Time-dependent Finite Element Model Research Articles

Temperature field and cooling rate of laser cladding with wire feeding

Temperature field and cooling rate are important parameters to influence the properties of clad layer and the heat affected zone. In this paper the temperature field and cooling rate of laser cladding are studied by a two-dimensional time-dependent finite element model. Experiment has been carried out by Nd:YAG laser cladding with wire feeding. Research results indicate that at the beginning of cladding, the width and depth of melt pool increase with cladding time. The cooling rate is related to position, cladding time, cladding speed, and preheating temperature. The temperature near melt pool changes rapidly while the temperature far from melt pool changes slowly. With the increase of cladding time, cooling rate decreases. The further the distance from the melt pool, the lower the temperature and the slower the cooling rate. The faster the cladding speed, the faster the cooling rate. The higher the preheating temperature, the slower the cooling rate. The FEM results coincide well with the experiment results.

The role of the periodontal ligament in bone modeling: The initial development of a time-dependent finite element model

Current remodeling theories, as applied to long bones, suggest that such processes are controlled by mechanical strains either within or on the bone surface. In this study, the stresses and strains within the periodontal ligament and surrounding bone, consequent to orthodontic loading of a tooth, were investigated by application of the finite element method. Previously, various authors have applied two and three dimensional instantaneous (essentially static) models to analyze the problems. The study reported in this article describes an initial time-dependent (continuous/dynamic) finite element model for tooth movement that uses newly developed software, the results being cross-referenced against historical data. These early results, from a two-dimensional mathematical model of a loaded canine tooth, suggest that the remodeling process may be controlled by the periodontal ligament rather than the bone. In the finite element model, bone was found to experience a low strain of 1 x 10(-5), whereas the periodontal ligament experienced a strain of 0.1 when the "tooth model" is loaded. Only this latter figure is above the threshold usually reported to be necessary to initiate the remodeling process. Further developments in this rapidly advancing area of biomechanical research should facilitate a greater increase in our knowledge of tissue stress and strain after loading.

Measurement and interpretation of strain relaxation in passivated Al–0.5% Cu lines

X-ray diffraction has been used to measure the strain relaxation in passivated Al–0.5% Cu lines at 200 °C after cooling directly from an anneal at the passivation deposition temperature of 380 °C. Fits to the measured X, Y, and Z components of strain are summed to obtain the hydrostatic component, which exhibits a decay over time. Three mechanisms are considered to explain the decay of the hydrostatic strain in the metal line: Cu precipitation from the solid solution, the presence and growth of voids in the lines, and time-dependent deformation of the passivation. Calculations of the effect of Cu precipitation from the solid solution demonstrate that it plays an insignificant role in the relaxation. A high-voltage scanning electron microscope is used to image the presence and growth of voids through the passivation. The time scale of the growth of stress-induced voids is not the same as the hydrostatic relaxation, indicating that voiding is not solely responsible for the observed relaxation. The relaxation of the line is modeled using a time-dependent finite element model, allowing elastic compliance of the passivation. The magnitude of the calculated relaxation agrees with the measurements. It is suggested that a combination of voiding and passivation compliance is responsible for the measured hydrostatic strain relaxation in the metal line.

NATURAL CONVECTION OF WATER NEAR THE DENSITY EXTREMUM FOR A WIDE RANGE OF RAYLEIGH NUMBERS

A time-dependent penalty finite element model was used to investigate natural convection of pure water in a rectangular enclosure with vertical end walls differentially heated near the temperature of maximum density. Attention was focused on the main features of the flow at high Rayleigh numbers not considered previously (Ra = 105−108). Water in a rectangular enclosure for the aspect ratio of 1.25 was initially kept at 4°C. The enclosure was then suddenly heated and cooled on the opposing vertical walls, i.e., 8°C and 0°C. The Rayleigh number was varied by the size of the enclosure. In the Rayleigh number range considered here, steady state was reached within a time of the order of 2tf, where tf is the time to steady state suggested by Patterson and Imberger [1]. The steady state flow field and temperature structure were symmetric at about the enclosure's midpoint, and a stable sinking jet was formed in the interior of the enclosure as a result of density inversion. The velocity profile near the vertical ...

Potash mining and seismicity: a time-dependent finite element model

Potash mining and seismicity: a time-dependent finite element model

Potash mining and seismicity: A time-dependent finite element model

This paper attempts to answer questions associated with induced seismicity over underground excavations with special reference to potash mines in Saskatchewan, Canada. These seismic disturbances are widely understood to be generated in the competent, carbonate Dawson Bay Formation and are induced by potash mining activity. The earthquake initiation process, subsequent development and the associated failure mechanism(s) must be better understood to minimize the potential consequences. In this regard, a realistic finite element model based on viscoelasticlviscoplastic material behaviour has been developed. This model is specifically designed to include those capabilities required to model the complex fabric of stratified and jointed rock associated with potash mining and includes the ability to model time-dependent closure of excavations. Possible modes of failure are investigated with the aid of this numerical model. From the results of various models, it is suggested that the seismicity is caused by the brittle failure of intact carbonate rock. Slip along existing discontinuities is a second possible mode responsible for seismic activity.

Transient finite element analysis of thermal methods used to estimate SAR and blood flow in homogeneously and nonhomogeneously perfused tumour models

A two-dimensional time-dependent finite element model was developed to evaluate thermal techniques for estimating blood flow and specific absorption rate (SAR). In these computer simulations, homogeneously and nonhomogeneously perfused tumour models were heated by a 915 MHz interstitial microwave antenna array. Representative blood flow values were assigned within the tumour, and the applied SAR distribution was based on a previously developed antenna theory. SAR values were estimated from the power-on transient temperatures, and blood flow values were estimated from thermal clearance data after power was discontinued. These estimated parameters were then compared to the known 'true' blood flow and SAR values throughout the treatment region. SAR values could be predicted with reasonable accuracy throughout most of the heated region independent of local blood flow. For a homogeneous model, thermal clearance was found to yield reasonably accurate blood flow estimates at high perfusion rates and less accurate estimates at lower perfusion rates. However, for the inhomogeneous model, the blood perfusion estimates were generally poor, and an average blood flow value for the tumour was obtained with little ability to resolve the differences in perfusion between regions. Using temperatures observed early in the cool-down curve resulted in improved spatial resolution, but increased the contribution of thermal conduction to the blood flow estimates. A single time-constant exponential thermal decay curve was found to be a necessary but not sufficient condition for reliable blood flow estimates using this technique.