Critical Energy Density Research Articles

A peridynamic compensated critical energy density criterion for mixed-mode fracturing in quasi-brittle materials

This study integrates a compensated critical energy density criterion (CCED) into the ordinary state-based peridynamics framework to enable detailed analysis of mode I, mode II, and mixed-mode fracturing. The proposed bond failure criterion builds upon the advantages of the traditional critical energy density (CED) to enable precise calculation of strain energy density. Additionally, the critical bond rotation criterion (CR) is employed to account for shear bonds that the CED might overlook. Using the peridynamic differential operator (PDDO) format in formulating the entire computational framework enhances both accuracy and numerical stability. The model’s validation is conducted through benchmark examples, including the mode I double cantilever beam test, the mode II compact shear test, and a mixed-mode mechanical fracturing test in pre-notched specimens with central borehole loading. Convergence studies, comparative analyses with finite element method simulations and theoretical solutions thoroughly examine the proposed model’s performance and accuracy.

Ignition of Coal Microparticles by Laser Pulses of The Second Harmonic of a Ndodymium Laser in the Q-Switched Regime

The ignition of pelletized samples of hard coals of the long-flame gas (DG), gas (G), fat (L), coke (K) grades with particle sizes ≤63 μm by laser pulses (λ = 532 nm, τi = 10 ns) was studied. When the critical radiation energy density Hcr(1), specific for each grade of coal, is exceeded, an optical breakdown occurs and a dense plasma with a continuous emission spectrum is formed. As the plasma expands and rarefies, the spectra show the emission of carbon ions CII, excited nitrogen atoms N, excited carbon molecules C2, and carbon monoxide CO. The plasma glow intensity peaks at the end of the laser pulse, and the glow relaxation time is ~1 μs. The plasma glow amplitude increases nonlinearly with increasing laser pulse energy density. At radiation energy density H ≥ Hcr(2), specific for each grade of coal, thermochemical reactions are initiated in the volume of microparticles and coal particles are ignited in a submillisecond time interval.

Multiaxial fatigue rule applied to disc specimens with variable thickness subjected to an equibiaxial stress state

AbstractAssessing multiaxial fatigue theories requires experimental verification of a failure criterion, posing a significant challenge. This study aims to investigate the validity of a multiaxial fatigue method based on the Lagoda‐Macha‐Sakane (LMS) theory. The LMS theory links the critical strain energy density to the fatigue crack initiation cycles through a non‐linear equation defined by a set of empirical parameters calibrated by a strain‐controlled uniaxial fatigue test. This work adopts the LMS formulation, numerically calibrating the fatigue curve based on strain energy density from uniaxial fatigue experimental data and considering only the LMS theory for the critical strain energy density computation. This method avoids compatibility condition uncertainties and previous identification of material parameters. The study uses bi‐axial bending tests on AISI 316 L steel plate specimens with 3D finite element analyses to support computational assessment. The predictive capability of the model and the effectiveness of the testing method are presented and discussed.

Unruh-DeWitt particle detectors in bouncing cosmologies

We study semi-classical particle production in non-singular bouncing cosmologies by employing the Unruh-DeWitt model of a particle detector propagating in this class of spacetimes. The scale factor for the bouncing cosmology is derived analytically and is inspired by the modified Friedmann equation employed in the loop quantum cosmology literature. We examine how the detector response varies with the free parameters in this model such as the equation of state during the contraction phase and the critical energy density during the bounce phase. We also investigate whether such a signature in the particle detector survives at late times.

Active ballistic orbital transport in Ni/Pt heterostructure

Orbital current, defined as the orbital character of Bloch states in solids, can travel with larger coherence length through a broader range of materials than its spin counterpart, facilitating a robust, higher density and energy efficient information transmission. Hence, active control of orbital transport plays a pivotal role in the progress of the evolving field of quantum information technology. Unlike spin angular momentum, orbital angular momentum couples to phonon angular momentum efficiently via orbital-crystal momentum (L-k) coupling, allowing us to control orbital transport through crystal field potential mediated angular momentum transfer. Here, leveraging the orbital dependant efficient L-k coupling, we have experimentally demonstrated the active control of orbital current velocity in Ni/Pt heterostructure. We observe terahertz emission from Ni/Pt heterostructure via long-range ballistic orbital transport, as evidenced by the delay, and chirping in the emitted THz pulse correlating with increased Pt thickness. Additionally, we also have identified a critical energy density required to overcome collisions in orbital transport, enabling a swifter flow of orbital current. Femtosecond light driven active control of the ballistic orbital transport lays the foundation for the development of dynamic optorbitronics for transmitting information over extended distance.

Dynamic shear resistance and its dependence on geometrical imperfection of high entropy Cantor alloy and BJAM 316L stainless steel

This paper examines the adiabatic shear resistance of recently popular Cantor alloy and Binder Jetting Additive Manufacturing (BJAM) 316L, with emphasis on their dependence on geometrical imperfection. A series of shear tests were conducted by using the long Split Hopkinson bar and shear compression specimen (SCS). Both alloys present strain rate dependent shear behaviour with the large dynamic shear failure strain of about 104 %–132 %. Microstructural characterizations reveal that both Cantor and BJAM 316L alloys fail by adiabatic shear band. Introduced by the varying notch root radius, the sharpness significantly affects the dynamic shear resistance of the Cantor and BJAM 316L alloys. The linear functions are proposed to describe the drop of critical strain and energy density with the designed inverse root radius.

Order-disorder on cluster dynamics in the Q2R-Potts cellular automaton

Cellular automata (CA) are mathematical models that allow the study of emergent behavior from a bottom-up point of view, while the Potts model is renowned for its rich dynamics capable of developing both first and second order phase transitions. Here, we study the Q2R-Potts cellular automaton, which is a model that merges cellular automata and the Potts model through a microcanonical ensemble characterized by a conservative energy-like function. Our study, conducted via numerical simulations, focuses on the one-dimensional Q2R-Potts CA with three (q = 3) states, examining its dynamics through both macroscopic and microscopic quantities. We discover that the model exhibits a first-order phase transition from order to disorder around of a critical energy density, characterized by a discontinuity in a phase diagram and self-organizing clusters that follow a power-law behavior.

Quasi-Static and Dynamic Crack Propagation by Phase Field Modeling: Comparison with Previous Results and Experimental Validation

In this paper, experimental tensile tests for pre-cracked high Carbon steel ‘C90’ specimens were performed for quasi-static and dynamic loading. High loading velocity affects the crack patterns by preventing deflection. On the other hand, an efficient numerical tool based on the phase field model was developed and validated to predict brittle fracture trajectories. A staggered numerical scheme was adopted to solve the displacement and damage fields separately. Implementation efficiency in initiating and propagating cracks, even from an undamaged microstructure, was proved. The effect of the critical fracture energy density Gc on the crack path was tested; with smaller Gc, the crack patterns become more complex. In addition, the impact of loading velocities was examined, and earlier and faster crack formation and greater crack branching is observed with higher impact velocity. In this study, bidimensional plane stress cases were treated. The phase field model with hybrid formulation was able to predict crack pattern and especially crack arrest and branching found in the literature. The developed model accurately determined the transition zone of the crack path topology that has been observed experimentally.

Predicting mechanical failure of polycrystalline dual-phase nickel-based alloys by numerical homogenization using a phase field damage model

Brazing of nickel-based alloys plays a major role in the assembly of turbine components, e.g., abradable sealing systems. In a brazed joint of nickel-based alloys a composition of brittle and ductile phases can be formed if the brazing conditions are not ideal. This heterogeneous microstructure is a crucial challenge for predicting the damage behavior of a brazed joint. The initiation and evolution of microdamage inside of the brittle phase of a virtual dual-phase microstructure representing the material in a brazed joint is studied by means of numerical simulations. A phase field approach for brittle damage is employed on the microscale. The simulation approach is capable of depicting phenomena of microcracking like kinking and branching due to heterogeneous stress and strain fields on the microscale. No information regarding the initiation sites and pathways of microcracks is needed a priori. The reliability of calculating the effective critical energy quantities as a microstructure-based criterion for macroscopic damage is assessed. The effective critical strain energy density and the effective critical energy release rate are evaluated for single-phase microstructures, and the approach is transferred to dual-phase microstructures. The local critical strain energy density turns out to be better suited as a model input parameter on the microscale as well as for a microstructure-based prediction of macroscopic damage compared to a model employing the energy release rate. Regarding the uncertainty of the model prediction, using the effective critical energy release rate leads to a standard deviation which is five times larger than the standard deviation in the predicted effective critical strain energy density.

Research on less temperature flawing resistance of steel residue asphalt composition based on SCB test

In view of the increasing application of steel residue in asphalt pavement construction in China, in order to analyze the less temperature flawing resistance of steel residue asphalt composition, the less temperature semi-circular bending test (SCB) was used to analyze the less temperature flawing resistance of steel residue asphalt composition (SSAC-13) with various residue content based on the stress peak value and stress attenuation, rupture toughness, rupture energy and critical rupture energy density. The results show that the content of steel residue has a noticeable influence on the less temperature flawing resistance of steel residue asphalt composition. Considering the less temperature flawing resistance, the recommended steel residue content is 40%.

Fracture analysis of orthotropic functionally graded materials using element-based peridynamics

A fracture model of orthotropic functionally graded materials (FGMs) based on element-based peridynamics (EBPD) is proposed. Two-dimensional (2D) orthotropic FGMs use three-node triangular elements to describe the force density of EBPD. Due to the gradient difference of material properties inside the element, the Gauss integral formula is used to average the node performances to the integral point of the element. The equations of motion for EBPD is established, which is also applied to orthotropic FGMs by the Gauss integral formula. The micromodulus coefficient of the EBPD is derived for orthotropic FGMs. The critical strain energy density criterion is used as the failure criterion to simulate the quasi-static and dynamic fracture problems. A series of numerical examples, including displacement analysis, stress analysis, dynamic crack propagation of FGM beam, and crack growth of orthotropic FGMs under four-point bending load, are used to validate the accuracy of the fracture model of orthotropic FGMs. The proposed model can be helpful to the material gradient design for FGMs satisfying certain requirements.

Ordinary state-based peridynamic model for out-of-plane deformation and damage analysis of composite laminates

An ordinary state-based peridynamic (PD) model for predicting out-of-plane mechanical behaviour of composite laminates has been proposed, in which three types of PD bonds are used to describe the reinforcement properties. The non-local strain energy density and peridynamic formulations are obtained based on the principle of virtual work by using Total Lagrange formulation, and the force density is reformulated by interpolation technique. Since the Mindlin plate is regarded as the research object of this PD model, the transverse shear deformation of laminates is considered. Also, the dilatation term is included in the force density vector, and flaws in Poisson's ratio of materials can be overcome. In the proposed PD, the critical strain energy density rather than the critical curvature is adopted as the failure criterion. The capability of the developed PD model was demonstrated by the bending examples of composite laminates with different fiber orientations, and damage analysis was further conducted to demonstrate the strong capability of proposed PD model in replicating the damage process of laminates. In addition, a single-layer material point model (SLMPM) can be implemented in the proposed PD algorithm, and the computational efficiency of numerical models will be greatly improved.

Numerical Modeling of Progressive Damage and Failure of Tunnels Deeply-Buried in Rock Considering the Strain-Energy-Density Theory

Exploring the rock failure mechanism from an energy perspective is crucial for ensuring the safe construction of tunnels under complex geological conditions. In this study, a progressive damage and failure model of rock elements is established using the strain-energy-density theory based on the thermodynamic theory. Specifically, the rock elements are considered to have failed when the strain energy density absorbed by the element is greater than the critical strain energy density. Besides, the damage evolution of rock elements is reflected through the reduction of elastic modulus, until the element only has a certain residual strength. Based on the above theory, the calculation program of rock damage and failure is developed in FLAC3D using the FISH language. The validity of the method for simulating the process of rock damage and failure is verified through the numerical simulation of Brazilian splitting tests. Finally, the model was applied to the overload test of the geo-mechanical model of the Liangshui Tunnel on Lanzhou-Chongqing Railway. The comparison between the numerical simulation and the test results has not only confirmed that the feasibility and accuracy of the model in simulating the progressive failure process of tunnel surrounding rock under high ground stress, but also its ability to visually display the damage degree, failure scope and evolution process of the surrounding rock. The research findings are of great significance in ensuring the safe construction of tunnel and will promote the efficient development of the underground engineering construction.

Cutting soft matter: scaling relations controlled by toughness, friction, and wear.

Cutting mechanics of soft solids is gaining rapid attention thanks to its promising benefits in material characterization and other applications. However, a full understanding of the physical phenomena is still missing, and several questions remain outstanding. E.g.: How can we directly and reliably measure toughness from cutting experiments? What is the role of blade sharpness? In this paper, we explore the simple problem of wire cutting, where blade sharpness is only defined by the wire radius. Through finite element analysis, we obtain a simple scaling relation between the wire radius and the steady-state cutting force per unit sample thickness. The cutting force is independent of the wire radius if the latter is below a transition length, while larger radii produce a linear force-radius correlation. The minimum cutting force, for small radii, is given by cleavage toughness, i.e., the surface energy required to break covalent bonds in the crack plane. The force-radius slope is instead given by the wear shear strength in the material. Via cutting experiments on polyacrylamide gels, we find that the magnitude of shear strength is close to the work of fracture of the material, i.e., the critical strain energy density required to break a pristine sample in uniaxial tension. The work of fracture characterizes the toughening contribution from the fracture process zone (FPZ), which adds to cleavage toughness. Our study provides two important messages, that answer the above questions: toughness can be estimated from wire-cutting experiments from the intercept of the force-radius linear correlation, as previously explored. However, as we discovered, this only estimates cleavage toughness. Additionally, the force-radius slope is correlated with the work of fracture, giving an estimation of the dissipative contributions from the FPZ.

EFFECT OF COAL PARTICLE SIZE DISTRIBUTION ON LASER IGNITION CHARACTERISTICS

The ignition of hard coal grades DG, G, Zh, and K under the action of laser pulses (1064 nm, 120 μs, 1.3 J) was studied for the fractions of microparticles with a narrow size distribution in the range of 0.25-44 μm. The kinetic characteristics of the glow of samples from the entire size range were measured for each coal rank. Three stages of ignition are distinguished for each fraction. The duration of the first stage coincides with the duration of the laser pulse. The duration of the second takes a time interval of 10-15 ms (DG, G and Zh coal ranks) and 3-5 ms (K coal rank). The duration of the third stage is 60-80 ms (DG, G, and G coals) and 20 ms (K coal rank). It has been established that the threshold ignition energy densities (ignition thresholds) at all three stages depend non-monotonically on coal particle sizes. The minimum values of ignition thresholds at all three stages are achieved at particle sizes equal to 2.2 (for DG rank coal), 4.0 (for G rank coal), 0.7 (for Zh rank coal) and 2.0 μm (for K rank coal). Using the results of the proximate analysis of coals, the observed dependences of critical energy densities on the size of coal particles are interpreted.

Effect of scanning speed on fatigue behavior of 316L stainless steel fabricated by laser powder bed fusion

The effect of the scanning speed on the fatigue behavior of Laser Powder Bed Fusion (LPBF)-fabricated 316L steel is investigated in this paper. To this end, fatigue limits of specimen manufactured by different scanning speeds are determined by the self-heating approach. EBSD experiments and relative density measurements are carried out to characterize the microstructure and porosity. To analyse the influence of scanning speed on the microstructure (grain morphology, texture, dislocation density and stored energy) and fatigue property, a dislocation-density, crystal plasticity and stored energy-based fatigue model is developed. The inverse optimization method is combined with EBSD experiments and uniaxial tension experiments to identify the model parameters. The experimental results show a critical scanning speed, below which the fatigue limit stays almost unchanged and decreases drastically while the scanning speed is increased beyond. Furthermore, the simulation results show that the predicted fatigue limits correspond well to the experimental fatigue ones. From experimental and numerical results, it is deduced that the critical stored energy density and maximum temperature variation are functions of the porosity and can be used to differentiate the types of fatigue: microstructure-dominated or defect-dominated. This article provides new insights which can be further used in the optimization of fatigue behavior of LPBF 316L steel with respect to the scanning speed.

Thermo-mechanical and metallurgical preliminary analysis of SiC MOSFET gate-damage mode under short-circuit based on a complete transient multiphysics 2D FEM

For the first time, a complete 2D transient multiphysics electro-thermo-mechanical and metallurgical model of a 1.2 kV-80mΩ gate-planar SiC MOSFET power chip has been developed in a single FEM software. This model is used to quantify the short-circuit critical time and energy density with respect to the local SiO2 interlayer strength at high temperatures and the Al source-metal solidus-liquidus phase transition temperature. Repetitive experimental short-circuits were conducted to confirm the gate-aging existence in coherence with the critical values extracted from the proposed model.

Research on femtosecond laser welding process of silver nanowire transparent electrodes

With the continuous development of flexible transparent electrodes, silver nanowires have been widely used due to their excellent optoelectronic properties and flexibility. However, their progress has been hindered by high contact resistance. In this study, femtosecond laser post-processing was applied to the silver nanowire transparent electrodes, and the effect of laser power density on the welding of silver nanowires was investigated. The results showed that femtosecond laser could achieve welding between silver nanowires, but excessively high laser energy density could cause the melting of the nanowires. When the femtosecond laser energy density reached the critical energy density of approximately 2546 J·m−2, at which nanowires underwent spheroidization, the average sheet resistance of the silver nanowire electrodes was minimized to 18.89 Ω·sq−1, and the figure of merit (FoM) of the electrodes reached its maximum at 126.99, which was close to twice the initial value. Moreover, the non-uniformity factor (NUF) was also small, at 1.6%, indicating good conductivity and uniformity. Additionally, the influence of femtosecond laser irradiation on the transmittance of the silver nanowire transparent electrodes was insignificant, and the number of effective pulses had no obvious effect on the welding efficiency of the silver nanowires.

A robust life prediction model for a range of materials under creep-fatigue interaction loading conditions

This paper develops a robust creep-fatigue interaction (CFI) life prediction model which is superior to the existing methods. Specifically, the newly proposed creep damage incorporates the effect of creep strain, which introduces the critical creep strain energy density rate and creep strain evolution term. The predictions are carried out for various materials, including martensitic heat-resistant steel, austenitic stainless steel, nickel-based superalloy, and different loading conditions, including conventional CFI and hybrid-controlled CFI loadings. The results show that all of the tested data falls within ± 2.5 error band, demonstrating the broad applicability of the proposed model. Based on the proposed model, a continuous CFI failure envelope independent of material, temperature, and CFI loading type is proposed, with almost all the data points lying outside the envelope.

Sensitivity analysis of notch shape on brittle failure by using uni-bond dual-parameter peridynamics

The brittle failure of components weakened by sharp or blunt notches is a topic of active and continuous research. Notches created during the design and manufacturing of structural components give rise to localized stress concentrations, which can generate a crack leading to catastrophic failure or to a shortening of the assessed structural life. To investigate how notches influence the fracture and bearing capacity of brittle materials by using peridynamics (PD), an extended uni-bond dual-parameter peridynamic (UDPD) model that can overcome the fixed Poisson’s ratio in bond-based PD and address the attenuation effect of the nonlocal PD force is developed. The expressions of normal stiffness and tangential stiffness with elastic modulus and Poisson’s ratio are derived and rewritten. Additionally, the critical microstrain energy density for the extended UDPD model is given to judge the fracture initiation, and the validity and accuracy of the proposed model are verified by four examples. Ultimately, six typical types of notches, i.e., rectangular notches, sharp V notches, U notches, blunt V notches, keyhole notches, and VO notches, were selected and investigated in brittle plates with four different tip radii to study the notch sensitivity of brittle failure to notch shape by using the extended UDPD model. The results show that the crack path and bearing capacity of the structure are sensitive to the notch shape and the tip radius of the notch, and a blunt notch with a larger tip radius (U notch, blunt V notch, keyhole notch, and VO notch, tip radius ρ⩾2mm) offers better performance in terms of structural safety than a sharp notch or a notch with a smaller tip radius.