variations of the observation interval in which PLC instabilities could be detected in the present indentation experiments J. Mater. Res., Vol. 16, No. 4, Apr 2001

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