Khaled W. Shahwan

Compressive response and failure of braided textile composites: Part 2—computations

Abstract In this, the second part of a two part paper, results obtained by using the finite element (FE) method in conjunction with micromechanics to predict the effective elastic stiffness and strength of a carbon 2D triaxially braided composite (2DTBC), are presented. The 3D FE based micromechanics study was carried out on one representative unit cell (RUC) of the carbon 2DTBC (the “micromodel”). The FE models were first used to determine the macroscopic elastic orthotropic stiffnesses of the 2DTBC. The micromodel was deemed acceptable (in terms of the number of elements used in the mesh of the micromodel) if the elastic stiffnesses it displayed were within 5% of the elastic properties found experimentally. Subsequently, buckling eigenmodes were determined for the FE RUC under uniaxial and biaxial loading states, corresponding to the experimental investigation reported in part I of this two part paper. The lowest symmetric modes were identified and these mode shapes were used as imperfections to the FE model for a subsequent nonlinear response analysis using an arc-length method in conjunction with the ABAQUS commercial FE code. The magnitude of the imperfections was left as a parameter and its effect on the predicted response was quantified. The present micromechanics computational model provides a means to assess the compressive and compressive/tensile biaxial strength of the braided composites and its dependence on various microstructural parameters. It also serves as a tool to assess the most significant parameter that affects compressive strength.

Compressive response and failure of braided textile composites: Part 1—experiments

Abstract Experimental results obtained by examining the planar biaxial compression/tension response of carbon 2D triaxial braided composites (2DTBC) are reported in this paper. These experiments were motivated by a need to examine the failure of 2DTBC in a state of stress that would be similar to what is experienced by the walls of a tubular member under compressive crush loads. Results obtained from a series of biaxial tests that were conducted with different proportional displacement loading ratio combinations of compression and tension are reported. In all cases, the dominant failure mechanism under such a stress state is the buckling of the bias and axial tows within the composite. Full field surface displacement data is acquired concurrently during all biaxial and some uniaxial tests using the technique of digital speckle photography. Digital images of the specimen surface that is illuminated with a He–Ne laser are acquired at discrete time intervals during the loading history using a high-resolution digital camera. These images are stored and analyzed to obtain the incremental inplane surface displacement field, Δu(x,y) and Δv(x,y). From these, the incremental inplane surface strains Δex, Δey and Δγxy are obtained by numerical differentiation. The present paper, which is the first in a two part series, is devoted to the biaxial experimental results pertaining to 2DTBC failure.

NON–SELF–SIMILAR DECOHESION ALONG A FINITE INTERFACE OF UNILATERALLY CONSTRAINED DELAMINATIONS

We have presented a novel and unified approach for the analysis of delaminated structures in a compressive load environment. Previous studies have addressed delamination buckling, postbuckling and growth as three separate events with respect to remote load, with an appropriate criterion to demarcate the separate regimes. We show that a unified treatment of this problem is possible so that the evolution of the delaminated areas is obtained as a part of the calculation process. The unified approach is made possible by the introduction of an interface decohesion law that is appealing both as a computational device to regularize an otherwise singular problem, and as a physical model of the decohesion process. This type of modelling is known in fracture mechanics as Barenblatt–Dugdale (BD) models. Employing BD models, we were able to overcome some of the limitations of linear elastic fracture mechanics approaches in predicting general delamination growth. Using a virtual work formulation, the delamination–interphase–substrate system was modelled as one, resulting in a system of integral equations that was solved using an approximate method. The present treatment is new and demonstrates a successful departure from traditional fracture mechanics based concepts that require empirical relations for non–self similar delamination growth studies. The problem formulation places no distinction between the phenomena of buckling (and postbuckling) and non–self–similar growth. That is, the same equations were found to govern the entire behaviour from beginning (starting to load/displace the structure) to end (complete decohesion and/or loss of stiffness) without specification to certain regimes of validity. We have demonstrated that the use of nonlinear elastic foundation models to characterize unilateral constraints and the use of interphase models to analyse delamination decohesion and growth are indeed viable. Non–self–similar delamination growth patterns were simulated without resorting to fracture mechanics concepts and it was found that unilateral contact can occur at buckling or in the postbuckling regime, as well as prior to delamination growth or after delamination growth. Several examples are presented to illustrate this new treatment.

Compression Response of 2D Braided Textile Composites: Single Cell and Multiple Cell Micromechanics Based Strength Predictions

This article is concerned with the development of a finite element (FE) based micromechanics model for the prediction of compressive strength and post-peak compression response of 2D triaxial braided carbon fiber polymer matrix composites (2DTBC). This micromechanics based study was carried out on a series of single and multiple representative unit cell (RUC) 3-D FE models. The uniaxial compressive response, including unstable equilibrium paths, was studied using an arc-length method in conjunction with the ABAQUS commercial FE code. In the reported study, explicit account of the braid microstructure (geometry and packing) and the measured inelastic properties of the matrix (the in-situ properties) are accounted for via the use of the FE method. This enables accounting for the different length scales that are present in a 2DTBC. The computational model provides a means to assess the compressive response of 2DTBC and its dependence on various microstructural parameters. The model provides a means to compute the compression strength allowable for a 2DTBC structure. In particular, the dependence of compressive strength on the axial fiber tow properties and axial tow geometrical imperfections is discussed and shown to be significant in capturing the mechanism of damage development. Results are presented for 1, 4, 9, and 16 RUC representations of the 2DTBC, enabling to examine the dependence of compressive strength (or lack thereof) on the size of the region that is modeled. The predicted results are found to compare favorably against experiment.

Buckling of unilaterally constrained plates: Applications to the study of delaminations in layered structures

Abstract The results from a combined experimental and analytical investigation of the problem of buckling of unilaterally constrained, finite, rectangular, elastic plates is reported. The plates are modeled along the lines of classical plate theory employing the Kirchhoff-Love hypothesis. The presence of a unilateral constraint is accounted for through the use of a nonlinear elastic foundation model that exhibits a deformation sign dependent force-displacement relation. Using Galerkins method, the resulting system of governing nonlinear equations are solved iteratively. Different boundary conditions are considered and the results for some boundary conditions are compared and shown to be in good agreement with ‘exact’ results reported earlier for infinite plates. The results from an experimental investigation has further revealed that the buckling mode of the plate may involve regions or points of contact with the substrate beneath the buckling plate. The shadow Moire technique is used to show clearly that the mode shape is periodic and contains points and/or regions of contact. The results obtained from the theoretical investigation are found to bound the experimental values. It is clear that the stiffness of a post-buckled plate with unilateral constraints is highly influenced by whether the buckled portion involves points (or regions) of contact or not. Thus, in analytical model development, associated with addressing the problem of delamination buckling in layered plates, the possibility of the delaminated portion contacting the substrate beneath cannot be excluded. The present study has demonstrated the validity of using nonlinear foundation models in the buckling analysis of unilaterally constrained rectangular plates.

Effects of Matrix Microcracking on the Response of 2D Braided Textile Composites Subjected to Compression Loads

This article is concerned with the implementation of a coupled damage-elastic-plastic constitutive model for the matrix material of a 2D triaxial braided carbon fiber composite (2DTBC) subjected to compression loads. Damage in the matrix of 2DTBC is in the form of matrix microcracking which is observed in laboratory experiments of 2DTBC coupons subjected to cyclic loading. In the model, the matrix is treated as a continuously evolving solid governed by a coupled elastic-plastic damage theory which is modified from the classical elasto-plastic theory. With this description of the matrix, the response of 2DTBC to compression loading is studied through the adoption of a representative unit cell that consists of a progressively damaging matrix and elastic-plastic progressively damaging fiber tows. Results from the analysis are compared against a model without evolving damage and also against available experimental data to understand the significance of matrix damage and its influence on compression load bearing capability.

Instabilities in Braided Textile Composites Under Uniaxial Compressive and Biaxial Loadings

This paper discusses the results of a finite element (FE) based study of the multiaxial compressive instabilities in braided glass fiber composites. The micro mechanics study was carried out on a 2-unitcell size 3-D FE model. Computational tests were carried out to first determine the elastic moduli of the system. Once the computational model was validated with experimental data for the elastic moduli, the uniaxial compressive response of the micromodel was established using the RIKS option available in the ABAQUS commercial FE code. Subsequently, the response of the micromodel to biaxial loading was investigated. The present approach is different from those reported in the literature where classical methods based on the technique of homogenization is used to model the elastic and inelastic response of braided composites. In this work, explicit account of the braid microstructure (geometry and packing) and the inelastic properties of the matrix are accounted for via the use of the FE method. The macromechanical data pertaining to the braided composites were obtained through traditional means. Tensile tests were performed on the composites through the use of ASTM D 3039 standard to obtain the macroscopic orthotropic moduli and macroscopic response. For each test, the average data is reported in this paper. A separate test was conducted to obtain the in-situ matrix properties of the braided glass composites. The computational model provides a means to assess the compressive and biaxial strength of the braided composites and its dependence on various microstructural parameters. It also serves as a tool to assess the most significant parameter that affects compressive strength.

Delamination buckling instability near a circular hole in laminated composite plates

The motivation for the present study stems from the importance of delamination buckling as a viable mode of failure in laminated composite plates. This part of the study focuses on the prediction of the buckling loads and modes of unilaterally constrained rectangular plates. The laminated plates were modeled along the lines of classical lamination plate theory. Due to the out-of-plane thickness ratio of the delaminated near surface plies to that of the sublaminate (parent), the sublaminate was modeled as an infinitely rigid foundation which constrained the plates out-of-plane response t o be of one sign. The foundation was modeled as extensional springs exhibiting a nonlinear force-displacement relationship such that its stiffness as well as the plates buckling mode sign can be controlled in a continuous fashion allowing the simulation of a rigid and tensionless foundation. Preliminary investigations of the buckling loads and modes of rectangular plates attached to such foundations and subjected to a uniform inplane stress field showed the validity of this model for the cases investigated and compared t o previous exact results reported in the literature.