Effective stiffness concept in bending modeling of laminates with damage in surface 90-layers

Pupurs, Andrejs; Vārna, Jānis; Loukil, Mohamed Sahbi; Kahla, Hiba Ben; Mattsson, David

doi:10.1016/j.compositesa.2015.11.012

Cited by 25 publications

(24 citation statements)

References 24 publications

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“…This configuration will be used in this article to produce numerical data needed for CSD analysis and for validation. Therefore, we present the expressions obtained by analytical treatment of expressions in “Formulation of the problem and summary of results of the GLOB-LOC approach” section for this relatively simple case of damaged laminates (Loukil et al., 2013; Pupurs et al., 2016; Varna, 2015) …”

Section: Determination Of Thermo-elastic Constants In Glob-loc Formulmentioning

confidence: 99%

Crack face sliding displacement (CSD) as an input in exact GLOB-LOC expressions for in-plane elastic constants of symmetric damaged laminates

Loukil

Vārna

2019

International Journal of Damage Mechanics

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The crack opening and crack sliding displacements of both faces of an intralaminar crack are the main parameters defining the significance of each crack in laminate stiffness degradation, according to the previously published GLOB-LOC approach for symmetric laminates with an arbitrary number of cracks in all plies. In the exact stiffness expressions of this approach, the crack density is always multiplied by crack opening displacement and crack sliding displacement. The dependence of crack opening displacement on geometrical and elastic parameters of adjacent plies was studied previously and described by simple fitting functions. The crack sliding displacement has been analyzed for low-crack densities only and the proposed finite element method-based fitting expressions are oversimplified not including the out-of-plane ply stiffness effects. Based on finite element method analysis, more accurate expressions for so-called non-interactive cracks are suggested in the presented article. For the first time the shear stress perturbations are analyzed and interaction functions are presented with the feature that they always lead to slightly conservative predictions. The presented simple fitting functions, when used in the GLOB-LOC model, give predictions that are in a good agreement with finite element method results and with experimental data for laminates with damaged off-axis plies in cases when crack face sliding is of importance. The significance of including crack sliding displacement in stiffness predictions is demonstrated.

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Section: Determination Of Thermo-elastic Constants In Glob-loc Formulmentioning

confidence: 99%

Crack face sliding displacement (CSD) as an input in exact GLOB-LOC expressions for in-plane elastic constants of symmetric damaged laminates

Loukil

Vārna

2019

International Journal of Damage Mechanics

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“…The experimental lay-up was more like a laminated beam than a plate. It has been shown in several papers, [10][11][12] that for cross-ply laminates approximation with beam (geometry with xas only in-plane coordinate and z as the thickness coordinate) is rather accurate. In this approximation, we assume that in equations in the Modified laminate expressions section, the Poisson's ratios are equal to zero.…”

Section: Cross-ply Beam Approximationmentioning

confidence: 99%

“…Therefore, only the summary average VP and VE strains developed after certain number of loading cycles is documented and described by fitting functions. The effective stiffness dependence on crack density is used in unsymmetrical laminate theory, an approach which was proven accurate by Pupurs et al 10 An approximate ''quasi-elastic'' Hook's law is used for layers in mechanically unloaded specimens where the previously accumulated average viscoplastic strains are not changing during the measurement, and therefore they are incorporated in the same way as the free thermal expansion strains.…”

Section: Introductionmentioning

confidence: 99%

Curvature of unsymmetric cross-ply laminates: Combined effect of thermal stresses, microcracking, viscoplastic and viscoelastic strains

Vārna

Persson

Claudel

et al. 2016

Journal of Reinforced Plastics and Composites

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Curvature of unsymmetrical [0/90] specimens caused by thermal stresses changes if the specimen is subjected to large axial strains introducing intralaminar cracks in the 90-layer. It is shown that the large curvature reduction can not be explained by cracking related stress release only. The large irreversible viscoplastic strains introduced during the axial tensile loading (with 5 min holding at high strain for crack counting) give the main contribution to the curvature change. The effect of transient viscoelasticity (VE) was found to be of minor significance. Simple approach based on effective damaged layer stiffness and constant irreversible strain is used in the framework of laminate theory to extract the viscoplastic and VE strains from experimental curvature data. The obtained fitting expressions for viscoplastic- and VE-strain development are successfully used to describe curvature change in [0/902] laminate subjected to the same test procedure. It is suggested that the used curved beam tests could be efficient to characterize the viscoplastic strain development in the thin 90-layers.

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“…Moreover, stress transfer in cracked un-symmetric laminates under flexural loads has also been addressed leading to determination of bending thermo-elastic properties [12][13][14][15][16][17] of general cracked laminates. In addition, cracked laminates under out-of-plane normal (through-thickness) applied loads are also investigated and, thus, the effective out-of-plane axial properties of cracked laminates can be determined [5].…”

Section: Introductionmentioning

confidence: 99%

Model to accurately predict out-of-plane shear stiffness reduction in general cracked laminates

Hajikazemi

Garoz

Paepegem

2019

Composites Science and Technology

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The practically important problem of the modification of laminate out-of-plane shear stiffness by ply cracks is hardly investigated in the literature. In this paper, out-of-plane shear stiffness reduction of laminates containing uniform and non-uniform distributions of ply cracks is studied. A novel variational model is developed to determine accurately stress transfer mechanisms and consequently out-of-plane shear stiffness reduction of general cracked laminates under applied out-of-plane shear loads. It is shown that the presence of ply cracks in a laminate under out-ofplane shear loads, perturbs the uniform distribution of shear stresses and induces high gradients of in-plane stresses leading to large shear stiffness reductions. The results are compared with those of the finite element method (FEM) implementing periodic boundary conditions. It is shown that there is excellent accordance between the results obtained from these approaches. The outcome of the paper provides necessary information for determination of damage-based constitutive laws for composites.

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Effective stiffness concept in bending modeling of laminates with damage in surface 90-layers

Cited by 25 publications

References 24 publications

Crack face sliding displacement (CSD) as an input in exact GLOB-LOC expressions for in-plane elastic constants of symmetric damaged laminates

Crack face sliding displacement (CSD) as an input in exact GLOB-LOC expressions for in-plane elastic constants of symmetric damaged laminates

Curvature of unsymmetric cross-ply laminates: Combined effect of thermal stresses, microcracking, viscoplastic and viscoelastic strains

Model to accurately predict out-of-plane shear stiffness reduction in general cracked laminates

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