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Measurement of residual stresses around Vickers indentations in a ruby crystal using a Raman luminescence microscope

This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2001 J. Phys. D: Appl. Phys. 34 L122 (http://iopscience.iop.org/0022-3727/34/22/103) View the table of contents for this issue, or go to the journal homepage for more

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INSTITUTE OF PHYSICS PUBLISHING

JOURNAL OF PHYSICS D: APPLIED PHYSICS

J. Phys. D: Appl. Phys. 34 (2001) L122–L124

PII: S0022-3727(01)28445-9

RAPID COMMUNICATION

Measurement of residual stresses around Vickers indentations in a ruby crystal using a Raman luminescence microscope G K Banini1 , M M Chaudhri1 , T Smith2 and I P Hayward2 1

Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB3 0HE, UK 2 Renishaw plc, Spectroscopy Products Division, Wotton-under-Edge, Gloucestershire GL12 7DW, UK

Received 31 August 2001 Published 6 November 2001 Online at stacks.iop.org/JPhysD/34/L122 Abstract A Raman luminescence microscope has been used to determine the residual stresses around Vickers diamond indentations in a relatively large, ¯ ruby single crystal. The principle of the method well-polished, R-cut (1012) is based on the fact that the frequencies of the luminescence R lines of the ruby shift in a systematic manner with applied stress. It is shown that the hydrostatic component of the residual stress around a 25 N Vickers indentation can be as high as about 2 GPa, and that its magnitude decreases as A/r 3 , where r is the distance from the centre of indentation and A is a constant. These measurements are shown to be in qualitative agreement with the predictions of the current analytical models, although the magnitudes of the measured residual stresses are an order of magnitude smaller than those predicted by theory. Possible reasons for these differences are discussed. (Some figures in this article are in colour only in the electronic version; see www.iop.org)

Although indentation hardness testing provides a useful and relatively quick method for determining the mechanical properties of solids, the indented surface is left in a state of residual stress. Such residual stresses play an important role in the strength degradation and erosion of brittle solids, which are caused by quasi-static or dynamic contact with hard, sharp particles [1, 2]. The residual stresses around an elasto-plastic indentation are, however, difficult to measure. Nevertheless, in recent years a limited amount of success has been achieved with some ceramics and semiconductors using Raman and luminescence microscopy [3–5]. This approach of stress determination makes use of the fact that there is a systematic shift in the luminescence/Raman peaks of the test solid due to the applied stress. At present the magnitude of the residual stress around elasto-plastic indentations and its variation with the distance from the indentation centre are not fully known. It was, therefore, the main objective of this investigation to obtain this information, and in this note we describe the measurements of the residual stress in and 0022-3727/01/220122+03$30.00

© 2001 IOP Publishing Ltd

around Vickers diamond micro-indentations in a ruby single crystal. The red colour of ruby is due to the presence of the trivalent chromium ions substitutionally incorporated in a single crystal of α-Al2 O3 . These ions give rise to two sharp luminescence lines (R1 and R2 ) in the visible region [6, 7], which shift linearly with the applied stress according to the relation [8] νR1 = 7.590P − 1.5S

νR2 = 7.615P − 0.6S (1)

where νR1 and νR2 are the respective shifts in the R1 and R2 lines of ruby (in cm−1 ) and P and S are the hydrostatic and nonhydrostatic components of the stress (in GPa), respectively. If the stresses are purely hydrostatic (i.e. S = 0), both the R-lines shift by nearly equal amounts with the applied hydrostatic stress P (see equation (1)). In this work Vickers diamond indentations were made on a flat, mechanically polished surface of an unannealed R-cut ¯ ruby crystal 19 mm in diameter and 3 mm in thickness (1012)

Printed in the UK

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(a)

(b)

A B

A B 50µ µm

RC RC

50µ µm 0.2GPa

-1.9GPa

Figure 1. (a) Optical photomicrograph taken with reflected light of a 25 N Vickers diamond indentation in an R-cut ruby single crystal 19 mm in diameter and 3 mm in thickness. Radial cracks, RC, lateral cracks (halos around the indentation) and some crystallographic features AA and BB, which are probably twin traces [4], appear. The arrow indicates the line, drawn through the centre of indentation, along which the frequencies of the luminescence lines R1 and R2 were measured at several points, each separated by a distance of 5–10 µm from its nearest neighbour. Vickers hardness is 23 ± 1 GPa. (b) A Raman luminescence microscope map, represented in a colour scale, of the residual surface stresses around the indentation shown in (a). This stress map was obtained using the R1 luminescence peak of the ruby. A stress scale key in colour is given below the main frame. On this scale, a positive figure represents hydrostatic tension whereas a negative figure represents hydrostatic compression. Note that the maximum hydrostatic compression is located close to the edge of indentation, whereas there is hydrostatic tension at the tips of the radial and lateral cracks. In regions relatively distant from the indentation, the residual stress is zero, as would be expected.

and containing 0.5% by weight of Cr2 O3 (Union Carbide, USA). The indenter loads used were in the range of 1 to 25 N and the dwell time was 30 s. After unloading the indenter and removing it from the specimen, the diagonals of the residual indentations were measured using an optical microscope. Also, photomicrographs of some of the selected indentations were made. The luminescence in the ruby crystal specimen was excited with a 20 mW HeNe laser (λ = 632.8 nm), whose power at the specimen surface had been reduced to 0.05 mW by using a neutral density filter. The incident beam was focused onto the sample surface through a ×50 objective lens of a Renishaw Raman Microscope (RM2000). The luminescence was also collected by the same objective and then analysed by the grating spectrometer of the Raman microscope. The data were recorded with a frequency resolution of 1 cm−1 but by assuming that each peak was of a Lorentzian shape, curve fitting to the data gave the frequencies of the R-lines to an accuracy of 0.1 cm−1 . The frequencies of the luminescence lines of the ruby were measured for several positions on the specimen surface and lying along a radial line through the indentation centre. Some of these positions were inside the indentation and some were outside. For each test position on the sample surface, the incident beam was focused on to the surface manually. The diameter of the focused beam spot was about 1 µm. Maps of the frequency shift (i.e. residual stress) of either the R1 or the R2 line of the indented surface around various

indentations were made using an automatic displacement specimen stage of the microscope. Each complete mapping amounted to taking several thousand spectra, and without the automatic stage it would have been extremely difficult to carry out such mapping. The results obtained from all the indentations in the ruby crystal were quite similar in nature and so here we discuss only those obtained from a 25 N indentation (figure 1(a)). In this figure RC show radial cracks and the lighter regions, caused by reflected light, around the indentation are sub-surface lateral cracks. The luminescence spectra recorded from the stress-free regions of the ruby crystal showed two sharp peaks with wavenumbers at 14 404.8 cm−1 and 14 434.8 cm−1 in the visible spectrum and with a peak separation of 30 cm−1 ; these peaks were thus confirmed to be the R-lines of the unstressed ruby [9, 10]. A residual stress map of the 25 N indentation is represented in a colour scale in figure 1(b). The colour scale key at the bottom of the figure represents the residual hydrostatic stress for the R1 luminescence line only. It will be seen from the figure that the distribution of the residual stress is asymmetric about the load axis. A comparison of figures 1(a) and 1(b) suggests that the asymmetry of the residual stress may be caused by the radial and sub-surface lateral cracking. In addition, the anisotropy of the crystal and the indentation shape may contribute to this asymmetry. The largest compressive residual stress is located close to the edge L123

G K Banini et al

r/a 1

2

3

4

5

6

7

8

region outside indentation 0.8

region within indentation

Hydrostatic stress component, P (GPa)

0 1

0.6

0.4

0.2

Best fit to experimental data P = A/r

3

0

-0.2 0

40

80

120

160

Distance from centre of indentation, r (µm) Figure 2. Variation of the hydrostatic component of the residual stress measured at several points lying along the radial line indicated by the arrow in figure 1(a). r and a are the distance from the indentation centre and one-half of the residual indentation diagonal, respectively. Note that in the region outside the indentation, the stress decreases in a qualitative manner as A/r 3 . Here a negative value represents hydrostatic compression, while a positive value represents hydrostatic tension.

of indentation. Within the indentation itself, the residual stress is also compressive. Furthermore, at the tips of the radial and lateral cracks there is residual hydrostatic tension. However, at sufficiently large distances from the indentation centre there is no residual stress, as would be expected. A plot of the measured surface hydrostatic component in the region outside the 25 N residual indentation and along the line indicated by the arrow in figure 1(a) is shown in figure 2. In this figure, a negative stress value represents hydrostatic compression while a positive value corresponds to a hydrostatic tension. The maximum residual stress of 0.8 GPa is located at the edge of indentation. This value is approximately in agreement with the residual stress measurements reported by Molis and Clarke [4] and by Ostertag et al [8]. The former group studied the frequency shift of the R1 and R2 lines around a 10 N indentation in a ¯ crystal, with the luminescence being excited by ruby (1010) the beam of a krypton laser of wavelength 647.1 nm, and used an effective piezospectroscopic coefficient of 3.0 cm−1 GPa−1 ; they reported a value of 2 GPa at the indentation edge. On the other hand, Ostertag et al [8] studied the shift of the R1 and R2 ¯ single crystal around a 2 N Vickers lines of a ruby (1120) diamond indentation and the cathodoluminescence from a region around the indentation was excited with an electron beam of 20 keV. They estimated the residual stress using (1). These authors reported a maximum hydrostatic component of 0.6 GPa at the edge of the indentation. However, the scatter in their data is very large. It will also be seen from figure 2 that the hydrostatic stress component outside the residual indentation varies approximately as A/r 3 , where r is the radial distance from the centre of the indentation and A is a constant. This observation L124

is in qualitative agreement with the predictions of the models by Yoffe [11] and Chiang et al [12], which were developed for the case of an axisymmetric indentation in an isotropic solid. However, the magnitude of the measured hydrostatic stress component reported here is considerably smaller than the values predicted by the two theoretical models [11, 12]. In our experiments, the value of A was determined to be 9.07 × 10−6 nm. From the Yoffe [11] and the Chiang et al [12] models, the values of A are 7.17×10−4 nm and 1.38×10−4 nm respectively. This discrepancy between the theoretical models and experiment may possibly be due to the cracking around the indentation (figure 1(a)), which will cause some stress relaxation. It would be particularly interesting to study lowload indentations without any cracking at all. From the above observations and measurements, the following conclusions may be drawn: (i) within the indentations in the ruby crystal the hydrostatic component of the residual stress is compressive; (ii) outside the indentation, the hydrostatic component of the residual stress is also compressive and its magnitude varies as A/r 3 , where r is the radial distance from the centre of the indentation and A is a constant; this observation is in qualitative agreement with the theoretical models of Yoffe [11] and Chiang et al [12]; (iii) at the tips of lateral and radial cracks, there is a significant component of surface hydrostatic tensile stress, as would be expected; (iv) it has been shown that the use of a Raman luminescence microscope provides a non-destructive method for the determination of residual hydrostatic stress in and around indentations in some solids; and (v) the stress mapping of the region around an indentation provides an important overall view of the residual stresses.

Acknowledgments One of us (GKB) would like to thank the Association of Commonwealth Universities and the Government of Ghana for a postgraduate scholarship.

References [1] Chaudhri M M and Phillips M A 1990 Phil. Mag. A 62 1 [2] Chaudhri M M and Brophy P A 1980 J. Mater. Sci. 15 345 [3] Hayward I P, Baldwin K J, Hunter D M, Batchelder D N and Pitt G D 1995 Diamond Related Mater. 4 617 [4] Molis S E and Clarke D R 1990 J. Am. Ceram. Soc. 73 3189 [5] Williams K P J, Pitt G D, Smith J E, Whitley A, Batchelder D N and Hayward I P 1994 J. Raman Spectrosc. 25 131 [6] Grabner L 1978 J. Appl. Phys. 49 580 [7] Schawlow A L 1961 Advances in Quantum Electronics ed J R Singer (New York: Columbia University Press) p 50 [8] Ostertag C P, Robins L H and Cook L P 1991 J. Eur. Ceram. Soc. 7 109 [9] Kaplyanskii A A and Przhevuskii A K 1962 Sov. Phys. Dokl. 7 37 [10] Munro R G, Piermarini G J, Block S and Holzapfel W B 1985 J. Appl. Phys. 57 165 [11] Yoffe E H 1982 Phil. Mag. A 46 617 [12] Chiang S S, Marshall D B and Evans A G 1982 J. Appl. Phys. 53 298