A Theory for Fatigue Failure under Multiaxial Stress-Strain Conditions

Abstract

A new theory for multiaxial fatigue is presented that is based on a physical interpretation of the mechanisms of fatigue crack growth. It may be represented graphically by contours of constant life, which are expressed mathematically by

where ε₁, ε₂ and ε₃ are the principal strains, •ε₁ ≥ ε₂ ≥ ε₃.

This equation underlines the importance of strain parameters in correlating fatigue data. It illustrates the effect of both the shear strain and the tensile strain normal to the plane of maximum shear.

The theory is compared with several classical and recent theories, which are briefly reviewed. It is shown that classical theories of fatigue failure cannot correlate experimental data, and may be dangerous if used for design purposes.

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References

Evans

W. J.

‘Deformation and failure under multiaxial stresses—A survey of laboratory techniques and experimental data’, N.G.T.E. Note N.T. 833, 1972.

Parsons

M. W.

‘Cyclic straining of steels under conditions of biaxial stress’, Ph.D. Thesis, 1971 (University of Cambridge).

Ellison

E. G.

Andrews

J. M. H.

‘Biaxial cyclic high strain fatigue of aluminium alloy RR 58’, J. Strain Analysis 1973 8, 209.

McDiarmid

D. L.

‘Failure criteria and cumulative damage in fatigue under multiaxial stress conditions’, PhD. Thesis, 1972 (City University, London).

Pascoe

K. J.

de Villiers

J. W. R.

‘Low cycle fatigue of steels under biaxial straining’, J. Strain Analysis 1967 2, 117.

de Villiers

J.W.R.

‘Low cycle fatigue failure of steels under biaxial straining’, Ph.D. Thesis 1966 (University of Cambridge).

Pascoe

K. J.

‘Low cycle fatigue in relation to design’, Proc. 2nd Int. Conf. Fracture 1969, Brighton, 677 (Chapman and Hall Ltd., London).

Andrews

J. M. H.

Ellison

E. G.

‘A testing rig for cycling at high biaxial strains’, J. Strain Analysis 1973 8, 168.

Liddle

Miller

K. J.

‘Multiaxial high strain fatigue’, Proc. 3rd Int. Conf. Fracture 1973, Munich.

10.

Taira

Inoue

Takahashi

‘Low cycle fatigue under multiaxial stresses (in the case of combined cyclic tension-compression and cyclic torsion in the same phase at elevated temperature)’, Proc. 10th Japan. Cong. Test. Mater. 1967, 18.

11.

Taira

Inoue

Yoshida

‘Low cycle fatigue under multiaxial stresses (in the case of combined cyclic tension-compression and cyclic torsion out-of-phase to reach elevated temperature’, Proc. 11th Japan. Cong. Mater. Res. 1968, 60.

12.

Kikukawa

Ohji

Kotani

Yokoi

‘A comparison of axial and reversed-torsional strain cycling low cycle fatigue strength of several structural metals’, Bull. J.S.M.E. 1972 15, 889.

13.

Miller

K. J.

Chandler

D. C.

‘High strain torsion fatigue of solid and tubular specimens’, Proc. Instn mech. Engrs 1969–70 184 (Pt 1), 433.

14.

Zamrik

S. Y.

‘An investigation of strain cycling behaviour of 7075-T6 aluminium under combined state of strain’, 3rd Annual Progress Report, Dept of Engng Mechanics, Pennsylvania State University, 1967.

15.

Shewchuk

Zamrik

S. Y.

Marin

‘Low cycle fatigue of 7075-T651 aluminium alloy in biaxial bending’, Expl Mech. 1968 8, 504.

16.

Zamrik

S. Y.

‘An investigation of strain cycling behaviour of 7075-T6 aluminium under combined state of strain—The effects of out-of-phase, biaxial strain cycling on low cycle fatigue’, NASA tech. Rep. CR-72843, 1972.

17.

Libertiny

G. Z.

‘Short life fatigue under combined stresses’, J. Strain Analysis 1967 2, 91.

18.

Krempl

‘On deformation behaviour and failure laws for structural metals at elevated temperatures’, Extension Seminar on high temperature strength of materials, Int. Conf. Mechanical Behaviour of Materials, Kyoto, 1971.

19.

Gough

H. J.

Pollard

H. V.

‘The strength of metals under combined alternating stresses’, Proc. Instn mech. Engrs 1935 131, 3.

20.

Gough

H. J.

Pollard

H. V.

‘The effect of specimen form on the resistance of metals to combined alternating stresses’, Proc. Instn mech. Engrs 1936 132, 549.

21.

Gough

H. J.

Pollard

H. V.

Clenshaw

W. J.

‘Some experiments on the resistance of metals to fatigue under combined stress’, Aero. Res. Council Rep. Memo 2522, 1951.

22.

Guest

J. J.

‘The problem of combined stress’, Engineering, Lond. 1943 155, 21–3, 101, 102, 281, 282, 303, 304.

23.

Stanfield

Contribution to discussion, Proc. Instn mech. Engrs 1935 131, 93.

24.

Stolen

F. B.

Cummings

H. N.

‘A failure criterion for multiaxial fatigue stresses’, Proc. Am. Soc. Test. Mater. 1954 54, 822.

25.

Findley

W. N.

Coleman

J. J.

Hanley

B. C.

‘Theory for combined bending and torsion fatigue with data for SAE 4340 steel’, Proc. Int. Conf. Fatigue Metals 1956, 150 (American Society of Mechanical Engineers and Institution of Mechanical Engineers, London).

26.

Findley

W. N.

‘Combined stress fatigue strength of 76S-T61 aluminium alloy with superimposed mean stresses and corrections for yielding’, Tech. Notes natn. Advis. Comm. Aeronaut., Wash. 2924, 1953.

27.

Findley

W. N.

Mitchell

W. I.

Martin

D. E.

‘Combined bending and torsion fatigue tests of 25S-T aluminium alloy’, Proc. 2nd U.S. Nat. Cong. appl. Mech. 1954, 585 (American Society of Mechanical Engineers).

28.

Blass

J. J.

Findley

W. N.

‘The influence of the intermediate principal stress on fatigue under triaxial stresses’, Bull. Am. Soc. test. Mater. Res. Std. 1967 7, 254.

29.

Halford

G. R.

Morrow

‘Low cycle fatigue in torsion’, Proc. Am. Soc. test. Mater. 1962 62, 695.

30.

Morrow

Tuler

F. R.

‘Low cycle fatigue evaluation of Inconel 713C and Waspaloy’, J. bas. Engng, Trans. Am. Soc. mech. Engrs 1965 87 (D), 275.

31.

Findley

W. N.

Mathur

P. N.

Szczepanski

Temel

A. O.

‘Energy versus stress theories for combined stress—a fatigue experiment using a rotating disc’, J. bas. Engng, Trans. Am. Soc. mech. Engrs 1961 83 (D), 10.

32.

Joshi

S. R.

Shewchuk

‘Fatigue crack propagation in a biaxial-stress field’, Expl Mech. 1970 10, 529.

33.

Kibler

J. J.

Roberts

‘The effect of biaxial stresses on fatigue and fracture’, J. Engng Ind., Trans. Am. Soc. mech. Engrs 1970 92 (B), 727.

34.

Morrison

J. L. M.

Crossland

Parry

J. S. C.

‘Fatigue under triaxial stress: Development of a testing machine and preliminary results’, Proc. Instn mech. Engrs 1956 170, 697.

35.

Crossland

‘Effect of large hydrostatic pressures on the torsional fatigue strength of an alloy steel’, Proc. Int. Conf. Fatigue Met. 1956, 138 (American Society of Mechanical Engineers and Institution of Mechanical Engineers, London).

36.

Burns

D. J.

Parry

J. S. C.

‘Effect of large hydrostatic pressures on the torsional fatigue strength of two steels’, J. mech. Engng Sci. 1964 6, 293.

37.

Welter

Choquet

J. A.

‘Triaxial tensile stress fatigue testing’, Weld. Res. Suppl. 1963 28, 565s.

38.

Plumbridge

W. J.

Ryder

D. A.

‘The metallography of fatigue’, Metall. Rev. 1969 14, 119.

39.

Plumbridge

W. J.

‘Review: Fatigue-crack propagation in metallic and polymeric materials’, J. Mater. Sci. 1972 7, 939.

40.

Cox

H. L.

Field

J. E.

‘The initiation and propagation of fatigue cracks in mild steel pieces of square section’, Aeronaut. Q. 1952 4, 1.

41.

Nadai

Theory of flow and fracture of solids 1950 1, ch. 15 (McGraw-Hill Book Co., New York and London).

42.

Miller

K. J.

‘High-strain torsional fatigue in metals’, Ph.D. Thesis, 1969, University of London.

43.

Wilson

I. H.

White

D. J.

‘Cruciform specimen for biaxial fatigue tests: An investigation using finite-element analysis and photoelastic coating techniques’, J. Strain Analysis 1971 6, 27.

44.

Little

R. E.

‘A note on the shear stress criterion for fatigue failure under combined stress’, Aeronaut. Q. 1969 20, 57.

45.

Findley

W. N.

‘A theory for the effect of mean stress on fatigue of metals under combined torsion and axial load or bending’, J. Engng Ind., Trans. Am. Soc. mech. Engrs 1959 81 (B), 301.