Constitutive Model for a Fiber Tow Bridging a Delamination Crack

Cox, B. N.

doi:10.1080/107594199305584

Cited by 52 publications

(33 citation statements)

References 12 publications

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“…If a Z-pin is subjected to high longitudinal-transverse shear stresses it is susceptible to split into strands that can slide relative to each other and accommodate further loading before failure [14]. In the present modelling method, columns of zero-thickness cohesive elements with their normal direction oriented in the Mode II loading direction are inserted in the Z-pin at potential splitting locations.…”

Section: Z-pin Splitting Definitionmentioning

confidence: 99%

“…Cox [4,14,15] established a comprehensive analytical model for the mixedmode bridging analysis by taking into account the pin actual orientation with respect to the fracture plane and the consequent "snubbing" effect (enhanced friction). In Cox's model, the constitutive equations are derived by assuming that the Z-pin behaves as a linear-elastic/perfect-plastic body; the embedding laminate is described as a perfectly plastic medium.…”

Section: Introductionmentioning

confidence: 99%

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Micro-mechanical finite element analysis of Z-pins under mixed-mode loading

Zhang

Allegri

Yasaee

2015

Composites Part A: Applied Science and Manufacturing

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This paper presents a three-dimensional micro-mechanical finite element (FE) modelling strategy for predicting the mixed-mode response of single Z-pins inserted in a composite laminate. The modelling approach is based upon a versatile ply-level mesh, which takes into account the significant micromechanical features of Z-pinned laminates. The effect of post-cure cool down is also considered in the approach. The Z-pin/laminate interface is modelled by cohesive elements and frictional contact. The progressive failure of the Z-pin is simulated considering shear-driven internal splitting, accounted for using cohesive elements, and tensile fibre failure, modelled using the Weibull's criterion. The simulation strategy is calibrated and validated via experimental tests performed on single carbon/BMI Z-pins inserted in quasi-isotropic laminate. The effects of the bonding and friction at the Z-pin/laminate interface and the consequences of the internal Z-pin splitting are discussed in detail. The primary aim is to develop a robust numerical tool, as well as guidelines for designing Z-pins with optimal bridging behaviour. .

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Section: Z-pin Splitting Definitionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Micro-mechanical finite element analysis of Z-pins under mixed-mode loading

Zhang

Allegri

Yasaee

2015

Composites Part A: Applied Science and Manufacturing

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“…The bridging traction vector, p; can be expressed as a function of the jump in displacement, 2u; across the crack faces. 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%

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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“…The case used for illustration is motivated by recent tests on pipe joints [6]. The model combines the finite element method and a previously developed analytical model for the pins, which can account for pins of arbitrary initial orientation, subject to large mixed-mode deformations [20][21][22][23]. The model is incorporated here as prescribed bridging tractions, which act on the surfaces of the adherends when a debond crack exists.…”

Section: Introductionmentioning

confidence: 99%