PSI - Issue 5

Tomasz Trzepieciński et al. / Procedia Structural Integrity 5 (2017) 562 – 568 Mojtaba Biglar et al./ Structural Integrity Procedia 00 (2017) 000 – 000

6

567

a)

b)

Fig. 3. Average horizontal stress versus average strain for two different types of polycrystalline aggregates..

Fig. 4. Comparison of the influence of element length on the numerical results.

In Fig. 4, the size of the elements in the BEMs are compared. As can be seen in Fig. 4, the different sizes of elements do not have a significant influence on the final results and that is why Lm = 8.52 × 10 -7 was chosen as the length of the elements in all the investigations in the current work.

7. Summary

In this study, an image processing technique was applied by developing a complicated numerical algorithm for analysing SEM images of obtained BaTiO 3 pellets and preparing a suitable model for BEM. Due to the low ratio of grain boundaries to grain size the grain boundaries were not considered as a separate part, which means that the study of the behaviour of grain boundaries can be ignored. It is clear from Fig. 2b that the gap between grains has its own boundaries. So, the distances between grains must be eliminated and the grains must have the same boundaries along the lines at which they make contact with one another. To achieve this goal, another numerical algorithm was designed. The developed method and generated numerical codes incorporating BEM have sufficient accuracy and can be generalized for more complicated investigations such as crack initiation and propagation. Acknowledgements This work was supported by the People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme FP7/2007-2013, grant number PITN-GA-2013-606878. Benedetti, I., Aliabadi, M.H. 2013a. A Three-dimensional Cohesive-frictional Grain-boundary Micromechanical Model for Intergranular Degradation and Failure in Polycrystalline Materials. Computer Methods in Applied Mechanics and Engineering 265, 36 – 62. Benedetti, I., Aliabadi, M.H., 2013b. A Three-dimensional Grain Boundary Formulation for Microstructural Modeling of Polycrystalline Materials. Computational Materials Science 67, 249 – 260. Benedetti, I., Aliabadi, M.H., 2015. Multiscale Modeling of Polycrystalline Materials: A Boundary Element Approach to Material Degradation and Fracture. Computer Methods in Applied Mechanics and Engineering 289, 429 – 453. Cruse, T.A., 1973. Application of the Boundary-integral Equation Method to Three Dimensional Stress Analysis. Computers & Structures 3, 509 – 527. Garcia-Sanchez, F., Sáez, A., Dominguez, J., 2005. Anisotropic and Piezoelectric Materials Fracture Analysis by BEM. Computers & Structues 83, 804 – 820. Groh, U., Kuna, M., (2005). Efficient Boundary Element Analysis of Cracks in 2D Piezoelectric Structures. International Journal of Solids and Structures 42, 2399 – 2416. Jafari, M., Saeed, Z.R., Nima, N., 2013. Modeling of the Plastic Deformation of Polycrystalline Materials in Micro and Nano Level Using Finite Element Method. Journal of Nano Research 22, 41 – 60. Liew, K.M., Sun, Y., Kitipornchai, S., 2007. Boundary Element ‐ free Method for Fracture Analysis of 2D Anisotropic Piezoelectric References