Estimation of the Performance Level of a Stretchable Plate Weakened by a Transverse Crack

Research output: Contribution to journalArticleResearchpeer-review

Abstract

We considered a rectilinear crack in a thin elastic plate in this work. Stretching the plate in the direction perpendicular to the crack, compressive stresses appear in the vicinity of the crack, which lead to stability loss in the plain form of plate equilibrium at a certain tension level. This study is aimed at clarifying whether the stability loss contributes to crack growth or leads to deformation stabilization. The stress state of the plate in the initial post-critical stage is studied. An approximate analytical solution is proposed. The finite element method is used for solving the problem of stretching a plate after stability loss. The effect of the loss of a plain deformation form when a plate with a central crack is stretched to the level of the stress state in the vicinity of the crack tip is estimated. An analysis of the stressed state in the vicinity of the tip of the central crack under uniaxial tension suggests that, at possible local buckling near the crack, there is an increase in stretching stresses in the vicinity of the crack tip and so the load leading to fracture decreases.

Original languageEnglish
Pages (from-to)220-226
Number of pages7
JournalVestnik St. Petersburg University: Mathematics
Volume52
Issue number2
DOIs
StatePublished - 1 Apr 2019

Keywords

  • finite element method
  • loss of plain deformation form
  • plate

Scopus subject areas

  • Mathematics(all)

Cite this

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title = "Estimation of the Performance Level of a Stretchable Plate Weakened by a Transverse Crack",
abstract = "We considered a rectilinear crack in a thin elastic plate in this work. Stretching the plate in the direction perpendicular to the crack, compressive stresses appear in the vicinity of the crack, which lead to stability loss in the plain form of plate equilibrium at a certain tension level. This study is aimed at clarifying whether the stability loss contributes to crack growth or leads to deformation stabilization. The stress state of the plate in the initial post-critical stage is studied. An approximate analytical solution is proposed. The finite element method is used for solving the problem of stretching a plate after stability loss. The effect of the loss of a plain deformation form when a plate with a central crack is stretched to the level of the stress state in the vicinity of the crack tip is estimated. An analysis of the stressed state in the vicinity of the tip of the central crack under uniaxial tension suggests that, at possible local buckling near the crack, there is an increase in stretching stresses in the vicinity of the crack tip and so the load leading to fracture decreases.",
keywords = "finite element method, loss of plain deformation form, plate",
author = "Morozov, {N. F.} and Semenov, {B. N.} and Tovstik, {P. E.}",
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pages = "220--226",
journal = "Vestnik St. Petersburg University: Mathematics",
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}

Estimation of the Performance Level of a Stretchable Plate Weakened by a Transverse Crack. / Morozov, N. F.; Semenov, B. N.; Tovstik, P. E.

In: Vestnik St. Petersburg University: Mathematics, Vol. 52, No. 2, 01.04.2019, p. 220-226.

Research output: Contribution to journalArticleResearchpeer-review

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AU - Morozov, N. F.

AU - Semenov, B. N.

AU - Tovstik, P. E.

PY - 2019/4/1

Y1 - 2019/4/1

N2 - We considered a rectilinear crack in a thin elastic plate in this work. Stretching the plate in the direction perpendicular to the crack, compressive stresses appear in the vicinity of the crack, which lead to stability loss in the plain form of plate equilibrium at a certain tension level. This study is aimed at clarifying whether the stability loss contributes to crack growth or leads to deformation stabilization. The stress state of the plate in the initial post-critical stage is studied. An approximate analytical solution is proposed. The finite element method is used for solving the problem of stretching a plate after stability loss. The effect of the loss of a plain deformation form when a plate with a central crack is stretched to the level of the stress state in the vicinity of the crack tip is estimated. An analysis of the stressed state in the vicinity of the tip of the central crack under uniaxial tension suggests that, at possible local buckling near the crack, there is an increase in stretching stresses in the vicinity of the crack tip and so the load leading to fracture decreases.

AB - We considered a rectilinear crack in a thin elastic plate in this work. Stretching the plate in the direction perpendicular to the crack, compressive stresses appear in the vicinity of the crack, which lead to stability loss in the plain form of plate equilibrium at a certain tension level. This study is aimed at clarifying whether the stability loss contributes to crack growth or leads to deformation stabilization. The stress state of the plate in the initial post-critical stage is studied. An approximate analytical solution is proposed. The finite element method is used for solving the problem of stretching a plate after stability loss. The effect of the loss of a plain deformation form when a plate with a central crack is stretched to the level of the stress state in the vicinity of the crack tip is estimated. An analysis of the stressed state in the vicinity of the tip of the central crack under uniaxial tension suggests that, at possible local buckling near the crack, there is an increase in stretching stresses in the vicinity of the crack tip and so the load leading to fracture decreases.

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