Propagation of plasticity bands from the tip of a semiinfinite crack of mixed type

Savruk, M. P.; Rytsar, R. B.

doi:10.1007/bf02355558

Cited by 2 publications

(1 citation statement)

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“…3c). For small loads [F/((~yRt)< 0.3], the procedure of numerical calculations is unstable and, as asymptotic solutions, we use the corresponding results obtained for the case of a semiinfinite crack [ 15].…”

Section: Plane Deformationmentioning

confidence: 99%

Tension of an elastoplastic disk. Part 1. Central crack

Panasyuk¹,

Savruk²,

Ivanyts'ka³

et al. 1999

Mater Sci

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539.375 Within the framework of the model of plasticity bands, we consider an elastoplastic problem of fracture mechanics of the development of plasticity bands near the tips of a central crack in a disk. We assume that, in the plane stressed state, plastic strains in the vicinity of the crack tip are localized along three plasticity bands (L I , L 2 , and L~ ) one of which is located on the continuation of the crack and the other two make nonzero angles with the direction of the crack and that, under the conditions of plane deformation, plastic strains are localized along two plasticity bands (L I and ~ ). The band (~) is modeled by a line of discontinuity of normal and tangential displacements and the bands (L l and L 2) are modeled by lines of discontinuity of tangential displacements. The lengths and orientations of these lines are determined in the process of numerical solution of the problem by the method of singular integral equations. The values of the crack tip opening displacement are also determined.Disk specimens with notches or cracks are used in the investigation of the processes of initiation and development of cracks under static and cyclic loading [1][2][3][4]. The level of local strains near a concentrator characterized by the jump of normal displacements (opening displacement) at its tip 6 can be regarded as a parameter that controls these processes in elastoplastic materials. To find this parameter, it is necessary to solve the problem of determination of the strain-stress state of the disk taking into account elastoplastic strains near the tip of the concentrator. For this purpose, we use the model of plasticity bands (see, e.g., [5-1 1]) according to which the plasticity zone is localized along narrow bands lying on the continuations of the crack. As follows from the experimental data presented in [5][6][7], this model reflects the actual process of deformation in the first stage of the development of plastic strains in thin plates. However, in many cases (in particular, in disks with central cracks [6]), under loads of certain types, we observe the appearance of new bands inclined to the line of continuation of the crack. Neglecting these inclined bands, we get underestimated values of the displacement ~ [12].In the present work, within the framework of the model of plasticity bands, we solve the problem of elastoplastic equilibrium of a disk with central crack and study the influence of inclined plasticity bands on the crack tip opening displacement. Plane Stressed StateA thin disk of radius R containing a central crack L 1 of length 2/1 is related to a Cartesian coordinates xOy. The disk is subjected to tension by two concentrated forces F applied at points Zo = + ih (Fig. 1). The material of the disk is perfectly elastoplastic.In the disk subjected to tension, near the crack tips, we first observe the appearance of plastic bands directed along the continuation of the crack. Further, as the load increases, we observe the appearance of two additional bands at each tip making nonzero an...

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Section: Plane Deformationmentioning

confidence: 99%