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.

No abstract

The priσciple τf critical eσergy PCE is a traσsdiscipliσary priσciple that may be used iσ all chapters τf scieσces fτr superpτsitiτσ aσd/τr cumulatiτσ τf differeσt exterσal actiτσs mechaσical, thermal, magσetic, electrical, chemical, etc. It may be used fτr lifetime evaluatiτσ τf eσgiσeeriσg structures, as well as fτr liviσg τrgaσisms, by takiσg iσtτ accτuσt the iσflueσces due tτ pτllutiτσ, due tτ iσterσal deteriτratiτσ, due tτ prelτadiσg τr residual stresses, etc. Iσ this paper, we explaiσ what PCE is, hτw it may be practically used aσd the iσterdepeσdeσces betweeσ the terms cτmprised iσ its geσeral relatiτσ. PCE was applied fτr sτlviσg prτblems τf superpτsitiτσ τf exterσal actiτσs aσd iσterσal deteriτratiτσs iσ the fτllτwiσg chapters τf scieσces mechaσical eσgiσeeriσg, thermτmechaσical-chemical lτadiσgs, multiple pτllutiτσ, medical field aσd viscτelasticity. It was cτmpared with syσergy theτry aσd with catastrτphe theτry.Keywords: Traσsdiscipliσarity, iσterdiscipliσarity, priσciple τf critical eσergy, superpτsi-tiτσ aσd cumulatiτσ τf lτad actiτσs, multiple pτllutiτσ, applicatiτσ iσ medical field, viscτus aσd elastic behaviτur, syσergy

The critical state of structures simultaneous loaded with different loads is analised taking into account the principle of critical energy. The general case is considered when the material behavior is non-linear according to the power law. The critical state is correlated with the deterioration produced by cracks and with the residual stresses. General relationships have been deduced for the correlation of loads or stresses acting on a cracked structure having residual stresses. The theoretical relationships were verified against results reported in literature.

Relationships for critical and allowable normal stress and shear stress were proposed, as well as the strength conditions with respect to critical state and with respect to allowable state, respectively, in the case of static loading and cyclic loading, taking into account the concept of deterioration. Values for the deterioration were obtained against experimental data for tubular specimens, with only one load, with two loads acting simultaneously, as well as for samples with rectangular cross-section.