Mathematical modeling of damage in unidirectional composites

Dharani, Lokeswarappa R.; Jones, W. F.; Goree, James G.

doi:10.1016/0013-7944(83)90115-7

Cited by 73 publications

(14 citation statements)

References 9 publications

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“…(29) with b = d m /2, is also shown by a solid line exhibiting a similar behavior. The behavior shown in this figure for cracked fiber composites is in complete agreement with the analytical results obtained from the shear lag theory (Dharani et al, 1983;Beyerlin et al, 1996). It is also in agreement with the data obtained by the improved shear lag model of Beyerlein and Landis (1999).…”

Section: Crack In a Fiber Reinforced Compositesupporting

confidence: 91%

“…The shear lag analysis provides a good approximation of the average stresses in the fiber and matrix regions in the case of a sufficiently large contrasts between the fiber/matrix elastic moduli. This method was employed by Hedgepeth (1961), Hedgepeth and Van Dyke (1967), Dharani et al (1983), Hikiami and Chou (1990), Sastry and Phoenix (1993) and Beyerlin et al (1996) for example. One of the limitations of the classical shear lag method is the neglect of the axial stress in the matrix.…”

Section: Introductionmentioning

confidence: 99%

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A continuum approach to the analysis of the stress field in a fiber reinforced composite with a transverse crack

Ryvkin

Aboudi

2007

International Journal of Solids and Structures

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The stress field in a periodically layered composite with an embedded crack oriented in the normal direction to the layering and subjected to a tensile far-field loading is obtained based on the continuum equations of elasticity. This geometry models the 2D problem of fiber reinforced materials with a transverse crack. The analysis is based on the combination of the representative cell method and the higher-order theory. The representative cell method is employed for the construction of Green's functions for the displacements jumps along the crack line. The problem of the infinite domain is reduced, in conjunction with the discrete Fourier transform, to a finite domain (representative cell) on which the Born-von Karman type boundary conditions are applied. In the framework of the higher-order theory, the transformed elastic field is determined by a second-order expansion of the displacement vector in terms of local coordinates, in conjunction with the equilibrium equations and these boundary conditions. The accuracy of the proposed approach is verified by a comparison with the analytical solution for a crack embedded in a homogeneous plane.Results show the effects of crack lengths, fiber volume fractions, ratios of fiber to matrix Young's moduli and matrix Poisson's ratio on the resulting elastic field at various locations of interest. Comparisons with the predictions obtained from the shear lag theory are presented.

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Section: Crack In a Fiber Reinforced Compositesupporting

confidence: 91%

Section: Introductionmentioning

confidence: 99%

A continuum approach to the analysis of the stress field in a fiber reinforced composite with a transverse crack

Ryvkin

Aboudi

2007

International Journal of Solids and Structures

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“…The point stress criterion was proposed by Nuismer and Whitney [16] for notched composites. This criterion has been extended to shear lag models for unidirectional composites [13,17] Figures 6 and 7 show the remote strain required to extend an inherent transverse crack, as a function of the 90 degree layer thickness for [Om/9On] s and [45k/Om/90n] , laminates respectively. The tendency of the laminate for microcracking in the transverse plies increases with the transverse ply thickness.…”

Section: Analytical Resultsmentioning

confidence: 99%

Micromechanics characterization of sublaminate damage

Dharani

Tang

1990

Int J Fract

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A micromechanics analytical model is developed for characterizing the fracture behaviour of a fibre reinforced composite laminate containing a transverse matrix crack and longitudinal debonding along 0/90 interface. Both the matrix and the fibres are considered as linear elastic. A consistent shear lag theory is used to represent the stress-displacement relations. The governing equations, a set of differential-difference equations, are solved satisfying the boundary conditions appropriate to the damage configuration by making use of an eigenvalue technique. The properties of the constituents appear in the model explicitly. Displacements and stresses in the fibres and the matrix are obtained, and the growth of damage is investigated by using the point stress criterion. The investigation includes fibre stress distribution in zero degree plies, transverse crack and debonding intitiation as functions of laminate geometry, and the effect of fibre breaks in the zero degree ply on damage growth. The predicted damage growth patterns and the corresponding critical strains agree with the finite element and experimental results.

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“…The shear-lag approach was first used by Hedgepeth [1] over 20 years ago to consider a linear elastic, fully bonded monolayer of infinite extent. Since then, this original analysis has undergone numerous extensions (see Reference [2] which reviews much of the work prior to 1980, as well as References [3][4][5][6], which were published subsequently).…”

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confidence: 99%

Fiber Stresses in a Cracked Monolayer: Comparison of Shear-Lag and 3-D Finite Element Predictions*

Reedy

1984

Journal of Composite Materials

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Shear-lag and 3-D finite element predictions for the fiber stresses in a cracked monolayer are compared. Results are given for 5-fiber wide boron/aluminum and Kevlar 49/epoxy monolayers containing a single broken fiber. Both methods of analysis are found to predict nearly the same fiber stress distribution along the cracktip fiber when the monolayer is fully elastic. Results for highly loaded monolayers with extensive matrix yielding are not in quite as good agreement, but even then the predicted stress distributions are within 5%. These calculations show that a shear-lag analysis is accurate even when 1) the matrix is relatively stiff and can carry substantial loads (e.g., boron/aluminum), and 2) the fiber is highly anisotropic, (e.g., Kevlar 49/epoxy). INTRODUCTIOÑ~J~

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Mathematical modeling of damage in unidirectional composites

Cited by 73 publications

References 9 publications

A continuum approach to the analysis of the stress field in a fiber reinforced composite with a transverse crack

A continuum approach to the analysis of the stress field in a fiber reinforced composite with a transverse crack

Micromechanics characterization of sublaminate damage

Fiber Stresses in a Cracked Monolayer: Comparison of Shear-Lag and 3-D Finite Element Predictions*

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