Issue 47

V. Rizov, Frattura ed Integrità Strutturale, (2047) 468-481; DOI: 10.3221/IGF-ESIS.47.37 469 bonded joints has also been considered. It has been shown the importance of using of reliable failure criteria for widening the application of adhesively bonded joints in load-bearing composite and sandwich structural members and components in different industries [1]. A through review of recent publications on failure behaviour of different type of fiber reinforced composite materials has been presented in [2]. Various aspects of fatigue and life prediction of fiber reinforced composites have been discussed in detail. The effects of inherent and environmental factors such as temperature, moisture and corrosion on fatigue and failure of composites have been analyzed. A summary of commonly used failure criteria for life prediction of composite structures subjected to static and fatigue load conditions has been reported. A progressive fatigue model has also been considered in the review. Models for prediction of residual mechanical properties of composites under different loading conditions have been described and discussed [2]. The thermomechanical behaviour of a carbon fiber composite laminated sheet that is irradiated by using a continuous wave chemical oxygen iodine laser has been analyzed in [3]. A potential delamination of the composite sheet makes the analysis of the influence of the laser an important practical task. The temperature distribution in the composite has been studied. The peak temperature of irradiated region has been evaluated. It has been found that the model developed is suitable for simulating of laser ablation of carbon fiber epoxy composite materials. The study has indicated that the laser beammachining is an appropriate process for manufacturing of fiber reinforced composite materials [3]. However, multilayered materials and structures have low interlaminar strength which is a premise for development of delamination cracks [4, 5]. Delamination fracture or separation of layers is the predominant failure mode of multilayered structures. The service lifetime of laminated composite structural members and components is limited by their delamination fracture behavior under certain loading conditions [4]. Delamination fracture of multilayered material systems under mode II crack loading conditions with considering of the creep behavior has been studied in [4]. For this purpose, the methods of linear elastic fracture mechanics have been applied. An elevated temperature has been used to accelerate the delamination fracture under constant external loads. Delamination behavior of a double cantilever beam configuration has been analyzed. By using of the Paris power law, a methodology for predicting the service lifetime of multilayered beam structures in terms of service load, temperature and initial delamination crack length has been developed [4]. A review of techniques for modeling and analysis of functionally graded single layers and sandwich beam configurations has been presented in [5]. Various solutions which are based on the assumption for linear-elastic behavior of the functionally graded material have been presented and discussed. Analyses of beam structures under both static and dynamic loading conditions have been considered. Free and forced vibrations of functionally graded sandwich constructions have been studied. Investigations of functionally graded sandwich beams resting on two-parameter elastic foundation have been reported. Studies of buckling behaviour of sandwich beams have been reviewed too. Various analyses of bending behaviour of viscoelastic sandwich structures have been discussed. Works dealing with static analyses of functionally graded sandwich beams resting on a Pasternak elastic foundation have also been presented. Solutions of linear-elastic beams made of functionally graded materials under tension and bending have been considered [5]. The main goal of the present paper is to derive the strain energy release rate for a delamination crack in multilayered four- point bending beam configurations assuming that each layer exhibits smooth material inhomogeneity in width and length directions. The beam under consideration is made of an arbitrary number of adhesively bonded lengthwise vertical layers which have non-linear mechanical behavior of the material that is treated by applying the Ramberg-Osgood equation. It should be mentioned that in his previous works, the author has studied delamination fracture behavior of various multilayered beam structures made by lengthwise vertical inhomogeneous layers usually by applying power law stress-stain relations for modeling the non-linear mechanical behavior of the material [6, 7]. The solution to the strain energy release rate derived in the present paper can be applied in fracture mechanics based structural design of multilayered beams made of inhomogeneous materials such as functionally graded materials which have been widely used in recent years as advanced structural materials in many engineering applications [8, 9, 10, 11, 12, 13, 14, 15]. D ETERMINATION OF THE STRAIN ENERGY RELEASE RATE multilayered four-point bending beam configuration containing a delamination crack of length, 2 a , is shown schematically in Fig. 1. The external loading consists of two vertical forces, F , applied at the two ends of the beam. The beam cross- section is a rectangle of width, b , and height, h . The length of the beam is   1 2 2 l l  . It is assumed that the beam is made A