Strength of single-lap-joint assemblies of continuous unidirectional carbon fibre-reinforced thermoplastic matrix tapes under tensile loading

Abstract

Unidirectional tape-placement technologies appeared as a promising alternative due to their potential in large-scale component production. While the optimization strategies used to define the tape lay-out can be of different nature, the utilization of tape-to-tape joints is inevitable. Whereas several studies have focussed their efforts on the process and design stages, no study has yet addressed the influence of the manufacturing process on the mechanics of unidirectional tape joints. In this study, the strength of single-lap-joint assemblies of carbon fibre-reinforced thermoplastic tapes under tensile loading was analysed. The dependence of the strength on the overlap geometry and the manufacturing pressure was of main focus. Single-lap-joint assemblies with rectangular and rounded overlaps of the same overlap area were prepared employing a pre-heating stage at 250℃ and forming pressures from 3 to 100 bar. Failure of the assemblies was not observed on the overlap itself but instead on the zone near the overlap end on the adherend. Traditional determination of strength of single-lap-joint assemblies is not applicable in this case. Consequently, a typical Hashin failure criterion was used to model the failure of the assemblies. The study showed that although cohesive failure is not likely within the analysed pressure range, overlap geometry and forming-pressure affect the strength of single-lap-joint assemblies under tensile loading.

Keywords

Unidirectional tapes carbon fibre strength failure criterion joining manufacture

Introduction

Unidirectional (UD) composites offer maximum capabilities in terms of improvement of stiffness and strength compared to the polymeric matrix. Tape-placement process appears as one of the few alternatives to fully exploit the properties of UD composites with potential for large-scale applications. The process also offers the advantage of tailoring mechanical properties directly at the production line.¹

The location and orientation of tapes is usually defined according to the stress distribution on the component under service conditions. Different strategies to optimize the fibre orientation in order to maximize a specific design variable (e.g. stiffness) can be found in literature.^2–10 Figure 1 illustrates the case of a plate with a hole under tensile loading. The desired fibre orientation and the tape placement alternatives are shown. Two main challenges not yet addressed in literature arise from the example shown in Figure 1: (a) independently of the strategy employed to optimize the tape placement, tape-to-tape joints will be inevitable present on the final part; (b) in order to follow an optimal path, overlaps will surely not be rectangular in all cases. Whereas tape-to-laminate cohesion has received much attention in the last years,^1,11–13 studies on the strength of tape-to-tape joints with special regard of the manufacturing conditions are scarce in literature although these joints are also present in tailored components. On the other hand, the literature assessing the influence of overlap geometry is also limited. Laminate joints with rectangular overlaps have been widely studied^14–22 but studies addressing different overlap geometries either in tapes or laminates joints are hard to find.

In addition to the typical rectangular overlaps, rounded overlaps might be preferred to maximize material utilization in cases where the load path changes direction. Consequently, the question arises whether the strength of the joint is affected by these different overlap geometries.

The cohesion of the structure is of primary importance since it determines its ability to efficiently transfer interlaminar stresses. Typically, fibre-placement optimization algorithms are developed on the basis of perfectly bonded interfaces. In this way, large-scale manufacture of optimized tailored components will not be reliable as long as design and manufacture guidelines considering the joint strength are not defined.

The aim of the present work is to evaluate the strength of single-lap-joint (SLJ) assemblies of carbon fibre (CF) tapes produced by thermoforming. The study focusses on the strength dependence on the adherend (i.e. overlap) geometry and the manufacturing pressure of a commercial 60% (by weight) CF/polyamide 6 UD tape of nominal thickness of 0.19 mm. A tensile characterization of the tape material was first carried out. As cohesive failure was not detected, definition of strength based on the in-plane shear stresses developed in the interface between adherends is no longer relevant. The mechanisms behind the failure of the assemblies are a complex combination of the thermo-mechanical events occurred during the thermoforming stage and their effects on the composite microstructure (local fibre orientation, fibre waviness, etc.).²³ Nevertheless, as the failure was identified on the adherend and cohesive failure did not occur, a typical UD composite failure criterion can provide a good enough approach to support the technology-development process. In this way, Hashin failure criterion²⁴ with dependence on the manufacturing pressure was used to model the observed strength variations.

Experimental

Tape tensile characterization

Tensile specimens of UD tape material were produced according to ASTM D 3039²⁵ with three different fibre orientations: 0° (also referred to as longitudinal), 45° and 90° (also referred to as transversal). Tabs were needed in order to avoid grip-induced fracture. These were made of epoxy/glass fibre laminate prepared by hand lay-up and cured at room temperature for 24 h. The tape-tab interface was previously sandpapered to improve adhesion. Tabs dimensions were in concordance to the standard.²⁵

CF-tape was characterized under tensile loading at room temperature. At least five specimens for each loading angle were tested. Longitudinal tests were done employing a servo-hydraulic MTS 852 Damper Test System equipped with a 50 kN load cell. Transversal and 45° tests were carried out using a BOSE Electroforce 400N LM1 TB A-T actuator equipped with 55 and 450 N load cell, respectively. Full-field strain measurements were done employing digital image correlation (DIC). Figure 2 schematises the experimental setup. Tests were done at 2 mm/min as specified in the standard.²⁵

SLJ assemblies characterization

Two different joint geometries were prepared employing seven different manufacturing pressures. The influence of the geometry was studied using rectangular and rounded overlaps of the same overlap areas. The nominal dimensions of the jointed assemblies are presented in Figure 3. Tabs were also required for testing the SLJ assemblies. The manufacture of the tabs was the same as employed for the tape tensile characterization.

The joint-preparation process for all SLJ specimens is given as follows:

The two adherends were placed according to Figure 3 on a polished metal plate.

A second polished metal plate was placed on the adherends. The specimens were placed now between both metal plates.

The package was heated in infrared oven up to 250℃, and the temperature was kept constant for 5 s.

The package was removed, compressed and cooled in a cooling press at different pressures.

Table 1 summarizes all conditions covered by the SLJ characterization.

Table 1.

SLJ assemblies description.

Specimen description	Overlap geometry	Manufacturing pressure (bar)
RECT-P003	Rectangular	3
RECT-P005		5
RECT-P010		10
RECT-P020		20
RECT-P030		30
RECT-P060		60
RECT-P100		100
ROUN-P003	Rounded	3
ROUN-P005		5
ROUN-P010		10
ROUN-P020		20
ROUN-P030		30
ROUN-P060		60
ROUN-P100		100

SLJ assemblies were tested in tension at the Transfercenter für Kunststofftechnik using a Zwick/Roell Z020 machine at a nominal cross-head speed of 1.27 mm/min.²⁶ The displacement was monitored using a clip-on extensometer over a gauge length of 50 mm. The overlap of the assembly was approximately centred in the gauge region (Figure 4). All specimens were tested until rupture registering the load–displacement response.

Tape constitutive modelling and model calibration

Due to the thin thickness of the studied tapes, it is reasonable to work under plane stress assumption. Under these conditions, the transversely isotropic elastic behaviour is completely defined by four parameters, namely E₁, elastic modulus in longitudinal direction; E₂, elastic modulus in transversal direction; ν₁₂, Poisson’s ratio; and G₁₂, in-plane shear modulus.

Initial guess of E₁ and E₂ was obtained by least-squares correlation of the longitudinal and transversal tensile tests data, respectively. Likewise, an initial estimation of ν₁₂ was computed from the axial and lateral strain measurements obtained from the longitudinal tensile data. The calculation of G₁₂ is not such a straightforward process since pure shear tests are almost no feasible in the case of very thin tapes. Available standards^27,28 recommend the test of a ±45° laminate. However, response of a laminate might differ from that of a single ply due to inter-ply effects. Alternatively, 45°-specimens were tested in tension. All four elastic parameters were afterwards reverse engineered considering tensile data at all three loading angles using a minimization algorithm based on the Nelder–Mead simplex method.²⁹

Mechanical characterization

Tape tensile tests

Initial guess of elastic parameters, obtained as described previously, is shown in Table 2. Reverse-engineered elastic parameters are shown in Table 3. The coefficient of determination (denoted as R² and calculated according to equation (1)), taking into account all loading cases, was 0.953

R 2 = 1 - \frac{\sum_{i} (y_{i} - f_{i}) 2}{\sum_{i} (y_{i} - \bar{y}) 2}

(1)

Table 2.

Initial estimation of elastic parameters of the tape material.

	E₁ (MPa)	E₂ (MPa)	ν₁₂ (−)
Mean	87958	2245	0.411
CV (%)	4.15	5.97	15.6

Mean values and coefficient of variation in percentage, denoted as CV (%), are shown.

Table 3.

Reverse-engineered elastic parameters of the tape material.

E₁ (MPa)	E₂ (MPa)	ν₁₂ (−)	G₁₂ (MPa)
92652	2182	0.465	1143

In equation (1), y_i are the observed stress values of each test, $\bar{y}$ is the arithmetic mean of y_i and fi are the stress values obtained employing transversely isotropic elasticity.

Ultimate stresses are shown in Table 4. S₁₁, S₂₂ and S₁₂ indicate the maximum stress reached during the tensile test at loading angles of 0°, 90° and 45°, respectively. Large scatter on ultimate stresses was found when testing 45°- and 90°-specimens.

Table 4.

Ultimate stresses of tape tests.

	S₁₁ (MPa)	S₂₂ (MPa)	S₁₂ (MPa)
Mean	1375	2.81	9.30
CV (%)	5.53	29.2	20.0

Mean values and coefficient of variation in percentage, denoted as CV (%), are shown.

SLJ assemblies tests

Independent of the manufacturing pressure and the adherend geometry, no cohesive failure was observed. Figure 5 shows a rectangular and a rounded joint after testing. It can be seen, especially at the overlap ends, that both adherends remained bonded while several cracks propagated through the matrix, parallel to the fibre. Fibre fracture was identified preferentially also at the end of the overlap, agreeing with the results of Wang et al.¹⁹ However, axial stresses on the adherend are mainly responsible for the assembly failure in the present case and not only a combination of shear and peel stresses as it would be normally expected. The distributions of peel/shear stresses causing cohesive failure and axial stresses, main root of adherend fracture, are shown schematically in Figure 6.

Kim et al.¹⁶ tested SLJs of UD CF/epoxy laminates with different bonding methods. Although co-cured specimens showed the highest strength, delamination was still observed as a main root of failure. In the other cases, adhesive failure or interlaminar failure of the adherends reduced the joint strength. Similar results have been found for thermoplastic matrix laminates where cohesive failure or intralaminar failure takes place depending on the welding procedure.³⁰ Adherend fracture, as observed in present work, has not yet been reported since when strong interfaces are present, the interlaminar failure in the adherend and/or interface cohesive failure precedes the fibre fracture.

As cohesive failure was not present in any case, the strength of the assemblies was characterized in terms of the ultimate tensile strength (UTS), which was ad hoc defined according to equation (2), as the maximum load reached during the test (P_max) per unit of cross-sectional area of one adherend (A₀)

UTS = P_{max} / A_{0}

(2)

The UTS for all tested assemblies is presented in Figure 7. Some main observations can be made on these results:

For the same overlap area, assemblies with rounded adherends exhibit in general lower strength;

Manufacturing pressure has geometry-dependent impact on joints;

Strength of rectangular joints is not severely affected by the manufacturing pressure;

A threshold-manufacturing pressure can be identified for rounded joints beyond which the strength is reduced drastically.

Such threshold does not exist in the case of rectangular adherends.

According to the above-mentioned observation, three clear regions can be identified in Figure 7: (a) for manufacturing pressures up to 10 bar, almost no difference between strength of rectangular and rounded joints is observed; (b) a transition takes place between 10 and 20 bar where strength becomes geometry dependent; (c) for manufacturing pressures of 20 bar and higher, the strength of the rounded assemblies is significantly lower.

The transition between 10 and 20 bar is of high importance. Considering the case of tape-placement process integrated in a thermoforming line, these results allow defining forming limits for such operation. Depending on the geometry of the joint, the strength can be estimated and allowable stresses (i.e. forming conditions) consequently defined.

The strength of rounded joints showed strong pressure dependence while the rectangular practically did not exhibit changes with the manufacturing pressure. Thus, it can be said that the geometry of the adherend is a relevant parameter and affects the strength of the assembly. Fibre lateral constraint during the pressing/forming stage depends on the overlap geometry, and consequently, the local alterations induced on the fibre orientation are different. In addition, different overlap geometries induce different stress distributions. The combination of these two facts results in the observed pressure/geometry dependence. Figure 8 presents the shear stress distribution for both geometries under equal tensile loads. It can be seen that due to the different overlap geometries, tensile stresses are transferred differently from one adherend to the other. While shear stresses near the rectangular overlap can be practically neglected, they are one order of magnitude higher around the rounded overlap under the same applied nominal stress.

The above-described experimental observations provide a novel insight in the SLJ strength dependence on the manufacturing pressure. However, they are not enough to design tailored components. Therefore, a failure criterion, which predicts the assembly strength as a function of the processing condition, is mandatory in order to define maximum allowable loads.

Failure dependence on manufacturing pressure

Failure criterion and calibration procedure

Decohesion of the SLJ was not observed in any case as it was already pointed out. Both adherends remain bonded and instead of joint failure, adherend fracture near the overlap end takes place. Based on these observations, an UD composite failure model, Hashin failure criterion²⁴ is used, and the material strength values are estimated for each manufacturing pressure. It must be noted that only tension modes are analysed here as the compression testing of studied tape is not possible without using a ground structure due to instability of the testing specimen. The failure criterion for the analysed modes (fibre and matrix tension) is expressed as²⁴

Fibre tension [\frac{σ_{11}}{X T}] 2 + [\frac{τ_{12}}{S L}] 2 = 1

(3)

Matrix tension [\frac{σ_{22}}{Y T}] 2 + [\frac{τ_{12}}{S L}] 2 = 1

(4)

where X^T, Y^T and S^L, respectively, represent the longitudinal tensile strength, transversal tensile strength and longitudinal shear strength.

Failure parameters under tension in longitudinal and transverse directions, X^T and Y^T, respectively, were initially approximated as the maximum stresses (S₁₁ and S₂₂) reached during the tensile tests of tapes at the respective loading angles. The remaining parameter, the longitudinal shear strength (S^L), was first estimated considering the maximum shear stresses reached during the 45°-tests.

In order to capture the dependence of the material strength with the manufacturing pressure, an optimization routine was developed. The failure parameters were obtained combining finite element (FE) analysis and numerical optimization algorithms. An overall cost function G was defined, which was additively decomposed in G_rect in regard to rectangular joint and G_roun concerning the rounded joint. Since the stiffness of the joint assemblies showed to be independent of the manufacturing pressure, and furthermore, no variations with respect to the adherend geometry were observed, the cost function was defined only in terms of ultimate load regardless the load–displacement behaviour. Both G_roun and G_rect are based on the minimization of the square differences between the average experimental ultimate load and the maximum load achieved in the corresponding FE simulation. The cost function is only dependent on the failure variable $\overset{⇀}{x}$ , which in our case is defined as a vector containing the engineering failure parameters (X^T, Y^T, S^L). The above-mentioned definitions are expressed in equations (5) and (6)

G_{rect} = (\bar{P_{rect}^{\exp}} - P_{rect}^{FE} (x)) 2

(5)

G_{roun} = (\bar{P_{roun}^{\exp}} - P_{roun}^{FE} (x)) 2

(6)

It was assumed that the longitudinal strength (X^T) is not affected by the pressing process. Therefore, maximum X^T value during the optimization was constrained to S₁₁, which is observed experimentally. No such boundaries were set for Y^T and S^L.

The calibration of the failure parameters can then be given by the following optimization function

min (G_{rect} (x) + G_{roun} (x))

(7)

For solving the above-explained problem, an iterative procedure, where both joint cases are iteratively solved and compared with experimental data, is schematised in Figure 9.

The average maximum loads reached during the test of the rectangular $\bar{P_{rect}^{\exp}} androunded \bar{P_{roun}^{\exp}}$ joints are calculated from experimental data for a determined manufacturing pressure. FE simulations of the tests considering the initial guess of failure parameters $\overset{⇀}{x} 0$ are carried out. The maximum loads in the rectangular and rounded case (denoted as $P_{rect}^{FE} and P_{roun}^{FE}$ , respectively) are computed and compared with the experimental results for each pressure case. Convergence conditions were set in terms of G and $\overset{⇀}{x}$ . In case, the reduction of the cost function or the improvement of the solution is less than the established tolerances, the process stops. If the convergence conditions are not satisfied, failure parameters are modified using a trust-region³¹ optimization algorithm and the simulation is rerun with the updated parameters. This process is recomputed iteratively until one of the convergence conditions is achieved.

FE analysis

Rectangular SLJ was modelled using quadratic quadrilateral shell elements (S84). Quadratic, quadrilateral and triangular shell elements (S8R and STRI65) were used for the rounded joint. The corresponding meshes are shown in Figure 10.

Cohesive contact³² was employed on the overlap area. In this way, the stiffness observed in the SLJ tests can be easily reproduced. Fracture loads were determined as the maximum load reached during the non-linear incremental analysis. Brittle fracture was simulated in the usual way by employing small damage evolution energy.³²

The computation time should be reduced as much as possible in order to provide an accurate calibration of the failure criterion in a reasonable time. Therefore, a sensitivity analysis on mesh size and damage stabilization³² was previously performed to determine the optimal simulation conditions, which provide the fastest computation time with 10% repeatability on the fracture load between conditions.

Hashin results and strength parameters variation

The model predictions are shown in dotted lines in Figure 7. The employed model works well up to 30 bar but does not describe accurately enough the strong geometry dependence found for 60 and 100 bar. The found failure parameters and their dependence on the manufacturing pressure are presented in Figure 11. It can be seen that the drop on the strength of rounded assemblies in Figure 7 is accompanied by an important decrease in the S^L in Figure 11.

The obtained values of Y^T, as well as S^L in the low-pressure range, differ significantly from the ultimate stresses observed in the tape off-axis test (S₁₂ and S₂₂). However, under off-axis, loading matrix failure determines the tape ultimate stress leading to a premature fracture of the specimen mainly as a consequence of the very thin thickness of the tested tapes (0.19 mm). Due to local defects, which are induced in the manufacturing process of tapes, the strength parameters are much lower than those measured in the consolidated joint. In this way, the values of S₁₂ and S₂₂ cannot be directly correlated to the parameters Y^T and S^L, and they must be determined from SLJ test.

The ability of the model to predict the observed differences between both geometries lies mainly on the variation of S^L with the manufacturing pressure. However, the difference in the predicted UTS can be as high as the difference between the shear stresses developed in rectangular and rounded overlaps. The additional drop of the UTS is attributed to the fact that for high-forming pressures (60–100 bar), joint geometry is severely altered.

Summary and conclusions

CF tapes were successfully characterized under tensile loading. Using DIC techniques, a complete description of their transversely isotropic elastic behaviour was introduced. SLJs were also characterized under tensile loading. Overlap geometry and manufacturing pressure effects were taken into account.

Cohesive failure of SLJ of the analysed tapes did not occur under the processing conditions studied. On the contrary, brittle tape failure was repeatedly observed at the zone near the overlap end. It could be shown that geometry is of special importance. While strength of rectangular assemblies did not exhibit dependence on the manufacturing pressure, a significant reduction of the strength of rounded assemblies was found for high-manufacturing pressures. Local structural alterations introduced by the forming process are different for each geometry. Moreover, the presence of rounded overlaps promotes shear stresses in the zone near the overlap end (Figure 8). It seems that rounded assemblies can undergo such stresses as long as the local structural alterations introduced by the forming process reach a certain degree of severity. In the present work, this threshold was identified on the forming pressure range between 10 and 20 bar. For higher manufacturing pressures, since the load-bearing capability of the material was somehow degraded during the forming stage, the strength of the rounded SLJ was found to be lower.

The observed effects of the manufacturing pressure on the tape material could be successfully modelled employing Hashin failure criterion. The presented results offer the possibility to improve the design of patch-tailored composite structures. Maximum allowable loads of such structures can be defined now subjected to their processing conditions (i.e. manufacturing pressure). Furthermore, overlap geometry has proven to play an important role on the strength of the joint. In this way, definition of optimized tape lay-out in a tailored structure should also consider the geometry of the generated overlaps, avoiding pressure/geometry combinations (e.g. high-forming pressure and rounded overlaps) that clearly showed to reduce the strength of the assembly.

Footnotes

Acknowledgements

The authors thank the cooperation of Transfercenter für Kunststofftechnik in part of the experimental work.

Funding

Financial support by the Austrian Federal Government for research and development in the framework of the Austrian Competence Headquarter Program operated by ENGEL AUSTRIA GmbH is gratefully acknowledged.

Conflict of interest

None declared.

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