Irreversible Strain Research Articles

The Role of Transition Metals on Chemo‐Mechanical Instabilities in Prussian Blue Analogues For K‐Ion Batteries: The Case Study on KNHCF Versus KMHCF

AbstractPrussian blue analogues (PBAs) cathodes can host diverse monovalent and multivalent metal ions due to their tunable structure. However, their electrochemical performance suffers from poor cycle life associated with chemo‐mechanical instabilities. This study investigates the driving forces behind chemo‐mechanical instabilities in Ni‐ and Mn‐based PBAs cathodes for K‐ion batteries by combining electrochemical analysis, digital image correlation, and spectroscopy techniques. Capacity retention in Ni‐based PBA is 96% whereas it is 91.5% for Mn‐based PBA after 100 cycles at C/5 rate. During charge, the potassium nickel hexacyanoferrate (KNHCF) electrode experiences a positive strain generation whereas the potassium manganese hexacyanoferrate (KMHCF) electrode undergoes initially positive strain generation followed by a reduction in strains at a higher state of charge. Overall, both cathodes undergo similar reversible electrochemical strains in each charge–discharge cycle. There is ~0.80% irreversible strain generation in both cathodes after 5 cycles. XPS studies indicated richer organic layer compounds in the cathode‐electrolyte interface (CEI) layer formed on KMHCF cathodes compared to the KNHCF ones. Faster capacity fades in Mn‐based PBA, compared to Ni‐based ones, is attributed to the formation of richer organic compounds in CEI layers, rather than mechanical deformations. Understanding the driving forces behind instabilities provides a guideline to develop material‐based strategies for better electrochemical performance.

Simplified Phenomenological Model for Ferroelectric Micro-Actuator.

As smart structures are becoming increasingly ubiquitous in our daily life, the need for efficient modeling electromechanical coupling devices is also rapidly advancing. Smart structures are often made of piezoelectric materials such as lead zirconate titanate (PZT), which exhibits strong nonlinear behavior known as hysteresis effect under a large applied electric field. There have been numerous modeling techniques that are able to capture such an effect; some techniques are suitable for obtaining physical insights into the micro-structure of the material, while other techniques are better-suited to practical structural analyses. In this paper, we aim to achieve the latter. We propose a simplified phenomenological macroscopic model of a nonlinear ferroelectric actuator. The assumption is based on the direct relation between the irreversible strain and irreversible electric field, and the consequently irreversible polarization. The proposed model is then implemented in a finite element framework, in which the main features such as local return mapping and the tangent moduli are derived. The outcomes of the model are compared and validated with experimental data. Therefore, the development presented in this paper can be a useful tool for the modeling of nonlinear ferroelectric actuators.

Deformation Behaviour and Damage Evolution of Carbonaceous Phyllite under Cyclic Triaxial Loading.

Rocks present complex deformation behaviours and damage processes under triaxial cyclic loading-a subject not yet sufficiently researched. This paper performed triaxial multistage constant-amplitude cyclic loading experiments under different confining stresses on carbonaceous phyllite. The degradation process is analysed by investigating the variation of elastic modulus ES, Poisson's ratio υ, irreversible strain εirr and energy. Moreover, the rock's failure mode is explored from both macro and micro perspectives. The results showed that the increase in stress level caused the decrease of ES in a step-like form, and the constant-amplitude cyclic loading in each stress level caused a slow decrease of ES, while the υ increased with stress level and constant-amplitude cycles in a similar form. εirr accumulated rapidly at first and then slowly at each stress level; the stress level and irreversible axial strain are related by an exponential function. In terms of energy evolution analysis, the damage to rock can be represented by the cumulative damage energy, there were deceleration accumulations and stability accumulation stages of damage at all stress levels, and an acceleration accumulation stage occurred when the rock was close to failure. The failures of rock under cyclic loading are mainly shear failures, accompanied by grain crushing.

Area effect during the fracture process of high-Niobium-Titanium-Aluminum alloys under continuous tension loading-unloading

Based on the extracted results of the continuous tension loading-unloading testing, and observations of the corresponding cracks and fracture surfaces for the high-Niobium-Titanium-Aluminum alloys, both tensile damage and fracture mechanism were systematically studied. From the acquired results, it was demonstrated that the continuous tension loading-unloading did not affect the elastic modulus of the alloy. However, it decreased in fracture stress, fracture strain, and fracture work per unit area, and increased in irreversible strain. This result shows that the irreversible strain is not mainly caused by the volume effect of microcracks, but by the plastic strain of the materials. Although the density of the micro-cracks produced by multi-loading and unloading was small, most of the micro-cracks were concentrated on a certain section area, which results in an obvious area effect caused by the damage of the microcrack. In addition, the further propagation of the main crack under lower re-loading stress was not caused by the application of higher normal stress but by the residual tensile stress, which depends on the deterioration of the material at the crack tip during the unloading process of the alloy. These small amounts of microcracks are usually concentrated on the cross-sectional area, and the area effect caused by the microcracks damage is also obvious, which leads to a reduction of the fracture performance. Therefore, the area effect ultimately induces a decrease in fracture stress.

Revealing the microstructure evolution of the deformed superelastic NiTi wire by EBSD

The generation of irreversible macroscopic strains in superelastic NiTi alloys is an important issue closely related to the crystallography of the transformation from B2 austenite to B19’ martensite under stress. Although widely investigated at micro and nano scales by transmission electron microscopy (TEM), the observation of this phase transformation at the mesoscale is still lacking. In the present study, a superelastic NiTi wire was maintained in bending condition and investigated by electron backscattered diffraction (EBSD) technique. A strong variant selection and a formation of martensite texture were observed and quantified using the interaction work (IW) based on the distortion matrix of a single variant. A new habit plane between martensite and parent B2, {114}B2 || (201¯)M, was experimentally measured. It was explained by the Phenomenological Theory of Martensite Crystallography (PTMC) using dislocation slip {110}<001>B2 as lattice invariant shear (LIS). Some new B2 domains were also found in {114}B2 twinning relation with primary B2 grain. Two scenarios are proposed to explain them: a) the direct formation of {114}B2 deformation twin in B2, and b) a more complex one in which a primary B2 grain is transformed into a martensite variant, a (201¯)M deformation twin is formed inside this variant; then the (201¯)M twinned martensite reversely transforms into a new {114}B2 twinned B2 domain. The scenario b) permits to explain some uncommon (130)M, (201)M, and (101¯)M twins observed by EBSD between the martensite variants of the two {114}B2 twin-related B2 phases.

A thermodynamic-based model for modeling thermo-elastoplastic behaviors of saturated clayey soils considering bound water dehydration

The non-isothermal deformation of soft mudrocks or clay soils is one of the most critical issues in energy and environmental related geotechnics. Clay-related geomaterials hold complex microstructure and mineral composition, which brings difficulty in investigating their thermo-mechanical behaviors. Previous studies pay little attention to the difference between a thermal plastic strain and the strain from clay dehydration. In this study, a new constitutive model is proposed for describing the thermo-elastoplastic behaviors of clayey soils under water-saturated condition. The effect of temperature variation and mechanical loading on elastoplastic strains and dehydration are investigated. The thermodynamics laws and the unconventional plasticity are applied to quantify the thermo-mechanical behavior. The irreversible strain is captured by using Cam-Clay plasticity and subloading yield surface concept. The dehydration strain is described by utilizing a novel method based on generalized thermodynamics approach and Helmholtz free energy function. The internal variables, and the first and second laws of thermodynamics are applied in the model. The hardening rule is established by implementing the laws of physical conservation, energy dissipation, and plastic flow. The proposed model is validated using specially designed thermal consolidation tests on laboratory prepared heavily consolidated clayey soils and some published data of clayey soils with different geological origins.

Studies on the Deformation and Macro-Micro-Damage Characteristics of Water-Bearing Sandstone under Cyclic Loading and Unloading Tests.

The study of the deformation characteristics and damage evolution law of the underground water-bearing rock mass under reciprocating loads such as mine earthquake and mechanical vibration is a very crucial aspect of underground engineering. In this pursuit, the present study was envisaged to assess the deformation characteristics and damage evolution law of sandstone with different water contents under various cycles. Specifically, the uniaxial and cyclic loading and unloading tests, X-ray diffraction (XRD), and scanning electron microscope (SEM) tests of the sandstone under dry, unsaturated, and saturated conditions were carried out under laboratory conditions. Subsequently, the change laws of elastic modulus, cyclic Poisson's ratio, and irreversible strain in the loading section of sandstone under different water content conditions were analyzed. Based on the two-parameter Weibull distribution, the coupled damage evolution equations of sandstone under water content and load were established. The results showed that with an increase in the water content in the sandstone, the loading elastic modulus of the corresponding cycles exhibited a gradual decrease. Microscopic analysis revealed that kaolinite was present in the water-bearing sandstone in a lamellar structure, with flat edges and many superimposed layers, and the proportion of kaolinite gradually increased with an increase in the water content. The poor hydrophilicity and strong expansibility of kaolinite are the key factors in reducing the elastic modulus of sandstone. With the increase of the number of cycles, the cyclic Poisson's ratio of sandstone experienced three stages: an initial decrease, followed by a slow increase, and finally a rapid increase. The decrease was mainly observed in the compaction stage; the slow increase existed in the elastic deformation stage; and the rapid increase was seen in the plastic deformation stage. Furthermore, with the increase of water content, there was a gradual increase in the cyclic Poisson's ratio. The concentration degree of the distribution of the rock microelement strength (the parameter m) under the corresponding cycle of sandstone with different water content states exhibited an initial increase followed by a subsequent decrease. With the increase in the water content, the parameter m under the same cycle gradually increased, and the change rule of parameter m corresponded to the development of internal fractures in the sample. With an increase in the number of cycles, the internal damage of the rock sample gradually accumulated, and the total damage increases gradually but the growth rate decreases gradually.

Structural health monitoring of carbon nanotube-modified glass fiber-reinforced polymer composites by electrical resistance measurements and digital image correlation

A method based on changes of electrical resistance was used to evaluate non-visible damage inflicted to multiscale hierarchical composites subjected to monotonic and cyclic bending loads. The composites comprise glass fiber weaves modified by carbon nanotubes in a vinyl ester matrix. Damage sensing is achieved by placing an array of electrodes close to the surfaces of four-point bending specimens and is correlated to strain fields measured by digital image correlation (DIC). The top (compressive) surface exhibited lower electrical resistance changes than the bottom (tensile) one. Spatial measurements of electrical resistance allowed identification of the most severely damaged zones, which coincided with those pinpointed by DIC. DIC also indicated an important presence of irreversible interlaminar shear strains accumulating close to the supports and/or loading introduction elements, which coincided with the location of delamination. The electrical technique allowed not only the detection of the onset of damage in the form of initial fiber breakage and matrix cracking, but also the detection of damage progression under cyclic loading and low-velocity impact.

Influence of the Crack Angle on the Deformation and Failure Characteristics of Sandstone under Stepped Cyclic Uniaxial Compression with a Constant Lower Limit

Engineering rock structures containing joints and fissures are frequently subjected to discontinuous periodic disturbances of varying amplitudes. To attain the quantitative relationship between the crack angle and the mechanical and deformation properties of rock under complex stress paths, uniaxial cyclic loading and unloading tests with increasing stress gradients were conducted on sandstone specimens containing a single crack of different angles. Our results showed that the bearing capacity of the sandstone increased as the crack angle increased. The irreversible strain and elastic moduli of the rock presented a sudden increase when entering the next cycle of the stepped loading. However, the entire loading process can be divided into three stages according to their respective trends. These three stages correspond to the three stages of rock deformation, i.e., the pore crack compaction stage, the elastic deformation to the stable micro-elastic crack development stage, and the unstable crack development stage. In addition, the crack angle of sandstone showed a negative correlation with the irreversible strain, but a positive correlation with the elastic modulus. With the increasing crack angle, the failure mode of the rock changed from the tensile-shear failure to the shear failure, and then to the interlayer dislocation failure.

Influence of volume compression on the unloading deformation behavior of red sandstone under damage-controlled cyclic triaxial loading

A reasonable evaluation of unloading deformation characteristics is of great significance for the effective analysis of deformation and stability of surrounding rocks after underground excavation. In this study, the damage-controlled cyclic triaxial loading tests were conducted to investigate the pore compaction mechanism and its influences on the unloading deformation behavior of red sandstone, including Young's modulus, Poisson's ratio, volumetric strain, and irreversible strain. The experimental results show that the increases of volumetric and irreversible strains of rocks can be attributed to the compaction mechanism, which almost dominates the entire pre-peak deformation process. The unloading deformation consists of the reversible linear and nonlinear strains, and the irreversible strain under the influence of the porous grain structure. The pre-peak Young's modulus tends to increase and then decrease due to the influence of the unloading irreversible strain. However, it hardly changes with the increasing volumetric strain compaction under the influence of reversible nonlinear strain. Instead, the initial unloading tangent modulus is highly related to the volumetric strain, and clearly reflects the compaction state of red sandstone. Furthermore, both the reversible nonlinear and irreversible unloading deformations are independent of confining pressure. This study is beneficial for the theoretical modeling and prediction of cyclic unloading deformation behavior of red sandstone.

Experimental Study on Mechanical Characteristics of Li2TiO3 Pebble Beds Under Cyclic Loading

The lithium titanate (Li2TiO3) ceramic pebble bed is one of the main tritium breeder candidates in the solid blankets of fusion reactors. Under the extreme operating conditions of fusion blankets, such as neutron irradiation, high temperatures, structural material extrusion, and stress concentration, the mechanical characteristics of tritium breeding pebble beds not only affect the mechanical performance of the blanket but also affect tritium production and extraction. Therefore, an experimental apparatus was built to characterize the mechanical behavior of 0.47 and 0.99 mm Li2TiO3 pebble beds. A uniaxial compression test was performed under the cyclic mechanical loads of 4, 6, and 8 MPa, respectively. It was shown that large irreversible residual strain appeared in the Li2TiO3 pebble bed with the increase of loading cycles and that the mechanical characteristics of the pebble beds were greatly affected by different mechanical loads and particle sizes. The current results provide relevant experimental data that can support the design of fusion blankets.

Mechanical properties and failure characteristics of sandstone under ramp loading paths

The revelation of the mechanical behaviors of rock in complex stress conditions is of vital importance for the safe exploitation of underground resources. In this paper, the ramp loading path was designed to elaborate the mechanical properties and failure characteristics of sandstone under the compound action of linear loading path and cyclic loading and unloading path. The strength, deformation, AE and failure characteristics of sandstone under ramp loading paths were obtained. The research achievements indicate that with the increase of the amplitude and decrease of the stress change rate, the peak stress decreases. Elastic modulus is more greatly affected by the linear path stress than by the cyclic disturbance. The irreversible strain curve is L-shaped under a single loading and unloading cycle. Under lower amplitudes and higher stress change rates, the loading and unloading response ratio fluctuates largely and decreases slightly. Under lower amplitudes and higher stress change rates, the deformation and failure of sandstone caused by stress growth under the linear path is the leading cause for total deformation and failure of sandstone. Under higher amplitudes and lower stress change rates, cyclic loading and unloading are the dominant factor for the failure of sandstone. The research results are of scientific value for evaluating rock failure.

The effect of cyclic stress amplitude on macro‐meso failure of rock under triaxial confining pressure unloading

AbstractThis work aims to explore the impact of cyclic stress amplitude (CSA) on the macro‐meso failure characteristics of deeply buried rock under confining pressure unloading process. The experimental results show that the deterioration of rock structure is influenced by the disturbed stress amplitude. It is found that the lateral expansion induced by confining pressure unloading has a great impact on rock volumetric deformation, damage propagation, and failure characteristics. Additionally, a damage evolution model is proposed and expressed using the irreversible lateral strain. The model is available to express the progressive damage evolution pattern. Finally, CT images investigate the complexity of the crack network, and it decreases with increasing CSA. It is suggested that the final volumetric deformation does not simply depend on the stimulated crack pattern but also on the failure modes. A specimen with the pure shear failure mode has the largest volumetric deformation.

Deformation characteristics of muddy sandstones during cyclic loading and unloading with different stress lower limits under pore pressure

This paper studies the effect of stress lower limit on deformation characteristics of muddy sandstones during cyclic loading under pore pressure. The cyclic loading tests with pore pressure were conducted including increasing, constant, and decreasing stress lower limits. The results indicate that the relationship between deviatoric stress and volumetric strain can be divided into four cases during cyclic loading. The increase in the stress lower limit could reduce the peak strength, accumulate the irreversible strain, and accelerate the failure of muddy sandstones. After failure, both the elastic modulus and Poisson's ratio decrease and fluctuate within a certain range.

Functional properties of NiTi / Kapton nanocomposites deposited by electronic beam evaporation

Shape memory effects were studied in a NiTi / Kapton composite produced by deposition of a thin layer of NiTi on a Kapton substrate by electronic beam evaporation. It was shown that after preliminary deformation by bending at room temperature, the composite demonstrated strain recovery on heating. An increase in preliminary strain increased the recoverable strain the maximum value of which was 2.1 %. The two-way shape memory effect was not observed due to a small thickness of the NiTi layer that did not exceed 300 nm. It was shown that the recoverable strain variation on cooling and heating under a stress was not observed due to the polymer creep on heating. The functional properties of the NiTi / Kapton composite produced by e-beam evaporation were compared to the behaviour of the NiTi / Kapton composite produced by the flash evaporation technique. It was shown that the value of the shape memory effect was comparable for both composites, whereas the irreversible strain was smaller in the samples produced by e-beam evaporation.

Development of a generalised creep-recovery test and a back-calculation method for determining the permanent deformation of asphalt mixtures in the time domain

The measured strain during a creep-recovery (CR) test comprises both reversible and irreversible strains; therefore, adequate treatment is required to accurately separate them. In this paper, a generalised version of the CR test was proposed to investigate the permanent deformation behaviour of asphalt mixtures exerted by a variety of loading patterns in the time domain. The companion back-calculation algorithm was also proposed to separate with improved accuracy and repeatability the pure viscoelastic (VE) and viscoplastic (VP) strains. First, the creep compliance (CC) was back-calculated based only on the recovery data by using an approximate analytical creep compliance function of the Huet-Sayegh model as the solution function in the optimisation process. Then, the pure VE and VP strains were determined. The results show that the proposed method attains a good level of reliability although relatively short durations of the recovery period have been used.

Experimental investigation on mechanical characteristics of red sandstone under graded cyclic loading and its inspirations for stability of overlying strata

The horizontal stress in the fractured blocks of a fractured zone is in a stress relief status under repeated mining disturbances. To investigate the effect of the horizontal stress in fractured blocks on the stability of the overlying strata, uniaxially graded cyclic loading and unloading experiments on red sandstone with different initial stress level were carried out. First, the evolution of the loading and unloading elastic modulus, irreversible strain and load-unload response ratio were analyzed. Then, the strain energy evolution and damage variable characteristics were examined. Finally, the stability of a voussoir beam structure under repeated mining disturbances was discussed. The results showed that with increasing cycle number, the elastic modulus showed a nonlinear decreasing trend, the load-unload response ratio always fluctuated at approximately 1, and the irreversible strain showed a rapid and steady increasing trend. The proportion of elastic energy tended to increase linearly with increasing cycle number, while the proportion of dissipated strain energy tended to decrease. Moreover, the damage variable, based on the dissipation strain energy definition, showed a parabolic growth trend with increasing cycle number. The irreversible strain and damage variables showed an “increasing–decreasing-increasing” trend as the initial stress level increased. Finally, a stability criterion of the voussoir beam structure based on the effect of repeated mining disturbances on horizontal thrust was proposed. This research has important implications for overlying strata stability.

Critical current degradation behaviour of various REBCO tapes under uniaxial strain

REBCO coated tapes have become one of the most practical superconducting materials, which have been considered in the design of high-field magnets for fusion in the future. At present, several manufacturers are able to produce commercial REBCO tapes. During the fabrication and operation of REBCO magnets, REBCO tapes are subjected to tension, compression, bending, and torsion loads, resulting in applied strains. However, the critical current (Ic) of REBCO tape is strain dependence. Therefore, the clear Ic performance of a single REBCO tape under applied uniaxial strain is required before designing REBCO conductors/magnets in order to help select an appropriate tape specification and manufacturer. In this paper, several measurements of Ic and n-value versus applied uniaxial strain were performed on different kinds of REBCO tapes, which were produced by Shanghai Superconductor Technology and Fujikura at 77 K with self-field on the U-spring device. The width of the REBCO tape is from 3 mm to 5 mm, and the thickness of the substrate is from 25 μm to 50 μm. The results show that the Ic of most of the tapes are reversible under applied uniaxial compressive strain. The width of the tape and the thickness of the substrate affects the irreversible tensile strain limit. The n-value of the REBCO tape hardly depends on the strain condition.

An advanced constitutive model for transversely isotropic rock - Evaluation of two different regularization approaches

The mathematical description of the material behavior of rock is a demanding task in engineering practice. Rock is classified as a frictional cohesive material characterized by highly nonlinear mechanical behavior with irreversible deformation, strain hardening, strain softening and degradation of stiffness. In addition, depending on the origin of a particular rock type, the orientation of minerals and grains as well as the formation of stratification planes lead to inherent anisotropic behavior. Especially in stratified rock types like shales or phyllites, often the special case of transversely isotropic material behavior is encountered. In a previous work, a novel continuum-based material model for describing both, the highly nonlinear and transversely isotropic material behavior of rock, denoted as TI-RDP model, was presented. By means of the linear mapping of the Cauchy stress tensor into a fictitious isotropic configuration, an established isotropic damage plasticity model for rock was extended. In this contribution two different regularization approaches, which are well established for isotropic models, i.e., the mesh-adjusted softening modulus and the implicit gradient-enhancement, are adopted for the TI-RDP model. Based on uniaxial tension and triaxial compression tests considering different orientations of the principal material directions with respect to the direction of axial loading, their capabilities are assessed in terms of predicting the direction-dependent mechanical behavior in a mesh-insensitive manner.

Effect of prior cyclic damage on rock failure exposed to triaxial multistage unloading confining pressure and cyclic loads

AbstractA series of triaxial alternative unloading and damage‐controlled cyclic loading tests were conducted on deeply buried granodiorite. The testing results reveal that the prior cyclic loading damage influences rock volumetric deformation, stiffness degradation, damage evolution, and failure modes. Rock volumetric deformation and hysteresis ratio increase with increasing prior cyclic damage, and the subsequent damage propagation is the most severe for a sample subjected to high cyclic damage. A larger hysteresis ratio indicates large plastic deformation and energy loss. In addition, a damage evolution model was proposed based on the irreversible radial strain, and it well describes the damage propagation at the respective cyclic loading stage (CLS) and unloading confining pressure stage (UCPS). Moreover, as prior damage increases, the dominant failure mode changes from shear failure to mixed shear–tensile failure and then to tensile failure. It is suggested that rock failure is cyclic damage dependent; damage fully develops under high cyclic damage.