Ductile crack propagation by plastic collapse of the intervoid ligaments

In the present study ductile crack initiation and propagation is investigated by means of a micro-mechanical model under small-scale yielding conditions. Voids are resolved discretely in the fracture process zone where steep gradients occur during the loading history and are taken into accounted by a homogenized porous plasticity law elsewhere. The size of the region of discrete voids is not set a priori but is determined consistently. The results show that effective crack growth occurs by plastic collapse, i.e. purely geometric softening of the intervoid ligaments without incorporating material separation. Due to this mechanism a limit load exists coinciding with the maximum fracture toughness. In addition, it turns out that the shielding due to the growth of voids around the crack plane has a considerable influence on the computed R-curves compared to models neglecting this effect. Depending on the void arrangement a diffuse softening zone or even crack branching is observed. A comparison with experimental data from literature indicates that plastic collapse and the formation of diffuse zones of void growth are realistic mechanisms of ductile crack propagation.     

Residual Stresses in Fiber-Reinforced Ceramics due to Thermal Expansion Mismatch

Principles for the calculation of residual stresses due to thermal expansion mismatch and previous solutions are reviewed. A general model for this subject is proposed. Considering the effective thermoelastic properties of a unidirectional composite in axial and transverse directions allows a more comprehensive treatment of the residual stress situation in fiber-reinforced composites. Parameter variations show the important influence of the thermomechanical properties of an interfacial layer, which is disregarded in most of the conventional calculations.     

Three-dimensional cell model analyses of void growth in ductile materials

Three-dimensional micromechanical models were developed to study the damage by void growth in ductile materials. Special emphasis is given to the influence of the spatial arrangement of the voids. Therefore, periodical void arrays of cubic primitive, body centered cubic and hexagonal structure are investigated by analyzing representative unit cells. The isotropic behaviour of the matrix material is modelled using either v. Mises plasticity or the modified Gurson-Tvergaard constitutive law. The cell models are analyzed by the large strain finite element method under monotonic loading while keeping the stress triaxiality constant. The obtained mesoscopic deformation response and the void growth of the unit cells show a high dependence on the value of triaxiality. The spatial arrangement has only a weak influence on the deformation behaviour, whereas the type and onset of the plastic collapse behaviour are strongly affected. The parameters of the Gurson-Tvergaard model can be calibrated to the cell model results even for large porosity, emphasizing its usefulness and justifying its broad applicability.     

Determination of deformation and failure properties of ductile materials by means of the small punch test and neural networks

This paper describes an approach to identify plastic deformation and failure properties of ductile materials. The experimental method of the small punch test is used to determine the material response under loading. The resulting load displacement curve is transferred to a neural network, which was trained using load displacement curves generated by finite element simulations of the small punch test and the corresponding material parameters. The simulated material behavior of the specimen is based on the ductile elastoplastic damage theory of Gurson, Tvergaard and Needleman. During a training process the neural network generates an approximated function for the inverse problem relating the material parameters to the shape of the load displacement curve of the small punch test. This technique was tested for three different materials (ductile steels). The identified parameters are verified by testing and simulating notched tensile specimens.     

A mixed hybrid finite element for three-dimensional elastic crack analysis

A new three-dimensional crack tip element is proposed, which is based on a mixed hybrid stress/displacement model. A truncated series expansion of eigenfunctions for the straight semi-infinite crack is deduced and assumed for the internal stress and displacement fields in the element. The basic approach of constructing these hybrid elements is outlined. Their good capability, efficiency and accuracy for analyzing three-dimensional elastic crack problems are demonstrated by first numerical examples.

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Résumé On propose un nouveau type d'élément tridimensionnel pour l'extrémité d'une fissure, basé sur un modèle mixte contraintes hybrides/déplacements. On en tire un développement en séries tronquées des eigenfonctions relatives à une fissure droite semi-infinie, et on suppose qu'elle est représentative des champs de contraintes internes et de déplacements dans l'élément. L'approche de base utilisée pour construire ces éléments hybrides est soulignée. On démontre par de premiers exemples numériques qu'ils ont la capacité, l'efficacité et la précision nécessaires à l'analyse des problèmes élastiques et tridimensionnels de fissuration.

     

Multi-phase hydration model for prediction of hydration-heat release of blended cements

Recently, the heat release during cement hydration and the so-caused temperature rise was exploited for (i) identification of material properties of early-age cement-based materials (stiffness, strength), and (ii) determination of the diameter and the cement content of jet-grouted structures. In this paper, the underlying hydration model for determination of the heat release and its rate is refined for Ordinary Portland Cements (OPC) and extended towards blended cements. Hereby, the overall degree of hydration with one kinetic law is replaced by a multi-phase hydration model, taking the hydration kinetics of the main clinker phases into account. As regards blended cements, which are commonly used in engineering practice, the effect of slag hydration is incorporated into the presented multi-phase model. The developed hydration model for both plain and blended cement is validated by means of differential-calorimetry (DC) experiments.     

An Analytical Approach to Determine the Pressure Distribution During Chemical Mechanical Polishing

During chemical mechanical polishing the distribution of wear is primarily affected by the pressure distribution on the wafer surface. Moreover, understanding the effects that influence the contact pressure plays a key role in improving the process quality. In this paper a multizone chuck is considered. Two ways to calculate the distribution of contact pressure between wafer and pad are shown. First, an analytical approach is presented, which uses the plate theory to describe the behavior of the carrier. Secondly, a finite-element simulation, which is able to handle more details, is performed to verify that the included assumptions have a negligible impact on the results. It is found that both approaches produce similar results. The reasons for the differences can be explained.     

Transient dynamic analysis of interface cracks in layered anisotropic solids under impact loading

Transient elastodynamic crack analysis in two-dimensional (2D), layered, anisotropic and linear elastic solids is presented in this paper. A time-domain boundary element method (BEM) in conjunction with a multi-domain technique is developed for this purpose. Time-domain elastodynamic fundamental solutions for homogenous, anisotropic and linear elastic solids are applied in the present time-domain BEM. The spatial discretization of the boundary integral equations is performed by a Galerkin-method, while a collocation method is adopted for the temporal discretization of the arising convolution integrals. An explicit time-stepping scheme is developed to compute the unknown boundary data and the crack-opening-displacements (CODs). To show the effects of the crack configuration, the material anisotropy, the layer combination and the dynamic loading on the dynamic stress intensity factors and the scattered elastic wave fields, several numerical examples are presented and discussed.