Accumulated Strain Energy Research Articles

Revealing the oxidation growth mechanism and crack evolution law of Si-HfO2/Yb2Si2O7/Yb2SiO5/high-entropy hafnate thermal/environmental barrier coatings during thermal cycling

The Si-HfO2/Yb2Si2O7/Yb2SiO5/(Dy0.2Ho0.2Er0.2Tm0.2Lu0.2)2Hf2O7 thermal/environmental barrier coating (T/EBC) protects ceramic matrix composites (CMCs) from turbine multi-corrosive media erosion. Challenges persist in the thermal cycling performance of multi-layered T/EBC, notably in understanding the oxidation of the Si-HfO2 bond coat, compatibility of its mixed thermally grown oxide (m-TGO) with adjacent layers, and the evolution of cracks caused by thermal cycling. Utilizing plasma spraying physical vapor deposition (PS-PVD), this T/EBC on CMC substrates withstands up to 200 hours at 1450 ℃ to 1550 ℃. The m-TGO oxidation follows a parabolic growth curve, with oxygen diffusion activation energies of 160.31 kJ/mol from 1450 ℃ to 1500 ℃, and 125.16 kJ/mol from 1500 ℃ to 1550 ℃. Thermo-mechanical calculations indicate that elastic strain energy accumulation causes interlaminar cracks between m-TGO and adjacent layers. Controlling mud crack density is key to preventing the stress attraction at the tips of bifurcated cracks, thereby avoiding the formation of interlaminar cracks.

Microstructural evolution of GH4079 superalloy during hot deformation and heat treatment

Through hot compression and subsequent heat treatment experiments on GH4079 superalloy, the influence of different hot deformation and heat treatment conditions on the evolution of GH4079 superalloy microstructure was studied. The evolution of grains and γ′ phases under different thermomechanical conditions was investigated. The results indicate that at deformation temperatures above 1100 °C and strain rates ranging from 0.01 to 0.1 s−1, the primary mechanism of dynamic softening in the alloy is discontinuous dynamic recrystallization (DDRX). When the deformation temperature is below 1100 °C and strain rates range from 0.01 to 0.1 s−1, both continuous dynamic recrystallization (CDRX) and DDRX are the main dynamic softening mechanisms. Due to high strain energy accumulation, the samples deformed at lower temperatures (below 1100 °C) and then solution-treated at 1120 °C for 8 h exhibit significant increases in recrystallization volume fraction and recrystallization grain size. Conversely, the samples deformed at higher temperatures (above 1100 °C) and then solution-treated at 1120 °C for 8 h show minimal changes in recrystallization volume fraction and recrystallization grain size. After solution treatment at 1140 °C, the grain size of the alloy significantly increases. The samples deformed at higher strain rates exhibit the evolution of fine γ′ phases into elongated rod shapes during solution treatment, while larger γ′ phases undergo splitting processes.

Energy Evolution Characteristics and Hydraulic Fracturing Roof Cutting Technology for Hard Roof Working Face during Initial Mining: A Case Study

In the process of mining, a large area of hard roof will be exposed above a goaf and may suddenly break. This can easily induce rock burst and has a significant impact on production safety. In this study, based on the engineering background of the hard roof of the 2102 working face in the Balasu coal mine, the spatial and temporal characteristics of the strain energy of the roof during the initial mining process were explored in depth. Based on a theoretical calculation, it is proposed that hydraulic fracturing should be carried out in the medium-grained sandstone layer that is 4.8–22.43 m above the roof, and that the effective fracturing section in the horizontal direction should be within 30.8 m of the cutting hole of the working face. The elastic strain energy fish model was established in FLAC3D to analyze the strain energy accumulation of the roof during the initial mining process. The simulation and elastic strain energy results show that, as the working face advances to 70–80 m, the hard roof undergoes significant bending deformation. The energy gradient increases with the rapid accumulation of strain energy to a peak value of 140.54 kJ/m3. If the first weighting occurs at this moment in time, the sudden fracture of the roof will be accompanied by the release of elastic energy, which will induce rock burst. Therefore, it is necessary to implement roof cutting and pressure relief before reaching the critical step of 77 m. To this end, the comprehensive hydraulic fracturing technology of ‘conventional short drilling + directional long drilling’ is proposed. A field test shows that the hydraulic fracturing technology effectively weakens the integrity of the rock layer. The first weighting interval is 55 m, and it continues until the end of the pressure at the 70 m position. The roof collapses well, and the mining safety is improved. This study provides an important reference for hard roof control.

Physical model investigation of a hybrid GRS integral bridge abutment under cyclic thermal stresses

GRS integral bridge abutments develop large lateral earth pressure on the facing during seasonal/diurnal thermal expansion/contraction, causing significant surface settlements. To mitigate these issues, researchers prefer the use of different kinds of facing to withstand lateral pressure in conjunction with reinforcing of backfill to reduce surface settlement. The present research investigates the performance of a hybrid integral abutment under lateral movement of the facing due to cyclic thermal expansion/contraction of the bridge deck through scaled down 1 g physical model tests. Using the optimized facing and reinforcement configuration, an integral abutment model was proposed and analyzed under varying rate of loading and different loading offsets for three displacement modes till 100 cycles of excitation. The assessment included the development of lateral pressure on facing, surface settlement, magnitude and location of peak reinforcement forces, followed by evaluating long-term performance in terms of permanent strains, stiffness degradation, and strain energy dissipation. The observations revealed that the proposed model having strong connection between the reinforcement and facing along with inclusion of secondary reinforcements along the entire height of abutment in the bearing zone exhibits rapid dissipation of accumulated strain energy, leading to a 48 % reduction in surface settlement under cyclic thermal stresses.

Application of Singular Spectrum Analysis to InSAR time-series for constraining the postseismic deformation due to moderate magnitude earthquakes: the case of 2019 Mw 6 Mirpur earthquake, NW Himalaya

Summary Detection and separation of the subtle postseismic deformation signals associated with moderate magnitude earthquakes from Interferometric Synthetic Aperture Radar (InSAR) time-series is often challenging. Singular Spectrum Analysis (SSA) is a statistical non-parametric technique used to decompose and reconstruct signals from complex time-series data. We show that the SSA analysis effectively distinguished the postseismic signal associated with the 2019 Mw 6 Mirpur earthquake from periodic and noise components. The SSA derived postseismic deformation signal is smoother and fits better to an exponential model with a decay time of 34 days. The postseismic deformation is confined to the southeast of the rupture area and lasted for ∼90 days following the mainshock. Inversion of the postseismic deformation suggests an afterslip mechanism with a maximum slip of ∼0.07 m on the shallow, up-dip portions of the Main Himalayan Thrust. The 2019 Mirpur earthquake and afterslip together released less than 12 per cent of the accumulated strain energy since the 1555 Kashmir earthquake and implies continued seismic hazard in the future.

Design and molecular dynamics of biocompatible WPU/PVA composite hydrogels with enhanced fatigue resistance: Energy dissipation of intermolecular clusters for elastomers

To engineer a hydrogel elastomer for use as an in vivo tissue replacement, it is imperative to ensure superior fatigue resistance, guaranteeing a prolonged service life. Investigating the molecular mechanisms of strain energy accumulation and transmission, which occur during the compression of elastomeric materials, is instrumental in elucidating the causes of hydrogel material fatigue. Such insights are of immense value for the development of durable artificial tissue replacements, ensuring their longevity and sustained functionality within the human body. We synthesized hydrogel elastomers through polyvinyl alcohol (PVA) and waterborne polyurethane (WPU) with good biocompatibility, and studied their fatigue behavior through molecular dynamics (MD). The results of this analysis demonstrate that the introduction of energy dissipation structures between mechanically supported molecular frameworks can enhance the relaxation efficiency of polymers. This improvement leads to enhanced resistance of hydrogels to compression fatigue. A total of 1,000,000 cycles of compression tests were conducted to verify that WPU/PVA did not exhibit any significant compression fatigue under high stress of 50 % strain. In contrast, PVA hydrogel exhibited obvious fatigue due to the absence of an energy dissipation structure. These results revealed the source of compression fatigue resistance of hydrogel elasticity and provided powerful guidance for the design and synthesis of artificial tissues.

Effects of various long-term thermal aging levels on the morphology, rheology and self-healing performances of high-viscosity asphalt

Large macroporous structures of permeable asphalt pavement made high-viscosity asphalt (HVA) more susceptible to aging and failure. However, the standard pressure aging vessel (PAV) test was difficult to accurately emulate the long-term aging behavior of HVA. Hence, 1–5PAV aging levels of two HVAs (i.e. HVA-1 and HVA-2) were emulated by the simple aging test (SAT). Rheological analysis indicated that asphalt oxidation consistently dominated regardless of the long-term aging levels of HVAs. Combined with the fluorescence microscopy observation, HVA-2 with meticulous and uniform granular distribution was more resistant to aging than HVA-1 with coarse and continuously strip-like structures. Stress-strain curve analysis in linear amplitude sweep (LAS) test revealed that the accumulated strain energy (ASE) representing the overall mechanical properties of HVAs first increased and then decreased as the long-term aging level grew. The continuous repeated LAS (RLAS) test further reflected that the yield stress, yield strain and ASE of HVAs gradually decreased as the LAS loading number increased at initial long-term aging states; but as the sustained growth of aging level, the stress-strain curve of HVAs become increasingly chaotic until remarkable strain hardening occurred. Furthermore, RLAS-based self-healing (RLASSH) test was developed by introducing intermittent time into RLAS test. The variation of ratio of ASE decrease can characterize the self-healing performance of HVAs. RLASSH test showed that the self-healing performance of HVAs was unstable at 1–3PAV aging level, and the HVAs with 4 or 5PAV aging levels completely lost their self-healing performance. Overall, with the increase in long-term aging levels, significant differences were observed in the evolution characteristics of morphology, rheology and self-healing performances of different HVAs. This study helps to understand the rheology and self-healing performance evolution pattern of HVA during long-term service.

Optimizing misfit dislocation glide kinetics for enhanced threading dislocation density reduction in Si1−xGex/Si(001) layers through dynamic growth rate control

Relaxed Si1−xGex layers on Si(001) serve as virtual substrates for strained Si or Ge layers. However, plastically relaxed layers inevitably contain misfit and threading dislocations, negatively affecting devices. Deposition of a SiGe layer on the backside of the substrate introduces a dislocation reservoir at the wafer edge that can reduce the threading dislocation density (TDD) of Si0.98Ge0.02/Si layers, as these preexisting dislocations start gliding toward the wafer center upon reaching the critical thickness. Here, we show that this low-strain system can be used effectively to study dislocation glide kinetics. In agreement with the literature, dislocation glide is a thermally activated process with an activation energy of 2.12–2.16 eV. Near the critical thickness, relaxation is sluggish and inefficient due to the linear dependence of the glide velocity on excess stress. At lower growth rates, dislocations from the edge reservoir are activated in a lower density due to the increase in the critical thickness through partial strain relaxation by already activated dislocations. Contrary to common models, here, the lowest possible growth rate is not essential for minimizing the TDD. Instead, a careful balance between low and high growth rates is beneficial. Overcoming the initial sluggish and inefficient relaxation phase is critical while also avoiding accumulation of strain energy, and, therefore, the activation of dislocation sources. Only in a later stage of buffer growth, the growth rate should be reduced to a minimum. With this method, the TDD of strain relaxed Si0.84Ge0.16 layers is reduced to 7 × 104 cm−2.

Heat-assisted friction stir incremental sheet forming of thermoplastics

Incremental sheet forming (ISF) has been attracting increasing interests for customised manufacture of thermoplastics, but the application in high-performance and hard-to-form thermoplastics is still a challenge. This paper develops a new heat-assisted friction stir incremental sheet forming (HAFS-ISF) process to form polyether ether ketone (PEEK) and polymethyl methacrylate (PMMA, acrylic). Flexible heating tapes and tool rotational friction heat the thermoplastic sheet on both bottom and top surfaces, which maintain the sheet material at high temperature and reduce the through-thickness temperature gradient. Results are given for the effect of key parameters on forming temperature, force, accuracy and thickness distribution. Spindle speed has the most significant effect on all the studied aspects, followed by the pre-heating temperature, while feed rate and step size have less effect. With lower spindle speed of 100 rpm, the through-thickness temperature gradient is improved. Compared with PEEK parts, more uniform forming temperature and smaller forming force can be observed for PMMA parts. But the material brittleness causes worse formability, and the severer twist and stretching effect affect the forming accuracy of PMMA parts. Forming accuracy, fracture and twist are discussed by developing analytical models. The model for forming accuracy considers the initial bending effect and springback. The fracture is discussed by modelling the stress triaxiality and equivalent strain distribution under contact. While the model for twist considers effect of the applied torque on shear strain energy and continuous accumulation of twist along the tool path. By comparing analytical models and testing observations, the effectiveness of the models is confirmed to understand the underlaying mechanisms and to address a few challenges.

Study on damage and fracture characteristics of wood based on acoustic emission b-value and seismic magnitude difference entropy

To assess the damage and fracture behavior of wood under load, a wood damage assessment method was proposed based on acoustic emission (AE) b-values and seismic magnitude difference entropy. First, AE signals from Pinus sylvestris var. mongolica (softwood) and Zelkova schneideriana (hardwood) specimens were collected separately at a sampling frequency of 500 kHz in a three-point bending test. Then, 52 dB was taken as the threshold of the AE event, and the b-value and seismic magnitude difference entropy were calculated at 4-s intervals. Finally, by comparing with the load‒time curve, the b-value and seismic magnitude difference entropy were used to evaluate the damage fracture degree. The results showed that an increase in the b-value indicates the accumulation of strain energy, and vice versa, corresponding to the concentrated release of strain energy. At the same time, the test process can be divided into three stages—elastic, elastic‒plastic and plastic—based on the level of the seismic magnitude difference entropy.

Assembly of Large Flip Chip Die in Ceramic Packages

Hermetic packaging is required to ensure the reliability of processors and application specific integrated circuit (ASIC) chips that are used in strategic systems, whose operating lifetimes typically exceed thirty years. Performance requirements for emerging system applications are dictating the need for one thousand or more I/O, which precludes the use of wire bonded devices. These packaging requirements can be met by flip chip bonding die onto multilayer, high temperature cofired ceramic substrates. The hermetic environment is provided by a Kovar metal ring that is brazed onto the ceramic and sealed in the final assembly step, by welding on a metal cover. Several process and design requirements must be met to achieve high reliability flip chip assemblies. Reflowed devices must be free of flux residues because they are corrosive, provide a path for ion diffusion, are a source of moisture and degrade the adhesion of underfill to chip and substrate. Removal of flux residues by cleaning is problematic because the gap between chip and substrate is very small relative to chip area. A better approach is to bond chips without flux, as we do, by reflowing them in a formic acid environment. An important reliability requirement for strategic hardware is the ability to sustain many cycles over extended temperature ranges. Temperature cycles induce plastic deformation in the solder connections as a result of stresses generated by the mismatch in thermal expansion coefficients of the chip and package. These stresses can be reduced significantly by underfilling the bonded chip with a filled adhesive. Choice of material as well as process execution impact the effectiveness of underfill enhancement of reliability. Optimization of both the physical design and composition of the solder connections is essential to producing reliable flip chip assemblies. We make extensive use of finite element analyses (FEA) in which we track the accumulation of plastic strain energy in the solder connections as they are subjected to temperature cycle induced stresses. Good correlations between the energy accumulated per cycle and the number of cycles to failure can be achieved if accurate state models of the solder are used. We have a catalog of Anand models for the solder compositions that we use in our FEA simulations. One of the more challenging aspects of designing high performance flip chip packages is matching the size and pitch of the bond pads on the ceramic with those on the chip. Current devices use 90 micron diameter pads on 200 micron pitch, but newer designs are migrating towards 80 micron diameter pads on 180 micron pitch. It challenging to maintain tight tolerances on pad geometries in these higher density packages and to route all the additional signals. Thermal management is also an important component of the package design. Thermal vias and thermally conductive underfills are used to remove heat from the front side of the chip. On the backside of the chip, the gap between chip and cover is minimized and filled with a high thermal conductivity interface material. High fidelity FEA modeling is necessary to ensure that the chip can be adequately cooled in its hermetic environment. This paper discusses the impact of these design and assembly factors on the reliability of high performance, hermetically packaged flip chip assemblies.

Effects of length-to-diameter ratio and strain rate on strain energy accumulation and dissipation in sandstone

To investigate the influence of the length-to-diameter (L/D) ratio and strain rate on the evolution of strain energy of sandstone under uniaxial compression, experimental tests were conducted using the RMT-150B rock mechanics test system. Specifically, uniaxial compression experiments (UCE), uniaxial loading-unloading experiment(ULUE) and uniaxial cyclic loading-unloading experiments (UCLUE) were performed. The results show that: 1) Based on an investigation of the Kaiser effect in UCLUE, it is postulated that a small degree of loading-unloading has negligible impact on the storage of strain energy in rock masses. The hypothesis regarding the limited influence of loading-unloading on the elastic strain energy storage of rocks is confirmed through a comparative analysis between the elastic strain energy storage in UCLUE and ULUE. 2) By analyzing the ESED and ISED of sandstone under different L/D ratios and strain rates, it is found that it follows the linear energy storage law. The evolution of elastic strain energy is not affected by strain rate. Therefore, the UCLUE at any strain rate can analyze the elastic strain energy of uniaxial compression experiment with the same size at any strain rate, and provide a new method for strain energy analysis at different length-diameter ratios and strain rates. 3) When the stress of sandstone samples of equal size is equal, the smaller the strain rate, the longer the loading experiment of sandstone, the more time the friction development and interconnection of cracks in sandstone are, and the more dissipated strain energy and input strain energy are generated. 4) Smaller L/D ratios are associated with larger ESED and DSED values in sandstone. As the stress intensifies, the ESED and DSED of certain sandstones with larger L/D ratios experience a sharp increase when approaching the failure stress. Under equal stress levels, it is possible for sandstones with larger L/D ratios to exhibit higher ESED and DSED values compared to those with smaller L/D ratios.

Strain accumulation and relaxation on crack formation in epitaxial AlN film on Si (111) substrate

The formation of cracks is often observed in the epitaxial growth of ultrawide-bandgap aluminum nitride (AlN) semiconductor films on economical and versatile silicon (Si) substrates due to the significant differences in in-plane lattice parameters and thermal expansion coefficients between the film and the substrate, which hampers the development of template, buffer layer, and device structure with a relatively thick AlN layer for devices. The present study aims to elucidate the conditions of crack formation through a simple but comprehensive estimation of strain energy accumulation and relaxation by lattice strain, misfit dislocation density, and crack formation. Strain energy in the epitaxial film from lattice and thermal mismatches is evaluated by an elastic strain equation tailored to the epitaxy of the hexagonal crystal structure. The effects of temperature, thickness, and dislocation density on the lattice and dislocation strain energies of the film are also considered. Finally, the comparison in the changes in the total strain energy and cleavage energy with decreasing temperature shows that cleavage energy is higher than strain energy if the film is thinner than 400 nm but becomes lower than the strain energy if the film is thicker than 400 nm during cooldown, suggesting the crack formation, which matches well with experimental observations.

Analytical Estimation of Strain Energy Accumulation in Retreating Longwall Mining and Sensitivity Analysis Using the Orthogonal Testing Method

AbstractExcessive strain energy accumulation in the coal seam is one of the essential conditions for rockbursts to occur. It is imperative to understand the parameters that affect the strain energy accumulation in retreating longwall mining to optimise the design and minimise rockbursts occurrences. In this paper, new analytical models were developed to calculate the strain energy accumulation considering the current state-of-the-art longwall machinery being used in the industry. Seven parameters, i.e., mining depth, length of the cantilever roof, coal seam thickness, thickness of the immediate roof, Young’s modulus of coal and the roof, and Poisson’s ratio of the coal seam, were identified as the parameters affecting the strain energy accumulation. A detailed statistical analysis of the parameters was conducted using the orthogonal testing method, which revealed that mining depth, Young's modulus of coal and the coal seam thickness significantly influence the strain energy accumulation within a 99% confidence interval.

Force decomposition and toughness estimation from puncture experiments in soft solids.

Several medical applications, like drug delivery and biosensing, are critically preceded by the insertion of needles and microneedles into biological tissue. However, the mechanical process of needle insertions, especially at high velocities, is currently not fully understood. Here, we explore the insertion of hollow needles into transparent silicone samples with an insertion velocity v ranging from 0.1 mm s-1 to 2.3 m s-1 (with needle radius R = 101.5 μm, thus strain rates ∼v/R ranging from 1 s-1 to 2.3 × 104 s-1). We use a double-insertion method, where the needle is inserted and re-inserted at the same location, to estimate the fracture properties of the material. The deflection of the specimen's free surface is found to be different between insertion and re-insertion experiments for identical needle positions, which is associated with different force magnitudes between insertion/reinsertion. This aspect was previously neglected in the original double-insertion method, thus here we develop a method based on imaging, image analyses and force measurements to decompose the measured force into individual force components, including deflection force Fd, frictional and spreading force Ff + Fs, and cutting force Ft. We estimate that the toughness Γ of our silicone samples, calculated using the cutting force Ft and the crack dimensions, increases with needle velocity, and ranges within observed values in previous literature for the same material and for some soft biological materials. In addition to toughness Γ, other parameters, such as critical force Fc and mechanical work Wc, also show strain-rate dependence, suggesting tissue stiffening, due to accumulated strain energy, at high speeds.

Effects of thermal aging level on the morphological structures, rheological properties and fatigue characteristics of high-viscosity asphalts

High-viscosity asphalt (HVA) provides excellent cracking and rutting resistance for ecological permeable pavement. However, HVA suffers from severe aging due to higher construction temperatures and rich porous structures, which limited its applications for urban sustainability. Currently there is still a lack of knowledge about the thermal aging effects and mechanisms of HVA. In this study, the effects of thermal aging on the morphological structures, rheological and fatigue properties of two HVAs (i.e. HVA-1 and HVA-2) at five aging levels via Simple Aging Test (SAT) are systematically investigated. HVA-1, characterized by loosen and coarse reticulated structures, undergoes significant structural changes during aging, whereas HVA-2, characterized by dense and fine reticulated structures, experiences fewer alterations. The changes in the modulus master curves of HVAs become more gradual after aging, indicating the reduced temperature sensitivity. Multiple stress creep recovery results reflect that two types of HVAs exhibit totally different dominance of oxidation or polymer degradation depending on aging level. Liner amplitude sweep (LAS) results based on damage mechanics analysis reveal that aging leads to an increase in the accumulated strain energy observed in stress-strain curves for both HVAs. As aging progresses, the proportion of elastic energy decreases due to polymer degradation, resulting in a reduction in fatigue life. Especially, the fatigue life of aged HVAs significantly decreases after SAT40. LAS results based on fracture mechanics analysis show that the crack length increases with aging due to polymer degradation and asphalt phase hardening. Aging effect on crack length was limited at initial stage but becomes more significant as crack extends. As aging deepens, the crack initial stage of HVAs tends to lengthen while the crack extension stage tends to shorten. Moreover, the crack growth process of HVAs follows a two-stage behavior of crack initiation and propagation under certain aging levels from the relationship between energy release rate and crack propagation rate. Overall, the thermal aging kinetics of various HVAs differ significantly in the structures, rheological and fatigue properties as aging deepens. HVA-2 with loosen and coarse structures exhibits greater aging resistance and lower temperature sensitivity than HVA-1 with dense and fine structures.

Emergence and growth of faults during earthquakes: Insights from a dynamic elasto-plastic continuum model

I use a dynamic two-dimensional plane strain model of an elasto-plastic (Mohr-Coulomb) material with velocity-weakening friction to numerically simulate the emergence and propagation of shear fractures that accumulate slip intermittently during earthquakes. The model considers a 10 × 10 km block of homogeneous crust with a small weak inclusion, subjected to slow simple shear. Results show that deformation is distinctly bimodal, consisting of long periods (lasting ca. 50–200 years) where deformation is dominantly elastic separated by rapid sliding events lasting a few seconds during which time deformation is strongly localised on narrow plastic shear bands (faults). In terms of energy expenditure, the interseismic period is overwhelming dominated by accumulation of elastic strain energy whereas during earthquakes, most of the drop in elastic strain energy is consumed (dissipated) by plastic work. Model earthquakes have maximum slip rates of a few meters per second, involve a few meters of slip and result in drop of mean differential stress of several megapascals. Most earthquakes are complex events involving near-simultaneous rupture of multiple fault segments that propagate at supershear velocities (close to the P-wave speed) while they also induce a significant amount of more diffuse off-fault inelastic deformation. Earthquakes may involve formation of new faults and/or reshear on previously formed faults, which are favourably reactivated owing to their low pressure. Most individual faults establish much of their length early, whereas during subsequent events they continue to accumulate displacement at virtually constant length. As the confining pressure is increased, ruptures are more dynamic, which leads to increasingly widespread inelastic deformation. Overall, the models highlight the complex temporal and spatial interactions that exist between different faults within an array that communicate especially during earthquakes through static and dynamic changes in the stress field.

Strain based damage indicators for finite element analysis of reinforced concrete structures

Numerical analysis conducted using a finite element model provides a quantitative and detailed evaluation of damage in concrete. As a result, the performance verification based on the local damage obtained numerically is considered an effective method for achieving a rational design of RC structures. Stresses and strains computed from numerical analysis are suited to indicators for representing local damage in concrete instead of sectional forces calculated from design equations; however, the performance evaluation using stresses and strains lack versatility owing to their dependency on constitutive equations and mesh discretization in numerical models. This study presents two types of strain-based damage indicators for performance verification in the design of RC structures using nonlinear finite element analysis. The second strain invariant of the deviatoric strain tensor is used to assess tensile damage, such as the opening of flexural cracks and the development of shear cracking in concrete, whereas the normalized accumulated strain energy is used to evaluate compressive damage, i.e., concrete crushing. These scalar indicators have high general usefulness, with calculation as non-local values by a weighted average, to reduce their mesh dependency. Furthermore, numerical analyses were performed to evaluate the damage condition and failure modes of RC beams, and the proposed damage indicators helped accurately understand flexure and shear failure. Lastly, we propose threshold values of the damage indicators for the performance verification of safety, represented by the load-carrying capacity in the design of RC structures.

Numerical modeling on strain energy evolution in rock system interaction with energy-absorbing prop and rock bolt

The interaction mechanism between coal and rock masses with supporting materials is significant in roadway control, especially in deep underground mining situations where dynamic hazards frequently happened due to high geo-stress and strong disturbed effects. This paper is to investigate the strain energy evolution in the interaction between coal and rock masses with self-designed energy-absorbing props and rock bolts by numerical modeling with the finite difference method. The interaction between rock and rock bolt/prop is accomplished by the cables element and the interface between the inner and outer props. Roadway excavation and coal extraction conditions in deep mining are numerically employed to investigate deformation, plastic zone ranges, strain energy input, accumulation, dissipation, and release. The effect on strain energy input, accumulation, dissipation, and release with rock deformation, and the plastic zone is addressed. A ratio of strain energy accumulation, dissipation, and release with energy input α, β, γ is to assess the dynamic hazards. The effects on roadway excavation and coal extraction steps of α, β, γ are discussed. The results show that: (1) In deep high geo-stress roadways, the energy-absorbing support system plays a dual role in resisting deformation and reducing the scope of plastic zones in surrounding rock, as well as absorbing energy release in the surrounding rock, especially in the coal extraction state to mitigate disturbed effects. (2) The strain energy input, accumulation is dependent on roadway deformation, the strain energy dissipation is relied on plastic zone area and disturbed effects, and strain energy release density is the difference among the three. The function of energy-absorbing rock bolts and props play a key role to mitigate strain energy release density and amount, especially in coal extraction condition, with a peak density value from 4×104 to 1×104 J/m3, and amount value from 3.57×108 to 1.90×106 J. (3) When mining is advanced in small steps, the strain energy accumulation is dominated. While in a large step, the released energy is dominant, thus a more dynamic hazards proneness. The energy-absorbing rock bolt and prop can reduce three times strain energy release amount, thus reducing the dynamic hazards. The results suggest that energy-absorbing props and rock bolts can effectively reduce the strain energy in the coal and rock masses, and prevent rock bursts and other hazards. The numerical model developed in this study can also be used to optimize the design of energy-absorbing props and rock bolts for specific mining conditions.

Experiment and particle flow simulation on mechanical properties and crack evolution mechanism of Brazilian discs containing two flaws

Abstract The mechanical behavior of fractured rock in tensile stress environment is a hot topic in underground mining engineering. Here, real surrounding rock of coal mine roadway was simulated by using rock-like materials and the tensile failure behavior of Brazilian discs with intermittent double fissures was investigated experimentally. The deformation response, fracture evolution, and failure mode of rock were analyzed. The fissured disc specimen's discrete element model was proposed in particle flow code (PFC2D). The microforce field, crack, and energy evolution processes of model specimens were discussed. The results showed that the load-displacement curves exhibit single-peak and double-peak types, corresponding to the splitting penetration and wing crack penetration damage modes of the specimen. The fissure angle or rock bridge angle showed a great influence on the evolution of main cracks and secondary cracks. The double-fissured Brazilian disc failed due to the initiation and transfer of microcracks in the stress concentration zone, combined with the continuous propagation and convergence of those microcracks. The splitting failure of the Brazilian disc is a continuous process of strain energy accumulation from the early stage of loading and instantaneous release of strain energy after obtaining the peak strength as the dissipative energy sharply rises.