Biaxial Straining Research Articles

Analysis of Experimental Biaxial Surface Wrinkling Pattern Based on Direct 3D Numerical Simulation.

This paper presents a direct 3D numerical simulation of biaxial surface wrinkling of thin metal film on a compliant substrate. The selected compliant substrate is a commercial Scotch tape on which a gold metal thin film has been transferred by using low adhesion between the thin metal film and polyimide substrate. Compared with the previous fabrication of a cylindrical thin-film wrinkling pattern, an undulated wrinkling pattern has been implemented by increasing the width of the thin metal film in order to create biaxial straining in the thin film. To understand the wrinkling behavior due to biaxial loading, a simple direct numerical simulation based on material imperfections defined in the compliant substrate has been conducted. Through modeling and simulation, it was found that the wrinkling mode is determined by the biaxiality ratio (BR), the ratio between transversal strain and longitudinal strain. Depending on the BR, the wrinkling mode belongs to one of the cylindrical, undulated (or herringbone), checkerboard, or labyrinth modes as a function of applied strain. The cylindrical wrinkling is dominant at the input of BR less than 0.5, while the undulated (or herringbone) ones become dominant just after the onset of the wrinkling pattern at BR greater than 0.9. Through the comparison of the wrinkling patterns between simulation and experiment, the applied BR of the fabricated thin film has been successfully estimated.

Fostering mica exfoliation through biaxial straining strategy with monovalent cation substitution

Efficiently exfoliating mica for 2D applications remains a challenge, partly due to a lack of comprehensive design principles based on atomistic modelling of its solid mechanics. In this investigation, we employed a threefold approach: (1) Biaxial straining principles were utilized to compute electron–electron, electron–phonon, and phonon–phonon interactions at crack tips, (2) first-principles calculations were employed to explore the intrinsic relationship between muscovite mica's crystalline structure, electronic properties, ion exchange energy, and exfoliation energy, particularly in the context of various interlayer cations, and (3) experiments were conducted to corroborate the theoretical forecasts. Our findings reveal a compelling correlation between the unit cell size and the ionic radius of the interlayer cation, a phonon-dependent parameter, whereas the bandgap energy, an electron-dominant parameter, remains relatively unaffected. The electron–phonon interactions, characterized by the dihedral angle and size of the hexagonal tetrahedral ring, are influenced by the properties of the interlayer cation, crucially governing ion exchange and exfoliation energy. Significantly, mica featuring H+ interlayer cations demonstrates substantial biaxial strains, aligning with the lowest exfoliation energy, thereby facilitating efficient exfoliation. Our experimental endeavors validate that Li+ intercalation prompts a reduction in number of layers in resulted nanosheets, observed in the order of Li+ nanosheets < Na+ nanosheets < K+ nanosheets. Notably, Li+ intercalation enhances mica's exfoliation into thinner nanosheets. We propose a strategic biaxial straining approach: either replacing the interlayer cation with the smallest cation (H+) or employing larger cations within the boundaries of ion exchange. These outcomes contribute valuable insights into mica's exfoliation mechanisms and furnish a comprehensive guideline for proficiently exfoliating layer-structured materials.

Strain-Induced SiP–PtS2 Heterostructure with Fast Carrier Transport for Boosted Photocatalytic Hydrogen Conversion

Earth-abundant silicon-, phosphorus-, and sulfur-related compounds are crucial for optoelectronic application. Specifically, experimentally proven monolayer SiP has attracted a great deal of attention in above listed field owing to its unique properties but is plagued with challenges such as photocorrosion and poor charge separation. Moreover, theoretical understanding on the relationship of the interface and photocatalytic activity in SiP-based chemicals is not well understood. In this work, hybrid functional first-principles calculations were used to explore the photocatalytic hydrogen evolution activity of SiP–PtS2 heterostructure. Further examination of phonon, ab initio molecular dynamics (AIMD), and elastic property simulations confirms its dynamical stability. Its computed band gap of 1.59 eV is suitable for maximizing solar energy conversion efficiency, with noticeable strong absorption coefficients of 105 cm–1 order across visible–ultraviolet domains, asymmetric decent carrier mobility (∼103 cm2 V–1 s–1), and low exciton binding energy (0.56 eV). Differences in charge density and Bader and Mulliken population analyses reveal that charge flows from the SiP to the PtS2 layers, performing the dual functions of segregating photoinduced charge carriers and increasing their lifetimes. The relative band alignment of the monolayers promotes a spatial separation of the charges. An important feature of this heterostructure is that the band edges cross the water redox potential at pH of 0 upon −2% of compressive biaxial straining, with ΔG for hydrogen evolution reaction (HER) barrier lower than −0.2 eV. The quadratic relationship between biaxial strain and atomic energy indicates that both the system and strains are elastic. Redox thermodynamic analysis predicts facile hydrogen production on the heterostructure. In particular, the calculated maximum solar power conversion efficiency (PCE) and solar-to-hydrogen (STH) efficiency can reach 22.9 and 23.8%, respectively.

Engineering the light absorption spectrum and electronic properties of black and blue phases of a SiSe monolayer via biaxial straining

Engineering the light absorption spectrum and electronic properties of black and blue phases of a SiSe monolayer via biaxial straining

Film thickness and architecture effects in biaxially strained polymer supported Al/Mo bilayers

Multilayers on polymer substrates are of interest for several technical applications. However, the true understanding of how one layer affects the other during mechanical loading is still unknown. In order to address this lack of knowledge, single and bilayer thin films of Al (250, 125, and 75 nm) and Mo (50 nm) were sputter deposited onto polyimide (PI, 50 µm) and biaxially strained in-situ with X-ray diffraction. The technique allows for the simultaneous measurement of lattice strains of Al and Mo to correlate the observed mechanical behavior of both materials. Using the evaluated film stress and full width at half maximum evolutions, four domains of mechanical behavior are identified. The presence of the domains in either Al or Mo depends on the thickness of the Al films and, more importantly, the bilayer architecture (Al/Mo/PI vs. Mo/Al/PI). Domain boundaries in Al were found to correspond well with domain boundaries in the Mo, such as necking in Al with fracture in Mo or simultaneous fracture in both materials. The maximum stress achieved in the Mo layers during biaxial straining was also found to highly depend on the architecture and depend less on the Al film thickness. Results will demonstrate that the film architecture (layer order) is more important than the film thickness to enhance fracture resistance.

In situ electrical and mechanical study of Indium Tin Oxide films deposited on polyimide substrate by Xe ion beam sputtering

Four series of Indium Tin Oxide (ITO) thin films 600 nm thick were deposited on polyimide substrates by Xe ion beam sputtering under different deposition conditions: with or without O2 flow, and at room temperature or 100 °C heated substrates. Both electrical and mechanical properties of the four different films were investigated in situ by electrical resistance measurements and synchrotron x-ray diffraction during equibiaxial deformation tests. The ITO films are found to have a low elastically anisotropy, i.e. an elastic anisotropy index slightly smaller than 1. The elastic regime domain is quite small and is associated to a small effective negative gauge factor. During biaxial straining, electrical measurements show that all films are very brittle with crack onset strains corresponding to applied strains ranging from 0.15 to 0.3%. The introduction of oxygen flow during deposition delays the crack onset as the decrease of deposition temperature does.

Microstructure and Formability of Laser Welded Dissimilar Butt Joints of Austenitic-Ferritic Stainless Steels

Dissimilar laser welding of ferritic, type EN 1.4509, and austenitic, type EN 1.4307, stainless steel sheets was conducted at different energy inputs 30 and 80 J/mm and under different shield gases Ar and N and without shielding gas to evaluate the microstructure and hardness of the welded zone. The formability tests, using Erichsen principle, were carried out to determine the deformation behaviour of the dissimilar welded joints under biaxial straining. The fusion zone microstructure analysis revealed that the predominant phase structure is columnar coarse ferritic grains with slightly small content of austenite in the ferrite grain boundaries. The formability of the welded joints under Ar and N shielding gases is significantly improved, i.e., higher plasticity, compared with welded joints without shielding gas at both energy inputs.

A computationally tractable framework for nonlinear dynamic multiscale modeling of membrane woven fabrics

AbstractA general‐purpose computational homogenization framework is proposed for the nonlinear dynamic analysis of membranes exhibiting complex microscale and/or mesoscale heterogeneity characterized by in‐plane periodicity that cannot be effectively treated by a conventional method, such as woven fabrics. The framework is a generalization of the “finite element squared” (or FE2) method in which a localized portion of the periodic subscale structure is modeled using finite elements. The numerical solution of displacement driven problems involving this model can be adapted to the context of membranes by a variant of the Klinkel–Govindjee method1 originally proposed for using finite strain, three‐dimensional material models in beam and shell elements. This approach relies on numerical enforcement of the plane stress constraint and is enabled by the principle of frame invariance. Computational tractability is achieved by introducing a regression‐based surrogate model informed by a physics‐inspired training regimen in which FE2 is utilized to simulate a variety of numerical experiments including uniaxial, biaxial and shear straining of a material coupon. Several alternative surrogate models are evaluated including an artificial neural network. The framework is demonstrated and validated for a realistic Mars landing application involving supersonic inflation of a parachute canopy made of woven fabric.

Spontaneously Ordered Hierarchical Two-Dimensional Wrinkle Patterns in Two-Dimensional Materials.

Achieving two-dimensionally (2D) ordered surface wrinkle patterns is still challenging not only for the atomic-thick 2D materials but also in general for all soft surfaces. Normally disordered 2D wrinkle patterns on isotropic surfaces can be rendered via biaxial straining. Here, we report that the 1D and 2D ordered wrinkle patterns in 2D materials can be produced by sequential wrinkling controlled by thermal straining and vertical spatial confinement. The various hierarchical patterns in 2D materials generated by our method are highly periodic, and the hexagonal crystal symmetry is obeyed. More interestingly, these patterns can be maintained in suspended monolayers after delamination from the underlying surfaces which shows the great application potentials. Our new approach can simplify the patterning processes on 2D layered materials and reduce the risk of damage compared to conventional lithography methods, and numerous engineering applications that require nanoscale ordered surface texturing could be empowered.

Damage Analysis in Dual-Phase Steel Using Deep Learning: Transfer from Uniaxial to Biaxial Straining Conditions by Image Data Augmentation

Microstructural damage can occur during metal forming, but how and where this happens vary with the local microstructure and strain path. Large-scale analysis of such damage mechanisms is particularly important in advanced steels with a heterogeneous phase distribution. In our previous work, we demonstrated that deep learning enables a mechanism-based, statistical analysis by classifying many individual damage sites. The aim of this work is to generalize this approach to different stress states, e.g., biaxial instead of uniaxial tension, without manually labeling a large new ground-truth dataset of further micrographs and to thereby assess the changes in damage behavior with respect to stress state. Data augmentation and regularization allow us to directly apply our approach to the new, biaxial loading case. Overall, the network performance could be greatly improved and an analysis of changes in damage behavior, here the martensite crack angle distribution, with stress state can now be performed.

Microstructural evolution of 316L austenitic stainless steel during in-situ biaxial deformation and annealing

Austenitic stainless steel 316L was investigated by a combination of in-situ biaxial straining and subsequently by in-situ annealing within a Carl Zeiss Sigma FEG-SEM. A Micromecha Proxima stage was used to impart biaxial strain on the sample, results were compared with macro scale testing to validate the method, and physical properties were established in close correlation to macro scale tests. Samples were subsequently subjected to annealing cycles using a Gatan Murano 525 heated stage to assess the influence of imparted strain on the recrystallization kinetics of the material. Following annealing trials the material was observed to initiate recrystallization around 100 °C earlier within heavily strained samples at 750 °C in comparison to 850 °C within unstrained samples.

Enhanced photocatalytic activity for water splitting of blue-phase GeS and GeSe monolayers via biaxial straining.

The structural, electronic, dipole-induced internal electric field, optical and photocatalytic properties of monolayer GeS and GeSe under external biaxial strain were investigated by using first-principles calculations. The monolayer GeS and GeSe are indirect semiconductors with the band gaps of 3.265 eV and 2.993 eV, respectively. The band alignment of the monolayer GeS and GeSe manifests the photocatalytic activity for water splitting. Especially, it is effective to tune the properties including structures, band gaps, surface potential difference, dipole moment P, dipole-induced internal electric field, absorption and photocatalytic activity of the monolayer GeS and GeSe via biaxial strain. Our results suggest that monolayer GeS and GeSe possess photocatalytic properties for water splitting, and strain engineering, especially tensile strain, can enhance the photocatalytic activity under ultraviolet and visible light.

Relaxation mechanisms in a gold thin film on a compliant substrate as revealed by X-ray diffraction

The fact that the polymeric substrate does not relax after a load jump allows realizing an original relaxation experiment of a metallic thin film. Thanks to the combination of two strain probes done at different scales, namely, X-ray synchrotron diffraction and digital image correlation techniques, the apparent activation volumes are monitored and their values help to capture leading deformation mechanisms in thin films. Such experiments have been performed on a nanocrystalline gold thin film, and deformation mechanisms involved during a biaxial straining have been distinguished between different texture components.

The role of extrusions and intrusions in fatigue crack initiation

The profiles of persistent slip markings produced by uniaxial and biaxial cyclic straining in four different polycrystalline materials with f.c.c. structure were investigated using focused ion beam (FIB) cutting and TEM observation of oriented surface foils. Typical shapes of persistent slip markings are extrusions accompanied by parallel intrusions. In some cases only extrusions were developed and intrusions were produced later in fatigue life. In polycrystalline copper extrusions and intrusions appear on the surface of the grain where persistent slip band characterized by ladder-like dislocation structure egress on the surface. Similar features were observed in fatigued austenitic 316L and Sanicro 25 steels but the extrusion and intrusion shapes were more complicated. Crack-like intrusion shapes produce high stress and strain concentration and primary stage I crack starts to grow from the tip of intrusions. The experimental observations were compared with the predictions of the existing crack initiation models.

Assessment of X-ray diffraction and crystal plasticity lattice strain evolutions under biaxial loading

A methodology to simulate X-ray diffraction lattice strains using crystal plasticity, replicating in-situ synchrotron experimental measurements during the deformation of a low-carbon steel, has been developed. Uniquely, the model calculated lattice strains for full Debye–Scherrer diffraction rings, providing the in-plane lattice strain distributions determined from crystal plasticity. Thus, a direct method of comparison between experimental and crystal plasticity results becomes possible. The model considered two forms of hardening whilst subjecting the material to two dissimilar proportional strain-paths; uniaxial and balanced biaxial deformation. Both deformation paths showed influence on resulting lattice strain distributions which were also found to depend upon texture. Biaxial straining led to a stronger dependence on the material's hardening behaviour and this was attributed to the higher rate of work hardening seen under biaxial compared to uniaxial straining. However, biaxial deformation showed quite isotropic lattice strains distribution, irrespective of initial texture or hardening. Quantitatively, good agreement between the computed and experimentally determined lattice strain distributions was obtained for each strain path. This success demonstrates the possibility of calibrating crystal plasticity model parameters using such methodologies, or simply to provide insight into the governing mechanisms in polycrystal deformation.

Impurity-Induced Grain Boundary Strengthening in Polycrystalline Graphene

First-principles density functional theory (DFT) calculations were performed to investigate the effects of boron (B) and nitrogen (N) doping on the fracture behaviors of a series of symmetric graphene grain boundaries (STGBs) under biaxial straining. Doping was found to generally enhance the fracture strength of STGBs, which was shown to be attributed to dopants mechanically lowering the local stretching energy or chemically strengthening the critical bond. We also showed that doping may also induce crack deflection to further improve the fracture resistance of graphene grain boundaries (GBs). Furthermore, we showed that the presence of multiple B and N dopants in the pentagon-heptagon ring(s) can contribute to promoting intergranular fracture in the presence of a small prestrain along the GBs. Our findings clarify the role of B and N dopants in GBs strengthening of polycrystalline graphene.

The asymptotic solution of particle growth in the convective undercooled melt driven by a biaxial straining flow

A dynamical system of particle growth in the convective undercooled melt driven by a biaxial straining flow is modeled. A uniformly valid asymptotic solution for the interface evolution in particle growth is obtained by means of the multiple variable expansion method. The analytical solution as a function of both azimuth angle and polar angle shows that the interface shape of particle growth in the biaxial straining flow is significantly deformed by the biaxial straining flow. The biaxial straining flow results in higher local growth rate near the surface where the flow comes in and leads to lower local growth rate near the surface where the flow goes out. Due to the difference in local growth rate, an initially spherical particle will evolve into a prolate barrel-like shape in the biaxial straining flow.

Experimental Investigation of the Formability of Organic Coated Steel Sheet Metal

Application of the coating to material in a flat condition has economical, technological and ecological advantages. As the material is subsequently formed into shape not only the base material needs to withstand this process but the coating as well. Development of forming tools for coated metals is mainly concerned with the prediction of performance of the base material and does not analyse the condition of the coating. However, during the forming process, major surface damage can occur when the coated sheet is bent and unbent around the die geometry. To reduce surface damage of coatings, proper control of the parameters during forming and a detail study of the surface conditions is required. This research is conducted on metallically and organically coated sheet material which is commonly used for structural applications. The crack density of the coating is analysed during a deep drawing process and a forming limit diagram is obtained from the biaxial straining of the prepainted steel samples. The results show that cracks initiate from within the organic coating and are linked to the strain in the base material.

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

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

Texture, hardening and non-proportionality of strain in BCC polycrystal deformation

Non-proportionality of straining, initial texture and hardening has been investigated in single- and polycrystal BCC steel using a crystal plasticity finite element framework. The effect of hardening on achievable ductility is also predicted for a BCC polycrystal. Two extreme forms of hardening have been investigated; namely, isotropic latent hardening and anisotropic self-hardening. Dislocation density evolutions on all independent slip systems have been calculated in order to investigate the establishment of dislocation distributions and their dependence on non-proportionality, hardening and initial texture. Results for a BCC single crystal are considered first in order to provide insight into subsequent polycrystal investigations.The degree of non-proportionality during straining, whilst maintaining in all cases the identical, final strain state, has been shown to lead to moderately differing final stress states, with a higher degree of non-proportionality giving the largest divergence from the corresponding proportional stress states. The nature of the hardening is also found to influence the strength of the non-proportionality effect, with isotropic latent hardening leading to the development of greater non-proportionality effects on stress than those for anisotropic self-hardening in polycrystals. The polycrystal dislocation distributions established are found to depend on the degree of non-proportionality, particularly under uniaxial straining conditions (as opposed to biaxial straining), and very strongly on the nature of the hardening assumed, but less so on the initial texture. In addition, the predicted limit strain is moderately affected under non-proportional biaxial strain paths as opposed to more significant increases under non-proportional uniaxial strain paths. It has been shown that that non-proportionality plays a key role in the establishment of strain localization and hence on forming limits.