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A review on numerical optimization in liquid composite moulding processes
Materials Today: Proceedings xxx (xxxx) xxx
Contents lists available at ScienceDirect
Materials Today: Proceedings journal homepage: www.elsevier.com/locate/matpr
A review on numerical optimization in liquid composite moulding processes Anita Zade, Raghu Raja Pandiyan Kuppusamy ⇑ Department of Chemical Engineering, National Institute of Technology Warangal, Telangana 506004, India
a r t i c l e
i n f o
Article history: Received 14 June 2019 Accepted 22 July 2019 Available online xxxx Keywords: Liquid Composite Moulding Optimization Meta-heuristic algorithm Curing Mould filling
a b s t r a c t Liquid Composite Moulding (LCM) processes became popular for producing near-net shape structural composite parts over traditional methods. However, some critical issues arise during making of the composite part using LCM processes. This article presents the literature review on prevention methodologies of process induced defects in LCM which arises mainly in the mold filling and curing stage. Different numerical methods are developed for reducing the flow induced defects like macro-voids, dry spot and micro-voids formation and cure induced defects like matrix micro-cracks and geometrical distortions. Currently, researchers are attracting towards heuristics techniques such as Genetic Algorithm (GA), especially for the development of Multi-objective optimization (MOO) problems, to optimize multiple conflicting objectives simultaneously. The lack of connection between the selection of optimization technique and process induced defects are highlighted in the future work. Ó 2019 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the 1st International Conference on Manufacturing, Material Science and Engineering.
1. Introduction
1.1. Optimization problems
Nowadays, optimization is become a crucial parameter in the engineering design. The designing parameters like Light weight, less expensive material, high strength etc. are taken into consideration for designing mechanical structures. The applications of composite materials are increasing in different industries like aeronautics & automotive industries due their high specific strength. Thus, different optimization studies carried out on composite structures using various types of algorithms. Algorithm represents the procedure of optimizing the parameters to achieve the desired objective function. The selection of algorithm is problem specific. Thus, for designing the optimum composite structures depends on type of optimization problem and selection of proper optimization algorithm. Though there are various optimization algorithms proposed by researchers but according to No-FreeLunch (NFL) theorem there is not the best algorithm for all applications. Hence, this area of research is still active for different types of optimization problems [1,2].
An optimization problem consists of objective function, design variables or constraints. Based on these attributes optimization problems can be classified as follows [3,4]: 1. Single dimensional & multi-dimensional optimization problems contain one design variable & more than one design variable respectively. 2. When the design variables are discrete are called discrete optimization problems, for example the number of layers. Whereas, in continuous optimization problems, design variables are continuous. 3. In the constrained optimization approaches design variables changes by satisfying certain constraints whereas in unconstrained optimization problems design variables are free to change without any constraints. 4. When there is single objective to optimize such problems are called as single objective optimization problems and the problems which contain multiple conflicting objectives to optimize such problems are called as multi-objective optimization problems.
⇑ Corresponding author. E-mail address: [email protected] (R.R.P. Kuppusamy). https://doi.org/10.1016/j.matpr.2019.07.605 2214-7853/Ó 2019 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the 1st International Conference on Manufacturing, Material Science and Engineering.
Please cite this article as: A. Zade and R. R. P. Kuppusamy, A review on numerical optimization in liquid composite moulding processes, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.07.605
2
A. Zade, R.R.P. Kuppusamy / Materials Today: Proceedings xxx (xxxx) xxx
5. If optimality procedure of a problem is depends on time and it changes with respect to time such problems are called dynamic optimization problems in contrast for static type of optimization problems optimal design does not depend on time. To address these optimization problems there are various optimization algorithms can be used which are classified as follows [5]: 1. Deterministic algorithms: These are rigorous types of algorithms, if we solve the problem for specific design parameters today or tomorrow the solution will not change. For example Gradient based algorithms such as Newton’s method, secant method and non-gradient based algorithms such as simplex method, box-complex method. Though these methods are effective for good convergence but may stuck in local optima for complex problems. 2. Stochastic algorithms: These methods are random in nature, which gives different solution as number of times as we run the program. These methods start with random initial guesses and converge to the global optimal solution. For example, Genetic Algorithm (GA), Particle Swarm Optimization (PSO) algorithm, Ant Colony Optimization (ACO) algorithm and Cuckoo Search (CS) algorithm etc. Although these methods are computationally costly they are very popular for addressing real world applications [6–8]. 3. Hybrid algorithms: In this method two or more algorithms are combined by taking into account the potential aspects of each method and eliminating the weak aspects. For example, hybrid Box-Complex method with Cuckoo Search (BC-CS) algorithm, A hybrid PSO with Genetic algorithm, A hybrid Nelder-Mead PSO (NM-PSO) algorithm etc. Proposing such hybrid type of algorithms is still an active area of research to address the complexity of the real world applications [9–11].
1.2. Composite structures Composite materials are the combination of two or more constituents having different properties. The main constituents are reinforcement fibre which carries the structural load and resin matrix which holds the fibre together. Polymer Matrix Composite (PMC) [12] uses a polymer as the matrix and a fibre as the reinforcement. The main purpose of all polymer composite processing methods is to bring the resin and reinforcement fibre together in the required shape of the product targeting minimum void with maximum resin-fibre wet-out. The mechanical strength and the stiffness of a composite component come primarily from the reinforcement fibres, making a higher volume fraction desirable. However, increase in fibre volume fraction, decreases the degree of resin impregnation due to reduced porosity as a cause of reduced space between the fibre bundles. Consequently, this poor resin distribution can result in entrapment of air and formation of voids, affecting the final product quality. The proper selection of processing parameters of manufacturing method helps to maximize the fibre volume content. The viscosity changes and the cure kinetics during fiber wet-out are the main resin characteristics to be considered during production process. Lower the viscosity, easier the resin flow and the saturation of reinforcement fiber. Cure kinetics increases the viscosity with increase in degree of cross-linking. Moreover, cure kinetics directly affects the process efficiency, as the time for complete cure governs the production rate.
The product geometry can often dictate the selection of production process, by its size and complexity. As the geometry becomes more complicated, it becomes more difficult to force the resin and saturate the whole product domains. The resin flow can be hindered in the presence of with ribs and design features of varying thickness. The presence of uneven surfaces and hollow structures has the impact to select one process over another. Various composite production techniques such hand lay-up, filament winding, pultrusion, Compression molding, Liquid composite molding (LCM), Autoclave are currently in use. However, the choice of the composite production process for a particular application is governed by a trade-off between lower manufacturing cost, high performance part, high production rate, and ease in making complex geometries. Liquid Composite Moulding (LCM) processes such as Resin Transfer Moulding (RTM) and Vaccum Assisted Resin Transfer Moulding (VARTM) has taken promising interest over traditional methods [13]. Thus, various numerical studies have been carried out to optimize the process particularly in the mould filling and curing stage to produce a void free part within optimum process time.
2. Motivation With increase in scope of LCM processes in different industries, numerous studies performed in the literature. Hamidi and Altan (2017) reviewed the process induced defects in LCM processes and classified them as preform, flow induced and cure induced defects. Preform defects arises due to irregularities in reinforcement path geometry. Hence, appropriate selection of the fibre/matrix system with acceptable cooling rates helps to reduce these defects. Flow induced defects arises due to non-uniform impregnation of preform through resin which results into dry spot and void formation. These defects can be reduced by analysis of capillary number with combination of other applicable methods. Cure induced defects arises during curing cycle which includes matrix micro-cracks and geometrical distortions. Prevention of these defects can be achieved by using appropriate constitutive models and numerical simulations to optimize the cure cycle [14]. Zhang and Friedrich (2003) reviewed the application of Artificial Neural Networks (ANN) in polymer composites. In this review various principles of ANN are discussed to predict the certain properties of polymer composite material such as fatigue life, wear performance, response under combined loading situations, and dynamic mechanical properties [15]. Jahromi (2012) et al, trained dynamic Artificial Neural Network using the numerical results obtained by 3-D finite volume method with the aim of achieving uniform degree of cure and temperature within the composite part. A non-linear optimization problem is developed to minimize the temperature overshoot during the curing process with a constraint on achieving maximum degree of cure [16]. Nikbakht (2018) et al, presented the review article on optimization of Functionally Graded (FG) composite structures. It has been observed that meta-heuristics algorithms such as GA and PSO were the most commonly used techniques for the optimal design of FG structures. The coupling of ANN and Adaptive Neuro-Fuzzi Interference System (ANFIS) with these meta-heuristic techniques used to optimize the objectives like stress distribution, buckling load, fundamental frequency, and the weight of FG structures [17]. C.H. Park (2015) presented the numerical modelling and simulation approaches to increase the productivity and reduce the process cycle time for the resin flow analysis in textile composite manufacturing processes. Resin flow characterization was presented at different scales. At macroscopic scale the computational domain is greater than 0.1 m and considered as homogeneous
Please cite this article as: A. Zade and R. R. P. Kuppusamy, A review on numerical optimization in liquid composite moulding processes, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.07.605
3
A. Zade, R.R.P. Kuppusamy / Materials Today: Proceedings xxx (xxxx) xxx
porous media where Darcy’s law is applied. At mesoscopic scale computational domain is 1–10 mm and the resin flow in open gap modelled as viscous flow represented by Stokes’ flow equation. At microscopic scale computational domain is 0.01–1 mm and modelled by Stokes’ flow equation with surface tension [18]. Luisa SILVA (2016) et al, presented the modelling and simulation of mold filling which involves multi-phase and multi-physics flow problems and for addressing such problems Finite Element Method (FEM) and Finite Difference Method (FDM) are commonly used [19]. Ruiz and Trochu (2011) also presented the numerical simulation methodology for tracking the moving resin flow front through the finite element mesh of the composite part [20]. Many researchers have developed the heuristic and numerical techniques to determine the optimal locations of gate and vent to minimize mold filling time and reduce dry spot and macro-void formation [21–25]. S. Shevtsov (2012) et al, developed an mathematical model of epoxy-based composite structure during curing cycle and simulated in COMSOL Multiphysics FEM software. This model takes into account the kinetics of thermoset resin, phase state, thermal capacitance during cure and heat transfer equation [26].
of an optimal strategy for designing the complex mould. This will enable the industry to use RTM technology instead of hand layup method for large and complex composite structures.
3. Conclusion The use of numerical optimization in LCM processes is reviewed here. The mold filling and curing step are considered as the crucial steps for making qualitative and productive component. To prepare a defect free component with best operating parameters number of optimization techniques has been used. It has been observed that the use of meta-heuristics techniques is increasing due to its ability to optimize the properties of complex structure. The use of hybrid optimization algorithm for making stable and defect free composite part will be the promising area of research. Development of a sophisticated multi-objective optimization strategy for large and complex composite structures will be the future work.
Appendix A Table 1 Objective function categorization for LCM process optimization. LCM process optimization Curing process Single objective optimization Process time Temperature overshoot, Degree of cure, Residual stresses
Multi-objective optimization process time/degree of cure process time/temperature overshoot process time/cost tensile load/flexural strength
Mold filling process
Numerical Techniques
references
filling time voids resin flow front injection flow rate warpage shrinkage rate
Trial & error, Finite Element Method (FEM), Finite Volume Method (FVM), Finite Difference Method (FDM), Sequential Quadratic Programming (SQP), Volume of Fluid (VOF) model, GA, ANN, Direct Differential Method (DDM), Taguchi Experimental Design, Analysis of Variance (ANOVA), Response Surface Methodology (RSM), Gradient based algorithm, Lloyd’s algorithm, Graph based two phase heuristic (GTPH) method, QuasiNewtonian method, Control Volume Finite Element (CVFE) algorithm, stochastic algorithm
[15,16,35–44,19,45– 47,20,21,26,31–34]
voids/filling time filling time/vents number Gates number/Vents number Fill time/weld line Fill time/waste resin
Non-dominated Sorting Genetic Algorithm (NSGA), NSGA-II, Multi-objective Optimization Genetic Algorithm (MOOGA) toolbox
[22,27,30,48–50]
G. Seretis (2018) et al., developed an Multi-objective optimization (MOO) problem to investigate the optimum curing condition of glass-fibre/epoxy composite part using Poisson regression and Genetic Algorithm (GA). Heating rate, temperature of the 1st curing step and duration of the 1st curing step are treated as design variables whereas tensile load and flexural strength are considered as objectives to optimize [27]. Struzziero, Skordos (2016) et al, developed an MOO problem to optimize the cure process time and temperature overshoot for thick and ultra-thick composite parts using MOOGA by selecting appropriate thermal profile [28]. Tomonaga Okabe (2016) et al, proposed and MOO approach to investigate the optimum gate locations using FEA with MOOGA [29]. Tifkitsis (2018) et al, developed a novel MOO optimization method where surrogate model is coupled with Monte-Carlo simulator and then integrated with MOOGA to optimize the cure process time and temperature overshoot of thick flat carbon fibre/epoxy laminates [30]. Currently, modelling, simulation and optimization of RTM process is developed for simple geometries like T-shape, L-shape, rectangular and rib model. Hence there is large scope for development
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[18] C.H. Park, Advances in Composites Manufacturing and Process Design, Woodhead Publishing, 2015, 317-378. [19] L. Silva, P. Laure, T. Coupez, D. Hugues, Heat transfer in polymer composite materials, Forming Processes (2016). [20] E. Ruiz, F. TRochu, Composite reinforcements for optimum performance, 2011, 588–615. [21] B.J. Henz, R.V. Mohan, D.R. Shires, Compos. Part A 38 (2007) 1932–1946. [22] V. Achim, F. Ratle, F. Trochu, Appl. Soft Comput. 9 (2009) (2009) 817–823. [23] F. Sánchez, L. Domenech, V. García, N. Montés, A. Falcó, E. Cueto, F. Chinesta, P. Fideu, Compos. Part A (2015). [24] F. Sanchez, J.A. Garcıa, F. Chinesta, L. Gascon, C. Zhang, Z. Liang, B. Wang, Compos. Part A 37 (2006) 903–912. [25] R. Mathur, B.K. Fink, S.G. Advani, Polym. Compos. 20 (1999). [26] S.N. Shevtsov, I. Zhilyaev, I.A. Parinov, Adv. Mater. Res. 569 (2012) 185–192. [27] G. Seretis, G. Kouzilos, D. Manolakos, C. Provatidis, Mater. Res. 21 (2018). [28] G. Struzziero, A.A. Skordos, Compos. Part A 93 (2016). [29] T. Okabe, Y. Oya, G. Yamamoto, J. Sato, T. Matsumiya, R. Matsuzaki, S. Yashiro, S. Obayashi, Compos. Part A (2016). [30] K.I. Tifkitsis, T.S. Mesogitis, G. Struzziero, A.A. Skordos, Compos. Part A 112 (2018) 383–394. [31] A. Bebamzadeh, T. Haukaas, R. Vaziri, A. Poursartip, J. Compos. Mater. (2010). [32] T. Porto, W. Junior, A.G.B. De Lima, W.M.P.B. De Lima, H.G.G.M. Lima, Adv. Mater. Sci. Eng. (2018). [33] E. Ruiz, V. Achim, S. Soukane, Compos. Sci. Technol. 66 (2006) 475–486.
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Please cite this article as: A. Zade and R. R. P. Kuppusamy, A review on numerical optimization in liquid composite moulding processes, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.07.605
Contents lists available at ScienceDirect
Materials Today: Proceedings journal homepage: www.elsevier.com/locate/matpr
A review on numerical optimization in liquid composite moulding processes Anita Zade, Raghu Raja Pandiyan Kuppusamy ⇑ Department of Chemical Engineering, National Institute of Technology Warangal, Telangana 506004, India
a r t i c l e
i n f o
Article history: Received 14 June 2019 Accepted 22 July 2019 Available online xxxx Keywords: Liquid Composite Moulding Optimization Meta-heuristic algorithm Curing Mould filling
a b s t r a c t Liquid Composite Moulding (LCM) processes became popular for producing near-net shape structural composite parts over traditional methods. However, some critical issues arise during making of the composite part using LCM processes. This article presents the literature review on prevention methodologies of process induced defects in LCM which arises mainly in the mold filling and curing stage. Different numerical methods are developed for reducing the flow induced defects like macro-voids, dry spot and micro-voids formation and cure induced defects like matrix micro-cracks and geometrical distortions. Currently, researchers are attracting towards heuristics techniques such as Genetic Algorithm (GA), especially for the development of Multi-objective optimization (MOO) problems, to optimize multiple conflicting objectives simultaneously. The lack of connection between the selection of optimization technique and process induced defects are highlighted in the future work. Ó 2019 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the 1st International Conference on Manufacturing, Material Science and Engineering.
1. Introduction
1.1. Optimization problems
Nowadays, optimization is become a crucial parameter in the engineering design. The designing parameters like Light weight, less expensive material, high strength etc. are taken into consideration for designing mechanical structures. The applications of composite materials are increasing in different industries like aeronautics & automotive industries due their high specific strength. Thus, different optimization studies carried out on composite structures using various types of algorithms. Algorithm represents the procedure of optimizing the parameters to achieve the desired objective function. The selection of algorithm is problem specific. Thus, for designing the optimum composite structures depends on type of optimization problem and selection of proper optimization algorithm. Though there are various optimization algorithms proposed by researchers but according to No-FreeLunch (NFL) theorem there is not the best algorithm for all applications. Hence, this area of research is still active for different types of optimization problems [1,2].
An optimization problem consists of objective function, design variables or constraints. Based on these attributes optimization problems can be classified as follows [3,4]: 1. Single dimensional & multi-dimensional optimization problems contain one design variable & more than one design variable respectively. 2. When the design variables are discrete are called discrete optimization problems, for example the number of layers. Whereas, in continuous optimization problems, design variables are continuous. 3. In the constrained optimization approaches design variables changes by satisfying certain constraints whereas in unconstrained optimization problems design variables are free to change without any constraints. 4. When there is single objective to optimize such problems are called as single objective optimization problems and the problems which contain multiple conflicting objectives to optimize such problems are called as multi-objective optimization problems.
⇑ Corresponding author. E-mail address: [email protected] (R.R.P. Kuppusamy). https://doi.org/10.1016/j.matpr.2019.07.605 2214-7853/Ó 2019 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the 1st International Conference on Manufacturing, Material Science and Engineering.
Please cite this article as: A. Zade and R. R. P. Kuppusamy, A review on numerical optimization in liquid composite moulding processes, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.07.605
2
A. Zade, R.R.P. Kuppusamy / Materials Today: Proceedings xxx (xxxx) xxx
5. If optimality procedure of a problem is depends on time and it changes with respect to time such problems are called dynamic optimization problems in contrast for static type of optimization problems optimal design does not depend on time. To address these optimization problems there are various optimization algorithms can be used which are classified as follows [5]: 1. Deterministic algorithms: These are rigorous types of algorithms, if we solve the problem for specific design parameters today or tomorrow the solution will not change. For example Gradient based algorithms such as Newton’s method, secant method and non-gradient based algorithms such as simplex method, box-complex method. Though these methods are effective for good convergence but may stuck in local optima for complex problems. 2. Stochastic algorithms: These methods are random in nature, which gives different solution as number of times as we run the program. These methods start with random initial guesses and converge to the global optimal solution. For example, Genetic Algorithm (GA), Particle Swarm Optimization (PSO) algorithm, Ant Colony Optimization (ACO) algorithm and Cuckoo Search (CS) algorithm etc. Although these methods are computationally costly they are very popular for addressing real world applications [6–8]. 3. Hybrid algorithms: In this method two or more algorithms are combined by taking into account the potential aspects of each method and eliminating the weak aspects. For example, hybrid Box-Complex method with Cuckoo Search (BC-CS) algorithm, A hybrid PSO with Genetic algorithm, A hybrid Nelder-Mead PSO (NM-PSO) algorithm etc. Proposing such hybrid type of algorithms is still an active area of research to address the complexity of the real world applications [9–11].
1.2. Composite structures Composite materials are the combination of two or more constituents having different properties. The main constituents are reinforcement fibre which carries the structural load and resin matrix which holds the fibre together. Polymer Matrix Composite (PMC) [12] uses a polymer as the matrix and a fibre as the reinforcement. The main purpose of all polymer composite processing methods is to bring the resin and reinforcement fibre together in the required shape of the product targeting minimum void with maximum resin-fibre wet-out. The mechanical strength and the stiffness of a composite component come primarily from the reinforcement fibres, making a higher volume fraction desirable. However, increase in fibre volume fraction, decreases the degree of resin impregnation due to reduced porosity as a cause of reduced space between the fibre bundles. Consequently, this poor resin distribution can result in entrapment of air and formation of voids, affecting the final product quality. The proper selection of processing parameters of manufacturing method helps to maximize the fibre volume content. The viscosity changes and the cure kinetics during fiber wet-out are the main resin characteristics to be considered during production process. Lower the viscosity, easier the resin flow and the saturation of reinforcement fiber. Cure kinetics increases the viscosity with increase in degree of cross-linking. Moreover, cure kinetics directly affects the process efficiency, as the time for complete cure governs the production rate.
The product geometry can often dictate the selection of production process, by its size and complexity. As the geometry becomes more complicated, it becomes more difficult to force the resin and saturate the whole product domains. The resin flow can be hindered in the presence of with ribs and design features of varying thickness. The presence of uneven surfaces and hollow structures has the impact to select one process over another. Various composite production techniques such hand lay-up, filament winding, pultrusion, Compression molding, Liquid composite molding (LCM), Autoclave are currently in use. However, the choice of the composite production process for a particular application is governed by a trade-off between lower manufacturing cost, high performance part, high production rate, and ease in making complex geometries. Liquid Composite Moulding (LCM) processes such as Resin Transfer Moulding (RTM) and Vaccum Assisted Resin Transfer Moulding (VARTM) has taken promising interest over traditional methods [13]. Thus, various numerical studies have been carried out to optimize the process particularly in the mould filling and curing stage to produce a void free part within optimum process time.
2. Motivation With increase in scope of LCM processes in different industries, numerous studies performed in the literature. Hamidi and Altan (2017) reviewed the process induced defects in LCM processes and classified them as preform, flow induced and cure induced defects. Preform defects arises due to irregularities in reinforcement path geometry. Hence, appropriate selection of the fibre/matrix system with acceptable cooling rates helps to reduce these defects. Flow induced defects arises due to non-uniform impregnation of preform through resin which results into dry spot and void formation. These defects can be reduced by analysis of capillary number with combination of other applicable methods. Cure induced defects arises during curing cycle which includes matrix micro-cracks and geometrical distortions. Prevention of these defects can be achieved by using appropriate constitutive models and numerical simulations to optimize the cure cycle [14]. Zhang and Friedrich (2003) reviewed the application of Artificial Neural Networks (ANN) in polymer composites. In this review various principles of ANN are discussed to predict the certain properties of polymer composite material such as fatigue life, wear performance, response under combined loading situations, and dynamic mechanical properties [15]. Jahromi (2012) et al, trained dynamic Artificial Neural Network using the numerical results obtained by 3-D finite volume method with the aim of achieving uniform degree of cure and temperature within the composite part. A non-linear optimization problem is developed to minimize the temperature overshoot during the curing process with a constraint on achieving maximum degree of cure [16]. Nikbakht (2018) et al, presented the review article on optimization of Functionally Graded (FG) composite structures. It has been observed that meta-heuristics algorithms such as GA and PSO were the most commonly used techniques for the optimal design of FG structures. The coupling of ANN and Adaptive Neuro-Fuzzi Interference System (ANFIS) with these meta-heuristic techniques used to optimize the objectives like stress distribution, buckling load, fundamental frequency, and the weight of FG structures [17]. C.H. Park (2015) presented the numerical modelling and simulation approaches to increase the productivity and reduce the process cycle time for the resin flow analysis in textile composite manufacturing processes. Resin flow characterization was presented at different scales. At macroscopic scale the computational domain is greater than 0.1 m and considered as homogeneous
Please cite this article as: A. Zade and R. R. P. Kuppusamy, A review on numerical optimization in liquid composite moulding processes, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.07.605
3
A. Zade, R.R.P. Kuppusamy / Materials Today: Proceedings xxx (xxxx) xxx
porous media where Darcy’s law is applied. At mesoscopic scale computational domain is 1–10 mm and the resin flow in open gap modelled as viscous flow represented by Stokes’ flow equation. At microscopic scale computational domain is 0.01–1 mm and modelled by Stokes’ flow equation with surface tension [18]. Luisa SILVA (2016) et al, presented the modelling and simulation of mold filling which involves multi-phase and multi-physics flow problems and for addressing such problems Finite Element Method (FEM) and Finite Difference Method (FDM) are commonly used [19]. Ruiz and Trochu (2011) also presented the numerical simulation methodology for tracking the moving resin flow front through the finite element mesh of the composite part [20]. Many researchers have developed the heuristic and numerical techniques to determine the optimal locations of gate and vent to minimize mold filling time and reduce dry spot and macro-void formation [21–25]. S. Shevtsov (2012) et al, developed an mathematical model of epoxy-based composite structure during curing cycle and simulated in COMSOL Multiphysics FEM software. This model takes into account the kinetics of thermoset resin, phase state, thermal capacitance during cure and heat transfer equation [26].
of an optimal strategy for designing the complex mould. This will enable the industry to use RTM technology instead of hand layup method for large and complex composite structures.
3. Conclusion The use of numerical optimization in LCM processes is reviewed here. The mold filling and curing step are considered as the crucial steps for making qualitative and productive component. To prepare a defect free component with best operating parameters number of optimization techniques has been used. It has been observed that the use of meta-heuristics techniques is increasing due to its ability to optimize the properties of complex structure. The use of hybrid optimization algorithm for making stable and defect free composite part will be the promising area of research. Development of a sophisticated multi-objective optimization strategy for large and complex composite structures will be the future work.
Appendix A Table 1 Objective function categorization for LCM process optimization. LCM process optimization Curing process Single objective optimization Process time Temperature overshoot, Degree of cure, Residual stresses
Multi-objective optimization process time/degree of cure process time/temperature overshoot process time/cost tensile load/flexural strength
Mold filling process
Numerical Techniques
references
filling time voids resin flow front injection flow rate warpage shrinkage rate
Trial & error, Finite Element Method (FEM), Finite Volume Method (FVM), Finite Difference Method (FDM), Sequential Quadratic Programming (SQP), Volume of Fluid (VOF) model, GA, ANN, Direct Differential Method (DDM), Taguchi Experimental Design, Analysis of Variance (ANOVA), Response Surface Methodology (RSM), Gradient based algorithm, Lloyd’s algorithm, Graph based two phase heuristic (GTPH) method, QuasiNewtonian method, Control Volume Finite Element (CVFE) algorithm, stochastic algorithm
[15,16,35–44,19,45– 47,20,21,26,31–34]
voids/filling time filling time/vents number Gates number/Vents number Fill time/weld line Fill time/waste resin
Non-dominated Sorting Genetic Algorithm (NSGA), NSGA-II, Multi-objective Optimization Genetic Algorithm (MOOGA) toolbox
[22,27,30,48–50]
G. Seretis (2018) et al., developed an Multi-objective optimization (MOO) problem to investigate the optimum curing condition of glass-fibre/epoxy composite part using Poisson regression and Genetic Algorithm (GA). Heating rate, temperature of the 1st curing step and duration of the 1st curing step are treated as design variables whereas tensile load and flexural strength are considered as objectives to optimize [27]. Struzziero, Skordos (2016) et al, developed an MOO problem to optimize the cure process time and temperature overshoot for thick and ultra-thick composite parts using MOOGA by selecting appropriate thermal profile [28]. Tomonaga Okabe (2016) et al, proposed and MOO approach to investigate the optimum gate locations using FEA with MOOGA [29]. Tifkitsis (2018) et al, developed a novel MOO optimization method where surrogate model is coupled with Monte-Carlo simulator and then integrated with MOOGA to optimize the cure process time and temperature overshoot of thick flat carbon fibre/epoxy laminates [30]. Currently, modelling, simulation and optimization of RTM process is developed for simple geometries like T-shape, L-shape, rectangular and rib model. Hence there is large scope for development
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Please cite this article as: A. Zade and R. R. P. Kuppusamy, A review on numerical optimization in liquid composite moulding processes, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.07.605