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Abstract

Thermoplastic composites were applied to one of the more challenging and highly loaded fittings in aircraft structures, bathtub fittings. Bathtub fittings with multiple intersecting walls were designed using finite element analysis and special purpose software and were subsequently manufactured using press-forming of pre-heated flat blanks with varying thickness. Non-destructive Computed Tomography (CT) scans were used to evaluate the quality of the resulting parts. Subsequent static tests demonstrated strength 5% lower than the design strength and in close agreement with analysis predictions. Fatigue tests showed excellent performance with the failure mode not caused by the out-of-plane stresses in radius regions. A recently developed methodology for fatigue predictions based on the amount of energy dissipated per cycle was applied and was in very good agreement with the test results.

Keywords

Composite fittings fatigue performance press forming static failure

Introduction

Thermoplastic composites have been applied on aircraft since the 1980s, with the F-22 weapons bay and landing gear doors¹ and the Westland helicopter 30–300 stabilizer and fin assembly.² Since then, their application has remained relatively limited for decades (less than 20% of airframe structure). Recently, renewed interest in the superior out-of-plane damage resistance, low-cost high rate production and recyclability potential of thermoplastic composites has led to using them in larger quantities. Simple parts, such as tension and shear clips currently used on the Boeing-787 and the Airbus A-350,³ have evolved to more complex applications such as co-consolidated stiffened panels and leading edges.⁴

The present study focuses on advanced, highly loaded fittings. In general, fittings are relatively small (with longest dimension typically smaller than 200 mm), three-dimensional parts connecting a minimum of two other components. They are, usually, loaded in all three directions and they can be critical for airframe structures as their failure may lead to catastrophic failure of the vehicle. For these reasons, the historical practice has been to include extra safety factors in their design and analysis⁵ such as fitting factors, which are also used for joints.

We will focus here on bathtub fittings, typical configurations of which are shown in Figure 1. They are, primarily, tension fittings, transmitting tension load, and are similar to angle fittings but have at least three intersecting walls. The metal versions of these fittings have been employed since the 1940s and mostly approximate methods to analyze them have been available in the open literature, for decades.⁶ In general, the main tension load is transmitted to the end pad through a bolt and fasteners are used to connect one or more of the remaining walls to adjacent structure. The use of fasteners makes it easy to remove and replace them during maintenance and repair actions. Thermoplastics provide one advantage in that respect because welded connections can be used instead of fasteners. This reduces weight and permits disassembly by subsequent melting of the welded connections as necessary.

Figure 1.

Representative bathtub fittings.

Traditional manufacturing methods for metallic fittings are either assembling fastened sheet metal pieces or machining, both of which are labor-intensive. Thermoplastics offer the possibility of stamping such geometries at a fraction of the cost of the metallic equivalent. In addition, their lower density and high out-of-plane strength would lead to lower weight.

Given that industry has more experience with thermoset materials, the question that arises is whether, for fittings of this complexity, thermoset materials should be preferred over thermoplastic materials. Thermoset fittings of this complexity would use either a labor-intensive hand layup process or resin transfer molding with an expensive fiber preform. In both cases, from our own experience, the cost of the thermoplastic fitting would be lower and the rate of production (number of units per hour) much higher. In addition, the hand laid up thermoset version would have problems with high interlaminar stresses at the radius regions connecting the end pad with the vertical wall(s) and the resin transfer molding process would require a stitched, and thus expensive, preform with an accompanying reduction of in-plane strength properties.

In this study we focus on a generic, highly loaded, bathtub fitting as shown in Figure 2. The overall dimensions shown in the Figure are representative of regions with highly loaded tension connections in airframe structures. Press-forming was selected as the manufacturing process. Two major challenges must be overcome: (1) Maintaining high quality and consolidation at the radius region despite the relatively deep draw near the end pad with height 51 mm and width 57 mm and (2) Pressing a flat pre-consolidated laminate into the right shape and minimizing the wrinkles that will be created at the corners.

Figure 2.

Basic geometry of bathtub fitting evaluated in this study.

Unlike metals where deep drawing for various alloys has been studied extensively, deep drawing of thermoplastic parts is still an area of active research mostly focusing on automotive applications. In one of the earlier works, Gutowski et al⁷ studied wrinkling of thermoset and thermoplastic composites during diaphragm forming and established scaling laws using ideal kinematics accounting for relative movement and the magnitude of shear forces required. Robroek⁸ carried out a detailed study of the inter-ply slippage and intraply shear mechanisms which come into play during press-forming and provided details on how matrix viscosity and intra-ply shearing resistance can be tailored through careful choice of layup, applied pressure, stamping material and temperature. Ozdemir et al⁹ researched deep drawing and spring-back on a standard (Nakajima) set up varying pressure and temperature. They concluded that deep draws up to 25 mm were possible. Haanappel et al¹⁰ investigated the formability of quasi-isotropic laminates made of uni-directional or eight harness satin (8HS) material for parts with compound curvature. The 8HS material performed better showing wrinkles only on curved flanges.

The die and stamp material selection and the radii used at corners are also very important in parts like the fitting shown in Figure 2. The relative stiffness of stamp and die and the local geometry will determine whether defects such as wrinkles, waviness, thickness variations, voids and delaminations will appear in the finished product. Brooks et al¹¹ provide a detailed discussion of the material choices for stamp forming of thermoplastic composites, quality of resulting parts and effect of process parameters. Addressing the defects and attempting to predict their creation, Wilkinson¹² developed a simulation process accounting for the material behaviour during the stamping process and found good correlation with experiments. Jamin et al,¹³ carried out an experimental study which evaluated the effect of local thickness and part radius on overall part quality for different process parameter choices. They provided ranges of acceptable tool radii minimizing defects. Today, there are many software codes developed with thermoplastic draping and forming in mind especially when it comes to deep drawing. Bergsma’s¹⁴ early work in this area deserves mention.

Achieving a thermoplastic component that meets the required loads while also being cost-effective and consistently high-quality, is a complex challenge. It demands careful consideration of geometry, process parameters, and material selection to optimize the design and manufacturing process. In addition to an understanding of the material behavior and manufacturing process, there is a need for rapid and accurate analysis methods that will assess the static and fatigue strength of the candidate designs. Because of the frequent use of metal bathtub fittings in airframe structures, accurate semi-empirical methods were developed in the 1940s and were kept proprietary in aerospace company manuals. As these methods were based on assumptions which do not necessarily carry over to composites without appropriate adjustments and re-definition of terms, detailed analysis of such composite fittings is performed by finite element methods.¹⁵

In what follows, the approach to design and manufacture highly loaded thermoplastic composite bathtub fittings using press-forming is described. The quality of the fittings is assessed with CT scans and their mechanical performance under static and fatigue loads is experimentally quantified. In addition, methods to accurately predict static and fatigue failure are presented.

Design

A design load of 14,400 N was selected as representative of moderately to highly loaded such fittings. The design of Figure 2 was based on the premise that a flat blank with the appropriate layup would first be made in a press. This would then be stamped in a metal die to the required shape. It was recognized that this process, while extremely efficient, would lead to the creation of wrinkles at corners where the blank is folded. This is shown in Figure 3.

Figure 3.

Material folding at corners and forming wrinkles.

Software which enabled tracking plies as they deform onto a die was used to predict the wrinkle creation. This is simple pre-processing software within the Composite Design workbench in the CATIA V5 which enables monitoring the stretching, scissoring and folding actions of plies given initial (flat) and final (target) geometries. The predicted locations of wrinkles are highlighted (in red) in the last image in Figure 3. Note the visualization in Figure 3 only shows the regions where the wrinkles are expected and not their size which was part of tabular output. The size of the wrinkles was predicted to vary almost linearly from each corner at the bottom of the end pad to a maximum size of 20 mm at the top. This was in reasonable agreement with CT scans which showed approximately 25 mm maximum wrinkle size. The CT scan is shown in Figure 4. The wrinkle in Figure 4 seems to be nearly vertical and constant at 25 mm instead of being inclined with length increasing from the bottom to the top. This difference could either be a result of how the CT scan slices are taken relative to the viewer or, more likely, resulting from the fact that the orientation and attitude of the blank during stamping were not precisely the same as in the simulation. Small differences amplify when material is folded around closed corners.

Figure 4.

CT scan of vertical wall of fitting (end pad is on the right).

The TC1200/PEEK Five Harness Satin (5HS) material with nominal ply thickness 0.31 mm was selected with 10 plies at the end pad (layup: 60% 0/90, 40% 45/−45) and 7 plies (70% 0/90, 30% 45/−45) everywhere else. An alternating approach of overlapping plies around corners (with 12 mm inside radius) was selected to minimize thickness build-up and provide continuous fibers around radius regions. This is shown in Figure 5. The local layups and radii of wall intersections were selected through an iteration process which allowed sequencing of the failure modes such that in-plane failure preceded delaminations. This minimized bending stiffness reductions after initial failure which, in turn, minimize deflections and rotations, which could lead to an early fatigue failure.

Figure 5.

Repeating pattern of plies around the end pad edges (only portions of the complete flat blank are shown for clarity).

As a final note on the design, it should be mentioned that the location of the bolt hole was selected such that the local bending moment due to the bolt eccentricity is minimized.

Manufacturing

The selected layups and basic process steps are shown in Figure 6.

Figure 6.

Layups and manufacturing steps (I. Consolidation II. Thermoforming). Mat’l: TC1200/PEEK 5HS).

Manufacturing took place in two separate steps: Flat laminate consolidation into the blank consisting of multiple plies, and hot press forming (shaping) of the blank to the final shape. During each of the steps, differing only in the process cycle time, the material is heated above the melting point (T_m) and then cooled to the glass transition temperature (T_g) under an applied pressure over the entire surface of the laminate/component. The consolidation and hot press process consist of the steps in Table 1. (see also Figures 6 and 7).

Table 1.

Steps of consolidation and hot press forming processes.

Step	Consolidation	Hot press forming
1	Preparation of a stack with the desired number and orientation of prepreg plies	Cutting out blank into desired shape
2	Preheating the press to consolidation temperature T_c	Preheating mold to mold temperature T_md
3	Loading prepreg to press when T_c is reached	Mounting the blank in the transporting frame
4	Closing the press with the lowest possible initial pressure and increasing temperature to the processing temperature T_p	Moving the blank into the IR heater
5	Applying the required pressure	Heating up the material in IR oven for time t_h
6	Maintaining consolidation temperature T_c and pressure for time t_c	Transporting the blanket into the given position in the press
7	Cooling to T_r while maintaining applied pressure	Thermoforming with the pressure P for time t_c
8	Removing consolidated laminate	Releasing the part

Figure 7.

Fitting manufacturing. Press flat charge, attach with tensioning springs, stamp into die, remove and trim.

A steel die with a silicone stamp was used to press the consolidated preform to the final shape. The same steps were followed as for the flat laminate consolidation, see also Figure 7. Twenty-one specimens were fabricated with the geometry shown in Figures 2 and 6. Of them, three were used for static and 18 for fatigue tests. Four additional specimens with tapering thickness in the vertical walls and base were fabricated successfully to verify part quality for more complex geometries. These were ultrasonically welded on stiffeners of “L” cross-section, see bottom left of Figure 7. A PEEK foil was used as an energy director and a specially-manufactured metal anvil held the surfaces to be welded together. The void content was less than 1.5% and the quality, as evidenced by visual inspection, which verified the thickness, and C-scan, which showed the wrinkle was as expected, was very good.

Static and fatigue tests

For the static tests, a back-up steel fitting was used to connect the test specimen at the end pad. The metallic back-up fitting was designed to have the same stiffness as the composite fitting such that, under the same load, displacements and rotations at the bolt location were matched. The test specimen and back-up fitting were fastened on steel plates which were gripped by the test machine as shown in Figure 8. Three specimens were tested after having been welded on the stiffener to check the strength of the welds between fitting vertical wall and base to stiffener web and flange. Failure was in the fitting, as intended, and not in the weld lines, thus confirming that the welds were sufficiently strong. Three additional specimens were tested without being welded to the stiffener to give baseline failure load and mode for the fatigue test.

Figure 8.

Static tensile test configuration (right after failure).

The average test failure load, for specimens without stiffener, was 13,700 N with 6.0% coefficient of variation. The average failure load is 5% lower than the design load of 14,400 N. Given the multiplicity of failure modes and their interaction, which are discussed in some detail in the next section, it can be seen that the methodology is accurate and only minor improvements are needed. The failure location, between the radius region and the loading pin in the end pad, is shown in Figure 10.

For the fatigue tests shown here, all done with specimens not welded on L-stiffeners, three specimens were tested at each load level. Loading was tension-tension with R (=σ_min/σ_max) = 0.1. Each load level was selected as a percentage of the average static strength. Two identical specimens were loaded back-to-back into the fixture as shown in Figure 9. This saved time in testing. If one specimen failed, another specimen would replace it and the test would continue until the next specimen failed. For the last specimen of each set of three, a steel back-up fitting was used. The fatigue failure mode was the same as for the static tests with one exception: Once failure started, there was complete separation of the end pad from the rest of the fitting as shown in Figure 10.

Figure 9.

Tension-tension fatigue test configuration.

Figure 10.

Fatigue test failure.

Results of the fatigue tests are shown in Figure 11. The fatigue failure curve is close to horizontal for high loads (loads higher than 85% of the average static strength). At lower loads, between 60 and 85% of the static strength, there is a relatively steep drop. The best fit curve to the experimental data shown in the Figure was a polynomial least square fit of the geometric means of the fatigue tests at each load level.

Figure 11.

Fatigue test results.

Analysis and correlation of tests with predictions

Static analysis and comparisons with tests

The stand-alone fitting, without attachment to the “L” stiffener, was analyzed with finite elements. The local stresses and strains predicted by NASTRAN were used with separate special-purpose software to check for the following failure modes:

1. Material strength, in-plane, using the Tsai-Hill failure criterion.

2. Out-of-plane strength in the radius regions using the anisotropic elasticity solution by Lekhnitskii¹⁶ combined with a maximum stress failure criterion for the interlaminar stresses.

3. Pull-through failure at the loading bolt and connection fasteners by comparing the maximum out-of-plane shear stress at the edge of the washers to the material interlaminar shear strength.

4. Bearing strength of loading bolt and attachment fasteners.

The finite element model represented closely the static and fatigue test configurations of Figures 8 and 9. The composite bathtub, steel bathtub (whenever used), two steel plates and six bolts (connecting bathtub fittings to steel plates) and one loading bolt between the two bathtub fittings were all included in the model. The finite element analysis was done using the MSC NASTRAN 2017 solver. The non-linear SOL400 simulation with non-friction contact was carried out to better capture the contact and interaction between the end pads of the back-to-back bathtubs and prevent self-penetration. This contact is caused by the bending moment created by the offset of the applied displacement at the loading bolt and the axis of the connecting fasteners at the base of each fitting. The model included 8060 CQUAD4, 56 CTRIA3, 7 CBUSH and 14 RBE3 elements and 8423 nodes with 67,581 degrees of freedom. The boundary condition represented the static and fatigue test configurations of Figures 8 and 9 with clamping of the edges of the steel plates in the grips of a test machine. The model was fixed at one edge of one steel plate and the load was applied to the end of second one in the form of an applied displacement. The finite element model is shown in Figure 12.

Figure 12.

Finite element model of the fitting in the static and fatigue test configuration.

Each laminate layup used PCOMPG properties allowing for different thicknesses according to the number of plies at each location. As mentioned earlier in the section on design, the shape of the fitting and the method of stamping a flat charge leads to wrinkles at the edges of the end pad and makes it difficult to determine the local fiber direction. At the same time, it is necessary to approximate the changes in fiber direction as closely as possible. This was done by combining the desired fiber orientation for each ply and the selected overlapping pattern (see for example Figure 5) with the expected wrapping action around radius regions and the location of ply drops. A transition region was thus created at one corner where the end pad meets the base and one vertical wall. This is shown in Figure 13. The transition region was then sub-divided into sections with different material properties also shown in Figure 13. The other half of the fitting was created by using symmetry.

Figure 13.

Zones with different material properties approximating fiber orientations and ply drops in the transition region.

CBUSH spring element properties were determined for fasteners using PBUSH property cards with associated stiffness for each axis. Basic material properties for the thermoplastic 5HS fabric are given in Table 2.

Table 2.

Material properties for TC1200/PEEK 5HS material.

Property	Symbol	Design value
0˚ tensile Young's modulus, (GPa)	E11	64
90˚ tensile Young's modulus, (GPa)	E22	55
In-plane shear modulus, (GPa)	G66	4,5
Poisson's ratio, [-]	v12	0.05
0˚ tensile strength, (MPa)	F1t	830
0˚ compression strength, (MPa)	F1c	615
90° tensile strength, (MPa)	F2t	622
90˚ compression strength, (MPa)	F2c	660
In-plane shear strength, (MPa)	F12	140
Interlaminar shear strength, (MPa)	Fils	90
Interlaminar tension strength, (MPa)	Filt	88
Open hole compression, strain [-]	eOHC	0.0064
Open hole tension, strain [-]	eOHT	0.0095

The analysis was carried out to determine (a) the displacement value corresponding to the load that would cause first-ply failure and (b) to obtain local loads for separate analysis of the failure modes discussed at the beginning of this section. The analysis results showed failure for an applied displacement which corresponds to a failure load of 14,400 N applied at the connection bolt. These results are shown in Figure 14. The failure location is in the end pad, half-way between the radius region at the bottom and the connecting bolt. The critical stress at that location, in terms of the stress with magnitude closest to its ultimate strength value is 90-degree (or fill direction) compression. This occurs in one of the plies towards the inner wall of the end pad which is locally under compression in that direction. It is important to note that the fitting was designed to not have an out-of-plane, interlaminar, failure as the critical failure mode. The results from the tests confirmed the design and analysis with in-plane failure being critical. This was possible because of the high out-of-plane strength of thermoplastics.

Figure 14.

Failure location predicted by analysis compared to test results.

Fatigue analysis and comparisons with tests

Instead of relying on curve fitting models and extensive coupon testing to establish S-N curves or da/dN curves, the approach used here was based on the realization that, during fatigue testing, there is a certain amount of energy dissipated during every cycle as indicated by the area enclosed in each loading/unloading cycle. This is shown schematically in Figure 15.

Figure 15.

First two loading/unloading cycles and dissipated energy per cycle (R = 0 shown for clarity).

The non-linearity of the stress-strain curve in Figure 15 is exaggerated for clarity. The example in this Figure is for R = 0. Even with a slight non-linearity, when unloading to zero from the maximum applied stress σ, there will be a small non-zero residual strain ε_m1. Re-loading and unloading would lead to a new residual strain ε_m2. The area in the enclosed shape AHBIA is energy per unit volume or specific energy dissipated during this cycle. After a number of cycles, usually a few dozen, the loading/unloading cycle stabilizes to a shape with constant enclosed area or specific energy dissipated. Fatigue failure will occur when the sum of the dissipated specific energies equals the area under the static stress-strain curve. For high cycle fatigue, dividing the total area under the static stress-strain curve by the stabilized dissipated energy gives a sufficiently accurate prediction. This approach was implemented successfully for metals in Ref. 17 and is applied here also. Following,¹⁷ the cycles to failure are given by:

N_{f} = \frac{8 U_{d f}}{σ ε \frac{σ}{E_{o} ε} {(1 - \frac{σ}{E_{o} ε})}^{2} (2 - \frac{σ}{E_{o} ε}) (3 - \frac{σ}{E_{o} ε}) {(1 - R)}^{n_{1} + 1}}, R > 0

(1)

N_{f} = \frac{8 U_{d f}}{σ ε \frac{σ}{E_{o} ε} {(1 - \frac{σ}{E_{o} ε})}^{2} (2 - \frac{σ}{E_{o} ε}) (3 - \frac{σ}{E_{o} ε})}, R = 0

(2)

where σ is the applied maximum stress, ε is the applied nominal strain (before cycles stabilize), E_o is the initial Young’s modulus of the static stress-strain curve, n₁ is the Ramberg-Osgood exponent of the first reloading cycle assuming that the stress-strain curve up to the applied stress can be represented by a Ramberg-Osgood model, and U_df is the specific energy at static failure, i.e., the area under the static stress-strain curve.

The above equations were derived in Ref. 17 for simple uni-axial loading. In a situation with complex stress interactions as in a bathtub fitting, the local stress and strain at the failure location must be known. The finite element model, discussed in the previous section, showed a three-dimensional stress state at the failure location shown in Figure 14. However, as already mentioned in that section, the critical stress was the in-plane compression stress in the 90-degree direction. This, and its corresponding stress-strain curve were used in applying equation (1) and were found to be sufficient. This will be shown below. More refined predictions can be obtained by making the strength values corresponding to the stresses present at the failure location into functions of cycles and combining them in an interaction criterion.¹⁸

It was assumed here, and was confirmed by the fatigue tests, that the fatigue failure was at the same location and in the same failure mode as the static failure. If, due to load redistribution, the failure location and mode are different under fatigue than under static loading, the inputs to the equations above must be modified accordingly. Note also that these equations are not valid for R <0.

As discussed in Ref. 17, for the method to give accurate predictions, it is necessary to have very accurate stress and strain values. Changes of less than 1–2 percent in the strain value can cause huge changes (by a factor of 5 or 10) in the predicted fatigue life. This can also be an advantage. If, for different applied stress levels accurate values of strain are available, predictions reproducing experimental scatter in fatigue can be obtained.

The static stress strain curve for the thermoplastic material used here was obtained in a number of tests during material characterization. The corresponding stress-strain curves for nominally identical specimens are shown in Figure 16. There are records from 10 different tests shown in this Figure. It is observed that while at low loads, less than 150 MPa, the curves are very close to each other, at higher loads they depart. Even in the region 150–250 MPa which corresponds to the maximum stresses exerted during some of the fatigue tests, there are small differences in the strains from one specimen to the other for the same applied stress. This means that each specimen, if its material were used in a bathtub fitting being tested, it would give a different fatigue life prediction. Each of the curves in Figure 16 was digitized. Then, for a given applied load in the connecting pin in the fitting, the local stress at the failure location was obtained from the finite element model. The strain corresponding to this local stress was determined for each of the specimens in Figure 16 using the digitized curves. Next, equation (1) was applied and a life prediction was obtained. The procedure was repeated for all specimens for the same applied load to the fitting. Then, the same approach was used for different applied loads. The predictions thus obtained are shown on the left of Figure 17 along with a curve obtained by connecting the geometric means of the predictions at each stress level. On the right of Figure 17, the test results are shown.

Figure 16.

Typical stress-strain curves for transverse (fill) compression of TC1200/PEEK 5HS material.

Figure 17.

Fatigue life predictions (left) and test results (right) for thermoplastic bathtub fittings.

The different stress-strain curves result in different fatigue life predictions as indicated by the filled circles on the left Figure 17. It is interesting to observe that the scatter as predicted by this approach covers about three orders of magnitude and is in close correspondence to the three orders of magnitude scatter shown by some of the test results.

As a final comparison, the predicted curve on the left Figure 17 is plotted with the test results and best fit curve from the right Figure 17. This is shown in Figure 18. There is a small difference between the test and prediction curves. This is partly because there are not enough test data points for applied loads between 90% and 100% of the static failure load. In addition, both the test results and the predictions suggest a rather steep drop of the fatigue curve around the 10K cycles. This appears to be related to accumulation of broken fibers in the tension-loaded portion of the fitting. Once a certain threshold has been reached, which for uni-directional material is between 11% and 22% of the fibers in tension,¹⁹ load is redistributed and the neutral axis moves towards the compression side increasing the compressive stress (in the fill direction). This, in turn, precipitates final failure. As the material here is fabric, the details of the mechanism and the threshold of broken fibers, if there is one, need to be further investigated. The conclusion is that good modeling of the local stress field, combined with the fatigue model which accounts for the energy density dissipated during each cycle, can lead to accurate fatigue life predictions for such structures with local three-dimensional stress fields.

Figure 18.

Fatigue life predictions compared to test results.

Summary and conclusions

Highly loaded thermoplastic composite bathtub fittings were designed, analyzed, fabricated and tested under static and fatigue loading. Press forming was used to press a flat charge and, in a second press forming step, the charge was stamped into the final shape using a metal die and a Silicone stamp. The design process accurately predicted the location and size of wrinkles created. Taking advantage of increased out-of-plane strength of the PEEK matrix used (compared to thermoset materials), the layup and geometry were selected such that out-of-plane failure due to delaminations in the radius regions of the fitting was not possible. The fitting was analyzed using non-linear finite elements and the internal stresses were used for in-plane and out-of-plane failure mode analysis: Material strength, corner delamination, pull-through, and bearing strength. An approach to calculate the energy dissipated during each fatigue cycle was used to predict fatigue life. The predicted failure location matched exactly the failure location observed in tests. The static test failure load was within 5% of the predicted load. The fatigue predictions were very close to the test results. It was also shown that accurate knowledge of the stress and strain during fatigue testing can be combined with a model predicting the strain energy density dissipated per cycle to lead to a good estimate of the fatigue life scatter. Such models, with proper generalization to other structures and loading configurations can be used to provide insight in the static and fatigue behavior of thermoplastic materials and minimize the number and duration of tests needed.

Footnotes

Author contributions

Wojtuszewski: Finite element models. Farbaniec: Design and Manufacturing. Kassapoglou: Static and fatigue analysis, design and project coordination. Ahsan: Design.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Ethical considerations

This article does not contain any studies with human or animal participants.

ORCID iDs

Radosław Wojtuszewski

Christos Kassapoglou

Data Availability Statement

Data used in this paper are available upon request to the authors.*

References

Harris

Starnes

Shuart

, “An assessment of the state-of-the-art in the design and manufacturing of large composite structures for aerospace vehicles”, NASA TM-2001-210844, 2001.

Spurway

Duthie

. The use of fibre reinforced thermoplastics for helicopter primary structures and their engineering substantiation. Proceedings of 45^th American Helicopter Society Forum 1989: 497–597.

Gardiner

. TPCs on the boeing 787 and airbus A350. Composites. 2011.

Offringa

. Thermoplastics in aerospace, new products through innovative technology. SAMPE J 2005; 41: 19–27.

Federal Aviation Regulation Part 25 – Airworthiness Standards: Transport Category Airplanes . Washington DC: Federal Aviation Administration Department of Transportation, 2024.

Fuselage structural analysis vol III, frames, bulkheads and fittings, Report No 144, Cincinnati, OH, 1964.

Gutowski

Dillon

Chey

, et al. Laminate wrinkling scaling laws for ideal composites. Compos Manuf 1995; 6: 123–134.

Robroek

LMJ

. The development of rubber forming as a rapid thermoforming technique for continuous fibre reinforced thermoplastic composites. Amsterdam, Nethernalds: Delft Univ Press, 1994.

Ozdemir

Subasi

Karataw

. Investigating the effects of forming parameters on molding force and springback in deep drawing process of thermoplastic composite laminates. JK Sci 2021; 34: 506–515.

10.

Haanappel

ten Thije

RHW

Sachs

, et al. Formability analyses of uni-directional and textile reinforced thermoplastics. Composites 2014; 56: 80–92.

11.

Brooks

Wang

Ding

, et al. A review on stamp forming of continuous fibre-reinforced thermoplastics. Int J Lightweight Mater Manuf 2022; 5: 411–430.

12.

Wilkinson

. Optimization of the stamp forming process for thermoplastic composites. Bristol: Univ, 2021. PhD Thesis.

13.

Jamin

Dubé

Laberge Lebel

. Stamp forming of thermoplastic composites: effect of radius and thickness on part quality. ECCM 16, 16^th European conference on composite materials, Seville, 2014.

14.

Bergsma

. Three-dimensional simulation of fabric draping. PhD thesis Delft University of Technology, 1995.

15.

Faile

Hollis

Ledbetter

, et al. “Development and test of advanced composite components”. NASA, 1985, vol TM 86512.

16.

Lehknitskii

. In: Tsai

Cheron

(eds). Anisotropic Plates, Translated. New York: Gordon and Breach Science Publishers, 1968, pp. 23–24.

17.

Kassapoglou

. Determination of energy dissipation during cyclic loading and its use to predict fatigue life of metal alloys. Fatigue & fracture of engr matls & structures, 2023, pp. 3667–3679.

18.

Philippidis

Vassilopoulos

. Fatigue strength prediction under multiaxial stress. J Compos Mater 1999; 33: 1578–1599.

19.

Socci