About the applicability of a simple model to predict the fatigue life and behavior of woven-ply thermoplastic laminates at T > Tg
Introduction
In advanced engineering fields such as aeronautics or aerospace, thermosetting resin (TS)-based composite materials have been extensively used over the past 30 years. Even if they have interesting mechanical properties, they are also characterized by undeniable drawbacks such as the need for low-temperature storage of raw materials, a difficult-to-control reticulation process, a very long curing process and a handmade draping that generates most of the non-reversible defects of manufacturing process. One projected breakthrough in the composites industry cost equation is expected to involve large scale manufacture of continuous fiber thermoplastic (TP) composites [1]. TP matrices offer improved raw materials and processing costs, as well as improved functional performance. Because the processes of material consolidation do not involve exothermic curing reactions, they can use shorter autoclave cycle times (which are ideal for large production), although the temperatures involved are generally higher than those for TS matrices. The meltability of TPs also provides better potential for recycling purposes. In such context, high-performance thermoplastic resins (e.g. PEEK and PPS) offer a promising alternative to TS resins [2]. Further growth of TP-based composites is also directly linked to the knowledge of their potentially highly ductile behavior of the matrix. The fundamental understanding of the mechanisms of deformation and failure in [±45°] TP-based laminates, and their dominance under service conditions, is essential for engineering design [3], [4], [5], [6]. Angle-ply laminates loaded in tension have shown promise of high strains to failure, but often fail prematurely due to matrix microcracking or plasticization, and high free-edge stresses lead to an extensive delamination [7]. The effect of fiber reorientation via a scissoring action has been shown to strongly influence the tensile behavior of angle-ply laminates. Thus, a “pseudo-ductile” behavior can be observed as the fiber rotation itself, combined with matrix yielding, leads to large strains. Such behavior is exacerbated when TP-based materials are applied at service temperatures above their glass transition temperature [8]. It usually results in a pronounced non-linear degradation of their structural properties, and the thermo-mechanical response strongly depends on the architecture of the reinforcement (UD- or woven-ply).
Most of the studies available in the literature on the fatigue of TP composites deal with the behavior of UD-ply laminates. Woven-fabric composites have been finding increasing use in advanced structural applications in recent years, because of their enhanced through-thickness stiffness and strength properties, impact resistance, dimensional stability, fracture toughness, damage tolerance and ease of manufacturing. Although there are a few studies on the fatigue behavior of woven-ply TS-based composites [9], it is still an open question for woven-ply TP-based composites for which the fatigue behavior is strongly influenced by the ductility of the matrix. Indeed, the distribution of the matrix in woven-ply laminates initially results from the non-planar interply structure of woven plies, in which the weft fiber bundles undulate over the warp fiber bundles according to a given weave pattern [10]. An interlaminar crack will interact with matrix regions and the weave structure during its propagation, resulting in substantial crack growth resistance and a better resistance to delamination [11]. The concept of introducing soft regions, sometimes referred to as softening strips, into a fiber composite to provide barriers to crack growth and so raise the intrinsic toughness of the material has been well established [12], [13]. From the fatigue performances standpoint, it is therefore potentially interesting to associate woven fabrics with highly ductile thermoplastic matrices [14], [15], which effect is even more noticeable when service temperature is higher than the material glass transition temperature [16]. The effects of matrix toughness on fatigue response of carbon fiber reinforced composite laminates was extensively studied in the eighties and nineties [17], [18], [19], [20], [21]. In particular, the transferability of matrix toughness and fatigue resistance to fatigue growth in TP composites has been investigated in UD-ply laminates [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], in woven-ply laminates [14], and at high temperatures lower than Tg [4], [34], [35], [36], [37]. Another aspect that is closely related to the fatigue behavior of TP-based composites is the dependency on strain rates or load frequencies [23], [25], [38], [39], [40], [41], [42]. From these works, it appears that the fatigue life of TP-based laminates decreases as loading frequency increases, because the specimens heat up and the matrix eventually becomes more compliant and yields at lower stresses. The temperature might even exceed the glass transition temperature locally in regions of high stress concentration [12], making essential to evaluate the contribution of viscous effects (viscoelasticity and viscoplasticity) to the fatigue behavior of TP-based laminates at high frequencies. The fatigue behavior of carbon woven-ply PPS laminates has already been investigated at room temperature [42], [43], [44], [45], [46], in the case of both on-axis and off-axis tensile loadings on [(0,90)]4s laminates. Be that as it may, very few authors have investigated the high-temperature fatigue behavior of such materials [15], [47]. In addition, considering the ductile nature of the PPS matrix at temperatures close to its Tg, the observations of failure surfaces shows that the matrix is characterized by a plastic deformation aspect, suggesting that PPS matrix yields until fatigue failure. Finally, there are very few references available in the literature dealing with the fatigue behavior of UD-ply and woven-ply PMCs when temperature is near or higher than their glass transition temperature Tg [34], [48], [49], [50], [51].
Under cyclic loading, composite materials, unlike metals, accumulate damage in a generalized rather than a localized way, and failure does not always occur by the propagation of a single macroscopic crack [12], ultimately causing failure. In laminated composite materials, the micro-structural damage accumulation is characterized by multiple damage modes, such as crazing and cracking of the matrix, fiber/matrix debonding, fiber fracture, transverse-ply cracking, delamination, and void growth. These modes occur sometimes independently and sometimes interactively, and the predominance of one or the other may be strongly affected by both material variables and testing conditions. They usually appear rather early in the composite fatigue life, and degradation may occur gradually or catastrophically. As damage accumulates in the material, both stiffness and strength of composite materials are adversely affected by repeated loading, and the higher the maximum stress level during cycling is, the more rapid the decrease in mechanical properties. Thus, the damage initiation mechanisms and growth are quite complex for composite materials, and the concept of damage accumulation may be used as a suitable approach to predict the fatigue life of composite materials structures [3]. A comprehensive review of the fatigue damage modeling of fiber-reinforced composite materials is given in [6], [52], [53]. The brief literature review herein is focused on TP-based composites. Combining a general extended Tsai–Hill fatigue failure criterion with the Classical Laminate Theory, Jen et al. have tried to predict the fatigue strength and life [33]. Even though this approach gives acceptable results in the case of quasi-isotropic and cross-ply laminates, the coupling effect of plastic deformation and friction between the layers results in a relatively poor agreement with experimental data. Such a coupling is instrumental in ruling the mechanical response of angle-ply TP-based laminates [5], [6], particularly at temperatures higher than Tg [8]. Loverich et al. have developed a life prediction methodology for PPS composites subjected to cyclic loading at elevated temperatures (at T = 90 °C close to Tg). This method is based on the assumption that damage accumulation progressively reduces the residual strength of UD cross-ply laminates [48]. Based on a physical phenomenon of damage growth, Chen and Hwang developed a fatigue damage model including the nonlinear effects of stress ratio and stress frequency on the damage index for UD-ply composites [54]. However, this approach is not convenient to account for the rapid increase in damage growth during the last stage of fatigue life. In order to predict the three stages of the damage evolution, Nouri et al. proposed a model built in the framework of the continuum damage mechanics [53]. Through an extension of the model initially proposed by Ladeveze and LeDantec [55], they combined Norton-like power and an exponential laws expressing the damage rates as a function of the associated thermodynamic dual forces. Petermann and Plumtree proposed a unified fatigue failure criterion based on strain energy densities, satisfying the conditions of continuum mechanics [56]. Being load path independent (only peak values are needed), this methodology accounts for the mean stress effects, and considerably reduces the number of parameters to be determined experimentally. This model successfully predicts the fatigue lives of different UD laminates under cyclic tension considering various combinations of fiber load angle and stress ratio. Nevertheless, such fatigue criterion does not quantitatively evaluate the fatigue damage as a function of the cycles, and then it is not adequate to capture the primary phases of damage growth in Polymer Matrix Composites (PMCs). Apart from the models built in the framework of the continuum damage mechanics which are more complex to be implemented, cumulative damage theories have often been used to predict the fatigue life of composite materials [12]. They usually consist of the formulation of a damage summation rule to predict fatigue life without recourse to experimental observation of the damage accumulation process. Because of its simplicity, the Palmgren–Miner rule is still widely used but fails to predict the effect of load history [3]. Based on cumulative damage, Tang et al. also developed a simple a fatigue model applied to orthotropic laminates. This model is classically defined from the loss in material’s stiffness, the stress amplitude and loading frequency [57]. Mao et al. proposed a fatigue cumulative damage model based on mean strain development in the case of angle ply laminates. This nonlinear model captures the damage evolution in composite materials subjected to fatigue loadings, and fatigue damage can be evaluated at any time with the parameters obtained from experimental data. Montesano et al. have applied this model to predict the fatigue life of woven-ply TD laminates at high temperature. They conclude that the model was able to accurately capture the three-stage damage development with excellent correlation to the experimental data [6].
Substantial databases exist on many factors (geometrical, constituents, environmental, type of loading) contributing to the fatigue behavior of [±45°] TP-based laminates. The fundamental understanding of the mechanisms of deformation and failure in [±45°] layers of laminated composites, and their dominance and interactions under service conditions, is essential for engineering design, and justifies a scientific engagement [3]. Fatigue tests conducted on [±45] woven-ply laminates allowed the authors to investigate specifically the contribution of the matrix ductile and viscous behavior, exacerbated at temperatures higher than Tg (e.g. 120 °C), to the high-temperature fatigue behavior of A–P laminates. Such temperature was chosen because advanced aeronautics structures, particularly nacelles, require high-performance fiber-reinforced polymer matrix composites, which can be used at temperatures up to about 120 °C. The basic idea was to investigate the specific fatigue behavior and damage accumulation in woven-ply laminates consisting of pure matrix regions at the crimps. Lastly, through the application of a simple analytical model, the concept of damage accumulation was used to quantitatively evaluate the fatigue damage within the laminates as a function of the cycles [58].
Section snippets
Materials
The studied composite materials are carbon fabric reinforced laminates consisting of a semi-crystalline high-performance PPS matrix. The toughened PPS resin (Fortron 0214) is supplied by Ticona. The woven-ply prepreg, supplied by SOFICAR, consists of 5-harness satin weave carbon fiber fabrics (T300 3 K 5HS), such as the volume fraction of fibers is 50%. A DMTA analysis showed that the glass transition temperature is 95 °C. The experimental method used to determine the value of Tg is based on the
Monotonic off-axis tensile behavior
In laminates subjected to monotonic off-axis tensile loadings, the matrix-dominated response results in an elastic-ductile behavior (See Fig. 2) [8]. The highly ductile behavior of PPS can be observed because the test temperature (120 °C) is higher than its Tg. Load–unload tensile tests performed on A–P laminates show a gradual decrease in material’s longitudinal modulus as well as an increase in residual strains [8]. Fatigue tests were conducted at four stress levels where laminates display a
Tension–tension fatigue behavior of woven-ply laminates
The description of damage evolution in [±45°]S laminates indicates that monotonic and fatigue tensile damage evolution is very similar, and can be called a matrix mode because the types of damage (matrix cracking, debonding and delamination) are not only governed by the matrix properties but are also located in matrix-rich regions (See Fig. 5).
From the tension–tension fatigue behavior of woven-ply laminates standpoint, it seems that these pure matrix regions play a significant role depending on
Conclusion
The present work is directed towards the improvement of the material understanding about the off-axis tension–tension fatigue behavior of woven-ply C/PPS laminates at test temperatures higher than its Tg. Thanks to matrix-rich regions resulting from the non-planar interply structure of woven plies, the obtained results show that ductility and time-dependent behavior of PPS matrix exacerbated at T > Tg are instrumental in ruling the fatigue behavior of woven-ply C/PPS laminates. Thus, the fatigue
Acknowledgement
The authors would like to acknowledge Professor L. Taleb for his financial support. They are also grateful to the Aircelle Company for supplying the composite materials.
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