X-RAY DIFFRACTION STUDY OF ANISOTROPIC STATE OF RESIDUAL STRESS AFTER DOWN-CUT AND UP-CUT FACE GRINDING

Transcription

1 34 X-RAY DIFFRACTION STUDY OF ANISOTROPIC STATE OF RESIDUAL STRESS AFTER DOWN-CUT AND UP-CUT FACE GRINDING Zdenek PALA 1, Nikolaj GANEV 1, Jan DRAHOKOUPIL 1,2 1 Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Department of Solid State Engineering, Trojanova 13, Prague 2, CZECH REPUBLIC 2 Institute of Physics of the Academy of Sciences of the Czech Republic, Na Slovance 2, Prague 8, CZECH REPUBLIC ABSTRACT Differences between up-cut and down-cut grinding are usually not considered since both modes are alternating during conventional face grinding. Nevertheless, there is a pronounced distinction in the fashion of material removal which could lead to unequal states of surface residual stress. By means of X-ray diffraction analysis, ground plates made from three types of steel were investigated in order to compute, and compare, both macroscopic and microscopic residual stress, and domains of coherent scattering. In respect to the main sources of residual stress generation, i.e., plastic and thermal deformation, machining process was carried out in two types of cooling environment. The results indicate significant influence of heat removal since differences between the two grinding modes are virtually nonexistent for liquid cooling, whereas dry grinding results in higher compressive normal residual stresses for down-cut mode in comparison to the up-cut. INTRODUCTION Machining by face grinding is inherently an anisotropic surface treatment and, therefore, ground surfaces are palpable examples of residual stress (RS) anisotropy. In particular, normal RSs frequently vary significantly in value and character (i.e., tensile or compressive), appreciable shear RSs may occur in the direction of grinding due to tangential cutting forces [1] and gradients of RSs are present even in shallow depths of several micrometers in thickness [2, 3]. Moreover, during face grinding two fundamentally different processes of material removal are alternately in

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3 3 progress up-cut and down-cut grinding. The significant difference lies in the direction of applied forces causing the plastic deformation as can be seen in Fig. 1. The purpose of the performed experiments was to ascertain, by means of X-ray diffraction analysis, whether the above mentioned modes of grinding lead to any differences in final state of surface residual stress. A B Figure 1: Schematic depictions of up-cut (A) and down-cut (B) face grinding. Investigation of ground surfaces even resulted in the description of the so-called psi splitting about half a century ago [4]. In their experiment, Fuks and Gladkikh rotated the sample by 180 in order to align the diffractometer, the initial position was such that the primary X-ray beam impinged the surface in the direction of grinding. The aligning job was to be considered accomplished when the plots of 2è versus sin 2 ø were the same within the experimental inaccuracy for both orientations. However, such desired situation was not achieved and the psi splitting was later [] explained by occurrence of shear stresses in the irradiated volume. Several attempts have been made to theoretically explain the generation of shear stresses in metals, mostly as a consequence of anisotropy, gradient or coupled stress effects on the residual strains at the surface. Another interpretation of this phenomenon is based on inhomogenities of the distribution of the Burgers vector of dislocations with strong density gradients from the surface [6]. It should be emphasized that shear stresses are recorded in multi-phase materials; singlephase ground surfaces of pure aluminium or silver usually do not exhibit psi splitting [7]. SAMPLES AND GRINDING PROCESSES Studied samples in form of square-shaped plates with dimensions 0 0. mm 3 were manufactured from three types of steels mild carbon steel C4, corrosion-resistant steel M300

4 36 and high speed steel M41. The set of twelve plates, which were cut from cast ingots, underwent annealing at 0 C in argon atmosphere for two hours in order to reduce surface residual stresses before the actual grinding. The finish surface grinding was conducted on the BPH 320 A face grinding machine equipped with a corundum abrasive wheel under following parameters: the wheel speed - 3 m/s, tangential speed of table drift - 10 m/min, axial table drift - 1 mm per stroke, and thickness of removed layer mm. The samples were fixed on a magnetic table, which was moving in respect to the grinding wheel rotation axis, each plate was subjected either to down-cut or up-cut grinding (Fig. 1). In order to consider the effects of thermal deformation, either emulsion of water and synthetic fluid for machining operations or ambient air were used as coolants. X-RAY DIFFRACTION ANALYSIS Since the face grinding is almost exclusively done by alternating up-cut and down-cut modes, the last direction of sample movement and wheel sense of rotation is not usually taken into account because it is not known. Hence, there exist two possibilities for grinding direction assignment. Being aware of this freedom and having the information about the geometry of grinding, the diffraction measurements were performed for both options, i.e. in two coordinate systems mutually rotated by 180. In order to obtain full stress tensor, the diffraction line {211} of á-fe phase was measured in both positive and negative tilts in three azimuths 0, 4, 90 on a è/è Bragg-Brentano ù-goniometer X Pert PRO with CrKá radiation. The goniometer was adjusted in respect to a strain-free reference specimen of á-fe powder. For all samples, the azimuth 0 was chosen in the direction of material removal progress (Fig. 2) and in the opposite one. Since the ground surfaces exhibit psi splitting, calculation of tensor for state of triaxial RS was done according to modified sin 2 ø (Dölle and Hauk) method [8]. X-ray elastic constants for measured á-fe {211} diffraction planes were computed following the Eshelby-Kröner theory [9]. The position of diffraction maximum was established as a centroid of diffracted doublet CrKá 1 á 2 after Lorentz, polarization and absorption corrections. Information about strain-free lattice spacing a 0 for the three materials was obtained from evaluation of strain-free direction in d öø (sin 2 ø ) plots of annealed samples. For comparison, and due to higher inaccuracy of the hydrostatic tensor, results of deviatoric tensor were considered as well.

5 37 DIRECTION OF MATERIAL REMOVAL PROGRESS PRIMARY X-RAY BEAM DIFFRACTED X-RAY BEAM Figure 2: Layout of diffraction measurement in azimuth ö = 0 assigned to the direction of material removal progress for both grinding modes. Microstrains and mean coherent scattering domain sizes were evaluated by single line profilefitting method [10] for each obtained {211} diffraction peak of ferrite in order to unveil possible direction-dependent dissimilarities. EFFECT OF COORDINATE SYSTEM ROTATION BY 180 Suppose that ó kl (k,l = 1,2,3) are components of stress tensor in reference frame x, y, z, while ó kl correspond to reference frame x, y, z. Using Einstein summation rule (m,n = 1,2,3), their mutual relation is given by [11] ó kl = a km a ln ó mn, where a kl are components of transformation matrix representing direction cosines between axes x, y, z and x, y, z : cos(x,x) cos(x, y) cos(x,z) cos(y,x) cos(y, y) cos(y,z). cos(z,x) cos(z, y) cos(z,z) As the reference frames are rotated by 180, the transformation matrix has the form

6 The components of the stress tensor ó kl can be therefore written as ó kk = ó kk, ó 13 = ó 13, ó 23 = ó 23, ó 12 = ó 12. Hence, the terminology of compressive and tensile shear stresses, in contrast to normal stresses, bears no physical meaning as it depends on the choice of coordinate system. RESULTS In particular, the ground surfaces were assessed in accordance with (i) differences between up-cut and down-cut ground plates, (ii) impact of cooling environment, (iii) ambiguity of choice of azimuth ö = 0 as the grinding direction. Backscattering Debye - Scherrer patterns were continuous homogeneous diffraction rings and gave evidence of crystallite size suitable for X-ray diffractometric measurements of RSs. Residual stress analysis of plates made from mild carbon steel C4 is displayed as a representative set of results. Table 1: Stress tensors of ground surface of sample made from mild carbon steel C4. UP-CUT DOWN-CUT LIQUID COOLING AMBIENT AIR ö = 0 in the direction of material removal progress ö = 0 in the opposite direction ö = 0 in the direction of material removal progress ö = 0 in the opposite direction

7 39 CONCLUSIONS Following principal conclusions could be drawn from the performed diffraction analysis for all three materials: Way of cooling has an appreciable impact on normal RSs ó 11 & ó 22 in respect to the grinding modes. Liquid cooling results in approximately the same values of RSs, whereas for down-cut dry grinding higher compressive normal RSs were recorded in comparison to the up-cut mode. Shear stress ó 31 computed from psi splitting in grinding direction indeed changes its sign when the reference frame is rotated by 180. Moreover, the negative ó 31 always occurs when the primary X-ray beam impinges the surface in the opposite orientation vis-à-vis the assumed sense of grinding wheel rotation. The sign of shear stress ó 31 can be, hence, used for determination of grinding wheel rotation direction. Negative shear stresses ó 31 are systematically lower, in an absolute value, in comparison with positive shear stresses. Causes for such behaviour can lie in an array of factors ranging from the absorption of X-rays to deviation from perfect sample alignment. Values of microstrains and mean coherent scattering domain sizes don t show any dependence on grinding modes for both cooling environment. The computed microstrains averaged 10-3 and mean coherent scattering domains were characteristically about 4 nm in size. REFERENCES [1] Dölle, H.; Cohen, J.B., Met. Trans. A, 1980,11A, [2] Hauk, V.; Oudelhoven, R.W.M.; Vaessen, G.J.H., Met. Trans. A, 1982, 13A, [3] Kraus, I.; Ganev, N.: Residual Stress and Stress Gradients, In: Industrial Applications of X- Ray Diffraction. New York: Marcel Dekker, 2000, [4] Fuks, M.; Gladkikh, L., Zav. lab., 196, 8, 978. [] Macherauch, E.; Müller, P., Zeitsch. angew. Physik, 1961, 13, [6] Gondi, P.; Mattogno, G.; Montanari, R.; Silli, A., Zeitsch. f. Metallk., 1990, 70 7 [7] Behnken, H.; Hauk, V., Mat. Sci. For., 2002, , [8] Dõlle, H.; Hauk, V., Materialprüf., 1976, 18, [9] Hauk, V.; Macherauch, E.; Advances in X-ray analysis, 1983,

8 40 [10] de Keijser, Th.H.; Langford, J.I.; Mittemeijer, E.J.; Vogels, A.B.P., J. Appl. Cryst., 1982, 1, 308. [11] Noyan, I.C.; Cohen, J.B.: Residual Stress Measurement by Diffraction and Interpretation. Springer, 1987,