by Codrington, John

Plate thickness can have a profound effect on fatigue crack growth following theapplication of an overload cycle. A modified strip-yield model is presented for determining the effects of plate thickness based on the mechanism of plasticity-induced crack closure and first-order plate theory. This approach eliminates the need for any empirical or fitting parameters. Comparisons are made with experimental data for the case of a single tensile overload applied under otherwise constant. ΔK loading. The theoretical crack growthpredictions are found to be in good agreement with the experimental data.

DOI: 10.1007/s10704-009-9322-y
Online Date: 2/27/2009
Print publication date: 1/1/2009
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by Zemri, M.; Mazari, M.; Bouchouicha, B.; Benguediab, M.; Ranganathan, N.

The growth of crack is related to the existence of a plastic zone at the crack tip; whose formation and growth is accompanied by energy dissipation. The estimation of this energy is generally done by the so called global methods (hysterisis loops) or the micro-gages. In the present study, the micro-hardness measures in the plastic zone are used to evaluate the energy dissipated in the fracture process zone by plastic deformation. The obtained results on the aluminium alloy 7075 T7 and E460 steel are compared to those obtained by other methods.

DOI: 10.1007/s10704-009-9319-6
Online Date: 2/18/2009
Print publication date: 1/1/2009
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by Roux, Stéphane; Hild, François

Considering a semi-infinite planar crack propagating along a plane where the local toughness is a random field, the addressed problem is to compute the effective (or homogeneous and macroscopic) toughness. After a brief introduction to the two regimes—strong and weak pinning—that are expected depending on the system size, a self-consistent homogenization scheme is introduced. It is shown that this scheme allows one to predict not only the mean value but also the standard deviation and even the complete probability distribution function of the toughness. A discussion about the quality of this prediction as compared with direct numerical simulations is proposed.

DOI: 10.1007/s10704-008-9271-x
Online Date: 2/17/2009
Print publication date: 11/1/2008
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by Vellinga, W. P.; Bosch, M.; Geers, M. G. D.

A discrete lattice based model for the interaction of cracking, delamination and buckling of brittle elastic coatings is presented. The model is unique in its simultaneous incorporation of the coating and of disorder in the interface and material properties, leading to realistic 3D bending (and buckling) behavior. Results are compared to the literature. In the case of cracking, the key role of a stress transfer correlation length ξ in establishing a scaling behavior for the brittle fracture of thin films is shown to extend to all geometrical and material properties involved. In the scaling regime of crack density in uniaxial tension cracking and delamination are found to occur simultaneously. In uniaxial tension of films with an internal biaxial compressive stress, the predicted initiation of buckles above delaminated areas near crack edges in the model is remarkably similar to experimental results.

DOI: 10.1007/s10704-008-9266-7
Online Date: 2/17/2009
Print publication date: 11/1/2008
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by Rosti, Jari; Koivisto, Juha; Traversa, Paola; Illa, Xavier; Grasso, Jean-Robert; Alava, Mikko J.

The dynamics of a “peeling front” or an elastic line is studied under creep (constant load) conditions. Our experiments show in most cases an exponential dependence of the creep velocity on the inverse force (mass) applied. In particular, the dynamical correlations of the avalanche activity are discussed here. We compare various avalanche statistics to those of a line with non-local elasticity, and study various measures of the experimental avalanche-avalanche and temporal correlations such as the autocorrelation function of the released energy and aftershock activity. From all these we conclude, that internal avalanche dynamics seems to follow “line depinning”-like behavior, in rough agreement with the depinning model. Meanwhile, the correlations reveal subtle complications not implied by depinning theory. Moreover, we also show how these results can be understood from a geophysical point of view.

DOI: 10.1007/s10704-009-9312-0
Online Date: 2/17/2009
Print publication date: 11/1/2008
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by Carpinteri, Alberto; Puzzi, Simone

Since the pioneering paper by Mandelbrot (Nature, 308:721–722, 1984) on the fractal character of the fracture surfaces in metals, the fractal aspects in the deformation and failure of materials have been investigated by several Researchers (see the reviews by Bouchaud (J Phys Condens Matter, 9:4319–4344) and Carpinteri et al. (Appl Mech Rev, 59:283–305, 2006)) and the attempts to apply fractals to fracture have grown exponentially. Aim of this paper is 2-fold: on one hand, it summarizes in a detailed yet concise fashion the major results of the fractal approach to the scaling of mechanical properties in solid mechanics; on the other hand, it reports some recent results concerning the size effect in the failure of reinforced concrete (RC) beams. These recent findings clearly show that the picture of the size-scale effects is much more complex when interaction among different collapse mechanisms occurs. The consequences on the size-scale effects are discussed in detail.

DOI: 10.1007/s10704-008-9278-3
Online Date: 2/17/2009
Print publication date: 11/1/2008
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by Chiaia, Bernardino M.; Masoero, Enrico

The analogy between structural progressive collapse and Fracture Mechanics is consistent either for phenomenological, technological and theoretical aspects. In this paper a general energy criterion suitable for fracture in heterogeneous materials is applied to study the progressive collapse of simple structures with cohesive post peak behavior: elementary frames and fiber bundles. The analyses put into evidence some interesting scale effects induced by ductility and dynamics. In particular, a power law describing the decrease of the reduced dynamic critical load with the structural scale and a second order ductile-brittle transition, have been found. These results can be usefully applied in robustness oriented structural design. Moreover, the study of the influence of the extent of the starting damage in structures with different sizes suggests that, the elementary cells of complex framed structures can play a role similar to the microstructure of materials. In conclusion, a new approach to the problem of collapse into complex structures by means of the tools of Fracture Mechanics is proposed.

DOI: 10.1007/s10704-008-9287-2
Online Date: 2/17/2009
Print publication date: 11/1/2008
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by Pang, Sze-Dai; Bažant, Zdeněk P.; Le, Jia-Liang

It is argued that, in probabilistic estimates of quasibrittle structure strength, the strength threshold should be considered to be zero and the distribution to be transitional between Gaussian and Weibullian. The strength histograms recently measured on tough ceramics and other quasibrittle materials, which have been thought to imply a Weibull distribution with nonzero threshold, are shown to be fitted equally well or better by a new weakest-link model with a zero strength threshold and with a finite, rather than infinite, number of links in the chain, each link corresponding to one representative volume element (RVE) of a non-negligible size. The new model agrees with the measured mean size effect curves. It is justified by energy release rate dependence of the activation energy barriers for random crack length jumps through the atomic lattice, which shows that the tail of the failure probability distribution should be a power law with zero threshold. The scales from nano to macro are bridged by a hierarchical model with parallel and series couplings. This scale bridging indicates that the power-law tail with zero threshold is indestructible while its exponent gets increased on each passage to a higher scales. On the structural scale, the strength distribution except for its far left power-law tail, varies from Gaussian to Weibullian as the structure size increases. For the mean structural strength, the theory predicts a size effect which approaches the Weibull power law asymptotically for large sizes but deviates from it at small sizes. This deviation is the easiest way to calibrate the theory experimentally. The structure size is measured in terms of the number of RVEs. This number must be convoluted by an integral over the dimensionless stress field, which depends on structure geometry. The theory applies to the broad class of structure geometries for which failure occurs at macro-crack initiation from one RVE, but not to structure geometries for which stability is lost only after large macro-crack growth. Based on tolerable structural failure probability of <10⁻⁶, the change from nonzero to zero threshold may often require a major correction in safety factors.

DOI: 10.1007/s10704-009-9317-8
Online Date: 2/17/2009
Print publication date: 11/1/2008
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by Wittel, F. K.; Carmona, H. A.; Kun, F.; Herrmann, H. J.

The brittle fragmentation of spheres is studied numerically by a 3D Discrete Element Model. Large scale computer simulations are performed with models that consist of agglomerates of many spherical particles, interconnected by beam-truss elements. We focus on a detailed description of the fragmentation process and study several fragmentation mechanisms involved. The evolution of meridional cracks is studied in detail. These cracks are found to initiate in the inside of the specimen with quasi-periodic angular distribution and give a broad peak in the fragment mass distribution for large fragments that can be fitted by a two-parameter Weibull distribution. The results prove to be independent of the degree of disorder in the model, but mean fragment sizes scale with velocity. Our results reproduce many experimental observations of fragment shapes, impact energy dependence or mass distribution, and significantly improve the understanding of the fragmentation process for impact fracture since we have full access to the failure conditions and evolution.

DOI: 10.1007/s10704-008-9267-6
Online Date: 2/17/2009
Print publication date: 11/1/2008
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by Bolander, John E.; Choi, Sokhwan; Duddukuri, Sri Ramya

Short-fiber reinforcement is commonly used to improve various properties of cement-based materials, including their resistance to shrinkage cracking, post-cracking strength, and toughness. The spatial distribution of fibers within a structural component exhibits local variations that depend on many factors, including the methods of production. Local measures of fiber volume fraction can be much lower than the global average and such regions can act as flaws within the composite material. In addition, fiber orientation is restricted by any near surfaces of the structural component. Such non-uniformities of the fiber distribution can significantly affect fracture behavior and complicate the interpretation of fracture test results. This paper concerns the computational modeling of fiber- reinforced cement composites (FRCC), with attention to the effects of non-uniform fiber distributions. The simulations utilize lattice models of the matrix phase of the composite, based on the Voronoi tessellation of irregularly positioned nodes within the structural domain. A crack band approach provides energy-conserving, mesh-insensitive descriptions of fracture through the irregular lattice. Each fiber is explicitly modeled within the lattice framework. The fiber distributions are synthetically constructed within the structural domain, although experimentally determined fiber positions could be used. Models of simple tensile tests demonstrate a dependence of post-cracking strength and toughness on the spatial distributions of the fibers.

DOI: 10.1007/s10704-008-9269-4
Online Date: 2/17/2009
Print publication date: 11/1/2008
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