Analysis Of Strain Localization Research Articles

Revisiting strain localization analysis for elastoplastic constitutive models in geomechanics

AbstractThe localization of deformations plays a crucial role in the failure of granular materials. Concerning classical continuum constitutive models, the localization of deformations is considered to be connected to the loss of ellipticity of the governing rate equilibrium equations, and entails mesh sensitivity in finite element simulations. While previous studies are often limited to strain localization analyses of individual tests, the focus of the present contribution lies on studying the localization properties in general constitutive states. For this purpose, a staggered optimization algorithm for determining the loss of ellipticity, considering both extreme values, minimum and maximum, of the determinant of the acoustic tensor, is proposed. Part of this algorithm representing a novel application of spherical Fibonacci lattices for discretizing the feasible domain of the associated optimization problem. In the presented localization study of the widely recognized modified Cam‐clay model, special attention is paid to determining the influence of the individual model parameters. Specifically, three factors favoring strain localization are found, namely (i) a low value of the ratio of the primary compression index and the recompression index, (ii) a large value of the critical state frictional constant, as well as (iii) a large value of Poisson's ratio. Moreover, a structural finite element study is performed, confirming the results of localization analyses at the constitutive level.

Numerical Analysis of Strain Localization in Granular Soils by Modified Cam-Clay Model Based on Micropolar Continuum Theory

Numerical Analysis of Strain Localization in Granular Soils by Modified Cam-Clay Model Based on Micropolar Continuum Theory

Analysis of strain localization and slip transfer based on composite Schmid factor in TA19 titanium alloy

The correlation between slip behavior and strain localization was investigated through in-situ tensile experiment. The relationship between slip transfer and crystallographic orientation was analyzed using the composite Schmid factor (CSF), where CSF=mout+minm' (min and mout represent the Schmid factor (SF) of incoming and outgoing slip systems, respectively, m' is the geometric compatibility factor). The results show that for adjacent equiaxed α (αeq) grains without slip transfer, it will induce significant strain localization around αeq/αeq grain boundary due to the accumulation of massive dislocations on grain boundary. The initiation of secondary slip in αeq grain would exacerbate strain localization within the grain, as it promotes the dislocation pile-ups and entanglement. The slip behavior is largely related to the crystallographic orientation of the two adjacent αeq grains. Based on statistical analyses, for slip transfer, the slip system with the largest CSF is more likely to act as an easily initiated outgoing slip system. It can be attributed to that the CSF could reflect the synergistic effect of applied stress and the local shear stress induced by incoming slip system on the slip transfer behavior. However, with the increase of strain, some outgoing slip systems without the largest CSF can also be initiated, which may be associated with the complicated local stress state induced by the initiation of slip systems in multiple adjacent αeq grains before the initiation of outgoing slip system.

Thermo-kinetic characteristics on stabilizing hetero-phase interface of metal matrix composites by crystal plasticity finite element method

Using dislocation-based constitutive modeling in three-dimension crystal plasticity finite element (3D CPFE) simulations, co-deformation and instability of hetero-phase interface in different material systems were herein studied for polycrystalline metal matrix composites (MMCs). Local stress and strain fields in two types of 3layer MMCs such as fcc/fcc Cu–Ag and fcc/bcc Cu–Nb have been predicted under simple compressive deformations. Accordingly, more severe strain-induced interface instability can be observed in the fcc/bcc systems than in the fcc/fcc systems upon refining to metallic nanolayered composites (MNCs). By detailed analysis of stress and strain localization, it has been demonstrated that the interface instability is always accompanied by high-stress concentration, i.e., thermodynamic characteristics, or high strain prevention i.e., kinetic characteristics, at the hetero-phase interface. It then follows that the thermodynamic driving force ΔG and the kinetic energy barrier Q during dislocation and shear banding can be adopted to classify the deformation modes, following the so-called thermo-kinetic correlation. Then by inserting a high density of high-energy interfaces into the Cu-Nb composites, such thermo-kinetic integration at the hetero-phase interface allows a successful establishment of MMCs with the high ΔG-high Q deformation mode, which ensures high hardening and uniform strain distribution, thus efficiently suppressing the shear band, stabilizing the hetero-phase interface, and obtaining an exceptional combination in strength and ductility. Such hetero-phase interface chosen by a couple of thermodynamics and kinetics can be defined as breaking the thermo-kinetic correlation and has been proposed for artificially designing MNCs.

Modelling of ductile failure in materials with heterogeneous particle structure using localization analysis

In this study, we evaluate the use of strain localization analysis based on the imperfection band approach to model the effect of heterogeneous particle distribution on the ductile failure of structural metallic materials. To this end, tensile tests are performed on smooth and notched samples made of aluminium alloy AA6110 with an equiaxed grain structure and an inhomogeneous distribution of the constituent particles. The constituent particles are assumed to be the main contributors to the ductile failure of the alloy. By varying the heat treatment of the alloy, three different materials are considered with different strength, work hardening, and ductility, while the grain structure and constituent particle distribution are unaltered. Finite element simulations of the tension tests are conducted using both metal and porous plasticity models and the stress–strain histories of the elements in the minimum section of the specimen are used in strain localization analyses. In these analyses, ductile failure is assumed to occur when the strain rate inside a thin, planar imperfection band becomes infinite. The imperfection band is modelled with porous plasticity, using either a higher initial porosity than in the bulk material or by adding void nucleation. It is found that the ductility of the materials is most accurately captured by modelling the imperfection band by stress-enhanced nucleation.

Automated slip system identification and strain analysis framework using high-resolution digital image correlation data: Application to a bimodal Ti-6Al-4V alloy

Statistical analysis of slip system identification and quantitative study on local plasticity is crucial to understand the collective deformation by the sub-grain-scale slip activities in polycrystalline metallic materials. In this study, an automated framework for identifying slip system and assessing strain localization of slip bands termed ASSISL (automated Slip System Identification and Strain Localization analysis of slip bands) is introduced, using the results from high resolution digital image correlation (HR-DIC), and is demonstrated on 1591 primary α grains of a bimodal Ti-6Al-4V alloy under tensile loading. The framework includes: (1) alignment of electron backscattered diffraction (EBSD) maps with strain field maps from HR-DIC through treatment of EBSD distortion, (2) slip band orientations identification from strain field map of each grain through a Radon-transform-based algorithm, (3) slip system assignment with combined Schmid factor and critical resolved shear stress analysis, (4) quantification of plasticity by slip activities which provides information on the numbers, positions and mean strain of slip bands in each grain. The confidence of ASSISL is validated through comparing current statistical results with existing literature, as well as examining reasons for grains assigned with wrong slip systems, which accounts for 9.6 percent (153 out of 1591) of the primary α grains. A comparison between ASSISL and other HR-DIC-based slip identification methods is also conducted. This framework provides a method for analyzing slip activities in a large number of grains of polycrystalline metals in a time-saving and automated fashion.

Strain localization of Mohr-Coulomb soils with non-associated plasticity based on micropolar continuum theory

To address the problems of strain localization, the exact Mohr-Coulomb (MC) model is used based on second-order cone programming (mpcFEM-SOCP) in the framework of micropolar continuum finite element method. Using the uniaxial compression test, we focused on the earth pressure problem of rigid wall segment involving non-associated plasticity. The numerical results reveal that when mpcFEM-SOCP is applied, the problems of mesh dependency can be effectively addressed. For geotechnical strain localization analysis involving non-associated MC plasticity, mpcFEM-SOCP in conjunction with the pseudo-time discrete scheme can improve the numerical stability and avoid the unreasonable softening issue in the pressure-displacement curves, which may be encountered in the conventional FEM. It also shows that the pressure-displacement responses calculated by mpcFEM-SOCP with the pseudo-time discrete scheme are higher than those calculated by mpcFEM-SOCP with the Davis scheme. The inclination angle of shear band predicted by mpcFEM-SOCP with the pseudo-time discrete scheme agrees well with the theoretical solution of non-associated MC plasticity.

Localized strain evolution and accumulation at the notch tip of an aluminum single crystal under cyclic loading

AbstractA synchronized analysis of strain localization and slip system interaction, with full‐field strain mapping, in the vicinity of a notch tip in aluminum single crystal is presented. Progressive strain accumulation, prominently along one of the slip shear bands, was demonstrated quantitatively under cyclic loading, using digital image correlation. This dominant slip band potentially critical for the nucleation and growth of a crack. Also, triple slip active regions found on the surface indicate the participation of all three in‐plane slip systems. Therefore, the use of either diagonal or weakly coupled hardening rule is recommended even in aluminum single crystals, instead of the commonly used isotropic models. Finally, the results from this work provide quantitative data on the progressive strain accumulation and localization around a notch under cyclic loading that can be used in model validation for single and polycrystal plasticity.

Failure and Mechanical Properties of Glassy Diblock Copolymer Thin Films

Block copolymer self-assembly is affected by nanoscale confinement, which has long been known to affect interchain entanglements and dynamics of polymers. While most previous work on confined polymer glasses has focused on the properties of homopolymers, the mechanical response of glassy block copolymer thin films is still relatively unexplored. By uniaxially deforming glassy lamellar diblock copolymer films with different morphologies via molecular dynamic simulations, we demonstrate that the toughness of the films with fingerprint morphologies is higher compared to homopolymers and oriented lamellar films due to the increase in the randomness of domain orientations and entanglements. We show that the thickness impact on the mechanical properties of the block copolymers is not as big as that of the homopolymer systems. In the strain localization analysis of the block copolymer films, there are the plastic rearrangements initially clustered at the boundary between the two phases of the lamellae until close to failure when the plasticity transitions to the center of a domain. In the block copolymer systems, crazes in the thinnest films exhibit distinct behaviors compared to thicker films. Our studies of the film mechanics provide molecular insights into how segmental mobility and entanglements interplay with position and morphology to control the mechanics of thin polymer films.

A shear modified enhanced Gurson constitutive relation and implications for localization

The most widely used phenomenological constitutive relation to model ductile failure of structural metals at room temperature is based on the work of Gurson (1977) and has the advantage of having both a micromechanics basis and sufficient simplicity to enable complex engineering calculations to be carried out. The predictions of this framework have been most successful in circumstances where the stress triaxiality, the ratio of mean normal stress to Mises effective stress, is relatively large. For stress states with smaller values of stress triaxiality, the predictive capability has typically been much reduced. We present a shear modified enhanced Gurson constitutive relation that combines the shear modification of Nahshon and Hutchinson (2008) with the second porosity concept of Gologanu et al. (1994). This maintains both the connection with micromechanics and the computational simplicity. The predictive capability of the framework is illustrated by the good agreement with cell model calculations for localization of deformation over a wide range of stress states. Strain localization analyses with an initial porosity imperfection predict that for axisymmetric stress states with a superposed hydrostatic tension, the minimum critical strain for the onset of localization follows the onset of coalescence, as defined within the context of the constitutive model here, if the value of the stress triaxiality is sufficiently small. For an imposed shear stress state with a superposed hydrostatic tension, the minimum critical strain for the onset of localization is predicted to precede the onset of coalescence. A strong sensitivity of the critical strain for localization of deformation to the strain or stress range over which void nucleation occurs is also predicted, with void nucleation and localization of deformation essentially coinciding for sufficiently abrupt nucleation.

Strain localization analysis using digital image correlation for PVA fiber-reinforced concrete-filled FRP tubes under compressive loading

This study presents the outcomes of the first experimental study on the strain localization of polyvinyl alcohol (PVA) fiber-reinforced concrete-filled fiber-reinforced polymer (FRP) tubes (CFFTs). 24 CFFT specimens were prepared and tested with various instrumentations, such as linear variable differential transformer (LVDT) and strain gauges (SGs), to record required full-field strains, i.e., axial, lateral and Von Mises strains. The strain evolutions over the surface of the specimens were recorded during axial compression loading. The FRPs were prepared with carbon, S-glass or basalt fiber to examine the influence of the fiber type and confinement stiffness on the behavior and strain localization of CFFTs. The evolution of Von Mises strains was determined and studied under axial compression. The obtained results show that although the general pattern of localization for both CFFTs without and with PVA fiber is nearly similar, the characteristics of the localization are different. The expansion of shear zone for insufficiently basalt FRP (BFRP)-confined concrete is more localized compared to the more homogenized behavior of sufficiently FRP-confined concrete. However, insufficiently BFRP-confined PVA fiber-reinforced concrete exhibits less localized behavior compared to insufficiently BFRP-confined plain concrete, which is due to the influence of the internal fibers on the concrete cracking behavior. At FRP rupture, hoop strains vary along the height and around the perimeter of the specimens, which results in the inability of SGs to consistently capture the actual hoop rupture strain.

Geotechnical Strain Localization Analysis Based on Micropolar Continuum Theory Considering Evolution of Internal Characteristic Length

Within the framework of second-order cone programming optimized micropolar continuum finite-element method (CosFEM-SOCP), the geotechnical strain localization can be adequately modeled. In most existing literatures, however, the constant internal characteristic length lc has been adopted and less attention has been paid to the evolution of lc. To more accurately predict the strain localization, response, and stability of a geotechnical system, one relationship for evolving lv that relies on the equivalent plastic strain is implemented and investigated. Based on one homogeneous slope example and one rigid strip footing example, it was found that geotechnical stability may not be significantly affected by evolving lv, indicating that constant lc can be simply applied to geotechnical stability analysis. For the rigid strip footing problem, nevertheless, the effects of evolving lv on the pressure–displacement response curves should not be ignored, and the influence range of the shear band predicted by CosFEM-SOCP with evolving lv is generally smaller than that predicted by CosFEM-SOCP with constant lc. Consequently, in order to more accurately predict the pressure–displacement response curves and the failure zone, the evolving lv will be adequately assessed and modeled.

Analytical strain localization analysis of isotropic and anisotropic damage models for quasi-brittle materials

Strain and damage localization are usually precursors of rupture. We present a three-dimensional method dedicated to quasi-brittle materials based on the works of Bigoni & Hueckel, and Jirásek and coworkers, aiming at simplifying the analysis of the localization properties of continuous damage models of a general form, and possibly anisotropic. The method reformulates the localization problem as a two-variable polynomial maximization problem, a strategy commonly used in softening plasticity models, but not so much in Continuum Damage mechanics. The quasi-brittle hypothesis is exploited to render the problem solvable in a fully analytical way, and a post-analysis criterion for the validity of the analysis is also exhibited. In this work, the method is fully established from a theoretical viewpoint, and examples illustrating its use are provided. Multiaxial calculations are performed for four continuous damage models (two isotropic and two anisotropic ones). The method applies to induced anisotropy and constitutive models representing isotropic linear elasticity before damage growth, and remains accurate when models display immediate softening after the elastic limit (and thus to multiaxial tensile cases). The analytical method is, however, entirely general and allows for the calculation of (i) the orientation of a potential localization plane, (ii) the mode angle of the weak discontinuity, and (iii) the validity domain of such a simplified analysis.

Microstructure-based finite element analysis of mesoscale strain localization and macroscopic mechanical properties of aluminum alloy 2024 laser weld joint

The microstructure and residual stress can be modified by laser welding, which significantly affect the strength and ductility of materials. In this work, a microstructure-based finite element model is established to investigate the mesoscale strain localization and the macroscopic mechanical properties of the 2024 aluminum alloy laser weld joint. The residual stress in different welding processes is predicted, and its effect on the elastic-plastic constitutive model of constituent phases is evaluated. The stress-strain curves of α-Al phase and eutectic phase are calculated using instrumented indentation method. Actual microstructure graphs of the joints are used as the representative volume elements in the model. The mesoscale strain distribution, macroscopic deformation response and the damage initiation are predicted quantitatively during uniaxial tensile deformation. The model is validated by comparing with experimental results, i.e., fusion profile, distortion, strain localization bands, tensile test curves, and good agreements are achieved. It is found that the strain and stress in the constituent phases of the fusion zone are extremely inhomogeneous. There are significant strain localization bands in the α-Al phase and high stress concentration zones in the eutectic phase. The dendritic arm spacing and eutectic phase size decrease, and the percent of eutectic increases during high power matching with high welding speed within certain limits. In this case, the bearing capacity of eutectic phase increases, and the strain inhomogeneity decreases. As a result, the strength (358.8 MPa) and ductility (6.21%) of the joint can be increased by the optimized laser power (5 kW) and welding speed (140 mm/s).

Strain localization analysis in materials containing randomly distributed voids: Competition between extension and shear failure modes

Strain localization is often a precursor to the ductile failure of materials. This paper investigates plastic strain localization phenomena in the case of random microstructures, namely cubic cells made of an elastic-perfectly plastic matrix embedding distribution of identical non-overlapping spherical voids. The consideration of random microstructures allows for a better representation of the interaction between voids and greater diversity of failure modes than single-void (or unit) cells. The cells are simulated by means of the finite element (FE) method for proportional stress loading paths with controlled stress triaxiality and Lode parameters. Strain localization is detected by Rice’s criterion computed at the cell level. This criterion is shown to accurately capture the onset of localization and the type of failure mode, either extension or shear banding. Moreover, the influence of the loading orientation, i.e. the orientation of the principal axes of the applied stress tensor with respect to the microstructure cube, is systematically studied. Significant anisotropy of failure behavior is observed, especially in the case of single void unit cells, which can be attributed to the intrinsic anisotropy of the simulation cells. Finally minimal failure strain values at localization with respect to all loading orientations are found. A zone of reduced ductility is observed under generalized shear loading conditions.

Strain localization criteria for viscoplastic geomaterials

AbstractThis work presents a viscoplastic localization criterion to detect quasi‐instantaneous (i.e., load‐induced) and delayed (creep‐induced) strain localization in rate‐dependent solids. The study is based on the theory of controllability and a viscoplastic description of the mechanical response. Analytical precursors of unstable states are defined through systems of ordinary differential equations (OEDs). The use of the proposed criteria is illustrated at the material point level through a set of strain localization analyses simulating active strain localization of a porous rock. In addition, full‐field finite element simulations of compression tests conducted under various pressures are reported to demonstrate the role of local unstable viscoplasticity in the spontaneous propagation of deformation bands under stationary boundary conditions. The study shows that the viscoplastic localization criterion maintains a negative sign as long as the behavior is unstable, that is, the rate of deformation is accelerating. The sign switch coincides with the transition to decelerating deformation. The analyses revealed that pulses of overstress always emerge in correspondence with the growth of unstable behavior, and the peak matches the transition to stable behavior. The local responses recovered from full‐field analyses were consistent with those observed in analyses at material point level and the predictions of the presented theory.

Theoretical and numerical plastic strain localization analysis at plane strain of isotropic dilating non-associated mediaat plane strain conditions

Theoretical and numerical plastic strain localization analysis at plane strain of isotropic dilating non-associated mediaat plane strain conditions

Microstructure-based analysis of residual stress concentration and plastic strain localization followed by fracture in metal-matrix composites

A numerical study is performed to investigate the deformation and fracture in metal matrix – ceramic particle composites using Al6061T6 and ZrC as an example of the compound materials. The step-by-step packing method is adopted for generating three-dimensional model microstructures of metal-matrix composites, with the irregular shape of particles and polycrystalline structure of the matrix being taken into account. The dynamic boundary-value problems are solved by the finite-element method. Constitutive models describing the mechanical behavior of the composite compounds include anisotropic elasticity, crystal plasticity with the strain hardening and strain fracture criterion for the matrix and isotropic elastic-brittle formulation with the stress fracture criterion for particles. A user-defined subroutine is developed to combine the anisotropic matrix and isotropic particle responses and implemented in the finite element calculations of the composite thermomechanical behavior. The interrelated plastic strain localization in the aluminum matrix and crack origination and growth in the matrix and ceramic particle are investigated under compression and tension, including the influence of the cooling-induced residual stresses. A detailed analysis is performed to evaluate the residual stress concentration in local regions of bulk tension formed under all-round and uniaxial compression of the composite due to the concave and convex interfacial asperities.

An adaptive multiscale finite element method for strain localization analysis with the Cosserat continuum theory

Strain localization analysis based on finite element method (FEM) usually requires an intensive computation to capture an accurate shear band and the limit stress, especially in the heterogeneous problems, and thus costs much computational resource and time. This paper proposes an adaptive multiscale FEM (AMsFEM) to improve the computational efficiency of strain localization analysis in heterogeneous solids. In the multiscale analysis, h- and p-adaptive strategies are proposed to update the fine and coarse meshes, respectively. The problem of mesh dependence is handled by the Cosserat continuum theory. In the fine-scale adaptive procedure, triangular elements are taken to discretize the fine-scale domain, and the newest vertex bisection is utilized for refinement based on the gradient of displacement. In the coarse-scale adaptive procedure, a multi-node coarse element technique is considered. By introducing a probability density function for each side of a coarse element, the optimal positions of the newly added coarse nodes can be determined. With the proposed adaptive multiscale procedure, the computational DOFs are reduced smartly and massively. Three representative heterogeneous examples demonstrate that the proposed method can accurately capture shear bands, with an improved computational efficiency and robust convergence.

Crushing of additively manufactured thin-walled metallic lattices: Two-scale strain localization analysis

The response of architectured structures is characterized by multi-scale kinematics, which complex relation and effect on the engineering load response is still not completely understood and therefore needs further investigations. More precisely, the lack of experimental methods enabling to provide multi-scale data remains a key issue. The paper presents an experimental and numerical analysis of crushing tests performed on thin-walled auxetic metallic lattices manufactured by Directed Energy Deposition. The work is focused on the two-scale strain localization occurring (a) at the microscopic scale of the unit cell and (b) at the macroscopic scale corresponding to the homogenized continuum. The structures of interest are defined as the extrusion of a 2D auxetic wireframe and allow the application of an adapted digital image correlation scheme dedicated to the identification of the kinematics at the two considered scales. In particular, the microscopic kinematics are studied by following the deformation of lattice crossings, while the macroscopic strains are deduced from the motion of virtual unit cell corners. The results show that the global elastic-plastic response of the lattices is completely driven by the formation of plastic hinges at specific locations, leading to characteristic deformation patterns and eventually a collective behavior of neighboring unit cells. Companion finite element computations show an excellent match with experiments and thus enable to assess the effect of modeling assumptions, unit cell geometry, strain rate and geometrical imperfections in the global response of the architecture material.