Thermo-elastic stress of a metal-matrix composite disc under linearly-increasing temperature loading by analytical and FEM analysis

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Abstract

In this study, the elastic stress analysis of a composite disc with aluminium matrix subjected to a linearly-increasing temperature distribution has been carried out. The values of tangential and radial stress components that have occurred under the effect of the temperature from the inner surface of the disc towards the outer surface have been obtained by two different methods, numerical and analytical. In the analytical analysis, a computer program has been developed to get the values of thermal stresses. But in the numerical study carried out with the finite-element method, Abaqus 6.8 package program has been used. As a result of these analyses, it has been observed that the stress values obtained from both methods support each other. It has been determined under this temperature distribution that tangential stress components are always on the condition of compression in the inner surface of the disc and of tensile in the outer surface. It has also been found out that radial stress components are always in the state of tensile along the whole profile of the disc. Finally, the stress analysis of the same composite disc subjected to this temperature distribution, but with a reduced mass, has also been examined numerically.

Introduction

In recent times, composite materials which are lighter and have higher specific strength than other materials have a wide field of use, especially in the aviation industry and in the automotive industry. Because of that, load-carrying capacities of the reinforced discs are higher than those of the isotropic steel discs with the same geometry. The discs with hole have been the subject of many scientific studies under different conditions.

Sayman [1] used an analytical method to investigate thermo-elastic stress analysis on an orthotropic composite disc with aluminium metal-matrix reinforced towards x and y direction. Singh and Ray [2] determined the creep on an orthotropic aluminium silicon carbide composite rotating disc according to the Tsai–Hill yield criterion. The results obtained from this study were compared with the ones from the Von Mises yield criterion used for isotropic composites. Stanley and Garroch [3] developed a new test method for the composite discs reinforced by moulded fiber and obtained thermo-elastic data from fiber-reinforced orthotropic disc in this study to find out the values of the orientation tensor. Karakuzu and Sayman [4] used the finite-element method and made an elasto-plastic stress analysis in the orthotropic rotating discs with holes. Bektaş et al. [5] realized the elastic–plastic stress analysis on a composite disc with an aluminium metal-matrix under internal pressure loads. Altan et al. [6] carried out an elastic–plastic thermal stress analysis of an orthotropic composite disc with a hole by using an analytical solution. The thermal load distribution was chosen as parabolically. Çallıoğlu et al. [7] studied stress analysis analytically on a circular orthotropic rotating disc under mechanical and thermal load. They obtained the solutions under parabolic temperatures along a radial section from the inner surface of the disc to the outer surface. Güven and Altay [8] studied thermal stresses in a linear hardening solid disc under a uniform heat source. Jain et al. [9] designed a constant thickness composite disc of uniform strength by tailoring the anisotropic elastic constants. Sen and Aldas [10] obtained thermal stresses in a thermoplastic composite disc unidirectionally reinforced by steel fibers. They used finite-element method to calculate the thermal stress distributions within the composite disc. Sen [11] investigated the effect on thermal and residual stresses of parabolic temperature loading in a thermoplastic composite disc.

In this study, the elastic stress analysis of the hollow composite disc under the linearly-increasing distribution of temperature has been carried out analytically with the help of a computer program [12]. At the same time, finite-element method with the Abaqus 6.8 program has been used to calculate the magnitude of thermal stresses.

Section snippets

Thermal elastic stress solution

As steel fiber-reinforced orthotropic aluminium composite disc is thin, the case of plane stress is valid. In this case, strain–stress correlation that takes place on an orthotropic composite disc under the influence of temperature can be written as follows:εr=dudr=arrσr+arθσθ+αrTεθ=ur=arθσr+aθθσθ+αθT

Here αr and αθ are thermal expansion coefficients in radial and tangential directions. T represents the magnitude of the temperature distribution. Constants of the arr, a and aθθ elasticity

Composite disc and mechanical properties

The composite disc has been manufactured at the Mechanical Laboratory of the Faculty of Engineering, Pamukkale University [12]. Aluminium matrix has been reinforced by the steel fibers of a circular form.

Composite disc manufacture has been carried out under pressure by means of a hydraulic press. The moulds have been heated up to 550 °C with the use of electrical resistances in the course of manufacture and 30 MPa pressure has been applied with the press on them for 10 min. Under these conditions,

Results and discussion

In the stress analysis that has been done, the elastic thermal stress analysis of a composite disc has been carried out under the linearly-increasing temperature distribution. To determine the accuracy of the stress analysis carried out, analytic and numerical solution methods have been used and compared with each other. Disc dimensions have been taken as a = 15 mm and b = 75 mm in the analysis. During the analysis, the thermal stresses at 0 °C have been taken as zero. At the same time, it has been

Conclusions

The following points are obtained from the analytical and numerical thermal elastic stress analysis of a composite disc with aluminium metal-matrix under the load of linearly-increasing temperature.

  • It has been observed that the results obtained from these two solution methods are very close. Therefore, both of these solution methods have been found to support each other.

  • As orthotropic composite discs have different thermal expansions, tangential and radial stress components occur.

  • The magnitudes

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