Numerical prediction of saturation in dual scale fibrous reinforcements during Liquid Composite Molding

This paper presents a fractional flow model based on two-phase flow, resin and air, through a porous medium to simulate numerically Liquid Composites Molding (LCM) processes. It allows predicting the formation, transport and compression of voids in the modeling of LCM. The equations are derived by combining Darcy’s law and mass conservation for each phase (resin/air). In the model, the relative permeability and capillary pressure depend on saturation. The resin is incompressible and the air slightly compressible. Introducing some simplifications, the fractional flow model consists of a saturation equation coupled with a pressure/velocity equation including the effects of air solubility and compressibility. The introduction of air compressibility in the pressure equation allows for the numerical prediction of the experimental behavior at low constant resin injection flow rate. A good agreement was obtained between the numerical prediction of saturation in a glass fiber reinforcement and the experimental observations during the filling of a test mold by Resin Transfer Molding (RTM).     

Simulation of coupling filtration and flow in a dual scale fibrous media

In this article, numerical simulation of suspension (particles filled-resin) flow through a fibrous media taking into account dual scale porosity in LCM (Liquid Composite Molding) processes is presented. During the flow, a strong interaction between the particle motion and the fluid flow takes place at the porous media wall (the fiber bundle surface). In this study, the Stokes–Darcy coupling is used to describe the resin flow at mesoscopic scale to treat the particles in suspension. A “fluid” model to describe the suspension flow, a “filtration” model to describe the particle capture and a “solid” model dedicated to the modeling of mass particles dynamics was used. The “solid” model is also operated to identify the particles retention.For validation, the numerical results of proposed model were compared with the experimental results from the literature and found in good agreement. Then, other numerical results studying the suspension’s rheological behavior are presented.     

An optically-based inverse method to measure in-plane permeability fields of fibrous reinforcements

Structural composite manufacturing relying on Liquid Composite Molding technologies is strongly affected by local variability of the fibrous reinforcement. Optical techniques using light transmission are used and allow field measurements of areal weight (and fibre volume fraction) of glass fibre reinforcement. The coupling of obtained areal weight mappings along with injection flow fronts is used to extract in-plane permeability fields. The current work presents results with a focus on glass random mats, but the method can be adapted to any glass fibrous medium. A study of convergence and error due to discretization is performed. Also the influence of the stacking of fibrous layers on the preform variability is analyzed. The major advantage of the proposed technique is a relatively fast acquisition of statistical data on reinforcement variability, which can be later utilized in stochastic based process simulations.     

Optimization of injection flow rate to minimize micro/macro-voids formation in resin transfer molded composites

Resin transfer molding (RTM) has become one of the most widely used processes to manufacture medium size reinforced composite parts. To further enhance the process yield while ensuring the best possible quality of the produced parts, physically based optimization procedures have to be devised. The filling of the mold remains the limiting step of the whole process, and the reduction of the filling time has an important impact on the overall cost reduction. On the other hand, the injection cycle has to be appropriately carried out to ensure a proper fiber impregnation. Indeed, a partial fiber impregnation leads to the creation of micro-scopic and macro-scopic voids.In the present work, based on a double scale flow model and the capillary number Ca, an optimization algorithm is proposed to minimize the micro/macro-voids in RTM composite parts. The optimized injection flow rate ensures an optimum Ca at the flow front during part filling. The implemented algorithm allows the use of various constraints such as maximum capabilities of the injection equipment (i.e., maximum pressure or flow rate at the injection gates) or maximum velocity to avoid fiber washing. Bounded by these constraints, the optimization procedure is devised to handle any injection configuration (i.e., injection gates or vents locations) for two or three-dimensional parts. The numerical model is based on a mixed (FE/CV) formulation that uses non-conforming elements to ensure mass conservation. The proposed algorithm is tested for two and three-dimensional parts while emphasizing the important void reduction that results from the optimized injection cycle.     

Intermetallic and void formation in gold wirebonds to aluminum films

Gold ball bonds attached to either pure Al films or Al films with Cu and Si additions were annealed at temperatures in the range 77–277°C for periods of up to 3,000 h and then shear tested. The resulting fracture surfaces were observed to change progressively with time and temperature of annealing. The intermetallic phases and voids present after each annealing treatment were characterized by microscopic examination of the bond cross sections. Shear test results are discussed in terms of the observed microstructures.     

Numerical simulation of void formation in LCM

The existence of void type defects in composite laminates manufactured using the liquid composite molding process alters the mechanical characteristics of the final product. The object of this paper is to present a procedure to simulate mold filling and to incorporate void formation. The model is composed of a unique combination of robust and accurate numerical algorithms for solving the transport equation. The saturation ratio is a macroscopic entity yet it is clearly the consequence of microscopic phenomena and especially of air entrapment within tows, hence the presence of micropores. In the model, the source term is dependent on the capillary number and is related to the micro–macro scale effects with the dual-porosity. The unsaturated flow and transport model was applied to a problem and was found to produce accurate, mass conserving solutions when compared to experimental results in void content.     

Influence of fabric shear and flow direction on void formation during resin transfer molding

In resin transfer molding, void type defect is one of common process problems, it degenerates the mechanical performances of the final products seriously. Void content prediction has become a research hotspot in RTM, while the void formation when the flow direction and the tow direction are not identical or the fabric is sheared has not been studied to date. In this paper, based on the analysis of the resin flow velocities inside and outside fiber tows, a mathematical model to describe the formation of micro- and meso-scale-voids has been developed. Particular attention has been paid on the influence of flow direction and fabric shear on the impregnation of the unit cell, so their effects on the generation and size of voids have been obtained. Experimental validation has been conducted by measuring the formation and size of voids, a good agreement between the model prediction and experimental results has been found.     

Effect of scale size,orientation type and dispensing method on void formation in the CUF encapsulation of BGA

Prediction of void occurrence during capillary underfill encapsulation process is vital to avoid package failure due to incomplete filling during the encapsulation process. Two design variables, namely the gap height and package orientations, together with different types of industrial standard design of dispensing methods were identified as possible influences to the void formation in encapsulated package. In this paper, all these factors have been closely related to the void formation and subsequently the best chip design has been formulated to improve package reliability. From the study, air entrapment is clearly visualized in the experiment, which can be detrimental as it contains trapped oxygen, which can combust at high temperature. A series of experiments eventually showed higher possibility of air void formation by U-type dispensing method compared with the L-type dispensing method. In addition, it is found that the chip design parameters that include the scaling size and ball grid array orientation have an effect on the size of void formed. Our experimental findings were validated using lattice-Boltzmann method simulation and great consensus is found between both approaches. These findings provide additional insights to the electronic packaging developer to effectively reduce the formation of void during encapsulation process.     

Simulation of void formation in liquid composite molding processes

Air entrapment within and between fiber tows during preform permeation in liquid composite molding (LCM) processes leads to undesirable quality in the resulting composite material with defects such as discontinuous material properties, failure zones, and visual flaws. Essential to designing processing conditions for void-free filling is the development of an accurate prediction of local air entrapment locations as the resin permeates the preform. To this end, the study presents a numerical simulation of the infiltrating dual-scale resin flow through the actual architecture of plain weave fibrous preforms accounting for the capillary effects within the fiber bundles. The numerical simulations consider two-dimensional cross sections and full three-dimensional representations of the preform to investigate the relative size and location of entrapped voids for a wide range of flow, preform geometry, and resin material properties. Based on the studies, a generalized paradigm is presented for predicting the void content as a function of the Capillary and Reynolds numbers governing the materials and processing. Optimum conditions for minimizing air entrapment during processing are also presented and discussed.     

A comparison of rescheduling policies for online flow shops to minimize tardiness

In practical situations, flow shops usually have some policies on rescheduling previously scheduled jobs. This article compares three of these rescheduling policies: an unrestricted one where previously scheduled jobs can be moved freely, one where jobs can only be moved forward in the schedule, and one where jobs that have already been scheduled cannot be moved at all. The comparison is performed by considering the minimization of tardiness. While unrestricted rescheduling should generally give the best solution, moving jobs only forward can be more practical as in general production, material orders can be delayed but seldom advanced. This article points out that moving jobs only forward is not significantly worse than the unrestricted scheduling. When cases with small numbers of jobs and machines are analysed both policies give similar tardiness. Numerical experiments show that the differences between these two rescheduling policies are rather small in larger problems as well.     

MD simulation of atom-order void formation in Ni fcc metal

Atom-order void formation in a defective crystalline material is studied by using molecular dynamics method (MD). Infinite long cylinder, which is constructed with nickel atoms with a line of vacancies, is subjected to multiaxial tensile strain field by moving periodic boundary and the atoms on the outer surface of the cylinder. When the load exceeds a critical value, sudden appearance of the void is observed and it develops rapidly. The developed void does not disappear by only unloading and relaxation, in spite of the system with the void has higher potential energy than that without void. The biaxial or the triaxial load is necessary to the atom order void formation. Moreover, the results by the MD simulations are compared with theoretical solution for nonlinear elastic solid. Received 26 August 1999     

Prediction of ductile fracture in axisymmetric tension by void coalescence

Fracture strains are predicted for ductile materials undergoing void growth and coalescence. The calculation scheme is based on Gurson–Tvergaard yield function and its associated flow rule. Fracture condition is identified by vanishing stress-carrying capacity of the material. The plastic flow parameters are all determined from experimental evidences for a variety of alloys. Comparison among predicted fracture strains and experimental ones is given for a wide range of conventional and superplastic materials as well as powder compacts. Finally an approximate fracture criterion is proposed.     

Application of electrical capacitance tomography to the void fraction measurement of two-phase flow

Based on the electrical capacitance tomography technique, a new method for the void fraction measurement of two-phase flow is proposed. A 12-electrode void fraction measurement system is established. A mathematical model of image reconstruction of electrical capacitance tomography is developed. To obtain the quantitative information of two-phase flow, combining the Tikhonov regularization principle and the algebraic reconstruction technique algorithm, a new image reconstruction algorithm is presented. The experimental results show that the accuracy of void fraction measurement is satisfactory. The proposed method is suitable for the void fraction measurement of many kinds of two-phase flow.     

Use of Centroidal Voronoi Diagram to find optimal gate locations to minimize mold filling time in resin transfer molding

In Resin Transfer Molding (RTM) processes, liquid resin is injected into a dry reinforcement structure to create a composite part within given time limits. To reduce the fill time, resin may be injected into the mold through multiple gates. The minimum number of gates and their locations needs to be determined. To reduce the number of scenarios to be simulated, an iterative method is implemented for multiple-gate injection optimization. The inlet nodes on the mesh surface are used to generate a Voronoi Diagram of the mold geometry. Then the optimal Centroidal Voronoi Diagram (CVD) of the mold surface is searched iteratively. It is shown that the generation points associated with the optimal CVD correspond with the gate locations that yield the shortest fill time. The results are compared with exhaustive search and genetic algorithms results to illustrate the efficiency and accuracy of CVD method.     

Experimental measurement of void fraction in cryogenic two phase upward flow

Experimental measurements of the void fraction in two-phase single component upward flow of both helium and nitrogen were carried out using the capacitance probe technique. An electronic circuit was designed and constructed to accurately detect small changes in the dielectric constant resulting from changes in density in the two-phase flow. A coaxial capacitance probe at the exit of the test section was used as the sensing element to pick up changes in void fraction.Tests were carried out at both adiabatic and diabatic conditions on two test section sizes (6.35 and 2.75 mm id and each 1000 mm long) with exit quality ranging from 0 to 100%, liquid flow of 5 to 35 lh^?1 and inlet pressures of 1 to 2 atm.Analysis of the data indicates that the slip ratio (obtained from quality and void fraction measurements) is affected primarily by pressure, mixture quality, superficial velocity and to a lesser degree by the size of the test section.The data of helium and nitrogen is also compared with the predictions of Lockhart-Martinelli, Levy and the homogeneous models.     

Bottleneck-based heuristics to minimize tardy jobs in a flexible flow line with unrelated parallel machines

This paper develops new bottleneck-based heuristics with machine selection rules to solve the flexible flow line problem with unrelated parallel machines in each stage and a bottleneck stage in the flow line. The objective is to minimize the number of tardy jobs in the problem. The heuristics consist of three steps: (1) identifying the bottleneck stage; (2) scheduling jobs at the bottleneck stage and the upstream stages ahead of the bottleneck stage; (3) using dispatching rules to schedule jobs at the downstream stages behind the bottleneck stage. A new approach is developed to find the arrival times of the jobs at the bottleneck stage, and two decision rules are developed to schedule the jobs on the bottleneck stage. This new approach neatly overcomes the difficulty of determining feasible arrival times of jobs at the bottleneck stage. In order to evaluate the performance of the proposed heuristics, six well-known dispatching rules are examined for comparison purposes. Six factors are used to design 729 production scenarios, and ten test problems are generated for each scenario. Computational results show that the proposed heuristics significantly outperform all the well-known dispatching rules. An analysis of the experimental factors is also performed and several interesting insights into the heuristics are discovered.     

Diameter dependence of the void formation in the oxidation of nickel nanowires

In this work, we show how the vacancy diffusion length scale must be considered, in the context of the diameter of a nanowire, when utilizing the Kirkendall phenomenon in the fabrication of metal oxide nanotubes starting from metal nanowires. We find that the diameter of the nanowire relative to the diffusion length scale of the vacancy will affect greatly the type of voids that can be generated. By using a larger diameter nickel nanowire, we show that segmented heterojunction void formation can be avoided and that the resulting structure will serve as a precursory 'template' for subsequent oxidation processes at high temperatures. In doing so, we can prevent the formation of bamboo-like structures and obtain uniform nickel oxide nanotubes through direct oxidation that has proven to be difficult previously. The result from this work is also significant as the interplay of vacancy diffusion length and nanostructure dimension is important in the oxidation of other types of metal nanostructures, especially when void formation and the Kirkendall effect are involved.     

Turbulent flow of a fibrous suspension in a pipe

The Henky-Ilyushin equations are used to describe the steady turbulent flow of an incompressible viscoplastic fluid in a pipe. A fibrous suspension is examined as the fluid.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 58, No. 2, pp. 223–229, February, 1990.     

利用注水前缘监测技术跟踪水推速度

讨论了红032井区注水前缘分布及微地震监测结果。结果表明,微地震注水前缘监测结果与油田地质数值模拟结果、地震波幅分布结果一致。由微地震监测结果可以确定注入水推进位置,为油田注水方案调整、改进注采措施、提高注水效率提供依据。     

Flow modeling of linear and nonlinear fluids in two scale fibrous fabrics

The fundamental macroscopic material property needed to quantify the flow in a fibrous medium viewed as a porous medium is the permeability. Composite processing models require the permeability as input data to predict flow patterns and pressure fields. As permeability reflects both the magnitude and anisotropy of the fluid/fiber resistance, efficient numerical techniques are needed to solve linear and nonlinear homogenization problems online during the flow simulation. In a previous work the expressions of macroscopic permeability were derived in a double-scale porosity medium for both Newtonian and rheo-thinning resins. In the linear case only a microscopic calculation on a representative volume is required, implying as many microscopic calculations as representative microscopic volumes exist in the whole fibrous structure. In the non-linear case, and even when the porous microstructure can be described by a unique representative volume, microscopic calculation must be carried out many times because the microscale resin viscosity depends on the macroscopic velocity, which in turn depends on the permeability that results from a microscopic calculation. Thus, a nonlinear multi-scale problem results. In this paper an original and efficient offline-online procedure is proposed for the efficient solution of nonlinear flow problems in porous media.