Theoretical Analysis of Ring-Core Method for Residual Stress Determination

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1 Konference ANSYS 2009 Theoretical Analysis of Ring-Core Method for Residual Stress Determination Adam Civín 1, Miloš Vlk 2 Institute of Solid Mechanics, Mechatronics and Biomechanics Faculty of Mechanical Engineering Brno University of Technology Abstract: The ring-core method is semi-destructive experimental method used for the residual stress measurement. This method depends on the calibration coefficients which need to be obtained by experiment or FE-analysis. This paper considers application of the general-purposed finite element model which is suitable for the calibration coefficients determination. The FEM model is convenient for determination of the depth varying residual stress too. The calibration coefficients are determined by the integral method. Key words: hole-drilling method, ring-core method, residual stress, calibration coefficients/ relaxation functions, relaxed strain, strain gauge rosette, finite element method Abstrakt: Metoda uvolňování sloupku patří mezi experimentální polodestruktivní metody k určování zbytkového napětí. Použití této metody závisí na vhodném určení kalibračních koeficientů, které lze získat jak provedením experimentu, tak simulací pomocí metody konečných prvků. Příspěvek se zabývá využitím univerzálně navrženého konečnoprvkového modelu, sloužícího ke stanovení kalibračních koeficientů pro homogenní a nehomogenní napjatost po tloušťce materiálu. Koeficienty jsou vyhodnocovány pomocí integrální metody. Klíčová slova: metoda vrtání otvoru, metoda sloupku, zbytkové napětí, kalibrační koeficienty, tenzometrická růžice, metoda konečných prvků 1. Introduction Residual stresses in the structural materials affect positively or negatively behavior of component parts. Existence of the residual stress in the structural material occurs by machining, heat treatment, history of loading and environmental effects such as temperature, radiation etc. The ring-core and the hole-drilling methods are semi-destructive methods used to quantify the principal residual stresses within a specified depth of material. Both techniques are relatively rapid and convenient in practice. They also allow determination of the principal residual stresses as a functi- 1 Ing. Adam Civín; Brno University of Technology, Institute of Solid Mechanics, Mechatronics and Biomechanics, Technická 2896/2, Brno, civin.adam@seznam.cz 2 doc. Ing. Miloš Vlk CSc.; Brno University of Technology, Institute of Solid Mechanics, Mechatronics and Biomechanics, Technická 2896/2, Brno, vlk@fme.vutbr.cz

2 TechSoft Engineering & SVS FEM on of depth. The specimen is not totally destroyed during measurement and in many cases could be used for another application (Civín, 2008). This paper compare basic differences between both methods and is focused how to determine magnitude and directions of principal residual stresses by the finite element method. All-purpose finite element model has been designed for the residual stress simulation and determination of the calibration coefficients/relaxation functions for specimens with uniform and non-uniform state of stress inside of material. Model is available to simulate cutting of the uniform or non-uniform depth increments too. Possible parameters with the influence to obtained results (calibration coefficients) are mentioned (i.e. basic dimensions of model, radius caused by the cutting tool at the bottom of the hole etc.) because they are essential for the residual stress determination. For the calibration coefficients determination has been used Integral method approach (Schajer, 1988). An application program for easier setting up and running the simulation with desired parameters of solution has been created too. 2. Ring-core vs. Hole-drilling method The hole-drilling and the ring-core methods are two of the most common methods for residual stress measurement. Both involve a localized removal of stressed material and measurement of strain relief in the adjacent material. Mathematical functions known as the relaxation functions or the calibration coefficients are related to the subsurface relaxed strains, measured on the surface. These functions are unique for a specific strain gage rosette and ring core diameter. They can be determined experimentally or by FE-analysis. Special strain gauge rosettes are used for the measurement of relaxed strains. These rosettes are bonded to the surface of the measured object and ring-shaped grooves are milled around them with special equipment (in case of the ring-core method). When the hole-drilling method is being used, small hole is drilled in the centre of strain gauge rosettes. The hole-drilling method (see Fig.1a) requires drilling a small hole (1-4 mm in diameter) to a depth approximately equal to its diameter. A specialized three-element rosette measures the surface strain relief in the material around the outside of the hole. a) The hole-drilling method b) The ring-core method Fig.1. Difference between semi-destructive methods

3 Konference ANSYS 2009 Relieved strains are then measured in vicinity of the hole and magnitude of residual stress could be determined. Method can be used to quantify only residual stresses that are less then nominally half of the yield strength of the material (Lu, 1996). The ring-core method (see Fig.1b) is similar, except that a ring-core, typically mm inner diameter, is drilled instead of the hole. Small annular groove in the surface of the specimen is drilled concentrically around a strain gauge rosette, leaving the upper part of the core separated from the surrounding material. This separation causes release of the residual stresses presented in core, which is represented by deformation of the core. These deformations can be measured by strain gauges designated for measuring relieved strains by the ring-core method. The annular groove needed to release the stresses can be machined with suitable cutter, like a ring saw. This method is less sensitive to errors involved in placement of the cutting tool relative to the strain gauge and stress can be measured accurately up to the yield stress of material. The ring-core method is more sensitive in comparison to the hole-drilling method because it involves almost complete relief of the surface strains. However, the size of annular groove is relatively large, causing much more damage than the hole-drilling method which allows more localized residual stress measurement. Despite its potential disadvantages, the hole-drilling method is the most common choice. Method is well established, experimentally and theoretically (Lu, 1996; Švaříček, 2003). 3. Theoretical approach Basics of the mathematical approach are almost the same for both methods. The evaluation of the ring-core method assumes that one of the principal directions of the residual state of stress is in a direction perpendicular to the specimen s surface and negligible stress exists in this direction. An unknown residual state of stress exists parallel to the surface. The stress field is almost uniform in the measuring plane within the core diameter but variable with depth. The material is isotropic and the relaxation of strains is elastic (Ajovalasit, 1996) The integral equation method is needed to construct a numerical calibration coefficients matrix in order to describe a non-uniform stress state. Analysis equations are based on fact that the total strain relaxation (Equation (1)) depends on the stress state of all previous depth increments. The calibration data, matrix F, are provided by a finite element calculation. where ε (H) is strain relieved on the surface after milling a groove having depth H, E is Young s modulus, σ (z) is residual stress acting at depth z and F (H,z) is the calibration coefficient which is proportional to the strain relieved on the surface due to the stress acting at the depth z when the groove have a total depth of H. Equation (1) can be modified to the bi-dimensional case in following way: in which A (H,z), B (H,z) are the calibration coefficients, σ 1(z) and σ 2(z) are the residual stresses acting at depth z and α k(z) is the angle between the maximum principal stress σ 1(z) and the measuring direction k (see Fig.2). (1) (2)

FE-analysis is based on the basic specimen volume with basic dimensions of 50 x 50 mm (may vary) and variable thickness.

4 TechSoft Engineering & SVS FEM 4. Finite element analysis Fig.2. Geometry and general notification for integral equation method Simulation by FEM is the only reasonable way how to obtain desired information or how to simulate real experiment. FE-analysis is based on the basic specimen volume with basic dimensions of 50 x 50 mm (may vary) and variable thickness. Due to symmetry, only a quarter was modeled with centre of the core on the surface as the origin. That considerable minimizes data storage capacity and computing time. Shape of the model is simply represented by block with planar faces with quarter off drilled annular groove (Siiriäinen, 2000). FE-model used for analysis is shown in Fig.3a. Suitable FE-mesh is created by specific elements (see Fig.3b). t r a a) Model b) Detail of finite element mesh Fig.3. Finite element model The ring-core method like the hole-drilling method has many restrictions in which cases could be used. A few possible parameters and restrictions, which have significant influence on obtained results, are described below:

5 Konference ANSYS Restrictions and assumptions of numerical model: a) material model is isotropic, linearly elastic b) no applied loads on the models surface (plane state of stress is required), c) a uniform state of stress over whole depth of removed material or the uniform state of stress in every removed layer, but with variable magnitude and the principal directions of residual stress of each removed layer (assumption for an integral method of measuring a non-uniform residual stress through every removed layer of the specimen), d) residual stress is homogeneous in planes parallel to the surface of the material, e) surface of the specimen is flat or nearly flat (cylindrical or spherical surfaces with large radius of curvature), f) no other residual stress is introduced into the specimen during material removal by cutting tool, 4.2 Parameters with influence on results: a) will be examined whether and how the following factors affect the measurement: thickness, height and width of body, radius caused by the cutting tool at the bottom of the hole (covered in 4.3 Testing of influence of model dimensions), hole location, size and depth of groove, diameter of drilled core, etc.), b) drilled hole must be concentric with the centre of the strain gauge rosette and must be located at sufficient distance from geometric discontinuity (the edge of body, fillet, additional holes, brackets, grooves etc.), c) appropriate types of the strain gauge rosettes for measuring residual stress must be used (different types of strain gauge grid shape, structure, size), d) type and geometry of cutting tool, particularly geometry of blades, 4.3 Testing of influence of model dimension: To judge the influence of the specimens dimensions to magnitude of released strains has been accomplished by many types of computations. Influence of the length, width and thickness of specimen and radius caused by the cutting tool at the bottom of the hole is considered. Isotropic, linearly elastic material model is used with material properties of Young s modulus 210 GPa and Poisson s ratio µ=0.3. Relieved strains, which are used for proper determination of the calibration coefficients, were calculated by the FE-analysis. Basic parameters of specimen were: thickness t = mm, length x width a = mm, inner ring-saw radius r 1 = 7 mm, outer ring-saw radius r 2 = 9 mm, drilled depth h = 0.5 mm, cutting-ring fillet r = mm. For every set of calculations has been changing only one of mentioned parameters (see Fig.3a), i.e.: t (Tab.1, Fig.4), a (Tab.2, Fig.5), r (Tab.3, Fig.6). Values of relaxed strains (ε x ) correspond to unity preassure of 1MPa, applied inside of annular groove to simulate equibiaxial stress and shear stress in every removed layer. As you can see, influence of specimen shickness (t) on relesased strains is significant only for thin models, then recommended thickness should be at least t = 30 mm. There is no more influence for thicker models. No obvious influence of model s dimesions like a length x width (a) is observed. But dimension at least a = 50 mm is recommendet for all simulations. There is an obvious influence of the cutting-ring fillet (r) created at the bottom of the hole by blunting the

TechSoft Engineering & SVS FEM cutting edge. During the rising of cutting-ring fillet the relieved strain is changing and then as well calculated calibration coefficients. Tab.1.

6 TechSoft Engineering & SVS FEM cutting edge. During the rising of cutting-ring fillet the relieved strain is changing and then as well calculated calibration coefficients. Tab.1. Influence of parameter t Fig.4.Thickness vs. plane tension and shear tension Tab.2. Influence of parameter a Fig.5.Length vs. plane tension and shear tension Tab.3. Influence of parameter r Fig.6. Cutting ting fillet vs. plane tension and shear tension

Application allows setting up model dimensions, solution specifications, direct start of solution (ANSYS software needs to be installed) or creation macro files necessary for solution. Fig.7a and Fig.

7 Konference ANSYS Ring-core user s application: For easier creation of own macro files with desired values of main parameters has been created an application program, appropriate for the ANSYS software. Application allows setting up model dimensions, solution specifications, direct start of solution (ANSYS software needs to be installed) or creation macro files necessary for solution. Fig.7a and Fig.7b show the interface of the application with important boxes for selection and edition. All numerical values are possible to edit only within specified range. Fig.7a shows the first part of the application with editable specimen and ring-saw dimensions. Fig.7b shows the second part with available definition of material properties, selection of uniform and non-uniform depth increment with number of removed layers and another users options. a) Model and cutting tool specification b) Material, solution and user s settings Fig.7. Ring-core application program 5. Conclusion This paper provides basic information about semi-destructive ring-core method with assessment of main distinctions from hole-drilling method. Both methods are used for residual stress determination. The ring-core method is suitable for measurement of under-surface stresses where standard hole-drilling method is less sensitive. All-purpose finite element model is designed for the calibration coefficients/relaxation functions which are necessary for the residual stress determination. More detailed are study possible parameters with the influence to obtained results (measured strains), i.e. basic dimensions of model and radius caused by the cutting tool at the bottom of the hole. An application program for easier setting up and running the simulation with desired parameters is presented too. Improvements of the mathematical model to reduce influence of possible restrictions as well as parameters affecting reliability and sensitivity of ring-core method should be solved during next years. By concentrating the research on the observed weaknesses and the ambiguous details, the ring-core method can be made an accurate and reliable method for residual stress measurement. Application of the integral equation method initially developed for the hole-drilling method permits to determine a non-uniform residual stress field, i.e. principal stresses and their orientation. To apply this method, a specific amount of the calibration coefficients need to be calculated by FE-analysis. Restrictions and assumptions of the numerical model were mentioned too.

8 TechSoft Engineering & SVS FEM 6. References 1. Civín, A. Stanovení zbytkové napjatosti metodou vrtání otvoru s využitím MKP. Brno, Diplomová práce, Vysoké učení technické v Brně, Fakulta strojního inženýrství. 93 p. 2. Lu, J. Handbook of Measurement of Residual Stresses, Society for experimental mechanics, Inc.,1996, pp Ajovalasit, A. - Petrucci, G. - Zuccarello, B. Determination of Non-Uniform Residual Stresses Using the Ring-Core Method, Transactions of the ASME Journal of Engineering Materials and Technology. University of Palermo, Italy Vol. 118, No.2, pp Siiriäinen, J. - Gripenberg, H. - Hänninen, H. Design and implementation of ring-core method for residual stress measurement, 6th Int. Conf. on Residual Stresses ICRS-6, 2000, Oxford, UK, pp Schajer, G.S. Measurement of Non Uniform Residual Stress Using the Hole Drilling Method Part I. Journal of Engineering Materials and Technology. october 1988, Sv. 110, pp Švaříček, K. Teoretické stanovení kalibračních konstant pro měření zbytkového napětí odvrtávací metodou Diplomová práce. VUT FSI Brno, 2003.

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