P.S. Wei

Shape of a pore trapped in solid during solidification

Abstract The axisymmetric shape of a pore resulting from a bubble trapped by a solidification front is experimentally and theoretically investigated. Accounting for momentum, energy, mass, and species transport and physico-chemical equilibrium at the moving cap surface of the pore and introducing a time-dependent mass transfer coefficient derived from a scale analysis, the results find the effects of dimensionless parameters governing mass transfer coefficient, the maximum and decaying rate of displacement of the solidification front, Henry’s constant, concentration in bulk liquid, surface tension, and cap angle on the shape of the pore. Comparisons between the computed and measured variations in the pore length and cap radius with time are also presented.

Beam focusing characteristics effect on energy reflection and absorption in a drilling or welding cavity of paraboloid of revolution

Abstract Energy flux absorbed by the cavity of a paraboloid of revolution subject to a focused high-intensity beam, is systematically and quantitatively investigated. The intensity of incident flux is a Gaussian distribution, which is specified by the convergence angle, energy distribution parameter at the focal spot, and focal spot location relative to the workpiece surface. Absorption and scattering within the plasma in the cavity is assumed to be negligible. Using both analytical and Monte Carlo methods, and accounting for specular and diffuse reflections, the results find that energies absorbed by the cavity exhibit distinct regions for the focal spot lying above the cavity base. On the other hand, if the focal spot is below the base, absorbed energy flux is similar to a Gaussian distribution, and the maximum absorption is achieved. The effects of the beam focusing characteristics on the distribution of absorbed flux are provided. Formations of weld defects such as spiking and abnormally expanded fusion zone are proposed.

Three-dimensional analytical temperature field and its application to solidification characteristics in high- or low-power-densitybeam welding

Abstract An analytical three-dimensional temperature field in the liquid and heat-affected zones around the welding cavity produced by a moving high-intensity beam is provided. The cavity is idealized by a paraboloid of revolution in a semi-infinite workpiece subject to an incident flux of a Gaussian distribution. A relevant image technique is introduced to account for the adiabatic top surface. Three-dimensional solidification characteristics of the fusion zone, therefore, are quantitatively determined. The results show the effects of welding parameters, such as the dimensionless beam power, Peclet number, cavity opening radius, preheating temperature, and the parameter approximating convection, on the shape of the fusion zone, the cooling rates, and morphological stability. The findings agree well with available experimental data and three-dimensional finite-difference results.

Mechanisms of Spiking and Humping in Keyhole Welding

The effects of power density, concentration of volatile alloying element (magnesium, Mg), and welding speed on the mechanisms of fusion-zone defects, i.e., spiking and humping (and coarse rippling) during keyhole mode electron-beam welding of Al 6061, Al 5083, and SS 304 are investigated experimentally. Spiking represents a sudden increase in penetration beyond the average penetration line. Rippling exhibits rather regular, arc-shaped topographic features on a solidified surface, whereas humping shows an irregular surface contour consisting of a series of swelled protuberance. These defects seriously reduce the properties and strength of the joint. The quantitative variations of humping, coarse rippling, and spiking defects with the beam-focusing characteristics, volatile element, and scanning speed are quite limited in the literature. The experiments in this paper confirm that average pitch of the humps or coarse ripples is approximately identical to that of the spikes. Thus, the frequency of spiking can be determined from the observation of the weld surface. The results show that the average pitches and amplitudes of humping or coarse rippling and spiking increase with decreasing welding speed and increasing content of volatile element Mg from Al 5083. The frequency and amplitude of spiking, however, are increased by lowering the focal-spot location. The measured amplitude and frequency of spiking and humping and fusion-zone depth are confirmed from good agreement with available scaled analysis. This paper provides quantitative results useful for understanding mechanisms of these defects, so that preventing spiking and humping during keyhole mode welding becomes possible.

Fusion Zone Shapes in Electron-Beam Welding Dissimilar Metals

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Contact melting by a non-isothermal heating surface of arbitrary shape

Contact melting a material by a moving heater of arbitrary shapes with non-isothermal working surface is systematically investigated. A pressure exerted by the heater continuously squeezes the molten layer out of the close-contact region. The melting material has non-linear physical properties including temperature dependent conductivity, viscosity and non-Newtonian behaviors. By using a scale analysis momentum and energy equations are simplified. An iterative numerical procedure based on a boundary elements method is developed. Computed results show a good agreement with the analytical solutions that are available for a parabolic isothermal heating surface and constant physical properties. Influences of temperature distributions along the working surface and lengths of the heater on the thickness of the molten layer are found. A comparison between these factors is made. An appropriate distribution of the heat source within the heater is also proposed.

Origin of wavy weld boundary

In conduction mode laser welding, the shape of the fusion boundary affects the solidification process, microstructure, and properties of the weld. Although significant progress has been made in the calculations of the shape and size of the fusion zone in recent decades, the conditions for the formation of the wavy fusion boundary are still not well understood. Here we examine the conditions for its formation in terms of important dimensionless numbers. In particular, the computed flow patterns, temperature fields, and molten pool shapes under the flat free surface are examined for various values of Marangoni, Prandtl, Peclet, and dimensionless heat input values. In the absence of electromagnetic force, it is shown that the wavy fusion boundary forms for specific ranges of Marangoni and Prandtl numbers.

Magnetic property effect on transport processes in resistance spot welding

This study investigates the effects of the Curie temperature and magnetic permeability on transport variables, solute distribution and nugget shapes during resistance spot welding. The Curie temperature is the temperature below which a metal or alloy is ferromagnetic with a high magnetic permeability, and above which it is paramagnetic with a small magnetic permeability. The model proposed here accounts for electromagnetic force, heat generation and contact resistance at the faying surface and electrode–workpiece interfaces and bulk resistance in workpieces. Contact resistance includes constriction and film resistances, which are functions of hardness, temperature, electrode force and surface condition. The computed results show that transport variables and nugget shapes can be consistently interpreted from the delay of response time and jump of electric current density as a result of finite magnetic diffusion, rather than through the examination of the variations of dynamic electrical resistance with time. The molten nugget on the faying surface is initiated earlier with increasing magnetic permeability and Curie temperature. A high Curie temperature enhances convection and solute mixing, and readily melts through the workpiece surface near the electrode edge. Any means to reduce the Curie temperature or magnetic permeability, such as adjusting the solute content, can be a good way to control weld quality. This study can also be applied to interpret the contact problems encountered in various electronics and packaging technologies, and so on.

Energy absorption in a conical cavity truncated by spherical cap subject to a focused high-intensity beam

Energy absorption of a conical cavity truncated by a spherical cap subject to a focused beam is systematically and quantitatively investigated. The incident flux on any transverse cross-section has a Gaussian distribution, which is specified by the convergence angle, energy distribution parameter at the focal spot, and focal spot location relative to the workpiece surface. Absorption and scattering within the plasma in the cavity are assumed to be negligible. By accounting for specular and diffuse reflections the results show the effects of the spherical cap and cone angles of the cavity, locations and sizes of the focal spot, and convergence angles of the energy-beam on absorption. Asymptotic results agree with available solutions of simple models. An explanation for the occurrence of spiking in welding is also proposed.

Scaling of spiking and humping in keyhole welding

Spiking, rippling and humping seriously reduce the strength of welds. The effects of beam focusing, volatile alloying element concentration and welding velocity on spiking, coarse rippling and humping in keyhole mode electron-beam welding are examined through scale analysis. Although these defects have been studied in the past, the mechanisms for their formation are not fully understood. This work relates the average amplitudes of spikes to fusion zone depth for the welding of Al 6061, SS 304 and carbon steel, and Al 5083. The scale analysis introduces welding and melting efficiencies and an appropriate power distribution to account for the focusing effects, and the energy which is reflected and escapes through the keyhole opening to the surroundings. The frequency of humping and spiking can also be predicted from the scale analysis. The analysis also reveals the interrelation between coarse rippling and humping. The data and the mechanistic findings reported in this study are useful for understanding and preventing spiking and humping during keyhole mode electron and laser beam welding.