In recognition of the differences of scale between the welding pool and the heat affected zone along the welding line on one hand, and the overall size of the components being welded on the other, a localglobal nite element approach was developed for the evaluation of distortions in laser welded shipbuilding parts. The approach involves the tandem use of a 'local' and a 'global' step. The local step involves a threedimensional nite element model for the simulation of the laser welding process using the Sysweld nite element code, which takes into account thermal, metallurgical, and mechanical aspects. The simulation of the laser welding process was performed using a non-linear heat transfer analysis, based on a keyhole formation model, and a coupled transient thermomechanical analysis, which takes into account metallurgical transformations using the temperature dependent material properties and the continuous cooling transformation diagram. The size and shape of the keyhole used in the local nite element analysis was evaluated using a keyhole formation model and the Physica nite volume code. The global step involves the transfer of residual plastic strains and the stiffness of the weld obtained from the local model to the global analysis, which then provides the predicted distortions for the whole part. This newly developed methodology was applied to the evaluation of global distortions due to laser welding of stiffeners on a shipbuilding part. The approach has been proved reliable in comparison with experiments and of practical industrial use in terms of computing time and storage. STWJ/339Mr Tsirkas is in the NOMENCLATURE A material dependent parameter b evolution of transformation process C p speci c heat, J kg 1 K 1 d thickness of plate, m D diameter of beam, m E Young's modulus, GPa E elasticity matrix G r Grashof number h height, m H convection coef cient, W m 2 K 1 I(0) initial incident intensity, W m 2 I(n) incident intensity on layer n, W m 2 k exponent associated with reaction speed L characteristic length of plate, m m factor of proportionality between drilling velocity and absorbed intensity M S initial transformation temperature, K N u Nusselt number p(n) depth of nth layer p(T,t) phase proportion p phase proportion obtained after in nite time p m (T) martensite phase proportion p m martensite phase proportion obtained at in nitely low temperature P full penetration depth of keyhole, m P e Peclet number P r Prandtl number q material dependent parameter q c heat loss by free convection, W m 2 q r heat loss by radiation, W m 2 Q in input power of heat source, W Q la s e r power of laser beam, W r radial distance, m r m a x maximum radius of keyhole, m r m in minimum radius of keyhole, m r 0 initial radius of keyhole, m s material dependent parameter t time, s T temperature, K T v vaporisation temperature, K T 0 ambient temperature, K v welding velocity, m s 1 w width of heat affected zone, m a thermal diffusivity, m 2 s 1 a t thermal expansion coef cient, K 1 b (n) tilt angle, deg e heat emissivity e to...

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This paper presents the computational modelling of welding phenomena within a versatile numerical framework. The framework embraces models from both the fields of Computational Fluid Dynamics (CFD) and Computational Solid Mechanics (CSM). With regard to the CFD modelling of the weld pool fluid dynamics, heat transfer and phase change, cell-centred Finite Volume (FV) methods are employed. Alternatively, novel vertex-based FV methods are employed with regard to the elasto-plastic deformation associated with the CSM. The FV methods are included within an integrated modelling framework, PHYSICA, which can be readily applied to unstructured meshes. The modelling techniques are validated against a variety of reference solutions.

Purpose ± A study of the influence of megasonic (MS) assisted agitation on Printed Circuit Boards (PCBs) electroplated using copper electrolyte solutions, to improve plating efficiencies through enhanced ion transportation. Design/methodology/approach-The impact of MS assisted agitation on topographical properties of the electroplated surfaces studied, through a Design of Experiments (DOE), by measuring surface roughness, characterised by values of the parameter Ra as measured by white light phase shifting interferometry and high resolution scanning electron microscopy. Findings ± An increase of Ra from 400 nm to 760 nm measured after plating, for an increase to acoustic power from 45 W to 450 W. Roughening increase due to micro-bubble cavitation energy, supported through direct imaging of the cavitation. Current thieving effect by the MS transducer induced low-currents, leading to large Cu grain frosting reducing the board quality. Current thieving was negated in plating trials through specific placement of transducer. Wavy electroplated surfaces, due to surface acoustic waves, also observed reducing the uniformity of the deposit. Research limitations/implications ± The formation of unstable transient cavitation and variation of the topology of the copper surface are unwanted phenomena. Further plating studies using megasonic agitation are needed, along with fundamental simulations, to determine how the effects can be reduced or prevented. Practical implications ± Identify manufacturing settings required for high-quality MS assisted plating and promote areas for further investigation, leading to the development of an MS plating manufacturing technique. Originality/value ± Quantification of the topographical changes to a PCB surface in response to megasonic agitation and evidence for deposited copper artefacts due to acoustic effects.

In this paper we propose an agitation method based on megasonic acoustic streaming to overcome the limitations in plating rate and uniformity of the metal deposits during the electroplating process. Megasonic agitation at a frequency of 1 MHz allows the reduction of the thickness of the Nernst diffusion layer to less than 600 nm. Two applications that demonstrate the benefits of megasonic acoustic streaming are presented: the formation of uniform ultra-fine pitch flip-chip bumps and the metallisation of high aspect ratio microvias. For the latter application, a multi-physics based numerical simulation is implemented to describe the hydrodynamics introduced by the acoustic waves as they travel inside the deep microvias.