A NEW APPROACH FOR THE NUMERICAL ASSESSMENT OF FAILURE OF THE COMPOSITE DOVETAIL JOINT UNDER TENSILE LOADING

Abstract


This paper proposes and tests a new approach to assessing stress-strain states and determining failure regions of thick-walled tapered composite elements. The mesostructure features of composites, such as ply drops and resin pockets, are not explicitly considered in this approach. The constitutive model based on the multiphase finite element approach was extended to describe the three-dimensional stress-strain state. The model consisted of orthotropic linear-elastic and isotropic elastic-plastic sub-elements which simulate the properties of the fibres and matrix, respectively. The assumption of independence of the shear curve from the type of stress state was adopted to describe the nonlinear deformation response in the model. The calibration of the interlaminar nonlinear response of the constitutive model was performed using the test results of V-notched specimens under combined loading. Then, the verified model was used to determine the delamination load of the dovetail specimens. The delamination load of the dovetail specimens was estimated with the Nouthwestern (NU-Daniel) and the Hashin failure criteria. Finite element analysis of the influence of interlaminar strength and taper angle on the failure load of the dovetail specimens was performed. Based on the results obtained, we proposed the method for determining the rational parameters of the dovetail specimen. It was shown that the new approach could be effective for strength assessment and nonlinear behaviour analysis of tapered thick-walled composite structures at interlaminar shear strains up to 6%.

Full Text

The carbon fibre-reinforced plastics (CFRP) are considered to be an alternative to metals in elements of new generation aircraft, where weight is one of the critical parameters. Due to significant progress in manufacturing technologies, significant number of load-bearing elements are currently made of composites. In particular, wide-chord fan blades of foreign engines GEnx from General Electric, Rolls-Royce Advance and UltraFan families are made of CFRP [1]. This significantly reduces the weight of the blades and reduces the inertial and dynamic loads transmitted to other engine elements. Currently, composite materials are also widely used in the design of the fan of Russian aircraft engines PD-14 and PD-35 [2]. Dovetail joint is most often used to connect wide-chord fan blades with an engine rotor [3]. The composite dovetail joint is a thick-walled multilayer structure that is subjected to a complex multiaxial loading during operation. The composite dovetail joint may include various manufacturing defects, such as ply drops, warped layers, and resin pockets [4]. Due to these structural inhomogeneities and low interlaminar strength, tapered composite elements are prone to delamination [5]. At the same time, experimental data have shown that the through-thickness compression effect can significantly increase the interlaminar shear strength [6]. The combination of loads (transverse compression and interlaminar shear) leads to a complex nonlinear response, which is largely determined not by the brittle elastic fibre, but by the polymer matrix [6]. Thus, the assessment of the strength of a dovetail joint is a complex scientific and technical problem. A large number of computational and experimental studies are required to solve it [7]. There are two general approaches to predict the delamination load and the delamination growth. They are the strength of materials approach and the strain-energy-release-rate approach. According to the strength of materials approach, local stresses or strains are compared to the allowable material strength. Various failure criteria are used, for example, the maximum stress criterion, the NU-Daniel criteria [8-9], Christensen [10], Puck [11], Mohr-Coulomb [12], Hashin [13], etc. [14]. The criterion approach of maximum stresses has become widespread in engineering practice for solving this kind of problems [12-15] due to its simplicity. In [15, 20-21], rational reinforcement schemes were selected for mesoscale modelling of thick-walled composite elements. The authors did not explicitly take into account defects such as ply drops and resin pockets in these finite element models. In [21], a two-fold safety factor was obtained using the maximum stress criterion for the outlet guide vane under operating loads. In [22], the experimental results of the outlet guide vane tests under different loading types were compared with the numerical results. It was concluded that the numerical method [21] predicted a reliable assessment of the mechanical state of the composite vane. In [20], the analysis of the strength of the composite frame using the maximum stress criterion demonstrated a difference between the numerical and experimental failure load of 8%. However, the assessment of the strength using the maximum stress criterion under combined transverse compression/shear predicts a very conservative failure load [23]. The researchers [23] have shown that the NU-Daniel failure criterion predicts a higher delamination load, since the criterion considers the effect of through-thickness compression in the taper part of the dovetail joint. In this case, it is necessary to use, for example, the Hashin criterion [13], which considers the effect of tensile transverse stresses on the interlaminar strength for an adequate assessment of the strength in the thin part. It should be noted that the delamination load was determined without taking into account the actual nonlinear behaviour characteristic of thick-walled composites in the numerical models [15–23]. The alternative strain-energy-release-rate approach is based on fracture mechanics. It is used to predict the delamination growth. The laminate is assumed to fail when the available strain energy of a delamination crack in a ply interface exceeds the critical strain energy release rate for the material. Most researchers [4, 24-29] have predicted the delamination growth in tapered composite elements using virtual crack-closure technique (VCCT) or cohesive zone model (СZM). However, the authors considered the through-thickness compression effect only in some studies [4, 29]. In these studies, high-fidelity finite element simulation was used to describe the layered mesostructure of the composite. The finite element models included ply drops and resin pockets explicitly. Cohesive elements were used to analyse delamination in these models. Unfortunately, there is uncertainty in the parameters of the cohesive element adhesion strength [30-32] and the coefficient of the through-thickness compression effect [33-34] for such models. These discrepancies can lead to an error in determining the delamination region, while the peak delamination load will be significantly underestimated [4]. The researchers [4, 29] have shown that the parameters of cohesive contacts largely determine the failure type and the failure force of severely tapered specimens. It was shown that a good correlation with the experiment can be achieved by varying the parameters of cohesive pairs within the limits known in the literature. In addition, the boundary conditions introduce significant uncertainty into the calculation results. In [4], the authors assessed the effect of the friction coefficient between the dovetail specimen and the disk on the ultimate failure load. Increasing the friction coefficient from 0.1 to 0.3 leads to the change in the failure load by 20%. It is worth noting that the matrix properties provided by the manufacturer are used when simulating resin pockets in these high-fidelity models. However, authors in [35] showed that the actual in-situ properties of the resin pocket differ significantly from those of the epoxy resin obtained on standard specimens. The disadvantages of the high-fidelity finite element models combined with the high complexity of their preparation and the duration of calculations make them too difficult for practical engineering calculations of real structures. This is especially critical for the initial design stages when engineers need to select rational reinforcement schemes and assess their impact on the strength and stiffness of the entire structure. For such tasks, it is advisable to develop low-parameter numerical models using the strength approach that considers the features of nonlinear deformation and failure inherent in tapered thick-walled composite elements. To describe the nonlinear response of composites, various deformation models, based on the approaches of nonlinear elasticity, progressive damage accumulation and elastoplasticity were developed [36]. The significant number of studies [37-43] are related to the description of the in-plane nonlinear response of composites. The algorithm for describing the interlaminar nonlinear response was presented in the papers [44-45]. The researches [44] developed a low-parameter constitutive model in ABAQUS VUMAT for describing the interlaminar nonlinear response of unidirectional glass- and carbon-fibre reinforced plastics. It was shown that the nonlinear response can be approximated by the Ramberg-Osgood power law under pure shear. Similarly, the interlaminar nonlinear response was described in the papers [4, 29] when assessing the strength of tapered thick-walled composite elements. In these studies, the parameters of the approximation of the nonlinear response were determined from the pure shear deformation curves. However, the interlaminar strength and nonlinear response of thick-walled composites under combined loading differ significantly from those under pure shear [6]. The multiphase finite element (mFEA) approach [46] demonstrated good predictive capabilities of the in-plane nonlinear response fabric composites under combined loading [47]. A small number of identifiable parameters makes this model attractive for practical calculations of large structures. In this study, the mFEA approach was modified and expanded to describe the fabric composite interlaminar nonlinear response under combined loading. Model elastic parameters were identified based on standard tensile, compression, and shear test methods. The interlaminar nonlinear response was calibrated based on the test results of V-notched specimens under combined loading. Finally, numerical calculations were performed to assess the static strength of the dovetail joint. The influence of such factors as interlaminar strength and taper angle of the dovetail specimen on the failure load was also studied.

About the authors

K. A Guseinov

South Ural State University (National Research University), Chelyabinsk, Russian Federation

O. A Kudryavtsev

South Ural State University (National Research University), Chelyabinsk, Russian Federation

S. B Sapozhnikov

South Ural State University (National Research University), Chelyabinsk, Russian Federation

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