Strain Energy Governed Damage Law for a Visco-Plastic Material
The inelastic strain energy which was shown by other authors to correlate fatigue data is used as an independent variable in a differential law of damage growth. A special form of this law is discussed, and material constants are evaluated to fit experimental data for low-cycle fatigue and creep of 304 stainless steel at 650° 0. Since the main goal of this study is to develop the method of life prediction for a wide range of practical applications, both uniaxial and multiaxial states of stress are evaluated. In the farmer case the effects of rate of loading, strain/stress control, wave shape, mean strain and hardening are considered. The multiaxial state of stress has been illustrated by a special case of combined axial-torsional deformation. In all these situations the inelastic strain energy was calculated according to the viscoplasticity theory based on overstress (VBO), which was shown to describe the cyclic deformation of 304 stainless steel in room as well as in elevated temperatures.
Advances in life prediction, Proc. Material Conference Albany, April 18-20, New York 1983, ASME, 1983.
Low cycle fatigue, Proc. Symposium on Low Cycle Fatigue, Bolton Landing, 30 Sept. - 4 Oct., New York 1985, ASTM STP, 942, 1987.
Low cycle fatigue and elasto-plastic behaviour of materials, Proc. Conference on Low Cycle Fatigue, Munich, September, 1987, Elsevier Appl. Sci.Publ., 1987.
R.P.SKELTON, High strain fatigue testing at elevated temperature, High Temp. Techn., 3, 4, 179-194, 1987.
J.L.CHABOCHE, Structure life prediction at high temperature; present and future capabilities, High Temp.Techn., 5, 2, 59-74, 1987.
O.KUJAWSKI, V.V.KALLIANPUR and E.KREMPL, An experimental study of uniaxial creep, cyclic creep and relaxation of AISI type 304 stainless steel at room temperature, J.Mech.Phys.Solids, 28, 129-148, 1980.
A.PINEAU, High temperature behaviour of engineering materials in relation to microstructure, in: Fatigue at High Temperature, [Ed.] R.P.Skelton, Appl. Sci. Publ., 305-364, 1983.
J.JANSON and J.HULT, Fracture mechanics and damage mechanics, a combined approach, J.Mech.Applique, 1, 1, 69-84, 1977.
J.LEMAITRE, So many definitions of damage, Euromech Colloquium on Damage Mechanics, Cachan, September 7-11, 1981.
J.LEMAITRE, Damage measurements, Eng. Fract.Mech., 28, 5/6, 643-661, 1987.
J.LEMAITRE and J.L.CHABOCHE, A nonlinear model of creep fatigue damage cumulation and interaction, in: Mechanics of Visco-elastic Media and Bodies, [Ed.] J. HULT, Springer V., 291-301, 1975.
M.CHRZAN0WSKI, Use of the damage concept in describing creep-fatigue interaction under prescribed stress, Int.J.Mech.Sci., 18, 69-73, 1976.
W.J.OSTERGREN and E.KREMPL, A uniaxial damage accumulation law for timevarying loading including creep-fatigue interaction, J.Press.Vess.Techn., 101, 118- 124, 1979.
P.S.MAYIA and S.MAJUMDAR, Elevated temperature low cycle fatigue behaviour of different heats of type 304 stainless steel, Mec.Trans., SA, 1651-1660, 1977.
M.SATOH and E.KREMPL, An incremental life prediction law for creep-fatigue interaction, Press.Vess. and Piping, 60, 71-79, 1982.
J.L.CHABOCHE, Continuum damage mechanics, J.Appl. Mech., 55, Part I: 57-64, Part II: 65-72, 1988.
D.KRATCINOVIC, Continuum damage mechanics, Appl. Mech.Rev., 37, 1, 1-6, 1984.
T.INOUE et all., Report of Bench-Mark project on inelastic deformaton and life prediction of 2 1/4 Cr-1 Mo steel at 600° C, in: Constitutive Laws for Engineering Materials, Theory and Applications, [Eds.] C.S.DESAI, E.KREMPL, P.D.KIOUSIS, T.KUNDU, Elsevier, 959-965, 1987.
M.C.IU and E.KREMPL, A uniaxial viscoplastic model based on total strain and overstress, J.Mech.Phys.Solids, 27, 377-391, 1979.
E.KREMPL, J.J.McMAHON and D. YAO, Viscoplasticity based on over stress with a differential growth law for the equilibrium stress, Mech.Mat., 5, 35-48, 1986.
W.OTT, H.NOWACK and H.PEEKEN, Advanced FEM-based fatigue analysis (FEMAT) for arbitrary multiaxial elastic-plastic loading conditions, in: Low Cycle Fatigue and Elasto-Plastic Behaviour of Materials, Ed. K.T.RJE, Elsevier Appl.Sci., PubL., 499-505, 1987.
M.A.MINER, Cummulative damage in failure, J.Appl.Mech., Al59-Al64, September 1945.
P.W.WHALEY, A thermodynamic approach to material Failure, in: Advances in Life Prediction, 41-50, ASME, 1983.
R.BLOTNY and J.KALETA, A method for determining the heat energy of the fatigue process in metals under uniaxial stress, Int.J.Fract., 8, 1, Part 1: 29-33, Part 2: 35-38, 1986.
C.E.FELTNER and J.D.M0RROW, Microplastic strain hysteresis energy as a criterion for fatigue fracture, J.Basic Engng., 83, 1, 15-22, 1961,
D.E.MARTIN, An energy criterion for low-cycle fatigue, J.Basic Engng., 83, 565- 571, 1961.
G.R.HALFORD, The energy required for fatigue, J.Materials, 1, 1, 3-18, 1966.
J.T.FONG, Energy approach to creep-fatigue interaction in metals at high temperatures, J.Press.Vess.Techn., 214-22, 1975.
W.J.OSTERGREN, A damage function and associated failure equations for predicting hold time and frequency effects in elevated temperature, low cycle fatigue, J.Test.Evaluation, 327-339, 1977.
B.N.LEIS, An energy-based fatigue and creep-fatigue damage parameter, J.Press.Vess.Techn., 99, 4, 524-533, 1977.
F.ELLYIN, A criterion for fatigue under multiaxial states of stress, Mech. Res. Comm., 1, 4, 219-224, 1974.
F. ELLYIN and D.KUJAWSKI, Plastic strain energy in fatigue failure, J.Press.Vess.Techn., 106, 342-347, 1984.
D.LEFEBVRE and F.ELLYIN, Cyclic response and inelastic strain energy in low cycle fatigue, Int. J.Fatigue, 6, 9-15, 1984.
F.ELLYIN, Effect of tensile-mean-strain on plastic strain energy and cyclic response, J. Eng.Mat.Techn., 107, 119-125, 1985.
K.GOLOS and F.ELLYIN, Generalization of cummulative damage criterion to multilevel cyclic loading, Theor.Appl.Fract.Mech., 7, 169-176, 1987.
D.LEFEBVRE, K.W.NEAL and F.ELLYIN, A criterion of low cycle fatigue failure under biaxial states of stress, J.Eng.Met. Techn., 103, 1, 1-6, 1981.
B.N.LEIS and J.H.LAFLEN, Problems in damage analysis under nonproportional cycling, J.Eng.Mat.Techn., 102, 127-134, 1980.
Y.S.GARUD, Multiaxial fatigue: a survey of the state of the art., J.Eng.Mat.Techn., 103, 118-125, 1981.
A.BENALLAL and D.MARGUIS, Constitutive equations for nonproportional cyclic elasto-viscoplasticity, J.Eng.Mat.Techn., 109, 326-336, 1987.
Y.S.GARUD, A new approach to the evaluation of fatigue under multiaxial loadings, J. Eng.Mat.Techn., 103, 118-125, 1981.
Z.MRÓZ, On the description of anisotropic workhardening, J.Mech.Phys.Solids, 15, 3, 163-175, 1967.
Z.MRÓZ, An attempt to describe the behaviour of metals under cyclic loads using a more general workhardening model, Acta Mechanica, 7, 2/3, 199-212, 1969.
J.HULT, Creep in continua and structures, [in] Topics in Appl. Cont.Mech., 137- 155, 1974.
S.MAJUMDAR, Designing against low-cycle fatigue at elevated temperature, Nucl.Eng.Des., 63, 121-135, 1981.
H.W.LIU, M.ZHENG and C.QI, Low cycle fatigue life - an analysis based on fatigue crack growth behaviour under general-yielding cyclic loading, in: Low Cycle Fatigue and Elasto-Plastic Behaviour, [Ed.] K.T.R.IE, Elsevier Appl.Sci.Publ., 556-561, 1987.
D.YAO, Theory of viscoelasticity based on overstress with applications, Ph.D.Thesis, RPI, February 1987.
C.F.CHENG, C.Y.CHENG, D.R.DIERCKS and R.W.WEEKS, Low-cycle fatigue behaviour of types 304 and 316 stainless steel at IMFBR operating temperature, in: Fatigue at Elevated Temperatures, ASTM STP, 520, 355-364, 1973.
Engineering properties of steel, [Ed.] P.D.HARVEY, ASTM, 1982.
K.KANZAWA, K.J.MILLER and M.W.BROWN, Low-cycle fatigue under out-of-phase loading conditions, J.Eng.Mat.Techn., 99, 3, 222-228, 1977.