Strain localization

In concentrically braced frames, gusset plate connections to rectangular hollow section braces are fabricated using welds both on the brace side and to connect the gusset plate to the flanges of the beam and column framing into the brace. The beam-to-column connection at the gusset plate is either welded or bolted. A welded beam-to-column connection could be considered as the best option for braced frame gusset plate connections, because the potentially considerable axial forces developed in the beam must be transferred through this joint. Even when a bolted connection is provided at the face of the column flange, a stiff gusset plate connected to the beam and the column could still provide a fully restrained beam-to-column connection as in the case of the welded connection. The past experimental studies have indicated that undesirable failure modes could occur in the gusset plate even using a linear clearance rule in the design of the gusset plate connection. For these reasons, this study investigates the local seismic performances of fully restrained gusset plate connections through detailed finite element models of a single storey single bay frame located at the ground floor of the four storey frame using the MIDAS FE program. The main goal of the study on the local performance of the gusset plate connection is to validate the design procedure presented in this chapter, proposing and alternative clearance rule for the accommodation of brace rotation. Finally, local performances of FE models are compared in terms of strain concentrations in gusset plates, beams and columns.

In situ microscopic-digital image correlation (μ-DIC) is used to investigate the strain partitioning and strain localization behavior in a medium manganese steel. Continuous yielding results from strain partitioning with higher strain in the reverted austenite (í µí»¾ R) islands and less strain in the tempered martensite (α ′ temp) matrix, both in hot and cold rolled material. μ-DIC experiments are performed to further understand the effects of texture and grain morphology on strain partitioning which cannot be locally resolved through high resolution x-ray or neutron diffraction experiments. Apart from strain partitioning, strain localization is observed in hot rolled samples within colonies of lamellar í µí»¾ R islands. This localization does not only depend on the crystallographic orientation, but also on the spatial alignment of an austenite island relative to the loading direction. The effects of texture, spatial and colony alignment are interpreted within the concept of a relative grain size effect resulting in different yield stresses in the hot and cold rolled samples showing continuous yielding. Strain partitioning and strain localization based on texture and spatial alignment can be extended to numerous dual phase morphologies with similar texture, colony and spatial alignment effects.

We present a combined experimental–numerical study on fracture initiation at the convex surface and its propagation during bending of a class of ferritic–martensitic steel. On the experimental side, so-called free bending experiments are conducted on DP1000 steel sheets until fracture, realizing optical and scanning electron microscopy analyses on the post mortem specimens for fracture characterization. A blended Mode I – Mode II fracture pattern, which is driven by cavitation at non-metallic inclusions as well as martensitic islands and resultant softening-based intense strain localization, is observed. Phenomena like crack zig-zagging and crack alternation at the bend apex along the bending axis are introduced and discussed. On the numerical side, based on this physical motivation, the process is simulated in 2D plane strain and 3D, using Gurson’s dilatant plasticity model with a recent shear modification, strain-based void nucleation, and coalescence effects. The effect of certain material parameters (initial porosity, damage at coalescence and failure, shear modification term, etc.), plane strain constraint and mesh size on the localization and the fracture behavior are investigated in detail.

A three-dimensional nonlocal multiscale discrete-continuum model has been developed for modeling
mechanical behavior of granular materials. In the proposed multiscale scheme, we establish an informationpassing
coupling between the discrete element method, which explicitly replicates granular motion of
individual particles, and a finite element continuum model, which captures nonlocal overall responses of
the granular assemblies. The resulting multiscale discrete-continuum coupling method retains the simplicity
and efficiency of a continuum-based finite element model, while circumventing mesh pathology in the postbifurcation
regime by means of staggered nonlocal operator. We demonstrate that the multiscale coupling
scheme is able to capture the plastic dilatancy and pressure-sensitive frictional responses commonly observed
inside dilatant shear bands, without employing a phenomenological plasticity model at a macroscopic level.
In addition, internal variables, such as plastic dilatancy and plastic flow direction, are now inferred directly
from granular physics, without introducing unnecessary empirical relations and phenomenology. The simple
shear and the biaxial compression tests are used to analyze the onset and evolution of shear bands in granular
materials and sensitivity to mesh density. The robustness and the accuracy of the proposed multiscale model
are verified in comparisons with single-scale benchmark discrete element method simulations.

This work is focused on the numerical implementation of thermo-elasto viscoplastic constitutive equations in small and finite strain contexts using the FEM. A length-scale parameter is introduced implicitly through viscosity in order to address strain localization and material instability in the (initial) boundary value problems. According to the second law of thermodynamics a dissipation inequality described in the rotated material

NiAl is a potential candidate for high temperature structural applications because of its high melting point, high thermal conductivity, relatively low density, and good high temperature oxidation resistance. However, it suffers from a high brittle-to-ductile transition (BDT) temperature and a low room temperature toughness. The present study focuses on understanding the mechanism of the BDT and investigating the effects of strain rate and prestraining on the BDT in stoichiometric NiAl single crystals. The results of this study indicated that the BDT temperature (BDTT) correlates with the onset of net-section yielding in the double-notched tension specimens. A strong dependence of the BDTT on the applied displacement rate was observed. It was proposed that the BDT arises from a reduction in strain hardening rate as well as in yield strength with temperature. The similarity found in activation energy values calculated based on the strain rate dependence of fracture toughness and tensile data supports this proposal. While the prestraining was found to increase the toughness at room temperature nearly two-fold, it also increases the BDTT of NiAl single crystals. This observation suggested that the BDT of NiAl is not limited by the dislocation density. Based on the fractographic analysis, it was found that localization of strain is responsible for crack nucleation in NiAl single crystals. It was suggested that the crack instability is "nucleation-controlled" at low temperatures whereas it is "propagation-controlled" at high temperatures. Based on this suggestion, the increase in room temperature toughness upon prestraining was attributed to the reduction in the localization of strain upon prestraining achieved due to the enhanced dislocation density. The increase in the BDTT upon prestraining was attributed to the increased yield stress caused due to prestraining. The cleavage plane for NiAl single crystals was found to be \{511\} for the specimen geometry and orientation used in the study. The observation of this cleavage plane is in agreement with the previously reported results. The cleavage plane was independent of heat-treatment, prestraining, and temperature; however, the size of the largest cleavage facet was found to decrease with increasing temperature.

After detailed field (stratigraphic and structural) and laboratory analyses of intact and deformed rocky outcrops, we studied the multi-scale properties of strike-slip faults nucleated and developed in Pleistocene carbonate grainstones of Favignana Island ( ...

In this second part, a state-of-the-art digital image correlation (DIC) technique was used to compute true stress-true strain curves beyond diffuse necking for friction stir processed AA5182-O and AA6111-T4 aluminum alloys. Of particular interest were differences in key tensile properties, such as initial yield point, and ultimate tensile strength, between the base and friction stir processed materials. Tensile coupons cut from the same material used to investigate crystallographic texture via the electron backscatter diffraction technique in Part 1, were strained to failure in a miniature tensile stage. The evolution of two-dimensional strain fields in both the base and friction stir processed materials was explored with incremental and cumulative strain maps computed from digital grids superimposed on each image after testing was completed. The impact of friction stir processing on strain localization just prior to fracture was revealed through changes in incremental strain map contour profiles. It is suggested that grain size refinement due to friction stir processing has a prominent effect on strength, while texture plays a secondary role.