A thermal stress analysis on plates produced by two materials with different thermal expansions

Composite materials used in many areas as structural elements are exposed to thermal effects during production and operation. Especially, these materials are subjected to different types of mechanical or thermal effects during service. Due to these various effects, defects occur in different positions and in different geometries on the materials forming these plates. When thermal or mechanical effects are not taken into account, important stress concentrations can occur around these defects. Therefore, the expected strength in design cannot be ensured during the service life. Although there are lots of works on mechanical loads in literature, studies on thermal stress state around defects occured by temperature distribution are few. In order to be able to safely design of the structures, the thermal stress distributions and the stress concentrations around the defect should be determined. In this study, the thermal stress analysis of the plate made of two materials with different temperature expansions was performed. This plate has a cavity in the direction perpendicular to the plane of the interface. Mechanical properties of the composites are the same except for thermal expansion coefficients. Such an application is seen in pressure vessels of nuclear reactors. These elements are produced by coating the steel body with stainless steel. When DT is the temperature difference, thermal stresses will occur due to the different expansions of the materials. The problem that has been addressed is firstly studied experimentally with the method of photoelasticity. In the experimental study, mechanical modeling method of photo-thermoelasticity was used. For the experimental modeling of the prototype, the analogy of deformation between two different thermoelasticity problems in the literature was used. The first of these problems is the combination of two different materials having different thermal expansions subjected to the same temperature change. The second is about the plate made of a single material which are exposed different temperature change. The first problem is the prototype, the latter is the experimental analysis model. According to this analogy, the differences of thermal strains occurring in these two cases are equalized. The situation of prototype in which two materials with different coefficients of thermal expansion are subjected to the same temperature change was modeled by the case in which the parts are subjected to different temperature changes in a single material. Considering this modeling, the experimental model is made of same two cylindrical plates. The problem of different temperature changes of these plates has been studied in this work. The use of this analogy provides great ease in experimental modeling, because the thermal expansion coefficients, optical sensitivity coefficients and viscoelastic temperature of the materials are the same. By this way, a model was obtained which can be used practically for the method of strain freezing in photoelasticity. The material used in the experimental model is an epoxy-based material Araldite, which is homogeneous, isotropic and optical sensitive material. Linear-elastic behaviour is only considered. The mechanical and optical properties of the material were determined before the model was created. Viscoelastic temperature value, the coefficient of optical sensitivity and modulus of elasticity of the material were obtained by some photoelastic tests. Some of them were also determined by DMA (Dynamic Mechanical Analyzer). The strain, aDT, is formed by the mechanical modeling method and the formed strains are fixed in the plate by the freezing method of photoelasticity. To create the part on which the thermal effect occurs, a cylinder specimen, made from the same material with the model, was used. This specimen was loaded by axial pressure in the furnace, which is suitable for the photoelastic examination. In the furnace, the sample was heated to the viscoelastic temperature by a special regime of heating and an axial compression load was applied at this temperature. Then, the sample was cooled to room temperature with the same regime, and the strains occurring at the viscoelastic temperature were fixed at room temperature. From this specimen, a part whose thickness is 3.9 mm was obtained by a precision cutting in order to create the thermal loaded part of the experimental model. The diameter of the part is the same with the diameter of the part on which the mechanical strains are frozen. These parts were bonded to each other with a special process. Then, a cavity is formed in the model which is perpendicular to the interface of the parts. This cavity was actually identified as one of the types of defect encountered in the industrial applicatoins. In this way, an experimental model having the cylindrical geometry, formed by the combination of two plates, has been obtained. When the model was heated by the special heating regime up to the viscoelastic temperature, the strains on the part, on which the thermal deformations were frozen, were released, but since the unloaded part did not allow this, a new stresses distribution was formed through the model. This obtained stress distribution shows the thermal stress distribution in the prototype. Then, when the model is cooled to room temperature with the same special cooling regime, these deformations are fixed in the model. For the analyses of the thermal stresses, the method of slicing of three-dimensional photoelasticity was used. A slice including the tip of the cavity with a thickness of 1.3 mm was cut out in the diameter direction. The distribution of thermal stresses were obtained in the slice along the free surfaces, on the interface of the parts, along the thickness in the region without the effects of the cavity and edges, around the cavity and along the direction perpendicular to the cavity. For each point, where the stress values were obtained, the number of fringes are measured by a polarizing microscope and the thickness values of the light passes through the slice at these points were determined by the digital micrometer. Since the optical sensitivity coefficient of the material, the number of fringes at the measurement points, and the thickness values of the light passes through the slice were known, the difference values of the principal stresses were calculated for all points by the related formula. These calculated stresses were transformed into dimensionless stresses dividing them by Ee = EaDT and the distributions of dimensionless stresses were plotted. Since one of the principal stress components is zero in the elements adjacent to the upper edge of mentioned slice, an extra slice was cut out along this edge. Stresses found in the previous slice were substituted in the difference values of the stresses taken from the extra slice in order to separate the stresses. A graph of seperated stresses was obtained along this edge. Also, the distribution of the tangential components of the stresses around the cavity was obtained. For the regions where the analytical solution is valid in the model, the stress distribution were obtained using the thermal stress equations in the literature given for the case where the function of temperature change is a function of the coordinate variable in the plate thickness direction. In the analytical solution, the material properties and dimensions of the model created in the experiment were used. The stress distributions obtained by the analytical solution were compared with the distributions obtained in the appropriate direction from the experiment to show the consistency of the experimental data. Numerical analysis was also performed using the finite element method to compare the experimental data in regions where analytical solution is not available. ABAQUS, a finite element package program, was used for this analysis. Variables of the finite element model were firstly determined by mesh refinement applying the solution given in the literature, which has no discontinuity. Then, a finite element model of the experimental model with a cavity was developed. From the obtained results, the stress values in the relevant directions were compared with the results obtained from the analytical solution. The results have good agreement. In the model, the maximum stress concentration factor is calculated at the tip of cavity. In addition, the stress distributions obtained by the finite element analysis were compared with the distributions in the corresponding regions obtained from the experiment. Thus, the results from numerical modeling were verified by those from the analytical solution and experimental model.