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Badania elastooptyczne oraz analiza odkształceń i naprężeń kompozytów warstwowych

Jaroniek M.

Zeszyty Naukowe. Rozprawy Naukowe / Politechnika Łódzka

2007

Z. 357

3-156

In the present paper the elastic and plastic defonnation in multi-layered composites of finite thickness has been analysed. Advanced mechanical and structural applications require accurate assessment of the damage state of materials during the fabrications as well as during the service. Due to the complex nature of the internl structure of the material, composites (including the layered composite) often fail in a variety of modes. The failure modes very often are influenced by the local material properties that may develop in time under heat and pressure, local defect distribution, process inducing residual stress, and other factors. Consider a laminate composite in pIane stress conditions, multi-layered beam bonded to planes having shear modulus Gi and Poisson's ratio VI respectively, subjected to bending. The behaviour of the cracks depends on the cracks configuration, size, orientation, material properties, and loading characteristic. The fracture mechanics problem will be attacked using the photoelastic visualisation of the fracture events in a model structure. The proposed analytical and experimental method will be developed for a layered composite fracture problem. Fabrication of the model of the TBC with FGM can be obtained by layered mixing of two photoelastic materials of different thenno-mechanical properties with different volume ratios gradually changed fonn layer to layer such that first layer has only a few particles of the other phase and last has maximum volume ratio of this other phase. The specimen can be built as layered beam, for example, glass layer at the bottom next particles of the same glass in the epoxy in several layers of various volume ratio of the glass in epoxy and pure epoxy at the top. The beam can be loaded in 4 point bending to generate cracks propagate through the FGM layer. Photoelastic examination of each state may be obtained for various crack configuration due to applied mechanical load (and if epoxy thermal expansion coefficient is different than the glass thermal expansion coefficient also thermal load should be applied). The development of the failure criterion for a particular application is also very important for the predictions of the crack path and critical loads. Recently, there has been a successful attempt to formulate problems of multiple cracks without any limitation. This attempt was concluded with the series of papers summarising the undertaken research for isotropic and non-homogeneous class of problems. In the present paper the elastic and plastic defonnation has been analysed using the Muskhelishvili' s complex potentials method. The elastostatic stress field is required to satisfy the well-known equilibrium equations using two analytic functions ψ(z) and χ(z). The distribution of stresses and displacements has been calculated using the finite element method (FEM). Finite element calculations were perfonned in order to verify the experimentally observed the isochromatic distribution during cracks propagation. The geometry and materials of models were chosen to correspond to the actual specimens used in the experiments. The numerical calculations were carried out using the finite element program ANSYS 6.1, 9, by applying the substructure technique. Two different methods were used: solid modeling and direct generation. For comparison the numerical and experimental isochromatic fringes distribution was shown in this paper. It is possible to fabricate a model using various photoelastic materials to model multi layered structure. Photoelasticity has shown to be promising in stress analysis of bearns with various number and orientation of cracks. Finite element calculations (FEM) were performed in order to verify the experimentally observed branching phenomenon and the isochromatic distribution observed during cracks propagation. The agreement between the finite element method predicted isochromatics-fringe pattems distribution and those determined photoelasticaly was found to be within 3ফ percent. Crack propagation in multi-layered composites of finite thickness is especially challenging and open field for investigation. The development of the failure criterion for a particular application is also very important for the predictions of the crack path and critical loads. Recently, there has been a successful attempt to formulate problems of multiple cracks without any limitation. This attempt was concluded with the series of papers surnmarising the undertaken research for isotropic and non-homogeneous class of problems. Crack propagation in multi-layered composites of finite thickness is especially challenging and open field for investigation.