Given Number Of Cycles Research Articles

Fatigue analysis of notched laminates: A time-efficient macro-mechanical approach

A coupled, transversely isotropic, deformation and damage fatigue model has been implemented within the finite element method and utilized, along with a static progressive damage model, to predict the fatigue life, stiffness degradation as a function of number of cycles, and post-fatigue tension and compression response of notched, multidirectional laminates. The material parameters for the fatigue model were obtained utilizing ply-level classical lamination theory simulations and the provided [0], [90] and [±45] experimental composite laminate S–N data. Within the fatigue damage model, the transverse and shear stiffness properties of the plies were degraded with an isotropic scalar damage variable. The stiffness damage in the longitudinal (fiber) ply direction was suppressed, and instead the strength of the fiber was degraded as a function of fatigue cycles. A maximum strain criterion was used to capture the failure in each element, and once this criterion was satisfied, the longitudinal stiffness of the element was eliminated. The resulting, degraded properties were then used to calculate the new stress state. This procedure was repeated until final failure of the composite laminate was achieved or a specified number of cycles was reached. For post-fatigue tension and compression behavior, four internal state variables were used to control the damage and failure. The predictive capability of the above-mentioned approach was assessed by performing blind predictions of notched multidirectional IM7/977-3 composite laminate response under fatigue and post-fatigue tensile and compressive loading, followed by a recalibration phase. Tabulated data along with detailed results (i.e. stress–strain curves as well as damage evolution states at given number of cycles compared to experimental data) for all laminates are presented.

Damage Detection of AA2124/SiC Metal Matrix Composites Using Electronic Speckle Pattern Interferometry

Metal matrix composites (MMCs) with aluminium alloy AA2124 matrix reinforced with 17 and 25% of SiC were investigated. Symmetric tension-compression fatigue tests at ambient temperature and tensile creep tests at elevated temperature were carried out. Specimens were subjected to fatigue or creep loading conditions. Tests were stopped after given number of cycles or strain values respectively. Electronic Speckle Pattern Interferometry (ESPI) was used in order to detect damage under fatigue and creep conditions. Strain fields were observed on specimens’ surfaces to localise strain concentrations that would indicate areas of damage development.

Investigation on the Interaction between Plasticity Response and Fretting Wear under Partial Slip Condition

The fretting wear behavior of Ti-6Al-4V is studied with the focus on cyclic plasticity effect under partial slip condition. The analysis is simulated using finite element based method with a new worn surface profile model represent a given number of cycles using a cylinder-on-flat geometry. The effect of surface modification on the stresses and plastic strain distribution is studied. As the profiles become deeper and wider, the contact pressure and shear stress increase at the stick zone. Due to this increment, the accumulation of plastic strain will become more significant. This may lead to material’s ductility exhaustion that could initiate the nucleation of crack. Plastic deformation is predicted to occur in the 6000th cycle model and onwards. Overall the relationship of fretting wear and plasticity has been defined qualitatively.

Generating restricted classes of involutions, Bell and Stirling permutations

We present a recursive generating algorithm for unrestricted permutations which is based on both the decomposition of a permutation as a product of transpositions and that as a union of disjoint cycles. It generates permutations at each recursive step and slight modifications of it produce generating algorithms for Bell permutations and involutions. Further refinements yield algorithms for these classes of permutations subject to additional restrictions: a given number of cycles or/and fixed points. We obtain, as particular cases, generating algorithms for permutations counted by the Stirling numbers of the first and second kind, even permutations, fixed-point-free involutions and derangements. All of these algorithms run in constant amortized time.

Fatigue Life of Graphite/Epoxy Laminates Subjected to Tension-Compression Loadings

A recent two-parameter fatigue model, aimed at the predictionof the fatigue behaviour of composite materials, was applied to fatigueresults available in the literature, concerning graphite/epoxy laminatessubjected to tension-compression loadings. It was found that the model,successfully applied in the case of tension-tension andcompression-compression fatigue, also works when the sign of stress isreversed during fatigue. However, the constants appearing in theproposed formula must be evaluated anew when the loading mode changesfrom pure tension to tension-compression. The probability of failure infatigue is predicted with reasonable accuracy by the model, which isvery conservative in calculating the residual strength after a givennumber of cycles.

Modelling permanent deformation behaviour of unbound granular materials

A state of the art is presented on modelling permanent deformation behaviour of unbound granular materials. The existing numerical models are verified by a series of laboratory repeated load tests. A new model is introduced expressing the accumulated permanent axial strain at any given number of cycles as a function of applied stresses, taking into account the maximum shear stress ratio and the length of the stress path in p- q space. The results show similarities with the concept of the shakedown theory. At low levels of stress ratios the accumulation of permanent strain ceases, resulting in an equilibrium state. However, there are indications of the existence of a threshold stress ratio, known as the shakedown limit, beyond which the material experiences incremental collapse or gradual failure.

The asymptotic distribution of short cycles in random regular graphs

The probability that a random labelled r -regular graph contains a given number of cycles of given length is investigated asymptotically. Cycles of a finite number of different fixed lengths can be handled simultaneously. For i ≠ j , the probabilities of an i -cycle and a j -cycle occurring are asymptotically independent. The results are actually derived in the more general setting of graphs which have any given degree sequence, as long as the maximum degree is bounded above by a constant. As a special case, an asymptotic formula results for the number of labelled r -regular graphs with a given girth.

New direct lyapunov-type method for studying synchronization problems

A new approach of the Lyapunov type is presented for the stability analysis of a class of time invariant, nonlinear dynamical systems, which are characterized by a periodic nonlinearity, and the existence of an infinite number of stationary states. In particular, the method can be applied for studying transient stability problems in power systems, and the synchronization of phase lock circuits. Frequency criteria are developed for the convergence of all solutions to an equilibrium state, and a procedure, based on these criteria, is outlined for constructing stability regions for a collection of neighboring equilibria. When applied to power—or phase lock systems, these regions can be interpreted as synchronization regions within an arbitrary, given number of cycles. Also, some new results are obtained with respect to synchronization conditions within the first cycle.

The Crystallography of Formed and Cycled PbO2 Electrodes

The discharge‐recharge cycle process of the lead dioxide electrode was followed by means of optical microscopy. The lead dioxide microstructure obtained from the original formation, using cured electrode materials consisting of a mixture of and basic lead sulfates, was different from that obtained by recharge from an electrode reduced to normal lead sulfate. The lead dioxide electrodes, obtained from various sources and with various microstructures in the original as‐formed condition, all converted to practically the same microstructure after receiving only a few cycles. Although the microstructure underwent further change with increasing cycling, the plates from different manufacturers continued to resemble one another after any given number of cycles.