by Radi, Enrico; Loret, Benjamin

A crack is steadily running in an elastic isotropic fluid-saturated porous solid at an intersonic constant speed c. The crack tip speeds of interest are bounded below by the slower between the slow longitudinal wave-speed and the shear wave-speed, and above by the fast longitudinal wave-speed. Biot’s theory of poroelasticity with inertia forces governs the motion of the mixture. The poroelastic moduli depend on the porosity, and the complete range of porosities n ∈ [0, 1] is investigated. Solids are obtained as the limit case n =  0, and the continuity of the energy release rate as the porosity vanishes is addressed. Three characteristic regions in the plane (n, c) are delineated, depending on the relative order of the body wave-speeds. Mode II loading conditions are considered, with a permeable crack surface. Cracks with and without process zones are envisaged. In each region, the analytical solution to a Riemann–Hilbert problem provides the stress, pore pressure and velocity fields near the tip of the crack. For subsonic propagation, the asymptotic crack tip fields are known to be continuous in the body [Loret and Radi (2001) J Mech Phys Solids 49(5):995–1020]. In contrast, for intersonic crack propagation without a process zone, the asymptotic stress and pore pressure might display a discontinuity across two or four symmetric rays emanating from the moving crack tip. Under Mode II loading condition, the singularity exponent for energetically admissible tip speeds turns out to be weaker than 1/2, except at a special point and along special curves of the (n, c)-plane. The introduction of a finite length process zone is required so that 1. the energy release rate at the crack tip is strictly positive and finite; 2. the relative sliding of the crack surfaces has the same direction as the applied loading. The presence of the process zone is shown to wipe out possible first order discontinuities.

DOI: 10.1007/s10704-007-9169-z
Online Date: 12/21/2007
Print publication date: 9/1/2007
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by Ferro, Giuseppe; Carpinteri, Alberto; Ventura, Giulio

The problem of the assessment of minimum reinforcement in concrete members has been examined both theoretically and experimentally by the bridged crack model. The model has been demonstrated to be an efficient numerical tool for investigating the behavior of structural elements in bending, and allowed to show the minimum reinforcement percentage depends on the structural element size, and decreases with increasing beam depths. In the model, Linear Elastic Fracture Mechanics concepts are used to determine the equilibrium and the compatibility equations of a beam segment subjected to bending in presence of a mode I crack. Recently, the model has been extended to include the presence of closing stresses as a function of the crack opening in addition to steel reinforcement closing traction. This allows to characterize the mechanical behavior of fiber reinforced structural elements. A criterion for accounting for crushing in compression has been introduced as well, to bound from below (minimum reinforcement) and from above (maximum reinforcement) a region of stable and ductile mechanical behavior as a function of the mechanical properties as well as of the size of the structural element. Some experimental results are commented under this light.

DOI: 10.1007/s10704-007-9162-6
Online Date: 12/18/2007
Print publication date: 8/1/2007
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by Profant, T.; Ševeček, O.; Kotoul, M.; Vysloužil, T.

The problem of an edge-bridged crack terminating perpendicular to a bimaterial interface in a half-space is analyzed for a general case of elastic anisotropic bimaterials and specialized for the case of orthotropic bimaterials. The edge crack lies in the surface layer of thickness h bonded to semi-infinite substrate. It is assumed that long fibres bridge the crack. Bridging model follows from the assumption of “large” slip lengths adjacent to the crack faces and neglect of initial stresses. The crack is modelled by means of continuous distribution of dislocations, which is assumed to be singular at the crack tip. With respect to the bridged crack problems in finite dissimilar bodies, the reciprocal theorem (Ψ-integral) is demonstrated as to compute, in the present context, the generalized stress intensity factor through the remote stress and displacement field for a particular specimen geometry and boundary conditions using FEM. Also the application of the configurational force mechanics is discussed within the context of the investigated problem.

DOI: 10.1007/s10704-007-9164-4
Online Date: 12/12/2007
Print publication date: 9/1/2007
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by Kachanov, Mark

DOI: 10.1007/s10704-007-9170-6
Online Date: 12/12/2007
Print publication date: 8/1/2007
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by Lipperman, Fabian; Ryvkin, Michael; Fuchs, Moshe B.

The brittle fracture behavior of periodic 2D cellular material weakened by a system of non-interacting cracks is investigated. The material is represented as a lattice consisting of rigidly connected Euler beams which can fail when the skin stress approaches some limiting value. The conventional Mode I and Mode II fracture toughness is calculated first and its dependence upon the relative density is examined. To this end the problem of a sufficiently long finite length crack in an infinite lattice produced by several broken beams is considered. It is solved analytically by means of the discrete Fourier transform reducing the initial problem for unbounded domain to the analysis of a finite repetitive module in the transform space. Four different layouts are considered: kagome, triangular, square and hexagon honeycombs. The results are obtained for different crack types dictated by the microstructure symmetry of the specific material. The obtained results allowed to define the directional fracture toughness characterizing the strength of a material with many cracks for the given tensile loading direction. This quantity is presented in the form of polar diagrams. For all considered layouts the diagrams are found to be close to circles thus emphasizing quasi-isotropic fracture behavior. The deviation from isotropy in the case of a square honeycomb is essentially less than for the corresponding published axial stiffness polar diagram.

DOI: 10.1007/s10704-007-9171-5
Online Date: 12/11/2007
Print publication date: 8/1/2007
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by Wu, Chien H.

The title problem is considered for an elastic circular tube of inner radius A and outer radius B. The tube is made of a single component solid with vacancies as its second component. The mole fraction of the massive species is denoted by
¹, while that of the vacancies by
⁰ = 1 –
¹. The tube is completely surrounded by vacuum, serving as a reservoir of vacancies. One of the standard elasticity boundary conditions is applied at time t = 0, when the composition is uniform. The ensuing coupled deformation and diffusion leads to the evolving of A(t), B(t) and
¹(R, t) as functions of time. Since the single component solid is not in contact with its vapor or liquid, the diffusion boundary condition is always tied to the elasticity problem through a surface condition that involves the normal configurational traction. Our chemical potential has an energy density term that serves as a source in the interior and the boundary conditions for the diffusion problem are such that the time rates of boundary accretion Ȧ(t) and Ḃ(t) must simultaneously satisfy two dissipative inequalities, one governed by the gradient of the internal chemical potential and the other by the normal configurational traction.

DOI: 10.1007/s10704-007-9168-0
Online Date: 12/7/2007
Print publication date: 9/1/2007
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by Nagai, Masaki; Ikeda, Toru; Miyazaki, Noriyuki

New numerical methods were presented for stress intensity factor analyses of two-dimensional interfacial crack between dissimilar anisotropic materials subjected to thermal stress. The virtual crack extension method and the thermal M-integral method for a crack along the interface between two different materials were applied to the thermoelastic interfacial crack in anisotropic bimaterials. The moving least-squares approximation was used to calculate the value of the thermal M-integral. The thermal M-integral in conjunction with the moving least-squares approximation can calculate the stress intensity factors from only nodal displacements obtained by the finite element analysis. The stress intensity factors analyses of double edge cracks in jointed dissimilar isotropic semi-infinite plates subjected to thermal load were demonstrated. Excellent agreement was achieved between the numerical results obtained by the present methods and the exact solution. In addition, the stress intensity factors of double edge cracks in jointed dissimilar anisotropic semi-infinite plates subjected to thermal loads were analyzed. Their results appear reasonable.

DOI: 10.1007/s10704-007-9163-5
Online Date: 12/7/2007
Print publication date: 8/1/2007
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by Steigemann, Martin; Fulland, Markus

The accurate computation of stress intensity factors (SIFs) plays a decisive role in the determination of crack paths. The calculation of SIFs with the help of singular weight functions leads to pure Neumann problem for anisotropic elasticity in a plane domain with a crack. Here a method is presented to overcome the specific numerical difficulties which arises while calculating these solutions with Finite Element methods. The accuracy and advantage of this method are shown by a numerical example, the calculation of SIFs of a compact tension specimen.

DOI: 10.1007/s10704-007-9167-1
Online Date: 12/7/2007
Print publication date: 8/1/2007
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