Heterogeneous Deformation Research Articles

Critical Evaluation of Identified Flow Curves Using Homogeneous and Heterogeneous Solutions for Compression Test

BackgroundThe cylindrical profile model (CPM) is commonly used to convert the load–displacement measurement from the axis-symmetric compression test (ACT) to the flow curve. The model ignores the barrelling of the sample which results in serious flow curve distortion and underestimation of the effective stress and strain. To minimize these, a new solution of ACT with heterogeneous deformation is proposed in this work as an alternative to CPM.MethodRepresentative point is introduced in this new approach for better utilization of the new solution. Some key attributes of a typical flow curve are also considered to explore the sensitivity of the identified flow curve to the heterogeneous deformation. Sample flow curves are identified based on the new solution and compared with that of CPM.ResultsIt was found that CPM underestimates the maximum effective stress, strain and strain rate. Significant deviations were found between the reference flow curves and those of CPM. The model is unable to appropriately account for the rate-dependent behaviour of material and work hardening variations in the samples. Therefore, given its non-realistic homogeneous effective strain and strain rate in the sample, the CPM based flow curves are questionable. The new ACT solution provided more reliable flow curves than those of the CPM.ConclusionsConsidering the heterogeneous deformation at the centre of the sample, the new ACT solution provided flow curves that for strains bellow 0.4 closely resemble the reference curves obtained from the finite element model. Thus, the new ACT solution reduces the serious limitations of CPM and provides less error in the study of the hot deformation phenomena (e.g. recovery and recrystallization). Further recommendations were also given to limit the deviations in the identified flow curve.

Quantitative investigation on the heterogeneity of deformation fields in sandstone pre-existing cracks during damage evolution

The inherently heterogeneous microstructures of rocks lead to heterogeneity of the deformation distribution within the rock volume. In this study, experiments were conducted on red sandstone specimens with four different pre-existing crack inclinations stressed under uniaxial loading to investigate these features. Acoustic emission and digital image correlation techniques were used to confirm the damage process and obtaining deformation fields, respectively. The results showed that the heterogeneity of the deformation fields in the rock specimens amplifies with increasing stress magnitude, i.e., the displacement field heterogeneity shows two dense bands around the pre-existing crack, and the strain field heterogeneity shows localized regions with a numerical difference (quantified by the normalized standard deviation) and spatial concentration (quantified by the spatial correlation coefficient). The variations in the normalized standard deviation and spatial correlation coefficient were closely related to the damage process. The normalized standard deviation presented four evolution stages: relatively constant low value, steady growth, significant growth, and high rate growth. The spatial correlation coefficient changed from increasing at a relatively constant rate to increasing at a gentle rate and finally increasing rapidly. The evolution rate along with the strain showed two sharp fluctuations. The first could be used as precursor information of the damage. Finally, we confirmed the feasibility of the damage variable obtained from the heterogeneous deformation indicators used to calibrate or form damage evolution laws.

Experimental quantification of 3D deformations in sensitive clay during stress-probing

Unique four-dimensional (4D) deformation data are collected during drained triaxial tests on intact specimens of a natural sensitive clay. This requires the development of a miniature triaxial cell for advanced stress path testing, specifically designed for X-ray computed tomography. Salient features include the omission of a membrane, and a mounting procedure that minimises disturbance by the experimenter. Three distinct drained stress ratios are studied for pseudo-isotropic, K0, and highly deviatoric loading paths. The results indicate that the K0path shows the most uniform deformation mechanism, where the measured ratio of deviatoric and volumetric strain increments reach the stress ratio applied at boundary value level for large magnitudes of total strain. The pseudo-isotropic test also reaches a strain ratio close to η at large total strain levels; however, the deformation field is less uniform. Furthermore, the highly deviatoric stress path shows the most heterogeneous deformation fields commensurate with the applied stress ratio, although the ratio of deviatoric and volumetric strain increments falls above the η applied. The mean value of the three-dimensional spatial fields of strain corresponds well with the changes observed at boundary level, supporting prior research on drained stress-probing on clays for which there are no 4D deformation data available.

Origin of Goss texture in grain oriented electrical steel: Role of shear bands

Goss ((110)[001]) orientation is preferred in high silicon electrical steel used in transformer core to obtain superior magnetic properties with minimum hysteresis loss. The origin of Goss orientation along with its stability during the processing is crucial and not completely understood. Present study explores the possibility of the development of Goss orientation inside shear bands of a cold rolled polycrystalline Fe-3.78%Si steel by Electron Back Scatter Diffraction and crystal plasticity based analysis. Heterogeneous deformation in the form of shear bands has been observed during cold rolling of hot band annealed plate. Near Goss ((221) [1¯1¯4] ) and Rotated Cube ((001) [11¯0] ) orientations have been found to evolve inside the Type-I and Type-II shear bands of (111) [1¯1¯2] oriented grains, respectively. Crystal plasticity based study reveals that under pure shear loading on an inclined plane, Goss orientation may evolve inside the shear bands of (111) [1¯1¯2] oriented grain. Consideration of Taylor factor further indicates that geometrical softening is associated with shear banding and facilitate its development. Present study provides direct evidence on the evolution of Goss orientation inside shear band through EBSD analysis. These shear bands may alone accomplish the requirement of Goss orientation in the cold rolled grain oriented electrical steel.

Selective laser melting of bulk immiscible alloy with enhanced strength: Heterogeneous microstructure and deformation mechanisms

To overcome the dimension limits of immiscible alloys produced by traditional techniques and enhance their mechanical properties, bulk Cu-Fe-based immiscible alloy with abundant nanotwins and stacking faults was successfully produced by selective laser melting (SLM). The SLM-produced bulk immiscible alloy displays a heterogeneous microstructure characterized by micro-scaled γ-Fe particles dispersed in fine ε-Cu matrix with a high fraction (∼92%) of high-angle grain boundaries. Interestingly, abundant nanotwins and stacking faults are generated in the interior of nano-scaled γ-Fe particles embedded within ε-Cu matrix. The heterogeneous interface of soft domains (ε-Cu) and hard domains (γ-Fe) not only induces the geometrically necessary dislocations (GNDs) but also affects the dislocation propagation during plastic deformation. Therefore, the bimodal heterogeneous interface, and the resistance of nanotwins and stacking faults to the propagation of partial dislocation make the bulk immiscible alloy exhibit an enhanced strength of ∼590 MPa and a good ductility of ∼8.9%.

Frictional controls on the seismogenic zone: Insights from the Apenninic basement, Central Italy

Crustal seismicity is in general confined within the seismogenic layer, which is bounded at depth by processes related to the brittle-ductile transition (BDT) and in the shallow region by fault zone consolidation state and mineralogy. In the past 10-15 years, high resolution seismological and geodetic data have shown that faulting within and around the traditional seismogenic zone occurs in a large variety of slip modes. Frictional and structural heterogeneities have been invoked to explain such differences in fault slip mode and behaviour. However, an integrated and comprehensive picture remains extremely challenging because of difficulties to properly characterize fault rocks at seismogenic depths. Thus, the central-northern Apennines provide a unique opportunity because of the integration of deep-borehole stratigraphy and seismic reflection profiles with high resolution seismological data and outcrop studies. These works show that seismic sequences are limited within the sedimentary cover (depth < 9-10 km), suggesting that the underlaying basement plays a key-role in dictating the lower boundary of the seismogenic zone.Here we integrate structural data on exhumed outcrops of basement rocks with laboratory friction data to shed light on the mechanics of the Apenninic basement. Structural data highlight heterogeneous and pervasive deformation where foliated and phyllosilicate-rich rocks surround more competent quartz-rich lenses up to hundreds of meters in thickness. Phyllosilicate horizons deform predominantly by folding and foliation-parallel frictional sliding whereas quartz-rich lenses are characterized by brittle signatures represented by extensive fracturing and minor faulting. Laboratory experiments revealed that quartz-rich lithologies have relatively high friction, μ≈0.51, velocity-strengthening to neutral behaviour, and elevated healing rates. On the contrary, phyllosilicate-rich (muscovite and chlorite) lithologies show low friction, 0.23 <μ < 0.31, a marked velocity strengthening behaviour that increases with increasing sliding velocity and negligible rates of frictional healing.Our integrated approach suggests that in the Apenninic basement deformation occurs along shear zones distributed on thickness up-to several kilometres, where the frictionally stable, foliated, and phyllosilicate-rich horizons favour aseismic deformation and therefore confine the depth of major earthquake ruptures and the seismogenic zone.

Effect of bimodal grain size and gradient structure on heterogeneous deformation induced (HDI) stress and mechanical properties of Cu

In this study, two different types of heterogeneous structures were prepared by controlling different surface mechanical attrition treatment (SMAT) time (5 s, 10 s, 30 s, 60 s). The effect of heterogeneous Cu with bimodal grain size structure (BGSS) and gradient structure (GS) on heterogeneous deformation induced (HDI) stress and mechanical properties was investigated systematically. By combining surface morphology with microhardness distribution, it was found that the surface grains of the SMAT-ed Cu (5 s and 10 s) were partially refined to exhibit BGSS, while the surface grains of SMAT-ed Cu (30 s and 60 s) were sufficiently refined to form GS. The load-unload-reload (LUR) tests results showed that HDI stress for SMAT 60s Cu was much higher than that of the SMAT 10s Cu. Furthermore, microstructure characterizations revealed that SMAT-ed Cu with BGSS and GS suppressed strain localization, which resulted in high strength and reasonable ductility.

Slip system activity and lattice rotation in polycrystalline copper during uniaxial tension

The heterogeneous evolution of intragranular strain within polycrystalline copper grains is evaluated by in-situ electron back-scattering diffraction during uniaxial tension. Deformation heterogeneity between grains causes a proliferation of slip bands within grains and leads to lattice rotation within grains. The magnitude of intragranular orientation gradient development caused by lattice rotation is dependent on the initial grain orientation as well as grain interactions with its local neighbourhood. Uniaxial tensile deformation is accommodated by the activation of coplanar and non-coplanar slip systems with the highest and second highest Schmid factor values. Non-coplanar slip is predominantly observed in unstable 011 and “Other” (i.e.- those that do not belong to the 111, 001, and 011 fibres) grains. Viscoplastic self-consistent simulations revealed that the interactions with the homologous effective mediums provide additional rotation pathways for unstable 011 and “Other” grains to rotate towards more stable 111 and 001 orientations.

Significantly enhanced tensile ductility and its origin of a 〈0001〉 micro-textured extrusion bar of a powder metallurgy near alpha titanium alloy

This study investigated the tensile properties and deformation mechanism of a hot-extruded powder metallurgy near α-Ti alloy characterized by a regular lamellar microstructure in which some colonies present a unique 〈0001〉 micro-texture, i.e. c-axes are parallel to the extrusion direction. Compared with the alloy's wrought ingot metallurgy counterpart, ultimate tensile strength (UTS) of the extruded bar was increased by approximately 300 MPa, with an equivalent elongation to fracture (EI) of 15.0%, due to the micro-texture being favorable for extensive 〈c + a〉 wavy slips and associated abnormal rise of work hardening rate. Moreover, annealing at 880 °C brought about a bi-lamellar microstructure with βt domains full of ultrafine acicular α-laths, whereas 〈0001〉 micro-texture was still retained. Heterogeneous deformation induced (HDI) effect at α/βt interfaces led to an extra strain hardening, which resulted in simultaneously enhanced EI up to 22.0% and UTS of 1070 MPa.

Coupling Self-Adaptive Meshing-Based Regularization and Global Image Correlation for Spatially Heterogeneous Deformation Characterization

Coupling Self-Adaptive Meshing-Based Regularization and Global Image Correlation for Spatially Heterogeneous Deformation Characterization

A fully coupled crystal plasticity-cellular automata model for predicting thermomechanical response with dynamic recrystallization in AISI 304LN stainless steel

A microstructure-based multiscale framework was developed to physically correlate the microstructure evolution and mechanical behavior of AISI 304LN stainless steel during the thermomechanical process. The developed model couples a crystal plasticity finite element method (CPFEM) to simulate heterogeneous deformation and a probabilistic cellular automata (CA) approach with a dynamic recrystallization (DRX) model to simulate microstructure evolution. Specifically, the CA model was built with formulations with physical meaning and combined with CPFEM by updating algorithms with higher robustness. The developed model was validated by comparing it with the experimental results of AISI 304LN stainless steel under thermo-mechanical processing at various temperatures and strain rates. The predicted flow stresses, grain sizes, DRX volume fraction, and deformed texture match well with the experimental data. Additionally, the developed model can simulate microstructure evolution by the DRX process, whereby the evolutions of recrystallized grains and pole figures can be examined. Moreover, the mechanical responses during the nucleation and growth of recrystallized grains can be characterized by in-depth quantitative analysis considering grain-level deformation inhomogeneity.

A multiscale investigation on the preferential deformation mechanism of coarse grains in the mixed-grain structure of 316LN steel

Mixed-grain structure with millimeter-grade coarse grains (MCGs) is an intolerable defect often found in heavy forgings. Eliminating this microstructural defect through thermomechanical operations requires a thorough understanding on the microscopic deformation heterogeneity associated with the uneven grain size. Both in-situ and interrupted micro-tensile tests combined with a grain-level digital image correlation, microstructure tracking, surface slip tracing, and fractography examination were conducted on the intentionally prepared samples of mixed-grain structure with MCGs. Mesoscale full-field crystal plasticity (CP) modeling, incorporating a grain-level Hall-Petch law and a grain-size enhanced hardening rule, was proposed to describe the uneven grain size effect of mixed-grain structure. The agreements of simulation results with the experiments demonstrated that the proposed CP model is competent to capture the mesoscale deformation characteristics of the structures with MCGs. It was found that, during the deformation, the large deformation band covering the MCG and its surrounding fine grains (FGs) was preferentially generated because MCGs take the priority of plastic deformation, even if MCGs were hard-oriented. At large deformation, some FGs in the vicinity of MCGs inside the deformation band sustained more strain over the MCGs to coordinate the enforced deformation in the band, resulting in the intense strain and stress localizations. It was further found that the preferential and continuous deformation characteristic of the MCG is related to its ‘lake’ shape distribution of the number of activated slip systems (Ns), meaning that Ns is smaller in the interior than at the boundary of the MCGs. Both the TEM characterizations and CP simulations demonstrate that the MCG interior deformed in single-slip at early deformation and in primary-slip at large deformation. Compared with the FG structure, the MCGs have weaker initial slip resistance and hardening rate due to the less GB-related multiplication and storage of dislocations, and dislocation interaction in the multiple slip scenario.

The Effect of Grain Size on the Diffusion Bonding Properties of SP700 Alloy

Superplastic forming and diffusion bonding (SPF/DB) has been recognized as a viable manufacturing technology. However, the basic understanding of grain size and its effects on the quality of diffusion bonds is still limited. In this study, a certain type of SP700 alloy with different grain sizes is bonded at superplastic temperature. The experimental results indicate that the same materials, if coarse-grained, may not readily bond under identical conditions of pressure, temperature, and time. This type of bonding is possible because of the presence of many grain boundaries in fine-grained materials that act as short-circuit paths for diffusion. In addition, grain-boundary migration is also faster in fine-grained than in coarse-grained materials. Fractographic studies show that the dimples on the coarse-grained specimen have large dimensions compared with that in the fine-grained material, indicating that heterogeneous deformation develops in the coarse-grained specimen during tension.

Crystallographic orientation and spatially resolved damage for polycrystalline deformation of a high manganese steel

Deformation damage during tension and compression were revealed using in-situ neutron diffraction for a high manganese steel: (1) When the tensile stress is increased, an indication of damage is provided when the 111 and 422 lattice strains along the transverse direction give no more contraction or even expansion. This is because that the replacement of slip or twinning activities by crack propagation induces relaxation, which can outweigh contraction of the damaged slip or twinning planes. (2) For compression and also when the stress amplitude is decreased, the increase of the 111, 220, 311, 422 lattice strain amplitudes along the loading direction indicates damage. This is because micro-cracks can decrease the effective elastic modulus and crack propagation is not favored during compression. The identified damage grains for both cases belong to the same set. Distribution of the damaged grains in fractured samples is similar to that from grains featuring large Taylor factors. The cracks mainly distributed at the transverse surface. It is due to stronger deformation heterogeneity and ratcheting events at the surface rather than in the interior. During tension-compression fatigue loading, grain boundaries and the narrow deformation twins often correspond to different amplitudes of transversal contraction and expansion from those in other surface areas. This may trigger surface flaws as nuclei for cracks. The findings point to the important relations among damage, lattice strains, and plastic activities, as well as damage behavior differences between tension and compression.

Continuum modeling of dislocation channels in irradiated metals based on stochastic crystal plasticity

As a common feature observed in irradiated metallic materials, the formation of dislocation channels has been extensively studied and is considered to play a key role in irradiation embrittlement. However, modeling dislocation channels with the conventional crystal plasticity theory has been a theoretical challenge due to the difficulty of capturing microstructural inhomogeneities. Here a continuum crystal plasticity framework incorporating a stochastic distribution model of critical resolved shear stress (CRSS) is developed to describe the formation of dislocation channels and further plastic flow localization in irradiated materials. We show that the stochastic model is capable of capturing the heterogeneity of microscale plastic strain, which is an inherent feature of metallic materials during plastic deformation. It acts as an important microscale perturbation to trigger the dislocation channel nucleation in irradiated metals, especially for single crystals that lack mesoscale perturbations such as intergranular incompatibility and grain anisotropy. Without predetermining the potential nucleation position of dislocation channels, the stochastic irradiation crystal plasticity framework successfully simulates the dislocation channel formation and plasticity localization in both irradiated single- and polycrystalline copper (Cu), and further indicates the irradiation defect density threshold for the dislocation channel formation. This stochastic model broadens the application of the conventional crystal plasticity framework, and might provide new insights for other studies on plasticity localization, including shear bands formation of metals, mechanical behaviors with heterogeneous deformation and so on.

Heterogeneous Deformation and Microstructure of TWIP Steel under Damage and Fracture

Materials have always been a research hotspot in the chemical industry. With the continuous development of technology, the iteration of materials research has become faster and faster. Steel has strong toughness and tensile strength, and it is widely used in construction and other fields. However, one problem that cannot be avoided is the fracture of steel. The purpose of this paper is to analyze the damage and fracture of TWIP steel. In this paper, a microstructure characterization calculation method based on TWIP is proposed, which can effectively analyze the fracture surface, and for the performance of TWIP steel, this paper uses two different TWIP steels for comparative analysis. The results of this paper show that the HDI hardening rate of 22Mn0.6C TWIP steel is higher than that of 22Mn0.6C3Al TWIP steel.

Patient-Specific Quantification of Normal and Bicuspid Aortic Valve Leaflet Deformations from Clinically Derived Images.

The clinical benefit of patient-specific modeling of heart valve disease remains an unrealized goal, often a result of our limited understanding of the in vivo milieu. This is particularly true in assessing bicuspid aortic valve (BAV) disease, the most common cardiac congenital defect in humans, which leads to premature and severe aortic stenosis or insufficiency (AS/AI). However, assessment of BAV risk for AS/AI on a patient-specific basis is hampered by the substantial degree of anatomic and functional variations that remain largely unknown. The present study was undertaken to utilize a noninvasive computational pipeline ( https://doi.org/10.1002/cnm.3142 ) that directly yields local heart valve leaflet deformation information using patient-specific real-time three-dimensional echocardiographic imaging (rt-3DE) data. Imaging data was collected for patients with normal tricuspid aortic valve (TAV, [Formula: see text]) and those with BAV ([Formula: see text] with fused left and right coronary leaflets and [Formula: see text] with fused right and non-coronary leaflets), from which the medial surface of each leaflet was extracted. The resulting deformation analysis resulted in, for the first time, quantified differences between the in vivo functional deformations of the TAV and BAV leaflets. Our approach was able to capture the complex, heterogeneous surface deformation fields in both TAV and BAV leaflets. We were able to identify and quantify differences in stretch patterns between leaflet types, and found in particular that stretches experienced by BAV leaflets during closure differ from those of TAV leaflets in terms of both heterogeneity as well as overall magnitude. Deformation is a key parameter in the clinical assessment of valvular function, and serves as a direct means to determine regional variations in structure and function. This study is an essential step toward patient-specific assessment of BAV based on correlating leaflet deformation and AS/AI progression, as it provides a means for assessing patient-specific stretch patterns.

Heterogeneous Deformation Behavior of Hybrid Manufactured High Strength Titanium Alloy: Coordinate Deformation and Stress Concentration

Heterogeneous Deformation Behavior of Hybrid Manufactured High Strength Titanium Alloy: Coordinate Deformation and Stress Concentration

Evolution of fracture networks and connectivity during fault–bend folding: Insights from the Sinon Anticline in the southwestern Hongseong–Imjingang Belt, Korea

Crustal shortening in an elastico-frictional regime is mainly accommodated by contractional fault–fold systems with fracture networks. According to recent research, fracture networks in fold–thrust belts express complex internal strain states in response to thrusting and related folding. Furthermore, their connectivity and fluid flow characteristics likely depend on the structural positions and mechanical stratigraphy that control heterogeneous deformation processes. This study provides characteristics of fold-related fracture networks in the Sinon Anticline, which was formed by fault–bend folding in the southwestern Hongseong–Imjingang Belt, Korea. The fracture networks in the metamorphosed turbidites characterized by interbedded competent metasandstone layers and relatively thin incompetent schist layers have evolved through pre-, syn-, and post-folding fracturing events. Their complexity reflects the spatiotemporal variation in the strain pattern related to early layer-parallel shortening and subsequent fault–bend folding. Based on insights from detailed mapping and topological analysis of the fracture network, we conclude that strain partitioning that occurs during flexural folding results in a superposed tangential longitudinal strain expressed by fractures with a high (hydraulic) connectivity in the hinge zones. Strain partitioning is caused by flexural interlayer slip along incompetent schist layers in the fold limbs. Bed-parallel slip localization zones probably have low porosity and permeability and may act as barriers to fluid migration across beds. We suggest that heterogeneous vertical axis rotation, which occurred as the system's hanging wall slid over the footwall ramp, increased the complexity of fracture networks within the Sinon Anticline. Our findings indicate that the evolution, connectivity, and fluid flow properties of fracture networks can be characterized through careful interpretation of folding mechanisms and related strain states during formation of fault–bend fold systems.

Analysing the Interaction between Microscopic Deformation, Microstructure and Void Evolution of Near-α Titanium Alloys during Non-Superplastic Hot Deformation by an Integrated Crystal Plasticity Finite Element Model.

High-efficiency and low-cost hot forming technologies for titanium alloys have been developed for producing complex-shaped, thin-walled tubular components under non-superplastic forming conditions. Under these forming conditions, there exist complex and highly integrated material evolution processes including microscopic heterogeneous deformation, microstructure evolution and damage behaviour. This paper presents an integrated crystal plasticity finite element model of near-α titanium alloys during non-superplastic hot deformation conditions considering grain boundary sliding (GBS), dynamic recrystallisation (DRX), as well as void evolution. The polycrystalline model of a near-α TA15 titanium alloy was established, containing α phase, β phase and grain boundary (GB) regions, in which the GB region was a visualised representation of GBS. The quantitative strength ratio between the GB regions and α phase was calculated according to the Zener–Holloman parameter Z and grain size, which determined the microscopic deformation behaviour. There were found to be two high microscopic strain regions in the α phase: intragranular deformation bands through the most favourable slipping and near the GBs through multiple slipping, which promoted continuous and discontinuous DRX, respectively. With the decrease in parameter Z or grain size, the activated dislocations accommodating GBS were found to no longer pile up inside the grain, but instead travel across the grain interior. Finally, methods to improve the macroscopic plastic formability were proposed for the difficult-to-form titanium alloys experiencing non-superplastic hot deformation.