DETECTION AND QUANTIFICATION OF CRACKS IN PRESSURE VESSELS USING ESPI AND FEA MODELLS J GRYZAGORIDIS, DM FINDEIS, JR MYLES Department of Mechanical Engineering University of Cape Town Abstract Non destructive evaluation tools of the optical kind can reliably detect defects. Electronic speckle pattern interferometry (ESPI) is a fast, non-contacting optical NDE technique which can quantify the location of the flaw but essentially only provide qualitative information regarding the size of the defect. By combining finite element methods to evaluate the results obtained from ESPI, the authors attempt to provide quantitative information about the nature of the defects. Numerous thumbnail cracks, which vary both in size and orientation, are produced in the side walls of small pressure vessels. Out of plane ESPI is used to detect the surface displacement of the pressure near the defect. Using finite element techniques to model the pressure vessel, thumbnail cracks and loading parameters, a displacement field around the flaw is reproduced. The finite element deflection map is compared to that obtained experimentally using ESPI and areas of correlation are highlighted. 1. Introduction Non-destructive evaluation procedures which are capable of reliably detecting and quantifying flaws in manufactured products are of considerable importance in aiding toward residual life prediction in pressure vessels and piping. Electronic Speckle Pattern Interferometry (ESPI) is an interferometric measurement technique used in non-destructive evaluation (NDE). The technique is capable of detecting displacements of the order of 0.3 µm, producing a contour map of the surface displacement across the whole field of view. It can be used to measure both
static and dynamic variables such as strain, shape, vibration, and, most commonly, displacement. This technique can be used to reliably detect the location of a wide variety of flaws in objects such as surface and sub-surface cracks, debonds, delaminations and corrosion. The location of the flaw can be quantified, but the size of the flaw can only be assessed qualitatively. Finite Element methods have been employed in an attempt to assist in quantifying the flaw size by providing a quick and inexpensive method of investigating the effects of flaw configuration on the fringe patterns. This paper demonstrates the use of Finite Element Methods (FEM) for the evaluation of ESPI interferograms. For this purpose computer generated fringe patterns from FE models of flawed pressure vessels are compared to interferograms of the actual flawed component. 2. Electronic Speckle Pattern Interferometry ESPI is capable of measuring the total deformation on a component, however the measurement of only the out-of-plane displacement component will be dealt with here. The principle of measurement of the in-plane displacement component and their derivatives is similar. A more extensive and rigorous treatment of the subject may be found in Jones and Wykes (1983). 2.1 Laser light Two properties of laser light make ESPI possible: Laser light is monochromatic and coherent. When laser light strikes an optically rough surface, the tiny peaks and troughs of the surface scatter the light randomly. At any point in space the intensity of the light will be due to the complex addition of the random scatterings off the active surface. The path lengths of the beams arriving at the point vary and the resultant phase of the complex addition varies randomly from point to point. This results in a random intensity distribution which produces a grainy effect known as speckle pattern which is unique for given object surface, illumination and viewing conditions.
2.2 Out-of-plane ESPI A typical set-up used to measure out-of-plane displacement is shown in Figure 2-1. The laser beam is split into two by the beamsplitter; the one which passes through the splitter forms the object beam which is expanded to illuminate the test specimen. The other beam, known as the reference beam, is led, via the two mirrors, to a second beam expander which illuminates the partial mirror. The partial mirror recombines the reference and object beams before they are imaged on the CCD. The camera images are processed by the computer and the results are displayed on the monitor. Computer frame grabber Video monitor The image recorded by the camera is thus an image of the speckled interference pattern formed by the interference of the Figure 2-1 Possible layout for ESPI. speckled object and smooth reference beams. The speckled interference pattern recorded in this way is unique and is a function of the object s position in space. Mirror Laser Mirror Camera Beam Expander The process of making an electronic speckle interferogram is as follows: Partial mirror θc θi Object Mirror Beam Splitter Beam Expander An image of the speckle pattern associated with the object in its undisturbed state is recorded and stored digitally in the computer. The intensity of any point on the image is given by: 2 2 2 2 I = A + A + 2 A A cos( θ θ ) 1 1 2 1 2 1 2 The object is then stressed. This is achieved by either mechanical, pressure, vibratory or thermal loading. A second image of the speckle pattern is subsequently recorded with the object in it s deformed state. Any object surface deflection will alter the object beam path length between object and camera. A new random phased speckle pattern will form at the CCD image plane which is related to the original (undeformed) speckle pattern by the magnitude of the change in beam path length. The intensity of any point on this second image is given by: (1)
( θ θ φ) 2 2 2 2 I = A + A + 2 A A cos ( ) + 1 1 2 1 2 1 2 The two images are processed by the software to produce the interferogram. The two speckled images were captured using the same reference beam, so any intensity variations between image I and II are caused by a change in the object beam path length and associated phase distribution. By subtracting the two images one effectively subtracts out the reference beam, leaving only the object beam distribution. Areas of correlation will be visible as dark areas, and areas of decorrelation will be visible as bright areas. These bright and dark areas form bands known as fringes. The two images of the object are equally bright, so the subtraction process removes the object image by subtracting the two equal images from one another. All that remains is an interferogram which depicts areas of correlation and decorrelation. The intensity of the resultant image is given by: 1 1 ( θ θ 2 φ) ( 2 φ) 2 2 Ir = I1 I2 = 4 A1 A2 sin ( 1 2) + sin φ is dependant on the surface displacement and it can be shown that maximum correlation occurs along lines where (2) (3) d n = λ 2 (4) where n is an integer, λ the wavelength of illumination and d the surface displacement. The set-up shown in Figure 2-1 is insensitive to displacement perpendicular to the surface normal. The component of surface displacement perpendicular to the normal is a sine term which, for small angles θ 1 and θ 2, approaches zero. The set-up is therefore sensitive only to the normal or out-of-plane component of the surface displacement. 3. Experimental Procedure The investigation consists of three parts. Firstly the fringe patterns for a defect free pressure vessel are simulated under various internal pressure loads, using the finite element package ABAQUS and compared with the patterns obtained experimentally. The modulus of elasticity in the FE model is then calibrated within the range specified for the pressure vessel material to obtain the best possible correlation. Once satisfactory correlation is obtained, various thumbnail cracks are introduced and the results compared at various loads for each flaw configuration.
The comparisons are made visually and by plotting the out-of-plane displacement profile across the mid-section of the cylinder for the FE prediction and the experimental results. Four identical aluminium cylinders machined from solid bar as shown in Figure 3-were used for the experiments. The experimental and theoretical results were compared for all four cylinders before cracks were introduced to ensure that no uncontrolled flaws were present in the uncracked cylinders. Thumbnail flaws were then introduced using a 0.2 mm thick slitting saw. A single flaw was introduced into each cylinder and the experimental data collected, after which a second flaw was introduced into two of the cylinders to demonstrate the interaction of two flaws. The following flaw configurations were investigated: external parallel to the cylinder axis, internal parallel to the axis, external perpendicular to the axis, external at 45 to the axis, two parallel axial external flaws and a v-shaped flaw, one arm of the v parallel to the axis and the other at 45 to the axis. 200 30 58 74 64 Figure 3- Dimensions of aluminium pressure vessels 3.1 Finite Element Models Three basic criteria were used in the choice of elements for the finite element model: the fringes should be simulated as accurately as possible, the crack geometry should be simple to alter and the model should not require excessive computer time to run.
The cylinders used in the investigation can be accurately modelled using shell elements, which allows the ABAQUS line-spring element to be used to model the flaws. The line spring element, first proposed by Rice (1972), models the compliance of the crack as that of an edge-notched specimen in tension and bending. It was chosen over the more complex 3D crack models because of its simplicity of implementation in a shell model. It allows the crack size, geometry and position as well as which surface of the shell it appears on to be easily altered with little or no change to the original mesh. The final FE mesh thus consisted of 8 noded quadrilateral shell elements along with the 6 noded line spring elements. The FE mesh are shown in Figure 3-2 The whole cylinder was modelled so that the same mesh could be used in the non-symmetric cases. The aluminium cylinders were mounted in a jig so that both ends were effectively built-in. The end closures could thus be implemented by simply imposing boundary conditions on the ends of the model. 4. Results Figure 3-2 Finite Element mesh Typical examples of the results of this investigation are shown in the following figures. The graphs indicate the out-of-plane displacement profile across the diameter of the cylinder for the finite element prediction (solid line) and the experimental results (individual points). The deviation in displacement between experiment and FE prediction across the middle of the cylinder was typically of the order of 10%.
4.50E-06 4.00E-06 Out of Plane Displ. 3.50E-06 3.00E-06 2.50E-06 2.00E-06 1.50E-06 1.00E-06 5.00E-07 0.00E+00-4.00E-02-2.00E-02 0.00E+00 2.00E-02 4.00E-02 Position (m) Figure 4-1 External axial crack at 689.5 kpa 4.00E-06 3.50E-06 Out of Plane Displ. 3.00E-06 2.50E-06 2.00E-06 1.50E-06 1.00E-06 5.00E-07 0.00E+00-4.00E-02-2.00E-02 0.00E+00 2.00E-02 4.00E-02 Position (m) Figure 4-2 External circumferential crack at 689.5 kpa
3.50E-06 3.00E-06 Out of Plane Displ. 2.50E-06 2.00E-06 1.50E-06 1.00E-06 5.00E-07 0.00E+00-4.00E-02-2.00E-02 0.00E+00 2.00E-02 4.00E-02 Position (m) Figure 4-3 External angled crack at 552 kpa
3.00E-06 2.50E-06 Out of Plane Displ. 2.00E-06 1.50E-06 1.00E-06 5.00E-07 0.00E+00-4.00E-02-2.00E-02 0.00E+00 2.00E-02 4.00E-02 Position (m) Figure 4-4 Internal axial crack at 689.5 kpa 3.00E-06 2.50E-06 Out of Plane Displ. 2.00E-06 1.50E-06 1.00E-06 5.00E-07 0.00E+00-4.00E-02-2.00E-02 0.00E+00 2.00E-02 4.00E-02 Position (m) Figure 4-5 External V-shaped crack at 483 kpa
5. Conclusions It is suggested here that FE modelling is a valid and useful method of simulating the ESPI fringe patterns on objects such as pressure vessels. The ease with which the crack geometry can be altered suggests that the method will provide significant savings in time and expense in the study of the relationship between crack geometry and fringe pattern. The next steps is to attempt to quantify a flaw by matching the computer generated fringe pattern with the one obtained from the real object. References Hulett, C, Penny, RK (1992), Interferometric patterns at discontinuities in pressurised cylindrical shells, Proc. 11 th Symposium on Finite Elements in South Africa. Jones, R, Wykes, C, (1983), Holographic and Speckle Interferometry, Cambridge University Press, Cambridge Kaufmann, GH, Lopergolo, AM, Idelsohn, SR (1987), Evaluation of Finite Element calculations in a part-circular crack by coherent optical techniques, Experimental Mechanics, v27 p154-7, June 1987 Kumar, V, German, MD, Schumacher, BI, (1985), Analysis of Elastic Surface Cracks Using the Line Spring Model and Shell Finite Element Method, Journal of Pressure Vessel Technology, Trans. ASME, v107 p403-11, November 1985 Parks, DM, White, CS, (1982), Elastic-Plastic Line-Spring Finite Elements for Surface Cracked Plates and Shells, J. Pressure Vessel Technology, Trans. ASME, v104 p287-92, November 1982 Ratnam, MM, Evans, WT, (1993), Comparison of Measurement of Piston Deformation Using Holographic Interferometry and Finite Elements, Experimental Mechanics, v33 p336-42, December 1993 Rice, JR, Levy, N, The Part-through Surface Crack in an Elastic Plate, J. Of Applied Mechanics, Trans. ASME, p185-94, March 1972