Issue 29

M. Marino et alii, Frattura ed Integrità Strutturale, 29 (2014) 241-250; DOI: 10.3221/IGF-ESIS.29.21 244 stiffer and stronger than the matrix, can only fail due to loads acting in their axial direction. By omitting the subscript k discriminating different layers and addressing a single FRP layer, transversal failure occurs when 2 2 / 1 T AT AT T S S                   , (12) where / T S   is the laminate strength (rispectively in tension and compression) in the transverse-to-the-fibers direction, while AT S is the shear laminate strength. On the other hand, the fiber failure criterion is expressed by the following relationships: A A S    , A A S     (13) where A S  and A S  are the laminate strengths (respectively in tension and compression) along the fibers direction. The second criterion, provided by Huang [15], operates on the stress states in fibers ( ) f  and matrix ( ) m  , different in each layer and computed starting from the layer stress state k  by employing Eq. (11). Accordingly, it prescribes tensile failure for the constituent c if , eq c c S    , (14) where c S  is the tensile strength for the constituent c , and               1 2  1 , 1 2 2  0 0,  1                  c c c c c eq c q q q c c c c when when q       (15) c q being a power index accounting for the effects of a biaxial stress state on the bearing capacity, and   1 c  ,   2 c  are the first (maximum) and the second (minimum) principal stresses in the constituent c . Furthermore, a compressive failure of the constituent is assumed to occur if   2    c c S  (16) where c S  is the compressive strength for the constituent c . Material property degradation In this study, a simple degradation rule is employed by assuming that a damaged constituent reduces its elastic moduli by the factor 1   . When the Rotem failure criterion is used, the overall laminate stiffness matrix is locally degraded, while, by using the Huang failure criterion, the elastic moduli of fibers or matrix are locally degraded, depending on the damaged component. P ROBLEM STATEMENT he effectiveness of the proposed progressive damage model is verified by addressing as a benchmark the experimental study by Ascione et al. [10], carried out on a pin-plate system comprising a glass fiber reinforced polymer (GFRP) laminate with epoxy matrix. This experimental investigation aimed to analyze the influence of the fiber-to-load inclination angle, referred to as  , on the bearing failure load associated to the action of a steel pin (see Fig. 1). In particular the experiments in [10] considered three types of laminates, different in the stacking sequences of the plies. Herein reference is made to the laminate type denoted in [10] as Laminate 1 , consisting in a square-shaped plate (500 mm wide) and comprising eight equally-oriented plies of Continuous Strand Mat GFRP material placed between two plies of Chopped Strand Mat (CSM), resulting in the plying sequence 4 [ / 0 ] s CSM . The plate was tighten by two steel plates 500 mm wide and 50 mm thick, with a central circular hole of 300 mm in diameter (see Fig. 1). The higher stiffness of the T