Computation and Validation of the Stress Distribution around a Circular Hole in a Slab Undergoing Plastic Deformation
The aim of the current work was to employ the finite
element method to model a slab, with a small hole across its width,
undergoing plastic plane strain deformation. The computational
model had, however, to be validated by comparing its results with
those obtained experimentally. Since they were in good agreement,
the finite element method can therefore be considered a reliable tool
that can help gain better understanding of the mechanism of ductile
failure in structural members having stress raisers. The finite element
software used was ANSYS, and the PLANE183 element was utilized.
It is a higher order 2-D, 8-node or 6-node element with quadratic
displacement behavior. A bilinear stress-strain relationship was used
to define the material properties, with constants similar to those of the
material used in the experimental study. The model was run for
several tensile loads in order to observe the progression of the plastic
deformation region, and the stress concentration factor was
determined in each case. The experimental study involved employing the visioplasticity
technique, where a circular mesh (each circle was 0.5 mm in
diameter, with 0.05 mm line thickness) was initially printed on the
side of an aluminum slab having a small hole across its width.
Tensile loading was then applied to produce a small increment of
plastic deformation. Circles in the plastic region became ellipses,
where the directions of the principal strains and stresses coincided
with the major and minor axes of the ellipses. Next, we were able to
determine the directions of the maximum and minimum shear
stresses at the center of each ellipse, and the slip-line field was then
constructed. We were then able to determine the stress at any point in
the plastic deformation zone, and hence the stress concentration
factor. The experimental results were found to be in good agreement
with the analytical ones.
[1] W. D. Pilkey, Peterson’s Stress Concentration Factors, 2nd Ed. New
York: Wiley, 1997, ch.4.
[2] W. C. Young and R.G. Budynas, Roark’s Formulas for Stress and
Strain, 7th Ed. New York: McGraw-Hill, 2002, ch. 17.
[3] E.G. Thomsen, J.T. Lapsley, and J.B. Bierbower, “Experimental stress
determination within a metal during plastic flow, “in 1954 Proc.Am.
Soc. Exper. Stress Analysis, vol .VII, no.2, pp.59-68.
[4] S.D. El Wakil, “Deformation in bar cropping investigated by the visioplasticity”,
Journal of Mechanical Working Technology, vol 1, pp.85-98,
1977.
[5] W. Johnson, and P.B. Mellor, Plasticity for Mechanical Engineers.
London: Van Nostrand, 1970, ch.12.
[1] W. D. Pilkey, Peterson’s Stress Concentration Factors, 2nd Ed. New
York: Wiley, 1997, ch.4.
[2] W. C. Young and R.G. Budynas, Roark’s Formulas for Stress and
Strain, 7th Ed. New York: McGraw-Hill, 2002, ch. 17.
[3] E.G. Thomsen, J.T. Lapsley, and J.B. Bierbower, “Experimental stress
determination within a metal during plastic flow, “in 1954 Proc.Am.
Soc. Exper. Stress Analysis, vol .VII, no.2, pp.59-68.
[4] S.D. El Wakil, “Deformation in bar cropping investigated by the visioplasticity”,
Journal of Mechanical Working Technology, vol 1, pp.85-98,
1977.
[5] W. Johnson, and P.B. Mellor, Plasticity for Mechanical Engineers.
London: Van Nostrand, 1970, ch.12.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:70819", author = "S. D. El Wakil and J. Rice", title = "Computation and Validation of the Stress Distribution around a Circular Hole in a Slab Undergoing Plastic Deformation", abstract = "The aim of the current work was to employ the finite
element method to model a slab, with a small hole across its width,
undergoing plastic plane strain deformation. The computational
model had, however, to be validated by comparing its results with
those obtained experimentally. Since they were in good agreement,
the finite element method can therefore be considered a reliable tool
that can help gain better understanding of the mechanism of ductile
failure in structural members having stress raisers. The finite element
software used was ANSYS, and the PLANE183 element was utilized.
It is a higher order 2-D, 8-node or 6-node element with quadratic
displacement behavior. A bilinear stress-strain relationship was used
to define the material properties, with constants similar to those of the
material used in the experimental study. The model was run for
several tensile loads in order to observe the progression of the plastic
deformation region, and the stress concentration factor was
determined in each case. The experimental study involved employing the visioplasticity
technique, where a circular mesh (each circle was 0.5 mm in
diameter, with 0.05 mm line thickness) was initially printed on the
side of an aluminum slab having a small hole across its width.
Tensile loading was then applied to produce a small increment of
plastic deformation. Circles in the plastic region became ellipses,
where the directions of the principal strains and stresses coincided
with the major and minor axes of the ellipses. Next, we were able to
determine the directions of the maximum and minimum shear
stresses at the center of each ellipse, and the slip-line field was then
constructed. We were then able to determine the stress at any point in
the plastic deformation zone, and hence the stress concentration
factor. The experimental results were found to be in good agreement
with the analytical ones.", keywords = "Finite element method to model a slab, slab
undergoing plastic deformation, stress distribution around a circular
hole, visioplasticity.", volume = "9", number = "9", pages = "1634-4", }