Elastic Strain Energy Density Research Articles

Oxygen-induced decomposition of the body-centered cubic HfNbTaTiZr high-entropy alloy

The factors affecting the stability of an initially single-phase body-centered cubic (BCC) HfNbTaTiZr solid solution are investigated by heat treatments at 900°C up to 1000 h in different atmospheres. The BCC solid solution is stable but oxygen (O) contamination originating from the aging atmosphere leads to the co-precipitation of an O-enriched hexagonal close-packed (HCP) Hf-Zr-rich phase and a second Nb-Ta-rich BCC phase. As O from the atmosphere diffuses from the surface to the core of the sample at a much faster rate along grain boundaries than through the grain interior, this results in an inhomogeneous distribution of precipitates, which formed at grain boundaries by a monotectoid reaction. In contrast, coincidence-site-lattice boundaries are not affected by this transformation owing to their lower diffusivities and lower capacity for heterogeneous nucleation. Similar phases were observed in a HfNbTaTiZr enriched with 3 at.% O, thus confirming the role of oxygen in phase stability.In both alloys, the orientation relationship (OR) between the HCP and BCC phases is predominantly of Burgers type but our analyses further revealed the presence of two minor ORs. More interestingly, both alloys exhibit rod-shaped HCP precipitates in contrast to the plate-shaped precipitates observed in conventional Ti and Zr-based alloys. This result can be rationalized by calculations of elastic strain energy density, which suggest that the rods should grow along 〈100〉BCC to minimize the elastic strain energy. Deviations of up to 20° from this theoretical direction were observed and are likely related to relaxation by misfit dislocations or by plastic deformation.

Singularity distance computations for 3-RPR manipulators using intrinsic metrics

Avoiding singularities is a crucial task in robotics and path planning. This paper proposes a novel algorithm for detecting the closest singularity to a given pose for nine interpretations of the 3-RPR manipulator. The algorithm utilizes intrinsic metrics based on the framework's total elastic strain energy density, employing the physical concept of Green-Lagrange strain. The constrained optimization problem for detecting the closest singular configuration with respect to these metrics is solved globally using tools from numerical algebraic geometry implemented in the software package Bertini. The effectiveness of the proposed algorithm is demonstrated on a 3-RPR manipulator executing a one-parametric motion. Additionally, the obtained intrinsic singularity distances are compared with extrinsic metrics. Finally, the paper illustrates the advantage of employing a well-defined metric for identifying the closest singularities in comparison with the existing methods in the literature, highlighting its application in design optimization.

Exploring the structural mechanics of titanium nickel solid alloy using COMSOL Multiphysics: A Poisson equation and continuity equation perspective

This study investigates the structural mechanics of titanium-nickel (Ti-Ni) alloy thin film using computational modelling through COMSOL Multiphysics based on Poisson’s equation and continuity equation for stress check by considering its linear elastic, conservation of charge and providing insight into nanomaterial deformation. In the COMSOL environment the parameters for titanium nickel (Ti-Ni) are embedded in the COMSOL Simulink interface. The Thin film layer was designed by defining the layer geometry of the size and shape of the layer with a width of 500 μm, depth of 200 μm and height of 3 μm subjected to boundary conditions such as von – mises stress, surface temperature, iso-surface temperature, multi-slice electric potential, displacement component, surface elastic strain energy density and total enthalpy. The results displayed a trend that is, as the surface temperature increases there will be an increase in the current densities associated with high electrical conduction. On the same note, the designed thin film layer will pass the percolation threshold. The results of surface elastic strain energy density and total enthalpy imply that the designed thin film layer is effective and efficient as a structural pseudopotential device (photodiode).

Study on rock energy evolution and constitutive model under water–rock interaction

To explore the degradation in rock mechanical properties due to water–rock interactions and formulate a nonlinear damage constitutive model for the entire stress–strain curve of rocks, experiments involving saturated, dry-wet cycling, and uniaxial compression tests were conducted on granite and siltstone. Based on energy theory, the energy evolution of the rock throughout the testing process was scrutinized. The range of the compaction stage was identified through the analysis of the dissipation energy change curve. A nonlinear damage constitutive model for rocks subjected to water-rock interactions was then devised, drawing on concepts from statistical damage mechanics. The findings indicated a progressive reduction in uniaxial compressive strength and elastic modulus due to water–rock interactions, while the Poisson’s ratio was observed to increase. The energy density curve under these conditions delineated four distinct phases: compaction energy dissipation, linear energy accumulation, pre-peak gradient increase, and post-peak sudden change. The introduction of the unit elastic strain energy density metric underscored the deteriorating effects from an energy standpoint. A nonlinear damage constitutive model, incorporating the compaction stage based on a coupled damage variable, was formulated. The predictions of this model closely matched the empirical data, thereby affirming its validity. This model provides an enhanced depiction of rock deformation and failure mechanisms under the influence of water–rock interactions.

On the energy decomposition in variational phase-field models for brittle fracture under multi-axial stress states

AbstractPhase-field models of brittle fracture are typically endowed with a decomposition of the elastic strain energy density in order to realistically describe fracture under multi-axial stress states. In this contribution, we identify the essential requirements for this decomposition to correctly describe both nucleation and propagation of cracks. Discussing the evolution of the elastic domains in the strain and stress spaces as damage evolves, we highlight the links between the nucleation and propagation conditions and the modulation of the elastic energy with the phase-field variable. In light of the identified requirements, we review some of the existing energy decompositions, showcasing their merits and limitations, and conclude that none of them is able to fulfil all requirements. As a partial remedy to this outcome, we propose a new energy decomposition, denoted as star-convex model, which involves a minimal modification of the volumetric-deviatoric decomposition. Predictions of the star-convex model are compared with those of the existing models with different numerical tests encompassing both nucleation and propagation.

A computational method for tunnel energy evolution in strain-softening rock mass during excavation unloading based on triaxial stress paths

The squeezing deformation of deep soft rock tunnels is driven by energy. Few scholars have carried out theoretical research on energy evolution for deep soft rock tunnels. This study proposes a computational method for tunnel energy evolution in strain-softening rock mass during excavation unloading based on triaxial stress paths. The characteristics of energy distribution and energy evolution are further investigated. Results show that energy is input from the distant surrounding rock after tunnel excavation and converted into elastic strain energy in the elastic stage. In the plastic stage, the elastic strain energy density in the plastic zone reaches the storage limit, which is reduced due to the strain-softening behaviour. Thus the dissipated and released energy of the surrounding rock increases exponentially. For deep rocks with high peak strength, the energy evolution in the plastic stage is dominated by energy release, which indicates that rockburst mainly results from the energy release mechanism. In contrast, for the surrounding rock with low strength, the energy evolution during excavation unloading is dominated by energy dissipation due to the significant strain softening behaviour. Large squeezing deformation mainly stems from the energy dissipation mechanism.

On the origin of Sanchez-Lacombe equation of state theory in hydrostatic strain energy model for rubber-like materials

To capture the volume deformation of rubber-like materials, the strain energy density (SED) function of a compressible hyperelastic model is formulated as the hydrostatic/liquid-like term from interchain interaction changes plus the compressible elastic term owing to elastic deformation of crosslinking network. Notably, the former term dominates volume responses. Although the physics of the hydrostatic term is relatively clear, to our knowledge, few physically-based models are available. However, in our previous work (Liu and Lu, 2023), we constructed a physically-based hydrostatic SED function inspired by the Flory-Orwoll-Vrij equation of state (EOS) theory for pure polymer fluids, and proposed the general strategy for developing hydrostatic functions according to the EOS theories. Sanchez-Lacombe EOS theory (note: a type of lattice-fluid EOS theory) inspired this work. We assume: (i) a rubber-like material consists of polymer segments occupying lattice sites and unoccupied/vacant lattice sites, and the compressibility of the material corresponds to changes in vacant sites fraction; (ii) the hydrostatic strain energy is associated with the interchain interaction energy change and the mixing entropy change between network and vacant sites. According to the Helmholtz free energy in Sanchez-Lacombe EOS theory and limiting our attention to the isothermal condition, another physically-based hydrostatic SED function is constructed; a specific compressible hyperelastic model is provided by further combining compressible 8-chain elastic SED function. The basic framework of this compressible model is inherently consistent with the Flory-Rehner framework for swollen elastomers. Our model provides good predictions for volume deformation data of ten different rubber-like materials in hydrostatic compression (HC), uniaxial tension (UT), and constrained uniaxial compression (CUC). The proposed model reveals that HC, CUC, or uniaxial compression correspond to the entropy-decreasing process and they all are controlled by entropy changes; while for UT, equibiaxial tension, or pure shear, the entropy first increases and then decreases, and the interchain interaction energy and entropy changes control the responses for initial small stretches and remaining large stretches, respectively. This study aims to provide a new physical insight and a valid physically-based hydrostatic SED function for the compressibility of rubber-like materials.

A novel elastic strain energy density approach for fatigue evaluation of welded components

The averaged elastic strain energy density (SED) within a characteristic volume radius R has been investigated and applied for characterizing the fatigue strength of welded joints for decades. However, engineering applications are still relatively rare. The main reason is that the calculation process is cumbersome due to fine mesh size and circular pattern requirements. This study proposes a novel approach of SED without requiring special finite element size and special layout requirements. First, a novel approach of the notch stress solution is presented. As a result, the present solution differs from the conventional approach which has been focused on notch tip singular stress field. Then, an averaged strain energy density can be obtained analytically by taking advantage of the new notch stress solutions presented in this study. Both the closed-form notch stress solutions and resulting expression for average strain energy density have been validated by FEA results. Subsequently, a large number of fatigue tests published in the literature are selected to examine the effectiveness of the evaluation approach of SED on interpreting fatigue behaviors of welded joints. Finally, a procedure for practical engineering application is established and verified by a group of fatigue tests of 3D gusset welded components.

Determination of SIFs and application of a SIF-based fracture criterion for concrete-rock interface under sustained loading

This study proposes an effective method to determine the stress intensity factors (SIFs) of the interface crack considering the viscoelasticities of the bilateral materials and verifies the feasibility of the initial fracture toughness-based fracture criterion for the concrete-rock interface under sustained loading. Firstly, low-level sustained loading tests were conducted on the composite concrete-rock specimens with respect to two interface roughness degrees and two sustained load levels less than the initial cracking load. Then, an implicit creep equation was employed to characterise the viscoelasticities of bilateral materials and then calculate the mechanical responses of the concrete-rock interface in the low-level sustained loading test. The SIFs of the interface crack under sustained loading were determined by using the elastic strain energy density ahead of the crack tip. By averaging the SIFs over the radius of the core region of the crack tip, the representative SIFs under sustained loading were obtained. The test results indicated that the SIFs showed decreasing tendencies under sustained loading, and the initial fracture toughness can be considered as a material property of the concrete-rock interface. The initial fracture toughness-based fracture criterion was verified to be feasible to determine the initial cracking status of the concrete-rock interface under sustained loading. In addition, due to the reductions of the SIFs under sustained loading, additional loads were required to compensate the losses of the SIFs, leading to the enhancement of the initial cracking loads after experiencing the sustained loading.

A theoretical model for power generation via liquid crystal elastomers

Motivated by the need for new materials and green energy production and conversion processes, a class of mathematical models for liquid crystal elastomers (LCEs) integrated within a theoretical charge pump electrical circuit is considered. The charge pump harnesses the chemical and mechanical properties of LCEs transitioning from the nematic to isotropic phase when illuminated or heated to generate higher voltage from a lower voltage supplied by a battery. For the material constitutive model, purely elastic and neoclassical-type strain energy densities applicable to a wide range of monodomain nematic elastomers are combined, while elastic and photothermal responses are decoupled to make the investigation analytically tractable. By varying the model parameters of the elastic and neoclassical terms, it is found that LCEs are more effective than rubber when used as dielectric material within a charge pump capacitor.

Study on Rock Failure Criterion Based on Elastic Strain Energy Density

Uniaxial and five conventional triaxial compression tests were conducted on sandstone to obtain the evolution laws of the input energy density, elastic strain energy density, and dissipative energy density. The input and dissipative energy densities increased with increasing axial strain; the elastic strain energy density increased with increasing axial strain at the pre-peak stage and decreased after the peak. According to the linear change rule between the peak elastic strain energy density and confining pressure, the energy density failure criterion of sandstone was established, and the criterion has high precision and few parameters, and the parameters have clear physical meaning. Moreover, the expression of the energy density failure criterion was similar to the classical Hoek-Brown criterion, but its adaptability was more extensive. The strength calculation results for seven different rocks under different confining pressures calculated using the energy density failure criterion were consistent with the experimental values, and the calculation error was smaller than that of the Mohr–Coulomb criterion and Drucker–Prager criterion, verifying the accuracy and applicability of the criterion.

Irreversible thermodynamics of surfaces and interfaces: Special reference to the strained thin solid films on the substrates: Theory and practice

The realization of nanoscale devices largely depends on our ability to control and manipulate interfacial interactions and, thus, understanding of the mechanisms of surface/interface instabilities. In this work, theoretically as well as technologically important and distinct two thermodynamic systems, which are exposed to (isobaric) and isolated from (isochoric) external body forces and surface tractions, are formulated by using irreversible thermodynamics in combination with the generalized variational method. The starting point for the present formulation closely follows up the Fowler and Guggenheim [Statistical Thermodynamics (University Press, Cambridge, 1952)] interpretation of the Planck inequality [Über Prinzip Vermehrung Entropie: Ann. Phys. Series 2(32), 462 (1887)] for isothermal reversible and irreversible (natural) infinitesimal changes in heterogeneous systems (multi-phase and multi-component). By combining this fundamental principle with the interlink between the dissipation function and global internal entropy production postulates, two distinct sets of governing equations for the surface drift-diffusion flux as well as the rate of evaporation/condensation and/or the growth/recrystallization of amorphous solid thin films are obtained for isochoric and isobaric systems. The role of Eshelby's energy-momentum tensor in the generalized potential for the interface displacement is found to differ (opposite in sign) for isochoric and isobaric systems. To demonstrate the importance of these sign conflicts, two sets of computer experiments are performed on isochoric and isobaric systems. They showed us that the elastic strain energy density contribution to the generalized driving force for surface drift-diffusion alone favoring flat and smooth surfaces in isobaric systems regardless of the sign of the uniaxial stress (healing), rather than causing the surface roughness and even catastrophic crack initiation as the case in internally strained isochoric systems. Computer simulations allowed us to track down the dynamical behavior of test modules by furnishing surface and strain energy variations, combined with the Global Helmholtz free change, which indicates the existence of two regimes: initial smooth surface undulations followed up by the rather chaotic crack formation and propagation stage at the middle of the thin film supported by the stiff substrate. In this study, we mainly focused on the development kinetics of “Stranski–Krastanow” island-type morphology, initiated by the nucleation route rather than the surface roughening scheme. The physicomathematical model, which is based on the irreversible thermodynamics treatment of surfaces and interfaces with singularities [T. O. Ogurtani, J. Chem. Phys. 124, 144706 (2006)], furnishes us to have autocontrol on otherwise free-motion of the triple junction contour line between the substrate and the droplet without presuming any equilibrium dihedral contact (wetting) angles at edges. We have also demonstrated the formation of the Stranski–Krastanow (SK)-type doublet islanding (quantum dots) as a stationary nonequilibrium state in an epitaxially strained thin flat droplet on a rigid substrate by introducing the wetting potential—invoked by the quantum confinement—into the scenario and carefully selecting the system parameters (size and shape) for the isochoric system represented by [Ge/Si (100)]. It has been also shown that on the contrary to common perceptions, the Stranski–Krastanow islands are in genuine stationary nonequilibrium states in the sense of Prigogine if one invokes proper free-moving boundary conditions at triple junctions deduced from the irreversible thermodynamics rather than ad hoc periodic or reflecting constrains at the edges.

Composite collaborative acoustic metamaterials: Isolating shaft vibration of guide roller in printing machine

During the operation of the unit type gravure press, the violent mechanical vibration generated by the guide roller will seriously affect the stability of the unit operation, and causing transmission faults such as wrinkle, offset, scratch or fracture, and reducing the printing accuracy. To this problem, a novel multi-approach composite collaborative vibration isolator which combines the local resonator and multi-layer composite structure is proposed to solve the problems of vibration suppression in the single frequency and vibration energy dissipation in the full frequency band, respectively, and the theoretical model on the proposed isolator is established basing on dynamic stiffness method. For demonstrating isolation performance, the regularized normalized modal displacement, power loss density, elastic strain energy density, total kinetic energy, and vibration transmission ratio can be discussed. The results show that the composite vibration isolator has a wide vibration isolation band, and the vibration wave has two attenuation bands within 0–2000 Hz. The first attenuation band is 188–224 Hz and the width is 36 Hz; the second attenuation band is greater than 328 Hz. When the band of the vibration isolator is above 700 Hz, the vibration transmission ratio shows a monotonous decreasing trend. Furthermore, an experimental platform for the vibration isolation device of the guide roller is established to verify the vibration isolation performance. When the drive motor frequency is 20 Hz, the composite vibration isolator has the best vibration isolation effect. At the same time, the vibration isolation effect gradually decreases with the increase of the guide roller speed, but it still has preferable vibration isolation performance under various working conditions.

Mechanical Behavior of Bamboo-Like Structures under Transversal Compressive Loading.

Inspired by many biological structures in nature, biomimetic structures demonstrate significantly better mechanical performance than traditional engineering structures. The exceptional mechanical properties of natural materials are attributed to the hierarchical architecture of their structure. Consequently, the implementation of biomimetic structures in the design of lightweight structures with tailored mechanical properties has been constantly increasing in many fields of science and engineering. The bamboo structure is of particular interest because it combines a light weight and excellent mechanical properties, often surpassing those of several engineering materials. The objective of this study was to evaluate the mechanical behavior of bamboo-inspired structures subjected to transversal compressive loading. Structures consisting of bamboo-like thin-walled hexagonal building blocks (unit cells) with different dimensions were fabricated by stereolithography 3D printing and their mechanical performance was evaluated by mechanical testing, high-speed camera video recordings, and finite element simulations. The results of the elastic modulus, yield strength, and strain energy density at fracture were interpreted in terms of characteristic dimensions of the unit cell structure. The failure process was elucidated in the light of images of the fractured structures and simulation strain maps. The results of this study demonstrate that ultralight bamboo-like structures with specific mechanical characteristics can be produced by optimizing the dimensions and number density of the hexagonal unit cell.

Study of Local Fatigue Methods (TCD, N-SIF, and ESED) on Notches and Defects Related to Numerical Efficiency

The fatigue strength of structural components is strongly affected by notches and imperfections. Both can be treated similarly, as local notch fatigue strength methods can also be applied to interior defects. Even though Murakami’s √area approach is commonly used in the threshold-based fatigue design of single imperfections, advanced concepts such as the Theory of Critical Distances (TCD), Notch Stress Intensity Factors (N-SIF), or Elastic Strain Energy Density (ESED) methods provide additional insight into the local fatigue strength distribution of irregularly shaped defects under varying uniaxial load vectors. The latter methods are based on the evaluation of the elastic stress field in the vicinity of the notch for each single load vector. Thus, this work provides numerically efficient methods to assess the local fatigue strength by means of TCD, N-SIF, and ESED, targeting the minimization of the required load case count, optimization of stress field evaluation data points, and utilization of multi-processing. Furthermore, the Peak Stress Method (PSM) is adapted for large opening angles, as in the case of globular defects. In detail, two numerical strategies are devised and comprehensively evaluated, either using a sub-case-based stress evaluation of the defect vicinity with an unchanged mesh pattern and varying load vector on the exterior model region with optimized load angle stepping or by the invocation of stress and strain tensor transformation equations to derive load angle-dependent result superposition while leaving the initial mesh unaltered. Both methods provide numerically efficient fatigue post-processing, as the mesh in the evaluated defect region is retained for varying load vectors. The key functions of the fatigue strength assessment, such as the evaluation of appropriate planar notch radius and determination of notch opening angle for the discretized imperfections, are presented. Although the presented numerical methods apply to planar simulation studies, the basic methodology can be easily expanded toward spatial fatigue assessment.

Time-Dependent Fracture Behavior of Rock–Concrete Interface Coupling Viscoelasticity and Cohesive Stress Relaxation

This study investigated the time-dependent crack propagation of the rock–concrete interface under sustained loading. First, sustained loading tests were performed on the composite rock–concrete beams under three-point bending with respect to three interface roughness degrees, i.e., natural, 4×4, and 7×7 interfaces, and three sustained load levels, i.e., 80% of the maximum load, the initial cracking load, and 97% of the maximum load. Then, by employing the Norton-Bailey model and the time-dependent fictitious crack model, the constitutive relationships of bilateral materials and the rock–concrete interface were established and the mechanical responses of the rock–concrete interface under sustained loading were simulated. In addition, a crack propagation criterion proposed in this study was applied in the numerical procedure to simulate the time-dependent crack propagation process under sustained loading. The criterion implied that the interface crack propagated when the difference between the average elastic strain energy densities near the crack tip caused by the external load and cohesive stress exceeded that at the initial fracture status under quasi-static loading. The results indicated that the crack propagation under sustained loading could be interpreted from the view of energy balance between the driving energy from the external load and the resistance energy from the cohesive stress. The time-dependent crack propagation under sustained loading experienced three stages, i.e., decelerated propagation, uniform propagation, and accelerated propagation. A linear relationship between the logarithms of the crack mouth opening rate in the uniform propagation period and the failure time was established to predict the failure time of the rock–concrete interface under sustained loading.

Localizing gradient damage model based on a decomposition of elastic strain energy density

The simplest form of the localizing gradient damage model assumes the standard elastic strain energy, with an isotropic damage variable driven by a scalar equivalent strain. Such models are simple to implement, but become inadequate for quasi-brittle materials, when the loading conditions induce significant compressive stresses. In this contribution, the elastic strain energy density is decomposed into tension and compression parts by the spectral decomposition method for incorporated into the isotropic localizing gradient damage model. Firstly, the improved performance of the proposed decomposition model is illustrated by a cantilever beam problem. For the decomposition model, damage only evolves under tension conditions, while for the conventional model, the damage evolves in both tension and compression conditions. Next, a series of geometrically similar Double-Edge-Notched (DEN) specimens and the L-shaped panel are considered to show the predictive capability of the decomposition model, in terms of crack trajectories for concrete complex mixed-mode fractures. To further demonstrate the superiority of the decomposition model, a series of concrete Brazilian disc compression tests are considered, where the decomposition model captures the crack profile under strong compression loads most accurately.

New insights into the bond-based and ordinary state-based models in Peridynamics

Twenty years in since its introduction, Peridynamics established by Silling provides an attractive theory for modeling deformation and fracturing in solid materials. The paper aims to revisit the well-established bond-based Peridynamic (BPD) and ordinary state-based Peridynamic (OSPD) models and attempts to provide new insights into them. To this aim, a novel decomposition of the Peridynamic bond length change is developed, and the bond length change components are used to define a new micro-potential function. The macroscopic nonlocal elastic strain energy density (NESED) is computed through the integral of the micro-potential over the horizon. The constitutive relation is obtained by the Frechet derivative of the NESED with respect to the deformation state. The NESEDs and constitutive bond force densities are discussed with specific influence functions. The main foundings of the present work are as follows: (1) An explicit expression of bond micro-potential is proposed, and the NESED obtained by the integral of the micro-potential over the horizon can retrieve the ad hoc NESED in the OSPD model. It could pave the way for the development of micro-potential based bond failure criterion for the OSPD model. (2) It is proven that the constitutive relation in the OSPD model can be recovered by the present constitutive relation with specific influence functions in the case where the deformation is small. (3) As the Poisson ratio is 1/3 in plane stress condition or 1/4 in plane strain condition, the present Peridynamic model with specific influence functions is reduced to the BPD model in the case of small deformation, and thus the BPD model can be considered as a reduced form of an OSPD model. Moreover, numerical investigations on a single edge-notched plate under mode II dominated loading and three-point bending tests are conducted to illustrate the descriptive and predictive capabilities of the present Peridynamic model.

Analysis of the deterioration process of the dolomite with the interlayer in different directions during wetting

Taking the dolomite with anhydrite interlayer at the bottom of Huangcaoshan Tunnel in Shanghai-Wuhan-Chengdu high-speed railway as the research object, the wetting deterioration and uniaxial compression tests were performed to study the influence of different interlayer orientations on the hygroscopic deterioration characteristics of rock and to analyze the process of rock deterioration. The wetting cracking and deformation characteristics of dolomite with interlayer in different directions were analyzed respectively from the time effect of rock micro-expansion and the change of ultrasonic longitudinal wave velocity, and the uniaxial compression evolution process of samples with different moisture absorption conditions and interlayer directions was analyzed respectively from the aspects of crack volume strain and energy dissipation. The results show that the direction of interlayer had a significant effect on the wetting and deterioration of the rock. The sample with vertical interlayer cracked obviously during wetting, resulting in volume expansion along the axial and radial directions of the sample; However, the sample with horizontal interlayer had almost only axial volume expansion, and the expansion rate was small. After the rock was wet and deteriorated, the propagation velocity of ultrasonic longitudinal wave in the rock decreased, and the decrease amplitude in the sample with vertical interlayer was greater than that in the sample with horizontal interlayer. After rock wetting, its uniaxial compressive strength, crack initiation level, expansion level, and the threshold value of elastic strain energy density for failure decreased, while the radial peak strain, the energy conversion rate of dissipation increased, and the plastic characteristics of the sample were enhanced, and the sample with vertical interlayer changed significantly compared with the sample with horizontal interlayer.

Study on the mechanical properties of fiber-modified iron tailings stabilized by lime and fly ash based on energy analysis

After being cured by lime and fly ash and then modified by fiber material, waste iron tailings can obtain good road performance, which can not only reduce the accumulation of iron tailings but also save natural resources and can be used as a new road material with good performance. In this study, polypropylene fiber (0 %, 0.25 %, 0.5 %, 0.75 %, 1 %) was added to lime-fly ash solidified iron tailings (LHT) to produce a new type of road composite fiber modified two-ash iron tailings (LHTF). The mechanical properties of LHTF were analysed by unconfined compressive tests and splitting tensile tests, and the optimal ratio of LHTF was obtained. The internal failure mechanism of LHTF was explored and explained by analysing the transformation of the macroscopic failure mode and the change law of the energy absorption capacity of materials. The results show that with increasing fiber content, the unconfined compressive strength, splitting tensile strength and strength gain ratio first increase and then decrease. When the fiber content is 0.75 %, LHTF can achieve the best tension and compression performance and has the largest peak strain. With the increase in fiber content, the failure mode of LHTF gradually changes from brittle failure to ductile failure, and obviously different types of failure characteristics can be seen at the failure interface. The ductility failure characteristics of LHTF with the best fiber content are the most obvious, and the brittleness index is the lowest. The total strain energy density and elastic strain energy density of LHTF first increased and then decreased, while the change law of dissipated energy proportion showed the opposite situation. This study provides a reference for the recycling and utilization of waste iron tailings as road materials.