Eric R. Johnson

Effect of dropped plies on the strength of graphite-epoxy laminates

The reduction in the compressive and tensile strength of graphite-epox y laminates with thickness discontinuities due to dropped plies was studied by experiment and analysis. The specimens were fabricated with all the dropped plies lumped together in the center of a 16-ply quasi-isotropic layup, such that one surface was flat and the slope of the opposite surface changed abruptly at the dropped ply location to accommodate the thickness change. Even though the thick and thin sections are symmetrically laminated, there exists bending-extensioii coupling due to the geometric eccentricity of the middle planes of the thick and thin sections. Results from tests on 37 specimens are reported that differed in the configuration of the dropped plies only. The axial strength of a laminate with dropped plies is less than the strength of its thin section, and the compressive strength of a laminate with dropped plies is less than its tensile strength. The reduction in axial strength is directly related to the axial stiffness change between the thick and thin sections. To examine the mechanism of failure, the three-dimensional state of stress in the dropped ply region was evaluated by the finite element method. A tensile interlaminar criterion predicted the correct location of failure, but underestimated the failure load, and therefore is a conservative analysis procedure for design.

Intralaminar and interlaminar progressive failure analyses of composite panels with circular cutouts

A progressive failure methodology is developed and demonstrated to simulate the initiation and material degradation of a laminated panel due to intralaminar and interlaminar failures. Initiation of intralaminar failure can be by a matrix-cracking mode, a fiber-matrix shear mode, and a fiber failure mode. Subsequent material degradation is modeled using damage parameters for each mode to selectively reduce lamina material properties. The interlaminar failure mechanism such as delamination is simulated by positioning interface elements between adjacent sublaminates. A nonlinear constitutive law is postulated for the interface element that accounts for a multi-axial stress criteria to detect the initiation of delamination, a mixed-mode fracture criteria for delamination progression, and a damage parameter to prevent restoration of a previous cohesive state. The methodology is validated using experimental data available in the literature on the response and failure of quasi-isotropic panels with centrally located circular cutouts loaded into the postbuckling regime. Very good agreement between the progressive failure analyses and the experimental results is achieved if the failure analyses includes the interaction of intralaminar and interlaminar failures.

Analysis of Delamination Initiation in Postbuckled Dropped-Ply Laminates

The compression strength of dropped-ply, graphite-epoxy laminated plates for the delamination mode of failure is studied by a finite element analysis and corroborated with experiments

RESPONSE AND FAILURE ANALYSIS OF A GRAPHITE-EPOXY LAMINATE CONTAINING TERMINATING INTERNAL PLIES*

A change in laminate thickness due to terminating internal plies acts as a str-ess riser for both intralamina and interlamina stresses. This laminate configuration is referred to as a ply drop. The linear elastic, three-dimensional stress distributions in the vicinity of a ply drop are determined for a graphite-epoxy laminate subject to axial tension and compression by a finite element analysis. It is shown that the interlaminar stresses have a maximum magnitude at the ply drop-off, and decrease proceeding away from the drop. The interlaminar stresses vanish in regions sufficiently removed from the ply dropoff. Two modes of failure initiation are analyzed. In the pure resin regions surrounding the dropped plies, the maximum stress criterion is assumed to govern failure. The Tsai-Wu criterion is used for intralamina failure prediction. The influence of two laminate lay-ups and a variety of ply drop geometries on the rbsponse and failure are presented.

An Irreversible Constitutive Law for Modeling the Delamination Process using Interface Elements

An irreversible constitutive law is postulated for the formulation of interface elements to predict initiation and progression of delamination in composite structures. An exponential function is used for the constitutive law such that it satisfies a multi-axial stress criterion for the onset of delamination, and satisfies a mixed mode fracture criterion for the progression of delamination. A damage parameter is included to prevent the restoration of the previous cohesive state between the interfacial surfaces. To demonstrate the irreversibility capability of the constitutive law, steady-state crack growth is simulated for quasi-static loading-unloading cycle of various fracture test specimens.

Variable complexity design of composite fuselage frames by response surface techniques

Curved frame structures are often used as part of the internal skeletal structure in aircraft. Laminated composite materials offer potential weight savings for such structures, but composite frames have different and more complex failure mechanisms than metallic frames. In particular, failure mechanisms involving interlaminar stresses are important in composite structures. Interlaminar stresses can be directly computed from three-dimensional finite element models, but the computational expense of these models is prohibitive. In this work, two- and three-dimensional (2D and 3D) finite element models are combined to reduce the computational expense associated with designing composite frames. A response surface design approach is used to approximate the failure response of curved composite C-section frames subjected to an axial tensile loading using a minimum number of finite element analyses. Results are presented for two examples with two and five design variables, respectively.

A mixed variational formulation for interlaminar stresses in thickness-tapered composite laminates

Abstract Stress fields in laminated plates containing an abrupt thickness taper are determined following Paganos methodology of using the Hellinger-Reissner functional with the stress components approximated within layers by expressions explicit in the thickness coordinate [Pagano, N. J. (1978). Stress fields in composite laminates. Int. J. Solids Structures 14 , 385–400; Pagano, N. J. (1983). Axisymmetric stress fields in involute bodies of revolution. In Advances in Aerospace Structures, Materials and Dynamics; A Symposium on Composites, AD-06 , (eds U. Yuceoglu, R. L. Sierakowski and D. A. Glasgow) ASME, NY, pp. 57–64]. The Euler equations from the variational principle area set of variable coefficient, differential-algebraic equations (DAEs) in the longitudinal coordinate. Difficulties with the number of differential equations and boundary conditions are resolved. Solution of the system is by higher-order one-step finite difference scheme. Numerical ill-conditioning encountered when modeling layers that are thin relative to other layers in a model was remedied by choosing stress shape functions and displacement weighting functions that are different than those used by Pagano. The example problems discussed are dropped-ply laminates (laminates with terminated internal plies), that are subjected to in-plane compression or shear under the assumption that the response is adequately modeled by generalized plane deformation elasticity.

Buckling of imperfect, anisotropic, ring-stiffened cylinders under combined loads

The objective of this study is to develop an analysis to predict buckling loads of ring-stiffened anisotropic cylinders subject to axial compression, torsion, and internal pressure. This structure is modeled as a branched shell. A nonlinear axisymmetric prebuckling equilibrium state is assumed which is amenable to an exact solution within each branch. Axisymmetric geometric imperfections are included. Buckling displacements are represented by a Fourier series in the circumferential coordinate and the finite-element method in the axial coordinate. Application of the Trefftz criterion to the second variation of the total potential energy leads to a nonlinear eigenvalue problem for the buckling load and mode

Crack path bifurcation at a tear strap in a pressurized shell

Bifurcation of an initially longitudinal through crack in an internally pressurized cylindrical shell at a circumferential stiffener is investigated using a finite element analysis. The finite element model is developed from a fracture test of an aluminum shell having a 22.9 cm radius, a 1.02 mm wall thickness, and stiffened by two externally bonded circumferential straps spaced 40.6 cm apart. After initial stable crack growth in the longitudinal direction with increasing pressure, the crack propagated dynamically toward the strap, bifurcated near the strap into circumferential branches running parallel to the straps. Stable and unstable crack growth curves of pressure versus half-crack length are determined from the nonlinear analysis using a critical value of the crack tip opening angle as the criterion to predict crack growth. Although the crack growth curves are determined from a static analysis, they corroborate the test results for the location of crack path bifurcation. Also, the principal stress criterion for predicting crack turning is consistent with the test.

A Simple Homogenization of Degraded Micro-Cracked Plain Woven and Braided Textile Composites

In this study, three-dimensional shape equations for the 2-D plain woven and braided textile composites were derived to find degraded elastic properties using a simple model. The degraded elastic properties of the plain woven and braided textile composites with transverse micro-cracks were investigated, and reduced elastic properties of textile yarn structures were calculated by a crack density scheme based on micro-mechanical constitutive equations. In addition the iso-strain assumption is considered to describe the effective modulus in sub-domains consisting of cracked fill, warp yarns and resin components. To determine the geometry of textile fabric structures, the concept of repeating unit cell, surface equations of sinusoidal functions and geometrical parameters were used. Finally, our analytical predictions for cracked plain woven and braided textiles were compared to results extracted from the literature. The comparisons between our simple model and other models indicate an excellent agreement.