Three-Dimensional Stress Concentration Factor in Finite Width Plates with a Circular Hole

ABSTRACT

The
three-dimensional stress concentration factor (SCF) at the edge of elliptical
and circular holes in infinite plates under remote tension has been extensively investigated considering
the variations of plate thickness, hole dimensions and material properties,
such as the Poisson’s coefficient. This study employs three dimensional finite
element modeling to numerically investigate the effect of plate width on the
behavior of the SCF across the thickness of linear elastic isotropic plates with a
through-the-thickness circular hole under remote tension. The problem is
governed by two geometric
non-dimensional parameters, *i.e.*, the
plate half-width to hole radius (*W*/*r*) and the plate thickness to hole
radius (*B*/*r*) ratios. It is shown that for thin plates
the value of the SCF is nearly constant throughout the thickness for any plate
width. As the plate thickness increases, the point of maximum SCF shifts from
the plate middle plane and approaches
the free surface. When the ratio of plate half-width to hole radius (*W*/*r*) is greater than four,
the maximum SCF was observed to approximate the theoretical value determined
for infinite plates. When the plate width is reduced, the maximum SCF values
significantly increase. A polynomial curve fitting was employed on the
numerical results to generate empirical formulas for the maximum and surface
SCFs as a function of *W*/*r* and *B*/*r*. These equations can be applied,
with reasonable accuracy, to practical problems of structural strength and
fatigue, for instance.

Cite this paper

M. Vaz, J. Cyrino and G. Silva, "Three-Dimensional Stress Concentration Factor in Finite Width Plates with a Circular Hole,"*World Journal of Mechanics*, Vol. 3 No. 3, 2013, pp. 153-159. doi: 10.4236/wjm.2013.33013.

M. Vaz, J. Cyrino and G. Silva, "Three-Dimensional Stress Concentration Factor in Finite Width Plates with a Circular Hole,"

References

[1] R. C. J. Howland, “On the Stresses in the Neighbourhood of a Circular Hole in a Strip under Tension,” Philosophical Transactions of the Royal Society of London, Vol. 229, 1930, pp. 49-86. doi:10.1098/rsta.1930.0002

[2] S. Timoshenko and J. N. Goodier, “Theory of Elasticity,” 2nd Edition, McGraw-Hill Book Company, New York, 1951.

[3] N. I. Muskhelishvili, “Some Basic Problems of the Mathematical Theory of Elasticity,” Groningen, 1953.

[4] W. T. Koiter, “An Elementary Solution of Two Stress Concentration Problems in the Neighborhood of a Hole,” Quarterly of Applied Mathematics, Vol. 15, 1957, pp. 303-308.

[5] V. J. Parks and D. F. Mendoza, “Maximum Stress in a Tensile Strip with a Large Hole,” Experimental Mechanics, Vol. 15, No. 10, 1975, pp. 389-391. doi:10.1007/BF02319837

[6] A. M. Wahl, “Discussion of ‘Maximum Stress in a Tensile Strip with a Large Hole’,” Experimental Mechanics, Vol. 16, No. 11, 1976, pp. 439-440. doi:10.1007/BF02410352

[7] R. D. Cook, “Stresses in a Tensile Strip with a Large Circular Hole,” Computers & Structures, Vol. 24, No. 3, 1986, pp. 421-424. doi:10.1016/0045-7949(86)90319-6

[8] B. Pradhan, “Effect of Width and Axial to Transverse Elastic Stiffness Ratio on SCF in Uniaxially Loaded FRP Composite Plates Containing Circular Holes,” Fiber Science and Technology, Vol. 17, No. 4, 1982, pp. 245-254. doi:10.1016/0015-0568(82)90020-3

[9] W. D. Pilkey, “Peterson’s Stress Concentration Factors,” 2nd Edition, John Wiley & Sons, New York, 1997. doi:10.1002/9780470172674

[10] D. Bellett, D. Taylor, S. Marco, E. Mazzeo, J. Guillois and T. Pircher, “The Fatigue Behaviour of Three-Dimensional Stress Concentrations,” International Journal of Fatigue, Vol. 27, No. 3, 2005, pp. 207-221. doi:10.1016/j.ijfatigue.2004.07.006

[11] D. Bellett and D. Taylor, “The Effect of Crack Shape on Fatigue Limit of Three-Dimensional Stress Concentrations,” International Journal of Fatigue, Vol. 28, No. 2, 2006, pp. 114-123. doi:10.1016/j.ijfatigue.2005.04.010

[12] W. Altenhof, N. Zamani, W. North and B. Arnold, “Dynamic Stress Concentrations for an Axially Loaded Strut at Discontinuities Due to an Elliptical Hole or Double Circular Notches,” International Journal of Impact Engineering, Vol. 30, No. 3, 2004, pp. 255-274. doi:10.1016/S0734-743X(03)00068-X

[13] C. She and W. Guo, “Numerical Investigations of Maxi mum Stress Concentration at Elliptic Holes in Finite Thickness Piezoelectric Plates,” International Journal of Fatigue, Vol. 28, No. 4, 2006, pp. 438-445. doi:10.1016/j.ijfatigue.2005.06.046

[14] C. She and W. Guo, “Three-Dimensional Stress Concentrations at Elliptic Holes in Elastic Isotropic Plates Subjected to Tensile Stress,” International Journal of Fatigue, Vol. 29, No. 2, 2007, pp. 330-335. doi:10.1016/j.ijfatigue.2006.03.012

[15] P. Yu, W. Guo, C. She and J. Zhao, “The Influence of Poisson’s Ratio on Thickness-Dependent Stress Concentration at Elliptic Holes in Elastic Plates,” International Journal of Fatigue, Vol. 30, No. 1, 2007, pp. 165-171. doi:10.1016/j.ijfatigue.2007.02.007

[16] Z. Yang, C. B. Kim, C. Cho and H. G. Beom, “The Concentration of Stress and Strain in Finite Thickness Elastic Plate Containing a Circular Hole,” International Journal of Solids and Structures, Vol. 45, No. 3-4, 2008, pp. 713-731. doi:10.1016/j.ijsolstr.2007.08.030

[17] D. V. Kubair and B. Bhanu-Chandar, “Stressconcentration Factor Due to a Circular Hole in Functionally Graded Panels under Uniaxial Tension,” International Journal of Mechanical Sciences, Vol. 50, No. 4, 2008, pp. 732-742. doi:10.1016/j.ijmecsci.2007.11.009

[18] C. K. Chao, L. M. Lu, C. K. Chen and F. M. Chen, “Analytical Solution for a Reinforcement Layer Bonded to a Elliptic Hole under a Remote Uniform Load,” International Journal of Solids and Structures, Vol. 46, No. 14 15, 2009, pp. 2959-2965. doi:10.1016/j.ijsolstr.2009.03.025

[19] J. Rezaeepazhand and M. Jafari, “Stress Concentration in Metallic Plates with Special Shaped Cutout,” International Journal of Mechanical Sciences, Vol. 52, No. 1, 2010, pp. 96-102. doi:10.1016/j.ijmecsci.2009.10.013

[20] “ANSYS® User’s Manual. Structural Analysis Guide,” Release 10.0 Documentation, 2005.

[21] American Society for Testing Materials, “Standard Specification for Structural Steel for Ships,” A131/A131M, 2008.

[1] R. C. J. Howland, “On the Stresses in the Neighbourhood of a Circular Hole in a Strip under Tension,” Philosophical Transactions of the Royal Society of London, Vol. 229, 1930, pp. 49-86. doi:10.1098/rsta.1930.0002

[2] S. Timoshenko and J. N. Goodier, “Theory of Elasticity,” 2nd Edition, McGraw-Hill Book Company, New York, 1951.

[3] N. I. Muskhelishvili, “Some Basic Problems of the Mathematical Theory of Elasticity,” Groningen, 1953.

[4] W. T. Koiter, “An Elementary Solution of Two Stress Concentration Problems in the Neighborhood of a Hole,” Quarterly of Applied Mathematics, Vol. 15, 1957, pp. 303-308.

[5] V. J. Parks and D. F. Mendoza, “Maximum Stress in a Tensile Strip with a Large Hole,” Experimental Mechanics, Vol. 15, No. 10, 1975, pp. 389-391. doi:10.1007/BF02319837

[6] A. M. Wahl, “Discussion of ‘Maximum Stress in a Tensile Strip with a Large Hole’,” Experimental Mechanics, Vol. 16, No. 11, 1976, pp. 439-440. doi:10.1007/BF02410352

[7] R. D. Cook, “Stresses in a Tensile Strip with a Large Circular Hole,” Computers & Structures, Vol. 24, No. 3, 1986, pp. 421-424. doi:10.1016/0045-7949(86)90319-6

[8] B. Pradhan, “Effect of Width and Axial to Transverse Elastic Stiffness Ratio on SCF in Uniaxially Loaded FRP Composite Plates Containing Circular Holes,” Fiber Science and Technology, Vol. 17, No. 4, 1982, pp. 245-254. doi:10.1016/0015-0568(82)90020-3

[9] W. D. Pilkey, “Peterson’s Stress Concentration Factors,” 2nd Edition, John Wiley & Sons, New York, 1997. doi:10.1002/9780470172674

[10] D. Bellett, D. Taylor, S. Marco, E. Mazzeo, J. Guillois and T. Pircher, “The Fatigue Behaviour of Three-Dimensional Stress Concentrations,” International Journal of Fatigue, Vol. 27, No. 3, 2005, pp. 207-221. doi:10.1016/j.ijfatigue.2004.07.006

[11] D. Bellett and D. Taylor, “The Effect of Crack Shape on Fatigue Limit of Three-Dimensional Stress Concentrations,” International Journal of Fatigue, Vol. 28, No. 2, 2006, pp. 114-123. doi:10.1016/j.ijfatigue.2005.04.010

[12] W. Altenhof, N. Zamani, W. North and B. Arnold, “Dynamic Stress Concentrations for an Axially Loaded Strut at Discontinuities Due to an Elliptical Hole or Double Circular Notches,” International Journal of Impact Engineering, Vol. 30, No. 3, 2004, pp. 255-274. doi:10.1016/S0734-743X(03)00068-X

[13] C. She and W. Guo, “Numerical Investigations of Maxi mum Stress Concentration at Elliptic Holes in Finite Thickness Piezoelectric Plates,” International Journal of Fatigue, Vol. 28, No. 4, 2006, pp. 438-445. doi:10.1016/j.ijfatigue.2005.06.046

[14] C. She and W. Guo, “Three-Dimensional Stress Concentrations at Elliptic Holes in Elastic Isotropic Plates Subjected to Tensile Stress,” International Journal of Fatigue, Vol. 29, No. 2, 2007, pp. 330-335. doi:10.1016/j.ijfatigue.2006.03.012

[15] P. Yu, W. Guo, C. She and J. Zhao, “The Influence of Poisson’s Ratio on Thickness-Dependent Stress Concentration at Elliptic Holes in Elastic Plates,” International Journal of Fatigue, Vol. 30, No. 1, 2007, pp. 165-171. doi:10.1016/j.ijfatigue.2007.02.007

[16] Z. Yang, C. B. Kim, C. Cho and H. G. Beom, “The Concentration of Stress and Strain in Finite Thickness Elastic Plate Containing a Circular Hole,” International Journal of Solids and Structures, Vol. 45, No. 3-4, 2008, pp. 713-731. doi:10.1016/j.ijsolstr.2007.08.030

[17] D. V. Kubair and B. Bhanu-Chandar, “Stressconcentration Factor Due to a Circular Hole in Functionally Graded Panels under Uniaxial Tension,” International Journal of Mechanical Sciences, Vol. 50, No. 4, 2008, pp. 732-742. doi:10.1016/j.ijmecsci.2007.11.009

[18] C. K. Chao, L. M. Lu, C. K. Chen and F. M. Chen, “Analytical Solution for a Reinforcement Layer Bonded to a Elliptic Hole under a Remote Uniform Load,” International Journal of Solids and Structures, Vol. 46, No. 14 15, 2009, pp. 2959-2965. doi:10.1016/j.ijsolstr.2009.03.025

[19] J. Rezaeepazhand and M. Jafari, “Stress Concentration in Metallic Plates with Special Shaped Cutout,” International Journal of Mechanical Sciences, Vol. 52, No. 1, 2010, pp. 96-102. doi:10.1016/j.ijmecsci.2009.10.013

[20] “ANSYS® User’s Manual. Structural Analysis Guide,” Release 10.0 Documentation, 2005.

[21] American Society for Testing Materials, “Standard Specification for Structural Steel for Ships,” A131/A131M, 2008.