The problems of loading superposition of low cycle fatigue, finite cycle fatigue and high cycle fatigue on cracked structure are analyzed. The nonlinear power law behavior of the structure material has been considered. A strength criterion was established for a cracked structure under low cycle fatigue, finite cycle fatigue, and high cycle fatigue loading taking into account the deterioration. On the basis of concept of the specific energy participation and using Basquin’s law and Coffin–Manson’s law, a general relationship of fatigue life was established in the case of superposition of low cycle fatigue, finite cycle fatigue, and high cycle fatigue loadings on a mechanical structure deteriorated due to cracks. The derived relationships depend on the high cycle fatigue and finite cycle fatigue mean stress and on the low cycle fatigue mean strain, as well as on deterioration. Relationships for the deterioration calculation were established. Experimental work was performed for specimens with cracks, made of steel, statically and cyclically loaded. A numerical example shows how the established relationships may be used.
AlmarezGMDMoraRP (2013) Ultrasonic fatigue testing on high strength steel: Effect of stress concentration factors associated with corrosion pitting holes. International Journal of Damage Mechanics22: 860–877.
2.
BasquinOH (1910) The exponential law of endurance tests. Proceedings of-American Society for Testing Materials10: 623–630.
3.
BeckTLoeheDLuftJ, (2007) Damage mechanisms of cast Al-Si-Mg alloys under superimposed thermal-mechanical fatigue and high-cycle fatigue loading. Materials Science and Engineering A468–470: 184–192.
4.
ChattopadhyayJ (2006) Improved J and COD estimation by GE/EPRI method in elastic to fully plastic transition zone. Engineering Fracture Mechanics73: 1959–1979.
5.
CoffinLFJr. (1954) A study of cyclic-thermal stress in ductile metal. Transactions of the ASME76: 931.
6.
FlaceliereLMorelFDragonA (2007) Coupling between mesoplasticity and damage in high – Cycle fatigue. International Journal of Damage Mechanics16(4): 473–509.
7.
HammoudaMMIPashaRAFayedAS (2007) Modelling of cracking sites/development in axial dovetail joints of aero-engine compressor discs. International Journal of Fatigue29: 30–48.
8.
HarveyFT (1974) Theory and Design of Modern Pressure Vessels, 2nd ed. New York, NY: Van Nostrand Reinhold Comp.
9.
HerteléSWaeleWDeDenysR, (2012) Full – range stress – strain behavior of contemporary pipeline steels; part I. Model description. International Journal of Pressure Vessels and Piping92: 34–40.
10.
HuWPShenQAZhangM, (2012) Corrosion – Fatigue life prediction for 2024-T62 Aluminum alloy using damage mechanics-based approach. International Journal of Damage Mechanics21: 1245–1266.
11.
Iordăchescu VI (2013) Research about the strength of the cracked mechanical structures, with application to pressure equipment (Romanian language). PhD Thesis, Polytehnica University of Bucharest, Romania.
12.
JinLSunBGuB (2013) Cumulative fatigue damage for 3-D angle-interlock woven composite under three-point bending cyclic loading. International Journal of Damage Mechanics22: 3–16.
13.
JinescuVV (1989) The energy concept in critical group of loads calculation. International Journal of Pressure Vessels and Piping38: 211–226.
14.
JinescuVV (2011) Treatise on Thermomechanics, 1st ed. Bucharest: AGIR.
15.
JinescuVV (2012) Cumulation of effects in calculation the deterioration of fatigue loaded structures. International Journal of Damage Mechanics21(5): 671–695.
16.
JinescuVV (2013b) Critical energy approach for the fatigue life calculation under blocks with different normal stress amplitudes. International Journal of Mechanical Science67: 78–88.
17.
JinescuVV (2013c) The principle of critical energy, consequences and applications. Proceedings of the Romanian Academy, Series A14(2): 152–160.
18.
JinescuVVIordăchescuVI (2014) Calculation of deterioration due to crack in tubular specimens. U.P.B. Scientific Bulletin Series D76: 149–160.
19.
JinescuVVIordăchescuVITeodorescuN (2013a) Relations for the calculation of critical stress in pressure equipment with cracks. Revista De Chimie64(8): 858–863.
20.
KimNak-HyumChang-SikOhYun-JaeKim, (2011) Limit loads and fracture mechanics parameters for thick-walled pipes. International Journal of Pressure Vessels and Piping88: 403–414.
21.
KimYun-JaeDo-JunShimKamranNikbin, (2003) Finite element based plastic limit loads for cylinders with part-through surface cracks under combined loading. International Journal of Pressure Vessels and Piping80: 527–540.
22.
LiWWangPLuL-T, (2014) Evaluation of gigacycle fatigue limit and life of high-strength steel with interior inclusion – induced failure. International Journal of Damage Mechanics23: 931–948.
23.
MallSNicholasTParkT-W. Effect of predamage from low cycle fatigue on high cycle fatigue strength of Ti – 6Al – 4V. International Journal of Fatigue25: 1109–1116.
24.
MarinesIBinXBathiasC. An understanding of very high cycle fatigue of metals. International Journal of Fatigue25: 1101–1107.
25.
MashayekiMTaghhipourAAskariA, (2013) Continuum damage mechanics applications in low-cycle thermal fatigue. International Journal of Damage Mechanics22: 285–300.
26.
MinerMA (1945) Cumulative damage in fatigue. International Journal of Applied Mechanics67: A159–A164.
27.
NicholasT (1999) Critical issues in high cycle fatigue. International Journal of Fatigue21: 221–231.
28.
PalmgrenA (1924) Die lebensdauer von Kugellagern. Zeitschrift68: 339–410.
29.
Ramberg W and Osgood WR (1943) Description of Stress – Strain Curves by Three Parameters. Technical note No. 902, National Advisory Comitee for Aeronautics.
30.
SchweizerCSeifertTNiewegB, (2011) Mechanism and modeling of fatigue crack growth under combined low and high cycle fatigue loading. International Journal of Fatigue33: 194–202.
31.
SonsinoCM (2007) Course of SN-curves especially in the high-cycle fatigue regime with regard to component design and safety. International Journal of Fatigue29: 2246–2258.
32.
ViloticDAlexandrovSSidjaninL, (2014) The influence of torsional and tensile pre-straining on the validity of ductile fracture criteria. International Journal of Damage Mechanics23: 63–82.
33.
VuQHHalmDNadotY. High cycle fatigue of 1045 steel under complex loading: Mechanics map and damage modeling. International Journal of Damage Mechanics23: 377–410.
34.
YanaseKShojimaKOgataC (2013a) High-cycle fatigue threshold behaviors in notched plates. International Journal of Damage Mechanics22: 1006–1022.
35.
YanaseKShojimaKOgataC (2013b) High-cycle fatigue threshold behaviors in notched plates. International Journal of Damage Mechanics22: 1006–1022.
36.
ZerbstUAinsworthRASchawalbeKH (2000) Basic principles of analytical flaw assessment methods. International Journal of Pressure Vessels and Piping77: 855–867.
37.
ZhuS-PHuangH-ZLiY (2012) A novel viscosity-based model for low cycle fatigue – Creep life prediction of high-temperature structures. International Journal of Damage Mechanics21: 1076–1099.
38.
ZhuS-PHuangH-ZLiuY (2013) An efficient life prediction methodology for low cycle fatigue-creep based on ductility exhaustion theory. International Journal of Damage Mechanics22: 556–571.
