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Stresses Near a Disk-Shaped Sharp Slot with Tangential Contact Interaction Between Its Surfaces.

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Title: Stresses Near a Disk-Shaped Sharp Slot with Tangential Contact Interaction Between Its Surfaces.
Authors: Halazyuk, V.A.1, Sulym, H.T.1
Source: Materials Science. May2005, Vol. 41 Issue 3, p360-375. 16p.
Subjects: Strains & stresses (Mechanics), Contact transformations, Equilibrium, Surfaces (Technology), Pressure, Mechanics (Physics)
Abstract: We propose a new statement of the problem of elastic equilibrium of a disk-shaped slot whose surfaces are loaded by an arbitrary normal load vanishing on its front according to a certain law. By the method of discontinuous Weber-Schafheitlin integrals, it is shown that, in this case, there exists a unique state of elastic equilibrium with regular distribution of stresses over the front of the slot. According to the concept of boundary layer, the jump of tangential stresses formed on the surfaces of the slot due to the continuity of the components of the vector of local rigid rotation Ω on its front is continued in the plane of the slot and guarantees the validity of the equilibrium conditions provided that the normal stresses are equal to zero (the effect of boundary layer). The numerical analysis shows that the jump of tangential stresses in the boundary layer outside the slot rapidly decreases with the distance from the front in complete agreement with the Saint-Venant principle. If a jump of tangential stresses on the surfaces of the slot is absent (and exists outside the slot), then these surfaces have a kink in the front of the slot and the volume strains possess a logarithmic singularity. This situation can be regarded as the limiting state corresponding to the onset of plastic deformation or brittle fracture. If the tangential stresses do not have jump in the entire plane of the slot, then the solution of the problem does not exist. [ABSTRACT FROM AUTHOR]
Copyright of Materials Science is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: We propose a new statement of the problem of elastic equilibrium of a disk-shaped slot whose surfaces are loaded by an arbitrary normal load vanishing on its front according to a certain law. By the method of discontinuous Weber-Schafheitlin integrals, it is shown that, in this case, there exists a unique state of elastic equilibrium with regular distribution of stresses over the front of the slot. According to the concept of boundary layer, the jump of tangential stresses formed on the surfaces of the slot due to the continuity of the components of the vector of local rigid rotation Ω on its front is continued in the plane of the slot and guarantees the validity of the equilibrium conditions provided that the normal stresses are equal to zero (the effect of boundary layer). The numerical analysis shows that the jump of tangential stresses in the boundary layer outside the slot rapidly decreases with the distance from the front in complete agreement with the Saint-Venant principle. If a jump of tangential stresses on the surfaces of the slot is absent (and exists outside the slot), then these surfaces have a kink in the front of the slot and the volume strains possess a logarithmic singularity. This situation can be regarded as the limiting state corresponding to the onset of plastic deformation or brittle fracture. If the tangential stresses do not have jump in the entire plane of the slot, then the solution of the problem does not exist. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Materials Science is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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