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Abstract

Compared with layup techniques, thermo-hydroforming is shown to be a viable process for mass production of thermoplastic composite structures due to its relatively rapid cycle time and low impact on the microstructure of the material. However, unlike layup technique, thermo-hydroforming can produce wrinkles in the formed part. A research was conducted wherein ABAQUS/CAE (6.14-1) was employed to numerically study the impact of thermo-hydroforming process parameters on the formation of wrinkles in a thermoplastic helmet. The optimized properties of the fiber-reinforced polymer composite was previously determined by the authors using the preferred fiber orientation model implemented as a user material subroutine (VUMAT). To account for the interaction between different layers of the laminated composite, the cohesive zone model was employed. The objective of the study was to use the simulation tool to minimize the overall wrinkle density and wrinkle height in the formed helmet as a function of the fluid pressure, boundary conditions, and especially the blank shape and the relief cuts made in the blank.

Keywords

Thermo-hydroforming FRT composite FEA forming optimization blank cutting

Introduction

In recent years, various industries have shown great interest in applying composite material in structures, instead of conventional materials, due to the high specific strength and stiffness that they offer. Many composites use matrix systems such as polyester, vinyl ester, and epoxy. This type of plastic, known as thermosets, has several advantages such as relatively low cure temperature, low cure viscosity, high rigidity, and stability over a wide range of temperatures. However, curing cycles for thermosets can take a long time which reduces their viability for mass production. Also, damaged thermoset components are not easily repairable and may need to be replaced. These shortcomings can be solved using thermoplastic resin systems instead. The thermoplastic polymer can reach large deformations before it breaks, resulting in greater energy absorption compared with thermoset polymers.¹ Thermoplastics offer the added benefit of waste reduction since they can be easily recycled and reformed.² Many methods have been developed for the manufacturing of thermoset materials. These include wet layup, vacuum molding, resin transfer molding, vacuum-assisted resin transfer molding, autoclaves, and others. These methods utilize the low temperature and viscosity of the pre-cured resin. The need for a skilled workforce and a large autoclave significantly increases the price of the prepreg. However, thermoplastic composites surpass thermoset resins in manufacturing and cost. Moreover, the main advantage of thermoplastic matrix composites is their ability to be reheated and reformed several times before the final structure is made. This reforming method has been evaluated in many studies with various thermoplastic composite forming technologies such as die molding, vacuum molding, and hydraulic molding.³ Composite formability and the final part quality were also investigated in these studies for each of these forming methods. Pourboghrat et al. obtained a patent for a composite hydroforming process that demonstrated its ability to form composite structures.⁴ This process uses pressurized and heated hydraulic fluid to form thermoplastic composite materials. The main advantage of this process over other composite forming methods is that the fluid pressure uniformly acts on the entire surface of the composite sheet and reduces the out-of-plane warpage. Zampaloni et al. demonstrated the ability of this technique to form the kenaf-reinforced polypropylene natural composite⁵ and the glass fiber textile composite.^6,7 Pressurized fluids were used to directly heat and cool composite materials, which greatly reduced the process time. The authors concluded that composite hydroforming can be scaled to effectively manufacture automotive and aerospace composite structures.

In both thermoset and thermoplastic composites, the interfacial microstructure plays an important role in controlling the optimum properties of the composite. Thermoplastic polymers do not generally form strong bonds with the reinforcing fibers, instead they rely on an interlocked polymer chain network to transfer load between the matrix and the fibers. The effect of polymer viscosity has been studied on the mechanical behavior of fiber-reinforced composites and was shown to affect the strengthening of composites.⁸ Also, the influence of pyrolysis and the microstructure of the polymer on the matrix was studied and explained.⁹ Due to the complexity and high costs associated with performing life-size experiments, numerical methods have been developed to optimize the composite manufacturing process. Yu et al. developed a material model for the processing of plain weave synthetic fabrics, by considering the fabric structure directly.¹⁰ The warp and weft yarns were characterized by the number of fibers per tow and its material properties. This material model was further refined by introducing additional parameters to account for complex phenomena that occur in a deforming fabric. Considerable improvements have been made to the relief geometry between warp and weft.¹¹ This model considers a nonlinear shear behavior as shear stress increases. This nonlinear shear response enables a more accurate prediction of the extent and location of wrinkles when simulating the deformation of the fabric. Zampaloni developed a continuum model that accounted for the change in the orientation of fibers.⁶ In his model, the preferred fiber orientation (PFO) refers to the orientation along which the composite sheet material is stiffest. The PFO material model was used in the current optimization study. The hydroforming of metal sheets and the application of numerical models to control wrinkling were demonstrated previously.¹²

Various other studies have been conducted related to sheet forming processes. Especially, sheet metal forming has been used commercially for several decades, and many numerical models and analyses have been developed for them.¹³ To manufacture sheet metal parts, industry employs different forming processes such as hot and warm stamping, spinning, shear forming, flow forming, and incremental sheet forming. Moreover, over the years, numerous numerical models have been developed for metals to represent their properties. Spinning and flow molding have also been developed for metals to produce small to medium batches of engineering components. Parameters of sheet metal hydroforming have been optimized for part designs, reduce weight and cost, and implement mixed radial and fluid molding techniques.^14,15 Stamping (also known as press hardening) is one of the typical techniques in metal forming which has been studied to control various process parameters and interactions to produce high strength steel parts with desired properties. Incremental sheet forming was developed for large deformations, and various predictive and analytical tools were also developed for numerical investigation of this process.^16
–18 However, predictive analysis tools developed for sheet metal forming processes cannot be directly applied for composite materials, and the application of the forming method could be limited to just metals in many cases.

Numerical tools and theories have been developed specifically for composite material forming, especially fiber-reinforced composite structures.¹⁹ In the case of fiber-reinforced composite materials, it has been shown that the fiber structure has a significant influence on the mechanical properties and formability of the material.²⁰ A non-orthogonal material model was developed based on the homogenization method considering the microstructure of the composite including its mechanical and structural properties.²¹ In addition, many studies on metals have shown that processing conditions and process parameters significantly affect material properties after forming. To this end, several studies have been carried out that attempted to control processing parameters.^22,23 However, these researches have been all done for stamping, and no similar research has been found for thermo-hydroforming. Therefore, the current study focuses on the formability of fiber-reinforced composite material as a function of thermo-hydroforming conditions using test results from a recent study.²⁴ Furthermore, all the numerical analyses conducted in this study used the ABAQUS/Explicit, and the user material subroutine (VUMAT) developed for the PFO model. Optimization of the thermo-hydroforming process was conducted with the objective to minimize the amount of wrinkles forming in the composite helmet. The process parameters used to control the overall wrinkle density and wrinkle height in the formed helmet were the fluid pressure, boundary conditions, and especially the blank shape and the relief cuts made in the blank.

Composite thermo-hydroforming process

Thermo-hydroforming process

Thermo-hydroforming is a complex molding process developed and patented by Pourboghrat et al.⁴ This forming process has several advantages over the match die molding. The heated and pressurized fluid can be used to maintain the composite at the proper forming temperature and to eliminate the need for tool heating. Because the forming force is applied through a pressurized fluid, the direction of the load is always perpendicular to the surface of the material. Also, the forming force is uniformly distributed by the pressurized fluid, which greatly reduces out-of-plane distortion of the molded composite part, especially in the high shear zone. These advantages of thermo-hydroforming over other thermoplastic composite molding methods make the process amenable to the fabrication of deep-drawn parts. Although simple parts have successfully been formed with thermo-hydroforming, the process has not been optimized for the fabrication of complex parts. To avoid contact between the composite material and the forming fluid, a new bladder system was recently devised for this process.²⁴ This new system uses a nylon vacuum bag and a Teflon release film to vacuum and seal the composite material and effectively protect it from coming into contact with the forming oil during the deep drawing process. This bladder system also significantly reduced the amount of fiber debris that were accumulating and clogging the fluid pressurization and filtering systems. More information about the thermo-hydroforming system can be found in these patents.^4,25 In this study, the optimization process was performed based on the experimental data obtained from a previous research,²⁴ and Figure 1 shows a schematic diagram of the thermo-hydroforming equipment. In the preform fabrication process, same as previous study, during the consolidation process, the temperature of the platens was set to the desired forming temperature of 95°C. During the cooling process, once the temperature of all zones dropped below 60°C, pressure on the platens was released, the platens were opened, and the consolidated composite preform was removed. Also, the thermo-hydroforming process was performed using a 300-ton double acting hydraulic press which could provide a maximum clamping force of about 133,400 kgf (294 klbf) and a maximum hydroforming fluid pressure of up to 13,000 kPa (1885 psi).²⁴

Figure 1.

(a) A schematic diagram of the thermo-hydroforming press and (b) the thermo-hydroforming die and composite preform setup.^4,24

Composite materials and properties

Spectra Shield SR-3136 was used in this study to optimize the thermo-hydroforming process to form a helmet with minimum wrinkles. The material properties of the Spectra Shield SR-3136 were assumed to be linear elastic up to failure.²⁶ By assuming symmetric and orthotropic plane-stress shell material properties, the stress–strain relationship and the stiffness tensor for the material can be defined as

\begin{array}{l} [\begin{matrix} σ_{11} \\ σ_{22} \\ τ_{12} \end{matrix}] = [\begin{matrix} Q_{11} & Q_{12} & 0 \\ Q_{12} & Q_{22} & 0 \\ 0 & 0 & Q_{66} \end{matrix}] [\begin{matrix} ε_{11} \\ ε_{22} \\ γ_{12} \end{matrix}] \\ with Q_{11} = \frac{E_{11}}{1 - ν_{12} ν_{21}}, Q_{22} = \frac{E_{22}}{1 - ν_{12} ν_{21}}, Q_{12} = \frac{ν_{12} E_{11}}{1 - ν_{12} ν_{21}}, Q_{66} = G_{12} \end{array}

where $E_{i j}$ is the elastic modulus for each direction, $G_{12}$ is the shear modulus, and $ν_{12}$ is the Poisson’s ratio. As for directions, 1 is along the fiber and 2 is along the transverse direction. To calculate the stiffness matrix, E₁₁, E₂₂, v₁₂, and G₁₂ are needed. These properties were calculated based on the rule of mixture, as follows

E_{11} = E_{f} V_{f} + E_{m} (1 - V_{f}), E_{22} = {(\frac{V_{f}}{E_{f}} + \frac{1 - V_{f}}{E_{m}})}^{- 1}, G_{12} = {(\frac{V_{f}}{G_{f}} + \frac{1 - V_{f}}{G_{m}})}^{- 1}

where E_f and E_m are fiber and matrix moduli and V_f is the fiber volume fraction. In this study, a fiber volume fraction of 80%, a matrix modulus of 750 MPa, and a fiber modulus of 23.1 GPa were assumed. Shear modulus of the matrix was calculated based on isotropic elastic properties. Since a thin layer of pressurized oil always separates the blank from the die and the punch, a low friction coefficient of 0.1 was assumed for the whole part in the numerical simulations. Regarding the cohesive surface interaction, Liu et al.²⁷ developed a method to directly measure the traction separation curve needed for the numerical analysis. The material properties used in this study are the same as those reported in a recent publication,²⁴ which are also listed in Table 1.

Table 1.

Mechanical properties of SR-3136 composite laminar.²⁴

$E_{11}$	18.6 GPa
$E_{22}$	3.32 GPa
$ν_{12}$	0.46
$G_{12}$	0.1264 GPa
Fiber volume fraction	0.8
Laminate thickness	7.6 mm
Number of plies	6
Friction coefficient	0.1
Cohesive zone properties
$K_{n n}, K_{s s}, K_{t t}$	8.0 GPa/m
$δ_{n}^{0}, δ_{s}^{0}, δ_{t}^{0}$	0.2 mm
$δ_{n}^{f}, δ_{s}^{f}, δ_{t}^{f}$	0.4 mm

Numerical analysis and optimization of composite preform geometry

Numerical analysis method

In this study, the Spectra Shield SR-3136 preform was considered for the helmet. This material has two orthogonal PFOs along 0° and 90°, prior to deformation. Zampaloni et al. developed a squeeze flow test for determining the PFOs of fiber-reinforced thermoplastic (FRT) composites.⁶ The finite element simulation model of the thermo-hydroforming process²⁴ utilized the PFO model. The main advantage in using the PFO model is that it tracks the evolution of the property of the FRT composite during the molding operation by tracking the rotation of reinforcing fibers. In the finite element simulation, the PFO material model tracks the rotation of individual fibers and calculates an updated local stiffness tensor for the element. When the local stiffness tensors of all the PFOs in the finite element model are calculated, they are rotated into a common material frame and summed up to determine the updated total stiffness of the composite. Updating the total stiffness of the composite will result in modifying the mechanical behavior of the FRT composite after each deformation increment. These incremental changes in the mechanical properties of the composite material have been shown to be significant and cannot be ignored in a finite element simulation.

To model the interaction between the six layers of the preform, the cohesive surface contact behavior was used, and the transverse shear stiffness was updated according to the previous work.²⁴ The cohesive surface interaction model has been researched and validated for the simulation of adhesive bonding of composites.^28,29 Liu et al. developed a method using a double notch shear beam and characterized the traction separation behavior for ultra-high molecular weight polyEthylene (UHMWPE) composites.²⁷ These properties were used in the cohesive surface interaction model.

Optimization procedure

Figure 2 shows a Spectra Shield SR-3136 composite helmet formed with the thermo-hydroforming process. The numerical model used for the simulation of the thermo-forming process accurately predicted the deformation and wrinkling in the final part.²⁴ To reduce wrinkling, it seems intuitive to apply large holding forces on the clamped surfaces of the preform to prevent the blank from drawing inside the die cavity and essentially deform it under pure stretch condition. FRT composites, however, have limited formability and their reinforcing fibers fracture under excessive stretching or shear forces. Instead, in this research, it was decided to study the impacts that forming conditions, such as the fluid pressure and the initial preform shape, have on the formation of wrinkles. To further simplify, first the numerical simulations were performed with a hemispherical punch, instead of the more complex helmet shape. However, in the simulations, a square blank was considered, like that used in thermo-hydroforming experiments performed with a hemispherical punch, because its shape and dimensions were already optimized.²⁴ Regarding the fluid pressure in thermo-hydroforming, it was found that it has a significant impact on wrinkling. However, the fluid pressure that can be realistically applied to the blank in the thermo-hydroforming process is limited by the press tonnage. Therefore, in the numerical simulations, the fluid pressure variation was limited to the maximum capacity of the available thermo-hydroforming press.

Figure 2.

Blank shape comparison between experimental and numerical results with a helmet punch and 10-cm displacement. (a) Wrinkling is occurring in the same areas (red arrow) and dome of helmet appears to be forming wrinkle free and (b) overlay between the results shows that blank draw-in between the results is well predicted.²⁴

The optimization study also considered different initial preform shapes with relief cuts made in the blank in certain locations and directions to improve the formability and reduce wrinkling. Basically, the finite element simulation results showed that the FRT composite wrinkled in high stress concentration areas, and in areas where the fiber volume fraction was highest. Therefore, the optimization strategy revolved around reducing the wrinkling by controlling the initial blank shape and avoiding stress and fiber volume fraction concentrations. More specifically, the optimum forming conditions were investigated as a function of the number, location, and the geometry of the relief cuts made in the initial blank.

Also, the finite element results clearly showed that applying a fixed (stretch only) boundary condition will result in premature material failure, as shown in Figure 4(a). Therefore, a hybrid strategy was adopted in which a two-step boundary condition would be applied in different ratios in the simulation of the thermo-hydroforming process. The first step would involve applying a constant pressure on top of the flange area of the blank which would eventually allow the sheet to draw into the die cavity. The second step would involve applying a fixed (stretch only) boundary condition to the sheet until the deformation was completed. Furthermore, for the second step, two types of constraining motions were considered on the boundary of the sheet; symmetric and fixed boundary. The symmetric boundary allowed the deformation to take place with fixed transverse motion. For example, the horizontal edge has limited vertical movement and only horizontal movement is allowed. It can reduce shear stress concentration. However, the fixed boundary condition restricted the motion in both longitudinal and transverse directions, but the thickness direction motion still occurred due to the consideration of the layer-by-layer interaction. For the two-step model, the effect of the ratio of the time that each step was applied was also studied.

In this study, to quantify how much each change affects the quality of the formed parts, wrinkle density and wrinkle height parameters were calculated for comparison. The wrinkle density is defined as the ratio of wrinkled elements to the total elements in a designated area. The wrinkle height is defined as the longest distance between the punch surface and the upper layer shell in the wrinkled area. The reason for defining the wrinkle height in this way is to include both the deformation and separation of each layer in the designated area. The designated area corresponds to the total area in which the punch and the blank are still in contact. This is determined using the nodal coordinates at the end of the forming process or at the maximum punch travel of 12 cm. The wrinkle density and height are then calculated inside the designated area, as shown in Figure 3.

Figure 3.

A calculation method for wrinkle density and height. The calculation area was calculated to the limit of uniform forming area, which was selected up to the limit of contact between the punch and the blank based on the pristine blank. Wrinkle height is calculated relative to the pristine uncut blank forming result.

Results and discussions

Numerical results with a hemispherical punch

In this study, hydraulic pressure, boundary condition, and the blank shape were considered as parameters that influence the quality of the formed part. First, the influence of pressure on the formed part was considered by preforming finite element simulations of the thermo-hydroforming process. In the simulation, a square blank was considered like that used in previous experiments performed with a hemispherical punch. As shown in Figure 4(a), using a fully fixed boundary condition eliminated wrinkles, however, the formability of the material was significantly reduced due to the high strain energy required to form the part, as shown in Figure 4(c). In fact, the simulation stopped after 9.3-cm displacement (well short of the maximum 12-cm punch displacement) due to the high strain energy and stress concentration. Next, a maximum pressure of 12.41 MPa was applied as boundary condition to fully form the part. However, due to the relatively low strain energy needed to draw the sheet into the die cavity, wrinkles occurred in specific regions of the blank where high in-plane compressive stresses developed, as shown in Figure 4(b).

Figure 4.

Forming simulation results of square blank. Fully fixed boundary condition model cannot be processed beyond 9.3 cm due to the limitation of material properties resulting in numerical instability. In the case of pressure boundary condition, the formed part is highly wrinkled beyond 12 cm forming (a) fully fixed boundary condition, (b) pressure boundary condition same as the helmet hydroforming experiment, and (c) strain energy comparison between two models.

To study the effect of blank shape, a circular blank was used to reduce the effect of the boundary condition compared with a square blank. The circular blank had a 711-mm diameter which allowed us to use a symmetric mesh structure in the finite element simulation, as shown in Figure 5(a). The simulations were performed with pressures ranging from 8 MPa to 40 MPa. As shown in Figure 5(b) to (d), the wrinkling trend is similar, but the wrinkle density and height are different depending upon the hydraulic pressure. As shown in Figure 6(c), the application of higher pressure helped reduce the wrinkling density and height up to 20 MPa. However, the wrinkling density increased with the application of higher pressures. This can be attributed to the damage and delamination that occurred at the interfaces and the boundary when higher pressures were applied resulting in a larger wrinkled area. As can be seen from the plot, the wrinkle height, like wrinkle density, is optimized around 20 MPa. From these results, it was concluded that a forming pressure range between 17 MPa and 22 MPa would be the most optimum pressure for thermo-hydroforming of this material and structure. In this study, a 20.68-MPa pressure boundary condition was used in subsequent simulations.

Figure 5.

Representative simulation results showing the effect of thermo-hydroforming fluid pressure on wrinkling in a 711-mm (28 in) circular blank with pressure boundary condition. (a) Composite ply shape and mesh, (b) 8.274 MPa (1200 psi) forming pressure, (c) 12.41 MPa (1800 psi) forming pressure, and (d) 20.68 MPa (3000 psi) forming pressure.

Figure 6.

Plot of wrinkling density and height as a function of fluid pressure in thermo-hydroforming process. Relative wrinkle height is calculated based on 20.68-MPa pressure boundary model that has the lowest wrinkle height.

As evidenced by the numerical simulations, the blank shape has a significant influence on the formability of the part. To further reduce the formation of wrinkles, the wrinkling tendency of the pristine (uncut) and cut blanks were investigated next. The forming process is like the previous thermo-hydroforming process,²⁴ in which the maximum punch stroke was 12 cm. Figure 4(b) shows the effect of the boundary condition on the wrinkling of a pristine (uncut) square blank. Wrinkles occurred at the high stress and fiber density areas along the diagonal direction. Compared with Figure 4(b), Figures 7 and 8 show that by introducing relief cuts along perpendicular directions eliminated wrinkling in the diagonal directions, and also resulted in much smaller wrinkles in the perpendicular directions. It was concluded that wrinkles along the perpendicular direction were smaller since: (1) the effective length of the material that could wrinkle along that direction became shorter, and (2) the high density and concentration in those specific regions were also reduced. Although a relief cut in the blank can reduce the wrinkling tendency, a too wide or too deep of a cut can also adversely affect wrinkling. As can be seen from Figure 7, too large of a relief cut has led to early initiation and a more severe wrinkling. Also, a too wide of a relief cut resulted in a higher wrinkling density and a wrinkling height. On the other hand, too narrow of a relief cut width does not affect the wrinkle density. As shown in Figure 7(d), the blank with a very narrow cut width shows a wrinkling behavior similar to that in the pristine (uncut) blank with a higher wrinkle density and height. Cutting depth also affects wrinkle formation. As shown in Figure 8, the shape of the wrinkle varies depending on the depth of cut, and the positive effect of the cutting relief is less when the depth is shallow. Deeper cuts result in reduced wrinkles, but if they are too deep, it can also adversely affect the final forming structure. Therefore, deep cutting within a range, such that it does not affect the final structure, can be effective in reducing wrinkles. In addition, it can be concluded that since wrinkles appear only in the cutting direction and are dependent on the cutting geometry, a relief cut effectively controls the formation and direction of wrinkles.

Figure 7.

Representative simulation results showing the effect of the V-shape relief cuts on wrinkling for a 533-mm (21 in) square blank. V-shape dimensions (depth and width) are given as a percentage of the width of the square blank. All results are for 20.68-MPa pressure boundary condition and a 27.5% depth of cut and (a) 15% width cut, (b) 7.5% width cut, (c) 3.8% width cut, and (d) 1.1% width cut.

Figure 8.

Representative simulation results showing the effect of the V-shape relief cuts on wrinkling for a 533-mm (21 in) square blank. V-shape dimensions (depth and width) are given as a percentage of the width of the square blank. All results are for 20.68-MPa pressure boundary condition and a 3.8% width cut and (a) 29.4% depth cut, (b) 20% depth cut, and (c) 16.2% depth cut.

In the case of forming a square blank with a hemispherical punch, using four relief cuts was sufficient. Figure 9 shows that when eight cuts were used, additional wrinkles developed at the cutting point, and the wrinkle density increased. On the positive side, however, the wrinkle height in a blank with eight cuts is smaller than that in a blank with four cuts. Figure 10 summarizes the change in the wrinkle formation as a function of blank cutting properties. As can be seen, the best result can be obtained with the cutting width ratio of about 4% of the length of the blank. The relative wrinkle height is calculated based on the pristine (uncut) rectangular blank formed with the same pressure boundary condition. As shown in Figure 10(a), for width ratios smaller than 3%, the model shows wrinkling behaviors very similar to those in a pristine (uncut) blank. Regarding the cutting depth, Figure 10(b) shows that once this ratio exceeds 28% of the blank, the trend reverses and the wrinkle density and wrinkle height start to increase.

Figure 9.

Numerical result for the V-shape cuts in eight directions. A 20.75% wrinkle density and 0.802 relative wrinkle height were predicted. The result is for 20.68-MPa pressure boundary condition, and relative wrinkle density is calculated based on pristine blank wrinkle height as shown in Figure 6.

Figure 10.

Plot of wrinkling density and height as a function of the V-shape cut dimensions. All results are for 20.68-MPa pressure boundary condition, and relative wrinkle density is calculated based on pristine blank wrinkle height as shown in Figure 6. (a) Fixed 27.5% depth cut and (b) fixed 3.8% width cut.

The next process variable considered in this study was the boundary condition. In this study, a two-step boundary condition was used to improve the formability without neglecting the deep drawing advantage that hydroforming offers. In the first step, the pressure boundary condition was applied like the existing hydroforming process. However, somewhere during the forming process (i.e. step 2), the boundary condition was switched from pressure to boundary condition. In this analysis, an eight-cutting relief model was used for the blank to effectively track wrinkles, and the results are shown in Figure 11 and Table 2. The ratio represents the ratio of each step to the whole process. As shown in Figure 11, an eight-direction cut blank model was used in the simulations since wrinkles are easier to measure and compare for different forming conditions. Table 2 lists the predicted relative wrinkle height and density based on the two-step boundary condition model. The two-step forming model results show improvements compared with the one-step boundary condition, and the 1:1 time step ratio model is shown to have the best results based on the wrinkle density and wrinkle height. Figure 11 shows that the cut blank model has less stress concentration and strain energy which implies a more stable forming process. Finally, Figure 12 shows that using these optimal forming parameters, it is possible to alleviate the stress concentration and residual stress formation.

Figure 11.

Numerical results from a hybrid two-step boundary condition model. In step 1, the fixed boundary is applied, and in step 2, the fixed pressure boundary is applied. All results are for a 20.68-MPa pressure boundary condition applied to a composite square blank with the V-shape cuts in eight directions. The deformed blank shapes are shown in Figure 11 for three different ratios that each boundary condition was applied. (a) 1:2 step ratio boundary condition model, (b) 1:1 step ratio boundary condition model, and (c) 2:1 step ratio boundary condition model. Severe delamination of the blank can be seen in cases (a) and (c).

Figure 12.

Numerical results of the process parameter effect in thermo-hydroforming. (a) Stress distribution and forming result with 3.8% width and 27.5% depth of cut in a 533-mm square blank, and two-step boundary condition (optimized case), (b) stress distribution and forming result for the pristine (uncut) 533-mm square blank, (c) stress distribution and forming result for the pristine 711-mm round blank, and (d) comparison of strain energy for the three models.

Table 2.

Numerical results of two-step boundary condition.

Time step ratio	Wrinkle density (%)	Relative wrinkle height
2:1	15.90	0.919
1:1	15.18	0.852
1:2	16.58	0.820

Numerical simulations with an elliptical-shape helmet punch

As in the previous section, a square blank with 0/90 fibers aligned with its sides was used to simulate the hydroforming of a thermoplastic elliptical helmet with ears, as shown in Figure 13(a). Given the elliptical shape of the helmet punch with ears, a numerical study was conducted to study the effect of aligning the long axis of the punch with horizontal or diagonal axes of the square blank. Also, similar to the hemispherical punch model (Figure 11), a numerical study was conducted in which the punch was displaced a maximum of 12 cm to examine the effects of relief cuts (i.e. number and directionality) on reducing wrinkling height and wrinkling density in the formed part. The effect of the punch alignment is represented in Table 3. The relative wrinkle height is calculated based on a pristine (uncut) square blank forming result. Wrinkles generally form in the fiber-dense areas, such as the diagonal direction, where high compressive stresses develop. However, as shown in Figure 2, the wrinkles first appeared in the horizontal direction where the blank folded, before the wrinkles appeared in the diagonal direction, followed by the formation of small wavy diagonal wrinkles. The reason for this behavior is twofold; (1) the inhomogeneity of the curvature in the elliptical punch, especially in the ear portion of the helmet; and (2) the inhomogeneous deformation of the fiber-reinforced blank due to the diagonal alignment of the punch. To effectively reduce the wrinkles, first, the forming simulation with the elliptical punch was conducted with the pristine blank. This showed the wrinkling characteristics in the final formed structure as a function of punch direction. As shown in Figure 13(b), when the long axis of the punch was aligned with the diagonal orientation of the pristine blank, the results showed less number of wrinkles and a better formability. Therefore, further numerical simulations were conducted with the long axis of the punch aligned with the diagonal of the blank with relief cuts. The results of these simulations are shown in Figure 14. To compare the wrinkle reduction, blanks with four and eight relief cuts along diagonal and horizontal directions were simulated. As given in Table 3, the relative wrinkle height is smallest for the case of relief cuts in eight directions, but Figure 14(a) shows that wrinkles appear in all eight directions. In the case of four relief cuts, the diagonal cutting of the blank is more effective than the horizontal cutting. The horizontal wrinkling can be eliminated according to this cutting relief direction, thereby significantly reducing the overall number of wrinkles. Using such simulations, the optimum blank cutting configuration can be predicted for the hydroforming of structural parts.

Figure 13.

Numerical results showing the inhomogeneity effect for a helmet-shaped punch. (a) A helmet-shaped punch and pristine 533-mm blank, (b) forming simulation result for a 12-cm displacement with diagonal direction helmet punch, and (c) simulation result with horizontal direction helmet punch.

Table 3.

Numerical results of helmet-shape punch hydroforming.

Blank shape	Wrinkle density (%)	Relative wrinkle height
Reference pristine (uncut) blank with diagonal punch alignment	17.05	1.000
Reference pristine (uncut) blank with horizontal punch alignment	18.49	1.011
Eight directions cut relief model with horizontal punch alignment	15.93	0.785
Four diagonal direction cut relief model with horizontal punch alignment	11.30	0.851
Four horizontal direction cut relief model with horizontal punch alignment	12.69	1.051

Figure 14.

Numerical results for blanks with V-shape relief cuts formed with a helmet punch. All results are for 20.68-MPa pressure forming condition. The normalized wrinkle density is calculated relative to the pristine blank wrinkle height shown in Figure 13. For the horizontal direction, a 20% depth cut is used because larger depth cuts would interfere with the forming region. For the diagonal direction, a 27.5% depth cut was used based on the optimized results. (a) Eight direction blank cutting model, (b) diagonal cutting model, and (c) horizontal cutting model.

Conclusions

The thermo-hydroforming of multilayer-reinforced composite blanks were numerically investigated with the goal to reduce wrinkling by controlling important process parameters that affect the outcome. Compared with conventional molding processes, hydroforming has the advantage of forming deep-drawn structural parts with relatively rapid forming speed. The main disadvantage of the hydroforming process is the formation of wrinkles in the formed part due to increased fiber density and in-plane compressive stresses that develop during deep drawing. To overcome this problem, numerical modeling was systematically applied as shown in the following steps to improve the formability of the material and reduce wrinkling.

Applied the highest hydraulic pressure that was below the interfacial strength of the material.

Relief cut numbers and directions were decided based on the wrinkling behavior of a pristine (uncut) blank.

A two-step boundary condition strategy was used to reduce wrinkling. In step 1, only pressure was applied, and in step 2, the fixed boundary (stretching) condition was applied.

In the case of the elliptical punch, to reduce wrinkling, the blank cutting relief was applied in the areas with the largest curvature (ear portion) that showed the highest wrinkling densities in the pristine (uncut) case.

The modified hydroforming process reduced the amount of wrinkling density and wrinkling height in the final part and also resulted in improved formability through the abovementioned modifications in the process.

Footnotes

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the US Army TACOM under the contract no. W56HZV-07-C-0355.

ORCID iD

Farhang Pourboghrat

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Effects of pressure,boundary conditions,and cutting reliefs on thermo-hydroforming of fiber-reinforced thermoplastic composite helmet based on numerical optimization

Abstract

Keywords

Introduction

Composite thermo-hydroforming process

Thermo-hydroforming process

Composite materials and properties

Numerical analysis and optimization of composite preform geometry

Numerical analysis method

Optimization procedure

Results and discussions

Numerical results with a hemispherical punch

Numerical simulations with an elliptical-shape helmet punch

Conclusions

Footnotes

Funding

ORCID iD

References