INFLUENCE OF STRESS MACROCONCENTRATORS ON THE STRAIN LOCALIZATION IN Al6061/Al 2 O 3 COMPOSITES

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1 INFLUENCE OF STRESS MACROCONCENTRATORS ON THE STRAIN LOCALIZATION IN Al6061/Al 2 O 3 COMPOSITES Ye.Ye. Deryugin 1, V.E. Panin 1, V.I. Suvorov 1, G.V. Lasko 1,2 and S. Schmauder 2 1 Institute of Strength Physics and Materials Science, Siberian Branch of Russian Academy of Sciences; Pr. Akademicheskii 2/1, , Tomsk, Russia Institute of Materials Testing, Materials Science and Strength of Materials (IMWF), University of Stuttgart, Pfaffenwaldring 32, Stuttgart, Germany Keywords: Stress Macroconcentrator, Physical Mesomechanics, Plastic Strain Localization Abstract With the help of the optical-television measuring system TOMSC the influence of artificial stress macroconcentrators in the form of notches on the strain localization in alloys with clearly pronounced Portevin-Le Chatelier effect was investigated in Al+10%Al 2 O 3 polycrystals under tensile loading. In the case of a few number of notches (from 1 to 3) the strain localization is concentrated in small volumes of the specimen. Large number of notches (from 3 to 42) creates a set of stress concentrators in the working volume of the specimen. The increase of the number of notches leads to an increase of the stress flow and plasticity of the specimen. Introduction According to physical mesomechanics [1], stress concentrators in a material play a principle role in the development of non-homogeneous plastic flow in the volume of materials. Composites on the basis of aluminum alloys with Al 2 O 3 inclusions belong to the class of materials with internal interfaces. Typical peculiarities of these alloys in an annealed state is a pronounced Portevin-Le Chatelier effect at room temperature in the course of tensile testing within a definite interval of loading. In the laboratory of physical mesomechanics ISPMS a lot experimental findings have been obtained recently on these alloys [2-7]. The serrated shape of the stress-strain curve is shown to be a consequence of the formation of the band of plastic deformation. Each band is formed spontaneously and is oriented, as a rule, at an angle of 60 with respect to the tensile axis. The source of the macroband of plastic deformation are stress concentrators on different length scales. Junctions of the grain boundaries, hard phase particles and precipitates, caused by small additions of Mg and Si in the Al6061 matrix play the role of distributed stress concentrators in the material. The influence of these stress macroconcentrators on the process of strain localization can be found by testing of the specimens with notches, playing the role of artificial stress concentrators. In the present work, the effect of artificial stress concentrators (notches) put on the lateral edges of the specimen on the localization of plastic deformation in alloys with Portevin Le Chatelier effect will be investigated. The data on the quantitative influence of the notches on plasticity, strength and serrated flow of an Al+10%Al 2 O 3 composite will be obtained. The results are discussed from the point of view of physical mesomechanics of deformed solids [1]. Material and the technique of experiments The composite Al+10%Al 2 О 3 on the basis of technical Al6061-aluminum with the average size of hard Al 2 О 3 particles being equal to 15 μm, and produced by liquid-phase sintering, forging and extrusion have been used for the investigations. After intensive rolling of the initial material (in the form of rods of 20 mm diameter) bands with the width of mm have been ob- 41

2 tained. From these sheets of material the specimen have been processed by electro erosion technique in the form of spade with the radius of transition 2mm to the working part with crosssection 4х1.5 mm 2 and the length of 18 mm. Different numbers of notches were cut at the lateral surface of the specimens (1, 3, 14 and 42) with a depth of 0.3 mm and a width of 0.25 mm (Fig.1). Before testing, the prepared samples were annealed in vacuum at 550 С during 2 h and were cooled down in the furnace till room temperature. Mechanical polishing of the surface has been made with emery paper with gradual decreasing grain dimensions. Fig.1. Scheme of sample testing (а) and positions of the notches: а one notch, b 3, c 14 and d 42 notches. In the specimens with one stress macroconcentrator, the notch has been placed on the lateral edge at the center of the working part (Fig.1a). In the case of the specimens with 3 notches they were placed at the vertexes of the equilateral triangle (Fig.1b). Such a configuration was favorable for the formation of stress concentrators and conjugate bands of localized deformation at an angle of 60 with respect to the tensile axis and to an accelerated neck formation. In other cases the notches were placed along the lateral edges of the working part of the specimen at equal distances from each other. The notches at the different edges of the specimen were placed against each other (Fig.1 c, d). The specimen with notches and without notches were tested under uniaxial tensile loading with the rate of free movement of the clamps being 1.5 mm/h at the IMASH-device, equipped with an optical-television system TOMSC [8]. With the help of this system the image of the surface relief is input into a computer each 3s. By comparison of two consequent the surface images of the investigated segment of the surface in 3, 6, 9, 15s the displacement vectors fields have been obtained with an accuracy of 144 vect/mm 2. The area of observation embraced 1/3 of the part at the center of the specimen (Fig. 1а). Results Loading diagrams Shown in Fig.2 are the characteristic loading diagrams of the tested specimens with the different numbers of notches. The comparison shows that the presence of notches doesn t suppress the phenomenon of interrupted flow. In all cases the serrated flow has been observed, which is enhancing as the degree of plastic deformation increases. However, depending on the number of notches, the qualitative and quantitative differences of the characteristics of plasticity, strength and the character of plastic deformation development are observed. The following differences are essential: - The presence of a notch decreases the value of the conventional yield stress σ 0.05 by 20 MPa, independently on the number of notches. In the specimens without notches it is equal to σ MPa. 42

3 - Increase in the number of notches from one to three is accompanied by a decrease in plasticity and strength. However, any further increase of the number of notches of the specimen, in contrary, results in an increase in plasticity and strength. - A long-range stress modulation, typical for the specimen without notches, manifests itself only for the specimen with 42 notches. As for the rest of the specimen with notches, stress oscillations are less ordered and occur without clear periodicity. - The amplitude of stress oscillations in the specimen with one notch is much lower than that in the specimen with 3 notches (Fig.2, curves 5 and 4). However, further increase in the number of notches from 3 to 42, in contrary, results not to increase but to decrease the value of the amplitude of stress oscillations. A maximum amplitude of oscillations and a minimum frequency of stress oscillations are typical for the specimen without notches. The comparison of curves 1 and 2, for example shows, that the oscillatory characteristics for the specimen with 42 notches differs by several times from that for the specimen without notch. MPa Fig.2. Tensile diagrams of the composite Al+10%Al 2 О 3 : 1- without notch (1), with 42 (2), 14 (3), 3 (4) and with 1 (5) notches. - For the specimen with a small number of notches (from 1 to 3) the oscillations of the external stress doesn t stop also at the stage of decreasing stress (Fig.2, curves 5 and 4). This peculiarity is more pronounced in the specimens with three notches in comparison with that with one notch. Influence of notches on strain localization The analysis performed shows qualitative and quantitative distinctions of the loading curves for the specimen with small and large number of notches. It should be expected that it is connected, first of all, with the differences in the development of the bands of localized shear (BLS). In this connection, shown below are first results for the specimen with one and three stress concentrators, then the case of plastic strain localization for the specimen with a large number of notches (with 14 and 42 notches). The development of plastic strain localization has been analyzed on the basis of the data on displacement vector fields at the specimen surface. The analysis of displacement vector fields at the increasing stage of the loading diagram of the specimen with one notch shows, (see Fig.2, curve 5), that the notch defines the place and accelerates the process of neck formation. Non-homogeneous plastic deformations are recorded by displacement vector fields with the onset of macroplastic deformation. The process of plastic strain localization is concentrated in a couple of two macrobands, being oriented along the conjugate directions of tangential stresses, the origin of which is the notch itself. At that time, the consequent switching of the deformation process from one macroband to another, conjugate to 43

4 the first one (Fig.3), similar to the same as it takes place in the specimen without notches at the stage of neck formation. The observations show, that the influence of the notch as basic stress concentrator on the localization of plastic deformation is realized not during the whole time of loading. At the external applied stress, significantly exceeding the conventional yield stress of the specimen without notches, the instant of time comes, when localization of plastic deformation is recommenced not at the notch, but in the transition zone from the clamp to the working part of the specimen. The macroband of localized shear initiates at the head of the specimen and further jump-like propagates along the specimen, through the notch on the mechanism of the switching wave (Fig.4). In Figure 4а all the displacement vectors are directed from left to right, i.e. to the left, beyond the field of vision a spontaneous formation of BLS took place. After some time, the process of localization is displaced to the notch (Fig.8b). The successive macroband arises at the opposite site from the notch (Fig.4с). Fig.3. Consequence of the changing of the patters of displacement vectors in the process of plastic deformation localization in the zone of notch, ε p =2%. However, at a stress, close to the yield stress, the process of strain localization is concentrated finally in the zone of notch. The plastic strain rate in conjugate macrobands changes in antiphase and in pulsated manner. Along the same direction, the process of intensification of plastic deformation can be recommenced and faded several times, before the process switches into the conjugate one. In the specimens without notches there is no such a pulsation of plastic deformation in the macroband. Fig,4. The sequence of the changing of the displacement vector patterns in the course of BLS development beyond the notch, ε p = 4%. As distinct from the case of the specimen without a notch, a process of interrupted flow on the decreasing segment of the stress-strain curve doesn t stop (Figure 2, curve 5). Slowing down of the process of strain localization causes the serrated shape of the decreasing segment of the loading curve. Each jump of stress at this segment is also connected with a sharp localization of plastic deformation in the zone of the operation of an artificial stress macroconcentrator. Analyses shown that at the final stage of the formation of the neck, the process of strain localization embraces new volumes of not highly deformed material between two conjugate macrobands and consequently concentrated in the narrow region perpendicular to the specimen. Shears transfer to the plane at an angle of 60 to the tensile axis, intersecting the face surface of the specimen perpendicularly. Sharp localization of plastic shear in that plane results in rapid arising of a crack and quasi-brittle fracture of the specimen with shear along this plane. 44

5 The development of the localization of plastic deformation in the specimen with 3 notches has the same qualitative peculiarities, described for the specimen with one notch. At the initial stage also intensive plastic deformation occurs in the zone of 3 stress concentrators (Figure 5). Strain localization occurs in BLS, connecting the stress concentrators along the directions of maximum tangential stresses. Fracture of the specimen takes place along one of the conjugate macroband, in which the quickest accumulation of plastic deformation occurs. Figure 5. Formation of the conjugate BLS in the specimen with three notches. Specimen with a large number of notches The presence of a large number of notches (42 notches and 14 notches) doesn t change the qualitative character of strain localization development. The same way as for the case of the specimen without notches, macroplastic flow is defined mainly by the consequent formation of the macroband of localized shear. However the degree of the localization in macroband essentially depends on the number of notches. Shown in Figure 6 are the patterns of the displacement vector fields for the specimen without notch (a), with 42 (b) and 14 (c) notches. The comparison shows that the presence of notches doesn t cause the plastic strain localization. The localization of deformation is clearly pronounced in the specimen without notch (a). BLS in the displacement vector field for the case of the specimen with 42 notches is not clearly pronounced, Fig.6b. In the case of a specimen with 14 notches, the effect pointed out is less pronounced. The value of a separate jump of BLS is defined by the distance between the notches, independently on the stage of loading (Fig.6b, comp. frames 2 and 3). In the specimen without notches with increase in the stress the magnitude of the jump of BLS decreases [7]. In the case of the specimen with 42 notches, this value is 2 or 3 times the distance between the notches. In the case of a large number of notches, the propagation of BLS proceeds rarely without changing in orientation (Fig.6b). In the specimen with 14 notches the stable propagation of BLS is observed not so often from clamp to clamp (strain localization of type B). The probability of the random arising of BLS at the different locations of the specimen (C-Type) is high. Conclusion The obtained regularities testify to the principal role of stress concentrators in the development of non-homogeneous plastic flow in the investigated materials. A decrease in plasticity and strength of the specimen at the increase of the number of notches from one to three could be explained reasonably, because in the latter case the development of the macroband occurs under operation of two stress concentrators (SC), that result in more active localization of plastic deformation in the band. The geometrical location of the notches, placed at the vertexes of an equilateral triangle, is favorable for the quicker neck formation than in the case of one notch. The effective volume of the material, where intensive processes of strain localization occur, increases, if the number of notches increases further. As a consequence, the average degree of plastic deformation increases. Increase in the strength is connected with a decrease in the gradients of the non-homogeneous stress field as a result of superposition of the fields of stresses from the neighboring stress concentrators (notches). The gradients of stresses characterize the degree of the non-equilibrium state of the material and in that way is the driving force of mass transfer. 45

6 With the increase in the number of notches the width of the forming bands of localized shear increases (Fig.6) that testifies to a decrease of stress gradients. At that time the amplitude of the jumps of external stresses (Fig.2) essentially decreases (Fig.2). That means that the average degree of plastic deformation in a separate BLS essentially decreases [8]. Fig.6. Propagation of the band of localized strain in the specimen without notches (а) and with 42 (b) and 14 (c) notches. Experience shows, that the leading influence of one from three notches on the localization of plastic deformation is realized not at all time of loading. This fact is the direct evidence of the fact that during the process of plastic deformation stress relaxation within the zone of the notch takes place. The development of the band of localized shear, on one hand, is accompanied by a decrease in stress concentration in the vicinity of the notch, and on the other hand, results in strain-hardening of the material. A combined action of these two factors results in an increase in the external stress up to the level, favorable for the formation of BLS beyond the region of notch operation. As the external stress increases, the stress concentration in the zone of notches again becomes effective. Besides that, the third factor is essential, in particular, decreasing in the crosssection of the sample in the zone of notch location that causes a quick transition of loading diagram to the stage of decreasing stress. 46

7 It should be noted, that in all cases, the process of strain localization in the bunch from two conjugate BLS occurs on the scheme of phase wave of switching. It is observed as at the initial stage of macroplastic flow in the specimen with one or three notches, as well as at the initial stage of neck formation in the specimen with notches and without them. On the decreasing segment of the loading curve (Fig.2) an interrupted flow is caused by the involvement in the process of the volumes of material inside the V-shaped bunch of conjugate BLS, which on the previous stages of loading is not involved into intensive plastic deformation. Acknowledgements The work is supported by the German scientific Society (DFG), project DFG Schm 746/52-2, and Russian Foundation of basic Researches, project RFFI а. References 1. V.E. Panin, Synergetic principles of physical mesomechanics, Physical mesomechanics, 6 (3) (2000), Ye.Ye. Deryugin, S. Schmauder, I.V. Storozhenko, Meso- and Macroeffects of deformation localization in composites on the basis of Al with Al 2 O 3 inclusions, Proc. of Int. Conference «Physic-Technical problems of North (10-11 July 2000, Yakutsk), Ye.Ye. Deryugin, S. Schmauder, I.V. Storozhenko, Macroeffects of strain localization in composites on the basis of Al with Al 2 O 3, Physics of the processes of deformation and fracture on prediction of mechanical behavior of the materials (Proc. of ХХХVI Int. Workshop Actual problems of Strength P.1, September 2000, Vitebsk), Ye.Ye. Deryugin, V.E. Panin, S. Schmauder, I.V. Storozhenko, Effects of strain localization in composites on the basis of Al with Al 2 O 3 inclusions, Physical mesomechanics 3 (4) (2001), V.E. Panin, Ye.Ye. Deryugin, Mesomechanics of the Formation of Banded Structures on Mesoscopic and Macroscopic Levels, The Physics of Metals and Metallography, 1 (96) Suppl. (2003), S2-S L.S. Vasilenko, Ye.Ye. Deryugin, B.I. Suvorov, Influence of the rate of loading and geometrical dimensions of the specimens on the characteristics of serrated flow in Al+ 10%Al 2 O 3 alloy, New materials, structure and properties (IV All-Russian Workshop, 2004, Tomsk), Ye.Ye. Deryugin, V.Е. Panin, S. Schmauder, B.I. Suvorov, Investigation of the local characteristics of interrupted flow in disperse-hardened aluminum as multilevel system, Physical mesomechanics 9 (5) (2006), V.E. Panin, V.I. Syryamkin, Ye.Ye. Deryugin et al. Optical-television methods of the investigation and diagnostics of materials on mesolevel, Phys. Mesomechanics and computer-aided design of materials, ed. V.E. Panin (Novosibirsk: Nauka, 1, 1995),