A Traction Law for Inclined Fiber Tows Bridging Mixed-Mode Cracks

Cox, B. N.; Sridhar, Nigamanth

doi:10.1080/15376490290096973

Cited by 54 publications

(43 citation statements)

References 8 publications

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“…It was observed that the rods deformed with the following characteristics, which were included in the model of Ref. [22].…”

Section: Summary Of Existing Knowledge Of Mechanismsmentioning

confidence: 99%

“…Following the terminology in Ref. [22], loading where u and f have the same sign will be called loading 'with the nap' while loading where u is of opposite sign to f will be called loading 'against the nap'. It was observed that the rods deformed with the following characteristics, which were included in the model of Ref.…”

Section: Summary Of Existing Knowledge Of Mechanismsmentioning

confidence: 99%

“…Optimal design of the throughthickness reinforcement requires knowledge of the material and geometrical factors that determine the relation pðuÞ: Since the bridging tractions are proportional to the area density, c s ; of the bridging tows, a more fundamental relation is that between the tractions, T; acting over the section of a single tow on the fracture plane and u: Following observations of the deformation of a bridging fibrous tow (stitch or fibrous rod) during delamination crack propagation, a simple model has been proposed to predict TðuÞ for mode II crack displacements [20]. This model has recently been generalised to treat fibrous bridging tows that are initially canted at an angle to the delamination fracture plane and are subjected to mixed mode crack displacements [21,22].…”

Section: Introductionmentioning

confidence: 99%

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Mechanisms of crack bridging by composite and metallic rods

Cartié

Cox

Fleck

2004

Composites Part A: Applied Science and Manufacturing

142

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Experiments are reported that explore the mechanics of single pins or rods that bridge a delamination crack in a miniature model specimen. The effects of material and geometrical parameters are determined by varying the angle of the rod, its material, and the material in which it is embedded. Different tests represent mode I and mode II loading, with respect to a pre-existing delamination crack.Many observed mechanisms are similar to those previously reported for stitches and in limited studies on rods. They include debonding and sliding of the rod relative to the substrate, lateral deflection of the rod into the substrate (when mode II is present), rod pullout, and rod rupture.Sliding in mode I can be explained by assuming that pullout is resisted by uniform friction, which has a modest value (, 1 -20 MPa). However, when mode II loading is present and the rod deflects laterally, a more complicated friction behaviour is suggested. Peak load occurs well after the whole rod has begun to slide out of the specimen, implying that the pullout process is stable in mode II to large displacements. This, together with the high values observed for the peak loads and displacements suggest the presence of an enhanced friction zone (snubbing effect) extending over the segment of the rod that has been laterally deflected by mode II loading. This zone can grow under increasing shear displacements even after the whole rod begins to slide, leading to increasing shear loads (stable pullout). Various characteristics of the pullout experiments are consistent with this model. q

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“…It was observed that the rods deformed with the following characteristics, which were included in the model of Ref. [22].…”

Section: Summary Of Existing Knowledge Of Mechanismsmentioning

confidence: 99%

Section: Summary Of Existing Knowledge Of Mechanismsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Mechanisms of crack bridging by composite and metallic rods

Cartié

Cox

Fleck

2004

Composites Part A: Applied Science and Manufacturing

142

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“…Approaches to describe the through thickness reinforced (TTR) pin bridging mechanisms analytically have been attempted by a number of [13][14][15][16][17]. In all these cases the TTR bridging models have been calibrated against experimental data carried out either on mode I pin array pull-out tests [16], standard mode I fracture toughness tests [7], T-Joint pull-out tests [2,5,6,15] or mode I and mode II single pin tests [11,14].…”

Section: Introductionmentioning

confidence: 99%

Experimental characterisation of mixed mode traction–displacement relationships for a single carbon composite Z-pin

Yasaee

Lander

Allegri

2014

Composites Science and Technology

103

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This paper presents an experimental characterisation of the mechanical performance and behaviour of through-thickness reinforced composite laminates. To achieve this, composite blocks with individual reinforcing pins were manufactured, quality assessed and tested. Individual specimens were inspected using X-ray ComputedTomography and only the specimens with acceptable quality pin insertions were tested experimentally under a range of mode mixities. Two stacking sequences, unidirectional (UD) and quasi-isotropic (QI) were investigated. It was found that the pins inside the UD samples experienced significantly larger pin/matrix bond strength than those in the QI laminates. The resulting experimental data indicates that a non-UD laminate type may experience pin pull-out and thus increased energy absorption for a wider range of mode mixities than a UD laminate type. Energy plots show a clear transition from a pull-out to a pin rupture region for both laminate types. Specimens that experienced pin rupture during low mode mixity tests exhibited similar failure energies to those loaded in pure mode II.

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“…Such a traction acts against the direction that the fiber is tilted, causing the fiber to rotate into alignment with the crack plane normal. This type of deformation has been termed 'against the nap' by previous studies of bridging of cracks by inclined fibers (Cox and Sridhar, 2002). 'With the nap' deformation of the fiber cannot arise in the problem under present consideration: it would require a different relationship between the orientations of the traction vector, the fiber axis, and the crack plane normal.…”

Section: Free Body Analysismentioning

confidence: 99%

Matrix cracking of fiber-reinforced ceramic composites in shear

Rajan

Zok

2014

Journal of the Mechanics and Physics of Solids

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a b s t r a c tThe mechanics of cracking in fiber-reinforced ceramic matrix composites (CMCs) under general loadings remains incomplete. The present paper addresses one outstanding aspect of this problem: the development of matrix cracks in unidirectional plies under shear loading. To this end, we develop a model based on potential energy differences upstream and downstream of a fully bridged steady-state matrix crack. Through a combination of analytical solutions and finite element simulations of the constituent stresses before and after cracking, we identify the dominant stress components that drive crack growth. We show that, when the axial slip lengths are much larger than the fiber diameter and when interfacial slip precedes cracking, the shear stresses in the constituents are largely unaffected by the presence of the crack; the changes that do occur are confined to a 'core' region within a distance of about one fiber diameter from the crack plane. Instead, the driving force for crack growth derives mainly from the axial stresses-tensile in the fibers and compressive in the matrix-that arise upon cracking. These stresses are wellapproximated by solutions based on shear-lag analysis. Combining these solutions with the governing equation for crack growth yields an analytical estimate of the critical shear stress for matrix cracking. An analogous approach is used in deriving the critical stresses needed for matrix cracking under arbitrary in-plane loadings. The applicability of these results to cross-ply CMC laminates is briefly discussed.

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A Traction Law for Inclined Fiber Tows Bridging Mixed-Mode Cracks

Cited by 54 publications

References 8 publications

Mechanisms of crack bridging by composite and metallic rods

Mechanisms of crack bridging by composite and metallic rods

Experimental characterisation of mixed mode traction–displacement relationships for a single carbon composite Z-pin

Matrix cracking of fiber-reinforced ceramic composites in shear

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