A New Approach to Fibrous Composite Laminate Strength Prediction

A method of predicting the strength of cross-plied fibrous composite laminates is based on expressing the classical maximum-shear-stress failure criterion for ductile metals in terms of strains. Starting with such a formulation for classical isotropic materials, the derivation is extended to orthotropic materials having a longitudinal axis of symmetry, to represent the fibers in a unidirectional composite lamina. The only modification needed to represent those same fibers with properties normalized to the lamina rather than fiber is a change in axial modulus. A mirror image is added to the strain-based lamina failure criterion for fiber-dominated failures to reflect the cutoffs due to the presence of orthogonal fibers. It is found that the combined failure envelope is now identical with the well-known maximum-strain failure model in the tension-tension and compression-compression quadrants but is truncated in the shear quadrants. The successive application of this simple failure model for fibers in the 0/90 degree and +/- 45 degree orientations, in turn, is shown to be the necessary and sufficient characterization of the fiber-dominated failures of laminates made from fibers having the same tensile and compressive strengths. When one such strength is greater than the other, the failure envelope is appropriately truncated for the lesser direct strain. The shear-failure cutoffs are now based on the higher axial strain to failure since they occur at lower strains than and are usually not affected by such mechanisms as microbuckling. Premature matrix failures can also be covered by appropriately truncating the fiber failure envelope. Matrix failures are excluded from consideration for conventional fiber/polymer composites but the additional features needed for a more rigorous analysis of exotic materials are covered. The new failure envelope is compared with published biaxial test data. The theory is developed for unnotched laminates but is easily shrunk to incorporate reductions to allow for bolt holes, cutouts, reduced compressive strength after impact, and the like

Optimized bolted joint

A method is disclosed for joining segments of the skin of an aircraft. The ends of the skin are positioned in close proximity or abutt each other. The skin is of constant thickness throughout the joint and is sandwiched between splice plates, which taper in thickness from the last to the first bolt rows in order to reduce the stiffness of the splice plate and thereby reduce the load transfer at the location where bypass loads are the highest

Decay estimates for variable coefficient wave equations in exterior domains

In this article we consider variable coefficient, time dependent wave equations in exterior domains. We prove localized energy estimates if the domain is star-shaped and global in time Strichartz estimates if the domain is strictly convex.Comment: 15 pages. In the new version, some typos are fixed and a minor correction was made to the proof of Lemma 1

Critical joints in large composite aircraft structure

A program was conducted at Douglas Aircraft Company to develop the technology for critical structural joints of composite wing structure that meets design requirements for a 1990 commercial transport aircraft. The prime objective of the program was to demonstrate the ability to reliably predict the strength of large bolted composite joints. Ancillary testing of 180 specimens generated data on strength and load-deflection characteristics which provided input to the joint analysis. Load-sharing between fasteners in multirow bolted joints was computed by the nonlinear analysis program A4EJ. This program was used to predict strengths of 20 additional large subcomponents representing strips from a wing root chordwise splice. In most cases, the predictions were accurate to within a few percent of the test results. In some cases, the observed mode of failure was different than anticipated. The highlight of the subcomponent testing was the consistent ability to achieve gross-section failure strains close to 0.005. That represents a considerable improvement over the state of the art

Bolted joints in graphite-epoxy composites

All-graphite/epoxy laminates and hybrid graphite-glass/epoxy laminates were tested. The tests encompassed a range of geometries for each laminate pattern to cover the three basic failure modes - net section tension failure through the bolt hole, bearing and shearout. Static tensile and compressive loads were applied. A constant bolt diameter of 6.35 mm (0.25 in.) was used in the tests. The interaction of stress concentrations associated with multi-row bolted joints was investigated by testing single- and double-row bolted joints and open-hole specimens in tension. For tension loading, linear interaction was found to exist between the bearing stress reacted at a given bolt hole and the remaining tension stress running by that hole to be reacted elsewhere. The interaction under compressive loading was found to be non-linear. Comparative tests were run using single-lap bolted joints and double-lap joints with pin connection. Both of these joint types exhibited lower strengths than were demonstrated by the corresponding double-lap joints. The analysis methods developed here for single bolt joints are shown to be capable of predicting the behavior of multi-row joints

Adhesive-Bonded Single-Lap Joints

For abstract, see N74-13195

The role of biaxial stresses in discriminating between meaningful and illusory composite failure theories

The irrelevance of most composite failure criteria to conventional fiber-polymer composites is claimed to have remained undetected primarily because the experiments that can either validate or disprove them are difficult to perform. Uniaxial tests are considered inherently incapable of validating or refuting any composite failure theory because so much of the total load is carried by the fibers aligned in the direction of the load. The Ten-Percent Rule, a simple rule-of-mixtures analysis method, is said to work well only because of this phenomenon. It is stated that failure criteria can be verified for fibrous composites only by biaxial tests, with orthogonal in-plane stresses of the same as well as different signs, because these particular states of combined stress reveal substantial differences between the predictions of laminate strength made by various theories. Three scientifically plausible failure models for fibrous composites are compared, and it is shown that only the in-plane shear test (orthogonal tension and compression) is capable of distinguishing between them. This is because most theories are 'calibrated' against the measured uniaxial tension and compression tests and any cross-plied laminate tests dominated by those same states of stress must inevitably 'confirm' the theory

Adhesive-bonded double-lap joints

Explicit analytical solutions are derived for the static load carrying capacity of double-lap adhesive-bonded joints. The analyses extend the elastic solution Volkersen and cover adhesive plasticity, adherend stiffness imbalance and thermal mismatch between the adherends. Both elastic-plastic and bi-elastic adhesive representations lead to the explicit result that the influence of the adhesive on the maximum potential bond strength is defined uniquely by the strain energy in shear per unit area of bond. Failures induced by peel stresses at the ends of the joint are examined. This failure mode is particularly important for composite adherends. The explicit solutions are sufficiently simple to be used for design purpose

Non-classical adhesive-bonded joints in practical aerospace construction

Solutions are derived for adhesive-bonded joints of non-classical geometries. Particular attention is given to bonded doublers and to selective reinforcement by unidirectional composites. Non-dimensionalized charts are presented for the efficiency limit imposed on the skin as the result of the eccentricity in the load path through the doubler. It is desirable to employ a relativly large doubler to minimize the effective eccentricity in the load path. The transfer stresses associated with selective reinforcement of metal structures by advanced composites are analyzed. Reinforcement of bolt holes in composites by bonded metal doublers is covered quantitatively. Also included is the adhesive joint analysis for shear flow in a multi-cell torque box, in which the bond on one angle becomes more critical sooner than those on the others, thereby restricting the strength to less than the total of each maximum strength when acting alone. Adhesive plasticity and adherend stiffness and thermal imbalances are included. A simple analysis/design technique of solution in terms of upper and lower bounds on an all-plastic adhesive analysis is introduced

Adhesive-bonded scarf and stepped-lap joints

Continuum mechanics solutions are derived for the static load-carrying capacity of scarf and stepped-lap adhesive-bonded joints. The analyses account for adhesive plasticity and adherend stiffness imbalance and thermal mismatch. The scarf joint solutions include a simple algebraic formula which serves as a close lower bound, within a small fraction of a per cent of the true answer for most practical geometries and materials. Digital computer programs were developed and, for the stepped-lap joints, the critical adherend and adhesive stresses are computed for each step. The scarf joint solutions exhibit grossly different behavior from that for double-lap joints for long overlaps inasmuch as that the potential bond shear strength continues to increase with indefinitely long overlaps on the scarf joints. The stepped-lap joint solutions exhibit some characteristics of both the scarf and double-lap joints. The stepped-lap computer program handles arbitrary (different) step lengths and thickness and the solutions obtained have clarified potentially weak design details and the remedies. The program has been used effectively to optimize the joint proportions