SAFETY ASSESMENT OF PRESSURE VESSELS

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1 SAFETY ASSESMENT OF PRESSURE VESSELS Kateřina MACUROVÁ a, Richard TICHÝ b a VŠB TU, CPIT - Structural Integrity and Materials Design, 17. listopadu 15/2172, Ostrava-Poruba, The Czech Republic, katerina.macurova@simd.cz b VŠB TU, CPIT - Structural Integrity and Materials Design, 17. listopadu 15/2172, Ostrava-Poruba, The Czech Republic, richard.tichy@simd.cz Abstract The article deals with the study conditions breach of pressure vessels and determining the safety of using the modified criteria of Leak Before Break when a residual stress is found in the material of vessel. Design criterion is based on a critical crack length, which must be less than the thickness of the vessel wall. In this case it is guaranteed that there will not be uncontrolled breach of the container. Superposition of residual stress, which occurs in the production of vessel by impact extrusion, with wall stress loaded internal pressure affects significantly the life and conditions of technical use. Size and character of the distribution of residual stresses were determined experimentally by hole-drilling method. Hole-drilling method is based on the disturbance of power and torque balance inside the body by drilling out blind or walk-through circular hole. This causes deformation of the surface. Deflection is measured strain gauge rosette in three specified directions before and after drilling. Analytical solution of stress intensity factor in case of elliptical cracks of different geometry and different distribution of residual stress in the wall was verified with numerical solution. The numerical simulation and mathematical calculations used programs ANSYS and MATLAB. It has been shown that the results of numerical solutions are in very good agreement with the analytical solution INTRODUCTION The residual stress generates nearly at all technological processes. Its knowledge is important for determining the actual state of the load of components during operation. The residual stress in the wall of the pressure vessel has an impact in the initiation, crack propagation. Application of residual stress in the FE model based on experimentally measured values is a new alternative when it is not necessary to simulate the process of forming technology for their findings. The general restrictions of the applicability of the hole-drilling method are given by the complexity of the geometry of the examined components. 1. CONCEPTION OF SOLUTION The input numerical analysis of the stress-strain response for analysis of fracture mechanics was developed. The aim was to determine the individual components of stress tensor in a critical place in order to locate a crack for the calculation of stress intensity factor. Based on the input stress-strain analysis of the entire vessel, the solution was addressed the cylindrical part of the vessel at the first step, where the maximum hoop stress occurs and the failure occurs most often during a pressure test. The simplified solution of the cylindrical part of vessel, taking into account the residual stress, was treated by entered boundary conditions, reached in solving of the entire vessel without residual stresses. In the cylindrical part of the pressure vessel plane stress was anticipated. Determined reduced stress from the sum of residual stress and stress from the external load may be useful impact or harmful effect. Harmful effect occurs when the superposition of the reduced stress is greater than reduced stress from the external load. Useful impact occurs in the opposite case.

2 Fig. 1: Geometry of CT- sample The main attention was focused on the application of residual stress in the numerical analysis, based on values obtained by experimental measurements hole drilling method. 2. MATERIAL OF PRESSURE VESSEL The experiment and numerical simulation used pressure vessels of type LA4-0592, made of steel 34CrMo4. In order to determine experimental values of J-integral of the pressure vessel, wall samples of material (according to ASTM E399) were made which were subsequently machined to form of CT-samples (Fig. 1). After the tests were carried out, the curves of resistance of materials to crack propagation J-Δa were determined from the recorded data set. The value of initiation J-integral J 0,2 = MPa.m was determined from the curves. It was established that the initiation value J 0,2 integral is equal to the critical value of the J IC thus we are on the conservative and safe side. If we consider only linear-elastic deformations, the value of initiation integral can be converted to the value of stress intensity factor, K J : 1/ 2 K E J 0,2 = J 2 (1 μ ). (1) Where E =217 GPa is the modulus of plasticity, and µ=0.3 is the Poisson ratio. 3. HOLE-DRILLING METHOD Size and character of the distribution of residual stresses were determined experimentally by holedrilling method. The relaxed stress during drilling causes deformations which were measured strain gauge rosette on the surface in three specified directions before and after drilling. Based on the measured deformation it was possible to identify two main residual stresses and their direction with respect to the strain gauge (a) of rosette (Fig. 2). Fig. 2: Main residual stresses and their orientation Measurements were made on the outer and inner cylindrical surface of the vessel. The curvature of the surface was not necessary to consider in assessing the residual stress, because the outer and inner radius of the cylindrical surface of the container meets the minimum condition 17.5 multiple of the diameter hole [1]. It was the assumption of non-homogeneous distribution of residual stress through a thickness of the cylindrical wall of the vessel when we measured. Evaluation of residual stress was carried out by the integral method.

3 From the experimentally observed values of the size and nature of the distribution of main residual stresses σ 1 and σ 2 through the thickness of the cylindrical wall of the vessel the stress components σ x '(σ z ), σ y ' (σ y ) and τ xy '(τ zy ) were calculated using the Mohr circle, which were put into the calculation ( Fig. 3). Fig. 3: Strain-gauge rosette on the outer and inner surface of the vessel, Mohr's circle 4. RESIDUAL STRESS IN FEA For the numerical analysis and data processing programs ANSYS and MATLAB were used. It was used the concept of 3D crack mesh in a defined mesh in bonded contact with a brick mesh of elements of the cylindrical vessel when mesh of model was created. The residual stress was applied into the analysis as an initial state using INISTATE order to read the data file containing the size of the components of residual stress in the Gaussian integration points of elements [2]. The residual stress was applied using the inverse distance weighted IDW 3D interpolation method from the elements of specified crack mesh to the elements of specified mesh without crack [3] by the relationships: F (x, y, z) is the value of residual stress in interpolation Fig. 4: Revolved coordinate systems of elements, FE model of vessel point of coordinates [x, y, z], n is the number of neighboring points in the selected area with a known value of residual stress f i and w i are the weights calculated using the distance interpolation point to the surrounding points in the selected areas. The location of Fig. 5: Dimension of elliptical crack in the cylindrical part of vessel

4 neighboring points is expressed by coordinates [x i, y i, z i ]. Exponent p is a positive number, usually 2. When applying the residual stress it was necessary to take into account the rotational nature of the vessel. The rotary segments (columns of elements) of vessel were assigned revolved coordinate systems x N ', y N ', z N ', where N is the number of segments (Fig. 4). 5. LEAK BEFORE BREAK The numerical analysis of cylindrical part of pressure vessels with crack was made to compare two cases - with and without application of residual stress. Based on the input numerical analysis of the entire vessel the maximum hoop stress was designed. The elliptical crack was modeled (Fig. 5). Calculation of J-integral was carried out in both cases of numerical analysis. In the case of elastic analysis, the value of the J-integral along the crack front for both cases was converted to the value of stress intensity factor K I by the relationship (1) and compared. For the critical position in the cylindrical part of pressure vessel the value of stress intensity factor K I can be determined on the base of the work of Raju and Newman [4], according to the relation: (5) Where p is the internal pressure, R the internal radius at the vessel wall thickness, Q and Y are correction factors, including geometric parameters and load cracks. The estimate of minimum wall thickness of the vessel, taking into account that while a = t and K I = K J from the relation (5) can be expressed by: (6) After putting down the value of stress intensity factor (5) to (6) the critical height of the elliptical crack was calculated for both cases and compared to: (7) To calculate the critical height of the elliptical crack a cr in both cases the corresponding maximum hoop stresses from FEA were established. Other values could be computed, or selected according to [4] taking into account the geometric assumptions and a / c = 0.4, φ = 90, a / t = 0.6. The value of the correction factor Y was determined using numerical solution of the stress intensity factor of the greatest depth, ie at angle 90 º. Reached critical heights of elliptical crack for both cases were compared and evaluated by LBB. 6. ANALYSIS RESULTS AND DISCUSSION Crack in the cylindrical part of the vessel was oriented so that its plane is perpendicular to the hoop stress from the working pressure. It was simulated Fig. 6: Behaviour of the residual hoop stress to the depth 1 mm of wall thickness

5 a situation where the crack grows from the inner to the outer surface of the vessel. The measurement of the residual stress by the hole-drilling method on the inner surface vessels detected tensile component of residual hoop stress σ z (σ x ) (Fig. 6). Superposition of residual stress and stress form the working pressure proved its harmful effect. From the combined results of the ANSYS crack mesh finite element analysis the crack front J-integral and stress intensity factor were calculated during post-processing. The results showed the increase stress crack front stress intensity. 7. CONCLUSION It was used the concept of 3D crack mesh in a defined mesh in bonded contact with a brick mesh of elements of the cylindrical vessel. The residual stress measured by the experimental hole-drilling method was applied into the FE crack mesh analysis using the inverse distance weighted IDW 3D interpolation method. The residual stress of the non-homogeneous behavior through a wall thickness was applied to the integration points of elements of the vessel wall. Superposition of residual stress with the hoop stress from the working pressure caused an increase of stress intensity factor. It resulted in increasing demands for the vessel security, the selection of material and geometry optimization. ACKNOWLEDGEMENT This research work has been supported by Ministry of Education, Youth and Sports No. SP/ LITERATURE [1] MONTAY, G. et al. Determining Residual Stress in Spherical Components: A New Application of the Hole-Drilling Method. Journal of Testing and Evaluation. Vol. 32, No. 1. January pp [2] THORWALD G., ANDERSON T. L., Analysis of 3D Crack in an Arbitrary Geometry with Weld Residual Stress, Structural Relaibility Technology, Boulder, CO [3] SHEPARD D. A two-dimensional interpolation fiction for irregularly-spaced data, Proceeding of the 23 rd National Conference ACM, ACM [4] NEWMAN J. C., RAJU, S. I., Stress-intensity factor equations for cracks in three-dimensional finite bodies subjected to tension and bending loads, NASA Technical Memorandum, 1984.

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