PSI - Issue 43

Dragan Pustaić et al. / Procedia Structural Integrity 43 (2023) 252 – 257 Author name / Structural Integrity Procedia 00 (2022) 000 – 000 Mathematica was used for its determining. From the non-singularity stress condition (1), at the point ( ) p ,0 , a r + the exact analytical solution for the plastic zone magnitude, p , r was found and it was written in an inverse form (7). 257 6

Fig. 4. Dependence of plastic zone magnitude, p r a , around the crack tip on monotonously increasing external loading of the crack, F , for the different values of strain hardening exponent, n.

(

)

0 , F a   according to the expression (7), is presented through the

The non-dimensional loading of the crack,

variable, P , and the strain hardening exponent, n . By using the software Mathematica , the family of curves is calculated and presented in Fig. 2. By applying the algorithm, described at section 4, for n = 2, the explicit drawing is obtained, ( ) p 1 , r f F = in a non-dimensional form, as it is presented in Fig. 4. Generally, it could be say, the methodology described in these article is applicable for the stress analysis and the fracture mechanics parameters determination in the thin plates with incorporated crack in which the plane state of stress is occurred and for different boundary conditions. The few such problems the authors Pustaić, D. , and Lovrenić Jugović , M., solved and published earlier, (2018, 2019). The next problem which we are going to solve is in-plane loading of a crack with uniformly distributed continuous loads across the crack surface. References Chen, X. G., Wu, X. R., Yan, M. G., 1992. Dugdale Model for Strain Hardening Materials. Engineering Fracture Mechanics 41 (6), 843 - 871. Guo, W., 1993. Elastoplastic Three Dimensional Crack Border Field - I. Singular structure of the field, Eng ineer. Fracture Mechanics 46 (1), 93 - 104. Guo, W., 1995. Elasto -Plastic Three- Dimensional Crack Border Field - III. Fracture Parameters. Engineering Fracture Mechanics 51 (1), 51 - 71. Hoffman, M., Seeger, T., 1985. Dugdale Solutions for Strain Hardening Materials. The Crack Tip Opening Displacement in Elasti c- Plastic Fracture Mechanics. In: Proceedings of the Workshop on the CTOD Methodology. Geesthacht, 57 - 77. Neimitz, A., 2000. Dugdale Model Modification due to the Geometry Induced Plastic Constraints. Engineering Fracture Mechanics 67, 251 - 261. Neimitz, A., 2004. Modification of Dugdale Model to Include the Work Hardening and in - and out-of- Plane Constraints. Engineering Fracture Mechanics 71 (11), 1585 - 1600. Neimitz, A., Graba, M., 2008. Analytical - Numerical Hybrid Method to Determine the Stress Field in Front of the Crack in 3D E lastic-Plastic Structural Element. In: Proceedings of the 17 th European Conference of Fracture (ECF 17), Brno, Czech Republic, 514 - 521. Pustaić, D., Lovrenić - Jugović, M., 2019. Mathematical Approach of Crack Tip Plasticity, In: Abstract Booklet of the 9 th International Conference on Materials Structure & Micromechanics of Fracture (MSMF9), p . 162 and poster presentation, Šandera , P., ed., Brno, Czech Republic. Pustaić, D., Lovrenić - Jugović, M., 2019. More accurate Mathematical Description in the Assessment of Plastic Zone Magnitude around the Crack Tip. Procedia Structural Integrity 23, 27 - 32. Pustaić, D., Lovrenić - Jugović, M., 2018. Mathematical Modeling of Cohesive Zone in the Ductile Metallic Materials. In: Proceedings of the 9 th International Congress of Croatian Society of Mechanics. Marović, P. et al. (Eds.). Croatian Society of Mechanics. USB, Split, Croatia. Pustaić, D., Lovrenić, M., 2006. Analytical and Numerical Investigation of Crack Opening in Strain - Hardening Material. In: Proceedings of the 5 th International Congress of Croatian Society of Mechanics. Matejiček, F. et al. (Eds.). Croatian Society of Mechanics. CD - ROM. Trogir, Croatia. Pustaić, D., 1990. Contribution to the Stress Analysis in the thin Plates in a non - linear Range. PhD Thesis, University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture. Zagreb, Croatia. Wolfram Mathematica, Version 7.0, 2017. Wolfram Research Inc., Champaign II, http://www.wolfram.com/products/mathematica/