Inhomogeneous Deformation Research Articles

Cryogenic mechanical behavior and FCC → HCP phase transformation mechanism in a Si-added CrCoNi medium-entropy alloy under quasi-static and dynamic tension

The CrCoNiSi0.3 MEA exhibits excellent cryogenic mechanical properties upon both quasi-static and dynamic tension. Under quasi-static tension at cryogenic temperature, the engineering yield and ultimate tensile strengths (UTS) reach 980 MPa and 1800 MPa, respectively, with notable ductility (62 %). The product of UTS and total elongation (TE) is 111.6 GPa %, surpassing most cryogenic high strength-ductility alloys. The significant mechanical strength enhancement is attributed to the denser deformation twins (DTs), multiple twinning, and extensive face-centered-cubic to hexagonal-close-packed (HCP) phase transitions, resulting in a high work hardening capacity. Upon dynamic tension at cryogenic temperature, the strength and strain hardening are further improved, which originates from the thickening DTs and HCP sequence and localized plastic deformation. The effects of temperature and strain rate on phase transition are studied. It is proposed that there is a competing relationship between high strain rate and increased stacking fault energy (SFE) due to temperature rise. The coupling effect of cryogenic temperature and high strain rate inhibits phase transition due to the deformation inhomogeneity in CrCoNiSi0.3 MEA. The findings make a valuable contribution to understand the influence of temperature and strain rate on the mechanism of FCC-to-HCP phase transition.

Plastic Shakedown Behavior and Deformation Mechanisms of Ti17 Alloy under Long Term Creep–Fatigue Loading

Ti17 alloy is mainly used to manufacture aero-engine discs due to its excellent properties such as high strength, toughness and hardenability. It is often subjected to creep–fatigue cyclic loading in service environments. Shakedown theory describes the state in which the accumulated plastic strain of the material stabilizes after several cycles of cyclic loading, without affecting its initial function and leading to failure. This theory includes three behaviors: elastic shakedown, plastic shakedown and ratcheting. In this paper, the creep–fatigue tests (CF) were conducted on Ti17 alloy at 300 °C to study its shakedown behavior under creep–fatigue cyclic loading. Based on the plasticity–creep superposition model, a theory model that accurately describes the shakedown behavior of Ti17 alloy was constructed, and ABAQUS finite element software was used to validate the accuracy of the model. TEM analysis was performed to observe the micro-mechanisms of shakedown in Ti17 alloy. The results reveal that the Ti17 alloy specimens exhibit plastic shakedown behavior after three cycles of creep–fatigue loading. The established finite element model can effectively predict the plastic shakedown process of Ti17 alloy, with a relative error between the experimental and simulation results within 4%. TEM results reveal that anelastic recovery controlled by dislocation bending and back stress hardening caused by inhomogeneous deformation are the main mechanisms for the plastic shakedown behavior of Ti17 alloy.

Strain dependence of adiabatic shearing behaviors of CoCrFeNi high-entropy alloy fabricated via laser powder bed fusion under impact loads

Adiabatic shearing represents a prevalent mode of deformation failure in metals when subjected to impact loading. In this work, dynamic shearing interruption tests considering various shear displacements (i.e., shear strains) were conducted on of the CoCrFeNi high-entropy alloy (HEA) produced by laser powder bed fusion (LPBF) to analyze the microstructural evolution during adiabatic shearing. From the results, it was observed that the columnar grains in the shear region only distorted to different degrees at the lower levels of shear strain. Then, it was also found that the increase in shear strain caused severe distortion and refinement of the columnar grains, ultimately leading to adiabatic shearing band (ASB) at a critical shear strain threshold. During inhomogeneous deformation at high strain rate, the ASB formation was predicated on enough plastic deformation work. The interconnection between microstructural softening mechanisms and macroscopic mechanical behavior during ASB evolution and fracture was also highlighted. The nano-sized equiaxed recrystallized grains within the ASB were formed by rotational dynamic recrystallization (RDRX) rather than migratory recrystallization. Moreover, a large number of nano-twins were formed in these nano-sized recrystallized grains to motivate the mechanism of slip within nano-twins, thus accommodating the continuous plastic deformation. These results are the main reasons for the outstanding resistance to shear deformation of CoCrFeNi HEA produced by LPBF.

Atomic strain concentration induced by interfaces in extruded carbon nanotube reinforced 2024Al matrix composite

Inhomogeneous deformation occurs in aluminum matrix composite, resulting in strain concentration near reinforcement/matrix interfaces. In this work, for the CNT/2024Al composite extruded by porthole die extrusion, the effects of reinforcements (CNTs and Al4C3) and intermetallic (Al2Cu) on atomic strain concentration and grain boundary migration were systematically studied. The results indicate that obvious atomic strain concentration appears near the CNT/Al and Al4C3/Al interfaces, and then, the strain is transferred from the interfaces to Al matrix. Mirco-Al2Cu phases are mainly distributed at grain boundaries, increasing Zener force, and thus inhibit grain growth of the composite. In addition, the Al4C3/Al and Al2Cu/Al interfaces are observed, and the (111)Al atom plane is parallel to 1̄107Al4C3, while large number of misfit dislocations are observed near the Al2Cu/Al interface. Transmission Kikuchi diffraction and transmission electron microscope observations indicate that the grains, which contains more second phases, exhibit higher dislocation density than neighboring grains, providing driving force for grain boundary migration. High extrusion temperature brings about Al2Cu dissolution, leading to grain growth, and interfacial bonding strength decreases with increasing extrusion speed. Consequently, the composite extruded at low-temperature and low-ram speed has ultrafine grains, high dislocation density, and strong interfacial bonding, exhibiting high hardness, tensile strength and elongation.

Effect of heat treatments on inhomogeneous deformation of the melt-pool structure of Al–Si alloy manufactured via laser powder bed fusion

Laser powder bed fusion (L-PBF) is an additive manufacturing technology widely applied to the manufacture of metallic parts. The L-PBF processed aluminum-silicon (Al–Si) cast-type alloy components exhibit an anisotropic tensile ductility. In this study, we investigated the influence of heat treatments on the microstructural features of an Al–12%Si binary alloy fabricated via L-PBF and the associated inhomogeneous deformation of its melt-pool structure, which contributes to the resulting anisotropic tensile ductility. The mechanical inhomogeneity of the melt-pool structure and the change induced by annealing at various temperatures (300 and 530 °C) were characterized using microscale digital-image correlation analyses of scanning electron microscopy images obtained in situ during tensile deformation and nanoindentation hardness mapping. In the specimen fabricated via L-PBF, the high strain was concentrated at the locally coarsened microstructure (the soft region) along the boundaries of the melt pools rather than at the refined solidification microstructure (the hard region) within the melt pools. The localized strain varied depending on the geometrical relation between the orientation of the melt-pool boundary and the tensile direction, thus contributing to the anisotropic tensile ductility. This tendency appeared less pronounced in the specimen annealed at 300 °C, which exhibited a slightly homogenized melt-pool structure. The reduced strain localization is associated with a reduced difference in local strength between the melt-pool boundary (soft region) and the melt-pool interior (hard region). The slight homogenization of the melt-pool structure emphasized the effect of grain morphologies in the α-Al matrix on the inhomogeneous deformation within melt pools. In the specimen annealed at 530 °C, which exhibited a homogenized α-Al/Si two-phase microstructure, the uniformly distributed Si phase would be responsible for the homogenous deformation, resulting in an isotropic tensile ductility. This study advances our understanding of the correlation between the melt-pool structure and the deformation behavior of Al–Si alloys processed using L-PBF, which provides new insights for controlling the ductility by post-processing.

Influence of Mechanical Loading on the Process of Tribochemical Action on Physicochemical and Biopharmaceutical Properties of Substances, Using Lacosamide as an Example: From Micronisation to Mechanical Activation.

Many physical and chemical properties of solids, such as strength, plasticity, dispersibility, solubility and dissolution are determined by defects in the crystal structure. The aim of this work is to study in situ dynamic, dispersion, chemical, biological and surface properties of lacosamide powder after a complete cycle of mechanical loading by laser scattering, electron microscopy, FR-IR and biopharmaceutical approaches. The SLS method demonstrated the spontaneous tendency toward surface-energy reduction due to aggregation during micronisation. DLS analysis showed conformational changes of colloidal particles as supramolecular complexes depending on the loading time on the solid. SEM analysis demonstrated the conglomeration of needle-like lacosamide particles after 60 min of milling time and the transition to a glassy state with isotropy of properties by the end of the tribochemistry cycle. The following dynamic properties of lacosamide were established: elastic and plastic deformation boundaries, region of inhomogeneous deformation and fracture point. The ratio of dissolution-rate constants in water of samples before and after a full cycle of loading was 2.4. The lacosamide sample, which underwent a full cycle of mechanical loading, showed improved kinetics of API release via analysis of dissolution profiles in 0.1 M HCl medium. The observed activation-energy values of the cell-death biosensor process in aqueous solutions of the lacosamide samples before and after the complete tribochemical cycle were 207 kJmol-1 and 145 kJmol-1, respectively. The equilibrium time of dissolution and activation of cell-biosensor death corresponding to 20 min of mechanical loading on a solid was determined. The current study may have important practical significance for the transformation and management of the properties of drug substances in solid form and in solutions and for increasing the strength of drug matrices by pre-strain hardening via structural rearrangements during mechanical loading.

Photocycloaddition of Zero-Dimensional Metal Halide Hybrids with Reversible Photochromism.

In this work, two zero-dimensional (0D) metal halide hybrids L2ZnBr4 [1, L = (E)-4-(2-(1H-pyrrol-3-yl)vinyl)-1-methylpyridin-1-ium] and L6Pb3Br12 (2) were prepared, which demonstrated photochromism and photoinduced cracking. Upon irradiation at 450 nm, a single crystal-to-single crystal transformation occurred as a result of the [2 + 2] photocycloaddition of L. Interestingly, compared to the complete photocycloaddition of L in 1, only two-thirds of L monomers could be photodimerized in 2 because of the difference in L orientation. 1 shows reversible photochromic behavior including rapid response time, few cracks, high conversion rate, and good reaction reversibility, while 2 exhibits no significant color change but distinct photoinduced cracking because of the large local lattice strain induced by inhomogeneous and anisotropic deformation. Moreover, the photocycloaddition of L results in the distinct shift of photoluminescence of 1 and 2, attributed to the variation in conjugation of π electrons and distortion of metal halide clusters. As a proof-of-concept, reversible optical writing is demonstrated for 1. These findings provide new insights into the design of stimuli-responsive multifunctional materials.

Quantification of microscale factors for fatigue failure in NiTi shape memory alloys

Fatigue behavior is intrinsically linked to microstructural alterations induced by cyclic loading. However, the quantification of microstructural defects associated with fatigue damage of NiTi shape memory alloys (SMAs) is lacking, which hinders the development of a physically based fatigue criterion. To this end, a multi-scale experimental analysis was conducted on cyclically deformed NiTi SMAs, which evidenced a strong correlation between microstructural inhomogeneity and localized deformation behavior. The microstructural change associated with fatigue was quantified in terms of stored strain–energy, with the highest values observed in the regions where fatigue cracks initiate. Consequently, stored energy is deemed as an effective fatigue indicator, offering valuable insights for future work in the design and optimization of SMAs’ structures against fatigue.

Deformation inhomogeneity evolution and crack formation mechanism analysis in ultra-high strength steel by crystal plasticity simulations

Understanding deformation inhomogeneity and the formation mechanism of crack are crucial for fully exploiting the potential of ultra-high strength steel (UHSS). In this paper, the deformation inhomogeneity and microscopic crack formation mechanism of UHSS were investigated by combining high-fidelity crystal plasticity models with microscopic experiments. The simulation results at grain level show that the deformation strain of the UHSS is non-uniform, characterized by distinct deformation bands. A broad deformation band extends between multiple grains at an angle of approximately 40 degrees to the rolling direction, while a sharp deformation band is observed within a single grain. These features are intricately linked to the initial orientation (Taylor factor) distribution of the grains and their rotational behavior. The locations with greater Taylor factor deviations become potential crack initiation sites. In addition, as the deformation proceeds, the α-fiber reinforcement exacerbates the deformation inhomogeneity of the UHSS.

Achieving Superior Strength–Ductility–Conductivity Combination in TiB2p/6201 Composites via Particle Rotation and Subgrain Refinement

The key factor in the material design of overhead power transmission lines is to obtain a desired balance among strength, ductility, and electrical conductivity. Herein, TiB2 particulate‐reinforced aluminum matrix composites are prepared to find a way out of the intrinsic dilemma behind this balance by tailoring the subgrain refinement. The interaction in the form of inhomogeneous deformation induced by the flexibility discrepancy between the rigid particles and soft matrix is studied. On the one hand, the hexagonal plate‐like TiB2 particles rotate with the inhomogeneous deformation, forcing the biggest exposed plane ((0001) basal plane) parallel to the plastic flow direction, which is beneficial for the dislocation multiplication and hindrance of dislocation slipping. On the other hand, inhomogeneous deformation generates plentiful geometry necessary dislocations and divides the microstructure into two types: in the particle‐rich region ultrafine grains are formed and in the particle‐free region significant subgrains refinement is observed. The subgrains with 3 wt% TiB2 are refined from ≈897 to ≈248 nm. Thanks to these microstructural benefits, the composites achieve the following strength–ductility–conductivity combination: ultimate tensile strength is 370 MPa, elongation after fracture is 11.2%, and electrical conductivity is 51.79% IACS. Besides, the elastic modulus reaches 75.43 GPa.

Effect of aspect ratio on the metal flow behaviour during forming process: A numerical simulation approach

This paper presents results on the effect of aspect ratio on the flow stress of 42CrMo4 steel using Deform™ 3D Version 11 simulation software. The FEM simulation process conditions were upsetting temperature of 1000 °C and 10 s⁻¹ strain rate. The sample aspect ratios (height/diameter) varied within commonly used ranges during conventional Gleeble experimentations. The aspect ratio did not affect the flow stress behaviour during forming. Generally, the forming conditions influence the flow stress-strain field and distribution behaviour, causing inhomogeneous deformation. A negligible effect of aspect ratio on typical industrial forging process is only attainable between 1.0 and 2.0. The implications of the results for industrial forging are elucidated.

Thermomechanics of phase transformation induced localization in NiTi tubes. Part I experiments

This two-Part study aims to illustrate and elucidate the effects of thermomechanical interactions in pseudoelastic NiTi structures that arise in the course of the reversible transformations between the austenitic and martensitic phases. Transformation leads to inhomogeneous deformation with the two phases coexisting and to latent heat-induced local heating/cooling. Part I first presents the results of displacement-controlled isothermal tension and compression experiments on NiTi tubes covering the pseudoelastic temperature regime. The experiments are conducted in a constant temperature circulating bath which suppresses thermomechanical interactions so the transformation front velocity is governed strictly by the applied displacement rate. The load/unload hystereses traced, quantify the transformation stresses and strains and will be used to calibrate the constitutive model of Part II. A set of isobaric experiments in which NiTi tubes are taken through a cool/heat cycle under constant stresses of different levels follow. The experiments are conducted in a custom small-scale environmental chamber with a circulating air stream run by a feedback temperature controller, coupled to load-controlled mechanical loading. The evolution of helical bands of the alternate phase is captured using digital image correlation. The results demonstrate that under such loading histories a strong interaction develops between the evolving inhomogeneous deformation, the latent heat and the surrounding environment. The speed of propagation of the helical fronts slows down or accelerates so as to match the rate at which heat is removed/added to the specimen by the airflow. Thus, here the evolution of localized deformation is strongly coupled to the interaction between the latent heats and heat transfer from the environment. The effect of the stress level on these events is examined through eight isobaric experiments, which provide a rich data set for evaluating constitutive models and structural analyses of these experiments such as those in Part II.

Thermomechanics of phase transformation induced localization in NiTi tubes. Part II constitutive modeling and simulations

In an isobaric test, typically used for establishing the transformation temperatures of SMAs, a specimen is taken through a cool/heat cycle at a prescribed stress level. The companion paper, Part I, demonstrated that such tests on NiTi tubes result in rather complex interactions between the helical bands of localized deformation induced by phase transformations, the associated latent heat, and the thermal exchange with the environment. These interactions were quantified using accurately controlled testing conditions and full-field diagnostics, and provide a challenging platform for evaluating analyses. In Part II this challenge is met by first extending the thermomechanical constitutive framework developed by our group to include variations of transformation stress, strain, and latent heat with temperature. Unique features of the model include: modeling the reversible phase transformations of NiTi through a single surface in the deviatoric stress–temperature space with the transformation strain and entropy as the internal variables; and use of softening to model the inhomogeneous deformation exhibited in tension. The model is calibrated to the isothermal results of Part I. The constitutive model is then incorporated into a fully coupled static displacement-thermally transient finite element analysis that is used to simulate the isobaric experiments on NiTi tubes of Part I over a range of stresses. The clamped ends of the experiment are idealized as radial constraints. Heat exchange between the structure and the environment is strictly by convection. Isobaric testing is simulated by taking the model tube through the cool/heat cycle of the experiment at the prescribed stress level. A small thickness depression at one of the ends is used to initiate localized transformation. The temperature-strain response is reproduced with the two transformations initiating at essentially the same temperatures as in the experiments, producing the correct transformation strains for all stress levels. Transformation of M propagates via a helical band at similar speeds as in the experiments, while transformation of A is via multipronged fronts for all cases. Successful reproduction of the velocities of the banded transformations is governed by the value of the convection coefficient. Overall, the reproduction of the isobaric experiments over a range of stress levels, validates the constitutive and structural models. It also points to the limitations of modeling the heat exchange between the specimen and the environment only by convection.

Mechanics of single-network hydrogels with network imperfection

Polymer network is a crucial component of hydrogels, and network imperfection is a prominent feature of polymer networks, significantly influencing the performance of hydrogels. Two essential features of network imperfection are unequal chain lengths and dangling chains, both of which have a significant impact on the mechanical properties of single-network (SN) hydrogels. However, a theoretical framework considering network imperfection in SN hydrogels is still lacking. Here, we propose a theoretical model for SN hydrogels with network imperfection to study the damage behavior during deformation, in which we adopt different chain length distributions to accurately depict the real physical characteristics of the polymer network and incorporate the normalized critical chain force for a more precise measurement of network damage. To verify our theory, we discuss the effects of model parameters on the stress-stretch responses of SN hydrogels and predict the results of uniaxial loading-unloading tests of SN hydrogels, which agree well with experimentally measured stress-stretch behaviors. Finally, we implement the constitutive model into ABAQUS as a user subroutine to study the inhomogeneous deformation of hydrogels.

A thermodynamic theory coupling photo-chemo-mechano interactions for light-responsive hydrogel

Light-responsive hydrogel, as a typical functional hydrogel, is composed of crosslinked hydrophilic polymer chains, photosensitive molecules and water. Under illumination, the photosensitive molecules exhibit a transition in hydrophilic/ hydrophobic properties, leading to migration of water molecules and deformation of the hydrogel based on the temporal and spatial distribution of light. In this study, we propose a nonequilibrium thermodynamic framework to study the photo-chemo-mechano behaviors of light-responsive hydrogel. We firstly describe the light propagation in the hydrogel and the photochemical reaction kinetics. New free energy functions to expound the relationship between the photochemical reaction and thermodynamic process are established, and the constitutive equations are derived. Subsequently, we implant the model into a multi-field coupling analysis software, COMSOL, to conduct a spatio-temporal analysis of the hydrogel's response under uniform light exposure. Finally, we simulate the inhomogeneous deformation of light-responsive hydrogel strips under different illumination conditions and compare the results with experiments. The results highlight the importance of the photochemical reaction rate and the redistribution of light field caused by deformation. The present research holds potential for the precise manipulation and optimal design of light-responsive hydrogel in prospective applications, and offers insights for the synthesis of similar materials as well as the design of pertinent devices.

Notched Tensile Fracture of a Fe-15Mn-0.6C-2Al Twinning Induced Plasticity Steel at Room Temperature

The tensile fracture behavior of an Al-bearing TWIP steel was investigated by conducting a series of tensile tests on smooth and notched specimens with different notch geometries, focusing on the effects of evolution of the stress triaxiality and the effective strain during deformation. The flow curve and digital image correlation (DIC) analysis evidenced suppression of dynamic strain aging due to Al addition, and therefore, the effects of local inhomogeneous deformation associated with Portevin-Le Chatelier (PLC) band on fracture could be excluded. The smooth specimen fractured with negligible necking despite the absence of PLC bands. As a result, the effective strain was uniform through the gage section and the stress triaxiality (<i>η</i>) of ~0.33 was nearly unchanged over the entire cross-section up to the maximum load. This led to the fracture surface of the smooth specimen being entirely covered with fine equiaxed dimples. For notched specimens, the fracture strain was drastically reduced with decreasing notch radius, indicating the high notch susceptibility of the steel. The effective strain of the notched specimens was the highest at the edge of the notch root, regardless of the notch radius, so cracks first developed at the surface of the notch root. Although the <i>η</i> at the center of the notched specimens (0.40~0.48 depending on the notch radius) was higher than that of the smooth one, the center of the fracture surface of all notched specimens exhibited dimple features that were very similar to the smooth one, even in size. In contrast, in spite of the same <i>η</i> of ~0.33, fractography at the edge of the notched specimens revealed a fracture mode transition from dimple fracture to void sheet fracture to quasi-cleavage fracture as the notch radius decreased. The present results were rationalized in terms of the local evolution of stress triaxiality and effective strain during deformation, which were analyzed using the finite elemental method and DIC technique. It can be said that the fracture mode of TWIP steel, showing limited necking, was more influenced by the distribution and/or gradient of stress traiaxiality and effective strain rather than their local absolute values - that is, the severer their gradient is, the easier the quasi-cleavage fracture occurs.

Influence of Severe Plastic Deformation and Aging on Low Cycle Fatigue Behavior of Al-Mg-Si Alloys.

Strain-controlled low cycle fatigue (LCF) tests were conducted on conventionally grained (CG) and ultrafine-grained (UFG) Al-Mg-Si alloys treated under various aging conditions. In the cyclic stress response (CSR) curves, CG peak-aged (PA) alloys showed initial cyclic hardening and subsequent saturation, whereas CG over-aged (OA) alloys displayed cyclic softening behavior close to saturation. The UFG materials exhibited continuous cyclic softening except for UFG 3; it originates from the microstructural stability of the UFG materials processed by severe plastic deformation (SPD). Using a strain-based criterion, the LCF behavior and life of the CG and UFG materials were analyzed and evaluated; the results are discussed in terms of strengthening mechanisms and microstructural evolution. In the CG materials, the LCF life changed markedly owing to differences in deformation inhomogeneity depending on the precipitate state. However, the UFG materials displayed a decreasing LCF life as cyclic softening induced by dynamic recovery became more severe; additionally, a relationship between the microstructural stability of the UFG materials and the cyclic strain hardening exponent n' was suggested.

In-situ deformation inhomogeneity and damage evolution of mixed-grain structure with tempered sorbite/bainite in Fe–Cr–Mo–Mn steel

The inhomogeneous tempered sorbite/bainite (TS/B) with various morphologies and orientations play a significant role in deformation coordination and damage evolution. In this paper, the influence of distinct morphologies and orientations of the mixed-grain structure with TS/B on the deformation heterogeneity were extensively investigated by in-situ tensile testing. Furthermore, a multi-scale model of dislocation density-based crystal plasticity (CP) coupled with the phase field method (PFM) was developed to illustrate the damage nucleation and its evolution via the representative volume element (RVE) modelling. The results shows that mixed-grain structure with TS/B exhibits non-homogeneous deformation during the tensile process, and the coarse grains bear the main plastic deformation, resulting in cross-slip traces and the wrinkling phenomenon at the grain boundary and the interior of coarse grains. Furthermore, the activation of slip systems was determined through slip trace analysis, and the slip transfer behavior between adjacent microstructure was analyzed. According to the critical resolved shear stress (CRSS), the {123}<111> slip system was determined to be the most activated slip system during the in-situ deformation. Hard-orientated lath-shaped B (M1) is more prone to accumulate low angle grain boundaries (LAGBs) than hard-orientated TS (M2) and soft-orientated granular B (M3), resulting in higher orientation rotation degree and geometrically necessary dislocations (GNDs) density of M1 than M2 and M3. The M1 exhibits the nucleation of damage during the initial deformation stage. In addition, compared with the M2 and M3, the Schmid factor (SF) of M1 dominates the transformation from hard orientation to soft orientation and the higher value of damage factor (φ) of M1 results in the more activated slip systems and local damage at high strain levels. This study provides new insights into elucidate the effects of TS/B morphologies and orientations on deformation heterogeneity and damage evolution in large-scale forged spindles for offshore wind power.

Inhomogeneous deformations of Einstein solvmanifolds

AbstractFor each non‐flat, unimodular Ricci soliton solvmanifold , we construct a one‐parameter family of complete, expanding, gradient Ricci solitons that admit a cohomogeneity one isometric action by . The orbits of this action are hypersurfaces homothetic to . These metrics are asymptotic at one end to an Einstein solvmanifold. In the one‐parameter family, exactly one metric is Einstein, and exactly one has orbits that are isometric to .

Understanding the strain localization in additively manufactured materials: Micro-scale tensile tests and crystal plasticity modeling

Metallic parts fabricated by additive manufacturing (AM) usually exhibit unique microstructures and non-negligible residual stresses compared with the counterparts produced by conventional manufacturing. These inherent microstructural factors strongly affect the mechanical response of the as-built AM parts. In this study, we focus on the strain localization behavior of 316L stainless steel produced by laser powder-bed-fusion. In-situ tensile tests under a scanning electron microscope are performed, and the digital image correlation method is used to measure the strain distribution combined with electron backscatter diffraction. Meanwhile, a dislocation-based crystal plasticity finite element model incorporating residual stresses is developed to study the origins of the strain localization in the AM material. The results indicate that strain localization in AM materials is closely associated with microstructural features, encompassing behaviors related to slip activities, interactions with neighboring grains and dislocation evolutions. Additionally, the columnar grain features also render the strain distribution sensitive to the loading direction. The strain localization is serious in some small grains with high residual stresses, while in large grains the effect is less significant. These factors collectively contribute to the increasing likelihood of strain localization occurring in the AM microstructures with heterogeneous grain size and texture distribution. This work provides detailed insights into the strain localization in AM materials and would facilitate the manufacturing parameter optimization of AM materials by tuning the microstructure to reduce deformation inhomogeneity.