106 research outputs found

    Relaxation of thermal stress by dislocation motion in passivated metal interconnects

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    The development and relaxation of stress in metal interconnects strained by their surroundings (substrate and passivation layers) is predicted by a discrete dislocation analysis. The model is based on a two-dimensional plane strain formulation, with deformation fully constrained in the line direction. Plastic deformation occurs by glide of edge dislocations on three slip systems in the single crystal line. The substrate and passivation layers are treated as elastic materials, and therefore impenetrable for the dislocations. Results of the simulations show the dependence of the stress evolution and of the effectiveness of plastic relaxation on the geometry of the line. The dependence of stress development on line aspect ratio, line size, slip plane orientation, pitch length and passivation layer thickness are explored.

    A Critical Evaluation of Cohesive Zone Models of Dynamic Fracture

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    Finite element calculations of dynamic fracture based on embedding cohesive surfaces in a continuum indicate that the predictions are sensitive to the cohesive law used. Simulations were performed on a square block in plane strain with an initial edge crack loaded at a constant rate of strain. Cohesive laws that have an initial elastic response were observed to produce spontaneous branching at high velocity, but to modify the linear elastic properties of the body. As a consequence the cohesive surface spacing cannot be refined arbitrarily and becomes an important length scale in the simulations. Cohesive laws that are initially rigid do not alter the linear elastic response of the body. However, crack branching behavior was not observed when such a cohesive relation was implemented using a regular finite element mesh.Earth and Planetary SciencesEngineering and Applied Science

    Discrete dislocation analysis of size effects in thin films

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    A closed-form solution is presented for the plastic response of a single crystal thin film strained by its substrate during thermal loading, according to Gurtin’s strain gradient theory. The results are compared with those of discrete dislocation simulations.

    Ductile failure modeling

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    A finite strain, finite band method for modeling ductile fracture

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    We present a finite deformation generalization of the finite thickness embedded discontinuity formulation presented in our previous paper [A.E. Huespe, A. Needleman, J. Oliver, P.J. Sánchez, A finite thickness band method for ductile fracture analysis, Int. J. Plasticity 25 (2009) 2349–2365]. In this framework the transition from a weak discontinuity to a strong discontinuity can occur using a single constitutive relation which is of importance in a range of applications, in particular ductile fracture, where localization typically precedes the creation of new free surface. An embedded weak discontinuity is introduced when the loss of ellipticity condition is met. The resulting localized deformation band is given a specified thickness which introduces a length scale thus providing a regularization of the post-localization response. The methodology is illustrated through several example problems emphasizing finite deformation effects including the development of a cup-cone failure in round bar tension.A.E.H. and P.J.S. are grateful for financial support from ANPCyT and CONICET of Argentina through grants: PICT 2006-01232, PICT 2008-1228 and PIP 112-200901-00341. J.O. is grateful for financial support from the Spanish Ministry of Science and Innovation and the Catalan Government Research Department, under grants BIA2008-00411 and 2009 SGR 1510, respectively.Peer ReviewedPostprint (author's final draft

    A finite thickness band method for ductile fracture analysis

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    We present a finite element method with a finite thickness embedded weak discontinuity to analyze ductile fracture problems. The formulation is restricted to small geometry changes. The material response is characterized by a constitutive relation for a progressively cavitating elastic–plastic solid. As voids nucleate, grow and coalesce, the stiffness of the material degrades. An embedded weak discontinuity is introduced when the condition for loss of ellipticity is met. The resulting localized deformation band is given a specified thickness which introduces a length scale thus providing a regularization of the post-localization response. Also since the constitutive relation for a progressively cavitation solid is used inside the band in the post-localization regime, the traction-opening relation across the band depends on the stress triaxiality. The methodology is illustrated through several example problems including mode I crack growth and localization and failure in notched bars. Various finite element meshes and values of the thickness of the localization band are used in the calculations to illustrate the convergence with mesh refinement and the dependence on the value chosen for the localization band thickness.Peer ReviewedPostprint (author’s final draft

    A microstructurally motivated description of the deformation of vertically aligned carbon nanotube structures

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    Vertically aligned carbon nanotube’s extreme compliance and mechanical energy absorption/dissipation capabilities are potentially promising aspects of their multi-functionality. Mathematical models have revealed that a hardening-softening-hardening material relation can capture the unique sequential, periodic buckling behavior displayed by vertically aligned carbon nanotubes under uniaxial compression. Yet the physical origins of these models remain unknown. We provide a microstructure-based motivation for such a phenomenological constitutive relation and use it to explore changes in structural response with nanotube volume fraction

    Uniaxial Tension of a Class of Compressible Solids With Plastic Non-Normality

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    Motivated by a model that qualitatively captured the response of vertically aligned carbon nanotube (VACNT) pillars in uniaxial compression, we consider the uniaxial tensile response of a class of compressible elastic-viscoplastic solids. In Hutchens et al. [“Analysis of Uniaxial Compression of Vertically Aligned Carbon Nanotubes,” J. Mech. Phys. Solids, 59, pp. 2227–2237 (2011), Erratum 60, 1753–1756 (2012)] an elastic viscoplastic constitutive relation with plastic compressibility, plastic non-normality, and a hardening-softening-hardening hardness function was used to model experimentally obtained uniaxial compression data of cylindrical VACNT micropillars. Complex deformation modes were found in uniaxial compression, which include a sequential buckling-like collapse of the type seen in experiments. These complex deformation modes led to the overall stress-strain signature of the pillar not being of the same form as the input material hardness function. A fundamental question that motivates exploring the deformation of this class of materials—both experimentally and theoretically—is how to extract the intrinsic material response from simple tests. In this study we explore the relation between the input material response and the overall stress strain behavior in uniaxial tension using the constitutive framework of Hutchens et al. A simple one-dimensional analysis reveals the types of instability modes to be expected. Dynamic, finite deformation finite element calculations are carried out to explore the dependence of diffuse necking, localized necking, and propagating band deformation modes on characteristics of the hardness function. Attention is devoted to uncovering implications for obtaining intrinsic material properties of complex hierarchical structures; for example, vertically aligned carbon nanotubes (VACNTs), from uniaxial tension experiments
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