An Efficient Method for the Calculation of Interlaminar Stresses in Composite Materials

Abstract

A simple and efficient method is presented to determine the interlaminar stresses in a symmetric composite laminate under uniaxial loading. Expressions for the interlaminar stresses are assumed in terms of exponentials based on shapes that the interlaminar stresses must take in order to assure overall (integral) force and moment equilibrium. The boundary conditions and the traction continuity between plies are satisfied exactly. The exponential terms in the stress expressions are determined by minimizing the laminate complementary energy. Typical results are presented and compared with previous results found in the literature. The current method is shown to efficiently deal with the problem including the ability to perform the analysis of thick laminates (100 plies or more) with relative ease and cost-effectiveness.

Estimation of transverse/interlaminar stresses in laminated composites – a selective review and survey of current developments

“…Later Stein and Jegley [24] using this theory studied the eects of transverse shear on cylindrical bending of laminated composite plates and proved that this theory predicts the stresses more accurately than other theories. A simple technique to analyse symmetric laminates under tension or compression based on assumed stress distributions using the principle of minimum complimentary energy and the force balance method was presented by Kassapogolou and Lagace [25,26]. Later Kassapogolou [27] generalised this approach for general unsymmetric laminates under combined in-plane and out-of-plane (moment and shear) loads.…”

Progress in cold roll bonding of metals

“…Thus, the bond strength mentioned in this paper is determined by a tensile shear test, unless otherwise indicated. Kendall [45] addressed several methods for measuring interface properties using fracture mechanics by a cracking test, and much work has also been performed to calculate and predict the interface properties using the theory of material mechanics [46][47][48][49][50]. When applied, it will benefit greatly the development of new bonding processes and the improvement of bonding evaluation.…”

A variational model for free-edge interlaminar stress analysis in general symmetric and thin-ply composite laminates

“…[7], it is not possible to develop a software based on the current variational formulations. It simply means that the results obtained from the available variational models regarding the free-edge stress transfer [1,2,10,19] are approximate and thus, do not reproduce very refined finite element results. In addition, due to implementation of the minimum complementary energy principle, all of the developed stressbased variational models either for analyzing cracked laminates or free-edge stress fields are formulated for traction loading conditions.…”

“…This approach was first introduced by Hashin [14] in 1985 for the analysis of cracked two-layer cross-ply laminates under uniaxial tension and further developed by many authors for analyzing cracked laminates with general lay-ups, see for example [15][16][17][18] as the most complete variational models developed so far. Kassapoglou and Lagace [10,19] were the first who applied the variational approach for analyzing stress concentrations near free edges. The reader is referred to the recent publications [1,2,16,17] for a detailed review of the developments in variational approach for the free-edge [1,2] and matrix cracking [16,17] stress transfer problems.…”

“…Therefore, the interlaminar stress transfer problem can be reduced to a simple boundary value problem which is dependent only on the axial or transverse coordinate of the assumed laminate. For the variational free-edge stress transfer analysis [10,19] unlike the developed variational ply cracking models [15][16][17][18], this boundary value problem leads to a set of non-homogeneous differential equations as the Euler's equation(s) from the variational calculus.…”