Issue34

M. Ševčík et al, Frattura ed Integrità Strutturale, 34 (2015) 216-225; DOI: 10.3221/IGF-ESIS.34.23 218 laminates. The polyester resin (matrix) as well as glass fibers exhibit linear elastic behavior in tension up to brittle fracture [16], therefore, allowing the use linear elastic fracture mechanics for the analysis of the results. All the layers of the laminates were modeled according to the thicknesses estimated by the optical microscopy photos. The material properties and thicknesses of all layers of the laminate as well as the adhesive are listed in the Tab. 1. One of the failure mechanisms of the adhesively bonded GFRP pultruded laminates is the delamination cracking. The delamination usually occurs between 1 st and 2 nd combined mat. For the purpose of this paper four crack propagation paths are distinguished for the used laminate: Path 0 crack propagation in the middle of adhesive layer Path I crack propagation between adhesive and 1 st combined mat layer Path II crack propagation between 1 st combined mat and 2 nd combined mat layer Path III crack propagation between 2 nd combined mat layer and roving layer. Path 0 represent symmetrical MMB specimen whereas Path I, II and III represent increasing level of asymmetry. layer thickness [mm] E 11 [GPa] E 33 [GPa]  13 [-] G 13 [GPa] veil 0.05 3.2 3.2 0.38 1.2 1st combined mat 0.63 12.8 3.2 0.36 1.4 2nd combined mat 1.07 15.1 3.2 0.36 1.4 roving 2.5 38.9 3.2 0.35 2.7 adhesive 2 4.6 4.6 0.37 1.7 Table 1 : Material properties and thicknesses of all layers of the laminate and adhesive [17]. A NALYTICAL MODEL OF MMB TEST here exists analytical expression for the calculation of the total strain energy release rate of the symmetrical MMB specimen derived by Reeder and Crews in [18,19] in the following form:       2 2 11 2 32 2 2 3 34 16 3 L c L c ELhb Pa G     (1) This model has been successfully applied for the adhesively bonded laminate joins where the thickness of the adhesive layer was negligibly thin. However, for the structural applications the adhesive layer varies from millimeters to centimeters and therefore the adhesive layer induces asymmetric geometrical configuration and therefore the analytical model for asymmetrical MMB specimen has to be developed. Even though the Eq. (1) does not take the nonlinear effects (such as rotations of the arms or shear effects) into account it can serve as the reference equation for comparison with the proposed model derived later in this chapter. To derive the total strain energy release rate for the asymmetric MMB specimen following relation can be used [20]: a C b P G tot d d 2 2  (2) where P is the loading force, a is the crack length and C is the compliance of the specimen ( C =  / P , where  is the displacement of the lever below the applied force P ). The displacement of the lever  can be calculated using Castigliano’s theorem as follows: P W     (3) where W is total strain energy. To calculate the strain energy Maxwell-Mohr variant of Castigliano’s theorem can be used in general form: T