Modelling of the Monolithic Stiffener Forming Process from a Paek Thermoplastic Composite Matrix Using Pam-Form Software

The shaping of parts made of high-temperature thermoplastic composites (e.g. PAEK, PEEK, PEKK and PPS) is a demanding process and has limitations. These issues can be modelled by numerical analysis [1,2]. From the analysis, it is possible to monitor the course of the process and the behaviour of the material during the process, reduce the time to perform technological tests, optimise the forming tools and reduce the costs of implementation of the pressing process. One of the tools used to pressing processes of model composites is Pam-Form (Pam-Composites) software [3]. To perform an analysis using Pam-Form, it is necessary to define a material model based on experimental data. To reduce the weight of aircrafts, the aviation industry replaces classic construction materials with lighter composite materials [4]. Toray Cetex® TC1200 (Toray Group) is a well-described carbon thermoplastic composite with sufficiently good properties used in aviation structures. However, due to the high melting point of PEEK (T_m = 343°C), its processing technology is problematic. The processing temperature of a typical Toray Cetex TC1200 process ranges from 370°C to 400°C [5]. The process of producing flat composite panels used as prefabricated parts during pressing requires cyclic heating of the press, maintaining a constant temperature of approx. 385°C and then cooling with a speed factor to approx. 200°C [6]. This cycle is time-consuming and requires the use of high-power devices. The solution to this problem is the Toray Cetex® TC1225 thermoplastic composite with the same weave and fibre type (5HS, T300) in the PAEK thermoplastic matrix. Due to the same chemical family (polyaryletherketones), PEEK and PAEK [7,8] have similar physico-chemical properties, but PAEK has a lower melting temperature, T_m = 305°C. Its processing temperature ranges from 325 to 350°C [9]. This allows for a shorter, more stable and less energy-consuming process. In addition, Toray Cetex TC1225 is the first thermoplastic composite approved by the National Institute for Aviation Research (NIAR) for aviation applications [10]. At the Institute of Aviation, Łukasiewicz Research Network, as part of a project to produce thermoplastic inspection doors for the ILX-34 aircraft (Fig. 1), monolithic stiffening was formed using Toray Cetex® TC1225 [11]. The monolithic shape eliminates the need to produce separate stiffening parts, which would require the use of separate forming tools and the adaptation of subsequent processes, and eliminates the use of additional joints. Consequently, this reduces the weight of the structure. The monolithic structure ensures the continuity of the fibres in the area of the whole part, which gives high strength properties and shortens the overall process of its production. Due to the complicated shape, the technological process was preceded by numerical analysis. This allowed checking the possibility of making a stiffening frame during a single pressing process, assessing the quality of the manufactured part, optimising the forming tools and reducing the time and costs of implementing the process.

Figure 1.

To perform the analysis, it was necessary to build a model reflecting the pressing process and obtain material data that depict the behaviour of the actual material. When creating the material model, one had to rely on experimental data. Due to the innovation of the Toray Cetex® TC1225 material, it was difficult to find research papers or documentation describing the material properties necessary to create a material model by Pam-Form. The construction of the model was based on experimental results carried out on the Toray Cetex® TC1200 material. This was possible due to the similarity of both materials and their properties above the melting point. It is described in CompositesWorld [12]. The results of the analysis were compared with those of the produced part. The purpose of this work was to show how to adjust material data and how to build a model by Pam-Form to correctly model the pressing process (Fig. 2).

Figure 2.

In Table 1, a cross-sectional diagram of the door part is given together with the embossing dimensions of the stiffening part.

The thermoforming process uses previously consolidated composite panels cut to the right dimensions. The panels have specific layer arrangement that determines the thickness of the part. Trimmed panels are referred to as blanks in this article. Blanks are equipped with metal parts (‘cold spots’) attached with screws, which can be placed in their corners and on the side edges (Fig. 3).

Figure 3.

They perform the function of local heat collection and assembly. A blank is mounted on the transport frame with springs attached to the ‘colds pots’ parts (Fig. 4).

Figure 4.

The frame with the mounted blank is transported between infrared radiators, where the material is heated above the melting point of the thermoplastic matrix T_m. Then, the heated material is transported under the press. Under the pressure of the press, the blank assumes the shape of a punch and the mould used for forming. Steel or rubber/silicone punches are used for forming. After cooling, the press is opened [13]. The finished part requires cutting off technological allowances and can be further processed, e.g. grinding, drilling holes or painting. A block diagram of the thermoforming process is shown in Figure 5a.

Figure 5.

In Pam-Form, the laminate is considered as independent layers of the orthotropic material connected by contact constraints (friction, described in section 5.2). The orthotropic model used assumes a plane state of stress described by the following constitutive equation: 1 [ε1ε2γ12]=[1E1−ν12E10−ν12E11E20001G12][σ1σ2τ12]. \[\left[ \begin{matrix} {{\varepsilon }_{1}} \\ {{\varepsilon }_{2}} \\ {{\gamma }_{12}} \\ \end{matrix} \right]=\left[ \begin{matrix} \frac{1}{{{E}_{1}}} & -\frac{{{\nu }_{12}}}{{{E}_{1}}} & 0 \\ -\frac{{{\nu }_{12}}}{{{E}_{1}}} & \frac{1}{{{E}_{2}}} & 0 \\ 0 & 0 & \frac{1}{{{G}_{12}}} \\ \end{matrix} \right]\left[ \begin{matrix} {{\sigma }_{1}} \\ {{\sigma }_{2}} \\ {{\tau }_{12}} \\ \end{matrix} \right].\]

Shear strain is defined as the relative angle of rotation in radians between the principal directions of the fibres: 2 γ=θ0−θ. \[\gamma ={{\theta }_{0}}-\theta .\]

3.1.

Determination of material data

In addition to values such as density, Young’s modulus (in two directions: weft and warp) or thermoplastic viscosity, it is necessary to define additional properties whose existence has a key impact on the course of the forming process (e.g. buckling or wrinkle creation [14]).

The properties are as follows:

shear modulus in the plane of the layer – G (1)

bending behaviour – B

3.1.1.

Determination of shear stiffness in the plane of the layer – G

Shear stiffness is temperature-dependent. This parameter can be defined as shear stress as a function of shear angle. Indirectly, it can be determined using a unidirectional sample tensile test (uniaxial bias extension test). Due to the lack of availability of the results of the tensile test for Toray Cetex® TC1225, tensile test results for Toray Cetex® TC1200 were used [15]. A diagram of the tested sample is shown in Figure 6. Initially, the sample fibres are oriented at an angle of 45° to the direction of the tensile force. The test was performed at a speed of 30 mm/min. The sample was extended by 60 mm. Such a large deformation of the sample results from the arrangement of the fibres (very low tensile forces of the fibres) and very low shear stiffness in the plane of the layer of the thermoplastic matrix at a temperature close to T_m. The ratio of length to width of the sample should be 3:1. The length of the sample is 210 mm, width is 70 mm and thickness is 0.31 mm. The clean shear zone has been marked with C. In the zone marked with the symbol B, there is a semi-shear zone. There is no shear in the zone marked with the symbol A.

Figure 6.

The theoretical change of the shear angle during stretching is a function of the elongation of the sample and its geometric dimensions (2). The theoretical angle plot is shown in Figure 8. 3 γ=π−α, \[\gamma =\pi -\alpha ,\] [16] 4 γ=π2−2⋅cos−1(D+d2⋅D), \[\gamma =\frac{\pi }{2}-2\cdot {{\cos }^{-1}}(\frac{D+d}{\sqrt{2\cdot D}}),\] [16]

For the numerical analysis of the sample stretching, the following values were used: a Young’s modulus of 58 GPa for 0° and 59 GPa for 90° [9] and a thermoplastic matrix viscosity of 0.13 Pa/s [17]. Figure 7a shows the numerical model of the sample at 60 mm elongation with shear angle values. Model calibration allowed adjusting the stiffness so that the analysis results are as close as possible to the real tensile test.

Figure 7.

The graph in Figure 8 shows the theoretical change in the shear angle when stretching the sample (4).

Figure 8.

The results of the tensile test for selected temperatures are shown in Figure 9.

Figure 9.

The obtained results allowed determining the shear stiffness in the G plane (Fig. 10). The stiffness plot was generated using the conversion file provided with Pam-Form software. The area marked with dashed lines represents the change in stiffness in the shear angle range from 0° to approx. 30°. This is a value that is generally not exceeded in process with shallow moulds used.

Figure 10.

Calibration of shear stiffness allowed obtaining results comparable with the tensile test. Figure 11 presents a comparison of sample stretching diagrams for the real test and numerical analysis. Figure 12 presents a comparison of the theoretical shear angle and angle obtained during the analysis. The shear angle during the real tensile test can be measured using the digital image correlation (DIC) system [19].

Figure 11.

Figure 12.

The nature of the change in the shear angle is similar to the results of other works on this type of issues [18,20]. The change in the nature of the shear angle curve begins around 40°. The range of changes in the shear angle of the formed material does not exceed this value.

3.1.2

Determination of bending stiffness – B

Similar to shear stiffness G, bending stiffness B is temperature-dependent. Due to the lack of commonly available bending test results for the Toray Cetex® TC1225 composite, the bending test results for the Toray Cetex® TC1200 were used [21]. The bending stiffness test is carried out by free-hanging the sample at a given temperature and measuring the deflection of the end of the sample or measuring the curvature of the sample. Calibration of the model consists in determining the B value for which the deflection value obtained by means of numerical analysis will correspond to the value obtained in the bending test.

The conditions and the course of the bending test, as well as its results, are given in the study in Ref [21]. The calibration value of the end of the sample arrow was used to calibrate the model. Figure 13 presents a diagram of the test stand. The test is performed in a temperature chamber, where the sample is heated to the appropriate temperature.

Figure 13.

Using an accurate camera, it is possible to read the deflection value. For the bending test, samples with the dimensions were used: a length of 200 mm, a width of 50 mm and a thickness of 0.31 mm. The length of the bending part of the sample was 120 mm. The bending test was performed for a sample with a fibre orientation of 0° and 90° along the longer edge of the sample, determining the bending stiffness B in both directions, for a given sample temperature (Fig. 14).

Figure 14.

Figures 15 and 16 present graphs comparing the shape of the sample measured in a bending test at 360°C, for the 0° and 90° directions, and obtained by numerical analysis for the same deflection value. The same values of sample deflection were obtained for a stiffness B equal to: 0.39 Nm for the 0° direction and 0.555 Nm for the 90° direction.

Figure 15.

Figure 16.

Pam-Form v2019.0 software, version V1.9.N was used to simulate the moulding process.

Pam-Form enables modelling the processes of producing composite structures based on thermoforming, stamping, vacuum methods and automated fibre placement (AFP). It allows predicting the final orientation of the fibres, shape of the blanks and formation of wrinkles. Modelling in Pam-Form is based on two types of phenomena: the analysis of mechanical deformations and the analysis of heat transfer between parts, tools and the environment. The solver of Pam-Form uses an explicit type algorithm.

The following analysis ignores the thermal phenomena occurring in the pressing process of thermoplastic composites. For the sake of simplicity, a constant temperature of the composite was assumed, with no heat transfer between the composite and the tools and the environment. After cooling, the part hardens and retains the shape obtained during moulding.

4.1.

Boundary conditions and loads

The rigidity of forming tools in relation to the laminate being shaped is much higher, i.e. K_op > K₁. This is due to the fact that the process used a mould and stamp made of steel. It was assumed that the moulding surfaces of the tools were modelled as rigid bodies. Only the forming surfaces of the tools were applied in the numerical analysis. Friction modelling bonds were introduced between the forming surfaces and the outer layers of the laminate. Contact layers were introduced between the layers to model inter-layer friction. The determination of friction is described in section 5.2. Individual layers had areas imitating the ‘colds pots’ zone. Due to the fact that during the process layers in these areas remain immobile in relation to each other, contact bonds imitating their “gluing” were introduced between them. Springs were attached to the cold spots. The shaped blank was created from separate layers corresponding to the direction of fibres with the following arrangement: [0/45/–45/0]. This arrangement of layers results from the design assumptions adopted for the ILX-34 aircraft. The blank in relation to the mould was placed at a height of 35 mm, which corresponded to its position during the real process. The diagram of the numerical model is shown in Figure 17.

Figure 17.

Gravity was applied to the blank. The following boundary and initial conditions were adopted during the analysis:

die: u_x, uy, u_z, r_z, r_y, r_z¹ = 0;

punch: u_x, u_y, r_x, r_y, r_z=0;

free spring end: u_x, u_y, u_z, r_x, r_y, r_z=0.

velocity of punch: V_z

¹u – displacements, r – rotations, V – velocity

The profile of punch displacement is corresponding to the velocity of the press (0.032 [mm/ms], 0.0026 [mm/ms]) and is shown in the diagram in Figure 18.

Figure 18.

4.3.

Mesh parameters

Elements of meshes for individual layers were oriented in accordance with the direction of the fibres of a given layer. The layers of the composite are modelled using the created orthotropic model and are modelled with shell, 3 and 4 node finite elements of a given thickness of 0.31 mm. The size of the elements is the result of applying a factor. The same finite elements are used to model flat shaping surfaces without thickness. Pam-Form allows modelling of springs as bar parts with mass. They can be subjected to compression and tension. Their rigidity is described by a linear function (7): 7 k=(Fx+x0), \[k=(\frac{F}{x+{{x}_{0}}}),\] where F is the spring force, x is the spring elongation and x₀ is the initial elongation. Figure 19 shows the spring stiffness graph. The constant of the springs used was k = 0.0005 [kN/mm], x₀ = 40 [mm] and mass m = 0.01 kg.

Figure 19.

Springs were placed in the corners of the blanks at an angle of 45 to the direction of transport blanks under the press (Fig. 17).

The first observation from the analysis is the effect of gravity on the blank mounted in the transport frame and its fall by nearly 29 mm. This allows estimating the height at which the transport frame should be located in relation to the mould. The results are shown in Figure 20a. Figure 20b shows the influence of springs on the format mounted in the transport frame. Visible changes are observed in the shear angle in the 45° layer and deformations of the material before forming.

Figure 20.

Figure 21 shows a comparison of the shaped part with the simulation result. It can be seen that the warping of the material resulting from the pressing in the area of technological allowances coincide.

Figure 21.

To accurately reproduce the embossing and warping created on the edges of the blanks, the mesh had to be compacted in these areas. Figure 22 shows a comparison of the density of the meshes and the difference in representation of the pressed part.

Figure 22.

Figure 23 shows a comparison of shear angles in layers 45° and 0° at the end of the analysis. Shear angles do not exceed 16° in the usable area of the part.

Figure 23.

Figure 24 shows the value of bending moments in layers 0° and 45° during pressing. We can observe the formation of warping on the edges of the form. This can result in wrinkles in the finished item.

Figure 24.

Shear angles and bending moments affect the appearance of wrinkles.

Figures 25 and 26 show a comparison of the finished part with the result of the analysis during the process. The result of the analysis showed the possible appearance of wrinkles that can be observed on the finished part. Wrinkles are the result of shear angles and bending moments occurring in the material.

Figure 25.

Figure 26.

Figure 27 presents the values of the coefficient of friction in individual layers during the pressing process.

Figure 27.