Slip Field Research Articles

Hydromagnetic rotating flow in a porous medium with slip condition and Hall current

The slip effect on hydromagnetic rotating flow of viscous fluid through a porous space is investigated. The fluid is electrically conducting with the consideration of Hall current. The entire system rotates about the axis normal to a porous plate of uniform suction or injection with uniform angular velocity. The closed form solution is obtained using Laplace transform technique. The analytical expression for skin friction is evaluated. The graphical results are displayed to see the effects of various embedded flow parameters such as magnetic parameter , permeability parameter , Hall parameter , rotation parameter , suction or injection parameter , slip parameter and dimensionless time It is found that the magnetic field and slip parameter decrease the velocity magnitude whereas permeability and Hall parameters increase it. The slip and magnetic field play an important role in retarding the growth of both the primary and secondary flows, whereas Hall parameter enhances the flow. Key words: Slip effect, rotating flow, porous space, laplace transform.

Validation of a Modified Steel Bar Model Incorporating Bond-Slip for Seismic Assessment of Concrete Structures

In this paper the implementation and validation of a modified steel bar model including bond-slip of longitudinal bars that was proposed in a companion paper is discussed. The model is developed on the key assumption of linear slip field along the steel bar with different configurations at the ends of the bar. The simplified model is capable of predicting the axial slip displacement with suitable accuracy compared with a refined model but with considerably fewer computational steps. The proposed model avoids nested iterations in the context of fiber model discretization of a section that requires the representation of all actions in terms of stress and strain. The model is applied to two component tests—one with poor and another with improved reinforcing detailing. Findings from the simulations indicate that the proposed model is more suitable for use in connections with poor detailing and pronounced slip in the plastic hinge zones.

Plastic slip patterning through rate dependent non‐convex gradient‐enhanced plasticity

AbstractThe paper presents a non‐convex rate dependent strain gradient plasticity framework for the description of plastic slip patterning in metal crystals. The non‐convexity is treated as an intrinsic property of the free energy of the material. Departing from explicit expressions for the free energy, the non‐convex strain gradient crystal plasticity model is derived in a thermodynamically consistent manner, including the accompanying slip law. For the numerical solution of the problem, the displacement and the plastic slip fields are considered as primary variables. These fields are determined on a global level by solving simultaneously the linear momentum balance and the resulting slip evolution equation. The slip law differs from classical ones in the sense that it naturally includes a contribution from the non‐convex free energy term, which enables patterning of the deformation field. The formulation of the computational framework is partially dual to a Ginzburg Landau type of phase field modeling approach. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Displacement-based finite element formulations for material-nonlinear analysis of composite beams and treatment of locking behaviour

In this paper a numerical procedure is developed for the material-nonlinear analysis of composite beams composed of two Euler–Bernoulli beams juxtaposed with a deformable shear connection. In the displacement-based finite element analysis of composite beams, however, the coupling of the transverse and longitudinal displacement fields may cause oscillations in the interlayer slip field and reduction in optimal convergence rate, known as slip-locking. A very simple and novel procedure is introduced to develop an assumed strain formulation, which alleviates slip-locking in the numerical analysis of composite beams and provides superconvergent points for slip values. It is also shown that by changing the primary variable fields of Newmark's mathematical model, to interpolate the slip field directly, slip-locking can be completely eliminated. Numerical examples are presented to illustrate the performances and the numerical characteristics of the proposed methods.

Effect of secondary orientation on notch-tip plasticity in superalloy single crystals

Numerical and experimental evolutions of slip fields in notched Ni-Base Single Crystal superalloy tensile specimens are presented as a function of secondary crystallographic orientation. The numerical predictions based on three-dimensional anisotropic elasticity and crystal plasticity are compared with experimental observations. The results illustrate the strong dependence of the slip patterns and the plastic zone size and shape on the secondary orientation of notches, which can have important consequences on crack initiation. Specific orientations or non-symmetric notch geometries lead to non-symmetric patterns on both sides of the sample. The computations show that strongly different plastic zones are expected in the core of the sample and at free surfaces. The ability of the anisotropic elastic model to anticipate the plastic domains, based on identifying dominant slip systems, is confirmed by the crystal plasticity computations, at low load levels. An important observation is that kink shear banding is a real deformation mode operating at crack tips and notches in high strength nickel-based single crystal superalloys for specific orientations.

Surface deformation along the Carmel Fault System, Israel

The existing knowledge about the recent crustal deformations along the Carmel Fault in Northern Israel which passes the city of Haifa is to a certain degree ambiguous. Depending on geological, geophysical or geodetic sources the movement rates and senses range from 1 mm/yr sinistral up to 4 mm/yr dextral. In this paper we analyze GPS data from a regional network observed between 1999 and 2009 and derive global and regional velocities for 23 sites along the fault. The regional site velocities were estimated with respect to a local datum that was defined by a stable cluster of sites on one side of the fault and the horizontal velocity field shows deformations of up to 4.5 mm/yr dextral. In combination with an S-transformation the site velocities were used to estimate the parameters of a dislocation model based on elastic half space theory. We compare the results with expectations from slip rate analysis of seismicity parameters. In addition the resulting fault slip field is used to derive a fault-related velocity field.

Influence of grain boundary conditions on modeling of size-dependence in polycrystals

In this paper, a gradient crystal plasticity model in a polycrystalline grain structure is investigated. Hereby, the focus is on the influence of the grain boundary conditions. A new type of grain boundary conditions is introduced, the so-called micro-flexible boundary condition. In particular, it is compared to existing grain boundary conditions of plastic slip. Numerical results are given for the stress–strain response as well as for the plastic slip field in the grain structure.

Treatment of slip locking for displacement‐based finite element analysis of composite beam–columns

AbstractIn the conventional displacement‐based finite element analysis of composite beam–columns that consist of two Euler–Bernoulli beams juxtaposed with a deformable shear connection, the coupling of the transverse and longitudinal displacement fields may cause oscillations in slip field and reduction in optimal convergence rate, known as slip locking. This locking phenomenon is typical of multi‐field problems of this type, and is known to produce erroneous results for the displacement‐based finite element analysis of composite beam–columns based on cubic transverse and linear longitudinal interpolation fields. This paper introduces strategies including the assumed strain method, discrete strain gap method, and kinematic interpolatory technique to alleviate the oscillations in slip and curvature, and improve the convergence performance of the displacement‐based finite element analysis of composite beam–columns. A systematic solution of the differential equations of equilibrium is also provided, and a superconvergent element is developed in this paper. Numerical results presented illustrate the accuracy of the proposed modifications. The solutions based on the superconvergent element provide benchmark results for the performance of these proposed formulations. Copyright © 2010 John Wiley & Sons, Ltd.

Mixed-mode singularity and temperature effects on dislocation nucleation in strained interconnects

Dislocations can be nucleated from sharp geometric features in strained interconnects due to the thermal expansion coefficient mismatch, lattice mismatch, or stresses that arise during material processing. The asymptotic stress fields near the edge root can be described by mixed-mode singularities, which depend on the dihedral angle and material properties, and a transverse T-stress, which depends on how residual stress is realized in the interconnects. The critical condition for stress nucleation can be determined when an appropriate measure of the stress intensity factors (SIFs) reaches a critical value. This method, however, does not offer an explicit picture of the dislocation nucleation process so that it has difficulties in studying complicated structures, mode mixity effects, and more importantly the temperature effects. Using the Peierls concept, a dislocation can be described by a continuous slip field, and the dislocation nucleation occurs when the total potential energy reaches a stationary state. Through implementing this ad hoc interface model into a finite element framework, it is found that dislocation nucleation becomes more difficult with the increase of mode mixity, or the decrease of the T-stress, or the decrease of the length-to-height ratio of the surface pad, while the shape of the surface pad, being a square or a long line, plays a less important role. The Peierls dislocation model also allows us to determine the activation energy, which is the energy needed for the thermally activated, mechanically assisted dislocation nucleation when the applied load is lower than the athermal critical value. The calculated saddle point configuration agrees well with the molecular simulations in literature. Suggestions on making immortal strained interconnects are made.

Finite Element Studies of Homogeneous and Heterogeneous Dislocation Nucleation based on the Rice-Peierls Framework

ABSTRACTThe study of dislocation nucleation has gained increasing attentions recently primarily due to the advancement of small scale mechanical testing methods. Based on the classic Rice model of dislocation nucleation from a crack tip in which the dislocation core is modeled by a continuous slip field, a nonlinear finite element method can be formulated with the interplanar potential as the input, and the development of interplanar slip field can be solved from the resulting boundary value problems. The effects of geometric boundary conditions, loading patterns, etc. can be conveniently determined, as opposed to the time consuming molecular simulations. To validate the method, we compare the simulations results of homogeneous dislocation nucleation and heterogeneous dislocation nucleation from a two-dimensional crack tip to the literature results. As proposed by Rice and Beltz (J. Mech. Phys. Solids, 1994), the activation energy for dislocation nucleation from a three-dimensional crack tip depends on the finite thickness in the direction parallel to the crack tip, which has been successfully reproduced in the finite element simulation results reported here.

3D modeling of filtration process via polyurethane nanofiber based nonwoven filters prepared by electrospinning process

Full 3D particle filtration modeling at low pressures considering slip/transition/free molecular flow regime, particle–fiber interactions, air/particle slip, sieve and homogenous flow field has been performed for the polyurethane nanofiber filter prepared by electrospinning process and the obtained theoretical predictions for the filtration efficiency have been compared with the corresponding experimental data. Moreover, the effect of air velocity, viscosity, temperature, pressure and particle–fiber friction coefficient on the produced polyurethane nanofiber filter efficiency has been investigated in more details. In order to take all real structure features of the nanofiber filter into account (such as varying fiber diameter, curvature along its length, inhomogeneity and mat defects), a new approach for 3D nanofiber mat model construction from corresponding SEM images has been proposed and utilized.

Deformation patterning driven by rate dependent non-convex strain gradient plasticity

A rate dependent strain gradient plasticity framework for the description of plastic slip patterning in a system with non-convex energetic hardening is presented. Both the displacement and the plastic slip fields are considered as primary variables. These fields are determined on a global level by solving simultaneously the linear momentum balance and the slip evolution equation which is postulated in a thermodynamically consistent manner. The slip law differs from classical ones in the sense that it includes a non-convex free energy term, which enables patterning of the deformation field. The formulation of the computational framework is at least partially dual to a Ginzburg–Landau type of phase field modeling approach. The essential difference resides in the fact that a strong coupling exists between the deformation and the evolution of the plastic slip, whereas in the phase field type models the governing fields are only weakly coupled. The derivations and implementations are done in a transparent 1D setting, which allows for a thorough mechanistic understanding, not excluding its extension to multidimensional cases.

A Peierls perspective on mechanisms of atomicfriction

Stick–slip behavior observed from nanoscale asperity friction experiments are often modeled by the one-degree-of-freedom Tomlinson model, which is unable to explain the effects of lattice structure and interface defects, or by molecular simulations which suffer temporal limitations in modeling the velocity- and temperature-dependent frictional behavior. A Peierls-type model developed in this work views the atomic frictional process as the initiation and gliding passage of dislocations with diffused cores on the interface. As a consequence of loss-of-ellipticity instability, the occurrence of stick–slip behavior relies on the interaction among interface slip field, contact stress fields, and existing defects. The friction stress for commensurate interface under large contact area can be approximated from the Rice model of screw-dislocation nucleation from a planar crack tip. The spatially inhomogeneous nature of rate-limiting processes and the coupling effects between contact size and interface incommensurability are successfully determined, which cannot otherwise be tackled in the Tomlinsonmodel.

Elimination of slip-locking in composite beam-column analysis by using the element-free Galerkin method

In the numerical analysis of composite beam-columns inconsistencies in the shape functions of the transverse and longitudinal displacement fields may cause oscillations in the slip field and reduction in the accuracy of the results known as slip-locking which is typical of multi-field problems of this type. In order to eliminate slip-locking, matching field strategy is adopted herein by using the element free Galerkin method in which shape functions of the longitudinal displacement fields are obtained from the derivatives of shape functions of the transverse displacement fields. Continuous blending method is modified in order to couple element-free Galerkin and finite element methods when the matching field approach is used in the meshfree region. This modification allows for direct assembly of the stiffness matrices that are built for separate finite element and meshfree regions, the boundary conditions can be directly applied and the reaction forces can also be calculated directly from the structural stiffness matrix.

Locking-free finite element formulation for steel-concrete composite members

In the conventional displacement-based finite element analysis of composite beam-columns that consist of two Euler-Bernoulli beams juxtaposed with a deformable shear connection, the coupling of the transverse and longitudinal displacement fields may cause oscillations in interlayer slip field and reduction in optimal convergence rate, known as slip-locking. This locking phenomenon is typical of multi-field problems of this type, and is known to produce erroneous results for the displacement based finite element analysis of composite beam-columns based on cubic transverse and linear longitudinal interpolation fields. In this paper it will be shown that by simple change of the pair of dependent variables in the formulation the locking behaviour can be alleviated. An example is presented to illustrate the effects of connection stiffness on the behaviour of composite beams and the results show that the proposed approach is efficient in alleviating the locking behaviour.

Caracterização estatística de variáveis usadas para ensaiar uma semeadora-adubadora em semeadura direta e convencional

The objective of this work was to statistically characterize variables such as wheels slip, theoretical and effective field capacity of a planter in direct (DS) and conventional sowing (CS) systems, based on the verification of the adjustment of a series of data to a statistical distribution, aiming for the best form of representation and values be adopted so that these variables be used in agricultural practices operations. The experiment in CS was done with a speed of 1.5 m s-1 with 190 repetitions, and the experiment in DS was done with 1.8 m s-1 and 58 repetitions. It was concluded that differing values were not detected, and the variables in study can be represented by the function density of normal probability (Gaussian distribution), and the variables can be used for its representations.

Geometric effects on dislocation nucleation in strained electronics

Dislocation loops may be nucleated from sharp geometric features in strained micro- and nano-electronic devices. This process is investigated by a dissipative cohesive interface model which treats the dislocation core as a continuous, inhomogeneous lattice slip field. As a representative example, we calculate the critical external stress for dislocation nucleation from the edges/corners of a rectangular stress-free Si3N4 pad on a Si substrate as a function of geometric parameters such as the length-to-height ratio and the three-dimensional shape of the pad. The shapes of the dislocations are also simulated.

Evolution of plasticity in notched Ni-base superalloy single crystals

Numerical and experimental investigations of evolution of slip fields in notched Ni-base superalloy single crystal tensile specimens are presented as functions of load and secondary (notch) orientation. Three crystallographic orientations were investigated with the primary (load) orientation fixed along the [0 0 1] direction while the notch directions are parallel to [ 1 ¯ 10 ] / [ 1 1 ¯ 0 ] , [ 0 1 0 ] / [ 0 1 ¯ 0 ] , and [ 3 ¯ 1 0 ] / [ 3 1 ¯ 0 ] , respectively. A three-dimensional elastic anisotropic finite element analysis (FEA) was used to compute the triaxial stress fields in the neighborhood of the notch. The elastic solution is successful in identifying which slip systems are activated initially. Interestingly this procedure was found to be also successful in predicting slip evolution at higher loads, because of slip localization in the superalloy tested. Based on this analysis, the concept of “dominant slip system” is introduced and defined as the single slip system that experiences the highest resolved shear stress (RSS) at a given point near the notch. The dominant slip systems are seen to persist with increasing load and inhibit the activation of new slip systems, which implies that when plasticity is initiated in the dominant slip systems, either softening takes place and/or the rate of increase in RSS on the other slip systems is reduced significantly. The distribution of dominant slip systems in the neighborhood of the notch and on the surface is used to accurately predict the evolution of activated slip sectors and sector boundaries observed experimentally. The activated stress fields are shown to vary strongly through the specimen thickness. Elastic anisotropy governs the development of the elastic stress field and controls which slip systems become initially dominant/activated. Therefore inclusion of elastic anisotropy was found to be important for the prediction of stress field evolution as functions of load and crystal orientation.

Constraining earthquake source inversions with GPS data: 1. Resolution‐based removal of artifacts

We present a resolution analysis of an inversion of GPS data from the 2004 Mw 6.0 Parkfield earthquake. This earthquake was recorded at thirteen 1‐Hz GPS receivers, which provides for a truly coseismic data set that can be used to infer the static slip field. We find that the resolution of our inverted slip model is poor at depth and near the edges of the modeled fault plane that are far from GPS receivers. The spatial heterogeneity of the model resolution in the static field inversion leads to artifacts in poorly resolved areas of the fault plane. These artifacts look qualitatively similar to asperities commonly seen in the final slip models of earthquake source inversions, but in this inversion they are caused by a surplus of free parameters. The location of the artifacts depends on the station geometry and the assumed velocity structure. We demonstrate that a nonuniform gridding of model parameters on the fault can remove these artifacts from the inversion. We generate a nonuniform grid with a grid spacing that matches the local resolution length on the fault and show that it outperforms uniform grids, which either generate spurious structure in poorly resolved regions or lose recoverable information in well‐resolved areas of the fault. In a synthetic test, the nonuniform grid correctly averages slip in poorly resolved areas of the fault while recovering small‐scale structure near the surface. Finally, we present an inversion of the Parkfield GPS data set on the nonuniform grid and analyze the errors in the final model.

Fault slip and modern tectonic stress field in and around Kunming basin

Kunming basin is a Cenozoic faulted basin under the control of mainly SN-trending active faults. In and around the basin, there are a total of eight major active faults. Seismo-geological survey and fault slip observation show that the SN-and NE-trending active faults are mostly sinistral strike-slip faults, while the NW-trending faults are mostly dextral strike-slip faults. Using stress tensor inversion method with 706 active fault striation data at 22 measurement sites, we determined tectonic stress field of the study area. The result shows that modern tectonic stress field in and around Kunming basin is characterized by NNW-SSE compression, ENE-WSW extension, and strike-slip stress regimes. The maximum principal compressional stress (σ1) is oriented 335°–2°, with an average dip angle of 21°; the minimum (σ3) is oriented 44°∼93°, with an average dip angle of 14°, and the intermediate (σ2) has a high, or nearly vertical, dip angle. The inversion result from fault slip data is consistent with the result from focal mechanism solutions.