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The cumulative fatigue damage caused by uniaxial variable stress is considered. To facilitate the lifetime prediction at complex stress patterns, has been defined an effective stress ofconstant parameters, claimed to be equivalent to the sequence of original stresses in terms of fatigue life of material. The equivalence conditions are based on the theory of energy transformation systems. To the effective stress the Palmgren-Miner rule is applied. Thereby the cycle counting is not required
On the basis of modified Hooke’s law for multiaxial stress in viscoelastic solids, three-dimensional 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 flexibilityofviscoelastic materials is determined which depends on three material constants (Young modulus, Poisson’s ratio and coefficient of viscous damping of normal strain) and loadcircular frequency
Periodic stress with Cartesian components given in the form of Fourier series is considered. To account for the mean stress effect the modified Soderberg’s formula is employed.An equivalent stress with synchronous components is defined. The design criterionfor a finite fatigue life of metal elements is formulated. It covers the conditions of bothstatic strength and fatigue safety in the high-cycle regime and includes material constantswhich have simple physical interpretation, can be determined by uniaxial tests, are related directly to the applied loads, and can reflect material anisotropy
Uniaxial non-zero mean stress of constant circular frequency in the high-cycle fatigue regime is considered. It is assumed that equation of the S-N curve and modified Soderberg equation are applicable. For constant-amplitude stress, the fatigue-critical stress amplitude is defined as that which leads to failure during the required design life. For random-amplitude stress, expected values of the fatigue-critical stress amplitude and total fatigue damage accumulated during the required design life are estimated. It is found that the probability of fatigue failure is equal to the probability of exceedance of the fatigue- -critical stress amplitude. As an example, for stationary random stress the equivalent random-amplitude stress and probability of fatigue failure are determined
Random stress with Cartesian components of known statistical moments of their meanvalues and power spectral densities of stochastic stress processes is considered. To acco-unt for the mean stress effect the generalised Soderberg criterion for ductile materials isemployed. An equivalent stress with periodic (in the mean-square sense) components isdefined by means of the equivalence conditions based on the average strain distortionenergy. Also, is formulated the fatigue "safe-life" design criterion which covers the condi-tions of both static strength and fatigue safety and includes yield strengths and fatiguelimits which : have simple physical interpretation, can be determined by uniaxial tests, are directly relatedto the applied loads, and can reflect material anisotropy
Periodic stress with Cartesian components given in the form of Fourier series is conside-red. To account for the mean stress effect the generalised Soderberg criterion for ductilematerials is employed. An equivalent stress with synchronous components is defined bymeans of the equivalence conditions based on the average strain energy of distortion. Thefatigue "safe-life" design criterion is formulated which covers the conditions of both staticstrength and fatigue safety and includes material constants that have simple physical in-terpretation, can be determined by uniaxial tests, are related directly to the applied loadsand can reflect material anisotropy
On the basis of Hooke’s law for multiaxial stress in elastic solids, similar relationships for viscoelastic materials are considered. It is assumed that the material is homogeneous and isotropic, and that the Kelvin-Voigt’s model is applicable to normal strain components. An analogous model is also taken for shear strain components. It is shown that the ratio of coefficients of viscous damping of normal and shear strain components is equalto the ratio of Young modulus and shear modulus. As a result, the modified Hooke’s law for multiaxial stress in viscoelastic materials has been formulated which includes three material constants: Young modulus, Poisson’s ratio and coefficient of viscous damping of normal strain
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
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
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