PSI - Issue 13

Mor Mega et al. / Procedia Structural Integrity 13 (2018) 123–130 M. Mega et al. / Structural Integrity Procedia 00 (2018) 000–000

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structure with the desired properties, unidirectional (UD) or multidirectional (MD) laminates may be used. A UD laminate contains UD plies with fibers oriented in one specific direction. An MD laminate may be composed of plies whose fiber orientation varies between di ff erent plies. These plies may be either UD or woven. Multidirectional com posites containing woven plies are known to have higher impact resistance, fatigue resistance, fracture toughness and damage tolerance than UD laminates [5]. The interlaminar fracture toughness of MD composites made from various materials under mixed mode loading has been investigated. Yet, only a delamination along the interface between two UD plies oriented in di ff erent directions [6] - [9] or between two woven plies [10, 11] was considered. The frac ture toughness for a delamination between two dissimilar plies, namely a UD ply and a woven ply has not yet been discussed in the literature. A body containing an interface delamination may be subjected to any combination of three basic deformation modes, namely, opening, mode I, in-plane sliding, mode II and out-of-plane tearing, mode III. Only one standard exists for determination of interlaminar fracture toughness for mixed mode I / II conditions [12]. This standard utilizes the mixed mode bending (MMB) specimen and is limited to UD composites. Although the test setup is cumbersome, the main advantage of the MMB test is that various mode mixities may be achieved with one test setup. Many other beam type specimens have been suggested for this type of testing which have not been standardized, each produces only a small number of mixed mode ratios which limits their usefulness [13] - [21]. To obtain a wide range of mode mixities, using a simple test setup, as well as only one specimen type and fixture, the Brazilian disk (BD) specimen was used in the current investigation for mixed mode fracture tests. A methodology for measuring the interface fracture toughness of fiber-reinforced MD laminates using the BD specimen was first introduced in [22] and implemented for an interface between two transversely isotropic UD plies, namely, 0 ◦ // 90 ◦ , in [7]. Note that two slashes indicate the position of the delamination. In addition, a two-dimensional fracture criterion was presented. Two methods, the displacement extrapolation (DE) method and the conservative inter action energy or M -integral, were used to separate and calculate the stress intensity factors resulting from mechanical loading. With the DE method, the delamination opening displacements are used to calculate the stress intensity fac tors. By means of the M -integral, with use of auxiliary solutions, a su ffi cient number of equations to determine the mixed mode stress intensity factors are obtained. Both methods were extended to three dimensions for a + 45 ◦ // − 45 ◦ interface and a three-dimensional criterion was developed [23, 8]. A two-dimensional thermal M -integral was de rived in [24] and extended to three dimensions in [8]. In the current study, the first term of the asymptotic expansion was developed and used for the three-dimensional mechanical and thermal M -integrals, as well as the DE method to determine the mechanical and thermal stress intensity factors. The composite investigated here is composed of carbon fibers embedded in an epoxy matrix. The delamination is along an interface between an upper UD fabric ply with fibers oriented mainly in the 0 ◦ -direction and a lower woven ply with fibers oriented in the + 45 ◦ / − 45 ◦ -directions. Eight BD specimens have been tested at four loading angles leading to various mixed mode ratios. Two specimens were tested for each loading angle. The layup, material properties and dimensions of the specimens, as well as the experimental setup are discussed in Section 2. Based on the test results, finite element (FE) analyses were carried out in conjunction with the three-dimensional conservative mechanical and thermal M -integrals and the DE method. The stress intensity factors resulting from mechanical loads K ( f ) i , i = 1 , 2 , III , and from residual curing stresses K ( r ) i , along the delamination front for each specimen were obtained and superposed to obtain a total value K ( T ) i . The FE model, test results and the obtained stress intensity factors are presented in Section 3. Using these results, the interface fracture toughness G ic was determined as a function of the phase angle ψ which represents the in-plane mode mixity.

2. Specimen details and experimental procedure

In this study, a delamination along an interface between two materials was investigated. In Fig. 1, the delamination is presented where each material is denoted by k ( k = 1 , 2). The upper material ( k = 1) is a UD fabric composed of fibers embedded in an epoxy matrix. Approximately 97% of the fibers are carbon fibers oriented in the 0 ◦ -direction ( x 1 in Fig. 1); the remaining 3% are glass fibers oriented in the transverse, 90 ◦ -direction ( x 3 in Fig. 1). The lower material ( k = 2) is a plain balanced weave with carbon fibers oriented in the + 45 ◦ / − 45 ◦ -directions in the x 1 − x 3 -plane with reference to Fig. 1. These are also embedded in an epoxy matrix.