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Power-law Creep (power-law + creep)
Selected AbstractsA damage mechanics model for power-law creep and earthquake aftershock and foreshock sequencesGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2000Ian G. Main It is common practice to refer to three independent stages of creep under static loading conditions in the laboratory: namely transient, steady-state, and accelerating. Here we suggest a simple damage mechanics model for the apparently trimodal behaviour of the strain and event rate dependence, by invoking two local mechanisms of positive and negative feedback applied to constitutive rules for time-dependent subcritical crack growth. In both phases, the individual constitutive rule for measured strain , takes the form ,(t),=,,0,[1,+,t/m,]m, where , is the ratio of initial crack length to rupture velocity. For a local hardening mechanism (negative feedback), we find that transient creep dominates, with 0,<,m,<,1. Crack growth in this stage is stable and decelerating. For a local softening mechanism (positive feedback), m,<,0, and crack growth is unstable and accelerating. In this case a quasi-static instability criterion , , , can be defined at a finite failure time, resulting in the localization of damage and the formation of a throughgoing fracture. In the hybrid model, transient creep dominates in the early stages of damage and accelerating creep in the latter stages. At intermediate times the linear superposition of the two mechanisms spontaneously produces an apparent steady-state phase of relatively constant strain rate, with a power-law rheology, as observed in laboratory creep test data. The predicted acoustic emission event rates in the transient and accelerating phases are identical to the modified Omori laws for aftershocks and foreshocks, respectively, and provide a physical meaning for the empirical constants measured. At intermediate times, the event rate tends to a relatively constant background rate. The requirement for a finite event rate at the time of the main shock can be satisfied by modifying the instability criterion to having a finite crack velocity at the dynamic failure time, dx/dt , VR,, where VR is the dynamic rupture velocity. The same hybrid model can be modified to account for dynamic loading (constant stress rate) boundary conditions, and predicts the observed loading rate dependence of the breaking strength. The resulting scaling exponents imply systematically more non-linear behaviour for dynamic loading. [source] Polymer Viscoelasticity and Residual Stress Effects on Nanoimprint Lithography,ADVANCED MATERIALS, Issue 10 2007Y. Ding The decay kinetics of polystyrene (PS) gratings are monitored by tracking the intensity of the first-order laser diffraction peak as a function of annealing time. For low-molecular-mass PS (24,kg,mol,1, blue circles), an exponential response suggests that the pattern decay is a surface-tension- driven viscous flow. In high-molecular-mass PS (1007,kg,mol,1, green circles) a complicated response includes a rapid elastic recovery, a power-law creep, and a viscouslike flow (see figure). [source] Experimental Investigation of Eclogite Rheology and Its Fabrics at High Temperature and PressureJOURNAL OF METAMORPHIC GEOLOGY, Issue 2 2007J. ZHANG Abstract Eclogite plays an important role in mantle convection and geodynamics in subduction zones. An improved understanding of processes in the deeper levels of subduction zones and collision belts requires information on eclogite rheology. However, the deformation processes and associated fabrics in eclogite are not well understood. Incompatible views of deformation mechanism have been proposed for both garnet and omphacite. We present here deformation behaviour of eclogite at temperatures of 1027,1427 °C, confining pressures of 2.5,3.5 GPa, and strain rates of 1 × 10,5 s,1 to 5 × 10,4 s,1. We obtained a power-law creep for the high temperature and pressure deformation of a ,dry' eclogite (50 vol.% garnet, 40% omphacite and 10% quartz) with A = 103.3 ± 1.0, n = 3.5 ± 0.4, ,E =403 ± 30 KJ mol,1 and ,V = 27.2 cm3 mol,1. The two principal minerals of eclogite have greatly different strengths. Progressive increase of garnet results in a smooth increase in strength. Analysis by electron back-scattered diffraction shows that: (1) garnet displays pole figures with near random distributions of misorientation angle under both dry and wet conditions; (2) omphacite shows pronounced lattice preferred orientations (LPOs), suggesting a dominant dislocation creep mechanism. Further investigation into the water effects on eclogite show: (3) water content does not influence the style of omphacite fabric but increases slightly the fabric strength; (4) grain boundary processes dominate the deformation of garnet under high water fugacity or high shear-strain conditions, yielding a random LPO similar to that of non-deforming garnet, despite the strong shape preferred orientation (SPO) observed. {110} [001] slip may dominate the deformation of rutile. Quartz displays complicated and inconsistent LPOs in eclogite. These results are remarkably similar to observations from deformed eclogites in nature. [source] Impact of Thermal Diffusion on Densification During SPSJOURNAL OF THE AMERICAN CERAMIC SOCIETY, Issue 2009Eugene A. Olevsky Spark-plasma sintering (SPS) has the potential for rapid (with heating rates reaching several hundred K/min) and efficient consolidation of a broad spectrum of powder materials. Possible mechanisms of the enhancement of consolidation in SPS versus conventional techniques of powder processing are categorized with respect to their thermal and athermal nature. This paper analyzes the influence of thermal diffusion, which is an SPS consolidation enhancement factor of a thermal nature. The Ludwig,Soret effect of thermal diffusion causes concentration gradients in two-component systems subjected to a temperature gradient. The thermal diffusion-based constitutive mechanism of sintering results from the additional driving force instigated by spatial temperature gradients, which cause vacancy diffusion. This mechanism is a commonly omitted addition to the free-surface curvature-driven diffusion considered in conventional sintering theories. The interplay of three mechanisms of material transport during SPS is considered: surface tension- and external stress-driven grain-boundary diffusion, surface tension- and external stress-driven power-law creep, and temperature gradient-driven thermal diffusion. It is shown that the effect of thermal diffusion can be significant for ceramic powder systems. Besides SPS, the results obtained are applicable to the ample range of powder consolidation techniques, which involve high local temperature gradients. The case study conducted on the alumina powder SPS demonstrates the correlation between the modeling and experimental data. It is noted that this study considers only one of many possible mechanisms of the consolidation enhancement during SPS. Further efforts on the modeling of field-assisted powder processing are necessary. [source] Simulation of the Stress-Assisted Densification Behavior of a Powder Compact: Effect of Constitutive LawsJOURNAL OF THE AMERICAN CERAMIC SOCIETY, Issue 3 2008Héctor Camacho-Montes The densification of powders with linear and nonlinear viscous behavior (Scherer and Riedel models) and with power-law-deformation (Khun,McMeeking) behavior was studied under hot pressing and sintering forging conditions. Several numerical experiments, designated cases in this work, were performed to study the effect of (i) the uniaxial stress exerted by the piston and (ii) the rate of the uniaxial stress. The stress state was calculated using the finite-element program ANSYS for each case. Considering the mesoscopic behavior of the powders, densification rates were obtained. The similarities and differences between predictions from the three constitutive models are highlighted. The relationship between the constitutive behavior and the most effective stress state is one of the focuses of this study. For example, we show that under constant stress loading, hot pressing more effectively promotes densification than sinter forging for constitutive behaviors that do not follow the power-law creep. In general, as expected, the increase of uniaxial applied stress and piston velocity favored densification. However, the increase in densification depends strongly on the constitutive law. [source] | |||||||||||||