Strain Localization Bands Research Articles

Numerical investigation of the couplings between strain localisation processes and gas migrations in clay materials

Deep geological repository is the preferred solution in many countries to manage radioactive wastes, such as in France where the Callovo-Oxfordian (COx) claystone is the candidate host rock. In such clay rock formation, the drilling of storage gallery creates an Excavation Damaged Zone (EDZ) with altered flow properties in the short term, while corrosion processes release large amounts of gas in the long term. Assessing the evolution of gas pressures in the near-field and predicting the effect of the EDZ on gas transport remains a major issue. This paper presents a second gradient two-phase flow hydro-mechanical (H2M) model tackling the multi-physics couplings related to gas transfers and fractures development. The EDZ is reproduced by shear strain localisation bands using a microstructure enriched model with a second gradient approach. The gas migration is captured by a biphasic fluid transfer model. The impact of fracturing on the flow properties is addressed by relating the permeability and the water retention curve to mechanical strains. Using this tool, numerical modelling of a drift in the COx claystone is performed with the aim of emphasising the influence of the HM couplings on gas migrations at nuclear waste disposal scale.

Strain localization in titanium investigated via in situ digital image correlation with multiscale speckles

Strain localization in commercially pure titanium under uniaxial tension is investigated with in situ digital image correlation (DIC) at different length scales. Speckles in three different sizes are prepared on the surface of titanium specimens, referred to as microscale, mesoscale and macroscale speckles. The microscale and mesoscale speckles for scanning electron microscopy DIC analysis are fabricated by different electro-polishing procedures, and spray painting is used to prepare the macroscale speckles for the optical DIC measurement. Electron back scattering diffraction (EBSD) characterization is conducted for the microscale speckle case. The strain fields obtained at different length scales combined with the microscale EBSD examination establish the relationship between microscale strain localization and macroscale strain concentration bands. Strain localization tends to form at grain boundaries and inside deformation twins, especially at the large-angle grain boundaries, and the amplitude and rate of strain accumulation at grain boundaries are higher than inside deformation twins. The microscale strain-localized regions dispersed at grain boundaries and within deformation twins present themselves as the strain concentration bands observed with the macroscale speckles, and both the strain localization regions and strain concentration bands are at ±45 ∘ with the tensile direction. • Speckles in three different sizes are fabricated by electro-polishing and spray painting. • Digital image correlation measurements over a wide length scales are achieved. • Microscale scattered strain-localized regions present themselves as strain concentration bands on macroscale. • Strain localization tends to form at the large-angle grain boundaries. • Amplitude and rate of strain accumulation at grain boundaries are higher than inside twins.

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).

Improved virtual extensometer measurement method in complex multi-fracture situation

To overcome the limitation of the virtual extensometer method in measuring the crack opening displacement (COD) in the process of complex multi-crack propagation of rock, the measurement error of Digital Image Correlation (DIC) local deformation is theoretically analyzed. An improved virtual extensometer method for measuring the COD is proposed, which considers the temporal and spatial characteristics of crack development in the process of complex crack propagation. The accuracy of the proposed method is verified by the strain localization band numerical simulation test and indoor single crack simulation test. Furthermore, the method is applied to the two-dimensional similarity simulation test of simulating complex multi-fractures in rock stratum. The COD obtained by the traditional and improved methods is compared with the measured COD. The results show that in the case of multiple complex cracks, to obtain the COD accurately, the relative distance between the virtual extensometer measuring point and the crack should be greater than half of the sum of the width of the crack strain localization zone and the subset size. With the development of the crack, the relative distance between the virtual extensometer measuring point and the crack should increase with the increase of the width of the crack strain localization zone. The error of the COD measured by the traditional method increases with fracture development, and the maximum is 21.20%. The maximum relative error between the COD measured by the improved method and the measured crack opening is 3.61%. The research results improve the accuracy of the virtual extensometer in measuring the COD under complex multi-crack conditions.

Analysis of Failure Mechanics and Energy Evolution of Sandstone Under Uniaxial Loading Based on DIC Technology

Energy evolution process of rock deformation is conducive to essentially reveal the rock failure mechanism and is of great significance to uncover the breeding of dynamic disasters in rock engineering. To characterize the damage evolution of energy dissipation during rock failure, the digital image correlation (DIC) technique is proposed to describe the rock failure mechanics and its energy evolution process. The uniaxial compression experiment of sandstone specimen was carried out, and the whole field deformation and failure characteristics of the rock had been captured by the DIC system. Measurement accuracy was verified by the fiber Bragg grating (FBG) sensor, the elastic region of the specimen was divided according to the location of strain localization band (SLB), and the evolution process of elastic strain energy of the rock was analyzed. The results show that the time history development of rock strain obtained by the FBG and DIC system matches identically, and the deviation of peak axial strain of both means is less than 5%, which verifies the applicability of DIC system. The uncoordinated evolution of rock deformation displacement field is discussed to reveal the crack development and failure form of the sandstone specimen under uniaxial compression. The energy evolution of the elastic region of the specimen is revealed, and the development of releasable elastic strain energy would be divided into three stages, which correspond to the stress–strain characteristics of rock failure mechanics. This study could provide an alternative analytical method for the experimental rock mechanics research studies.

Non‐parametric stress field estimation for history‐dependent materials: Application to ductile material exhibiting Piobert–Lüders localization bands

AbstractEstimating stress in statically undetermined tests remains an issue in experimental mechanics. Most estimation methods rely on the a priori choice of a behaviour equation leading to an unavoidable model bias. Recently, efforts have been made to propose methods circumventing the parametric description of constitutive behaviours. In particular, Leygue et al. (2018) proposed a new paradigm called data‐driven identification (DDI). An extension of Leygue's method to history‐dependent materials is proposed in this paper. The formulation of the problem and its resolution are presented with emphasis on boundary conditions. The method is tested on real experimental data where the elasto‐plastic material is subjected to the formation of Piobert–Lüders bands. We finally show that the DDI allows to obtain balanced fields that are closer (more consistent) to the field measurements than the fields obtained by parametric identification strategies, even more in the presence of strain localization bands whose kinematics are usually not described by a standard constitutive model.

In-situ investigation of plasticity in a Ti-Al-V-Fe (α+β) alloy: Slip mechanisms, strain localization, and partitioning

As one of the representative characteristics of plastic deformation, microstructural plastic strain inhomogeneity has triggered a broad interest in uncovering the corresponding deformation micro-mechanisms. (α+β) titanium alloys enable fruitful mechanistic explorations of this dependency, since: (i) the plastic anisotropy of the α-phase drives distinctive dislocation gliding and/or mechanical twinning modes for plastic strain accommodation; and (ii) deformation transferability between α/β phase boundaries strongly relies on both microstructural and structural parameters. The present work carried out in a Ti-Al-V-Fe (α+β) alloy is an in-situ mechanistic study, aiming to elucidate the critical deformation micro-mechanisms that are responsible for strain localization, partitioning, as well as damage inception processes. It is revealed through statistical analysis of the in-situ strain mapping results that a moderate partitioning trend exists between α- and β-phases, and that the present alloy is characterized by the eminent strain localization bands that develop at the early stage of plastic straining. Deformation micro-mechanisms including texture-facilitated prismatic 〈a〉 slip activation together with the near-ideal slip transfer conditions across the α/β phase boundaries are found to be predominant in the strain localization regions. The combination of postmortem and in-situ damage analyses confirm the dominant role of these long-range strain localization bands in expediting surface cracking events.

Пластическая деформация титанового сплава ВТ6 в сложном напряженном состоянии при высокоскоростном растяжении

The article presents the results of a studies on mechanical behavior of titanium alloy Ti-6Al-4V (Ti Grade 5) in the range of strain rates from 0.1 to 103 s−1. Tensile tests were carried out on flat and notched specimens using the Instron VHS 40/50-20 servo-hydraulic testing machine. High-speed video recording was carried out with a Phantom 711 Camera. The strain fields in the measuring area of the sample were investigated by the Digital Image Correlation (DIC) method. Analysis of the deformation fields of Ti-6Al-4V specimens under uniaxial tension at high strain rates revealed the presence of stationary localized shear bands at the initial stages of strain hardening. The evolution of the deformation fields in the studied loading regime indicates that in the localization bands the plastic strain is significantly higher than the average values in the gage zone of the specimen. It was found that the value of strain before fracture of the Ti-6Al-4V alloy in the zone of strain localization increases with the tension strain rate. The fracture of the titanium alloy is a result of cracks formation in the zone of plastic strain localization bands oriented along the surface of the action of the maximum shear stresses. The results obtained confirm the ductile nature of fracture of Ti-6Al-4V at strain rates from 0.1 to 103 s−1, at the triaxiality stress parameter 0.33 < η < 0.44, and at an initial temperature of 295 K. At the same time, Ti-6Al-4V alloy demonstrates a tendency to embrittlement with an increase in the triaxiality stress parameter to 0.497 at the same loading condition.

Strain localization bands in fine-grained aggregates of germanate olivine and pyroxene deformed by a Griggs type apparatus

Strain localization bands are often observed in natural and experimentally deformed porous rocks in stress state of the transitional regime, from brittle faulting to cataclastic (or ductile) flow. The rock samples used in most of the previous studies were natural porous coarse sandstones. Meanwhile, fine-grained aggregates originating from powders were used as an initial sample for high-pressure coaxial deformation experiments. Generally, compaction for sintering these aggregates were performed before the experiments. No coaxial experiments have been performed the compaction of the powder under high pressure and low temperature during experiments (cold pressing). This stress state during sintering is close to the transitional regime from brittle faulting to cataclastic flow, hence, there is a possibility that compaction bands which are a type of strain localization bands may form at the cold-pressing stage of deformation in laboratory experiments. We conducted cold pressing experiments on the powder of fine-grained germanate olivine and pyroxene with approximately 30% porosity using a Griggs type apparatus. The experiments reveal that compaction bands form in the compacted and sintered sample. Microstructural analysis revealed that grains with a high dislocation density rotate and crush with shear strain concentration during compaction. At the end of the compaction, the grain size becomes small and bands are made of fine-grained material.

Influence of soil non-homogeneity on shear band evolution investigated by the numerical manifold method combined with the assumed enhanced strain method

The assumed enhanced strain (AES) method has been successfully used to deal with the strain localization or shear band problems. With AES treating the localization deformation as strong discontinuity in displacement field, the structural phenomenon and the associated strength loss manifested in strain localization could be reflected in a way independent of mesh density and alignment. On the other hand, the numerical manifold method (NMM) excels at dealing with non-homogeneity and discontinuity problems because of the two sets of covers. By combining the NMM with the AES method, this paper could investigate the influence of soil non-homogeneity on shear band evolution naturally and mesh independently. The Gauss Seidel projection contraction (GSPC) method is invoked because it is simple and efficient in tackling the integration difficulties induced by cutting the tensile part of the Drucker Prager (DP) model. Finally, this paper studies the influences of erratic boulders and weak soil layer on the evolution of shear band in the slope.

Strain localization under impulse load

Unknown characteristics of the strain localization process are determined by the study of the structure of localized strain bands and adjacent matrix metal. Interference of oncoming waves (compression and unloading) reflected from the sample faces are shown to induce oscillations of the sample in the standing wave mode at the nodes of which the localized strain bands (precursors of damage) arise. Strain localization is accompanied by the formation of a flow of particles (interstitial and substitution atoms, fine particles of the doping phase, and impurities), which migrate from the matrix to the zone of spall damage. The main property of a standing wave, namely, capability of preventing energy exchange through the nodal points, provides a long-term sample deformation after the shock wave front passed. The distance passed by the particles under impulse load exceeds the drift of particles under quasi-static load by several orders of magnitude.

Characterization of mechanical properties and deformation behavior of highly irradiated 316L stainless steel from target modules at the Spallation Neutron Source using digital image correlation analysis

Tensile specimens with irradiation doses ranging from approximately 0.7 to 7.6 displacements per atom (dpa) were fabricated from 316L samples removed from Spallation Neutron Source (SNS) target vessels after service. Tensile tests were performed in conjunction with digital image correlation (DIC) characterization, which permitted detailed analysis of the strain distribution and deformation behavior of the specimen gauge sections during testing. The results show, while considerable hardening (500–700 MPa increase in yield strength) occurred in the 316L SNS target material with increasing dose, appreciable ductility (19–23% total elongation) remained in the material after irradiation to 7.6 dpa in the mixed neutron/proton environment of the SNS target region. The DIC data showed the strain distribution and deformation behavior of all irradiated specimens were nonuniform during testing. Strain localization in the form of deformation bands or “hotspots” was observed during testing, and in some specimens, the bands propagated as deformation waves along the gauge section. The “traveling wave” deformation behavior affected the amount of elongation each specimen achieved, and the scatter in the elongation data was attributed to the large variation in deformation behavior observed among different specimens. Bands of localized strain, or deformation bands, oriented at specific angles were observed in two-dimensional plots of the strain distribution in the gauge sections of some specimens. This paper describes the experimental procedures, results, and deformation behavior of tensile specimens from SNS targets after service and illustrates the value of DIC characterization during tensile testing of irradiated materials.

Cohesive GTN model for ductile fracture simulation

The present work addresses the micromechanical modeling and the simulation of crack initiation and propagation in ductile materials failing by void nucleation, growth and coalescence. A cohesive–volumetric approach is used and the overall material behavior is characterized both by a hardening bulk constitutive law and a softening surface traction–separation law embedded between each mesh of a finite element discretization. The traction–separation law sums up across a surface all the ductile damage processes occurring in a narrow strain localization band, while the bulk behavior concerns the other elasto-plastic effects. The proposed cohesive zone model is based on a micromechanical approach where the Gurson–Tvergaard–Needleman ductile damage model is adapted to the reduced kinematics of a surface while ensuring the complete effect of the strain rate or stress triaxiality both on the local plasticity and on the void growth. The corresponding cohesive model is implemented in the XPER computer code using the Non-Smooth Contact Dynamics method where cohesive models are introduced as mixed boundary conditions between each volumetric finite element. The present approach is applied to the simulation of crack growth in a standard ferritic steel. Results are compared with available experimental data. The efficiency of the proposed cohesive-GTN model is underlined since the shape of the cohesive law and its mechanical parameters arise directly from the micromechanical approach without any ad hoc fitting parameter.

FEATURES STRAIN LOCALISATION UNDER IMPACT LOADS

The localization of plastic strain under impulse loads is determined by the sample geometry and is practically independent on the material properties. Deformation bands are a consequence of ultrasonic oscillations, which occurs when waves are reflected (compression and unloading) on the sample faces, and when the reflected waves interact with each other, and flows in the form of standing waves. Localized strain bands originate and develop at the nodes of standing waves under conditions of alternating deformation and are accompanied by mass transfer of particles from the matrix material (interstitial and substitutional atoms, impurity atoms, ultrafine particles of the hardening phase) to the sites of spall damage. The absence of energy transfer through the nodal points of the standing wave increases the duration of the sample deformation after the passage of the shock wave.

On the Localization of Plastic Strain in Microtextured Regions of Ti-6Al-4V

The equiaxed microstructure of Ti-6Al-4V contains nominally 10µm to 15µm α-phase grains. Depending on processing, these fine grains may aggregate into large, millimeter-scale regions of similar crystallographic orientation. These so-called microtextured regions are detrimental to quasi-static and fatigue properties. Their presence may facilitate the formation of long-range strain localization—bands of plastic strain that traverse grain boundaries and terminate at the boundaries of the microtextured region which compromises strength and ductility—and can cause early fatigue crack nucleation. Furthermore, the low angle boundaries within microtextured regions offer little resistance to crack growth, and corresponding increases in crack growth rates have been observed in these regions. Despite significant research into the effects of microtextured regions on macroscopic properties, there is still a lack of rigorous definition of what constitutes a microtextured region. To this end, we present a computational study in which deformation simulations are performed to study the effect of the intensity and character of microtexture on the localization of plastic strain. Mean orientation and intensity of microtexture are parameterized in a suite of simulations. Simulations indicate that strain localization is facilitated both by the presence of some amount of orientation spread within a microtextured region, and further by the intensity of microtexture in neighboring regions. Simulations are further discussed with respect to high resolution experimental measurements of intragrain strain in a microtextured Ti-6Al-4V specimen, which exhibit similar mechanical trends.

Effect of Lüders and Portevin–Le Chatelier localization bands on plasticity and fracture of notched steel specimens studied by DIC and FE simulations

The impact of the Portevin–Le Chatelier (PLC) effect on plasticity and fracture ahead of a severe notch is investigated by DIC field measurements for C–Mn steel. The PLC effect causes an intermittent activity of highly localized strain rate bands. This first high temperature investigation of the effect of a notch on the PLC localization bands is successfully reproduced numerically in terms of strain localization in 3D FE simulations. This thereby validates quantitatively the McCormick-type model under these complex conditions. It is found that, when the PLC effect is at play at elevated temperature (175°C), a flat to slant crack transition is observed. In contrast, at room temperature, when only Lüders bands are active, the crack remains mostly flat, i.e. normal to the loading direction of the SENT samples. This behaviour may be related to the early loss of symmetry and intermittency of the plastic zone that is found for PLC even affecting the initial Lüders bands at elevated temperature. During the slant fracture at high temperature, only half the fracture energy is absorbed compared to flat fracture at room temperature. The McCormick-type model simulations predict slant strain rate bands through the sample thickness, that are consistent with the slant fracture found at elevated temperature. Accordingly, no slant bands are found for simulations outside the PLC domain. Both experiments and simulations show PLC strain localization bands that are flip-flopping up and down during crack propagation. By combining the McCormick-type model with a Rousselier porous plasticity model, the flat fracture of the sample at room temperature and the associated macroscopic curve are reproduced successfully, but the toughness at elevated temperature is overestimated.

The Influence of Phase Composition and Phase Distribution on Crack Formation and Fracture Mechanisms of Cr–Ni Steels Produced by the Method of 3D Electron-Beam Printing

The features of crack formation near the fracture region and the fracture micromechanism are investigated during uniaxial tension of specimens of Ni–Cr stainless steels, Fe–19Cr–9Ni–0.1C and Fe–19Cr–9Ni–1.4Nb–0.1C, produced by the method of 3D wire-feed electron beam additive manufacturing (EBAM) as a function of the phase composition and phase distribution in the structure. It is found out that in the specimens with a twophase (austenite/δ-ferrite) microstructure the ferrite morphology and its volume content (up 25%) affect the plastic shear distribution in austenite and ferrite and exert a slight influence on the formation of strain localization micro- and macrobands in the pre-fracture stage, and the crack-formation mechanism is similar to that observed in cast stainless steels of similar compositions, which possess single-phase austenitic structure. In additively-manufactured steel containing niobium the formation of brittle niobium- and iron-based intermetallic phases favors the formation of pores and microcracks at the austenite/NbFeCrNi-phase or the δ- ferrite/NbFeCrNi-phase interfaces, while the processes of cracking in the strain localization bands (and their formation) turn out to be suppressed. Irrespective of the elemental and phase compositions of steel specimensformed by the method of 3D additive manufacturing, the principal micromechanism of their fracture, transgranular dimple fracture, is similar to that observed in the cast specimens of austenitic stainless steels.

The Metal Microstructure in Spall Plates

Ultrasonic oscillations of spall plates with a frequency of several MHz occur in the form of a standing wave. The reverberation of the plate is related to the ultrasound category with sufficiently large amplitudes of the vibrations. The periodic change of the compression–tension cycles, characteristic for oscillation processes, leads to the localization of the plastic deformation at the nodes of a standing wave. The self-healing effect is a consequence of the localized strain process: the interstitial elements and ultrafine particles of the alloying phase migrate from the matrix material into the zone of increasing spall destruction. The metal microstructure in the localized strain bands (LSBs) consists of a strongly deformed structureless material containing cup-shaped damage foci, 1 to 3 µm in size, with a large number of micropores. Physical and chemical processes, such as fragmentation, dissolution of the alloying phase particles, and carbidization, are responsible for the formation of the microstructure in the localization bands.

Effect of loading rate on fracture mechanics of NiTi SMA

Superelastic NiTi shape memory alloy is characterized by phase transformation under loading. In this work, the effect of loading rate on fracture mechanics of NiTi is investigated. First, to characterize the behavior of the material, tensile experiments are conducted on dog-bone specimens at different quasi-static-range loading rates and the transformation stresses–strains are calculated. An increase in forward transformation stresses–strains, and a decrease in the reverse transformation stresses–strains with increasing loading rate is observed. Surface mean temperature is measured using a thermal camera, and an increase in temperature difference is observed with increasing loading rate. Displacement field and strain maps are obtained simultaneously using Digital Image Correlation (DIC). The strain maps show strain localizations that change with increasing loading rate. At higher loading rates, localized strain bands increase in number. Fracture experiments are then conducted under Mode I loading on plane stress Compact Tension (CT) specimens, and for further confirmation of the behavior, Finite Element Analysis (FEA) is used with a user defined subroutine to account for thermomechanical coupling. Crack mouth opening displacements (CMODs) are measured and an increase with increasing loading rate is observed. Stress Intensity Factors (SIFs) are calculated using ASTM E399 equations, the displacement data obtained from DIC, and FEA. In all cases, stress intensity factors show an increasing-decreasing trend with increasing loading rate. Results are summarized in a figure to show the trend. Austenite to martensite transformation region sizes around the crack tip are evaluated experimentally, analytically and computationally, and are found to be decreasing with increasing loading rate as well. An interesting but coherent behavior in change of fracture parameters with increasing loading rate is obtained. This study is expected to stimulate new discussions on the subject.

Heavily twinned CoCrNi medium-entropy alloy with superior strength and crack resistance

The recrystallized and pre-deformed CoCrNi medium-entropy alloy (MEA), introduced with high-density deformation twins, exhibits an unprecedented high yield strength up to 2.1 GPa. We found that the highly distorted deformation twins provide strong resistance to crack propagation and the activated dislocation motion accommodates the further plastic deformation. Our in situ tensile tests of pre-notched sample reveal that crack propagation through strain localization band eventually leads to fracture. This result offers new insights on design and processing of MEA for desired mechanical performance.