Three-dimensional process cycle simulation of composite parts manufactured by resin transfer molding

A process cycle of resin transfer molding (RTM) consists of two sequential stages, i.e. filling and curing stages. These two stages are interrelated in non-isothermal processes so that the curing stage is dominated by the resin flow as well as temperature and conversion distributions during the filling stage. Therefore, it is necessary to take into account both filling and curing stages to analyze the process cycle accurately. In this paper, a full three-dimensional process cycle simulation of RTM is performed. Full three-dimensional analysis is necessary for thick parts or parts having complex shape. A computer code is developed based on the control volume/finite element method (CV/FEM). The resulting computer code can provide information regarding flow progression and pressure field during mold filling; and temperature distribution and degree of cure distribution for a process cycle. The computer code can also be used for process cycle simulation of composite structures with complex geometry and with various molding strategies including switching injection strategy, multiple gate injection strategy and variable mold wall temperature. Numerical examples provided in the present work show the capabilities of the computer code in analyzing the process cycle.     

Development of adaptive injection flow rate and pressure control algorithms for resin transfer molding

To prevent dry spot formation during fabrication of composite parts by Resin Transfer Molding (RTM), a control interface and four different adaptive control algorithms have been developed and tested with numerical simulations. The interface is capable of controlling the flow pattern of resin as it fills a mold containing a preform of fiber reinforcement, provided that the mold is equipped with multiple inlet gates, a single vent and a spinal sensor system that continuously feeds the interface with the resin flow front locations along the spine lines connecting the inlet gates to the vent. Four different adaptive control algorithms targeting on injection flow rate control, injection pressure control, linearly-corrected pressure control, and the combined flow rate and linearly-corrected pressure control have been proposed and incorporated with the control interface. To provide desirable controllability of the filling process and effective utilization of the resin dispensing equipment, the final formulations were optimized by means of numerical simulations of a rectangular RTM part containing different permeability distributions. The results were compared to investigate the strengths and weaknesses of the spinal adaptive control algorithms in terms of dry spot size, filling speed, and the minimum responding speed of injection pump. Finally, a complex geometry case study was conducted to validate and highlight the spinal adaptive control algorithms’ capability in handling flow disturbance for a complex RTM mold filling process which involves irregular mold geometry, multiple inserts, significant permeability and racetracking variations, and non-straight spinal sensors.     

Novel discretization methods for improved simulation precision in injection molding

Mold filling is an important stage of injection molding, which is one of the most commonly used manufacturing processes for the production of thermoplastic components in high volumes. As a consequence, the numerical simulation of this process based on computational fluid dynamics (CFD) is of great significance for production engineering [1, 2]. However, modeling of the mold filling is a tremendously demanding process, when considering interfacial physical phenomena, such as two‐phase flows, building a sharp interface between the molten plastics and the present air in the cavity or the dynamic wetting contact line at the cavity surface. A method for dealing with these phenomena is a local mesh refinement both in space and time. In this paper, the numerical solution of a mold filling problem using simplex‐type space‐time finite elements is presented and compared with experiments. These elements can be suited to increase efficiency, when used for the aforementioned refinement. In addition, a Navier's slip boundary condition is applied to the solid boundaries of the mold allowing the contact line to evolve along the boundary, while enabling a better prediction of the pressure distribution. The presented work was performed in collaboration of the subprojects B3 and B5 of the collaborative research center 1120 “Precision Melt Engineering”.     

有限元网格对RTM充模模拟的影响

本工作基于有限元控制体积法编写了模拟程序,研究了节点数量、网格密度对模拟过程的影响.以带圆孔的长方形为例,模拟比较了不同网格密度和注入口位置对充模时间、流动前沿以及干点形成区域的影响.结果表明,节点数量增加到一定程度时,只延长计算时间,对充模时间影响很小;网格疏密分布影响流动前沿的位置,根据流动前沿的形状可以确定排气口的位置和数量.     

A 3-D,symmetric, finite element formulation of the Biot equations with application to acoustic wave propagation through an elastic porous medium

A weak solution of the coupled, acoustic-elastic, wave propagation problem for a flexible porous material is proposed for a 3-D continuum. Symmetry in the matrix equations; with respect to both volume, i.e. ‘porous frame’–‘pore fluid’, and surface, i.e. ‘porous frame/pore fluid’–‘non-porous media’, fluid–structure interaction; is ensured with only five unknowns per node; fluid pore pressure, fluid-displacement potential and three Cartesian components of the porous frame displacement field. Taking Biot's general theory as starting point, the discretized form of the equations is derived from a weighted residual statement, using a standard Galerkin approximation and iso-parametric interpolation of the dependent variables. The coupling integrals appearing along the boundary of the porous medium are derived for a number of different surface conditions. The primary application of the proposed symmetric 3-D finite element formulation is modelling of noise transmission in typical transportation vehicles, such as aircraft, cars, etc., where porous materials are used for both temperature and noise insulation purposes. As an example of an application of the implemented finite elements, the noise transmission through a double panel with porous filling and different boundary conditions at the two panel boundaries are analysed. © 1998 John Wiley & Sons, Ltd.     

Post-filling flow in vacuum assisted resin transfer molding processes: Theoretical analysis

For rigid mold filling processes such as resin transfer molding, the resin flow stops when the preform is fully saturated with the resin. However, in vacuum assisted resin transfer molding process (VARTM), due to preform deformation the resin flow continues after the filling stage is complete as it does take a finite time for the pressure field to become uniform during this post-filling period. In this paper, the post-filling flow in the VARTM process with and without the membrane is examined. The governing equations for post-filling flow, in which the preform is allowed to deform, are developed with simplifying assumptions. A one-dimensional flow and deformation coupled process model is developed to simulate the time dependent pressure distribution during the post-filling stage. The model is implemented using finite differences, both in time and space, and utilizes the explicit time integration which is found to be conditionally stable. The change in pressure inside the mold during the post-filling stage is predicted for three different injection scenarios. The influence of the pressure distribution at the end of filling on the dwell time for the pressure to equilibrate and on the final thickness of the part is discussed. The effects of change in preform permeability and compliance on the dwell time and thickness are demonstrated and the extension of the model to more complex geometries and systems is outlined.     

Finite elements with displacement interpolated embedded localization lines insensitive to mesh size and distortions

A new finite element formulation aimed at the solution of problems involving strain localization is presented. The proposed formulation incorporates displacement interpolated embedded localization lines. Results are shown to converge to an ‘exact solution’ when the mesh is refined and also to be quite insensitive to mesh distortions.     

A numerical study of filling process through multilayer preforms in resin injection/compression molding

In resin injection/compression molding (RI/CM), a preform often comprises layers of different fiber reinforcements. Each fiber reinforcement has unique through thickness and in-plane permeabilities as well as compressibility, creating a heterogeneous porous medium in the mold cavity. In the present article, numerical simulation is utilized to investigate the filling process of RI/CM in such a heterogeneous porous medium. The filling stage is simulated in a full three-dimensional space by using control volume/finite element method and based upon an appropriate filling algorithm. The flow in the open gap which may be present in the mold cavity is modeled by Darcy’s law using an equivalent permeability. Numerical simulations of filling process for preforms containing two and three layers of different reinforcements in various stacking sequences are conducted with the aid of computer code developed in this study. Results show that the injection time as well as flow front progression depends on fiber types in the whole preform, fiber stacking sequence and open gap provided in the mold cavity. Simulated results also suggest that the presence of open gap at top of reinforcement can lead to both low injection time and uniform flow pattern.     

Analysis of non-isothermal mold filling process in resin transfer molding (RTM) and structural reaction injection molding (SRIM)

In this paper, we present a modeling and numerical simulation of a mold filling process in resin transfer molding/structural reaction injection molding utilizing the homogenization method. Conventionally, most of the mold filling analyses have been based on a macroscopic flow model utilizing Darcy's law. While Darcy's law is successful in describing the averaged flow field within the mold cavity packed with a porous fiber preform, it requires experiments to obtain the permeability tensor and is limited to the case of porous fiber preform-it can not be used to model the resin flow through a double porous fiber preform. In the current approach, the actual flow field is considered, to which the homogenization method is applied to obtain the averaged flow model. The advantages of the current approach are: parameters such as the permeability and effective heat conductivity of the impregnanted fiber preform can be calculated; the actual flow field as well as averaged flow field can be obtained; and the resin flow through a double porous fiber preform can be modelled. In the presentation, we first derive the averaged flow model for the resin flow through a porous fiber preform and compare it with that of other methods. Next, we extend the result to the case of double porous fiber preform. An averaged flow model for the resin flow through a double porous fiber preform is derived, and a simulation program is developed which is capable of predicting the flow pattern and temperature distribution in the mold filling process. Finally, an example of a three dimensional part is provided.     

‘Infinite domain’ elements

A parametric element is formulated which enables the economic modelling of ‘infinite domain’ type problmes. A typical problem is an opening in a stress field in an infinite medium, either in two or three dimensions. The strategy is to model around the opening with two or three layers of conventional isoparametric finite elements and surround these with a single layer of ‘infinite domain’ elements. Several sample problems has been analysed for circular, square and spherical openings in infinite media, and the results compared with either theoretical or boundary element solutions which include the ‘infinite’ boundary in their solution technique.     

A fractal patch test

Element consistency is generally checked using the patch test on an element patch of finite size. This condition may in certain cases be too restrictive, and disqualifies elements that appear to be convergent. A method termed ‘fractal patch test’ is presented, in which the patch size is maintained constant while the distorted mesh is refined. Examples are given for four-node quadrilateral elements used in plane stress and strain analysis, and for plate bending elements.     

Pressure-driven mold filling model of aluminum alloy melt/semi-solid slurry based on rheological behavior

The pressure-driven mold filling ability of aluminum alloy melt/semi-solid slurry is of great significance in pressure casting processes, and the rheological behavior of the alloy has a crucial effect on the mold filling ability according to fluid dynamics. In this work, a pressure-driven mold filling model is first proposed based on the rheological behavior of the alloys. A356 alloy is employed as an example to clarify the rheological behavior of aluminum alloys, which obeys the power law model and is affected by temperature. The rheological behavior of the alloy in semi-solid state is modelled with the coupling of shear rate and temperature. The stop of mold filling attributes to the pressure loss which is caused by the viscosity during the flow of the melt/semi-solid slurry. Pressure loss caused by viscous flow and heat transfer between the alloy and the mold are calculated and coupled during the mold filling of the melt/semi-solid slurry. A pressure-driven mold filling model of aluminum alloy melt/semi-solid slurry is established based on steady-state rheological behavior. The model successfully predicts the filling length of melt/semi-solid slurry in pressure casting processes. Compared with the experimental results,the model can provide a quantitative approach to characterize the pressure-driven mold filling ability of aluminum alloy melt. The model is capable of describing the stop filling behavior of other aluminum alloys in pressure casting processes with corresponding rheological parameters and heat transfer coefficient.     

Application of calcium carbonate in resin transfer molding process: An experimental investigation

The resin transfer molding (RTM) process is used to manufacture advanced composite materials made of continuous glass or carbon fibers embedded in a thermoset polymer matrix. In this process, a fabric preform is prepared, and is then placed into a mold cavity. After the preform is compacted between the mold parts, thermoset polymer is transferred from an injection machine to the mold cavity through injection gate(s). Resin flows through the porous fabric, and eventually flows out through the ventilation port(s). After the resin cure process (cross‐linking of the polymer), the mold is opened and the part is removed. The objective of this study is to verify the application of calcium carbonate mixed in resin in the RTM process. Several rectilinear infiltration experiments were conducted using glass fiber mat molded in a RTM system with cavity dimensions of 320 × 150 × 3.6 mm, room temperature, maximum injection pressure 0.202 bar and different content of CaCO₃ (10 and 40%) and particle size (mesh opening 38 and 75 µm). The results show that the use of filled resin with CaCO₃ influences the preform impregnation during the RTM molding, changing the filling time and flow front position, however it is possible to make composite with a good quality and low cost.     

基于非结构自适应网格技术的高超声速流动数值模拟

发展了一种基于非结构网格的自适应方法,对高超声速无粘流场进行了数值模拟。根据流场参数的变化梯度确定加密边,由加密准则进行自适应网格剖分后得到分布合理的较密网格。通过预先生成的初始极密表面网格将边界的加密点投影到边界上,使得边界保持初始外形。通过求解三维Euler 方程,对三维双椭球高超声速绕流问题进行了数值模拟,计算结果和实验数据相吻合,表明了该文所建立方法的正确性和可靠性。     

Branch and bound search to optimize injection gate locations in liquid composite molding processes

In liquid composite molding (LCM) processes the resin is injected into a mold cavity containing pre-placed reinforcement fabrics through openings known as gates, and the air leaves the mold through openings called as vents. The gate and vent locations play a crucial role as to whether the resin covers all empty spaces between the fibers in the mold, which dictates the quality and the properties of the final product. Optimization methods are used to find the gate and vent locations that will create a favorable flow that will prevent dry spots. In this paper, branch and bound search is adapted to mold filling in LCM processes and is used to find the optimal injection gate location that fulfill two different objectives. First, to find the gate locations that will yield the shortest fill time. Second, to find the auxiliary gate locations that will counteract a disturbance during filling and minimize the size of the dry spot. In each case, three geometries have been studied. The results are compared with exhaustive search and genetic algorithms results to illustrate the efficiency and accuracy of branch and bound search method.     

Effect of gate size on the melt filling behavior and residual stress of injection molded parts

This paper studies the effects of gate size on the cavity filling pattern and residual stress of injection molded parts. A total of three rectangular gates with different sizes were used. Experiments were carried out by using a dynamic visualization system. A flow visualization mold was specially designed and made for this study. A high-speed video camera was used to record the mold filling phenomena of cavities with different gate size and different processing parameters. In addition, a Stress Viewer was used to characterize the residual stress of molded samples. It was found that the undersized gate has many adverse effects on the filling behavior and residual stress of molded parts. With a larger gate, the cavity will be filled faster and residual stress of parts may be smaller. The result of the study also indicates that nozzle temperature and injection rate can significantly affect the above two aspects.     

视窗化RTM工艺充模过程模拟仿真技术研究

根据RTM工艺树脂流动充模模型,研究和开发了基于FEM/CV算法的RTM工艺复杂渗流充模过程数值模拟软件平台-BHRTM-2。BHRTM-2在视窗系统下运行,带有FEM网格捕捉器窗口可直观方便地设置注射口、溢料口和工艺参数,操作简单,能够模拟复杂边界制件的树脂流动充模过程、显示充模过程中任意时刻模腔内压力的分布场、流动前峰和预测充模时间及可能的干斑缺陷位置,为RTM工艺设计与优化提供了有效技术手段。文中对BHRTM-2的模拟结果的正确性和可靠性进行了理论与实验验证,并给出了具体算例。      

Micro-mechanical finite element analysis of Z-pins under mixed-mode loading

This paper presents a three-dimensional micro-mechanical finite element (FE) modelling strategy for predicting the mixed-mode response of single Z-pins inserted in a composite laminate. The modelling approach is based upon a versatile ply-level mesh, which takes into account the significant micro-mechanical features of Z-pinned laminates. The effect of post-cure cool down is also considered in the approach. The Z-pin/laminate interface is modelled by cohesive elements and frictional contact. The progressive failure of the Z-pin is simulated considering shear-driven internal splitting, accounted for using cohesive elements, and tensile fibre failure, modelled using the Weibull’s criterion. The simulation strategy is calibrated and validated via experimental tests performed on single carbon/BMI Z-pins inserted in quasi-isotropic laminate. The effects of the bonding and friction at the Z-pin/laminate interface and the internal Z-pin splitting are discussed. The primary aim is to develop a robust numerical tool and guidelines for designing Z-pins with optimal bridging behaviour.     

塑料注射成型流动过程中温度场数值模拟

采用有限差分方法进行塑料注射成型流动过程中温度场的计算机模拟,对能量方程中瞬态项和热传导项分别采用向后差分和隐式差分近似;同时,为保证数值计算过程的稳定性,采用上风法处理对流项。最后讨论了数值求解的稳定性。     

The gradient of the finite element variational indicator with respect to nodal and applications in fracture mechanics and mesh optimization

We derive a closed-form expression for the change in the variational indicator of a finite element mesh with respect to perturbations in nodal point co-ordinates. The expression is evaluated very effectively from standard finite element data obtained in one solution, and may be easily programmed as part of a general finite element code. We present the derivation for two- and three-dimensional isoparametric elements used in linear and nonlincar elasticity. The expression has practical applications in the computation of stress intensity factors in fracture mechanics and in the determination of the ‘optimal’ mesh with a given element-node connectivity. We demonstrate both applications by accurately determining the stress intensity factor of a Mode I crack using a finite element mesh which was improved using mesh optimization.