Residual strength of composite laminates containing scarfed and straight-sided holes

This investigation is motivated by the needs to quantify the load-carrying capacity of composite laminates with scarfed holes, a damage cut-out shape employed to achieve flush repairs of composites. Both experimental testing and analytical modelling were carried out to investigate the damage progression behaviour of composite laminates containing either straight-sided or scarfed holes. Hoop strains were recorded by strain gauges located along the scarf surface and the results indicate a much greater extent of damage progression than specimens containing straight-sided holes. Three different strength-prediction models were employed to quantify the residual strength, including an analytical cohesive zone model developed in this work, an analytical inherent-flaw fracture mechanics method and a finite element-based continuum damage model. Comparisons of the experimental results with the model predictions reveal that the continuum damage model, calibrated using data from coupons with straight-sided holes, provides promising correlation with experimental results.     

Two-dimensional strain-based interactive failure theory for multidirectional composite laminates

A 2-D strain-based interactive failure theory is developed to predict the final failure of composite laminates subjected to multi-axial in-plane loading. The stiffness degradation of a laminate during loading is examined based on the individual failure modes of the maximum strain failure theory, and a piecewise linear incremental approach is employed to describe the nonlinear mechanical behavior of the laminate. In addition, an out-of-plane failure mode normal to the laminate is also investigated to more accurately predict the failure of multidirectional laminates. The theoretical results of the failure model presented are compared with the experimental data provided by the World-Wide Failure Exercise, and the accuracy of the model’s predictive capabilities is investigated.     

Optimization of laminated composites considering different failure criteria

The purpose of the present work is to analyse how different the optimal structures are when different first ply failure criterion are considered in the optimization of laminated composites. Two problems are solved: the minimum weight and the minimum material cost of laminated plates subjected to in-plane loads. The failure criterion is taken into account by means of constraints introduced in the optimization problem. Three different failure criteria are tested independently: maximum stress, Tsai–Wu and the Puck failure criterion (PFC). Emphasis is given to the PFC as it appears to agree better with practical observations. The design variables are the ply orientations, the number of layers and the layer material, and the optimization problem is solved by a genetic algorithm (GA). The results show that optimal structures highly differ when different failure criterion are considered and that none of the failure criteria is always the most or the least conservative when different load conditions are applied.     

Experimental study on the stitching reinforcement of composite laminates with a circular hole

Experimental study is carried out on the stitching reinforcement of composite laminates containing a circular hole. First, the tensile strength and stiffness are measured, and their dependence on stitching parameters such as stitching needle span, row spacing, edge distance and stitching type are analyzed. Next, the strain distribution and concentration are investigated analytically and experimentally for different stitching parameters, external load and edge location of the hole. It is shown that the results of stitching reinforcement are quite different for composite laminates with a circular hole, which could provide proper stitching parameters for designers.     

Shear capacity of reinforced concrete members strengthened in shear with FRP by using strut-and-tie models and genetic algorithms

Substantial research has been performed on the shear strengthening of reinforced concrete (RC) beams with externally bonded fibre reinforced polymers (FRP). However, referring to shear, many questions remain opened given the complexity of the failure mechanism of RC structures strengthened in shear with FRP. This paper is concerned with the development of a simple automatic procedure for predicting the shear capacity of RC beams shear strengthened with FRP. The proposed model is based on an extension of the strut-and-tie models used for the shear strength design of RC beams to the case of shear strengthened beams with FRP. By the formulation of an optimization problem solved by using genetic algorithms, the optimal configuration of the strut-and-tie mechanism of an FRP shear strengthened RC beam is determined. Furthermore, unlike the conventional truss approaches, in the optimal configuration, compressive struts are not enforced to be parallel, which represents more consistently the physical reality of the flow of forces. The proposed model is validated against experimental data collected from the existing literature and comparisons with predictions of some design proposals are also performed.     

Numerical evaluation of shear strengthening performance of CFRP sheets/strips and sprayed epoxy coating repair systems

A numerical study is conducted to evaluate the shear strengthening performance of two repair systems: CFRP sheets/strips and a sprayed epoxy coating. Micromechanical constitutive models for the CFRP sheets/strips and sprayed FRP coating proposed by Liang et al. [Liang Z, Lee HK, Suaris W. Micromechanics-based constitutive modeling for unidirectional laminated composites. Int J Solids Struct 2006;43:5674–89] and Lee et al. [Lee HK, Avila G, Montanez C. Numerical study on retrofit and strengthening performance of sprayed fiber-reinforced polymer. Eng Struct 2005;27:1476–87] and Lee and Simunovic [Lee HK, Simunovic S. Modeling of progressive damage in aligned and randomly oriented discontinuous fiber polymer matrix composites. Composites: Part B 2000;31:77–86] in conjunction with damage models, are implemented into the finite element code ABAQUS to solve boundary value problems. Using the implemented computational model, numerical simulations of four-point bending tests on concrete beams repaired with the repair systems are conducted to quantify their strengthening abilities. The numerical tests yield load–deflection curves from which the shear strengthening performance of the repair systems is evaluated. Furthermore, the present prediction is compared with available experimental data to assess the accuracy of the proposed computational model.     

Three-layered plate: Elasticity solution

The subject of this paper is the plate composed of two identical isotropic outer layers and a more compliant inner interlayer, perfectly connected to one another at the interface (three-layered plate). This paper presents a model that describes the behavior of this plate by a system of exact analytical (explicit) equations.An analytical model is preferred over finite element models and simplified formulas if it is fast and easy-to-use. Thus, modeling has been developed within the framework of two-dimensional elasticity, instead of three. In so doing, the model also represents a means for attaining full comprehension of the involved phenomena, something that neither three-dimensional elasticity nor finite element models and simplified formulas can attain. The two-dimensional behavior is governed here by using assumptions that do not impose constraints on the behavior. Starting from these assumptions, the paper illustrates the relationships between displacements and interface stresses. The subsequent sections of the paper describe the model and present some real case applications.The contribution of this paper is to consider both the shear modulus and the elastic modulus of the interlayer. Thus, this model applies to three-layered plates with any interlayer, whether utterly compliant or relatively stiff. Conversely, the previous exact analytical models assumed zero elastic modulus, and hence they applied to utterly compliant interlayers only. Hence, not only does the new model predict the exact behavior of plates that the former analytical models described only approximately, but this model may also be used as a benchmark for finite element models, which cannot assign zero value to the elasticity modulus of the interlayer together with the actual shear modulus.