Keywords

1 Introduction

Carbon fiber-reinforced plastics (CFRPs) play an increasingly important role in the lightweight manufacturing of structural aviation and automotive components [1]. This leads to the growing need for rapid and reproducible mass production of CFRP parts. One way of scaling manufacturing quantity is fully automated production processes. The production line shown in Fig. 1 presented in this research is driven by Swinburne-CSIRO National Industry 4.0 Testlab as part of a Global Innovation Linkage (GIL) project funded by the Australian Department of Industry. The process chain includes an automated tape laying machine to produce 2D composite laminates, a double diaphragm former (DDF), a 300t press with resin injection capabilities, and a KUKA robot to shuttle the preform between the stations.

Fig. 1.
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Composite production chain at Swinburne/CSIRO Industry 4.0 Testlab [2]

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The industry-scale production line combines a novel multilayer system from FILL for automated tape laying (ATL). The multilayer is relevant to this research project because it offers unprecedented freedom in designing, deposition speed and creating the initial 2D composites laminates. The individual layers are ultrasonically spot welded together, allowing shuttling from the Multilayer to the forming stations. Multilayers can use materials ranging from binder dry-fiber tapes to thermoplastics and thermosets. The spools of the Multilayer can hold tapes of 49.5 mm width [3]. It cuts material waste and manufacturing time [2].

Accurate simulation of the SF process is essential for this work to implement parameterization in forming models. Such simulations require much time and can therefore be very costly. It is also where existing simulation environments are still lacking because of their direct relationship with the manufacturing process. The 2D tape stacks created in the multilayer are the basis for the forming simulations shown here. The SF process is typically used on thermoplastic prepregs and involves a blank holder that presses a flat workpiece against a metal tool. The stamp is then progressively lowered into the mold while being able to be heated during the forming process [4]. The given method uses the model to perform simulations [5,6,7]. This early work takes SF into account.

The SF process on tape-based layups induces defects such as wrinkles, layer separation, overlaps, and gaps between tapes, especially on thermoplastic tape-based sheets [8,9,10]. Therefore, optimizing the geometry, stacks of tapes, and process parameters are essential before forming. Optimization helps assess defects such as wrinkles, bridges, gaps, and overlaps. The optimization process repeats iteratively to ensure optimum structural performance with local drape effects. The iterative process is expensive, which includes material waste or virtual analysis, which causes computational time and accuracy. The finite element method (FEM) applied during the process uses data from actual situations to develop, mimic, and predict forming behavior [11]. In order to support FEM, different Design of Experiment (DoE) algorithms can be used to generate parametrized model simulations automatically [12]. These algorithms, such as Latin hypercube (LHC), full factorial, central composite design, box Behnken, etc., are commonly used in engineering and science to create samples to represent a much greater space of possibilities [13]. This work applies the LHC method to generate sets of parameters for different FE models. LHC aims to minimize the variety of parameter combinations needed to optimize the defect formation during forming.

In order to investigate the deformation behavior during the forming of tape laminates, it is necessary to categorize the deformation mechanisms. As a result, key deformation mechanisms are seen at the ply and laminate levels, which are often connected to mesoscopic and macroscopic approaches. The mechanism of Intra-ply occurs on a single tape of a multilayer laminate during the forming behavior. In comparison, the mechanism of inter-ply represents the deformation at the interfaces between the single tape of the stacked laminate [8,9,10]. It is necessary to evaluate formability that invariably depends on material properties such as Young’s modulus, Poisson ratio, friction coefficient, bending stiffness, etc., and process parameters such as tool velocity, temperature, gripper force, pressure, etc.

2 State of the Art

State of the art in automated CFRP manufacturing uses tape-laying machines, such as the Multilayer in this research, that can build customized 2D tape layups using up to sixteen spools at a time and a rotatable ground plate to allow for different orientations of the tape stripes.

Various solvers exist to solve a FEM model to compute the forming modeled parts’ stress, strain, and other responses. This research study is focused on four stagess, as shown in Fig. 2 below. The first stage includes preparing an initial FE model with material properties, initial conditions, and boundary conditions using Ansa v22.1.0 as a preprocessor. The second stage is followed by converting the FE model into the parametrized model by defining the parameters using Ansa inbuilt optimizer. The parameters are thickness, orientation, and position of the tapes, diameter, position, number of spot welds, tool velocity, material type, and gripping force. In the third stage, LS-DYNA R12 from the Livermore Software Technology Corporation (LSTC) is used to solve the FEM models. It is most suited solver for explicit and implicit simulations with many elements and contact conditions. An explicit solver is used in this research because it can solve the complex FEM model simultaneously. In the last stage, the data science approach concludes the results in the final section. It offers a variety of tools that can be applied to structure, cluster, and interpret the data based on mathematics. They range from simple linear regressions over advanced stochastics to machine learning.

Fig. 2.
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Scheme of the experiment process

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The following section describes the methodologies to build and execute the forming simulations in detail. Section 3 provides information on the setup of the FE models and how they are solved. In Sect. 4, the results are analyzed based on described methods. Section 5 includes the discussion of the results obtained on forming behavior. From that, Sect. 6 presents a conclusion and possible improvements.

3 Methodology

The research aims to enhance a stamp-forming process using simulations. The formed sheet is a tape-based layup as produced by Multilayer. It consists of multiple unidirectional (UD) tapes, making up four layers in total. 2D tapes preform positions between the mold and the blank holder. The blank holder has an opening for the forming tool. As seen in Fig. 3, the forming tool, which serves as the stamp, is positioned above the preform. The blank holder forces the preform against the mold during the forming process with a specific amount of pressure. Then the stamp is heated to the working temperature of the thermoplastic prepreg and lowered into the mold, forming the preform into the desired shape. The mold has a depth of 60 mm, and the blank holder has a size of 340 mm × 520 mm.

The tape design fits the mold’s dimensions. Each tape is 500 mm long (longitudinal), 300 mm long (horizontal), and 50 mm wide. The total number of tapes is 32 (20 longitudinal) and (12 horizontal).

Fig. 3.
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FE-model of forming process

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There are two basic categories for the evaluation of the simulations. The first is the quality, efficiency, and accuracy of the simulation itself, and the second is the quality of the resultant part of the forming process. Few wrinkles and gaps indicate that the overall forming outcome is satisfactory. In order to define quantitative criteria for evaluating the consequent part, it considers stress responses, displacement, internal energy, curvature, and other results. Thereby the result can be categorized for each criterion in different levels, for example: low, medium, and high. Table 1 gives the list of all requirements. All the qualitative measures must be as low as possible for an excellent forming process to mitigate the defects. It is necessary to run numerous simulations with various initial conditions, including material and process characteristics. The results of the corresponding simulations are then analyzed using statistical methods such as correlation and regression. Machine learning techniques assist in the discovery of a suitable SF model.

3.1 Initial Finite Element Model

A dynamic model for an SF process is produced to consider the material’s behavior and the formation of defects under predetermined boundary conditions [15]. Forming simulations frequently use flexible thin shell parts [16,17,18,19]. Thije and Akkerman found that fully integrated standard elements should align with the fiber direction to avoid contact problems and intra-ply locking [20]. In order to generate a realistic simulation of plastic deformation under stresses beyond the yield stress, detailed information about the plastic behavior, such as effective plastic strain or hardening curves, is needed [21,22,23,24]. Explicit solvers are preferable in this sector because formation simulations inherit contact criteria [25,26,27].

Table 1. Criteria for the assessment of the simulation and the results
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As already seen in Fig. 3, the 2D preform is composed of four layers of tapes. All modeled parts are rigid bodies in this model except for the 2D preform tapes. While the blank holder and the stamp are free to move in the direction of the stamp’s motion, the position of the mold is fixed. The rigid body force imparted to the blank holder parametrizes the forming model. The stamp is given a prescribed motion in the form of a displacement that depends on the termination time. Only the contact circumstances can limit the tapes. An anisotropic thermoplastic composite material uses (MAT 249 in LS-DYNA) to model them. The idea of using MAT 249 is to determine the bending stiffness by local integration points. It also defines the anisotropic hyperelastic material with up to three fiber directions. It is practical for this research since it utilizes the UD material model and matrix using a straightforward formulation of thermal elastic-plastic material.

Factors:

Tools speed, temperature, and the blank holder’s gripping force are process parameters. The tooling speed links with the simulation time since the displacement of the stamp are always the same. The geometrical parameters of the model are the position, thickness, and orientation of the tapes and the position and diameter of spot welds. Property-related parameters are the properties of the used materials. In order to keep things simple, the model considers only symmetrical cross-plies at various angles and symmetrically balanced angle plies concerning the longitudinal symmetry of the mold.

Design of Experiment:

The tapes mesh as shell elements using an automated approach. Their geometric parameters are considered controllable variables for the DoE. They include the initial gaps between tapes, their thickness, orientation, and the tapes’ horizontal position relative to the symmetry center. The width of the tape is kept constant at 50 mm to explore the limitation of the multilayer. Furthermore, the position and quantity of the spot welds are considered controlled variables, and beam elements model the spot welds. Morphing parameters are applied to parametrize the position, thickness, and orientation of the tapes and the spot welds for the DoE. Controllable process parameters are the selection of the material type for the tapes, the gripping force of the blank holder, and the force for the static test after the forming process. Simulation parameters are the simulation’s termination time and the tapes’ mesh size. The optimization tool used during the DoE utilizes polyamide (PA), polycarbonate (PC), and polyetheretherketone (PEEK) tape materials.

The DoE approach uses the controlled design parameters for sampling as in Table 2 [28]. The derived approach of LHC determines the most influential factors on the output response. Some of the factors occur multiple times for different layers of tapes. LHC minimizes the number of experiments needed while covering most inference space [29]. It enhances the possibility of not only post-process the geometries but also reverse-engineering the parameters defined.

Table 2. Design variables for the DoE as factors with corresponding levels
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3.2 Parametrization Setup

The materials used for the multilayer determine the tapes’ thickness (d). The chosen tapes are 0.14 mm, 0.17 mm, and 0.3 mm thick, as seen in Fig. 4.

Fig. 4.
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Position of different tape thicknesses

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Moving many layers of tape in the transverse direction is accomplished using the parameters for the tape’s position, as demonstrated in Fig. 5. Each layer has its defined parameter. For layer orientation, one parameter sets the angle of the outer layers, and one sets the angle of the interior layers. In a cross-ply layup, the internal layers have an angle 90° different from the outer layers. Suppose the layup is a cross-ply. The inner layers have an angle shifted by 90° for the outer layers. If the layup is an angle-ply, the inner layers’ orientation differs from the outer layer’s, leading to a balanced layup. The angles 0°, 45°, and 90° are not included in angle-plies since they would produce another cross-ply layup.

Fig. 5.
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2D preform with different tape angles

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The number of spot welds is defined for each layer of the tapes, as shown in Fig. 6. The number of spot welds per tape is determined separately for each symmetrical pair of tapes. Only one connection between each pair of tapes should be between the inner and outer layers. Tape length definition models the spot weld as stated in Sect. 3. Each tape initially has ten spot welds, modeled at a distance of 50 mm from each other. An absolute value of 3 mm, 6 mm, or 9 mm shift occurs in the position of the spot welds. The spotweld strength is affected by the use of cold forming. The initial weld strength has no bearing on hot forming.

Fig. 6.
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Spotwelds modeling on tapes laminate

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3.3 Analysis

We analyze the data with a Python script. The lasso. Dyna library reads the binout and d3plot files produced by LS-DYNA. Without loading the entire dataset, it is feasible to extract arrays containing the results for each node, shell element, or beam element using this library. It is also possible to plot the results of the forming simulation. The output log contains detailed information about the execution of the simulation, such as the used computational resources and timing information for the individual tasks of the simulation, e.g., element processing, contact algorithm, etc. Typical forming defects, such as wrinkles and gaps between the tapes, are evident. Simulation results conclude the desired mean, variance, and maximum absolute values of shell and beam elements such as bending moment, stress, shear, and axial force, as listed in Table 3.

Table 3. Single value results
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The linearized model chosen to predict the experiments is the quadratic approximation of the form shown in Eq. 1. This model has been chosen over the linear approximation because most DVs have at least three levels, making the model more suitable than the linear approximation. In this case, the linear term and the square term led to linear dependent columns in the factor matrix, which is why the second order is the best guess:

$$\mathrm{Y}={\upbeta }_{0}+\mathrm{DV}{\upbeta }_{1}+{\mathrm{DV}}^{2}{\upbeta }_{2}+\upepsilon =\left(1\left|\mathrm{DV}\right|{\mathrm{DV}}^{2}\right)\left({\upbeta }_{0}\left|{\upbeta }_{1}\right|{\upbeta }_{2}\right)+\upepsilon =\mathrm{X}\upbeta +\upepsilon $$
(1)

The calculation of parameter matrix β minimizes the prediction error ϵ. It calculates the error using Eq. (2) as described by Webers [28]. The error is the difference between the simulated and the predicted results. In order to calculate the result matrix, we use the previously calculated single values in Table 3. There are 21 single values for every simulation, leading to a response matrix of size 500 × 21.

$$\Rightarrow\upbeta ={\left({\mathrm{X}}^{\mathrm{T}}\mathrm{X}\right)}^{-1}{\mathrm{X}}^{\mathrm{T}}\mathrm{Y}$$
(2)

The K-Nearest Neighbors (KNN) approach is applied to the coordinates of each node at the most recent time step to analyze how similar the resulting geometry is to the original geometry. The nodes of each simulation are geometrically sorted, subsampled to the size of the smallest node array, then flattened to produce collections of the same size for each simulation [30]. In order to use a dimensionality reduction technique, the KNN method generates connectivity- and distance matrix that identifies groups of simulation results compared by Tenenbaum [31].

4 Results

The results shows that the ply-by-ply tape-based model, created by the combination of parameters, precisely replicates the multilayer ATL process. An analysis of relationships between the tape stack, forming models and the design factors shows a 3D scatter plot for each simulation. Figure 7 displays the maximum absolute values of the shell stress, shell shear force, and shell bending moment for the tape thickness. The majority of point cluster concludes that the thicker tape tends to have a lower maximum absolute stress and lower stress variance during forming. The conclusion is that choosing a thinner tape is an ideal option to reduce the shear forces and the bending moment.

Fig. 7.
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Max. Abs. Shell responses for different tape thicknesses

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Figure 8 compares a simulated geometry with similar design parameters to a created real geometry. Both parts display the recognizable wrinkles that develop during forming. This occurs because the spot welds link one tape on an upper layer to numerous tapes on the layer beneath. These tapes thus have more clearance as they are not perpendicular, resulting in the formation of gaps. The fringe pattern for the bending moment highlights the wrinkles in the simulation result. Both results also show a gap between the two middle tapes on the top layer. In particular, simulations of angle-plies with a 15° tape angle have shown severe gap creation, as shown in Fig. 9.

Fig. 8.
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SF rig results (left), simulation result (right)

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For both, more minor wrinkles appear along the double dome geometry’s edge, while more prominent ones appear on the outside tapes.

The quadratic function discussed in Sect. 0 correlates with the maximum absolute cross, and angle plies values. A 45° angle lowers the maximum absolute values for cross-plies, and a 75° angle decreases the maximum values for angle-plies. The Pareto plots created using the quadratic function, as shown in Fig. 10, corroborate the relationships between the tape thickness, the material ID, and the termination time. The relative root square mean error (rRMSE) for each value results assess the prediction function’s accuracy. In order to compare multiple design parameters, each design variable is normalized. It shows the predicted effect of different design variables on the max. Abs. Bending moment.

Fig. 9.
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Gap formation on angle-ply with 15°

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5 Discussion

The purpose of the research presented in this paper is to examine the thermoplastic UD tapes’ limits. Due to the limitations of the available SF rig, the temperature is not considered during the simulations. The rig is capable of producing temperatures up to 160 ℃. Utilizing a material with a low melting temperature is advised. Polycarbonate was the UD thermoplastic material employed in this study. The glass transition temperature of the tape is 140 ℃. As a result, the SF process is carried out at a temperature above the glass transition but below the melting point. Implementing the parameterization concept in the same forming simulation framework brings novelty to this research.

Polycarbonate tapes give the optimal forming results among the simulated materials under defined current boundary conditions. Once the temperature is included and forming is done at or above melting temperature, the model will get different results. It means that the resin will not be able to flow through the tapes, and the model will have a variety of flaws such as wrinkles, gaps, buckling, etc. The forming of ultrasonically spot-welded tapes at room temperature causes the defects such as wrinkles to emerge.

Fig. 10.
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Pareto plot of max. Abs. Bending moment for different normalized design variables

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If the forming occurs above the melting temperature, the weld spots melt. The spot welds are essential to this process and impact the wrinkles because of the SF rig’s limitations. Angle-plies with a 15° tape angle are more likely to cause gaps due to the different arrangement of spot welds. Thinner tapes seem to mitigate the defects independent of the material due to the higher flexibility of the tapes, which leads to lower bending moments. Higher termination times and smaller mesh size come at higher computational costs but most likely lead to fewer defects. The moving parts, such as the stamp and the blank holder, have lower inertial forces.

The considerable variance between the model parameters leads to the high error of the quadratic estimation. It means that the function cannot be used to predict the results but only to get a tendency of the impact of the parameters on an outcome. Results with fewer defects due to the tape angle explain the doubledome geometry’s curvature. An optimal angle is achieved with double curvatures on most tapes, leading to lower intra-ply shear stress. It seems to be the case for the doubledome geometry at 45° for cross-plies and 75° for angle-plies. The analysis with the KNN method failed. It can result from the high variation of the simulated models, leading to many differences in the results. This theory needs to be disproved by additional investigation.

6 Conclusion and Outlook

The model has successfully implemented individual tapes and a tape stack. Models are also used to generate ultrasonically welded tapes that are not pre-consolidated. The double dome model successfully predicts the defects when forming below the melting temperature. Current results show that thermoplastics tapes that are only spot welded are not formable without creating defects. The model and the simulations need further development to include the temperature and material card. Designing and simulating parametrized models for forming simulations with ANSA and LS-DYNA is possible. The bending stiffness and spot weld strengths depend highly on the temperature, and the material formed at the appropriate temperature should behave very similarly. The conclusion is that the forming results mainly depend on the fiber angles. Wrinkles, gaps, and overlaps are predicted with the simulations as observed by Vanclooster [15] and by Hamila and Boisse [19]. Simulations with higher bending moments have prominent wrinkles.

Creating and analyzing the parameter setup for the ultrasonic spot welds on the tapes is challenging. It is improved by assessing the layup for possible spotweld positions and activating or deactivating each spotweld. Testing other connection kinds, such as cohesive bonding, is also possible. For improved simulation accuracy and to take temperature into account during the forming process, the model can be expanded to incorporate more complex material models and a thermal solver [23]. It will result in a better understanding of the forming defects. These defects can be analyzed in more detail to prove that the fiber angles and their respective spotweld positions are significant concerns. Additionally, it is possible to explore the forming behavior using various tape widths and geometries.

The linearized model is helpful in understanding trends in the correlations between the design factors and the results, but it does not correctly represent the simulated findings. Additionally, different DoE algorithms can be used and compared to the LHC [12]. The Isomap dimensionality reduction with the KNN algorithm was inconclusive. Various machine learning algorithms such as convolutional neural network (CNN) could be applied to images of the results or on geometrically sorted arrays of shell responses. A user interface on top of the python script can simplify the search for simulations with specific design variables and results. The design variables may be iteratively optimized using PSO, GBO, RSM, and GA algorithms.