Statistical Strength Theory for Fibrous Composite Materials

Phoenix, S. Leigh

doi:10.1016/b0-08-042993-9/00056-5

Cited by 92 publications

(95 citation statements)

References 151 publications

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“…More specifically, we assume that load is transferred from the ductile phase back to broken elements of the brittle phase via an interfacial shear stress that equals the instantaneous average flow stress of the ductile phase in shear. This differentiates the present model from global load sharing models that have been proposed so far in the literature for brittle/ductile phase composites [16][17][18][19] because here the intact, ductile, phase hardens as it flows. Both the load it carries and the load it transmits to the brittle phase, wherever the latter has fractured, therefore increase as the composite deforms: we examine here how this influences ductile failure of the composite (or, in the parlance of composite mechanics, its failure by global load sharing [16,17]).…”

Section: Introductionmentioning

confidence: 96%

“…This differentiates the present model from global load sharing models that have been proposed so far in the literature for brittle/ductile phase composites [16][17][18][19] because here the intact, ductile, phase hardens as it flows. Both the load it carries and the load it transmits to the brittle phase, wherever the latter has fractured, therefore increase as the composite deforms: we examine here how this influences ductile failure of the composite (or, in the parlance of composite mechanics, its failure by global load sharing [16,17]). As will be seen, one finds that despite the many parameters needed to describe this two-phase system, in the end only two dimensionless parameters influence significantly its strain to failure.…”

Section: Introductionmentioning

confidence: 96%

“…The mechanics of this (complex) problem have been the subject of extensive work in composite micromechanics; Refs. [16] [17] give detailed in-depth reviews. The simplest ("shear-lag") view of the problem is that wherever the brittle phase has cracked, it is reloaded by the ductile phase via the shear stress that the latter exerts, along the stress direction, across the interface between the two phases.…”

Section: Statistical Model For the Damaging Brittle Phasementioning

confidence: 99%

“…We again consider the most basic and simple case, namely a strongly bonded unidirectional or laminated composite, which deforms slowly along the fibre or laminate direction. We describe load-sharing near a crack in the brittle phase using classical shear-lag theory, known to apply with good accuracy in fibre reinforced composites [16,17]. More specifically, we assume that load is transferred from the ductile phase back to broken elements of the brittle phase via an interfacial shear stress that equals the instantaneous average flow stress of the ductile phase in shear.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Tensile elongation of unidirectional or laminated composites combining a brittle reinforcement with a ductile strain and strain-rate hardening matrix

Cohades¹,

Mortensen²

2014

Acta Materialia

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We use the long-wavelength model of Hutchinson and Neale (Hutchinson JW, Neale KW. Acta Metall 1977;25:839) and Ghosh (Ghosh AK. Acta Metall 1977;25:1413) to estimate the uniform tensile elongation of two-phase composites deforming quasistatically according to the equistrain rule of mixtures, in which one phase is ductile while the other fractures progressively according to twoparameter Weibull statistics. We use shear-lag models in the literature to quantify load transfer from the ductile phase to the fractured brittle phase, to estimate the influence of matrix strain and strain-rate hardening, of brittle phase fracture characteristics, and of phase volume and strength ratios, on the composite strain to failure as dictated by the onset of unstable necking. Calculations show that strain and strain-rate hardening of the ductile phase do relatively little to increase the ductility of the composite. Two parameters play a dominant role, namely the brittle phase Weibull modulus and a dimensionless parameter describing load transfer across the two phases. The main practical implication of this analysis is that, to produce reasonably ductile two-phase composites, the best strategy is to aim for small layer thicknesses. IntroductionMany composite materials combine a ductile matrix with a brittle reinforcement: ceramic or carbon fibre reinforced metals fall in this category, as do some laminated metal composites and many other layered materials (such as thin film structures or ceramic-coated metals) [1][2][3][4]. When such composites are strained in tension the brittle phase develops cracks that cut its fibres or layers in two along a plane normal to the applied load; in laminated composites these are known as "tunnel cracks". Final fracture of the material may then happen in one of two ways. One is sudden brittle failure, caused by a propagative localization of internal damage that cuts abruptly the entire specimen in two; many strongly bonded ceramic or carbon fibre reinforced composites fail in this way [5][6][7], as do some particle reinforced composites [8]. Alternatively, internal damage accumulates stochastically throughout the material, in gradual and uncorrelated fashion. The composite is then likely to fail by strain localization, reaching its ultimate tensile strength at a smooth maximum along its stress-strain curve, and sometimes deforming significantly thereafter, while deformation concentrates in a portion of the sample's gauge length. Weakly bonded fibre reinforced composites (e.g., [5]), ceramic particle reinforced metals (e.g., [8,9]), two-phase metal alloys [10] or laminated metal composites [11] can all fail in this way. Strain hardening and strain-rate hardening then both play an important role: even small increases in a ductile material's strain hardening rate, or in its strain-rate sensitivity, can noticeably increase the tensile elongation when it is governed by the onset of strain localization.

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Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 96%

Section: Statistical Model For the Damaging Brittle Phasementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Tensile elongation of unidirectional or laminated composites combining a brittle reinforcement with a ductile strain and strain-rate hardening matrix

Cohades¹,

Mortensen²

2014

Acta Materialia

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“…Examples of such modelling include but not limited to modelling of laminated woven composites under quasi-static tension 2,3 and high strain rate compaction, 4 composites with braided reinforcement 5 and 3D composites. 6 However, the conventional unit cell approach cannot predict variability of the mechanical properties from sample to sample which is usually associated with variability in the intrinsic properties of constituents 7,8 and the geometry of reinforcements such as yarn and layer misalignments 9 arising from textile and composite manufacturing. This study focuses only on the effects of variability of textile reinforcement geometry, namely yarn paths and layer shift variability.…”

Section: Introductionmentioning

confidence: 99%

Effects of layer shift and yarn path variability on mechanical properties of a twill weave composite

Matveev

Long

Brown

et al. 2016

Journal of Composite Materials

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ArticleEffects of layer shift and yarn path variability on mechanical properties of a twill weave composite MY Matveev, AC Long, LP Brown and IA Jones Abstract Experimental and numerical analyses of a woven composite were performed in order to assess the effect of yarn path and layer shift variability on properties of the composite. Analysis of the geometry of a 12 K carbon fibre 2 Â 2 twill weave at the meso-and macro-scales showed the prevalence of the yarn path variations at the macro-scale over the meso-scale variations. Numerical analysis of yarn path variability showed that it is responsible for a Young's modulus reduction of 0.5% and CoV of 1% which makes this type of variability in the selected reinforcement almost insignificant for an elastic analysis. Finite element analysis of damage propagation in laminates with layer shift showed good agreement with the experiments. Both numerical analysis and experiments showed that layer shift has a strong effect on the shape of the stress-strain curve. In particular, laminates with no layer shift tend to exhibit a kink in the stress-strain curve which was attributed solely to the layer configuration.

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A probabilistic model of the tensile strength of a UD flax–fabric‐reinforced polymer composite

Andersons

Modniks

2016

Polymer Composites

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In order to fully realize the efficiency of bast fibers or their yarns as reinforcement of polymer composites, they should be aligned. Tensile strength of such composites in the direction of reinforcement has been found to exhibit size effect commensurable with that of unidirectionally reinforced (UD) composites with inorganic fibers, necessitating a probabilistic modeling approach. Strength distribution of a polymer matrix composite reinforced with aligned twisted bast fiber yarns is considered allowing for the strength scatter of elementary fibers, the presence of defects in the form of adjacent fiber breaks, and twist of the yarns. The model is applied to predicting the strength of flax/acrylated epoxidized soy oil resin composite specimens of different sizes. The theoretical prediction is found to be in a reasonable agreement with strength test results. POLYM. COMPOS., 39:2101–2109, 2018. © 2016 Society of Plastics Engineers

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Statistical Strength Theory for Fibrous Composite Materials

Cited by 92 publications

References 151 publications

Tensile elongation of unidirectional or laminated composites combining a brittle reinforcement with a ductile strain and strain-rate hardening matrix

Tensile elongation of unidirectional or laminated composites combining a brittle reinforcement with a ductile strain and strain-rate hardening matrix

Effects of layer shift and yarn path variability on mechanical properties of a twill weave composite

A probabilistic model of the tensile strength of a UD flax–fabric‐reinforced polymer composite

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