Ghazi Abu-Farsakh

A New Failure Criterion for Nonlinear Composite Materials

A new failure criterion based on the total strain energy density approach is introduced for an equivalent linear elastic material. The total strain energy is composed of the elastic strain energy and the plastic strain energy. The proposed criterion can be used to predict failure of fibrous composite materials subject to uniaxial, biaxial, or multiaxial stress state. The proposed criterion takes into account the different behavior of bimodular composites in tension and compression. Given the stress-strain diagrams in the principal material directions, the failure of the material at any fiber orientation angle under an imposed stress state can be predicted. The results are compared with the corresponding available experimental data. In addition, the predicted failure stresses are compared with those obtained using available failure criteria.

Buckling of glass-reinforced plastic cylindrical shells under combined axial compression and external pressure

The paper describes the results of a theoretical and experimental investigation into the buckling behavior of glass-reinforced plastic cylindrical shells under the action of combined axial load and internal pressure. A total of 20 shells were loaded to buckling. Initial imperfections, load-deflection response, and buckling modes and loads were determined experimentally and compared with the results of a finite element analysis. This analysis utilized a buckling criterion developed on the basis of the total potential energy. The proposed method of buckling load prediction is shown to give close agreement with the experimental results.

A micro-mechanical model for predicting the compressive strength of fibrous composite materials

Abstract A micro-mechanical model is proposed for the prediction of the compressive strengths of unidirectional fibrous composite laminates. In these laminates, it is assumed that the fibers have a small misalignment angle which ranges from 1 to 5 ° from the vertical direction. A fiber shear buckling mode is considered in the model formulation which is assumed to cause large shear deformation. A basic energy approach is utilized to determine the critical buckling load. Both fiber and matrix strain energies within the composite and the external work due to applied loads are considered during deformation. The model is tested by using various types of composites: wood/ductile wax, spaghetti/paraffin wax, glass/epoxy and carbon/epoxy. Results of the proposed model are compared with results given by the Rosen and Wisnom micro-models and with available experimental data. It is found that the proposed model yields reasonable results for the composite materials investigated.

The use of an energy-based criterion to determine optimum configurations of fibrous composites

Abstract The strength optimization of laminated composites under in-plane loading is considered. An effective application of a numerical optimization method has been demonstrated for the optimum laminate configuration to maximize the in-plane strength of laminated fibrous composites. Two composite materials are considered in this study; boron/epoxy and carbon/epoxy. An energy-based failure criterion is used as a first-ply-failure strength criterion. The optimization algorithm is based on the sequential linear programming method with small step limits with respect to the layer thickness. Layer thicknesses and orientations are chosen as the design variables and the total thickness of the laminate is selected as the objective function. Owing to the significance of the problem, the present paper also shows the interaction among various variables such as layer thickness, layer orientation angle, in-plane loading, stresses and energy components.

A triangular conforming element for laminated shells

Abstract A 30 degree of freedom (DOF) conforming shell element is developed for laminated composite materials. This element is 10-noded and has a triangular shape. Sanders thin shell theory is used. The element is used to perform both static and dynamic analysis on a composite cylindrical shell. Results obtained by the present element are compared with those available in the literature (exact, experimental, and numerical) for simple support and cantilever boundary conditions. These comparisons show that one can get reasonably accurate results with the present element and good convergence characteristics.

Effect of material nonlinearity in unidirectional composites on the behavior of beam structures

The present study is made to investigate the effect of material nonlinearity in unidirectional composites on the behavior of beams, where the fiber orientation is considered. The effect of these two factors on deflection, bending moment and external reactions is investigated. In order to achieve these objectives, a computer subroutine based on secant mechanical property is incorporated in a main computer program for beam and frame analysis. The program can solve structures made of unidirectional composite materials which exhibit general material nonlinearity. Several numerical examples including various beam structures having different fiber orientations are presented, for both linear and nonlinear analysis.

Modes of Failure of Fibrous Composite Materials as Affected by the Orientation-Angle of Fiber

An energy-based failure criterion has been recently developed by the authors. At any stress level, the model deals with the actual composite material as an equivalent linear elastic material. The total strain energy density of the system is considered to be composed of two parts, elastic and plastic. In this paper, the model has been used to identify the modes of failure based on the relative magnitudes of the various energy terms appearing in the failure criterion equation. Accordingly, three types of failure are anticipated: fiber failure, matrix failure (tension or compression), and matrix failure in shear. The critical fiber orientation for a given stress state can be predicted as well. The model has been verified using available experimental data in the literature and compared with other theoretical models as well. Good agreement has been obtained in both cases. The failure envelopes for boron-epoxy Narmco 5505 and glass-epoxy 3MXP 251S are predicted using several stress combinations and fiber orientations ranging from 0 to 90°. Seven failure envelopes are obtained, classified as A, B, C, D, E, F, and G.

Stress concentration around a central hole as affected by material nonlinearity in fibrous composite laminated plates subject to in-plane loading

Abstract The distribution of stresses in laminated composite plates with a central circular hole and having various stacking sequences, different geometric dimensions and subjected to in-plane axial tensile loading was investigated. The ANSYS computer program was utilized using the finite element method to study the linear and nonlinear material effects. A new method was proposed for the purpose of incorporating the material nonlinearity model into the ANSYS computer program using the secant modulus material model. The aim of the authors is to analyze the effect of D/b and a/b ratios (where D is hole diameter, b is plate width, and a is plate length) on stresses induced in such plates. Analysis was carried out for angle-ply, four-layered symmetric laminated rectangular plates with various stacking sequences [±θ]s.

An alternative model for nonlinear stress-strain behaviour of composite materials

An alternative model for the Jones-Nelson material model is developed, in which the secant mechanical property is assumed to be a function of the plastic strain energy density of an equivalent linear elastic system which replaces the total strain energy term in the Jones-Nelson model. The present model is capable of treating multiple mechanical property non-linearities which are generally exhibited by fibre-reinforced composite material. The new model is represented in two forms; the basic model and the iterative model. A comparison is carried out in order to correlate strains predicted by the present model with experimental data and other theoretical models cited from the literature. What makes the new model practical is that the plastic strain energy due to loading at any fibre-orientation is not allowed to exceed the fibre direction value obtained from the uniaxial loading test. Hence, the model does not require an extension of behaviour beyond the defined range of strain energy.

Experimental buckling of GRP cylindrical shells

During the setup of an experiment, errors may occur. Sources of such errors may be due to several factors which sometimes accumulate and then cause erroneous results. An experimental investigation on buckling of GRP (glass-reinforced-plastic) cylindrical shells, subject to axial compression and/or external pressure loading, has been carried out. At the beginning of the experiment, the initial geometrical imperfections were measured. Because of the small size of these quantities and the great effect these imperfections had on buckling loads, any small errors in the measurement procedure may lead to unreasonable results. Attempts have been made to detect these errors, and to identify and minimize their effect on experimental results. Tables are provided to show a comparison between the final experimental results and the corresponding theoretical ones.