by Yong, Huadong; Zhou, You-He

This paper presents an analysis of the static problem of model III crack of a functionally graded coating-substrate system with an internal crack perpendicular to the interface under antiplane shear loading when the coating layer and substrate have finite thickness. After the Fourier transform method is employed, the expressions of the displacement components can be obtained. Integral transforms are employed to reduce the problem to a singular integral equation that can be solved numerically. The influences of the nonhomogeneity constant, relative crack length and thickness ratio are quantitatively studied.

DOI: 10.1007/s10704-006-9007-8
Online Date: 10/31/2006
Print publication date: 10/1/2006
View article on SpringerLink

by Macleod, Niall; Bain, Maureen M.; Hancock, John W.

The mechanics and mechanisms of failure of hens’ eggs have been examined experimentally under contact loading conditions relevant to industrial conditions by testing eggs of known provenance in compression between stiff platens. Deformation was modelled computationally as a Hertzian contact problem between a thin walled elastic shell and a rigid plate. Contact damage was determined by scanning electron microscopy and by optical examination of transverse sections through the shell. Small stable micro-cracks were found to initiate in the contact area before structural failure, which was characterised by the propagation of one or more macroscopic cracks. Structural failure does not correspond to crack initiation, but crack propagation. Stable micro-cracks were not detectable by routine visual inspection or acoustic resonance, and combined with inconsistent cuticle coverage these could provide a pathway for pathogens to enter the egg contents and thus compromise egg safety.

DOI: 10.1007/s10704-006-9018-5
Online Date: 10/31/2006
Print publication date: 11/1/2006
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by Carpinteri, Alberto; Paggi, Marco; Pugno, Nicola

The problem of brittle crack propagation and fatigue crack growth in functionally graded materials (FGMs) is addressed. The proposed analytical approach can be used to estimate the variation of the stress-intensity factor as a function of the crack length in FGMs. Furthermore, according to the Paris’ law, the fatigue life and the crack-tip velocity of crack propagation can be predicted in the case of fatigue crack growth. A comparison with numerical results obtained according to the Finite Element method will show the effectiveness of the proposed approach. Detailed examples are provided in the case of three-point bending beam problems with either a FGM interlayer, or a FGM external coating. A comparison is presented between two types of grading in the elastic modulus: a continuous linear variation in the FGM layer and a discrete approximation with a multi-layered beam and a constant Young’s modulus in each layer.

DOI: 10.1007/s10704-006-9012-y
Online Date: 10/25/2006
Print publication date: 10/1/2006
View article on SpringerLink

by Tovo, R.; Livieri, P.; Benvenuti, E.

This paper proposes a new criterion for the prediction of static failure load of structural components made of linear brittle-elastic material affected by high stress concentrations. The static failure criterion is based on the definition of a non-local equivalent stress scalar. The approach starts with the definition of a spatial weighted average of a local stress scalar, called non-local equivalent stress. The non-local equivalent stress is then approximated through a spatial gradient expansion containing the Laplacian of the local equivalent stress multiplied by a non-local length. Thus the non-local equivalent stress is expressed as an implicit differential equation. We develop an analytical solution in the case of a one-dimensional stress state at a crack tip, assuming Neumann’s boundary conditions. Two-dimensional V-notched components are then considered and a numerical solution is found via a standard finite element procedure. We also relate the non-local length of the model to the ultimate tensile stress and fracture toughness of the material. Finally, we consider experimentally measured failure loads reported in the literature for brittle-elastic PMMA specimens. The failure loads numerically calculated for mode I and mixed-mode loading are compared with experimental data. For this purpose, different definitions of the local equivalent stress are taken into account. The accuracies of the numerically estimated failure loads are satisfactory for the considered loading modes.

DOI: 10.1007/s10704-006-9011-z
Online Date: 10/25/2006
Print publication date: 10/1/2006
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by Högberg, J. L.

A traction-separation relation to model the fracture process is presented. The cohesive law captures the linear elastic and softening behaviour prior to fracture. It also allows for different fracture parameters, such as fracture energy, strength and critical separation in different mode mixities. Thus, the fracture process in mode I (peel), in mode II (shear) or in mixed mode (a combination of peel and shear) can be modelled without the limitation of a common fracture energy in peel and shear. Examples are given in form of FE- implementations of the normalised cohesive law, namely for the Unsymmetrical Double Cantilever Beam (UDCB) specimen and the Mixed-mode double Cantilever Beam (MCB) specimen. Both specimens are adhesively bonded and loaded in mixed-mode.

DOI: 10.1007/s10704-006-9014-9
Online Date: 10/25/2006
Print publication date: 10/1/2006
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by Plaisted, Thomas A.; Amirkhizi, Alireza V.; Nemat-Nasser, Sia

The fracture strength of PMMA is studied using columns with rectangular cross- section that contain a central hole and are subjected to axial compression. Samples with geometries such that the width is 2, 3, 4, and 5 times the diameter of the hole are investigated. Cracks are initiated by introducing sharp notches in the axial direction at the crowns of the hole in each sample. The sample is then subjected to axial compression such that the axial cracks grow in a stable manner until a critical compression is attained, after which the cracks extend rapidly in the sample but do not reach its ends. To predict the experimental results, we have first sought to use several published models, but discovered that none would produce results in accord with our data, as they seem not to address the essential features of our beam-column experiments. We have then developed a simple model that consists of a suitably modified version of an elasticity solution based on a short-crack in an infinite plate, combined with a beam-column solution for a long-crack. This model yields results in good accord with our data and also gives reasonable values for the fracture toughness of the material. A comparative discussion of several published models is presented at the end of the paper, pointing out that linear elasticity is not an appropriate tool for solving the present beam-column problem.

DOI: 10.1007/s10704-006-9006-9
Online Date: 10/25/2006
Print publication date: 10/1/2006
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by Akarapu, S.; Zbib, Hussein M.

The classical linear elastic fracture mechanics is not valid near the crack tip because of the unrealistic singular stress at the tip. The study of the physical nature of the deformation around the crack tip reveals the dominance of long-range atomic interactive forces. Unlike the classical theory which incorporates only short range forces, a higher-order continuum theory which could predict the effect of long range interactions at a macro scale would be appropriate to understand the deformation around the crack tip. A simplified theory of gradient elasticity proposed by Aifantis is one such grade-2 theory. This theory is used in the present work to numerically analyze plane cracks in strain-gradient elastic materials. Towards this end, a 36 DOF C¹ finite element is used to discretize the displacement field. The results show that the crack tip singularity still persists but with a different nature which is physically more reasonable. A smooth closure of the structure of the crack tip is also achieved.

DOI: 10.1007/s10704-006-9004-y
Online Date: 10/25/2006
Print publication date: 10/1/2006
View article on SpringerLink

by Hofmann, M.; Bahr, H. A.; Linse, T.; Bahr, U.; Balke, H.; Weiss, H. J.

Tunneling cracks driven by drying in a ceramic precursor confined between two glass plates represent a simple type of three-dimensional (3D) crack pattern. They arrange themselves via mutual unloading which causes some cracks to stop whereby the remaining ones get the right spacing for further propagation. By extending a 2D-model of self-driven propagation of crack arrays, a fracture mechanical bifurcation analysis for 3D-crack patterns based on calculating the post-critical contour of the alternating bifurcation mode has been developed. Shrinkage due to drying is replaced here by a simplified thermo-mechanical model based on an effective heat flow whose related temperature field and thermal stresses drive crack propagation. By means of the finite element method, the propagation velocity and the minimum spacing between the steady-state parallel tunnelling cracks are determined. Comparison of theory and experiment suggests that propagation may be non-stationary in these experiments. The observed relation between crack spacing and layer thickness, p ~ e
^2/3, follows from a scaling analysis.

DOI: 10.1007/s10704-006-9001-1
Online Date: 10/25/2006
Print publication date: 10/1/2006
View article on SpringerLink

Welcome to the official blog of the International Journal of Fracture! You may remember the days when we had to wait for the printed copy of journals to show up physically at a nearby library; now archival information comes to us through a cable (and increasingly on wireless) connection. Old volumes of journals are getting converted to digital form for easy retrieval; for example, all back volumes of the International Journal of Fracture are now available in electronic form. Now we can browse the treasures of the archive with ease from practically anywhere. However, the information flow is unidirectional and somewhat static since we are just at the beginning of the digital information age. We have merely altered the mode of delivery, not the delivery itself. This blog is part of the process of evolution in archival journal publishing that aims to take the next steps in exploiting the digital platform to impact the content that is delivered.

I will moderate this blog in the early days in order to monitor the flow, but I expect that it will truly evolve into an open forum for discussions of problems related to structural integrity. The initial aims of the blog are as follows:

1. Each article published in the journal will have its own unique, linked blog entry created at the time of publication.
1. Authors will have an opportunity to include additional information regarding the article in the blog – background information, algorithms, details of methods and materials, movies and animations, images and data for use by others, etc can be added to the blog.
2. Errata may be included in the blog; since it is linked to the journal article, it is easy to track such entries.
3. Readers may compliment or critique the article, pose questions to the authors and thereby engage the authors in a discussion about the article. These will be monitored by the Blog Moderator; the discussion must be constructive.
2. The blog will serve as a forum for discussion of emerging issues of interest to the fracture community. These might be prompted by musings from the moderator or from questions posted by bloggers; discussions of interesting articles, books, conferences not necessarily connected to the journal, but of interest to the fracture community are encouraged.
3. New sections/classifications of specific subtopics in fracture may be organized depending on the level of activity; for example, discussions of pedagogical aspects of the discipline may be organized as a sub-topic within the blog.
4. The blog will have a section devoted to announcements; postings on upcoming conferences, new books etc.

The evolution of this medium is really under the control of the community and I encourage you to explore this opportunity to participate in this interesting experiment. I am open to suggestions from bloggers on what else we may accomplish with the blog.

The blog is now open to the public; the journal’s homepage can be found on Springer.com, and the full-text online version can be found on SpringerLink.com.

by Lan, Weiming; Deng, Xiaomin; Sutton, Michael A.; Cheng, Ching-Shan

Slant fracture is widely observed during crack growth in thin sheet specimens made of ductile materials, providing a good case for investigating three-dimensional criteria for mixed-mode ductile fracture. To gain an understanding of slant fracture events and to provide insight for establishing a slant fracture criterion, stable tearing fracture experiments on combined tension-torsion (nominal mixed-mode I/III) specimens and nominal Mode I Arcan specimens made of Al 2024-T3 are analyzed using the finite element method under three-dimensional conditions. Two types of finite element models are considered for the study of slant fracture: (a) combined tension-torsion specimens containing stationary, flat and slant cracks subject to loads corresponding to the onset of crack growth, and (b) stable tearing crack growth with slanting in a nominal Mode I Arcan specimen. Analysis results reveal that there exists a strong correlation between certain features of the crack-front effective plastic strain field and the orientation of the slant fracture surface. In particular, it is observed that (a) at the onset of crack growth in the combined tension-torsion experiments, the angular position of the maximum effective plastic strain around the crack front serves as a good indicator for the slant fracture surface orientation during subsequent crack growth; and (b) during stable tearing crack growth in the Mode I Arcan specimen, which experiences a flat-to-slant fracture surface transition, the crack growth path on each section plane through the thickness of the specimen coincides with the angular position of the maximum effective plastic strain around the crack front.

DOI: 10.1007/s10704-006-9008-7
Online Date: 10/20/2006
Print publication date: 10/1/2006
View article on SpringerLink