Geometric Compatibility Research Articles

Investigation of active slip modes via in-grain misorientation axis and strain compatibility of TA2 alloy during in-situ tensile deformation

Slip is an important mechanism to coordinate the deformation in metal materials. Grain boundary can hinder slip transfer, thus lead to strain concentration. This work focus on the law of slip coordination deformation, texture evolution and strain compatibility under different strains. Based on the electron backscattered diffraction (EBSD) technique, the in-situ tensile tests of TA2 alloy were carried out at strain of 2 %, 4 % and 6 %, the activate law of slip under different strains was analyzed by the in-grain misorientation axes (IGMA) method and was verified by Schmid factor (SF). The relationship between grain orientation and strain compatibility at grain boundaries was discussed by calculating the geometric compatibility factor (m′). The results show that the multi-system slip coordination deformation at initial deformation, and the prismatic slip dominates the deformation as the increase of strain. The texture is preferentially distributed in the transverse direction (TD) as the deformation proceeds. The strain concentration is mainly related to the lack of effective plastic deformation mechanism to complete strain transfer at grain boundaries.

On the superelastic behavior during spherical nanoindentation of a Ni-Ti shape memory alloy

Nanoindentation, the most widely-used probe for small-scall mechanical property evaluation, has been increasingly adopted for exploring the local behavior of shape memory alloys (SMAs). Herein, we explore the influence of the testing parameters (i.e., peak load, indenter radius, loading/unloading rate, and cyclic loading) on the superelastic behavior of a Ni-Ti SMA at room temperature, at which it is in the austenitic state, during spherical nanoindentation. The possible underlying mechanisms for measured response due to each of the testing parameters are discussed in terms of the roles of forward/reverse stress-induced phase transformations, dislocation activity, latent heat evolution, and geometric compatibility of the interfaces during the post-yield deformation.

High-entropy oxides for energy-related electrocatalysis

Electrocatalysis plays a crucial role in the conversion and storage of renewable energy, offering significant potential for addressing the energy crisis and environmental concerns. High-entropy oxides (HEOs), a class of emerging functional materials, have gained increasing attention in electrocatalysis due to their stable crystal structure, exceptional geometric compatibility, unique electronic balance factors, and abundant active sites. In this comprehensive review, we present recent advancements in utilizing HEOs as catalysts for various energy-based electrocatalytic reactions. We begin with an overview of HEOs that includes definitions, fundamental properties, and theoretical investigations. Subsequently, we describe different synthetic methods for HEOs while highlighting two newly-developed techniques. Furthermore, we extensively discuss recent developments in HEO-based electrocatalysts with diverse crystal structures such as rock-salt-type, rutile-type, spinel-type, perovskite-type, and other specially-structured HEOs. Special emphasis is placed on designed strategies aimed at enhancing performance and exploring correlations between structure/ composition and electrocatalytic performance. Finally, we provide concluding remarks along with perspectives on future opportunities in this exciting field.

Mesh-Based Double-Sided Freeform Lens Optimization

We present a mesh-based method for optimizing double-sided freeform lenses to control their caustic effects. Unlike traditional single-sided approaches, we optimize both sides of the lens simultaneously, using a bijective correspondence between the two sides to control light refraction paths. Our approach balances image fidelity, geometric compatibility, and physical constraints. Results demonstrate the method’s capability to accurately produce intricate light patterns, opening new possibilities in optical applications.

Pure measures of bending for soft plates.

This paper, originally motivated by a question raised by Wood and Hanna [Soft Matter, 2019, 15, 2411], shows that pure measures of bending for soft plates can be defined by introducing the class of bending-neutral deformations, which represent finite incremental changes in the plate's shape that do not induce any additional bending. This class of deformations is subject to a geometric compatibility condition, which is fully characterized. A tensorial pure measure of bending, which is invariant under bending-neutral deformations, is described in detail. As shown by an illustrative class of examples, the general notion of a pure measure of bending could be useful in formulating direct theories for soft plates, where stretching and bending energies are treated separately.

Effect of pre-strain on critical conditions for hydrogen-induced delayed cracking and crack nucleation characteristic of DP1180 steel

Hydrogen-induced delayed cracking represents a significant threat to the dependable performance of advanced high-strength steel. This study employed constant load tensile tests to uncover critical conditions for hydrogen-induced delayed cracking of DP1180 steel plate, establishing a precise relationship between pre-strain, threshold stress, and critical hydrogen concentration. Furthermore, this research explored dislocation slip transfer at grain boundaries, utilizing geometric compatibility factor (m') and residual Burgers vector (br), and analyzed slip characteristics at martensite/martensite, ferrite/ferrite, and martensite/ferrite interfaces. These findings provide valuable references for the safety assessment of DP1180 in hydrogen-exposed environments.

Estimating design positions of suspension bridge tower saddles in the completed bridge state: An analytical approach

Saddle position is an essential parameter in the form-finding of main cables and for the construction control of suspension bridges. In actual suspension bridges, the center of the arc-shaped tower saddle in the completed bridge state may sometimes deviate toward the river and the river bank. However, the influencing factors and the judgment method for the deviation have yet to be thoroughly studied. This study proposes an analytical approach for estimating saddles positions in the completed bridge state of suspension bridges under two definitions of the intersection point (IP) of the main cable in the tower top: (i) IP between the two extended catenary segments of the main cable and (ii) IP between the two extended straight lines of the main cable. For catenary-based IP, the calculation of the saddle position is separable from the form-finding of the main cable. Once the shape of the main cable is derived, equations can be established based on the geometric compatibility conditions for the saddle and main cable, their solving required for deriving saddles positions. For straight line-based IP, the calculation of the saddle position is inseparable from the form-finding of the main cable, and the two processes are conducted simultaneously. Equations can be established based on mechanical equilibrium and the geometric compatibility conditions for the saddle and the main cable and then solved. The relationship between the position of the center of the arc-shaped tower saddle and the centerline of the tower is analyzed, proving that the saddle deviates toward the side with a smaller catenary parameter. The eccentric compression of the tower is analyzed, implying that the eccentric moment acting on the tower in the completed bridge state is primarily produced by the self-weight of the saddle and the main cable segment in the saddle. Finally, the feasibility of the proposed method and the correctness of the above findings are verified through a suspension bridge with a main span of 730 m.

Microstructural insights into fatigue short crack propagation resistance and rate fluctuation in a Ni-based superalloy manufactured by laser powder bed fusion

The microstructural sensitivity of fatigue short crack path and its propagation rate in a Ni-based superalloy GH4169 manufactured by laser powder bed fusion (LPBF) was investigated at room temperature. In-situ digital image correlation (DIC) observation and post-mortem microstructural analysis around the crack path were performed. The results show that the intragranular cracks developed in the shear cracking mode are closely aligned along the activated slip bands in the γ-matrix grains with the crystallographic characteristics of parallel to the γ-{111} slip planes. Multiple slip was also activated, causing the crack retardation or deflection. Low-angle grain boundaries and subgrain boundaries were shown to cause deflections of intragranular cracking, while high-angle grain boundaries significantly arrested the short crack propagation. Moreover, the resistance of grain boundaries to short cracking was assessed using combined metrics including the crystallographic and microstructural parameters of twist angle, the Schmid factor and the geometrical compatibility factor. These site-specific microstructural analyses around the crack path provide insights into the microstructural origins of resistance to the short crack propagation as well as an interpretation of the observed significant fluctuations in the crack propagation rate.

Investigation into effect of grain sizes on deformation behavior of AZ31 alloys in different loading conditions

The AZ31 magnesium alloy with different grain sizes was prepared by adjusting the heat treatment process, and then the tension and compression tests were carried out to explore the effect of grain sizes and loading conditions on the microstructures and properties of the magnesium alloy. The Hall-Petch slope presented dramatic anisotropy under tension (181 Mpa· μm1∕2) and compression (115 Mpa· μm1∕2), the geometric compatibility factor (m′) and the difference in activation stress between the initiated deformation modes of two neighboring grains (σd) were calculated to analyze the anisotropy quantitatively. In compression, it was found that the elongation increased with further grain coarsening, which was attributed to the fact that more twins were initiated in the coarse grains and the preferred initiation of twinning to inhibit competitive crack initiation.

In-situ study of damage mechanisms in Mg–6Li dual-phase alloy

Interfaces play a crucial role in influencing the mechanical properties of Mg alloys. For Mg–Li dual-phase alloy, the type of interfaces is complex, which includes both grain boundary and phase boundary, and the influence of such interfaces on the damage nucleation is yet to be explored. In this paper, in-situ scanning electron microscopy (SEM) based measurements were carried out to investigate the meso‑scale damage nucleation mechanisms of the Mg–6Li dual-phase alloy. Results show that 94.8% of cracks are nucleated at the α-Mg grain boundary in the post-uniform elongation stage, while 5.2% are at phase boundary and almost no crack at the β-Li grain boundary. The initiation of α-Mg grain boundary cracks is attributed to strain incompatibility, which induces micro-strain localization, and then causes grain boundary sliding (GBS) and crack nucleation. Deformation compatibility analysis reveals that the geometric compatibility factor (Mk) can be used to predict the nucleation of α-Mg grain boundary crack. When Mk is lower than 0.075, α-Mg grain boundary cracks tend to form. Few cracks are generated at the phase boundary is due to the mild strain partitioning between α-Mg phase and β-Li phase and may also be partly attributed to multiple slip systems in body-centered cubic (BCC)-structured β-Li phase, which can accommodate well with the deformation of adjacent α-Mg phase.

Quasi-in situ observation of extension twinning of AZ31 magnesium alloy under co-directional dynamic compression

In this paper, twinning nucleation and microstructure evolution of AZ31 magnesium alloy were investigated during the quasi-in situ dynamic compression. The microstructure characterization of the sample before and after deformation was performed via electron backscatter diffraction and transmission electron microscopy. The strain accommodation was estimated by selecting twinning variants and using the geometric compatibility factor (m'). The nucleation behavior of 55.4% extension twinning obeyed Schmid's law under high strain rate compression. The non-Schmidt twinning variants with the highest geometric compatibility factor (m') in the active twinning system of adjacent grains were activated in paired twins that affected the twining nucleation and variant selections.

Structure-Chiral Selectivity Relationships of Various Mandelic Acid Derivatives on Octakis 2,3-di-O-acetyl-6-O-tert-butyldimethylsilyl-gamma-cyclodextrin Containing Gas Chromatographic Stationary.

Frequently, a good chiral separation is the result of long trial and error processes. The three-point interaction mechanisms require the fair geometrical fitting and functional group compatibility of the interacting groups. Structure-chiral selectivity correlations are guidelines that can be established via trough systematic studies using model compounds. The enantiorecognition of the test compounds was studied on an octakis 2,3-Di-O-acetyl-6-O-tert-butyldimethylsilyl-gamma-cyclodextrin (TBDMSDAGCD) chiral selector. In our work, mandelic acid and its variously substituted compounds were used as model compounds to establish adaptable rules for other enantiomeric pairs. The mandelic acid and its modified compounds were altered at both their carboxyl and hydroxyl positions to test the key interaction forces of the chiral recognition processes. Ring- and alkyl-substituted mandelic acid derivatives were also used in our experiments. The chiral selectivity values of 20 test compounds were measured and extrapolated to 100 °C. The hydrogen donor abilities of test compounds improved their chiral selectivities. The inclusion phenomenon also played a role in chiral recognition processes in several cases. Enantiomer elution reversals were observed for different derivatives of hydroxyl groups, providing evidence for the multimodal character of the selector. The results of our research can serve as guidelines to achieve appropriate chiral separation for other enantiomeric pairs.

Volumetric embedded entities for the IsoGeometric Analysis of complex structures

We propose a convenient methodology for the modeling and analysis of aircraft compressor blades. To meet this goal, IsoGeometric Analysis is put to good use, as it allows for an exact representation of the geometry, especially for the analysis. This work aims at developing numerical tools to handle mechanical analysis, and later on shape optimisation, of 3D aircraft engine compressor blades using IGA. More precisely, our final goal is to carry out shape optimisation of one precise patch belonging to a complex multipatch structure, while having other patches to follow automatically the geometric changes. To meet this goal, work on geometric and modeling aspects are needed, which is the objective of this paper. Using the proposed techniques to perform gradient-based shape optimisation constitutes a work in itself and is therefore not presented here, but will be detailed in a follow-up paper.In our case, the complete blade assembly is represented using several volumetric patches: the airfoil, the platform, the tenon and the fillet. In order to ensure the geometric compatibility between the different patches, we propose an embedded solid element formulation. A mortar method is implemented in order to guarantee the coupling between the various parts of the assembly. The results show a great potential for the proposed approach for blades design, while concurrently offering broad perspectives in terms of applications.

Achieving high strength-ductility synergy in a dilute Mg-Gd-Zn-Zr alloy with heterogeneous structure via hot extrusion

The common problem of low tensile yield strength (TYS) prevails in high ductility dilute-alloying Mg-RE alloys prepared by traditional hot extrusion. The design strategy of heterostructures in the microstructure of Mg alloys can effectively improve the strength-ductility synergy in mechanical properties, which is expected to break the trade-off dilemma between strength and ductility. In this work, we successfully prepared a series of high ductility as-extruded Mg-Gd-Zn-Zr alloys with all elongations (ELs) greater than 26.0% at room temperature. By controlling the extrusion process and thus introducing heterogeneous fiberous structure, we finally obtained a superior Mg-1.5Gd-0.5Zn-0.5Zr (wt.%) alloy with strength-ductility synergy, which exhibits a TYS of 246 MPa, ultimate tensile strength (UTS) of 274 MPa and an EL of 29.0%. The microstructure examination for the alloy with the heterostructure reveals that the structure consists of alternating filamentous deformed-grain and fine-grain layers. The overall fine grains in the microstructure, a large amount of nanoprecipitates and the relatively high density of residual dislocations contribute to the high TYS of the alloy. The alloy maintaining high ductility is attributed to the activation of multiple slip systems, especially the active and mobile <c+a> dislocations, the inhibition of the P-type dislocation to B-type dislocation transition, {10 1¯ 2} tensile twinning generated early during tensile testing, and full intergranular slip transfers caused by high geometric compatibility. The present work can further promote the development of dilute-alloying Mg-RE alloys with high strength-ductility synergy.

Experimental investigations of combustion oscillation modes in a large-aspect-ratio dual-mode combustor equipped with multi-strut

The annular scramjet combustor is considered one of the best configurations for a wide-speed-range combined engine, owing to its superior thermal protection performance and optimal geometric compatibility with rockets and turbines. To investigate the effect of fuel injection methods on the flame oscillation characteristics in the annular combustor, a scaled-down experiment was conducted on a fan-shaped combustor with a high aspect ratio equipped with multiple struts, utilizing liquid kerosene as the fuel. A series of experiments were conducted at the combustor inlet conditions of Ma = 2.7, Pt = 1.68 MPa, and Tt = 1640 K. High-speed cameras and pressure measurements were used in the experiments, and the flame images were processed using proper orthogonal decomposition. The findings revealed that under single-strut and multi-strut injection conditions, the flame oscillated in two modes: shear layer oscillation and central flame oscillation. As the equivalent ratio of injection strut increased, the oscillation frequency increased from 25 to 284 Hz, and the oscillation mode transition caused by the adverse pressure gradient occurred. The flashback was closely related to the combustion mode, and the distinct flame propagation processes under supersonic and subsonic flow conditions resulted in different oscillation characteristics. The experiment demonstrated that the flashback issue could be mitigated by increasing the spacing between the fuel injection struts. The study in this paper will provide important references for future research on flame oscillation and propagation characteristics in high-aspect-ratio annular combustors.

Crystallographic orientation-dependent dislocations slip during tensile testing of lath martensitic steel

Based on observations of slip traces and variant-pair boundaries obtained through the transformation of the Kurdjumov-Sachs (K-S) orientation relationship from quasi in-situ electron backscatter diffraction (EBSD), the corresponding slip systems, Schmid factors (SF), and geometric compatibility parameter (m') around the crack were calculated during tensile testing of lath martensitic steel. The occurrence of slip transfer, which typically happens at low values of m' or SF, resulted in stress concentration on crystallographic orientations of 50.5°, 60°, and twin-related orientations. However, more effective slip transfer and plastic deformation were observed at 20° due to larger m' and SF values.

Ultimate Load-Bearing Capacity of Rigid Two-Way Pavements Placed on Geosynthetic-Supported Soil Embankment

This study investigates the ultimate load-bearing capacity of rigid two-way concrete pavements placed on conventional and reinforced soil embankments using upper-bound limit analysis (UBLA). In the presence of the median strip, upper-bound solutions of rigid pavements resting on reinforced embankments did not draw much attention from previous researchers. Therefore, a rigorous UBLA is performed, adopting the multi-block failure mechanism for the intended purpose. The true upper-bound solution is achieved by satisfying the conditions of geometric compatibility and kinematic admissibility. The effects of the proximity of dual carriageways and embankment slopes on the load-bearing capacity of pavements are expressed in relation to interaction factors. The critical spacing beyond which the proximity effect ceases to exist is estimated for different slope angles of the embankment. A parametric investigation is performed to understand the influence of various soil parameters, embankment geometry, and layers of reinforcement. A notable improvement in the performance of two closely spaced rigid pavements can be observed by providing additional layers of reinforcement. The current outcomes are sensible and match well with the existing investigations.

Revealing the effect of misorientation on the deformation behavior of a Mg-Y alloy from the perspective of local strain

The addition of rare earth (RE) elements in magnesium alloys may significantly enhance the ductility of magnesium alloys, which is generally attributed to the decrease of stacking fault energy, the reduced critical resolved shear stress (CRSS) differences among different deformation modes and the weakening of basal texture. Rare earth elements also change the misorientation between adjacent grains of magnesium alloy, whose effects on the deformation behavior and thus the ductility of magnesium alloy were not emphasized before. In this work, ex-situ high-resolution digital image correlation (HR-DIC) coupled with electron backscatter diffraction (EBSD) was used to reveal the effect of the misorientation on the deformation behavior of a Mg-Y binary alloy from the perspective of local strain. It is shown that the heterogeneity of local strain is largely dependent on the misorientation between adjacent grains. For the intergranular deformation, three scenarios are observed, namely strain transfer, strain concentration and suppressed deformation, which mainly occurs at low misorientation, moderate misorientation and high misorientation, respectively. In addition, much more non-basal slip is found to be activated near the grain boundaries with moderate misorientation angles due to the high geometric compatibility factor (m’B-Pr/Py), which is favorable for the intergranular deformation compatibility, thus reducing the strain concentration near grain boundaries and achieving high ductility. For the intragranular deformation, a wide range of misorientation between adjacent grains in the Mg-Y alloy causes multiple basal slip systems to be activated within a grain, which also facilitates work hardening, thus contributing to improving ductility. Therefore, tailoring the misorientation between adjacent grains may be an effective way to improve the ductility of magnesium alloys.

Cucurbituril-Shaped Cd18(triazolate)12 Unit-Based Metal-Organic Framework Exhibiting an C2H2/CO2 Separation Ability.

Herein, a metal-organic framework (MOF), {[(Me2NH2)4][Cd(H2O)6][Cd18(TrZ)12(TPD)15(DMF)6]}n (denoted as JXNU-18, TrZ = triazolate), constructed from the unique cucurbituril-shaped Cd18(TrZ)12 secondary building units bridged by 2,5-thiophenedicarboxylic (TPD2-) ligands, is presented. The formation of the cucurbituril-shaped Cd18(TrZ)12 unit is unprecedented, demonstrating the geometric compatibility of the organic linkers and the coordination configurations of the cadmium atoms. Each Cd18(TrZ)12 unit is connected to eight neighboring Cd18(TrZ)12 units through 30 TPD2- linkers, affording the three-dimensional structure of JXNU-18. More interesting is that JXNU-18 displays an efficient C2H2/CO2 separation ability, as revealed by the gas adsorption experiments and dynamic gas breakthrough experiments, which afford insights into the potential applications of JXNU-18 in gas separation. The tubular pores composed of two Cd18(TrZ)12 units bridged by six 2,5-thiophenedicarboxylic linkers provide the suitable pore space for C2H2 trapping, as unveiled by computational simulations.

In-Situ Study on the Tensile Deformation and Fracture Mechanism of a Bimodal-Structured Mg-Gd-Y Alloy.

The as-extruded (EX) Mg-Gd-Y alloy studied here exhibited a bimodal structure, composed of fine dynamic recrystallized (DRXed) grains with random orientations and longitudinal coarse hot-worked grains. The slip analysis showed the DRXed grains exhibited mainly basal slips, while the hot-worked grains exhibited mainly prismatic slips during the tensile deformation. The distribution of geometrically necessary dislocations (GNDs) showed that there was strain partitioning between the fine and coarse grain regions. The hetero-deformation induced (HDI) hardening occurred between the two domains. It improves the strength and strain hardening capability of the alloy, leading to good strength-ductility synergy. Microcracks tended to nucleate at the DRXed grain boundaries, as well as at the interface between the two domains. The calculation of geometric compatibility parameter (m') indicated that strain incompatibility between the adjacent grains induced the crack nucleation. The toughening effect of the fine DRXed grains hindered the crack propagation. However, the major crack formed at the interface between the two domains propagated unstably, due to the high stress concentration and the large crack size, causing the final failure.