A model based on continuum theory for describing the cyclic deformation behaviour of grey cast iron under multi-axial loading is presented and compared with test results obtained from strain-controlled tension/torsion tests. The unsymmetrical stress-strain response of cast irons under tension and compression is modelled by taking into account the opening and closing of graphite flakes, the bulk stress of cast iron being directly related to the internal stress acting on the steel matrix. Predictions are compared with experimental results obtained from proportional and non-proportional biaxial tests. The method is simple yet able to describe the essential features of the deformation of grey cast iron, and can be easily integrated with existing elasto-plastic constitutive models.
ThumA.UdeH.‘Die-Elastizitat und die Schwingungsfes-tigkeit des Gusseisens’, Die Giesserei, 1929, 16, 547–556.
3.
CoffinL. F.Jr‘The flow and fracture of a brittle material’, Trans. ASME, J. Appl. Mech., 1950, 17 (3), 74.
4.
RussellE. S.‘Finite element simulation of the microstructure of gray cast iron’, Fracture Control Program, Report 33, College of Engineering, University of Illinois at Urbana-Champaign, December 1979.
5.
GilbertG. N.J.‘Stress/strain properties of cast iron and Poisson's ratio in tension and compression’, J. Br. Cast Iron Res. Ass., 1961, 9 (3), 347–363.
6.
GilbertG. N.J.‘The components of strain due to deformation of the matrix and due to volume changes in a flake graphite cast iron under uniaxial stress’, J. Br. Cast Iron Res. Ass., 1963, 11 (4), 512–524.
7.
DowningS. D.SocieD. F.‘Modelling cyclic deformation and fatigue behaviour of cast iron under uniaxial loading’, Materials Engineering — Mechanical Behaviour, College of Engineering, University of Illinois at Urbana-Champaign, January 1984.
8.
BrownM. W.MillerK. J.‘A biaxial fatigue machine for elevated temperature testing’, J. Testing Evaluation (JTEVA), 1981, 9 (4), 202–208.
9.
‘Determining the modulus of elasticity of flake graphite cast iron’, BCIRA Broadsheet 157–3, BCIRA, Alvechurch, Birmingham, 1977.
10.
GilbertG. N.J.‘Variation of the microstructure of a flake graphite cast iron after stressing in tension and compression’, J. Br. Cast Iron Res. Ass., 1964, 12 (1), 31–47.
11.
CloughW. R.ShankM. E.‘The deformation and rupture of gray cast iron’, Trans. Am. Soc. for Metals, 1957, 49, 241–262.
12.
FashJ. W.SocieD. F.RussellE. S.‘Fatigue crack initiation and growth in gray cast iron’, Proceedings of Fatigue 81, Society of Environmental Engineers, Fatigue Group Conference, Warwick University, 24–27 March 1981, pp. 40–51.
13.
GilbertG. N.J.KempS. D.‘The cyclic stress/strain properties of a flake graphite cast iron — a progress report’, BCIRA Report 1384, 1980.
14.
GilbertG. N.J.‘The cyclic stress/strain properties and fatigue properties of a flake graphite cast iron tested under strain control — a detailed study’, BCIRA Report 1621, 1985.
15.
GilbertG. N.J.‘Engineering data on grey cast iron — SI units’, J. Br. Cast Iron Res. Ass., Report 1285, Alvechurch, 1977.
16.
KachanovL. M.‘On rupture time under condition of creep’ (in Russian), Izvestia Akademi Nauk, SSSR, Otd. Tekhn. Nauk., 1958, 8, 26–31.
17.
RobotnovY. N.Creep Problems of Structural Members, 1969 (North-Holland, Amsterdam).
18.
HayhurstD. R.LeckieF. A.‘The effect of creep constitutive and damage relationships upon the rupture time of a solid circular torsion bar’, J. Mech. Phys. Solids, 1973, 21, 431–446.
19.
LemaitreJ.ChabocheJ. L.‘Aspect phenomenologique de la rupture par endommagement’, J. de Méc. Appliquee, 1978, 2, 317–365.
20.
HultJ.‘CDM — capabilities, limitations and promises’, inMechanisms of Deformation and Fracture, Edited by EasterlingK. E., 1979 (Pergamon, Oxford), pp. 233–247.
21.
KrajcinovicD.FonsekaG. U.‘The continuum damage theory of brittle materials, Parts 1 and 2’, Trans. ASME, J. Appl. Mech., 1981, 48, 809–824.
22.
ChabocheJ. L.‘Continuous damage mechanics — a tool to describe phenomena before crack initiation’, Nucl. Engng Des., 1981, 64, 233–247.
23.
MurakamiS.‘Notion of continuum damage mechanics and its application to anisotropic creep damage theory’, Trans. ASME, J. Engng Mater. Technol., 1983, 105, 99–105.
24.
ChabocheJ. L.‘Continuum damage mechanics: Parts I and II’, Trans. ASME, J. Appl. Mech., 1988, 55, 59–72.
25.
KachanovM.‘Continuum model of medium with cracks’, ASCE, J. Engng Mech. Div., 1980, 106 (EM5), 1039–1051.
LemaitreJ.ChabocheJ. L.Mechanics of Solid Materials, 1985 (Cambridge University Press, Cambridge).
28.
HughesP. M.The application of the finite element method to fatigue analysis of cast iron components containing stress concentrations’, ENDDURE Report, Personal Communication, 1992.
29.
WangC. H.BrownM. W.‘Experimental and theoretical study of the deformation behaviour of En15R steel under multiaxial loading’, inMultiaxial Plasticity, 1992 (Mecamat, Paris), pp. 256–277.
30.
LadevezeP.LemaitreJ.‘Damage effective stress in quasi-unilateral conditions’, The 16th International Conference onTheoretical and Applied Mechanics, Lyngby, Denmark, 1984.
31.
LavenderD. A.Deformation and rupture of structures due to combined cyclic plasticity and creep, PhD Thesis, Leicester University, 1986.
