Linear model of a plastic zone in the vicinity of a sharp notch under the conditions of longitudinal shear

Kryven, V. A.

doi:10.1007/s11003-005-0064-3

Cited by 7 publications

(2 citation statements)

References 4 publications

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“…Under low loads, for the investigation of plastic zones (in particular, strips) near pointed stress concentrators, one can use the linear model of plastic zone (LMPZ) [6] based on the use of the elastic solution. For its application, it is also necessary to have two corresponding auxiliary solutions of the problems that do not contain the parameters with dimension of length in the elastic and elastoplastic statements.…”

Section: Initial Stage Of the Development Of Plastic Stripsmentioning

confidence: 99%

Development of Plastic Strips in the Process of Shear Deformation of a Body with Narrow Rectangular Slot

2015

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We obtain analytic solutions of the antiplane problems for a body with semiinfinite rectangular slot in the elastic and elastoplastic (single-strip model of the zone) statements. The load is given in the form of the asymptotics of stresses at infinity equal to the asymptotics of a semiinfinite crack of longitudinal shear expressed via the stress intensity factor. It is established that the development of plastic strips starts in the direction of continuation of the bisectors of the notch angles. Their lengths of the plastic strips are found as functions of the stress intensity factor.To decrease the hazard of sudden fracture and provide the reliable operation of mechanical structures under high loads, it is customary to use materials characterized by the presence of plastic deformations. Hence, it is of interest to investigate the elastoplastic stress-strain state (SSS) of bodies and structural elements. At present, the main efforts of the researchers in the field of fracture mechanics are focused on the analysis of the SSS of bodies weakened by cracks, which are, as a rule, modeled by mathematical cuts. It is assumed that, prior to loading, the distance between the crack faces is equal to zero and the faces do not interact. The crack tip is regarded as a cuspidal point. An important continuation of these investigations is connected with the study of the distributions of elastoplastic strains near rectangular slots, which turn into a classical crack in the case of infinitesimally small width [1,2].In the present work, we study the development of plastic strips from the vertices of a narrow rectangular slot under the influence of shear loads applied at a great distance from its end faces. To analyze the SSS near the vertices of the slot, we assume that it is semiinfinite. The problem of development of continual plastic zones from the vertex of a semiinfinite rectangular notch was solved in [2]. In the cited work, the authors determined in particular, the shape of the plastic zones. Moreover, it was shown that, in the initial stage, the length of the zone is maximal on the continuation of the bisector of the notch angle, and its direction gradually approaches the axis of the notch as the load increases.We determine the direction of propagation of a single plastic strip from the vertices of a semiinfinite slotin an infinite body and investigate its development under quasistatically increasing shear loads (Fig. 1). The material of the body is assumed to be perfectly elastoplastic with yield limit in shear k .

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Section: Initial Stage Of the Development Of Plastic Stripsmentioning

confidence: 99%

Development of Plastic Strips in the Process of Shear Deformation of a Body with Narrow Rectangular Slot

2015

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“…The medium deforms under the action of a quasistatically monotonically increasing shear load τ xz = 0 , τ yz = τ ∞ , which acts at infinity in parallel to the faces of the prism that are free from stresses. We assume that the applied load is fairly small and use the linear model of a plastic zone (LMPZ) for an analysis of development of plastic strains [5].…”

Section: Initial Stage Of Plastic Exfoliation Of a Rectangular Inclusmentioning

confidence: 99%

Initial stage of plastic exfoliation of a rectangular inclusion under conditions of one-sided contact with a medium

Kryven

Valyashek

2012

J Math Sci

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We investigate the initial stage of quasistatic development of plastic deformations in the vicinity of the tips of a rigid rectangular inclusion whose pair of faces do not contact with a medium. Deformation is caused by shear forces that act at infinity in parallel with this pair of faces of the inclusion. The cases of plastic deformations localized in bands that develop from the tips of the inclusion and distributed continually are investigated. The characteristics of plastic zones for loads much smaller than the yield strength are obtained.The investigation of the stress-strain state in the vicinity of inclusions of finite sizes is necessary to study the deformation behavior of structural elements. It is important for fracture mechanics as a complement to the theory of thin inclusions [1,7,8] and mechanics of composite materials [9]. It is also necessary to take into account the almost unavoidable presence of imperfections of the contact of an inclusion with a medium as a result of an operation or a manufacturing process. Moreover, in contrast to a body with notches, in a body with inclusions, stress concentration is caused by not only corner points, but also points at which the contact with the medium undergoes qualitative changes. In investigating the stress-strain state of a body with an inclusion, one must foresee changes in its contact with the medium in the process of loading and, first of all, the emergence and development of plastic exfoliation on the interface.The problems of investigating the stress-strain state of a body with an inclusion that admit its plastic exfoliation remain inadequately studied [6].Let us investigate plastic exfoliation under conditions of antiplane deformation of a rigid rectangular inclusion − a ≤ x ≤ a , − b ≤ y ≤ b , − ∞ ≤ z ≤ + ∞ in an infinite ideally elastoplastic medium. Consider the case of incomplete mechanical contact of the medium and inclusion. Let the vertical faces x = ± a , − b ≤ y ≤ b , − ∞ ≤ z ≤ + ∞ of the inclusion be in ideal contact with the medium before loading, and assume that the horizontal faces − a ≤ x ≤ a , y = ±b , − ∞ ≤ z ≤ + ∞ do not contact at all. The medium deforms under the action of a quasistatically monotonically increasing shear load τ xz = 0 , τ yz = τ ∞ , which acts at infinity in parallel to the faces of the prism that are free from stresses. We assume that the applied load is fairly small and use the linear model of a plastic zone (LMPZ) for an analysis of development of plastic strains [5].Let us consider two possible schemes of development of plastic strains: namely, a scheme for strains localized in bands that emanate from the inclusion and a continual scheme with a continuous distribution in the vicinity of the tips of the inclusion.The thin-band scheme of development of plastic strains corresponds to the assumptions on the number of bands and their mutual location [4]. We assume that two plastic bands develop from each vertex. These are a vertical band of length d 1 , which leads to the slip of the medium over the surface of the in...

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Antiplane Deformation of Elastic Bodies with Notches and Cracks

Savruk

Kazberuk

2016

Stress Concentration at Notches

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Linear model of a plastic zone in the vicinity of a sharp notch under the conditions of longitudinal shear

Cited by 7 publications

References 4 publications

Development of Plastic Strips in the Process of Shear Deformation of a Body with Narrow Rectangular Slot

Development of Plastic Strips in the Process of Shear Deformation of a Body with Narrow Rectangular Slot

Initial stage of plastic exfoliation of a rectangular inclusion under conditions of one-sided contact with a medium

Antiplane Deformation of Elastic Bodies with Notches and Cracks

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