by Prasad, P.B.N.; Simha, K.R.Y.

The limiting situation of a pair of approaching circular arc crack tips in a homogeneous medium is examined to draw analogies with circular disc problems. As the crack tips approach each other, the narrow material ligament bridging the crack tips controls the stresses, stress intensity factors and energy release rates. In particular, this ligament sets up the length scale for singularity analysis for a given radius of the arc crack. Following a detailed analytical examination of approaching crack tips, a photoelastic visualisation of the stress field is presented. Experimental isochromatics are also compared with theoretical predictions for some specific cases. Finally, based on the ideas developed in this paper, existing notions on interacting cracks and cavities treated in the literature are reinterpreted.

DOI: 10.1023/B:FRAC.0000021085.27194.22
Print publication date: 1/1/2004
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by Itou, S.

A teflon tape (0.07 mm thickness) is placed at the center of an edge of an epoxy plate. The plate is used to fabricate a mold, and epoxy resin is cast in the mold so as to produce a cracked epoxy plate. A tensile test is conducted so as to determine the fracture toughness value of the epoxy plate. Next, a mold is fabricated from an aluminum plate having a teflon tape placed along its edge, and epoxy resin is cast in the mold so as to produce an epoxy-aluminum composite weakened by an interface crack. Tensile testing reveals that the crack always propagates into the epoxy plate at an angle measured from the interface. The stress intensity factor for an interface crack is defined in a manner similar to that for a crack in a homogeneous material, and is obtained for several values of a/h, 2a being the crack length and 2h being the width of the epoxy-aluminum composite.

DOI: 10.1023/B:FRAC.0000021081.21287.48
Print publication date: 1/1/2004
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by Sobczyk, K.; Trębicki, J.; Movchan, A.B.

This paper is devoted to the problem of interaction of a semi-infinite crack (propagating in elastic material) with a random array of small defects (e.g. inclusions, voids). This interaction manifests itself in changes of the crack orientation and, overall in randomly varying curvilinear crack trajectories.Making use of the asymptotic results proposed in (Movchan, 1991, 1995) the procedure for configurational averaging is presented which yields the mean crack path and the standard deviation from the mean. The general formulae for the mean crack path can serve as a basis for effective quantitative analysis for specific situations of practical interest. The illustrative examples elaborated in the paper show dependence of the shape of crack trajectory on the probabilistic characteristics of random locations of inclusions and on their elastic parameters. The analysis performed in the paper can be directly used in prediction of failure mechanisms of brittle materials containing small randomly distributed inclusions/voids.

DOI: 10.1023/B:FRAC.0000021077.36603.19
Print publication date: 1/1/2004
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by Forquin, Pascal; Rota, Laurent; Charles, Yann; Hild, François

An experimental procedure is developed to determine the scatter of the macroscopic toughness of brittle materials. First, samples are precracked to obtain a sharp precrack. The toughness is then determined by using a standard three-point flexural test. Digital image correlation is used to analyze displacement fields of cracked samples. Based upon the resolution and the spatial resolution of the measurement technique, a detection criterion is proposed and validated. It allows for an accurate estimate of the crack tip location so that the presence of a crack and its size at arrest can be monitored. As an example, the toughness distribution of 18 samples made of silicon carbide is evaluated. By using a simple macro-micro transition, an analysis of the scatter in toughness is related to that in strength for the material with no macrocracks.

DOI: 10.1023/B:FRAC.0000021076.76987.62
Print publication date: 1/1/2004
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by Banks-Sills, Leslie; Dolev, Orly

In this investigation, the conservative M-integral is extended to treat thermal-elastic, mixed mode problems. With it, stress intensity factors are obtained for cracks in homogeneous, isotropic materials, as well as isotropic and anisotropic, bimaterials. Excellent agreement is found between results determined in this study and those found in the literature. In addition, new results are obtained for interface cracks for a wide range of material properties and for a delamination in a composite material.

DOI: 10.1023/B:FRAC.0000021065.46630.4d
Print publication date: 1/1/2004
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by Suiker, Akke S.J.; Fleck, Norman A.

Steady-state tunneling and plane-strain delamination of an H-shape crack are examined for elastic, isotropic multi-layers. Both tunneling and delamination are analysed by employing linear elastic fracture mechanics within a 2D finite element framework. Failure maps are produced to reveal the sensitivity of cracking path to the relative toughness of layer and interface, and to the stiffness mismatch of layers. Closed-form expressions are derived for the critical stress level for steady-state plane-strain delamination. By means of a comparison with experimental results taken from the literature, it is demonstrated that these expressions serve as useful design criteria for elastic multilayers.

DOI: 10.1023/B:FRAC.0000021064.52949.e2
Print publication date: 1/1/2004
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by Colombi, Pierluigi

Stress intensity parameter and crack face displacements for compact tension (CT) and central cracked (CCT) steel specimens reinforced by composite patches are evaluated by a suitable analytical model based on fracture mechanics. Results at various crack length for the two analysed specimens configuration are validated through finite element analyses. The proposed analytical technique could then be used to evaluate reliable compliance information on CT and CCT steel specimens reinforced by composite patches.

DOI: 10.1023/B:FRAC.0000021043.74064.1a
Print publication date: 1/1/2004
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by Wang, Yue-Sheng; Huang, Gan-Yun; Gross, Dietmar

A new multi-layered model is developed for a functionally graded interfacial zone between two dissimilar elastic solids based on the fact that an arbitrary curve can be approached by a continuous but piecewise linear curve. The interfacial zone with both Young’s modulus and Poisson’s ratio varying continuously in an arbitrary manner is divided into multiple layers with the material properties varying linearly in each sub-layer and continuous at the interfaces between sub-layers. With this new model, we analyze the problem of a Griffith crack in the interfacial zone under plane stress-state deformation. The transfer matrix method and Fourier integral transform technique are used to reduce the mixed boundary-value problem to a set of Cauchy singular integral equations. The stress intensity factors are calculated. The paper compares the new model to other existing models and discusses its advantages.

DOI: 10.1023/B:FRAC.0000021042.28804.f1
Print publication date: 1/1/2004
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by Mishnaevsky Jr, L.; Weber, U.; Schmauder, S.

This paper presents a systematical computational study of the effect of microstructures of materials reinforced with brittle hard particles on their fracture behavior and toughness. Crack growth in particle-reinforced materials (here, in high speed steels) with various artificially designed arrangements of brittle inclusions is simulated using microstructure-based finite element meshes and an element elimination method. The following types of brittle inclusions arrangements are considered: (simple microstructures) net-like continuous, band-like, random with different inclusion sizes, and (complex microstructures) layered and clustered arrangements, with different inclusion sizes and orientations. Crack paths, force-displacement curves, fracture toughness and fractal dimension of fracture surfaces are determined numerically for each microstructure of the materials. It is demonstrated that extensive crack deviations from the initial cracking directions and an increase in the fracture toughness can most efficiently be achieved by using complex microstructures, such as alternated layers of fine and coarse inclusions.

DOI: 10.1023/B:FRAC.0000021031.67717.9f
Print publication date: 1/1/2004
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by Kudish, Ilya I.; Burris, Kenneth W.

A new mathematical model for lubricated elastic solids weakened by cracks is proposed. Surface and subsurface cracks are taken into account, and the interaction of lubricant with elastic solids within cavities of surface cracks is regarded as the most interesting aspect of the problem. The boundary conditions characterizing the behavior of lubricant within crack cavities such as pressure rise in crack cavities fully filled with lubricant as well as other boundary and additional conditions are derived. The problem is reduced to a system of integro-differential equations with nonlinear boundary conditions in the form of alternating equations and inequalities. A new iterative numerical method is developed for solution of the proposed problem. The method guarantees conservation of lubricant volumes trapped within closed crack cavities and allows for all three functions (normal and tangential displacement jumps and normal stress applied to crack faces) characterizing the problem solution to be determined simultaneously. Examples of numerical results for surface and subsurface cracks are presented and numerical and asymptotic results for small subsurface cracks are compared to each other. The numerical analysis indicates that depending on a surface crack orientation its normal stress intensity factor may be two or more orders of magnitude higher than the one for a similar subsurface one.

DOI: 10.1023/B:FRAC.0000021022.48417.a6
Print publication date: 1/1/2004
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