Modelling, Simulation and Validation of Plastic Zone Size during Deformation of Mild Steel
A model to predict the plastic zone size for material
under plane stress condition has been developed and verified
experimentally. The developed model is a function of crack size,
crack angle and material property (dislocation density). Simulation
and validation results show that the model developed show good
agreement with experimental results. Samples of low carbon steel
(0.035%C) with included surface crack angles of 45o, 50o, 60o, 70o
and 90o and crack depths of 2mm and 4mm were subjected to low
strain rate between 0.48 x 10-3 s-1 – 2.38 x 10-3 s-1. The mechanical
properties studied were ductility, tensile strength, modulus of
elasticity, yield strength, yield strain, stress at fracture and fracture
toughness. The experimental study shows that strain rate has no
appreciable effect on the size of plastic zone while crack depth and
crack angle plays an imperative role in determining the size of the
plastic zone of mild steel materials.
[1] K.J. Kang, H.G. Beom, “Plastic zone size near the crack tip in a
constrained ductile layer under mixed mode loading”, Engineering
Fracture Mechanics vol 66, pp 257 – 268, 2000.
[2] A. Tanaka and T. Yamauchi “Size Estimation of Plastic Deformation
Zone at the Crack Tip of Paper under Fracture Toughness Testing”, J.
Pack. Science and Technology, vol.6, no.5, pp 268 -275, 1997.
[3] N.Perez. Fracture Mechanics, Kluwer Academic Publisher, pp 95-112,
2004.
[4] Y.J Kim, G. Lin, A. Cornec, W. Brocks, K.H. Schwalbe. “The
Maximum Stresses in the Constrained Ductile Layer under Smallscale
Yielding Conditions”, Int. Journal of Fracture, vol 75, pp 9 – 16, 1996.
[5] Hill R. In: Mathematical theory of plasticity. Oxford: Oxford University
Press, pp 226 – 256, 1950.
[6] E.S Folias. “Estimating Plastic Zone Size” International Journal of
fracture, vol 10 no1, pp 109 – 111, 1974.
[7] D.K Choi and J.Kim, “A study on distribution of plastic region near a
crack tip using three-dimensional molecular dynamics simulation,”
Journals of Metals and Materials, vol. 4, No. 4, pp 925, 1998.
[8] M.T Welsch, M. Henning, M.Marx and H. Vehoff, “Measuring the
Plastic Zone Size by Orientation Gradient Mapping (OGM) and
Electron Channeling Contrast Imaging (ECCI)”. Adv. Eng. Material,
vol 9, pp 31–37, 2007.
[9] www.maplesoft.com/engineering/mechanical/monotonic plasticzonesize
[10] G.R. Irwin. “Plastic zone near a crack and fracture toughness”. In:
Proceedings of 7th Sagamore Conference. Pp 4 – 63, 1960.
[11] D.S. Dugdale. Yielding in steel sheet containing slits. Journal of Mech
Phys Solids; vol 8, pp 100 - 104, 1960.
[12] S. K. Nath, K. D. Uttam. Effect of Microstructure and Notches on the
Fracture Toughness of Medium Carbon Steel. Journal of Naval
Architecture and Marine Engineering, pp 15-22, 2006.
[1] K.J. Kang, H.G. Beom, “Plastic zone size near the crack tip in a
constrained ductile layer under mixed mode loading”, Engineering
Fracture Mechanics vol 66, pp 257 – 268, 2000.
[2] A. Tanaka and T. Yamauchi “Size Estimation of Plastic Deformation
Zone at the Crack Tip of Paper under Fracture Toughness Testing”, J.
Pack. Science and Technology, vol.6, no.5, pp 268 -275, 1997.
[3] N.Perez. Fracture Mechanics, Kluwer Academic Publisher, pp 95-112,
2004.
[4] Y.J Kim, G. Lin, A. Cornec, W. Brocks, K.H. Schwalbe. “The
Maximum Stresses in the Constrained Ductile Layer under Smallscale
Yielding Conditions”, Int. Journal of Fracture, vol 75, pp 9 – 16, 1996.
[5] Hill R. In: Mathematical theory of plasticity. Oxford: Oxford University
Press, pp 226 – 256, 1950.
[6] E.S Folias. “Estimating Plastic Zone Size” International Journal of
fracture, vol 10 no1, pp 109 – 111, 1974.
[7] D.K Choi and J.Kim, “A study on distribution of plastic region near a
crack tip using three-dimensional molecular dynamics simulation,”
Journals of Metals and Materials, vol. 4, No. 4, pp 925, 1998.
[8] M.T Welsch, M. Henning, M.Marx and H. Vehoff, “Measuring the
Plastic Zone Size by Orientation Gradient Mapping (OGM) and
Electron Channeling Contrast Imaging (ECCI)”. Adv. Eng. Material,
vol 9, pp 31–37, 2007.
[9] www.maplesoft.com/engineering/mechanical/monotonic plasticzonesize
[10] G.R. Irwin. “Plastic zone near a crack and fracture toughness”. In:
Proceedings of 7th Sagamore Conference. Pp 4 – 63, 1960.
[11] D.S. Dugdale. Yielding in steel sheet containing slits. Journal of Mech
Phys Solids; vol 8, pp 100 - 104, 1960.
[12] S. K. Nath, K. D. Uttam. Effect of Microstructure and Notches on the
Fracture Toughness of Medium Carbon Steel. Journal of Naval
Architecture and Marine Engineering, pp 15-22, 2006.
@article{"International Journal of Chemical, Materials and Biomolecular Sciences:71551", author = "S. O. Adeosun and E. I. Akpan and S. A. Balogun and O. O. Taiwo", title = "Modelling, Simulation and Validation of Plastic Zone Size during Deformation of Mild Steel", abstract = "A model to predict the plastic zone size for material
under plane stress condition has been developed and verified
experimentally. The developed model is a function of crack size,
crack angle and material property (dislocation density). Simulation
and validation results show that the model developed show good
agreement with experimental results. Samples of low carbon steel
(0.035%C) with included surface crack angles of 45o, 50o, 60o, 70o
and 90o and crack depths of 2mm and 4mm were subjected to low
strain rate between 0.48 x 10-3 s-1 – 2.38 x 10-3 s-1. The mechanical
properties studied were ductility, tensile strength, modulus of
elasticity, yield strength, yield strain, stress at fracture and fracture
toughness. The experimental study shows that strain rate has no
appreciable effect on the size of plastic zone while crack depth and
crack angle plays an imperative role in determining the size of the
plastic zone of mild steel materials.", keywords = "Applied stress, crack angle, crack size, material
property, plastic zone size, strain rate.", volume = "9", number = "2", pages = "381-6", }