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The purpose of this paper is to investigate the void coalescence and corrosion behaviour of titanium Grade 4 sheets during single point incremental forming (SPIF) process with various spindle rotational speeds. The development of corrosion pits in 3.5 (%) NaCl solution has also been studied during SPIF process.

In this current research work, the void coalescence analysis and corrosion behaviour of titanium Grade 4 specimens were studied. A potentio-dynamic polarization (PDP) study was conducted to investigate the corrosion behaviour of titanium Grade 4 processed samples with various spindle speeds in 3.5 (%) NaCl solution. The scanning electron microscope and transmission electron microscope analysis was carried out to study the fracture behaviour and corrosion morphology of processed samples.

The titanium Grade 4 sheets obtained better formability and corrosion resistance by increasing the CNC spindle rotational speeds. In fact that, the significant plastic deformation affects the corrosion rate with various spindle speeds were recorded.

The spindle rotational speeds and vertical step depths increases then the titanium Grade 4 sheets showed better formability, void coalescence and corrosion behaviour as the same is evidenced in forming limit diagram and PDP curves.

Microstructure void volume fraction is taken into account in finite element models developed for large strain elastoplastic problems. Void nucleation rate is related to matrix effective strain rate, void growth to material strain rate and associated elastoplastic potential available for porous material, void coalescence to matrix effective strain rate. The related radial return algorithm is described. Three types of computations are proposed: first, axisymmetric Q4 element traction are given as validation example; second, collar cylinder compression are computed as reference example; third, bulk forming are analysed as large strain specific example. Void volume fraction and hydrostatic stress are mainly discussed according to microvoids nucleation, growth and coalescence. Finally, the main interests of those computations are enhanced.

The mechanisms for void formation are investigated for applications involving solder paste in surface mount technology. Generally, voids are caused by the outgassing of entrapped flux in the sandwiched solder during reflow. The voiding is dictated mainly by the solderability of metallisation, and increases with decreasing solderability of metallisation, decreasing flux activity, increasing metal load of powder, and increasing coverage area under the lead of the joint. Decrease in the solder powder particle size has only a slightly negative effect on voiding. The data indicate that voiding is also a function of the timing between the coalescing of solder powder and the elimination of immobile metallisation oxide. The sooner the paste coalescence occurs, the worse the voiding will be. Increase in voiding is usually accompanied by an increasing fraction of large voids, suggesting that factors causing voiding will have an even greater impact on the joint reliability than shown by the total‐ void‐volume analysis results. Preliminary data suggest that certain predry treatment and flux solvent with higher boiling point appear to cause increased voiding.

We provide a method for automatically extending small‐strain state‐update algorithms and their correspondent consistent tangents into the finite deformation range within the framework of multiplicative plasticity. The procedure, when it applies, operates at the level of kinematics and, hence, can be implemented once and for all independently of the material‐specific details of the constitutive model. The versatility of the method is demonstrated by a numerical example.

The purpose of this paper is to perform a numerical assessment of two recently proposed extensions of the Gurson‐Tveegard‐Needleman ductile damage constitutive model under low stress triaxiality.

One of the most widely used ductile damage models is the so‐called Gurson‐Tveegard‐Needleman model, commonly known as GTN model. The GTN model has embedded into its damage formulation the effects of nucleation, growth and coalescence of micro‐voids. However, the GTN model does not include void distortion and inter‐void linking in the damage evolution. To overcome this limitation, some authors have proposed the introduction of different shear mechanisms based on micromechanical grounds or phenomenological assumptions. Two of these constitutive formulations are reviewed in this contribution, numerically implemented within a quasi‐static finite element framework and their results critically appraised.

Through the analysis of the evolution of internal variables, such as damage and effective plastic strain, obtained by performing a set of numerical tests using a Butterfly specimen, it is possible to conclude that the extended GTN models are in close agreement with experimental evidence.

Even though the results obtained with the modified GTN models have shown improvements, it can also be observed that both shear mechanisms have inherent limitations in the prediction of the location of fracture onset for some specific stress states.

From the results reported, it is possible to identify some shortcomings in the recently proposed extensions of the GTN model and point out the direction of further improvements.

Lead‐free soldering is becoming a common practice in the electronics industry because of the growing general opposition to lead‐containing solders. The reliability of lead‐free solders has been studied a lot recently, but knowledge of it is still incomplete and many issues related to them are under heavy debate. This paper presents results from a study of the formation of voids with regard to the number of reflow cycles in three different kinds of solder joints: first the ones prepared with lead‐free solder paste and lead‐free plastic ball grid array (PBGA) components, next the ones prepared with lead‐free solder paste and tin‐lead‐silver PBGA components, and last the ones prepared with tin‐lead solder paste and tin‐lead‐silver PBGA components.

This paper aims to present a geometrical void model in conjunction with a multiscale method to evaluate the effect of interraster distance, bead (raster) width and layer height, on the voids concentration (volume) and subsequently calculate the final mechanical properties of the fused deposition modeling parts at constant infill.

A geometric model of the voids inside the representative volume element (RVE) is combined with a two-scale asymptotic homogenization method. The RVEs are subjected to periodic boundary conditions solved by finite element (FE) to calculate the effective mechanical properties of the corresponding RVEs. The results are validated with literature and experiments.

Bead width from 0.2 to 0.3 mm, reported a decrease of 25% and 24% void volume for a constant layer height (0.1 and 0.2 mm – 75% infill). It is reported that the void’s volume increased up to 14%, 32% and 36% for 75%, 50% and 25% infill by varying layer height (0.1–0.2  and 0.3 mm), respectively. For elastic modulus, 14%, 9% and 10% increase is reported when the void’s volume is decreased from 0.3 to 0.1 mm at a constant 75% infill density. The bead width and layer height have an inverse effect on voids volume.

This work brings values: a multiscale-geometric model capable of predicting the voids controllability by varying interraster distance, layer height and bead width. The idealized RVE generation slicer software and Solidworks save time and cost (<10 min, $0). The proposed model can effectively compute the mechanical properties together with the voids analysis.

The fracture mechanism of S-07 steel was investigated by observing the fracture surface of the specimens with scanning electron microscope (SEM). Furthermore, the overall elastic–plastic behaviors and the stress state evolution during the loading procedure of all specimens were simulated by FE analysis to obtain the local strain at crack nucleated location and the average triaxiality of each type of specimen.

Three types of tests under various stress states were performed to study the ductile fracture characteristics of S-07 high strength steel in quasi-static condition.

Under tensile and torsion loading conditions, S-07 steel exhibits two distinctive rupture mechanisms: the growth and internal necking of voids governs the rupture mechanism in tension dominated loading mode, while the change of void shape and internal shearing in the ligaments between voids dominants for shear conditions.

The failure criterion for S-07 steel considering the influence of the triaxial stress state was established.

This study aims to examine both the population balance approach based on the MUltiple SIze Group (MUSIG) model and the average bubble number density transport equation (ABND) model for 3D, low pressure, gas‐liquid, subcooled boiling, vertical flows. The purpose is to assess the ability of both models to predict the radial profile of void fraction, bubble Sauter mean diameter and interfacial area concentration which characterise subcooled boiling.

Improvement in the ABND model to simulate gas‐liquid bubbly flows with heat transfer was achieved by combining the condensation expression with the gaseous mass transport equation within the CFD commercial code CFX4.4.

Overall, both the ABND model and the MUSIG model provided good results in terms of the above‐mentioned criteria when compared against experimental measurements. However, the ABND model was found to have limitations in predicting high‐subcooled boiling flows due to the lack of bubble size resolution to adequately capture the effect of condensation over a range of bubbles sizes.

It is shown that the ABND model provides an economic alternative to the MUSIG model in terms of complexity and computational time, as long as one is aware of the limitations in simulating high‐subcooling flow regimes.

The purpose of this paper is to investigate the strain distribution, stress-based fracture limit and corrosion behaviour of titanium Grade 2 sheets during single point incremental forming (SPIF) process, with various computerized numerical control (CNC) spindle rotational speeds and step depths. The development of corrosion pits in 3.5 (%) NaCl solution has also been studied during the SPIF process.

A potentiodynamic polarization (PDP) study was performed to investigate the corrosion behaviour of titanium Grade 2 deformed samples, with various spindle rotational speeds in 3.5 (%) NaCl solution. The scanning electron microscope (SEM) and transmission electron microscope (TEM) analysis was carried out to study the fracture behaviour, dislocation densities and corrosion morphology of deformed samples.

The titanium Grade 2 sheets exhibited better strain distribution, fracture limit and corrosion resistance by increasing the CNC spindle rotational speeds, tool diameters and vertical step depths (VSD). It was recorded that varying the spindle speed affected plastic deformation which in turn affected corrosion rate.

In this study, poor corrosion rate was observed for the as-received condition, and better corrosion rate was achieved at maximum speed of 600 rpm and 0.6 mm of VSD in the deformed sheet. This indicates that corrosion rate improved with increase in the plastic deformation. The EDS analysis report of corroded surface revealed the composition to be mainly of titanium and oxides.

This study discusses the strain distribution, stress-based fracture limit and corrosion behaviour by using titanium Grade 2 sheets during SPIF process.

This study is useful in the field of automobile and industrial applications.

With an increase in the spindle rotational speeds and VSD, the titanium Grade 2 sheets showed better strain distribution, fracture limit and corrosion behaviour; the same is evidenced in fracture limit curve and PDP curves.