Determine the stress intensity factor in a plate with a center crack under thermal and mechanical loading using isogeometric method based on the Bezier extraction operator

Subject Areas : Journal of New Applied and Computational Findings in Mechanical Systems

Mohammad Mehdi  Shoheib ¹ (Advanced computing Research Center, Department of Mechanical Engineering, Ahvaz Branch, Islamic Azad University, Ahvaz, , Iran.)
Peyman  Yousefi ² (Department of Mechanical Engineering, Islamic Azad University, Arak Branch, Arak, Iran)

Received: 2023-04-05 Accepted : 2023-05-30 Published : 2023-05-22

Keywords: Crack, Bernstein polynomial, Stress intensity factor, Extended IGA method, Bezier extraction operator,

Abstract :

     In this research, an analysis of the stress and stress intensity factor in a cracked plate under thermal and mechanical loading is done. For this purpose, using MATLAB coding, a plate with a center crack was modeled by the isogeometric method (IGA) based on the Bezier extraction operator. In this method, NURBS basis functions are generated as a linear combination of Bernstein polynomials using the Bezier extraction operator. Using this operator Bezier elements with Co continuity (similar to elements of the finite element method) were produced and Bernstein polynomials are defined on these elements. In order to model the crack, the extended isogeometric method (XIGA) was used. In this method, the control points that exist along the crack and at the tip of the crack are identified and extracted using the proper level set functions. Therefore, there is no need to re-meshing or modify the elements. By enriching the extracted control points with appropriate enrichment functions and applying boundary conditions, the analysis process was carried out and the strains and stresses were calculated. Finally, the value of the first mode stress intensity factor was obtained based on the interaction integral method. To check the accuracy of the obtained results, a similar analysis was performed using the finite element method and the results obtained from both methods were compared. These studies showed that the considered isogeometric method provides more accurate solutions with a much smaller number of elements and computational costs.

References:

[1] Dowling, N. E., (2012), Mechanical behavior of materials: engineering methods for deformation, fracture, and fatigue: Pearson.

[2]  Newman Jr, J. C., Raju, I. S., (1981), Stress-intensity factor equations for cracks in three-dimensional finite bodies. In ASTM Natl. Symp. on Fracture Mech., (No. NASA-TM-83200).

[3]  Shahani, A. R., Habibi, S. E. (2007), Stress intensity factors in a hollow cylinder containing a circumferential semi-elliptical crack subjected to combined loading, International journal of Fatigue, 29(1), pp.128-140.‏

[4]  Hughes, T. J., Cottrell, J. A., Bazilevs, Y., (2005), Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Computer methods in applied mechanics and engineering, 194(39), 4135-95.

[5]  Gong, Y. P., Dong, C. Y., Qin, X., (2017), An isogeometric boundary element method for 3D potential problems, Journal of Computational and Applied Mathematics, 313, pp.454-468.‏

[6]  Hao, P., Yuan, X., Liu, H., Wang, B., Liu, C., Yang, D., Zhan, S., (2017), Isogeometric buckling analysis of composite variable-stiffness panels, Composite Structures, 165, pp.192-208.

[7]  Huang, J., Nguyen-Thanh, N., Zhou, K., (2017), Extended isogeometric analysis based on Bézier extraction for the buckling analysis of Mindlin–Reissner plates, Acta Mechanica, 228, pp.3077-3093.‏

[8]  de Borst, R.,  Chen, L., (2018), The role of Bézier extraction in adaptive isogeometric analysis: Local refinement and hierarchical refinement, International journal for numerical methods in engineering, 113(6), pp. 999-1019.

 [9] Do, H. V., Nguyen-Xuan, H., (2017), Limit and shakedown isogeometric analysis of structures based on Bézier extraction, European Journal of Mechanics-A/Solids, 63, pp.149-164.‏

[10]  Moure, M. M., García-Castillo, S. K., Sánchez-Sáez, S., Barbero, E., Barbero, E. J. (2018), Matrix cracking evolution in open-hole laminates subjected to thermo-mechanical loads, Composite Structures, 183, pp. 510-520.‏

[11]  Narasimhachary, S. B., Bhachu, K. S., Shinde, S. R., Gravett, P. W., Newman Jr, J. C. (2018), A single edge notch specimen for fatigue, creep-fatigue and thermo-mechanical fatigue crack growth testing, Engineering Fracture Mechanics, 199, pp. 760-772.‏

[12]  Shoheib, M. M., Shahrooi, S., Shishehsaz, M., Hamzehei, M., (2022), Fatigue crack propagation of welded steel pipeline under cyclic internal pressure by Bézier extraction based XIGA, Journal of Pipeline Systems Engineering and Practice, 13(2), 04022001.

[13] McClaflin, D., Fatemi, A., (2004), Torsional deformation and fatigue of hardened steel including mean stress and stress gradient effects, International Journal of Fatigue, 26(7), pp. 773-784.‏

 [14] Sutradhar, A., Paulino, G. H., (2004), Symmetric Galerkin boundary element computation of T-stress and stress intensity factors for mixed-mode cracks by the interaction integral method, Engineering Analysis with Boundary Elements, 28(11), pp. 1335-1350.

‏ [15] Moës, N., Dolbow, J., Belytschko, T., (1999), A finite element method for crack growth without remeshing, International journal for numerical methods in engineering, 46(1), pp.131-150.

[16] Shoheib, M. M., Shahrooi, S., Shishehsaz, M., Hamzehei, M., (2022), Bézier base extended isogeometric numerical method for thermo elastic-plastic analysis of crack propagation in cracked plate under welding residual stress and thermal load, Mathematical Modelling and Analysis, 27(4), pp. 629-651.