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  • 1
    Electronic Resource
    Electronic Resource
    Lifetime statistics for single graphite fibres in creep rupture (1989)
    Springer
    Journal of materials science 24 (1989), S. 2151-2164 
    Details
    ISSN: 1573-4803
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Experimental results are presented for the lifetime in creep rupture of single graphite fibres. The fibres were extracted from unsized, Hercules IM6 tows and were tested at a gauge length of 5 cm under standard ambient conditions (21°C, 50% r.h.). The results were analysed using a theoretical model which embodies Weibull distributions for both strength and lifetime, and a power-law relationship for lifetime against stress level. Using maximum likelihood techniques, the Weibull shape parameter values for strength and lifetime were found to be about 4.6 and 0.015, respectively, and the power-law exponent was about 300, but could be as low as 250. As expected, this exponent was close in value to the ratio of the respective Weibull shape parameter values. Using the Kaplan-Meier estimator for censored data, the goodness of fit of the model to the data was found to be excellent.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02385436
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  • 2
    Electronic Resource
    Electronic Resource
    Temperature dependence of lifetime statistics for single Kevlar 49 filaments in creep-rupture (1988)
    Springer
    Journal of materials science 23 (1988), S. 1851-1860 
    Details
    ISSN: 1573-4803
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Experimental data are presented for the strength and lifetime under constant stress of single Kevlar 49 aramid filaments at two elevated temperatures, 80 and 130° C. As seen in previously published work performed at room temperature (21 °C), the strength data could be fitted to a two-parameter Weibull distribution; increasing the temperature caused a decrease in the Weibull scale parameter while the shape parameter remained relatively constant, indicating a decrease in the mean strength but no change in strength variability. Lifetime experiments at both 80 and 130°C were performed at different filament stress levels, ranging from 55 to 92.5% of the Weibull scale parameter for short-term strength at that temperature. These data were fitted to a two-parameter Weibull distribution with large variability (scale parameter values ⩽ 1), and evaluated using an exponential kinetic breakdown model in the spirit of Eyring and Zhurkov. Using this model, activation energies in the neighbourhood of 80 kcal mol−1 (3.35 × 105 J mol−1 ) were obtained, suggesting that scission of the C-N bond plays the dominant role in fibre failure at longer times under constant stress.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01115731
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  • 3
    Electronic Resource
    Electronic Resource
    Probability distributions for the strength of composite materials II: A convergent sequence of tight bounds (1981)
    Springer
    International journal of fracture 17 (1981), S. 601-630 
    Details
    ISSN: 1573-2673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Résumé Dans le cas de l'analyse de la distribution probable de la contrainte dans un matériau composite, on a développé une séquence de bornes supérieures convergentes. L'analyse est basée sur le modèle bien connu des chaines de bottes et la distribution locale des contraintes est supposée relative à des éléments de fibres non rompues dans chaque botte. Les limites sont définies en supposant queK ou d'avantage de fibres adjacentes sont rompues dans une botte et sur les conditions nécessaires mais non suffisantes pour que se produise la rupture des matériaux. Cependant, on trouve que pour une chargeL agissant sur le composite, une certaine valeur deK dénotée(L) est critique en ce que un groupe d'éléments rompus atteignant le nombre critiqueK(L) entrainera une croissance catastrophique dans la dimension et ce d'une manière presque certaine. SiL se trouve être approximativement la résistance moyenne du composite, la frontière calculée sur base deK =K(L) rupture adjacente est virtuellement identique à la distribution vraie des probabilités de la résistance des composites. En effet la convergence de la séquence des frontières devient virtuellement complète lorsqueK dépasseK(L). On montre que la distribution des contraintes dans le composite présente la structure de liaison la plus faible en se présentant comme une fonction de distribution caractéristiqueW(X),X ⩾ 0 dépendant de la redistribution de la contrainte et de la distribution de probabilités de résistance d'un élément fibreux. Divers cas sont considérés dans le cas d'une distribution de Weibull pour la résistance d'une fibre et sous une double version qui a pour effet de faire plafonner la résistance de la fibre. On montre que dans des situations typiques les prédictions utilisant la double distribution de Weibull ne sont pas ce qu'on pourrait en attendre et que leur utilisation n'est pas justifiée dans de nombreux cas.
    Notes: Abstract A sequence of convergent upper bounds is developed for the probability distribution of strength of composite materials. The analysis is based on the well-known chain-of-bundles model, and local load sharing is assumed for the nonfailed fiber elements in each bundle. The bounds are based on the occurrence ofk or more adjacent broken fibers in a bundle, an event which is necessary but not sufficient for the failure of the material. However, we find that given the loadL on the composite, some value ofk denotedk *(L) is critical in that a group of failed elements once reaching sizek *(L) will catastrophically increase in size with virtual certainty. IfL happens to be approximately the median strength of the composite, then the bound based onk =k *(L) adjacent breaks is virtually identical to the true probability distribution of composite strength; indeed, the convergence of the sequence of bounds becomes virtually complete ask exceedsk *(L). We show that the strength distribution for the composite essentially has weakest link structure in terms of a characteristic distribution functionW(x),x ≧ 0 which depends on the load sharing and on the probability distribution for fiber element strength. Typical cases are considered under a Weibull distribution for fiber strength and under a double version which has the effect of putting a ceiling on fiber strength. We show that in typical situations, predictions using the double Weibull distribution are not as one might guess, and its use is unjustified in many cases.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00681559
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  • 4
    Electronic Resource
    Electronic Resource
    Probability distributions for the strength of composite materials. III: The effect of fiber arrangement (1982)
    Springer
    International journal of fracture 20 (1982), S. 291-311 
    Details
    ISSN: 1573-2673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Résumé Dans le mémoire, on poursuit l'étude du modèle de succession de bottes pour établir la résistance statistique des matériaux composites. On met ici l'accent sur les composites à trois dimensions ou les fibres suivant une section droite sont réparties sur deux dimensions. En particulier, on considère des rubans à deux dimensions et des regroupements en forme hexagonale et l'on obtient les distributions des liaisons en se basant sur l'apparition d'au moins deux ruptures de fibres adjacentes dans le matériau. Comme dans un travail précédent, il apparait diverses distributions de Weibull approximatives et limitatives pour exprimer la résistance du composite. En comparant les nouveaux résultats avec ceux obtenus précédemment dans le cas de rubans et de tubes (distribution à une dimension), l'approche utilisée suggère que la résistance médiane est modérément accrue dans le cas de distributions à deux dimensions, tandis que les variations de la contrainte sont inchangées. Dans des situations où l'apparition de deux ruptures de fibres adjacentes conduit presque certainement à la rupture du composite, de telles conclusions sont confirmées. Dans les cas où les liaisons sont clairement conservatives, on s'attend aux mêmes résultats, bien que puisse survenir une légère diminution dans la variabilité de la résistance du composite. Néanmoins, les liaisons envisagées dans ce mémoire présentent une importance considérable.
    Notes: Abstract This paper continues the study of the chain-of-bundles model for the statistical strength of composite materials. The focus is onthree-dimensional composites where the fibers in a cross-section form atwo-dimensional array. In particular, two-layer tapes and hexagonal arrays are considered, and bounding distributions are obtained based on the occurrence of at least two adjacent fiber fractures in the material. As in earlier work, various approximate and limiting Weibull distributions arise for the strength of the composite. In comparing the new results with those obtained earlier for tapes and tubes (one-dimensional arrays), the bounds suggest that the median strength is moderately increased for the two-dimensional arrays, while the variability in strength is unchanged. In situations where the occurrence of two adjacent fiber fractures leads almost certainly to composite fracture, such conclusions are warranted. In cases where the bounds are clearly conservative, the same results are expected, although a slight decrease in the variability in composite strength may occur. Nevertheless, the bounds discussed in this paper yield considerable insight.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01130614
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  • 5
    Electronic Resource
    Electronic Resource
    Probability distributions for the strength of composite materials IV: Localized load-sharing with tapering (1983)
    Springer
    International journal of fracture 22 (1983), S. 243-276 
    Details
    ISSN: 1573-2673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Résumé Dans ce mémoire, on poursuit l'étude du modèle de groupage de bottes en série pour décrire la résistance statistique de matériaux composites, en se concentrant avec attention sur la redistribution locale des charges dans des composites à deux dimensions. On considère une règle plus souple pour le partage des contraintes, qui consiste à distribuer la charge nominale d'une fibre rompue sur les quatre fibres les plus proches, les deux fibres adjacentes absorbant la majeure partie de la charge. On considére trois techniques d'analyse probabiliste distinctes et on trouve que la structure probabiliste de base afférant à la distribution de la résistance dans le composite se présente comme la même que celle rencontrée lors du travail précédent où l'on étudiait un partage local idéalisé de la charge. Toutefois, la résistance médiane du composite s'accroit légèrement en raison de la surcharge moins sévère des fibres adjacentes à la rupture, tandis que la présence de faibles surcharges sur les fibres plus lointaines n'a pratiquement pas d'effet sur la résistance. En outre, la variation de résistance du composite tend à se réduire légèrement, vu le léger agrandissement de la zone sur laquelle se déroule la séquence critique des ruptures conduisant à rupture catastrophique. A nouveau, on constate que la distribution de Weibull apparait comme le modèle-clé pour décrire la résistance des composites unidirectionnels. Des approximations fiables de paramètres sont fournies.
    Notes: Abstract This paper continues the study of the chain-of-bundles model for the statistical strength of composite materials by focusing carefully on the localized load redistribution in two-dimensional composites. A tapered load-sharing rule is considered which distributes the nominal load of a failed fiber among its four nearest neighbors, with the two adjacent fibers taking a greater proportion of the load. We consider three distinct probabilistic techniques of analysis and find that the basic probability structure for the distribution for composite strength turns out to be the same as for the idealized local load-sharing in earlier work; however, the median strength of the composite rises moderately due to the milder overloads on the fibers adjacent to breaks, while the presence of small overloads on more distant fibers has almost no effect on strength. Also, the variability in composite strength tends to decrease mildly, due to a slight increase in the critical fracture sequence size leading to catastrophic failure. Again, the Weibull distribution arises as a key model for the strength of unidirectional composites, and we give accurate approximations for its parameters.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01140156
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  • 6
    Electronic Resource
    Electronic Resource
    Bounds on the probability of failure of composite materials (1979)
    Springer
    International journal of fracture 15 (1979), S. 321-336 
    Details
    ISSN: 1573-2673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Résumé On obtient les bornes d'une fonction de distribution cumulative de la résistance des matériaux composites. L'analyse est basée sur un modèle probabiliste d'une série de bottes assurant la résistance d'un composite. Les bornes sont calculées au départ d'une probabilité que deux ou d'avantage de fibres adjancentes dans une botte puissent se romprent. On suppose que la résistance d'une fibre répond à une distribution de Weibull et que les fibres adjacentes à la fibre rompue sont sujettes à une surcharge correspondant à une règle spécifiée pour le partage des charges. Quand le composite augmente de dimension, la liaison atteint une distribution de Weibull. Le paramètre de forme de Weibull pour le composite est double de celui pour la fibre, mais le paramètre d'échelle est quelque peu inférieur. Les caractéristiques de la borne limite de Weibull sont établies comme étant consistantes avec l'observation expérimentale, encore que numériquement la borne se révèle tout à fait conservative.
    Notes: Abstract Bounds are obtained for the cumulative distribution function of the strength of composite materials. The analysis is based on the chain-of-bundles probability model for composite strength. The bounds are computed from probabilities for the chance failure of two or more adjacent fibers in a bundle. A Weibull distribution is assumed for fiber strength, and fibers adjacent to failed fibers are subjected to overloading according to a specified load sharing rule. As the composite grows in size, the bound approaches a Weibull distribution. The Weibull shape parameter for the composite is double that for the fiber, but the scale parameter is somewhat less. Features of the limiting Weibull bound are shown to be consistent with experimental observation, though numerically the bound is quite conservative.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00033058
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  • 7
    Electronic Resource
    Electronic Resource
    Probability distributions for the strength of composite materials I: two-level bounds (1981)
    Springer
    International journal of fracture 17 (1981), S. 347-372 
    Details
    ISSN: 1573-2673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Résumé On obtient une borne supérieure dans la distribution des probabilités relatives à la résistance des matériaux composites. L'analyse est basée sur un modèle de probabilités de chaine de bottes et on suppose une redistribution locale des charges dans le cas d'éléments fibreux non rompus dans chaque botte. Le définition de la frontière se base sur l'apparition de deux ou de plusieurs fibres rompues adjacentes dans une botte. Cette circonstance est nécessaire mais pas suffisante pour entraîner la rupture du matériau. Deux distributions sont supposées intervenir dans la résistance de la fibre: la distribution habituelle de Weibull d'une part et une version plus réaliste dont l'effet est essentiellement de déterminer un plafond à la résistance de la fibre. Dans le cas de matériaux composites de grande dimension, la limite supérieure devient une distribution de Weibull mais avec un paramètre de forme qui équivaut à deux fois celui des fibres individuelles. La limite est toujours conservative mais peut être extrêmement étroite lorsque la variation de la résistance de la fibre est faible. Dans des cas typiques, l'utilisation de la double distribution de Weibull pour une résistance de fibre se révèle ne pas affecter le comportement de la frontière d'une manière significative. Vu les travaux expérimentaux et de calculs additionnels qui sont rendus nécessaires, son utilisation en pratique ne se justifie pas dans de tels cas. Cependant, cette utilisation permet de jeter la lumière sur des processus de rupture des matériaux composites.
    Notes: Abstract An upper bound is obtained on the probability distribution for the strength of composite materials. The analysis is based on the chain-of-bundles probability model, and local load sharing is assumed for the nonfailed fiber elements in each bundle. The bound is based on the occurence of two or more adjacent broken fibers in a bundle. This event is necessary but not sufficient for the failure of the material. Two distributions are assumed for fiber strength: the usual Weibull distribution and a more realistic double version which has much the effect of putting a ceiling on fiber strength. For large composite materials, the upper bound becomes a Weibull distribution but with a shape parameter which is twice that for the individual fibers. The bound is always conservative, but it is extremely tight when the variability in fiber strength is low. In typical cases, the use of the double Weibull distribution for fiber strength is shown not to affect the behavior of the bound significantly. In view of the additional experimental and computational labor involved, its use in practice may not be justified in such cases. However, its use does shed light on fracture processes in composite materials.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00036188
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  • 8
    Electronic Resource
    Electronic Resource
    Experiments on shear deformation, debonding and local load transfer in a model graphite/glass/epoxy microcomposite (1991)
    Springer
    Journal of materials science 26 (1991), S. 6655-6672 
    Details
    ISSN: 1573-4803
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Recent statistical theories for the failure of polymer matrix composites depend heavily on details of the stress redistribution around fibre breaks. The magnitudes and length scales of fibre overloads as well as the extent of fibre/matrix debonding are key components in the development of longitudinal versus transverse crack propagation. While several theoretical studies have been conducted to investigate the roles of these mechanisms, little has been substantiated experimentally about the matrix constitutive behaviour and mechanisms of debonding at the length scale of a fibre break. In order to predict the growth of transverse and longitudinal cracks using the same micromechanical model, we microscopically observed the epoxy shear behaviour around a single fibre break in a three-fibre microcomposite tape. The planar specimens consisted of a single graphite fibre placed between two larger glass fibres in an epoxy matrix. The interfibre spacing was less than one fibre diameter (〈6 μm) in order to reflect the spacing between fibres found in typical composites. The epoxy constitutive behaviour was modelled using shear-lag theory where the epoxy had elastic, plastic, and debond zones. The criteria for debonding were modified from conventional shear-lag approaches to reflect the orientational hardening in the epoxy network structure. The epoxy, which is brittle in bulk, locally underwent a shear strain of about 60% prior to debonding from the fibre.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02402659
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  • 9
    Electronic Resource
    Electronic Resource
    Matrix effects on lifetime statistics for carbon fibre-epoxy microcomposites in creep rupture (1991)
    Springer
    Journal of materials science 26 (1991), S. 1955-1970 
    Details
    ISSN: 1573-4803
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Experimental results are presented for the strength and lifetime in creep rupture of carbon-epoxy microcomposites consisting of seven carbon fibres (Hercules IM6) within an epoxy matrix (Dow DER 332 epoxy with Texaco Jeffamine T403 curing agent) in an approximately hexagonal configuration. Special attention was paid to clamping, specimen alignment, shock isolation and accurate lifetime measurement. The results were analysed using a previously developed model, which involves a Weibull distribution for fibre strength and micromechanical stress redistribution around fibre breaks where the matrix creeps in shear following a power law. The model yields Weibull distributions for both microcomposite strength and lifetime where the respective shape and scale parameters depend on model parameters such as the Weibull shape parameter for fibre strength, the exponent for matrix creep, and the effective load transfer length and critical cluster size for failed fibres. Experimental results were consistent with the theory, though a fractographic study suggested time-dependent debonding along the fibre-matrix interface as being a key mechanism. Arguments were given to suggest, however, that the overall analytical forms would essentially be preserved. The results were compared with earlier results using a different epoxy system (Dow DER 331 epoxy with DEH 26 curing agent). Values for the matrix creep exponent and the effective load transfer length were about double and triple respectively the values from the earlier study, leading to slightly reduced strength, about one-half the variability in lifetime, but almost one-half the value of the exponent for the power law relating microcomposite lifetime to stress level.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00543630
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  • 10
    Electronic Resource
    Electronic Resource
    Load redistribution near non-aligned fibre breaks in a two-dimensional unidirectional composite using break-influence superposition (1993)
    Springer
    Journal of materials science 12 (1993), S. 1596-1599 
    Details
    ISSN: 1573-4811
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00627024
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