Macroscopic Strain Localization Research Articles

Microstructure and Mechanical Properties of Biomedical Ti-Zr-Nb-Ta-Sn High-Entropy Alloys

Ti(50-x)Zr38NbxTa8Sn4 high-entropy alloys with x = 0, 10, and 20 at.% were produced by vacuum arc melting in a high-purity argon atmosphere. The initial microstructures consisted of equiaxial bcc grains with sizes of 115 ± 30 µm, 250 ± 60 µm, and 280 ± 70 µm for the Ti30Nb20, Ti40Nb10, and Ti50Nb0 alloys, respectively. The Ti30Nb20 and Ti40Nb10 alloys showed untypical mechanical behavior with a short strain-hardening stage followed by a gradual decrease in flow stress after reaching the yield point. Although these two alloys had some inclination toward macroscopic strain localization, their tensile elongation was similar to that obtained in the Ti50Nb0 alloy, which had a more extended stage of uniform deformation. The differences were associated with distinct microstructures observed after deformation to fracture. The formation of dislocation bands and the activation of cross-slip at the microscale, as well as the appearance of kink bands at the mesoscale, can result in plastic instability. In contrast, a lamellar-like microstructure with parallel dislocation bands, such as the one observed in the Ti50Nb0 alloy, can ensure a more stable mechanical behavior. The developed alloys (Ti30Nb20 and Ti40Nb10) have properties that make them highly attractive for biomedical application due to a combination of very high yield strengths (1090 and 930 MPa, respectively), low Young’s moduli (~78 and ~69 GPa, respectively), reasonable ductility, and excellent biocompatibility.

A study of macroscopic plastic strain localization during creep of polycrystalline aluminum

This paper studies the deformation behavior of commercially pure aluminum 1050A during creep tests at room temperature. The plastic flow parameters at the stage of steady-state creep at different stress levels are determined. The kinetics of localized plasticity zones in the creep mode is studied using the digital image correlation method. The stress dependence of the spatial period of plastic strain localization is established.

Mechanical Aspects of Nonhomogeneous Deformation of Aluminum Single Crystals under Compression along [100] and [110] Directions

The deformation behavior of aluminum single crystals subjected to compression along the [100] and [110] directions is numerically examined in terms of crystal plasticity. A constitutive model taking into account slip geometry in face-centered cubic crystals is developed using experimental data for the single-crystal samples with lateral sides coplanar to certain crystal planes. Two sets of calculations are performed using ABAQUS/Explicit to examine the features of plastic strain evolution in perfectly plastic and strain-hardened crystals. Special attention is given to the discussion of mechanical aspects of crystal fragmentation. Several distinct deformation stages are revealed in the calculations. In the first stage, narrow solitary fronts of plastic deformation are alternately formed near the top or bottom surfaces and then propagate towards opposite ends to save the symmetry of the crystal shape. The strain rate within the fronts is an order of magnitude higher than the average strain rate. The first stage lasts longer in the strain-hardened crystals, eventually giving way to an intermediate stage of multiple slips in different crystal parts. Finally, the crystal shape becomes asymmetrical, but no pronounced macroscopic strain localization has been revealed at any deformation stage. The second stage in perfectly plastic crystals relates to abrupt strain localization within a through-thickness band-shaped region, accompanied by macroscale crystal fragmentation. Stress analysis has shown that pure compression took place only in the first deformation stage. Once the crystal shape has lost its symmetry, the compressive stress in some regions progressively decreases to zero and eventually turns tensile.

Studying Deformation Behaviors in Austenitic Stainless Steels within a Temperature Range of 143 K < T < 420 K

This work deals with studying staging and macroscopic strain localization in austenitic stainless steel 12Kh18N9T within a temperature range of 143 K < T < 420 K. The visualization and evolution of macroscopic localized plastic deformation bands at different stages of work hardening were carried out by the method of the double-exposure speckle photography (DESP), which allows registering displacement fields with a high accuracy by tracing changes on the surface of the material under study and then comparing the specklograms recorded during uniaxial tension. The shape of the tensile curves σ(ε) undergoes a significant change with a decreasing temperature due to the γ-α'-phase transformation induced by plastic deformation. The processing of the deformation curves of the steel samples made it possible to distinguish the following stages of strain hardening, i.e. the stage of linear hardening and jerky flow stage. A comparative analysis of the design diagrams (with the introduction of additional parameters of the Ludwigson equation) and experimental diagrams of tension of steel 12Kh18N9T for different temperatures is carried out. The analysis of local strains distributions showed that at the stage of linear work hardening, a mobile system of plastic strain localization centers is observed. The temperature dependence of the parameters of plastic deformation localization at the stages of linear work hardening has been established. Unlike the linear hardening, the jerky flow possesses the propagation of single plastic strain fronts that occur one after another through the sample due to the γ-α' phase transition and the Portevin-Le Chatelier effect. It was found that at the jerky flow stage, which is the final stage before the destruction of the sample, the centers of deformation localization do not merge, leading to the neck formation.

Kinetics of Plastic Deformation Localization Bands in Polycrystalline Nickel

Jerky flow has recently aroused interest as an example of complex spatiotemporal dynamics resulting from the collective behavior of defects in Al- and Mg-based alloys under loading. This paper presents the results of the study of the macroscopic strain localization kinetics in Nickel 200 (99.5 wt % purity). Uniaxial tension of flat samples is monitored at room temperature in the load–unload mode at a constant strain rate and total deformation increment up to 5%. The stress–strain curves reveal jerky flow from the yield point to the formation of the neck. The digital speckle correlation method evidences the movement of localized plastic deformation bands under the conditions of the Portevin–Le Chatelier effect (PLC). It is shown that stress drops during jerky flow in Ni are accompanied by the formation of morphologically simple single PLC bands. It is established that, with an increase in total deformation, the number of PLC bands and their velocity of motion along the sample decrease, while their time period increases. Moreover, an increase in total deformation leads to an increase in the parameters of the force response (i.e., time period and stress drop magnitude). It is found that the criterion of damage for PLC bands as a function of the total strain has a sigmoidal shape.

Localization and coalescence of imperfect planar FCC truss lattice metamaterials under multiaxial loadings

This study investigates the effect of stress triaxiality on the failure mechanisms of an-isotropic perfect and imperfect planar FCC (Face Centred Cubic) truss lattice metamaterials. Three types of imperfection have been considered in the numerical modelling, namely, distorted struts, missing struts, and strut diameter variation. In order to maintain constant stress triaxiality during the simulations, a novel numerical framework was developed to overcome computational difficulties within the existing numerical approaches beyond elastic region. Three modes of microscopic localization were observed in perfect and imperfect lattices before failure: crushing band, shear band and void coalescence. A clear separation exists between the three modes of localization depending upon the type and level of defects, as well as the stress triaxiality. Under compressive loading, all lattices fail owing to crushing band; the distorted lattices are prone to shear band localization with increase in distortion, whereas missing lattices majorly fail due to void coalescence at high missing struts defect. Strut diameter variation, within the range of the strut diameters selected, shows no significant influence on the macroscopic mechanical response and strain localization. This work may open the door for predicting failure mechanisms of imperfect lattices under variety of loading conditions.

Millisecond dynamics of deformation bands during discontinuous creep in an AlMg polycrystal

Formation of bands of macroscopic strain localization during staircase creep in an AlMg polycrystal is studied by the acoustic emission (AE) technique and high-speed video recording with an image acquisition rate up to 50 000 frames per second. The simultaneous measurements by two methods allow us to distinguish different types of embryo deformation bands and concomitant AE signals, and to establish correlations between the band evolution and the acoustic response. It is found that the fastest stages of band formation, associated with its emergence to the surface and subsequent accelerated expansion, generate complex AE bursts in the frequency band ∼0.05-1 MHz. The correlations hidden in the complex structure of an individual acoustic burst are investigated by methods of statistical and fractal analysis. On the other hand, relationships between average parameters of various physical responses to discontinuous creep are assessed. Particularly, a close correspondence is found between the envelope of the acoustic burst and the rate of stress change during formation of a single deformation band. Evolution of dynamical behavior of embryo bands with increasing creep stress is discussed. Notably, a qualitative change in the AE waveform observed on approaching the ultimate stress is considered from the viewpoint of anticipation of the oncoming fracture.

A Numerical Study of Strain-Rate and Triaxiality Effects in Magnesium Alloys

We report a preliminary computational study of the rate-dependent behavior of a polycrystal magnesium alloy under varying levels of stress triaxiality conditions. Smooth and notched round bar specimens with a strong initial texture are considered to achieve different levels of stress triaxiality. Full three-dimensional crystal plasticity simulations are conducted, which mimic tensile Kolsky bar experiments. The results indicate that the material rate sensitivity couples with the stress state to produce qualitatively different macroscopic responses that are governed by the interacting microscale deformation mechanisms. While the smooth specimens show macroscopic strain localization resulting in stress softening immediately following the initial yield, notched bars exhibit increasingly stable responses with increasing notch acuity. Deformation anisotropy is tempered with increasing stress triaxiality and strain rate. A micromechanical analysis of the deformation activities is presented to explain the macroscale responses. Stress triaxiality distributions in the notch regions provide insights into probable damage mechanisms as a function of the imposed strain rate.

Investigation of the competition between void coalescence and macroscopic strain localization using the periodic homogenization multiscale scheme

In most voided metallic materials, the failure process is often driven by the competition between the phenomena of void coalescence and plastic strain localization. This paper proposes a new numerical approach that allows an accurate description of such a competition. Within this strategy, the ductile solid is assumed to be made of an arrangement of periodic voided unit cells. Each unit cell, assumed to be representative of the voided material, may be regarded as a heterogeneous medium composed of two main phases: a central primary void surrounded by a metal matrix, which can itself be assumed to be voided. The mechanical behavior of the unit cell is then modeled by the periodic homogenization multiscale scheme. To predict the occurrence of void coalescence and macroscopic strain localization, the above multiscale scheme is coupled with several relevant criteria and indicators (among which the bifurcation approach and an energy-based coalescence criterion). The proposed approach is used for examining the occurrence of failure under two loading configurations: loadings under proportional stressing (classically used in unit cell computations to study the effect of stress state on void growth and coalescence), and loadings under proportional in-plane strain paths (traditionally used for predicting forming limit diagrams). It turns out from these numerical investigations that macroscopic strain localization acts as precursor to void coalescence when the unit cell is proportionally stressed. However, for loadings under proportional in-plane strain paths, only macroscopic strain localization may occur, while void coalescence is not possible. Meanwhile, the relations between the two configurations of loading are carefully explained within these two failure mechanisms. An interesting feature of the proposed numerical strategy is that it is flexible enough to be applied for a wide range of void shapes, void distributions, and matrix mechanical behavior. To illustrate the broad applicability potential of the approach, the effect of secondary voids on the occurrence of macroscopic strain localization is investigated. The results of this analysis reveal that the presence of secondary voids promotes the occurrence of macroscopic strain localization, especially for positive strain-path ratios.

Study on the plastic anisotropy of advanced high strength steel sheet: Experiments and microstructure-based crystal plasticity modeling

For their versatile microstructure controlling techniques, advanced high strength steels (AHSSs) show great potential to be tailored for various application scenarios. The unique microstructure of AHSSs renders their complex plasticity behaviors and mechanical properties. In this work, uniaxial tensile tests combined with a 3D digital image correlation system were carried out to capture the mechanical anisotropy evolution of a cold-rolled dual-phase AHSS (DP980) sheet. In contrast to the conventional body centered cubic (BCC) steel sheets, the studied DP980 sheet shows much smaller Lankford coefficients and a mild strength anisotropy. The Lankford coefficients depend significantly on tensile directions and vary obviously with deformation; they increase with deformation first and then decrease after macroscopic strain localization takes place. Postmortem experimental characterizations as well as microstructure based full-field crystal plasticity simulations were employed to uncover the underneath mechanisms. Plasticity heterogeneities and micromechanical interactions between the soft ferrite matrix and hard martensite islands primarily account for the mechanical anisotropy of the studied steel sheet.

Ductile failure as a constitutive instability in porous plastic solids

A criterion for ductile rupture is derived using Rice’s theory for macroscopic strain localization, and a constitutive relation for porous plastic solids that accounts for inhomogeneous yielding at the mesoscale. At the microscopic scale, it is assumed that failure occurs by void coalescence along a band of voids. An approximate, parameter-free closed form expression for the failure criterion is derived as a function of a single scalar damage variable –the porosity– and the macroscopic stress state, characterized by the stress triaxiality and Lode parameters. For practical applications, an uncoupled approach is developed whereby the failure criterion is supplemented with a damage-free plasticity model and a loading path dependent damage evolution law. The predictive capabilities of the approach are illustrated by comparisons with finite element cell model studies. In particular, the influence of strain hardening is investigated in some detail.

Influence of strain rate sensitivity on localization and void coalescence

The onset of macroscopic strain localization limits the ductility of many ductile materials. For porous ductile materials, two distinct mechanisms of macroscopic localization have been identified: void growth induced softening and void coalescence. In this work we focus on analyzing the influence of material's strain rate sensitivity (SRS) on the two mechanisms of macroscopic localization or ductile failure as a function of the imposed stress triaxiality. To this end, three dimensional finite element calculations of unit cells have been carried out to model void growth and coalescence in an infinite block containing a periodic distribution of initially spherical voids in a band. The matrix material of the unit cell is considered to follow a strain rate dependent elastic perfectly plastic flow response. The unit cell calculations are carried out for a range of SRS parameter, imposed stress triaxiality and initial orientations of the voided band. Our results show that both the critical porosity and strain at the onset of localization and coalescence are strongly influenced by the SRS parameter and the imposed stress triaxiality values. Furthermore, the relative effect of the SRS parameter is found to increases with the increasing value of the imposed stress triaxiality.

Void-sheet analysis on macroscopic strain localization and void coalescence

An operational definition for the onset of macroscopic strain localization is established through the localization analysis on the overall response of a unit cell in a void-sheet. The constitutive relations are obtained from the homogenization of a representative volume element, which is taken to be a void-containing unit cell characterizing a void-sheet in a ductile solid. The unit cell is subjected to three macroscopic normal stresses and one macroscopic shear stress and is proportionally stressed under a maximum reduced shear stress condition. Together with the definition for the onset of void coalescence established previously, it is shown that the two onsets are distinct and separate, with the strain localization being a precursor to void coalescence. It is also shown that for Lode parameter −1≤L≤1, the difference between the effective strains for the onsets of strain localization and void coalescence decreases as stress triaxiality T increases, suggesting that both onsets may occur simultaneously for sufficiently large T. This difference in the effective strains are found to be large for moderate to lower T and in the range between generalized compression (L=−1) and generalized shear (L=0). For the range of T and L considered, there exists three scenarios involving strain localization and void coalescence: (1) both strain localization and void coalescence are possible, (2) strain localization is possible but void coalescence is not possible, and (3) both strain localization and void coalescence are not possible. The effects of orientation of the void-sheet on the onset of macroscopic strain localization are also investigated.

Microstructure-based modeling of tensile deformation of a friction stir welded AZ31 Mg alloy

The deformation and fracture behaviors of friction stir welded (FSWed) Mg alloys are topics under investigation. The microstructure and texture of a FSWed Mg alloy were characterized by electron back scattered diffraction. Four characteristic sub-zones with different orientations in the FSWed Mg alloy joint were identified. The texture distribution across the stir zones and transition zone were obviously inhomogeneous. For comparison, four sub-regions in the base material were also characterized. Based on the experimental microstructure and texture, a crystal plasticity finite element model was developed to represent the friction stir welded Mg alloy. Simulations were carried out to study the effect of texture variation on the deformation behaviors during transverse tension. Compared with the base material case, strong macroscopic strain localization was observed for the FSWed joint case after transverse tension. Strain localization may have contributed to the decayed elongation of the FSWed joint in the transverse tension. Texture variation in the thermal-mechanical affected zone did not change the deformation mechanism in the stir zones, while it did decrease the strain localization, thus assuming to improve the elongation of the friction stir welded Mg alloy.

Three dimensional simulations of texture and triaxiality effects on the plasticity of magnesium alloys

We investigate the synergistic effects of texture and intrinsic plastic anisotropy (at the level of single crystal) on the deformation of polycrystalline magnesium using three-dimensional crystal plasticity finite element simulations. Using rolled plate texture as a basis, we simulate the deformation using a range of synthetic textures. Smooth and notched round bar specimens are considered to achieve different levels of stress triaxiality. Two sets of constituent single crystal properties, representative of an Mg alloy and pure Mg respectively, are adopted in order to investigate the role of intrinsic plastic anisotropy. Our results reveal that textural variations couple into the intrinsic plastic anisotropy and triaxiality to determine the active deformation mechanisms. When loaded along the rolling direction of the plate, the deformation is accommodated by prismatic slip at low triaxiality and pyramidal 〈c+a〉 slip at high triaxiality. Softer mechanisms such as basal slip and extension twinning, which are not favored by the loading orientation, are activated due to the intergranular stresses. The smooth specimens show macroscopic strain localization the onset of which depends on initial texture. The deformed textures are strongly modulated by both triaxiality and intrinsic plastic anisotropy. We also briefly discuss the potential role of twinning in damage evolution.

Texture-dependent character of strain heterogeneity in Magnesium AZ31 under reversed loading

Depending on operational micromechanisms and crystallographic texture, the innate strain localization at microstructural length scales of a polycrystal can spatially coordinate to induce macroscopic strain localization. A challenge for material performance and modeling, this behavior is observed in wrought Magnesium alloys when they deform with heavy tensile twinning. With in-situ, multi-surface image correlation, a compression-tension experiment is implemented on samples with extrusion and rolling texture that have a consistent 11µm grain size. While samples of both textures exhibit a clear twin plateau with close stress levels (90/99MPa for rolled/extruded samples), the strain localization patterns are vastly different, both in terms of geometric structure and intensity. Rolled sample exhibits sharp shear banding structures with a fixed plane of shear. Extruded sample exhibits strain localization that is not in macroscopic ±45° shear form and much weaker in intensity (by about a factor of 2). Once the load is reversed and the tensile twin is deactivated, strain accommodation largely homogenizes for both textures during detwinning and subsequent high hardening stages.

Mechanical Properties of Ultrafine‐Grained Metals: New Challenges and Perspectives

Investigations of the behavior of ultrafine‐grained (UFG) materials manufactured by severe plastic deformation (SPD) have been greatly motivated by the expectations that they may have unique properties as well as by the desire to understand the fundamental mechanisms underlying the specific properties associated with extreme grain refinement. Although the concurrent improvement of both strength and ductility is possible via SPD, the most commonly observed high strength of UFG materials is paired with a very limited uniform elongation. Based on the dislocation kinetics and its relation with the Considère instability, an attempt is made to provide a unified view for the hardening behaviour and early macroscopic strain localization.

Hydrogen-induced Modification in the Deformation and Fracture of a Precipitation-hardened Fe–Ni Based Austenitic Alloy

Hydrogen-induced modification in the deformation and fracture of a precipitation-hardened Fe–Ni based austenitic alloy has been investigated in the present study by means of thermal hydrogen charging experiment, tensile tests, scanning electron microscopy (SEM) and transmission electron microscopy (TEM). It is found that the γ′ particles are subjected to the multiple shearing by dislocations during plastic deformation, which promotes the occurrence of the dislocation planar slip. Moreover, the alloy will be enhanced by hydrogen resulting in the formation of strain localization at macroscale. So, the mechanisms of deformation and fracture in the alloy have been proposed in terms of serious hydrogen-induced planar slip at microscale which can lead to macroscopic strain localization.

Anisotropic finite-strain models for porous viscoplastic materials with microstructure evolution

In this work, we propose a constitutive model for the finite-strain, macroscopic response of porous viscoplastic solids, accounting for deformation-induced changes in the size, shape and distribution of the voids. The model makes use of consistent homogenization estimates obtained by the “iterated variational linear comparison” procedure of Agoras and Ponte Castañeda (2013) to characterize both the instantaneous effective response of the porous material and the evolution of the underlying microstructure. The proposed model applies for general, three-dimensional loading conditions and can be implemented numerically for use in standard FEM codes. We also investigate the interplay between the evolution of the microstructure and the macroscopic stress–strain response, in the context of displacement-controlled, plane strain loading (bi-axial straining) of initially isotropic, porous, rigid-plastic materials with power-law hardening. We focus on the effect of strain triaxiality, and consider both extensional and contractile loading conditions leading to porosity growth and collapse, respectively. For both types of loadings, it is found that the macroscopic behavior of the material exhibits an initial hardening regime followed by a softening regime at sufficiently large strains. Consistent with earlier models and experimental results, the softening regime for extensional loadings is a consequence of porosity growth. On the other hand, the softening behavior predicted for contractile loadings is found to be a consequence of void collapse, i.e., of rapid changes in the average shape of the pores leading to crack-like shapes. For both types of loadings, the transition from hardening to softening in the macroscopic response can be identified with the onset of macroscopic strain localization. The associated critical conditions at the onset of localization are determined as a function of the strain triaxiality. The type of localization band ranges from dilatational to compaction bands as the bi-axial straining varies from uniaxial extension to uniaxial contraction.

Modeling of macroscopic strain localization in alloys with the L12 structure

Results of mathematical modeling of plastic strain superlocalization are presented with allowance for dislocation redistribution into dislocation walls. The model based on the concept of hardening and rest is used to construct equations describing kinetics of dislocations and substructure transformations. It is demonstrated that depending on the scenario of the strain model evolution in the microvolume of a deformable body, different types of localization are possible under the influence of stress concentrators.