Issue 30

Yu.G. Matvienko, Frattura ed Integrità Strutturale, 30 (2014) 311-316; DOI: 10.3221/IGF-ESIS.30.38 311 Focussed on: Fracture and Structural Integrity related Issues The effect of thickness on out-of-plane constraint in terms of the T-stress Yu.G. Matvienko Mechanical Engineering Research Institute of the Russian Academy of Sciences, Moscow, Russia ygmatvienko@gmail.com A BSTRACT . The plastic zone is theoretically and numerically analyzed for various combinations of the non- singular terms xx T to zz T ratios in connection with specimen thickness under mode I loading. The plastic zone size distribution is based on the Mises yield criterion for mode I conditions and mapped in the specimen thickness direction. It is shown that the plastic zone size is affected by the zz T -stress, i.e. there is strong effect of out-of-plane constraint (thickness) on crack tip plastic zones. In addition, to study the effect of thickness and loading mode mixity (mode I and II) of the specimen on the singular ( K I , K II ) and the non-singular ( xx T , zz T ) terms along the 3D crack front, three-dimensional stress fields are analyzed by means of finite element analysis. The strong effect of thickness and mixed mode loading conditions on the zz T -stress is observed. At the same time, there is not the effect of thickness on the non- singular xx T -stress at the same loading conditions. K EYWORDS . Non-singular T-Stresses; Thickness; Mixed Mode; In-plane and out-of-plane constraint; plastic zone; I NTRODUCTION he results of analytical and numerical calculations show that stress fields in the vicinity of the crack tip, in many cases, are strongly dependent on constraint. The source of a change of out-of-plane constraint is thickness. In contrast to out-of-plane constraint, the different sources of a change in in-plane constraint at the crack tip are associated with crack size, geometry of specimens and type of loading. To describe in-plane and out-of-plane constraint effects in fracture analysis, the following parameters can be used, namely, z T -parameter [1], local triaxiality parameter [2] and nonsingular components of the T-stresses ( xx T and zz T ) [3]. Not emphasize attention on merits and demerits of the above-mentioned parameters of constraint at the crack tip, this paper is concentrated on the nonsingular components of the T -stresses in the vicinity of the crack tip. It is well-known that the sign and value of the xx T -stresses considerably effect on the shape and size of the plastic zone at the crack tip. At the same time, there is no information about influence of thickness on the zz T component as well as the size of the plastic zone in literature. Moreover, an analysis of joint influence of the nonsingular T-stress ( zz T and xx T ) terms on the fracture mechanics parameters is not carried out yet. T

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