Variation-based cracked laminate analysis revisited and fundamentally extended

Li, Shuguang; Hafeez, Farrukh

doi:10.1016/j.ijsolstr.2009.03.031

Cited by 36 publications

(22 citation statements)

References 16 publications

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“…Vinogradov and Hashin (2010) extended the analysis to angle-ply laminates of type [θ m /φ n ] s containing intralaminar cracks in the middle laminae and found that prediction for the Young's modulus of cracked GFRP angle-ply [0/45] s is in good agreement with experimental results of Katerelos et al (2006). In the recent years the variational approach has gained significant attention (e.g., Li and Hafeez 2009;Katerelos et al 2015).…”

Section: Introductionmentioning

confidence: 80%

The effect of matrix cracking on mechanical properties in FRP laminates

Fikry

Ogihara

Vinogradov

2018

Mech Adv Mater Mod Process

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Background: Fiber Reinforced Polymer (FRP) laminates have properties, which are highly dependent on the ply fiber orientations and which can be designed for optimum laminate performance. The purpose of this study is to investigate the effect of matrix cracking on the mechanical properties of FRP laminates with various off-axis angles, and to provide a critical test for an analytical solution using variational stress analysis. Methods: Carbon and glass fiber reinforced polymer laminates (CFRP and GFRP) are tested. FRP prepregs are cured by using autoclave method to form laminates with layups [θ m / φ n ] s . The laminates are then loaded monotonically and cyclically to obtain their mechanical properties and the effect of matrix cracks on the properties. Some of the effects include reduction of laminates' stiffness and residual strains after unloading. In order to obtain higher crack densities in specimens, artificial cracks method was introduced in this study, where notches were made at the edges of some specimens before tested in tension. Cracks observation for CFRP laminates is done by using the X-ray technique, while for GFRP laminates a DSLR camera is used.

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Section: Introductionmentioning

confidence: 80%

The effect of matrix cracking on mechanical properties in FRP laminates

Fikry

Ogihara

Vinogradov

2018

Mech Adv Mater Mod Process

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“…Similar to what was demonstrated by Li and Hafeez, 9 the physical boundary conditions are generally insufficient to determine the unknown constants and the so-called "natural boundary conditions" are required, which in the variational calculus result from integration by parts of the perturbed functional. For the quadratic Lagrangian (29), these natural boundary conditions are given by dF…”

Section: Natural Bcmentioning

confidence: 68%

“…In all studies that adopted the generalized variational approach of Li and Hafeez, 9 two inherent steps are present: (1) derivation of natural boundary conditions, whose solution together with physical boundary conditions leads to the stress field in a cracked laminate, and (2) application of specific loading and integration of the resultant stress energy density to evaluate the complementary energy and corresponding compliances of the laminate. Analysis in the present paper addresses the problem of intralaminar cracks in an general laminate, when cracks are in plies with parallel fiber orientation.…”

Section: Introductionmentioning

confidence: 99%

A variational method for analysis of laminates with parallel arrays of intralaminar cracks

Vinogradov

2019

Numerical Meth Engineering

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This paper presents a robust variational method for prediction of the effective thermoelastic properties of laminates with parallel, but not necessarily coplanar intralaminar cracks. Arbitrary laminate layup, crack patterns, and any in-plane forces and bending moments, and temperature change can be treated simultaneously. The method is based on the principle of minimum complementary energy. The admissible in-plane stress components are assumed to be linear through the ply thickness. Simple matrix expressions are derived for the effective compliance matrix, thermal expansions and curvatures, and specific heat of a cracked laminate. Predictions for the Young's modulus, Poisson's ratio, shear modulus, flexural rigidity, and thermal expansion as functions of crack density for various laminates of symmetric and nonsymmetric layups demonstrated excellent agreement with experimental results of seven independently published studies. Accuracy and robustness of the method are complemented by the fact that no experimentally fitted parameters are required. It is shown that the same formalism can be applied to analysis of closed intralaminar cracks, as well as nonuniform and nonsymmetrical distributions of cracks.

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“…The one single fundamental assumption is that the inplane transverse and shear stresses are linear through-thickness of each ply. Akin to the variational models developed for ply cracking [15][16][17][18][19][20][21][22][23], the total stresses/displacements in a composite with free edges are partitioned to unperturbed (without free edge) and perturbation stresses/displacements. Therefore, it is possible to consider the effects of applied thermo-mechanical loads in the unperturbed state leading to a system of homogeneous differential equations that can be solved using standard methods.…”

Section: Introductionmentioning

confidence: 99%

Variational analysis of free-edge stress and displacement fields in general un-symmetric and thin-ply laminates under in-plane, bending and thermal loading

Hajikazemi

Paepegem

2018

Composites Part A: Applied Science and Manufacturing

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A variational approach based on the minimization of complementary energy is developed to determine accurately a complete solution for both free-edge stress and displacement distributions of a laminate with arbitrary lay-ups (possibly un-symmetric and made of thin plies) under combined in-plane, bending and thermal loading. The key idea is partitioning the total stresses/displacements in a laminate with free edges into unperturbed (without free edges) and unknown perturbation stresses/displacements caused by the presence of free edges. It enables the theory of variational stress-transfer to deal easily with both applied traction and displacement boundary conditions. A methodology is introduced to obtain displacement fields for a stress-based variational approach. The resulting stress and displacement fields exactly satisfy local equilibrium equations, strain-displacement relations together with all traction/displacement boundary and continuity conditions. By comparing the results with those obtained from the finite element method, the accuracy and computational efficiency of the developed model, is confirmed.

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Variation-based cracked laminate analysis revisited and fundamentally extended

Cited by 36 publications

References 16 publications

The effect of matrix cracking on mechanical properties in FRP laminates

The effect of matrix cracking on mechanical properties in FRP laminates

A variational method for analysis of laminates with parallel arrays of intralaminar cracks

Variational analysis of free-edge stress and displacement fields in general un-symmetric and thin-ply laminates under in-plane, bending and thermal loading

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