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.
Get full access to this article
View all access options for this article.
References
1.
EvansW. J.‘Deformation and failure under multiaxial stresses—A survey of laboratory techniques and experimental data’, N.G.T.E. Note N.T. 833, 1972.
2.
ParsonsM. W.‘Cyclic straining of steels under conditions of biaxial stress’, Ph.D. Thesis, 1971 (University of Cambridge).
3.
EllisonE. G.AndrewsJ. M. H.‘Biaxial cyclic high strain fatigue of aluminium alloy RR 58’, J. Strain Analysis19738, 209.
4.
McDiarmidD. L.‘Failure criteria and cumulative damage in fatigue under multiaxial stress conditions’, PhD. Thesis, 1972 (City University, London).
5.
PascoeK. J.de VilliersJ. W. R.‘Low cycle fatigue of steels under biaxial straining’, J. Strain Analysis19672, 117.
6.
de VilliersJ.W.R.‘Low cycle fatigue failure of steels under biaxial straining’, Ph.D. Thesis 1966 (University of Cambridge).
7.
PascoeK. J.‘Low cycle fatigue in relation to design’, Proc. 2nd Int. Conf. Fracture1969, Brighton, 677 (Chapman and Hall Ltd., London).
8.
AndrewsJ. M. H.EllisonE. G.‘A testing rig for cycling at high biaxial strains’, J. Strain Analysis19738, 168.
9.
LiddleM.MillerK. J.‘Multiaxial high strain fatigue’, Proc. 3rd Int. Conf. Fracture1973, Munich.
10.
TairaS.InoueT.TakahashiM.‘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.
TairaS.InoueT.YoshidaT.‘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.
KikukawaM.OhjiK.KotaniS.YokoiT.‘A comparison of axial and reversed-torsional strain cycling low cycle fatigue strength of several structural metals’, Bull. J.S.M.E.197215, 889.
13.
MillerK. J.ChandlerD. C.‘High strain torsion fatigue of solid and tubular specimens’, Proc. Instn mech. Engrs1969–70184 (Pt 1), 433.
14.
ZamrikS. 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.
ShewchukJ.ZamrikS. Y.MarinJ.‘Low cycle fatigue of 7075-T651 aluminium alloy in biaxial bending’, Expl Mech.19688, 504.
16.
ZamrikS. 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.
LibertinyG. Z.‘Short life fatigue under combined stresses’, J. Strain Analysis19672, 91.
18.
KremplE.‘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.
GoughH. J.PollardH. V.‘The strength of metals under combined alternating stresses’, Proc. Instn mech. Engrs1935131, 3.
20.
GoughH. J.PollardH. V.‘The effect of specimen form on the resistance of metals to combined alternating stresses’, Proc. Instn mech. Engrs1936132, 549.
21.
GoughH. J.PollardH. V.ClenshawW. J.‘Some experiments on the resistance of metals to fatigue under combined stress’, Aero. Res. Council Rep. Memo2522, 1951.
22.
GuestJ. J.‘The problem of combined stress’, Engineering, Lond.1943155, 21–3, 101, 102, 281, 282, 303, 304.
23.
StanfieldG.Contribution to discussion, Proc. Instn mech. Engrs1935131, 93.
24.
StolenF. B.CummingsH. N.‘A failure criterion for multiaxial fatigue stresses’, Proc. Am. Soc. Test. Mater.195454, 822.
25.
FindleyW. N.ColemanJ. J.HanleyB. 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.
FindleyW. 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.
FindleyW. N.MitchellW. I.MartinD. 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.
BlassJ. J.FindleyW. N.‘The influence of the intermediate principal stress on fatigue under triaxial stresses’, Bull. Am. Soc. test. Mater. Res. Std.19677, 254.
29.
HalfordG. R.MorrowJ.‘Low cycle fatigue in torsion’, Proc. Am. Soc. test. Mater.196262, 695.
30.
MorrowJ.TulerF. R.‘Low cycle fatigue evaluation of Inconel 713C and Waspaloy’, J. bas. Engng, Trans. Am. Soc. mech. Engrs196587 (D), 275.
31.
FindleyW. N.MathurP. N.SzczepanskiE.TemelA. O.‘Energy versus stress theories for combined stress—a fatigue experiment using a rotating disc’, J. bas. Engng, Trans. Am. Soc. mech. Engrs196183 (D), 10.
32.
JoshiS. R.ShewchukJ.‘Fatigue crack propagation in a biaxial-stress field’, Expl Mech.197010, 529.
33.
KiblerJ. J.RobertsR.‘The effect of biaxial stresses on fatigue and fracture’, J. Engng Ind., Trans. Am. Soc. mech. Engrs197092 (B), 727.
34.
MorrisonJ. L. M.CrosslandB.ParryJ. S. C.‘Fatigue under triaxial stress: Development of a testing machine and preliminary results’, Proc. Instn mech. Engrs1956170, 697.
35.
CrosslandB.‘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.
BurnsD. J.ParryJ. S. C.‘Effect of large hydrostatic pressures on the torsional fatigue strength of two steels’, J. mech. Engng Sci.19646, 293.
PlumbridgeW. J.RyderD. A.‘The metallography of fatigue’, Metall. Rev.196914, 119.
39.
PlumbridgeW. J.‘Review: Fatigue-crack propagation in metallic and polymeric materials’, J. Mater. Sci.19727, 939.
40.
CoxH. L.FieldJ. E.‘The initiation and propagation of fatigue cracks in mild steel pieces of square section’, Aeronaut. Q.19524, 1.
41.
NadaiA.Theory of flow and fracture of solids19501, ch. 15 (McGraw-Hill Book Co., New York and London).
42.
MillerK. J.‘High-strain torsional fatigue in metals’, Ph.D. Thesis, 1969, University of London.
43.
WilsonI. H.WhiteD. J.‘Cruciform specimen for biaxial fatigue tests: An investigation using finite-element analysis and photoelastic coating techniques’, J. Strain Analysis19716, 27.
44.
LittleR. E.‘A note on the shear stress criterion for fatigue failure under combined stress’, Aeronaut. Q.196920, 57.
45.
FindleyW. 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. Engrs195981 (B), 301.
46.
DugganT. V.‘Application of fatigue data to design—crack propagation in a simulated component’, Ph.D. Thesis 1973, Portsmouth Polytechnic.
47.
idem ‘Fatigue as a design criterion’ (Pt 2), Engng Mater. Des.196710, 875–8.
48.
FindleyW. N.TracyJ. F.‘The effect of the intermediate principal stress on triaxial fatigue of 7075-T6 aluminum alloy’, J. Testing Evaluation19731, 432.
49.
idem ‘Fatigue under pulsating hydrostatic pressure’, Proc. 1st int. Conf. Fracture19653, 1479.
50.
OhjiK.HaradaS.‘The effect of anisotropy in fracture ductility on uniaxial and biaxial low-cycle fatigue’, Proc. 17th Japan Nat. Symp. Strength, Fracture, Fatigue1972, 79–90.
51.
NisitaniH.YamasitaN.‘Influence of mean stress on crack initiation and propagation of 7: 3 brass’. Trans. Japan Soc. mech. Engrs1966, 1456–61.
52.
NisitaniH.MurakamiY.‘Torsional fatigue and bending fatigue of electropolished low carbon steel specimens’, Bull. J.S.M.E.1970, 325–33.
53.
EllisonE. G.AndrewsJ. M. H.‘Biaxial cyclic high-strain fatigue of aluminium alloy RR 58’, J. Strain Analysis19738, 209–19.
54.
RadhakrishnanV. M.‘Damage accumulation in low cycle fatigue’, Z. Metallk.197364, 705–10.
55.
TanakaK.‘Fatigue crack propagation from a crack inclined to the cyclic tensile axis’, Engng Fracture Mech.19746, 493–507.
56.
TairaS.InoueT.TakahashiM.‘Low cycle fatigue under multiaxial stresses (. at elevated temperature)’, Proc. 10th Jap. Congr. Test. Mater.1967, 18–23.
57.
idem ‘Low cycle fatigue under multiaxial stresses (. at room temperature)’, Trans. Japan. Soc. mech. Engrs196935, 526–32.
58.
FrostW. J.BurnsD. J.‘Effect of oil and mercury at high pressure on the fatigue behaviour of thick-walled cylinders of En 25 steel’, Proc. Instn mech. Engrs1967–68182 (Pt 3C), 65–71.
59.
TomkinsB.JonesP. M. Discussion on (58) ibid.309–12.
CoffinL. F.‘Fatigue at high temperature—prediction and interpretation’, Proc. Instn mech. Engrs1974188, 109–27.
62.
LittmanW. E.‘The mechanism of contact fatigue’, NASA Symp. Interdisciplinary approach to the lubrication of concentrated contacts 1969, 309–77 (Rensselaer Polytechnic Institute, New York).
DugdaleD. S.‘Yielding of steel sheets containing slits’, J. Mech. Phys. Solids19608, 100–4.
65.
BurdekinF. M.StoneD. E. W.‘The crack opening displacement approach to fracture mechanics in yielding materials’, J. Strain Analysis19661, 145–53.
66.
MillerK. J.KfouriA. P.‘An elastic-plastic finite element analysis of crack tip fields under biaxial loading conditions’, Int. J. Fracture197410, 393–404.
