Stress Concentrations from Single-Filament Failures in Composite Materials

Dyke, Peter Van; Hedgepeth, J. M.

doi:10.1177/004051756903900702

Cited by 68 publications

(4 citation statements)

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“…Since then, extensions of the Hedgepeth and Van Dyke model have also accounted for interfacial slipping and matrix cracking, as well as yielding. They can be found, for instance, in works by Van Dyke and Hedgepeth [19], Goree and Gross [8], Goree et al [ 7 ] , Rossettos and Olia [ 17 ] , Nairn [15 J,Beyerlein and Phoenix [ 3 ] , and Beyerlein et al [2]. Although these works indicate a mathematical structure that parallels, to some extent, our work, thereby suggesting solution methods, the physical and geometric aspects of the materials involved are quite different.…”

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confidence: 65%

Damage Growth in Prestressed Plain Weave Fabrics

Godfrey

Rossettos

1998

Textile Research Journal

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A simplified micromechanics approach is used to develop a mathematical model to predict damage growth in prestressed plain weave fabrics near sites where yams are broken. Stress concentration in the yams neighboring yarn breaks is determined as a function of increasing loading. An evaluation of the load redistribution around the damage region includes a determination of the frictional slip of broken yams. Consideration of equilibrium and deformation of constituent yams leads to linear differential equations for yarn displacements applicable to distinct regions where slipping does and does not occur. Slip frictional forces depend on yam normal contact forces at crossover points resulting from crimp interchange, Kawabata's model [12] is modified and used to motivate an analysis of frictional load transfer. The equations are nondimensionalized, and dimensionless parameters involving both geometry and material properties are identified.Biaxially stressed woven fabrics can be used for inflated fabric structures, parachute canopies, geotechnical structures, and numerous industrial applications. In many instances, fabrics are cut or punctured by accidental contact with a sharp edge or by impact with a moving object. Given sufficiently high biaxial tension in the region of the fabric surrounding the initial damage, the damage site provides a starting point for selfpropagating catastrophic tearing of the fabric. This situation is particularly untenable in gas-inflated fabric structures, where the tearing is accompanied by the sudden release of the stored energy of the compressed gas with explosive-like effects. Developing a model for damage growth in prestressed woven fabrics would significantly advance the state-of-the-art in selecting or designing new fabrics specifically for end-use as damage tolerant structural materials.A micromechanical analysis of damaged filamentary structures was first provided by Hedgepeth [10]. Although it was applied to fiber composite sheets, where the matrix transfers the load from broken to unbroken fibers by means of shear, he considered his shear lag model, where the fibers carry axial loads and the matrix is assumed to carry only shear, to apply to coated woven fabrics as well. In biaxially stressed uncoated woven fabrics, load transfer between yams of a given yam set is accomplished though a deformational stiffening effect involving the rotation of the tensioned crossing yarns in the fabric plane, while in the shear lag model, load transfer between neighboring yarns or fibers occurs through shearing of the coating or matrix. The ultimate transfer of the load to a given yarn arises through frictional contact at the cross-over point. This stress-induced shear stiffening effect has been noted by Christoffersen [ 4 ] and by Topping [ 18] . Christoffersen developed a finite deformation two-dimensional continuum model for a biaxially stressed ideal woven fabric (no slip occurs at yam cross-overs) and applied it to the problem of a slit parallel to a yarn direction. In our work, we incorporate...

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confidence: 65%

Damage Growth in Prestressed Plain Weave Fabrics

Godfrey

Rossettos

1998

Textile Research Journal

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“…In his model the effect of stress concentration due to fiber breaks was ignored (as GLS model was used) but in 1968 Zweben introduced this effect in the Rosen's model (Zweben [27]). Van Dyke and Hedgepeth [28] in 1969 investigated the influence of fiber-matrix debonding and matrix yielding on the stress concentration factor due to a single fiber break in a finite and an infinite lamina, both in 2D and 3D fiber arrangements.…”

Section: Methodsmentioning

confidence: 99%

Progressive damage of a unidirectional composite with a viscoelastic matrix, observations and modelling

Kotelnikova-Weiler

Baverel

Ducoulombier

et al. 2018

Composite Structures

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In this paper phenomenological observations of the creep rupture under maintained combined traction and torsion loading are first presented. They show the importance of the matrix's behavior in the long-term durability of the material. Understanding and foreseeing creep rupture of unidirectional fiber reinforced polymers (UD FRP) involves comprehension at the fibers' scale of various time-dependent interactions among the fibers and between the matrix and the fibers. Shear-lag models have been successfully applied in the modeling at the micro-scale of these interactions, some of them even introducing time dependence. Longterm durability of macro-scale structure demand further developments of such models to be able to predict the macro-damage cluster and their evolution. The aim of the present contribution that is an extension from existing models is to investigate the progressive damage of a 0o UD composite material subjected to combined shear-traction loading including a high number of interacting fibers, with a viscoelastic matrix, debondings and random distribution of fiber flaws. Results of simulations including different loadings and matrix viscoelastic properties will be shown and discussed for a better comprehension of the role of composite's components in the creep rupture phenomenon. In particular, the long-term influence of matrix's shear stiffness on the material's lifespan is shown, and the impact of an additional uniform shear stress is studied. This combined shear-traction loading is of interest in real-scale structures where shear stress can result from torsion or shear forces (such as those due to anchor points, misalignment and coupling). Moreover, this model is a first step to approach the long term failure of 0o composites subjected to torsion-bending loading, what is shown decisive in the second section of this work. Further experimental works in combined traction-torsion loadings are needed to validate this simulations with a specific attention on the identification of required parameters.

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“…The matrix material transfers only shear force between fibers. The shear-lag method was introduced by Hedgepeth (Hedgepeth and Van Dyke, 1967;Van Dyke and Hedgepeth, 1969) to analyze the multifilament failure problems of laminated composites. The shear-lag approach is based upon easy assumptions and usually provides adequate physical insights of complicated problems.…”

Section: The Shear-lag Methodsmentioning

confidence: 99%

Lattice of infinite bending-resistant fibers

Kobelev

2016

Multidiscipline Modeling in Materials and Structures

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This article present the double-periodical lattice made of infinite elastic fibers that withstand bending and tension. The model describes the elastic properties of flat periodic structure. With this model the behavior of a two-dimensional array of infinite fibers is simulated. The material that contains a row of broken fibers is considered. These broken fibers form the failure in the material that shapes like a long straight crack. The lattice is tensioned in the direction, which is orthogonal to the direction of straight crack. The conditions of fracture of this lattice are investigated. The closed form expression for the stress in the first unbroken fiber and the expression for fracture toughness are given. These values are the functions of mechanical parameters of lattice and tensions in both families of fibers. The closed form solution demonstrates a notable behavior of the material. Namely, the fracture behavior of two-dimensional lattice is cardinally depends upon the pre-stress in the material in the direction, parallel to crack direction. If the tension in fibers that parallel to the crack direction exists, it stabilizes the crack growth and makes the load distribution in the unbroken fibers more even. The two-dimensional lattice behaves in the presence of tension in both directions similarly to the plane elastic media. The finite length crack assumes the shape of the elongated elliptic split. Another behavior of lattice occurs if the fibers, parallel to crack direction, are unstressed. The character of stress concentration near the crack differs. The load distribution at the crack tip varies considerably. The first unbroken fiber carries higher load. The crack is lens-shaped and the crack borders form at the tip the finite angle

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Stress Concentrations from Single-Filament Failures in Composite Materials

Cited by 68 publications

References 1 publication

Damage Growth in Prestressed Plain Weave Fabrics

Damage Growth in Prestressed Plain Weave Fabrics

Progressive damage of a unidirectional composite with a viscoelastic matrix, observations and modelling

Lattice of infinite bending-resistant fibers

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