Comparative Study of Fatigue Damage Models Using Different Number of Classes Combined with the Rainflow Method

  • S. Zengah Department of Science and Technology, Mascara University, Algeria
  • A. Aid Department of Science and Technology, Mascara University, Algeria
  • M. Benguediab Department of Engineering Mechanics, Djillali Liabes University of Sidi Bel Abbes, Sidi Bel Abbes, Algeria
Keywords: damage models, damaged stress model, performance, random loading


Fatigue damage increases with applied load cycles in a cumulative manner. Fatigue damage models play a key role in life prediction of components and structures subjected to random loading. The aim of this paper is the examination of the performance of the “Damaged Stress Model”, proposed and validated, against other fatigue models under random loading before and after reconstruction of the load histories. To achieve this objective, some linear and nonlinear models proposed for fatigue life estimation and a batch of specimens made of 6082T6 aluminum alloy is subjected to random loading. The damage was cumulated by Miner’s rule, Damaged Stress Model (DSM), Henry model and Unified Theory (UT) and random cycles were counted with a rain-flow algorithm. Experimental data on high-cycle fatigue by complex loading histories with different mean and amplitude stress values are analyzed for life calculation and model predictions are compared.


Download data is not yet available.


ASTM E 1049-85, “Standard practices for cycle counting in fatigue analysis”, in: Annual Book of ASTM Standards, Vol. 03, No. 01, pp. 614–620, Philadelphia, 1997

N. E. Dowling, “Fatigue failure prediction for complicated stress-strain histories Journal of Materials, Vol. 7, No. 1, pp. 71–87, 1972

T. Lagoda, E. Macha, A. Nieslony, “Fatigue life calculation by means of the cycle counting and spectral methods under multiaxial random loading”, Fatigue & Fracture of Engineering Materials & Structures, Vol. 28, No. 4, pp. 409–420, 2005

P. H. Wirsching, M .C. Light, “Fatigue under wide band random stresses using rainflow method”, J. Struct. Division., Vol. 106, No. ST7, 1593–1607, 1980

E. Macha, T. Lagoda, A. Nieslony, D. Kardas, “Fatigue life under variable-amplitude loading according to the cycle-counting and spectral methods”, Materials Science, Vol. 42, No. 3, pp. 416-425, 2006

M. V. Borodii, “Life calculations for materials under irregular nonproportional loading”, Strength of Materials, Vol. 39, No. 5, pp. 560-565, 2007

M. A. Miner, “Cumulative damage in fatigue”, J. Appl. Mech., Vol. 67, pp. A159–A164, 1945

A. Fatemi, L. Yang, “Cumulative fatigue damage and life prediction theories: a survey of the state of the art for homogeneous materials”, International Journal of Fatigue, Vol. 20, No. 1, pp. 9–34, 1998

S. M. Marco, W. L. Starkey, “A concept of fatigue damage”, Trans. ASME, Vol. 76, No. 4, pp. 627–632, 1945

V. Dattoma, S. Giancane, R. Nobile, F. W. Panella, “Fatigue life prediction under variable loading based on a new non-linear continuum damage mechanics model”, International Journal of Fatigue, Vol. 28, No. 2, pp. 89–95, 2006

J. A. Bennett, “A study of the damaging effect of fatigue stressing on X4130 steel”, Proceedings, American Society for Testing and Materials., Vol. 46, pp. 693-714, 1946

D. L. Henry, “A theory of fatigue damage accumulation in steel”, Transactions of the ASME, Vol. 77, No. 6, pp. 913-918, 1955

H. T. Corten, T. J. Dolan, “Cumulative fatigue damage”, in Proceedings of the International Conference on Fatigue of Metals, Institution of Mechanical Engineering and American Society of Mechanical Engineers, pp. 235-246, 1956

A. M. Freudenthal, R. A. Heller, “On stress interaction in fatigue and a cumulative damage rule”, Journal of the Aero/Space Sciences, Vol. 26, No. 7, pp. 431-442, 1959

A. M. Freudenthal, “Physical and statistical aspect of cumulative damage”, in Colloquium on Fatigue, Stockholm, pp. 53-62, May, 1955

T. Bui-Quoc, “An interaction effect consideration in cumulative damage on a mild steel under torsion loading”, Proceedings of the 5th International Conference on Fracture, Pergamon Press, Vol. 5, pp. 2625-2633, 1981

T. Bui-Quoc, J. Dubuc, A. Barergui, A. Biron, “Cumulative fatigue damage under strain controlled conditions”, Journal of Materials, Vol. 6, No. 3, pp. 718-737, 1971

R. R. Gatts, “Application of a cumulative damage concept to fatigue”, J. Fluids Eng., Vol. 83, No. 4, pp. 529-534, 1961

F. R. Shanley, A theory of fatigue based on unbonding during reversing slip, report P-350, The Rand Corporation, Santa Monica, USA, 1952

S. R. Valluri, “A unified engineering theory of high stress level fatigue”, Aerospace Engineering, Vol. 20, No. 10, pp. 18-19, 1961

T. Bui-Quoc, “Cumulative damage with interaction effect due to fatigue under torsion loading”, Experimental Mechanics, Vol. 22, No. 5, pp. 180-187, 1982

J. Lemaitre, J. L. Chahoche, “Aspect phénoménologique de la rupture par endommagement”, Journal de Mécanique Appliquée, Vol. 2, No. 3, pp. 317-365, 1978

J. Lemaitre, A. Plumtree, “Application of damage concept to predict creep-fatigue failures”, Trans. ASME, J. Eng. Mater. Technol., Vol. 101, pp. 284-292, 1979

G. Mesmacque, S. Garcia, A. Amrouche, C. Rubio-Gonzalez, “Sequential law in multiaxial fatigue, a new damage indicator”, International Journal of Fatigue, Vol. 27, No. 4, pp. 461-467, 2005

A. Aid, Z. Semari, A. Amrouche, G. Mesmacque, M. Benguediab, “Nonlinear damage cumulative model in bloks loading conditions. Application for GS61 spheroïdal graphite cast-iron loaded by torsion and plane bending”, Journal of Theoretical znd Applied Mechanics, Vol. 38, No. 4, pp. 101-112, 2008

Aid, A. Amrouche, A. Bachir, B.A. and Benguediab, M, “Fatigue life prediction under variable loading based on a new damage model”. Materials & Design., 32(1),183–191, 2011

A. Aid, M. Bendouba, L. Aminallah, A. Amrouche, N. Benseddiq, M. Benguediab, “An equivalent stress process for fatigue life estimation under multiaxial loadings based a new non linear damage model”, Materials Science and Engineering: A, Vol. 538, No. 15, pp. 20-27, 2012

C. Amzallag, J. P. Gerey, J. L. Robert, J. Bahuaud, “Standardization of the rainflow counting method for fatigue analysis”, International Journal of Fatigue, Vol. 16, No. 4, pp. 287–93, 1994

ASTM E739-91, Annual book of ASTM standards 03.01, Philadelphia, pp. 614–620, 1998

A. Conle, T. Topper, “Fatigue service histories: techniques for data collection and history regeneration”, SAE Technical Paper 820093, Society of Automotive Engineers, 1983

F. E. Richart Jr, N. M. Newmark, “A hypothesis for the determination of cumulative damage in fatigue”, Proc. American Society for Testing and Materials, Vol. 48, pp. 767-800, 1948

J.B. Commerce, “The effect of overstress in fatigue on the endurance life of steel”, Proc. American Society for Testing and Materials, Vol. 45, pp. 532-541, 1945

A. Aid, J. Chalet, A. Amrouche, G. Mesmacque, M. Benguediab, “A new damage indicator: from blocks loading to random loading”, Fatigue Design Conf., Paris, France, November, 2005

O. Buxbaum, “Random load analysis as a link between operational stress measurement and fatigue life assessment. Service fatigue loads monitoring, simulation, and analysis”, American Society for Testing and Materials, Vol. 671, pp. 5-20, 1979

N. E. Dowling, “A Review of Fatigue Life Prediction Methods”, SAE Technical Paper Series, No. 871966, Passenger Car Meeting and Exposition, Dearborn, Michigan, USA, October, 1987

S. Kocanda, Fatigue failure of metals (fatigue and fracture), Sijthoff & Noordhoff International, 1978

E. Macha, A. Nieslony, “Random multiaxial fatigue loading”, in: Advances in Fatigue, Fracture and Damage Assessment of Materials, Chapter Eight, WIT Press, pp. 213–242, 2005

C. Lalanne, Mechanical Vibration and Shock. Vol. 4: Fatigue Damage, Hermes Penton Science, 2002

L. M. Kachanov, “Rupture time under creep conditions”, International Journal of Fracture, Vol. 97, pp. 11-18, 1999

Y. N. Rabotnov, Creep Problems in Structural Members, North-Holland, Amsterdam, 1969

A. Aid, Cumul d’endommagement en fatigue multiaxiale sous sollicitations variables, PhD Thesis, Universitè de Sidi-Bel Abbes, Algérie, 2006

X. Pitoiset, Méthodes spectrales pour une analyse en fatigue des structures métalliques sous chargements aléatoires multiaxiaux. PhD Thesis, Université Libres de Bruxelles, 2001

J. D. Clothiaux, N. E. Dowling, “Verification of rain-flow reconstructions of a variable amplitude load history”, NASA Contractor Report 189670, Virginia Polytechnic Institute and State University Blacksburg, VA, 1992



Abstract Views: 460
PDF Downloads: 90

Metrics Information
Bookmark and Share