Regimes of frictional sliding of a spring-block system

In the context of rate-and-state friction, we revisit the crossover between the creep and inertial regimes in the dynamics of a spring-block system as observed and described in the dry friction experiment of Heslot et al. (1994) and Baumberger et al. (1994). We show that the transition between the quasi-static motion of a spring-block and its dynamic motion occurs at a lower sliding velocity than that which minimises the steady-state friction coefficient. We perform a weakly nonlinear stability analysis combined with numerical studies with the continuation package Auto. In particular, attention is focused on the change of nature the Hopf bifurcation from supercritical to subcritical, as observed by Heslot et al. Comparing the results obtained for different friction laws, we conclude that the weakly nonlinear analysis provides a possible criterion for distinguishing which friction laws may be physically relevant.     

From dynamic modulus via different relaxation spectra to relaxation and creep functions

The main goal of the paper is to compare predictive power of relaxation spectra found by different methods of calculations. The experimental data were obtained for a new family of propylene random copolymers with 1-pentene as a comonomer. The results of measurements include flow curves, viscoelastic properties, creep curves and rubbery elasticity of copolymer melts. Different relaxation spectra were calculated using independent methods based on different ideas. It lead to various distributions of relaxation times and their “weights”. However, all of them correctly describe the frequency dependencies of dynamic modulus. Besides, calculated spectra were used for finding integral characteristics of viscoelastic behaviour of a material (Newtonian viscosity, the normal stress coefficient, steady-state compliance). In this sense all approaches are equivalent, though it appears impossible to estimate instantaneous modulus. The most crucial arguments in estimating the results of different approaches is calculating the other viscoelastic function and predicting behaviour of a material in various deformation modes. It is the relaxation and creep functions. The results of relaxation curve calculations show that all methods used give rather similar results in the central part of the curves, but the relaxation curves begin to diverge when approaching the high-time (low-frequency) boundary of the relaxation curves. The distributions of retardation times calculated through different approaches also appear very different. Meanwhile, predictions of the creep curves based on these different retardation spectra are rather close to each other and coincide with the experimental points in the wide time range. Relatively slight divergences are observed close to the upper boundary of the experimental window. All these results support the conclusion about a rather free choice of the relaxation time spectrum in fitting experimental data and predicting viscoelastic behaviour of a material in different deformation modes. Received: 15 March 2000 Accepted: 18 September 2000     

Dynamical measurements on viscoelastic behaviors of spiders in electro-dynamic loudspeakers

Spiders in electro-dynamic loudspeakers are most commonly concentrically corrugated fabric disks, and their viscoelastic behaviors affect the loudspeaker reproductions. A noncontact dynamic measuring technology is presented by a subwoofer closed box to excite the tested spiders pneumatically with a Laser Doppler Vibrometer (LDV) to measure the velocity of the moving spiders. Correlation techniques were employed to get an accurate and reliable acoustical transfer function between the measured velocity and sound pressure. The Young’s moduli of the tested spider composite materials were derived from the measured vibration modes. The creep effect and the level dependent behaviors of tested spiders were investigated. The results indicate that, the Young’s moduli of the tested spiders are frequency dependent. The mechanical stiffness increases with a small slope in low frequency range while a large slope in high frequency range. The loss factor exhibits the maximum around the resonance frequency, and after that it decreases with increasing frequency. The effective stiffness has a monotonic decrease with input voltage levels and the harder the spider, the less stiffness changes with input levels.     

Creep-constitutive behavior of Sn-3.8Ag-0.7Cu solder using an internal stress approach

The experimental tensile creep deformation of bulk Sn-3.8Ag-0.7Cu solder at temperatures between 263 K and 398 K, covering lifetimes up to 3,500 h, has been rationalized using constitutive equations that incorporate structure-related internal state variables. Primary creep is accounted for using an evolving internal back stress, due to the interaction between the soft matrix phase and a more creep-resistant particle phase. Steady-state creep is incorporated using a conventional power law, modified to include the steady-state value of internal stress. It is demonstrated that the observed behavior is well-fitted using creep constants for pure tin in the modified creep power law. A preliminary analysis of damage-induced tertiary creep is also presented.     

Impression recovery of amorphous polymers

The impression made by a loaded cylindrical flat-end punch on a polymer surface was observed to disappear with time at the same temperature after the load was removed. The depth-time relation appeared to obey second order kinetics. The temperature dependence of the rate constant shows two consecutive processes with activation energies, 906 kJ/mole (between 143 and 147°C) and 91 kJ/mole (between 150 and 160°C) for PC (Tg is at about 146°C) and 440 kJ/mole (between 104 and 110°C) and 95 kJ/mole (between 115 and 140°C) for PMMA (Tg is at about 112°C). These activation energies are probably associated with the motion and annihilation of conformational or structural defects of opposite signs. This kind of shape memory phenomena may be general for all amorphous polymers.     

High temperature materials for aerospace applications: Ni-based superalloys and γ-TiAl alloys

Two outstanding aerospace-oriented high-temperature materials, the single-crystal nickel-based superalloys for high-pressure turbine blades and the γ-TiAl-based alloys for low pressure turbine blades, are being presented here. In both cases, the optimisation of their mechanical properties is based on a high knowledge of metallurgy, mixing together different aspects such as processes, alloy design, deformation mechanisms, impact of oxidative environment or interaction between protective layers and protected alloy. Historical evolutions are recalled and put into perspective with more recent research activities.     

The creep of lead-free solders at elevated temperatures

Full implementation of the new generation of lead-free solders requires a detailed knowledge and understanding of their mechanical behavior. This paper reports an investigation of the creep behavior of three lead-free alloys: Sn-0.5 Cu, Sn-3.5 Ag, and Sn-3.8Ag-0.7Cu, at 75°C, and compares their response to that of Sn-37Pb at the same temperature. In terms of stress and time to rupture, the Sn-0.5Cu alloy behaves similarly to the eutectic Sn-Pb over the range of rupture lives considered (up to 1000 h). The silver-containing alloys exhibit much greater creep resistance, typically a hundred fold and a thousand fold for the binary and tenanary, respectively. These alloys are less ductile but their creep strains to failure are generally above ten percent. Their minimum creep rates are at least 100 times slower. When testing at the same homologous temperature (0.76), the silver-containing alloys retain the substantial superiority. The relationship between applied steady-state (or minimum) creep rate behavior is best described by a power law equation, although the steady state domain generally occupies less than 30 percent of life. The microstructural changes induced by creep are briefly described and used to explain some of the creep characteristics of the alloys.     

Chemically and mechanically driven creep due to generation and annihilation of vacancies with non-ideal sources and sinks

The classical concept of Nabarro creep is extended for a general dislocation microstructure. The specific mechanism of the creep consists in generation and annihilation of vacancies at dislocation jogs acting as non-ideal sources and sinks for vacancies. This mechanism causes the climb of dislocations, allowing for local volume and shape change. The final kinetic equations, relating the dislocation microstructure and the local stress state to the creep rate, are derived by means of the thermodynamic extremal principle. Closed-form equations for the creep rate are derived for isotropic polycrystals. Based on the model the creep rate in the ferritic P-91 type steel at very low applied stress is evaluated and compared with experiment.     

DYNAMICS IN POLY(OXYMETHYLENE) AND POLY(OXYMETHYLENE-CO-OXYETHYLENE) AS STUDIED VIA A COMBINED CREEP RATE SPECTROSCOPY/DIFFERENTIAL SCANNING CALORIMETRY APPROACH

The peculiarities and kinetics of segmental dynamics in a few semi-crystalline poly(oxymethylene) (POM) samples and in poly(oxymethylene-co-oxyethylene) with 1.5% ethylene oxide units were studied over the temperature range from 110 to 430K. Differential scanning calorimetry (DSC) and laser-interferometric creep rate spectroscopy (CRS) were used. The latter was operated under uniaxial tension or compression. A number of dynamic anomalies were observed. These included a suppressed glass transition (T _g) with its transformation into segmental relaxations below and above T _g, and a pronounced dynamic heterogeneity, with the dispersion of activation energies of segmental motion ranging from 60 to 500 kJ mol^?1. Formation of anomalous long folds in POM and the copolymer structure is assumed from DSC data, indicating a predominant contribution of “straightened out” tie chains to the structure of disordered regions in these isotropic polymers. Discrete high-resolution CRS analysis showed that numerous peaks (separate types of segmental motion) constituted dynamics in the interlamellar layers of the polymers under study. Considerable influence of comonomer or small additives, or preliminary treatments (quenching, small pre-straining) on discrete CR spectra was observed and are discussed in the text. All the anomalies observed could be treated in terms of the concept of the common segmental nature of α and β relaxations in flexible-chain polymers; as the breakdown of intermolecular motional cooperativity due to nanoscale confinement effect, and as a different constraining influence of crystallites on dynamics in the intercrystalline layers.     

Creep behaviour study of virgin and service exposed 5Cr–0.5Mo steel using magnetic Barkhausen emissions technique

Creep damage behaviour of water quenched 5Cr–0.5Mo steel has been studied using magnetic Barkhausen emissions (MBE) technique. The results were compared with the materials having same composition but used in service for 15 years to demonstrate the potentiality of the magnetic technique for in-situ evaluation of extent of creep damage of components. The rms voltage of magnetic Barkhausen signal for the virgin sample decreased at the initial stage of the expended creep life where new carbides are formed. As soon as the growth of the carbides took place at the expense of the smaller ones, MBE voltage started increasing due to the decrease of pinning density. However, in case of 15 years of service exposed sample, growth of carbides already took place and hence MBE voltage increased even during the initial stage of laboratory creep testing. As soon as the void started forming in the samples (both for virgin and service exposed one), the rate of increase of MBE voltage started decreasing. The formations of such cavities were observed through SEM micrograph analysis.