PSI - Issue 14

Dipankar Bora et al. / Procedia Structural Integrity 14 (2019) 537–543 Author name / Structural Integrity Procedia 00 (2018) 000–000

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engineering materials are ductile in nature. Ductile fracture occurs by three basic stages, namely void nucleation, void growth and finally void coalescence which leads to fracture. Nomenclature yield stress initial yield stress K hardening co-efficient n hardening exponent �� equivalent stress equivalent plastic strain  Lode angle F  Lode angle constant f  Lode angle function i D damage constant (i = 1, 2, 3, 4, 5) m temperature factor exponent C strain rate coefficient 1.1. Effect of Lode angle on ductile fracture It is found that Lode angle has an effect on the ductile fracture process. Therefore, Lode dependency must be included to describe the fracture process. The Lode angle effect has been used to account for internal shear localization of plastic strain ligaments between voids (Moxnes and Froyland (2016)). Barsoum et al. (2011) found that the Lode angle effect on the failure is prominent for high strength and low strain hardening material than the medium and high hardening material. Mirone et al. (2016) developed a new yield criteria based on the metals showing different hardening function under differently evolved Lode functions. They also backed their model with experimental results. Lode angle is the azimuth angle in the deviatoric plane, subtended by projection of any stress state with projection of principal stress axis on the deviatoric plane. Mathematically, it can be expressed as (Echávarri (2012)) Here,  is the Lode angle, J 3 is the third invariant of deviatoric stress and σ eq is the equivalent stress. Xue (2007) developed a Lode angle dependent function to incorporate Lode angle effect on ductile fracture given by 6 | | (1 ) f F F                     (2) Here µ f is the Lode angle function and � is the material constant. 1.2. Ductile fracture on thin walled cylindrical tubes There are various studies that has been carried out to study the response of thin-walled tubes subjected to dynamic compressive axial loading (Jones (1998)). If the impact velocity is not sufficiently large for the tube to fracture, the tube fails by bucking also referred to as the axial crushing . The problem of buckling of thin-walled   eq  1 3 3 1 3 27 sin 2 J             (1)