Technical notes. SP Swedish National Testing and Research Institute. Lars Jacobsson Bertil Enqvist

Transcription

1 Technical notes Lars Jacobsson Bertil Enqvist Deformation measurement on rock specimen during Brazilian test using White Light Speckle Photography (WLSP) SP Technical Notes 2004:38 Building Technology and Mechanics Borås 2004 SP Swedish National Testing and Research Institute

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3 Lars Jacobsson Bertil Enqvist 1 Deformation measurement on rock specimen during Brazilian test using White Light Speckle Photography (WLSP) SP Technical Notes 2004:38 Building Technology and Mechanics Borås Department of Structural Mechanics, Chalmers University of Technology, SE Gothenburg, Sweden

4 2 Abstract An indirect tensile strength test on a rock specimen has been carried out. The deformation field was measured during the loading with a certain time interval to a point right beyond failure using White Light Speckle Photography (WLSP), sometimes also called stereographic digital speckle photography. The speckle pattern was created by adding black speckles on a white background. Two CCD-cameras with 1280x1024 pixels were used to simultaneously capture the images of the specimen surface. The results show that the displacement and strain fields can be obtained with this method. However, the limited resolution makes it difficult to measure the deformations and strains at the initial stages of the loading, as the deformations are quite small. Moreover, the accuracy of the measurements is most likely too low in order to get quantitatively reliable results for the actual application. It is possible to increase the resolution by either using CCD-cameras with higher resolution and/or decreasing the measurement volume. The size of the speckles limits the theoretical resolution that can be obtained. It may therefore also be of importance to improve the method on how the speckles are made. Key words: Brazilian test, Rock mechanics, contactless deformation measurement, WLSP SP Sveriges Provnings- och SP Swedish National Testing and Forskningsinstitut Research Institute SP AR 2004:38 SP Technical Notes 2004:38 Borås 2005 Postal address: Box 857, SE BORÅS, Sweden Telephone: Telex: Testing S Telefax: info@sp.se

5 3 Contents 1 Introduction 5 2 Experimental set-up Mechanical loading Deformation measurements 7 3 Results of the deformation measurement 8 4 Discussion of results and conclusions 12 5 Acknowledgements 12 References 13 Appendix A Technical data of the deformation measurement system 14 Appendix B Additional results on the deformation measurement 16

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7 5 1 Introduction The modelling capabilities for the mechanical behaviour of rock materials are continuously increasing and there are nowadays possibilities to simulate the deformation and fracture process in greater detail. There are, for example, models in which the grain structure in the material is mimicked on a meso-scale, cf. e.g. [1]. These models contain a number of parameters that can be determined from mechanical tests on rock specimens. Examples of common tests are indirect tests for determining tensile strength (Brazilian tests) [2], uniaxial [3] and triaxial compression tests [4]. The results yield information of the macroscopic behaviour in the material. Additional information on e.g. localized deformations due to micro or macro cracking or stress concentrations is however needed in order to fully determine the model parameters in the advanced models. On the other hand, detailed information on the deformation and strain fields can be used to verify simulated results. There are different optical methods that can be used to measure the deformation field on a material surface. They are non-contact measurement methods. The most common are various holographic methods and speckle methods. One widely used holographic method is the electronic speckle pattern interferometri (ESPI), also called TV holography, where the image is captured on a video or CCD-camera, which can be used for measuring static, dynamic or transient deformations. The speckle methods are divided into speckle interferometry, shearing speckle interferometry and speckle photography. The speckles are obtained by illumination of the object with a coherent light from a laser and the image is recorded by a photographic film or a CCD-camera. Furthermore, the interference of two beams is used to determine the object deformation in the interferometric methods, whereas one beam is used to study the bulk movement of the speckles in the speckle photography method. A variant of speckle photography is the white light speckle photography (WLSP) in which the object is illuminated by a white light source and one or several CCD-cameras photograph the object. The WLSP-method was used in this study. Detailed descriptions of the various methods can be found in textbooks on optical metrology, e.g. [5]. A commercial system ARAMIS 1.3M by GOM mbh was used to carry out deformation field measurements using WLSP on a rock specimen during an indirect tensile strength test.

8 6 2 Experimental set-up 2.1 Mechanical loading The rock specimen used in the indirect tensile strength test was selected from a test series conducted on behalf of the Swedish Nuclear Fuel and Waste Management Co (SKB). The specimen comes from a test site in the Forsmark area and results from the entire series can be found in [6]. The specimen (KFM05A-110-5) is a cylindrical disc cut from a drill core with diameter 50.9 mm and thickness 26.3 mm. The rock type in the specimen is Medium-grained granite and it was water saturated prior to the mechanical test. The principle of the test is to apply a line load diametrically across the specimen and thereby obtain a tensile stress perpendicular to the line of loading, see Figures 1 and 2. The specimen was loaded with a prescribed deformation rate and the failure load was reached after about 90 s. The force at failure was 29.4 kn which can be recalculated to a indirect tensile strength of 14.0 MPa, cf. [2]. F F Figure 1 Loading during an indirect tensile strength test. Figure 2 Simulated fringe stress pattern induced by the indirect tensile strength test i) Shear stress; ii) Maximum principal stress; iii) Minimum principal stress. (The picture is reproduced from [1] with kind permission from the author.)

9 7 2.2 Deformation measurements Stereographic digital speckle photography was used in the deformation measurement. The surface of the specimen was prepared by first applying white retroreflective paint as a background. Small black stains were applied on top of the white background in order to create a characteristic speckle pattern. Two CCD-cameras with 1.3 Mega pixels resolution (1280x1024 pixels) was used to photograph the specimen, see Figure 3. The principle is to place the cameras at a certain distance from each other in order to obtain stereo photographs on the object (like the eyes of a human) in order to be able to determine out-of-plane displacements. The system needs to be calibrated with a reference speckle pattern. The calibration was made for a measurement volume of 75x60x40 mm 3. In total 98 image pairs were taken with a one second interval i.e. with a frequency of 1 Hz. The images are divided in sub-images, in this case with the size of 25x25 pixels with an overlap of 12 pixels. This yields a distance of 0.75x0.75 mm 2 between calculated points in the x- and y-directions. The grey scales in the subimages are used for the pattern recognition and for the computation of the displacement of each calculated point. A compensation for rigid body motions was done. Four points at the lower fixture part were selected as fixed reference points. The relative displacements were then obtained by subtracting the rigid body motions using the displacement data from the reference points. A filtering by a mean value calculation over three calculated points were done once in order to obtain smoother results. Figure 3 Experimental set-up containing the two CCD-cameras, test object and loading fixture.

10 8 3 Results of the deformation measurement Two sections have been defined for the results presentation in order to visualize the variation through a section; Section 0 is a horizontal cross section going from left to right and Section 1 is a vertical cross section going from top to bottom and both sections are intersecting with the centre point, see Figure 4. Figure 4 Definition of coordinate system and sections. The vertical displacements in the specimen, right before and after the fracturing, after 91 and 92 seconds of loading respectively, are shown in Figure 5. It can be concluded from the displacement field that the specimen has slightly rotated counterclockwise. Various strains in the specimen after 91 seconds of loading (right before fracturing), are shown in Figure 6. Moreover, the directions of the minor strain after 91 seconds are shown in Figure 7. It is seen that the direction of minor strain is still random like at 20 seconds of loading, but are starting to be orientated at 40 seconds of loading close to the contact surfaces and are almost fully oriented at 91 seconds of loading. Complementary results are found in Appendix B.

11 Figure 5 Vertical displacements in the specimen. The displacement variations along the sections are shown in the diagrams on the left and the displacement fields are shown on the right. 9

12 10 Figure 6 Strains in the specimen right before failure. Upper: strains in the horizontal direction, Middle: strains vertical direction, Lower: effective deviatoric strain (Mises strain). The strain variations along the sections are shown in the diagrams on the left and the strain fields are shown on the right.

13 11 Figure 7 Directions of the minor strain in the upper part of the specimen after 20 (upper figure), 40 (middle figure) and 91 seconds (lower figure) of loading.

14 12 4 Discussion of results and conclusions The maximum tensile strain recorded right prior to failure was approximately around 0.03% to 0.05% with a scatter of the same magnitude. It can be seen that the maximum tensile strain is located around the center with maximum along the vertical section. This corresponds with theoretical results as can be seen in Figure 2. The vertical compressive strain in the centre of the specimen was about 0.08% right prior to failure. This can be viewed with the knowledge that the Poisson ratio should be in the order of 0.25 to The strain concentrations around the loading areas can be seen in the results. The results show that the displacement and strain fields can be obtained with this method. However, it can be concluded that the given resolution in the displacement measurements is not high enough to obtain accurate results for the tested application. The strains just before to failure could be roughly estimated, but difficult to estimate at earlier stages during the loading when the values are smaller. It is possible to increase the resolution by either using CCD-cameras with higher resolution and/or decreasing the measurement volume. The size of the speckles limits the theoretical resolution that can be obtained. It may therefore also be of importance to improve the speckles made. Other optical methods such as electronic speckle pattern interferometri (ESPI), speckle interferometry or shearing speckle interferometry can detect small deformations and can be alternative methods for measuring the deformation field on a rock surface. The resolution of the displacement measurement in these alternative methods is down to the wavelength or parts of the wavelength of the coherent light sources used. In rough numbers a displacement change of 10 nm can be detected. There are however other drawbacks with these methods. For example they are more cumbersome to carry out and are sensitive to vibrations in a higher degree than the WLSP method. 5 Acknowledgements Thanks to Cascade Computing AB in Göteborg that has provided the equipment for the deformation measurements.

15 13 References [1] Liu, H, Numerical modelling of the rock fragmentation process by mechanical tools, Dr Thesis, Luleå Technical University, [2] ASTM a. Standard test method for splitting tensile strength of intact rock core specimens, [3] ISRM. Draft ISRM suggested method for the complete stress-strain curve for intact rock in uniaxial compression, Int. J. Rock. Mech. Min. Sci. 36(3), pp , [4] ISRM suggested method for determining the strength of rock material in triaxial compression: Revised version, Int. J. Rock. Mech. Min. Sci. & Geomech. Abstr. 20(6), pp , [5] Gåsvik, K J, Optical Metrology 2nd ed., Wiley, [6] Jacobsson, L, Forsmark site investigation, Borehole KFM05A, Indirect tensile strength test, Report P-05-98, Swedish Nuclear Fuel and Waste Management Co, (available at

16 14 Appendix A Technical data of the deformation measurement system The technical information about the system is obtained from the website of the manufacturer of the equipment, GOM mbh ( The system used in the measurements in this report was the ARAMIS 1.3M system. Technical information about the different systems are shown in Table A1 below. The system with the computer unit and the cameras are shown in Figure A1. Figure A1 Equipment for deformation measurements. Computer unit and CCD cameras. (Picture from Table A1 Technical information about different deformation measurement systems. (From Measuring Area Camera Resolution Frame Rate Exposure Time Strain Measuring Range Strain Measurement Accuracy Results Dimensions ARAMIS 1.3M ARAMIS 4M mm² up to > m² mm² up to > m² 1280x1024 pixel, 8 bit digital 2048x2048 pixel, 8 bit digital 12 Hz, 24 Hz optional 6 Hz 0.1 ms up to 1 s, computer-operated, asynchronus trigger 0.02 s up to 1 s, computer-operated, asynchronus trigger 0.1% up to > 100% 0.05% up to > 100% up to 0.02% up to 0.01% 2D/3D displacement fields, strains and contour 500x190x125 mm³ 2D/3D displacement fields, strains and contour 500x190x125 mm³

17 15 ARAMIS HS Measuring Area mm² up to > m² Camera Resolution 1280x1024 pixel, 8 bit digital Frame Rate 480 Hz at 1280x1024 pixel, 960 Hz at 1280x512 pixel,... Exposure Time ms up to 1s, computer-operated, asynchronus trigger Strain Measuring Range 0.1% up to > 100% Strain Measurement Accuracy up to 0.02% Results 2D/3D displacement fields, strains and contour Dimensions 500x190x125 mm³

18 16 Appendix B Additional results on the deformation measurement Vertical displacements The vertical displacement in the specimen at different stages of loading is shown in Figure B1. a) b) c) Figure B1 Vertical displacements after a) 0, b) 40 and c) 60 seconds loading. The displacement variations along the sections are shown in the diagrams on the left and the displacement fields are shown on the right.

19 17 Horizontal strain The horizontal strain in the specimen at different stages of loading is shown in Figure B2. a) b) c) Figure B2 Measured strain in the horizontal direction at a) 20, b) 40 and c) 60 seconds of loading.

20 18 Vertical strain The vertical strain in the specimen at different stages of loading is shown in Figure B3. a) b) c) Figure B3 Measured strain in the vertical direction at a) 20, b) 40 and c) 60 seconds of loading.

21 19 Effective deviatoric strain (Mises strain) The effective deviatoric strain in the specimen at different stages of loading is shown in Figure B4. a) b) c) Figure B4 Effective deviatoric strain at a) 20, b) 40 and c) 60 seconds of loading.

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