Mesoscale analysis of damage growth in woven composites
Introduction
Woven composites are increasingly used for lightweight aeronautical and automotive applications. The large variety in the choice of the reinforcing fabric allows the number of assembly operations to be reduced, which results in fewer weak points in a structure and lower production costs.
The behavior of woven composites may be optimized using design tools able to describe the change in their mechanical behavior from damage initiation to failure. Currently, design methods are based on macroscopic models predicting damage growth and failure in 2D [1], [2] and 3D [3], [4], [5], [6], [7] woven composites. These models require time consuming and expensive experimental tests in order to calibrate their parameters. Moreover, the model parameters must be recalibrated each time the constituents or the fiber architecture change. The number of tests may be reduced if some of the parameters can be determined by simulation of virtual tests with explicit modeling of damage initiation and propagation at the mesoscopic scale, at which the architecture of the fiber reinforcement architecture is defined.
Several strategies have been introduced to model damage at the mesoscopic scale. Gao et al. [8] proposed an analytical damage model using a mosaic laminate representation of the composite. This model allows for the calculation of the Young’s modulus of the damaged composite. However, yarn undulation, which has a major influence on damage location [9], [10], is neglected. Damage in woven composites at the mesoscopic scale is generally modeled using Finite Element (FE) approaches based on Continuum Damage Mechanics (CDM) [9], [10], [11], [12]. One drawback of such models is an erroneous prediction of damage propagation directions [12], [13]. Moreover, these models require regularization methods in order to avoid damage pattern dependence on the FE mesh [14], [15], and very fine meshes in order to obtain a good representation of localized cracks observed experimentally [16], [17], [18], [19]. Localized cracks can be modeled more accurately using discrete damage models [19], [20], [21], [22], which consist in directly inserting cracks in the FE mesh.
The modeling of damage growth requires tools that are able to determine damage initiation and propagation within the composite. Damage initiation in woven composites is generally modeled using a stress-based criterion [9], [10], [11], [12], [19], [23], which gives a good estimate of the crack locations [19], [23], [24]. However, the damage initiation strain is underestimated if only a stress criterion is used and a better estimate is obtained [24] if energetic considerations based on Finite Fracture Mechanics (FFM) [31] are also taken into account, as proposed by Leguillon [32], for instance. In a previous work [24], it has been shown that, in the studied composite, the energy criterion is dominant and thus Finite Fracture Mechanics can be used to accurately model the initiation of yarn cracks. Moreover, it also allows for the determination of the crack initiation configuration (e.g., length, orientation). The propagation of existing cracks in quasi-brittle materials can also be modeled using Fracture Mechanics. Yet, to the authors’ knowledge, damage propagation in woven composites has mainly been studied using models based on CDM [9], [10], [11], [12].
In this work, Finite Fracture Mechanics is followed to model damage growth in a composite consisting of four layers of glass fiber plain weave and epoxy matrix. In Section 2, optical micrographs of yarn cracks and debonding are presented. The crack and debond lengths are determined by means of digital image correlation (DIC). The algorithm developed to assess damage propagation is summarized in Section 3. It is used in Section 4 to determine the propagation of multiple cracks taking into account the possible coupling between several cracks. A comparison of the predicted damage growth to the experimental observations is presented in Section 5.
Section snippets
Material and testing
The composite under investigation was manufactured at Onera and consists of four layers of E-glass fiber plain weave reinforcement embedded in Araldite LY564/Hardener XB 3487 epoxy matrix. The plain fabric thread count is 2.2 warps/cm × 2 wefts/cm. The fabric mass per unit area is g/m2, the linear density of the yarns is 1200 TEX and the mass density of the fibers is 2.54 g/cm3. The dry fabric was compacted in a steel mold before matrix injection, which results in a mean fiber volume fraction
Crack propagation
Linear elastic fracture mechanics (LEFM) describes the propagation of cracks in (brittle) elastic materials. Brittle means in this case that the plastic zone around the crack tip is much smaller than the characteristic length of the material [29]. For the material under investigation, plastic deformation of the matrix in the yarns is only visible between the fibers at the microscopic scale. The size of the plastic zone is thus of only a few micrometers. Therefore, LEFM can be used for the crack
Hypotheses on crack configuration
Since the crack shape is not known a priori, hypotheses must be formulated in order to limit the number of possible crack configurations at damage initiation and therefore the number of calculations required to compute the incremental energy release rate. The first hypothesis is that the crack plane is parallel to the fiber direction since the fiber strength is much higher than that of the matrix. The cracks are also assumed to traverse the whole yarn width with straight crack fronts, and
Comparison between numerical and experimental results
In this section, the damage growth obtained taking into account the coupling between close cracks and debonding around the crack front is compared to the experimental observations. Fig. 12, Fig. 13 show the change in crack and debond densities as functions of the macroscopic strain. The critical energy release rate of the yarns was first taken from the work of Benzeggagh and Kenane [45] who studied a unidirectional glass fiber/epoxy matrix composite. Their value of J/m2 leads to a good
Conclusions
The proposed approach, which is based on discrete damage modeling in a representative unit cell of a woven composite at the mesoscopic scale, allows damage growth in the composite to be determined. Crack and debonding propagations are estimated by computing the incremental energy release rate for small surface increments. The propagation of a crack without debonding is stable after crack initiation. However, debonding initiation can make the propagation unstable and tends to accelerate crack
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