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About Unambiguity and Reliability of the Solution for Plastic Zone Magnitude around Crack Tip in Isotropic Strain Hardening Material

In this article, a review on the results of research of dependence of plastic zone magnitude around crack tip rp on strain – hardening exponent n is being carried out. For determining a plastic zone magnitude rp are used the analytical methods and the Dugdale´s model as well. Isotropic and non – linear strain – hardening of a material is assumed. The strain – hardening exponent n is changed among the discreet values n = 3, 5, 7, 10, 25 and ∞ . The authors X. G. Chen, X. R. Wu and M. G. Yan wrote about the same problem, but introducing an assumption about small plastic zone magnitude around crack tip (SSY assumption) and the results have been published in their paper [1]. The cohesive stresses within a plastic zone in isotropic strain – hardening material aren´t more constant but variable. They are changed in accordance with non – linear law. The stress intensity factor (SIF) of the cohesive stresses is determined by means of Green´s functions method. In our investigations we have fully exactly determined SIF by means of commercial software „ Mathematica“ , not introducing an assumption about small plastic zone as the above mentioned authors, had done in their paper [1]. An analytical solution is being given by means of gamma – function Г (x) and hypergeometric function . Afterwards, a hypergeometric function is expanded into a power. In further analysis we can take only first member, or first two members, or maybe three and more members of the series. How does it influence on an accuracy and reliability of a solution for plastic zone magnitude rp? It depends on how many members of series we include into calculation. We will get an algebraic equation of first, third, fifth, seventh, etc. degree for determining a magnitude rp. The roots of those equations we have determined also by using the commercial package „ Mathematica“ . The question is – are those solutions unambiguous ? This is a subject of our research and our intention is to present and publish the results exactly at this Conference.

Cohesive stress; Commerciale software Mathematica; Dugdale model; Elastic-Plastic Fracture Mechanics; HRR stress and strain field; Isotropic and non-linear strain hardening of material; Plastic zone magnitude around crack tip; Strain hardening exponent; Stress intensity factor (SIF)

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