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EN
In the article, the means of application of the direct spectral method for the identification of the stress cycles for multiaxial stress is discussed. Two cases are analyzed. The first, when components of stress tensor are in phase, and the second, when they are shifted in phase. The second case is associated with the practical application for the crane wheel.
PL
W artykule przedstawiono sposób zastosowania metody spektralnej bezpośredniej do identyfikacji cykli naprężeń o charakterze wieloosiowym. Rozważane są dwa przypadki. Pierwszy, gdy składowe tensora naprężeń są zgodne w fazie i drugi, gdy są one przesunięte w fazie. Drugi przypadek jest związany z praktycznym zastosowaniem dla koła suwnicy.
EN
The load capacity of homogeneous, isotropic viscoelastic materials subjected to multiaxial stresses is considered. For this purpose uniaxial equivalent stresses in selected load cases are determined and relevant criteria applied. It is shown that in the case of constant load the yield criterion does not differ from that for perfectly elastic materials. Similar conclusion has been drawn for the fatigue and yield criteria at in-phase and out-of-phase stresses. On the contrary, the criteria derived for viscoelastic materials subjected to periodic loads do not coincide with those for perfectly elastic materials.
EN
On the basis of modified Hooke’s law for multiaxial stress in viscoelastic solids, threedimensional constitutive equations for strains have been derived. It is shown that after application or removal of triaxial static load, normal and shear strain components vary in course of time proportionally to each other and that in-phase stress components produce in-phase strain components. Harmonic out-of-phase stress as well as multiaxial periodic and stationary random stresses are also considered. The matrix of dynamical flexibility of viscoelastic materials is determined which depends on three material constants (Young modulus, Poisson’s ratio and coefficient of viscous damping of normal strain) and load circular frequency.
EN
On the basis of the three-dimensional constitutive equations for strains resulting from the Kelvin-Voigt’s model and modified Hooke’s law for multiaxial stress in viscoelastic solids, the formulae for the energy dissipated in a given time per unit volume have been derived. It is shown that after application or removal of triaxial static load there is no difference in the time functions governing the dissipation of strain energy of volume change and the dissipation of strain energy of distortion. Harmonic in-phase stress and harmonic out-of-phase stress as well as multiaxial periodic stress are also considered. It is demonstrated that in the process of energy dissipation due to normal and shear stress components the role of the latter is dominant.
5
Content available remote Spectral Method in Multiaxial random fatigue
EN
The algorithm for fatigue life calculation with spectral method under random multiaxial loading has been shown. The method consists in extension of the known spectral formulae of fatigue life determination under uniaxial random loading. Power spectral density function of the equivalent stress or strain, determined according to a linear criterion of multiaxial random fatigue, was used. It has been shown that the reduction of the multiaxial stress or strain state to the equivalent one can be performed directly in the frequency domain.
EN
This paper describes a multiscale model able to predict the influence of multiaxial stress state and plasticity on the magneto-mechanical behaviour of ferromagnetic polycrystals. This multiscale model is based on localisation and homogenisation procedures, and on a magnetoelastic model for single crystal.
PL
Opisano model o wielu skalach pozwalajqcy na przewidywanie wpływu wieloosiowych naprężeń na właściwości magneto-mechaniczne materiałów ferromagnetycznych polikrystalicznych. Model ten wykorzystuje procedury ujednorodniania oraz magnetoelastyczny model kryształu.
EN
The paper deals with the safety criteria of design for an infinite fatigue life of machinery parts. Uniaxial and multiaxial zero mean stress are considered. In the latter case, constant-amplitude in-pase stress components, as well as random-amplitude synchronous stress components, are taken into account. Dimensionless and relative safety margins for these stress states are defined. The presented criteria refer to ductile materials showing true fatigue limits. Transformation rules in the plane are given for fatigue limits references to coordinate system different than the componets of the plane stress.
PL
Rozpatrywane są kryteria nieograniczonej trwałości zmęczeniowej części maszyn przy jedno- i wieloosiowych stanach wahadłowych naprężeń o zgodnych w fazie stałoamplitudowych składowych oraz o synchronicznych składowych z losowo zmiennymi amplitudami. Zdefiniowano bezwymiarowe i względne marginesy bezpieczeństwa dla tych stanów. Przedstawione kryteria dotyczą materiałów ciągliwych posiadających granice zmęczenia. Dla granic zmęczenia odnoszących sie do innego układu współrzędnych niż składowe płaskiego stanu naprężenia podano reguły transformacji na płaszczyźnie.
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