Optimal curing for thermoset matrix composites: Thermochemical considerations

A design sensitivity analysis is used to optimize the applied wall temperature vs. time in autoclave curing for thermoset matrix composites. The calculation minimizes the cure time and obeys a maximum temperature constraint in the composite. The transient, coupled thermal and cure problem is solved by a finite element method. Design sensitivity information is extracted efficiently from this primal analysis, based on an analytical, direct differentiation approach. The sensitivities are then used with gradient‐based optimization techniques to systematically improve the curing process. The optimal cure cycles for different numbers of temperature dwells may be similar (for a 2 mm thick part) or very different (for a 4 cm thick part), depending on the nature of the problem. In the latter case a large reduction of cure time is obtained when a three‐dwell cure cycle is used, and the optimizer has more flexibility to adjust the cure cycle. This systematic optimization approach provides a powerful and practical means of optimizing composite manufacturing processes.     

Preform shape and operating condition optimization for the stretch blow molding process

In this work, a new design approach was developed to automatically and consecutively predict optimal preform geometry and optimal operating conditions for the stretch blow molding process. The numerical approach combines a constrained gradient‐based optimization algorithm that iterates automatically over predictive finite element software. The strategy allows for targeting a specified container thickness distribution by manipulating consecutively the preform geometry (thickness and shape) and the operating parameters subject to process and design constraints. For the preform shape optimization, the preform geometry is mathematically parameterized for simplified treatment and the corresponding sensitivities are evaluated using a finite difference technique. A finite difference technique is also employed for the operating condition optimization. The constrained optimization algorithms are solved via the use of the sequential quadratic programming method that updates the design variables accordingly. Predicted optimization results obtained on an industrial case are presented and discussed to assess the validity when compared to experimental results and the robustness of the proposed approach. POLYM. ENG. SCI., 47:289–301, 2007. © 2007 Society of Plastics Engineers.     

Consolidation simulation of composite laminates: Formulation and validation verification

Advanced fiber‐reinforced polymer composites have been increasingly used in various structural components. One of the important processes to fabricate high‐performance laminated composites is an autoclave‐assisted prepreg lay‐up. Since the quality of laminated composites is largely affected by the cure cycle, selection of the cure cycle for each application is important and must be optimized. Thus, some fundamental model of the consolidation and cure processes is necessary to properly select the suitable parameters for each application. This article is concerned with the “flow‐compaction” model during the autoclave processing of composite materials. By using a weighted residual method, a two‐dimensional finite element formulation for the consolidation process of thick thermosetting composites is presented and the corresponding finite element code is developed. Numerical examples, including comparison of the present numerical results with one‐dimensional and two‐dimensional analytical solutions, are given to indicate the accuracy and effectiveness of the finite element formulation. In addition, a consolidation simulation of AS4/3501‐6 graphite/epoxy laminate is performed and is compared with the experimental results available in the literature. POLYM. COMPOS., 26:813–822, 2005. © 2005 Society of Plastics Engineers     

Cure simulations of thick adhesive bondlines for wind energy applications

Curing of adhesive bondlines is a critical and time-consuming operation in wind turbine blade manufacturing. Significant variation in adhesive thickness can lead to important differences in thermal histories trough the adhesive bonds due to the exothermic nature of the cure process. Reducing bondline cure cycle time and avoiding adhesive overheating are two competing factors in the design of cure temperature cycles. Predictive models on the impact of adhesive thickness variability in bondline cure temperature cycle is currently limited. Adhesive curing and temperature evolution can be simulated by finite element (FE) models coupling the heat transfer problem with the cure kinetics of the adhesive. The cure kinetics of the adhesive system was characterized by isothermal differential scanning calorimetry experiments and implemented in the FE software Abaqus/CAE by user subroutines. Predictions from the FE model were validated experimentally against temperature readings from the curing of 10, 20, and 30 mm thick adhesive bondlines. To highlight the role that predictive models potentially have in the optimization of bondline cure cycles a 2D cross section model representing the trailing edge of a wind turbine blade was used as case study. It was demonstrated that computational models enable customizing cure profiles for nonuniform adhesive thicknesses, ensuring fully cured bondlines with acceptable mechanical properties.     

Optimal cure cycles for the fabrication of thermosetting-matrix composites

Polymer-matrix composites using thermosetting resins as the matrix are increasingly finding use. However, a major impediment to their widespread commercial use is the high cost associated with their manufacture, arising from the long processing cycle times. This paper addresses the problem of determining cure temperature and pressure variations with time for a time-optimal manufacture of thermosetting-matrix composites subject to practical constraints. The optimal cure cycles are determined using the nonlinear programming scheme of sequential quadratic programming combined with a physical model base to simulate the process phenomena. The optimized cycles are shown to improve upon the manufacturer-recomended cycles as well as the improved cycles reported in the literature. The optimization results are reported for a wide range of resin materials, product specifications, and process constraints to illustrate their effects on the optimal cure cycles. Parametric studies are presented in terms of dimensionless groups to assess the combined effects of the product and process variables on the optimal cycles in a generalized manner.     

Optimal cure steps for product quality in a tire curing process

Numerical algorithms and computer programs have been developed to determine optimal cure steps in a tire curing process. A dynamic constrained optimization problem was formulated with the following ingredients: (1) an objective function that measures product quality in terms of final state of cure and temperature history at selected points in a tire; (2) constraints that consist of a process model and temperature limits imposed on cure media; (3) B‐splines representation of a time‐varying profile of cure media temperature. The optimization problem was solved using the complex algorithm along with a finite element model solver. Numerical simulations were carried out to demonstrate the procedure of determining optimal cure steps for a truck/bus radial tire. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 74: 2063–2071, 1999     

Resin flow analysis in the consolidation of multi-directional laminated composites

Advanced fiber reinforced polymer composites have been increasingly used in various structural components. One of the important processes to fabricate high performance laminated composites is an autoclave assisted prepreg lay-up. Since the quality of laminated composites is largely affected by the cure cycle, selection of the cure cycle for each application is important and must be optimized. Thus, some fundamental model of the consolidation and cure processes is necessary to properly select the suitable parameters for each application. This study applied the theory of consolidation and flow in a porous medium to provide a general model for the three-dimensional consolidation process of the laminates with fibers reinforced in multi-directions. Based on the model analysis, one can predict the pressure, velocity, and laminate thickness during consolidation process, which, as coupled with the curing analysis, can be used to properly select the cure cycle for applications of laminated composites.     

Experimental characterization of autoclave-cured glass-epoxy composite laminates: Cure cycle effects upon thickness,void content,and related phenomena

This article presents results from over 100 experimental autoclave curing fiber-glass-epoxy composite laminate curing runs. The primary objective was to verify shrinking horizon model predictive control—SHMPC—for thickness and void content control, using readily available secondary measurements. The secondary objective was to present and analyze the extensive experimental results obtained through this verification. Seven series of curing runs (16 per series) were performed, with cure settings governed by partial- or full-factorial orthogonal array based design of experiments. Through t-tests and two-way analysis of variance, it was found that pressure magnitude had the largest influence on laminate thickness and void content, while first hold duration/temperature, pressure application duration, and run delay influenced void content more than thickness. Thinner laminates with lesser void contents resulted from pressure application before the second temperature ramp. Prepreg age also affected thickness and void content. Photomicrographs revealed not one large void, but void clusters. Interrupted autoclave cure cycles revealed that significant laminate thickness reduction occurred during all curing cycle stages. The percentage of resin weight loss through laminate sides increased with pressure magnitude and application duration. Ten test curing runs indicated that SHMPC met difficult thickness targets while minimizing void content.     

Pressure window analysis for thin laminated composites in autoclave process

The curing temperature, pressure, and curing time have significant influence on finished thermosetting composite products. The external pressure and the time of pressure application are two major factors affecting the laminate thickness, fiber volume fraction, and void content. Based on the resin flow/fiber compaction model and corresponding program developed by our group, the genetic algorithm is accepted to design the pressure window for the consolidation of thin laminate. The objective of the optimization is to find the time of pressure application that achieves the desired average fiber volume fraction under given pressure. The pressure windows are analyzed for S‐2 glass fiber/5228 and T700S/5228 laminates with unidirectional and bidirectional lay‐up. It is found that no special viscosity region can be defined as pressure window for many factors affecting the consolidation process. The fiber and lay‐up type largely affect the time of pressure application. For laminates with the same fiber and lay‐up type, the fiber distribution is not much influenced by pressure cycle. The uneven degree of fiber distribution is larger for the fiber bed having higher deformation properties. With the genetic algorithm optimization system, the time of pressure application can be gotten quickly. It is helpful for the improvement of composite parts quality, reduction of the fabrication cost. POLYM. COMPOS., 2009. © 2008 Society of Plastics Engineers     

Numerical simulation of two‐dimensional flow and compaction during the consolidation of laminated composites

A new special finite element formulation and code are developed to simulate the two‐dimensional flow and compaction process during the autoclave processing of complex fiber‐reinforced thermosetting composite laminates. The numerical model is based on the Biot's consolidation principle, the fluid continuity equation, and Darcy's law. The simulation is performed for Hercules AS4/3501‐6 laminates and the predicted results are in good agreement with the results available in the literature. The laminate thickness and fiber volume fraction distribution of cured laminates are investigated from both the experiments and the simulations for T700S/5228 laminates. The simulations and experimental results are in good agreement for all the studied cases. A significantly uneven degree of consolidation along the laminate thickness direction is observed, and it is necessary to optimize the cure cycle to get uniformly compact and good quality laminates. POLYM. COMPOS., 2008. © 2008 Society of Plastics Engineers     

Consolidation and cure simulations for laminated composites

Fiber reinforced polymer composites have been increasingly used in various structural components. One of the important processes for fabricating high performance laminated composites is autoclave assisted prepreg lay-up. Since the quality of laminated composites is largely affected by the cure cycle, selection of the cure cycle for each particular application is important and must be optimized. Thus, some fundamental model of the consolidation and cure processes is necessary to properly select the suitable parameters for each application. This study used the viscoelastic solid model for the consolidation of the laminate. In addition, variations of permeability and thermal properties caused by the change of the fiber volume content during the consolidation process were also included. Simulated thickness variations of epoxy continuous carbon fiber prepreg (AS4/3501-6 from Hercules) laminate under consolidation were compared to the experimental results to test the model. Based on the model analysis, one can predict the pressure, velocity, and laminate thickness during the consolidation process, which can be used to properly select the cure cycle for applications of laminated composites.     

Three-dimensional simulations of the curing step in the resin transfer molding process

The curing step in resin transfer molding process involves heat transfer coupled with the curing reaction of thermoset resin. In order to examine the curing behavior under a specified cure cycle in the resin transfer molding process, numerical simulations are carried out by three-dimensional finite elements method. An experimental study for isothermal cure kinetics of epoxy resin is conducted by using differential scanning calorimetry. Kinetic parameters based on the modified Kamal model are determined from the calorimetric data for the epoxy system, and by using these parameters, numerical simulations are performed for a hat-shaped mold. It is found from the simulation results that the temperature profile and the degree of cure are well predicted for the region inside the mold. This numerical study can provide a systematic tool in the curing process to find an optimum cure cycle and a uniform distribution of the degree of cure.     

Simultaneous solution approach to model‐based experimental design

A model‐based experimental design is formulated and solved as a large‐scale NLP problem. The key idea of the proposed approach is the extension of model equations with sensitivity equations forming an extended sensitivities‐state equation system. The resulting system is then totally discretized and simultaneously solved as constraints of the NLP problem. Thereby, higher derivatives of the parameter sensitivities with respect to the control variables are directly calculated and exact. This is an advantage in comparison with proposed sequential approaches to model‐based experimental design so far, where these derivatives have to be additionally integrated throughout the optimization steps. This can end up in a high‐computational load especially for systems with many control variables. Furthermore, an advanced sampling strategy is proposed which combines the strength of the optimal sampling design and the variation of the collocation element lengths while fully using the entire optimization space of the simultaneous formulation. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4169–4183, 2013     

玻璃钢拉挤工艺过程非稳态温度场与固化度数值模拟与试验

玻璃钢拉挤成型过程中其固化度和温度变化为强耦合关系。根据固化动力学和传热学理论,建立了非稳态温度场与固化动力学数学模型。通过示差扫描量热实验计算出模型中固化动力学参数。采用有限元与有限差分相结合的方法,依据ANSYS求解耦合场的间接耦合法,编制了计算程序,对拉挤工艺不同工况玻璃钢非稳态温度场和固化度进行数值模拟。采用特殊设计制作的铝毛细管封装的布拉格光栅光纤传感器,屏蔽了荷载效应应变干扰,对玻璃钢温度场进行实时捡测;采用索氏萃取实验测定玻璃钢制品固化度。实验表明,模拟与实验结果基本吻合。为避开繁多试凑性实验而进行工艺过程优化提供理论依据。     

Development of heat-activated joining technology for composite-to-composite pipe using prepreg fabric

Owing to the lack of reliable and cost-effective joining methods, composite materials have not yet achieved their full market potential. The use of heat-activated thermal couplings offers a quick and cost-effective method for joining composite-to-composite pipe. In this study, a prepreg laminate containing thermoset resins and fiberglass reinforcements is wrapped around the ends of the components to be joined. A shrink tape, constructed of an oriented polyester film, is placed over the prepreg laminate. When heat is applied to the thermal coupling for curing, the shrink tape shrinks and compresses the prepreg to improve adhesion. Tests of the heat-activated thermal coupling in bending shows an increase of 29% over the currently used butt-weld method. A finite element model has been developed to assist in determining the most appropriate cure cycle required for different joint configurations. This reduces the need for experimentation when a variable has been changed. Based on the tested prepreg material properties and model, the FEA temperature distribution differs less than 10% from that of experimental results.     

Residual thermal stresses in bismaleimide/carbon fiber composite laminates

This is a study of residual thermal stresses in composite laminates, due to curing cycles. An extended formulation of Classical Lamination Theory (CLT) is adopted, which is able to take into account geometrical nonlinear effects owed to finite displacements. The approach is applied to square asymmetric laminates that have different dimensions and thicknesses. Final laminate shapes are evaluated after complete curing cycles; they can be cylindrical or saddle-like, and their equilibrium configuration stable or unstable depending on thickness vs. side length ratio. The same laminates are stacked, press-cured and the radii of curvature experimentally measured. In addition, they are modeled by means of finite element method (FEM) codes, using both linear and nonlinear techniques. Except for the thick laminates, the results obtained using nonlinear theoretical and numerical approaches show good agreement with experiment. Thermal residual strains are computed from non-mechanical strains by subtracting laminae free thermal deformations; the corresponding stresses are evaluated through layer stiffnesses. Residual stresses are evaluated both theoretically and experimentally. For thicker laminates the disagreement is mainly due to a mixed viscous phenomenon which takes place in resin interlaminar layers and matrix intralaminae. The share of relaxed stresses is evaluated and methods that include optimal cooling path techniques are suggested.     

Finite element modeling of curing of epoxy matrix composites

A two‐dimensional finite element model is developed to simulate and analyze the mechanisms pertaining to resin flow, heat transfer, and consolidation of laminated composites during autoclave processing. The model, which incorporates some of the best features of models already in existence, is based on Darcy's law, the convection–diffusion heat equation, and appropriate constitutive relations. By using a weighted residual method, a two‐dimensional finite element formulation for the model is presented and a finite element code is developed. Numerical examples, including a comparison of the present numerical results with one‐dimensional and two‐dimensional analytical solutions, are given to indicate the accuracy the finite element formulation. Moreover, using the finite element code, the one‐dimensional cure process of a laminate made of 228 and 380 plies of AS4/3501‐6 unidirectional tape is simulated and numerical results are compared with available experimental results. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 2310–2319, 2007     

Numerical analysis of parametric effects on consolidation of angle‐bended composite laminates

In the previous study, the finite element formulation has been developed by our group based on two‐dimensional resin flow and fiber compaction model. Good agreement between simulations and experimental results was found under the one‐dimensional flow condition. In this article, the two‐dimensional model was used to simulate the consolidation of angle‐bended laminates with the convex tool in autoclave process. The effects of material properties on the consolidation were studied. It was found that the fiber bed shear modulus significantly affects the compaction behavior in the corner section of angle‐bended laminate, the fiber bed compaction property decide the laminate deformation, and the resin viscosity and fiber bed permeability affect the rate of laminate compaction and consolidation time. The angle‐bended T700/BMI QY8911‐Ilaminates were manufactured in autoclave process. The experimental data validate the numerical simulation method for the consolidation of the angle‐bended laminates. These results are greatly helpful for the optimization of processing parameters, improvement of composite parts quality, and reduction of the fabrication cost. POLYM. COMPOS., 2009. © 2008 Society of Plastics Engineers     

纤维层合板梯度化后对弯曲刚度与层间应力的影响

本文介绍了纤维层合板力学梯度设计的新概念,以平纹正交织物复合材料为例,用板壳弯曲的有限元法,探讨了层合板的最佳弯曲刚度.     

Microwave and conventional curing of thick‐section thermoset composite laminates: Experiment and simulation

In conventional processing, thermal gradients cause differential curing of thick laminates and undesirable outside‐in solidification. To reduce thermal gradients, thick laminates are processed at lower cure temperatures and heated with slow heating rates, resulting in excessive cure times. Microwaves can transmit energy volumetrically and instantaneously through direct interaction of materials with applied electromagnetic fields. The more efficient energy transfer of microwaves can alleviate the problems associated with differential curing, and the preferred inside‐out solidification can be obtained. In this work, both microwave curing and thermal curing of 24.5 mm (1 inch) thick‐section glass/epoxy laminates are investigated through the development of a numerical process simulation and conducting experiments in processing thick laminates in a conventional autoclave and a microwave furnace. Outside‐in curing of the autoclave‐processed laminate resulted in visible matrix cracks, while cracks were not visible in the microwave‐processed laminate. Both numerical and experimental results show that volumetric heating due to microwaves promotes an inside‐out cure and can dramatically reduce the overall processing time.