by Ganne, P.; Vervoort, A.

The importance of the stress path on pre-peak (micro-) damage in rock material is addressed. Cracks, induced by macro-compressive stresses and macro-tensile stress fields are studied systematically on thin slices of crinoidal limestone samples. The effect of the sequence of macro-compressive and tensile stress fields, on the presence of the cracks is quantified. Firstly, samples damaged by compressive stresses only or tensile stresses only are studied. Hereafter, as a first case, a sample damaged firstly by compressive stresses and secondly by tensile stresses is studied. As a second case, samples damaged firstly by a tensile stress field, followed by compressive stresses are studied and compared to the first case. In the discussion, also the recorded cumulative acoustic emission energy and the clustering of acoustic emission events are used. The differences of both cases are highlighted: in the second case, more damage is observed than in the first case.

DOI: 10.1007/s10704-007-9081-6
Online Date: 5/22/2007
Print publication date: 3/1/2007
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by Shi, Weichen

By using direct calculation of the gradient and divergence of the Lagrangian of any quasicrystal, its dynamic conservation integrals are derived. These conservation integrals can be reduced to J- and M-integrals for plane and antiplane problems, which are calculated around the tip of an interfacial crack of antiplane sliding mode between a crystal and a quasicrystal.

DOI: 10.1007/s10704-007-9077-2
Online Date: 5/22/2007
Print publication date: 3/1/2007
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by Roy, Sébastien; Darque-Ceretti, Evelyne; Felder, Eric; Monchoix, Hervé

Cross-sectional nanoindentation (CSN) is a recent method for adhesion measurement of nanoscale thin films in ultra-large scale integrated circuits. In the case of ductile thin films, plastic deformation during the test and complex geometry of delaminated areas require 3D finite element modeling (FEM) for adhesion energy calculation. In this paper the adhesion of various copper (Cu) films on blanket and patterned structures is studied by CSN test. The experimental procedure and qualitative analysis of the test are presented in detail. Crack propagation is studied on blanket and patterned substrates. The dimensions of delaminated blisters are measured by scanning electron microscope (SEM) for each sample. Results show that a geometrical ratio can be used to give a quick and qualitative measurement of adhesion. A new 3D FEM model is then proposed to assess quantitative analysis of CSN test. The deformation energy of Cu blister is calculated for each sample. The mechanical properties of the Cu films required for numerical calculations are measured by instrumented indentation. The influence on these measurements of the evolution of the Cu deformation with penetration depth is discussed in detail with the aid of 2D numerical simulation. The results of numerical modeling correlate well with qualitative evaluation of adhesion.

DOI: 10.1007/s10704-007-9072-7
Online Date: 5/11/2007
Print publication date: 3/1/2007
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by Qasim, Tarek

This study investigates the influences of off-axis loading and of margin geometry on “margins failure” observed in loaded curved bi-layer structures, away from the contact loading point. Specimens of hemispherical bi-layer model consist of glass shells with varying margins geometry, and filled with epoxy resin substrate are prepared. These specimens are loaded with compliant PTFE Teflon cylindrical indenters, with a modulus of several orders of magnitude lower than the indented materials. Load is applied normally; axisymmetric to the dome apex, and at 45° from the axis of symmetry. In this fashion, the effect of off-axis loading and the influence of margin geometry on “margins failure” are studied. The onset of fracture is observed in situ using a video camera system. Finite element analysis is applied to determine basic stress distribution within the dome structures, and to confirm a shift in maximum tensile stress from the near-contact area to the dome sides with the use of more compliant indenters. Critical loads to initiate radial cracks and damage evolution are presented, and interpreted with the results of FEA.

DOI: 10.1007/s10704-007-9073-6
Online Date: 5/11/2007
Print publication date: 3/1/2007
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by Prokopiev, Oleg; Sevostianov, Igor

We consider connections between microstructure and elastic properties of porous/microcracked materials on the example of Fontainebleau sandstone. The microstructural information (average shapes of pores) required for adequate modeling of the isotropic elastic properties is identified. It is shown that, if this information is utilized, the usual effective media schemes provide satisfactory predictions of the effective elastic properties.

DOI: 10.1007/s10704-007-9069-2
Online Date: 5/9/2007
Print publication date: 2/1/2007
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by Anvari, Majid; Liu, Jun; Thaulow, Christian

The application of rate-dependent cohesive elements is validated in simulation of ductile fracture in aluminum round bars under dynamic loading conditions. Smooth and notched round bars made of AA6060-T6 are tested and simulated under quasi-static and dynamic loadings. The smooth round bar is modeled using finite elements that obey Gurson–Tvergaard–Needleman (GTN) formulation as the constitutive equation. Comparing with experimental results, corresponding GTN parameters and rate-dependent plasticity of the alloy are obtained. A single strain rate-dependent GTN element with the obtained parameters is examined under different values of stress triaxiality and loading rates. The resulting stress-elongation curves represent the traction separation law (TSL) for cohesive elements and the variations of the maximum traction and the energy absorbed are investigated.The notched round bars are modeled by axisymmetric continuum and cohesive elements. The undamaged bulk material is elastic-visco plastic and the cohesive elements obey the TSL defined from the single element calculations. The experiments are simulated by these models in which the cohesive elements are rate sensitive and automatically obtain the values of the total strain rate from their adjacent continuum elements to update the values of the cohesive strength during the analysis. The results of the analysis, including maximum load, time of failure and diameter reduction are validated with the experimental results. The effects of element size, rate-dependent plasticity of the material and stress triaxiality are also discussed.

DOI: 10.1007/s10704-007-9062-9
Online Date: 5/9/2007
Print publication date: 2/1/2007
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by Østergaard, Rasmus C.; Sørensen, Bent F.

Fracture of a sandwich specimen loaded with axial forces and bending moments is analyzed in the context of linear elastic fracture mechanics. A closed form expression for the energy release rate for interface cracking of a sandwich specimen with isotropic face sheets is found from analytical evaluation of the J-integral. An approach is applied, whereby the mode mixity for any combination of the loads can be calculated analytically when a load-independent phase angle has been determined. This load-independent phase angle is determined for a broad range of sandwich configurations of practical interest. The load-independent phase angle is determined using a novel finite element based method called the crack surface displacement extrapolation method.The expression for the energy release rate is based on the J-integral and certain stress distributions along the ends of the sandwich specimen. When the stresses from the crack tip interacts with the stresses at the ends, the present analytical calculation of the J-integral becomes inaccurate. The results show that for the analytically J-integral to be accurate the crack tip must be a certain distance away from the uncracked end of the specimen. For a sandwich specimen with face sheet/core stiffness ratio of 100, this distance is in the order 10 times the face sheet thickness. For sandwich structures with face sheet/core stiffness ratio of 1,000, the distance is 30 times the face sheet thickness.

DOI: 10.1007/s10704-007-9059-4
Online Date: 5/8/2007
Print publication date: 2/1/2007
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