Fracture Energy Density Research Articles

Research on the micro-mechanism and factors of hot recycled asphalt binder cracking

The poor low-temperature performance of recycled asphalt is the primary cause of the recycled asphalt disease. However, further strengthening is required to analyze the molecular-level cracking of recycled asphalt. This article presented a comprehensive investigation of the cracking phenomenon of recycled asphalt at both the macro and micro levels. This was achieved through the utilization of experimental tests and molecular dynamics simulations. In this study, pressure-aged asphalt was subjected to 40 h of aging. The aged asphalt was divided into three groups: 30% RAP (reclaimed asphalt pavement) recycled asphalt, 50% RAP recycled asphalt, and 70% RAP recycled asphalt. The three groups were then analyzed in terms of three major indexes. Linear amplitude scanning (linear amplitude sweep, LAS) was conducted on the three groups. The mechanical response law of asphalt was obtained, and it was found that the coefficient of strength of recycled asphalt increased with the increase of RAP dosage. At the same time, the fracture energy density decreased subsequently. Furthermore, the fracture energy density of aged asphalt was 7% lower than base asphalt's. Subsequently, this study examined the four fractions and C=O and S=O functional groups of five types of asphalt and constructed the molecular structures and models of stable base asphalt and aged asphalt. Subsequently, this article constructed a fusion model of new and old asphalt, analyzed the fusion process of new and old asphalt, and studied the factors affecting the blending degree of new and old asphalt. Finally, the factors affecting the cracking performance of rejuvenated asphalt, including the blending degree, the content of the four fractions, and the addition of the rejuvenator, were investigated. The impact of each influencing factor on the cracking performance of recycled asphalt was analyzed from multiple perspectives. In conclusion, the findings of this study provide a valuable guide for interpreting the tensile properties of reclaimed asphalt and the influence of rejuvenators.

Variational damage model: A novel consistent approach to fracture

The computational modeling of fractures in solids using damage mechanics faces challenge when dealing with complex crack topologies. One effective approach to address this challenge is by reformulating damage mechanics within a variational framework. In this paper, we present a novel variational damage model that incorporates a threshold value to prevent damage initiation at low energy levels. The proposed model defines fracture energy density (ϕ˜) and damage field (s) based on the energy density (ϕ), crack energy release rate (Gc), and crack length scale (ℓ). Specifically, if ϕ≤Gc2ℓ, then ϕ˜=ϕ and s=0; otherwise, ϕ˜=−Gc24ℓ21ϕ+Gcℓ and s=1−Gc2ℓ1ϕ. Furthermore, we extend the model with a threshold value to a higher-order version. Utilizing this functional, we derive the governing equation for fractures that evolve automatically with ease. The formulation can be seamlessly integrated into conventional finite element methods for elastic solids with minimal modifications. The proposed formulation offers sharper crack interfaces compared to phase field methods using the same mesh density. We demonstrate the capabilities of our approach through representative numerical examples in both 2D and 3D, including static fracture problems, cohesive fractures, and dynamic fractures. The open-source code is available on GitHub via the link https://github.com/hl-ren/vdm.

Decoding ceramic fracture: Atomic defects studies in multiscale simulations

Microstructural atomic defects, including voids, cleavage, and inclusions, are commonly observed in alumina materials, and their impact on mechanical properties, such as fracture stress and toughness, is significant. In this paper, we introduce novel alumina models that incorporate experimentally observed void features. An atomic model is established to study the effects of micro-structural void features on fracture properties and atomic structure changes using molecular dynamics simulations. The electron backscatter diffraction and scanning electronic microscopy analysis of experimental samples are used to evaluate microstructural features that are used as inputs to the simulations (e.g., void aspect ratio, void angle). We apply an innovative Atomistic-to-Continuum (ATC) method based on Riemann sums to bridge atomic and continuum mechanics theories, evaluating the resistance of materials with atomic defects to crack propagation. The results show the greatest effects of pore angles on weakening mechanical properties such as peak strength and fracture energy density. The accuracy and efficiency of the ATC method in evaluating stress intensity factors are used to calculate the mechanical responses. Additionally, we establish a multiple layer perceptron neural network to evaluate the complex relationship between void features (aspect ratio, pore angle, relative distance) and typical fracture properties (fracture stress, critical stress intensity factor). A meta-analysis of these results from both machine learning methods and molecular dynamics simulations reveals the significant impact of each void feature on the sensitivity of typical fracture properties (peak strength, critical stress intensity factor at peak strength) and highlights the critical role of aspect ratio on fracture properties.

An improved model for discrete element method simulation of spatial gradient distributions of freeze-thaw-induced damage to sandstone

The investigation into the freeze-thaw (F-T) damage holds paramount theoretical significance in comprehending the mechanisms underlying F-T disasters, predicting catastrophes, and devising engineering protection systems. F-T damage in rock evolves progressively from the surface towards the interior, however, current models exhibit conspicuous deficiencies in simulating such progressive damage. Drawing upon experimental findings concerning the evolution of F-T damage in water-saturated rock, an improved discrete element model (DEM) for rock F-T damage is developed. In this model, thermal conduction model and volume expansion theory are integrated to describe the volumetric expansion characteristics during the freezing of internal pore water, thus effectively simulating the initiation and progression characteristics of frost heave cracks. We validated this model through comparisons with theoretical analyses and experiments, exploring the effects of model parameters. Employing moment tensor, the spatial gradient distribution patterns of F-T damage in water-saturated rock from the vantage point of fracture energy was analyzed. The results reveal that at −20 °C, 20 F-T cycles are requisite for the propagation of damage from the outer layer to the center of the Sichuan sandstone samples. The extent of damage in the outer layer exceeds that of the center, with the maximum fracture energy density of the outer layer being approximately 38.7 times that of the center. This model aptly delineates the progressive development of F-T damage characteristics and holds promise for further applications in identifying and delineating F-T damage zones in cold region rock engineering.

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.

Integrated colloidal deformation to advanced polymer network design through polymer-nanoparticle alternating hybrids

Current polymer network design suffers from intrinsic trade-offs, where polymer networks with high modulus often turn out to be in short of stretchability or fracture toughness. Here, we show a novel polymer network design through polymer-nanoparticle alternating hybrids that enable integrating the non-polymeric colloid deformation into polymer network design. The new class of polymer network exhibits colloidal yielding at small deformation before conformational change at higher elongation ratios, enabling simultaneous achievement of high Young's modulus of E≈10−50MPa, high yield strength of σY∼3−5MPa, large stretchability of λ∼7−10, and high fracture energy density of Γ∼30MJ/m3. These results demonstrate a successful strategy to decouple the molecular mechanics for yield from that for stretchability or toughness, leading to new polymer networks design.

Study on low temperature crack resistance of warm-mixed recycled SBS modified asphalt mixtures

In view of the cold winter in northern China and the large temperature difference between day and night, the asphalt pavement has been in low temperature service for a long time, in addition to experiencing the aging effect of water and salt erosion, jointly leading to a particularly serious pavement cracking phenomenon. Therefore, a quantity of Reclaimed Asphalt Pavement (RAP) is produced for the repair and renovation of old roads. Faced with the problems of inadequate reuse rate of RAP and high energy consumption of thermal regeneration, it is of great practical significance to explore the technology of warm mix regeneration. In order to study the adaptability of recycled SBS modified asphalt mixtures to low temperature after complex environmental erosion (long-term aging, water freeze-thaw cycle, and salt freeze-thaw cycle), two mixing methods, including hot mixing and warm mixing, were selected, and a Semi-Circular Bending Test was performed. SCB and Digital Image Correlation (DIC) techniques were used to evaluate the low temperature properties of recycled asphalt mixtures by fracture toughness, fracture energy and horizontal strain density damage. Combined with an Atomic Force Microscope (AFM) test, the microscopic analysis of recycled asphalt was carried out to verify the mechanism of low temperature cracking. The results showed that the low temperature cracking resistance of the reclaimed asphalt mixtures with warm mix was slightly worse than that with hot mix. The overall low temperature cracking resistance of the reclaimed SBS modified asphalt mixtures decreased with the increase in RAP content. The low temperature performance of the warm-mixed reclaimed asphalt mixtures deteriorated greatly when the RAP content was 80 %. The influencing factors of environmental conditions on the low temperature cracking resistance of the warm-mixed recycled SBS modified asphalt mixtures were listed as below: long-term aging > salt freeze-thaw cycle > water freeze-thaw cycle. The influence of salt on the stress field of crack tip and the microstructure of recycled asphalt after freeze-thaw was greater than that of water erosion. The changes of the microscopic adhesion were in good agreement with the macroscopic test results, which could be employed as the index evaluating the low temperature crack resistance of the warm-mixed SBS modified asphalt mixtures. The addition of warm mixing agent would play a positive role in the low temperature crack resistance of recycled asphalt mixtures with a RAP content of less than 60 % to a certain extent, so warm-mixed recycled asphalt mixtures were more suitable for the application in northern areas.

Analyzing the Damage–Healing Performance of Asphalt Mixture from Macroscopic and Mesoscopic Scales

Owing to their self-healing ability, asphalt mixtures have great potential for improving the service life of asphalt pavement, and can play an important role in sustainable infrastructures. In this study, a semicircular bending damage-healing-fracture experiment was conducted to evaluate the healing effect of a 90# asphalt mixture and styrene-butadiene-styrene copolymer modified asphalt mixture. The digital image correlation technique was used to synchronously observe the semicircular specimen to analyze its surface displacement and strain changes during the healing process. The experimental results showed that, on the macroscopic scale, the healing index HIFE based on fracture energy density was recommended to evaluate the healing effect of asphalt mixtures, and the healing effect of the 90# asphalt mixture was better than that of the styrene-butadiene-styrene copolymer modified asphalt mixture. On the mesoscopic scale, the horizontal displacements of the notch of the specimen position gradually recovered under self-healing conditions. The strain concentration at the crack gradually weakened, and the strain degree in the non-cracked area of the specimen also decreased gradually under self-healing conditions. The recovery of the macromechanics of the specimen is related not only to the healing of the crack area but also to the recovery of the non-cracked area.

Mechanical properties and influence mechanism of hydroxyl‐terminated polybutadiene propellant under confining pressure

AbstractTo better understand the mechanical properties and influence mechanism of hydroxyl‐terminated polybutadiene (HTPB) propellant under various confining pressures, the uniaxial tension tests with low to medium strain rate and various confining pressures were carried out. The coupling effects of strain rate and confining pressure on mechanical properties were presented. Meanwhile, the confining pressure influence mechanism was analyzed and revealed using the meso numerical simulation method and scanning electron microscopy images of fracture surfaces. The meso damage evolution processes under various confining pressures were presented. The results show that strain rate and confining pressure affect mechanical responses of HTPB propellant significantly. As confining pressure increases, the maximum tension strength and fracture strength increase. The maximum tension strain and failure strain vary slightly with confining pressure under low strain rate, while they increase significantly with confining pressure at medium strain rate. The fracture energy density increases with the increase of strain rate and confining pressure. Meanwhile, the value of saturation pressure depends on strain rate. The confining pressure influence mechanism is to suppress dewetting damage initiation and evolution. Besides, the failure mode of HTPB propellant under different confining pressures is still particles dewetting.

A microstructure-sensitive analytical solution for short fatigue crack growth rate in metallic materials

Short fatigue crack growth in engineering alloys is among the most prominent challenges in mechanics of materials. Owing to its microstructural sensitivity, advanced and computationally expensive numerical methods are required to solve for crack growth rate. A novel mechanistic analytical model is presented, which adopts a stored energy density fracture criterion. Full-field implementation of the model in polycrystalline materials is achieved using a crystallographic crack-path prediction method based on a local stress intensity factor term. The model is applied to a range of Zircaloy-4 microstructures and demonstrates strong agreement with experimental rates and crack paths. Growth rate fluctuations across individual grains and substantial texture sensitivity are captured using the model. More broadly, this work demonstrates the benefits of mechanistic analytical modelling over conventional fracture mechanics and recent numerical approaches for accurate material performance predictions and design. Additionally, it offers a significant computer processing time reduction compared with state-of-the-art numerical methods.

Development of Strong and Tough β-TCP/PCL Composite Scaffolds with Interconnected Porosity by Digital Light Processing and Partial Infiltration.

Strong and tough β-TCP/PCL composite scaffolds with interconnected porosity were developed by combining digital light processing and vacuum infiltration. The composite scaffolds were comprised of pure β-TCP, β-TCP matrix composite and PCL matrix composite. The porous β-TCP/PCL composite scaffolds showed remarkable mechanical advantages compared with ceramic scaffolds with the same macroscopic pore structure (dense scaffolds). The composite scaffolds exhibited a significant increase in strain energy density and fracture energy density, though with similar compressive and flexural strengths. Moreover, the composite scaffolds had a much higher Weibull modulus and longer fatigue life than the dense scaffolds. It was revealed that the composite scaffolds with interconnected porosity possess comprehensive mechanical properties (high strength, excellent toughness, significant reliability and fatigue resistance), which suggests that they could replace the pure ceramic scaffolds for degradable bone substitutes, especially in complex stress environments.

Transition of rupture mode of strain crystallizing elastomers in tensile edge-crack tests.

We revisit the classical results that the fracture energy density (Wb) of strain crystallizing (SC) elastomers exhibits an abrupt change at a characteristic value () of initial notch length (c0) in tensile edge-crack tests. We elucidate that the abrupt change of Wb reflects the transition in rupture mode between the catastrophic crack growth without a significant SIC effect at c0 > and the crack growth like that under cyclic loading (dc/dn mode) at c0 < as a result of a pronounced SIC effect near the crack tip. At c0 < , the tearing energy (G) was considerably enhanced by hardening via SIC near the crack tip, preventing and postponing catastrophic crack growth. The fracture dominated by the dc/dn mode at c0 < was validated by the c0-dependent G characterized by G = (c0/B)1/2/2 and the specific striations on the fracture surface. As the theory expects, coefficient B quantitatively agreed with the result of a separate cyclic loading test using the same specimen. We propose the methodology to quantify the tearing energy enhanced via SIC (GSIC) and to evaluate the dependence of GSIC on ambient temperature (T) and strain rate (). The disappearance of the transition feature in the Wb-c0 relationships enables us to estimate definitely the upper limits of the SIC effects for T (T*) and  (*). Comparisons of the GSIC, T*, and * values between natural rubber (NR) and its synthetic analog reveal the superior reinforcement effect via SIC in NR.

Study on the Performances of Waste Battery Powder Modified Asphalt and Asphalt Mixture.

As an asphalt modifier, waste battery powder (WBP) has been proven to be possible. This paper studies the modification effect of WBP on asphalt. The Flight Test Instrumentation Requirements (FITR) of WBP, Dynamic Shear Rheology (DSR) test, and Full Section Fracture Energy Test (FSFET) of asphalt are carried out. The high-temperature rheological properties and low-temperature properties of WBP modified asphalt are analyzed. The high-temperature stability, low-temperature crack resistance and water stability of WBP modified asphalt mixture are tested. The research results show that the modification of asphalt by WBP is essentially physical modification but the mixing of WBP has a certain enhancement effect on the bond energy of the methylene group, which is helpful to improve the technical performance of modified asphalt. The proportion of elastic components in asphalt can be significantly increased by adding WBP, thus enhancing the deformation resistance of asphalt under high-temperature conditions. The dynamic shear modulus of 10% waste battery powder is about 1.5-2.0 times that of 0% waste battery powder. The mixing of WBP reduces the proportion of viscous components in asphalt which is unfavorable to the crack resistance under low temperatures. The greater the amount of WBP, the smaller the fracture energy density, the content of WBP is 6% and 10%, the fracture energy density is about 60-80% and 40-60% of the original asphalt, and the low temperature cracking resistance of asphalt decreases. The modification effect of WBP on asphalt is much lower than that of SBS.

The influence of microstructure on short fatigue crack growth rates in Zircaloy-4: Crystal plasticity modelling and experiment

Rates of fatigue crack growth in Zircaloy-4 are highly microstructurally sensitive and dependent upon texture. Crystal plasticity finite element modelling with the eXtended Finite Element Method and a stored energy density fracture criterion are used to simulate crack propagation in single crystals and polycrystalline microstructures for comparison with experimental crack growth rate data. Results demonstrate that growth rate fluctuations at microstructural features are driven primarily by elastic anisotropy and yield stress mismatch. Additionally, reduced rate of growth in soft hexagonal close packed grains (relative to the remote loading direction) can be linked with crack path tortuosity, which is shown to be controlled by the cyclic development of an in-plane shear back stress. Most importantly, stored energy density is shown to accurately capture major microstructure-driven differences in crack growth rate. Comparison of simulated fatigue crack growth rates with experimental data enables estimation of the critical stored energy density for crack propagation in Zircaloy-4 to be 250 J/m2.

A method for introducing mode II dissipation energy into mixed fracture analyses

AbstractThis paper presents a methodology to consider the mode II fracture energy density in those analyses in which the phenomenon of mixed fracture occurs. The method consists of using a fracture energy density calculated as the weighted average of the fracture energy densities in mode I and mode II, the weighting factors being the relative importance of the mode I and II deformations with respect to the total deformation. This methodology has been implemented in local damage models using the smeared crack approximation but can be implemented in more complex models such as nonlocal damage models. Since there is no specific experimental test to measure the mode II fracture energy density, this method allows this parameter to be measured indirectly by adjusting its value so that the numerical equilibrium curve matches the experimental results.

Assessment of Machinability in Aluminium Alloys Using the COPRAS Method

The most intriguing substance that offers the maximum mechanical force in the world of hard machining materials is aluminium alloys. Because of its superior "strength to weight ratio", it is widely used in the fabrication of aerospace and aeronautical products. Eco-friendly as well as cost-effective processing techniques have become increasingly necessary over time, and many experts have expressed a strong interest in developing ever-more-advanced machining techniques. Excellent machinability properties allow for faster cutting speeds, easy attainment of a good finish, and reduced tool wear when cutting certain materials. Manufacturing engineers must therefore figure out how to assess a material's processability, which primarily depends on its mechanical characteristics as well as other machining conditions, in order to make components affordably. In this work, "the COPRAS (Complex Proportional Assessment) approach" is used to examine the machinability properties of aluminium composite materials. In this instance, 8 different composites are taken into account, and their machinability is assessed based on various mechanical characteristics. With the aid of this process, it is now simpler for the producers to choose a composite material that is simple to machine. The rank of alternatives using the COPRAS method for A357FS is seventh, A357RS is fifth, A357FC is third, A357RC is first, A224FS is sixth, A224RS is eight, 7475FS is fourth, and 7475RS is second. It has been discovered that "aluminium alloy A357RC" is the specimen that is most straightforward to machine. Despite having a middling "yield strength and tensile strength" this alloy has the lowest "elongation at fracture and highest strain energy density" which places it at the top of the overall rating. " Aluminum alloy 7475FS", which has "higher yield and tensile strengths," is the trickiest material to perform machining.

Rise time of the 2018 MW 6.4 Hualien earthquake revealed by source time functions: A restrictive estimation of static stress drop

Using the ω−2 source model, the rise time of the 2018 Mw 6.4 Hualien earthquake is estimated from the corner frequency of the Fourier spectrum of the source time function. Two source parameters are also determined: average dynamic stress drop (∆σd) and static stress drop (∆σs). The results show that the rise time is 2.52 s, which is approximately 0.23 times the value of the entire source duration and then leads to a ∆σd of 3.03 MPa. In this study, we propose a method to confine the estimation of ∆σs through ∆σd. Because the radiated seismic energy exists, this leads to ∆σs<2∆σd−2μEgM0 (Eg is the fracture energy, M0 is the seismic moment, and μ is the rigidity) on average. Hence, we suggest that ∆σs for the 2018 Hualien earthquake should be less than 4.81 MPa. Because of ∆σs > ∆σd, the earthquake's rupture can be interpreted in a frictional overshoot model; then, the radiation efficiency near 0.5 suggests that 50% of the available energy is released to extend the fault. Furthermore, the lower fracture energy density (G) for the Hualien earthquake is probably due to the fact that an ML 5.9 foreshock disturbs the fault system beforehand.

An extended peridynamic model for dynamic fracture of laminated glass considering interfacial debonding

In this work, an extended peridynamic (PD) model considering interfacial debonding is proposed to investigate the dynamic fracture behavior of laminated glass under low-velocity and high-velocity impacting loads. The interaction between different materials is described by adding an interfacial force term into the governing equations, which is derived from the energy density function of the interfacial bonds. A potential function term sourced from the cohesive zone model (CZM) is reconstructed and then introduced into the peridynamic model to describe the cohesive interfaces. The failure criterion of interfacial debonding is determined by the calculation of interface fracture energy and interfacial energy density. Two benchmark examples, a through-cracked tensile test and a drop-weight test, have been conducted to establish the validity of the proposed model. The proposed model and approach are then employed to investigate the dynamic fracture mechanism of laminated glass under high-velocity impacting loads.

Size-Dependent Fracture Characteristics of Intermetallic Alloys

BackgroundLightweight alloys such as intermetallic titanium aluminide (TiAl) alloys are poised to be a potential candidate for replacing heavier nickel based super alloys in an aero engine. However, before an industry wide implementation is possible, it is indispensable to develop physically accurate computational material models which account for essential deformation and fracture mechanisms. This assists the virtual prototyping required for the new product development using TiAl components.ObjectiveThe objective of this work is to determine the effect of size of tested specimens on their fracture energy and provide a physically motivated scaling law.MethodsIn this work, the quasi-brittle behavior of TiAl alloys is experimentally and numerically investigated. A total number of 29 geometrically identical TiAl specimens of three different sizes are tested in a three-point bending setup. Since the final abrupt failure of each specimen is preceded by plasticity, a theoretical and numerical framework which accounts for both elastic and plastic work densities is applied in simulations.ResultsThe fracture energy density for each tested size is calculated numerically which is found to be lower for larger volumes, thereby, confirming the size effect in intermetallic TiAl alloys. A novel size effect law is proposed which is based on two physically motivated coefficients.ConclusionsThe work concludes with the quantitative knowledge of the size-dependent fracture energy of intermetallic alloys and an empirical scaling law to predict the same. Excellent predictive capability of the proposed law is successfully established with data of various quasi-brittle materials from literature.

Identification of parameter to assess cracking resistance of asphalt mixtures subjected to aging and moisture conditioning

This study comprehensively evaluated different parameters based on tensile strength testing to assess the cracking resistance of asphalt mixtures subjected to aging and moisture conditioning. For this purpose, two sources of aggregates were selected to produce hot and warm mix asphalt mixtures. Asphalt mixtures were subjected to short term and long term aging, three levels of moisture conditioning (freeze thaw cycles), and tested at two temperatures (15 °C and 25 °C). The load-displacement data was used to determine the fracture work density, fracture energy, toughness index, cracking resistance index, cracking tolerance index, and rate dependent cracking index. It was noticed that moisture conditioning increased the variability of the different parameters. The cracking tolerance index and rate dependent cracking index parameter had a much higher coefficient of variation (CoV) with a maximum value close to 50%. Indirect tensile strength, fracture energy, and fracture work density appropriately captured the effect of moisture on cracking resistance of mixtures. The cracking resistance index, cracking tolerance index, and rate dependent cracking index increased with an increase in the moisture conditioning level. The Statistical analysis showed that tensile strength, fracture work density, and fracture energy were significantly influenced by different aging and moisture conditions evaluated. Fracture energy showed better association with fatigue life of asphalt mixtures subjected to three freeze-thaw cycles compared to tensile strength. Further, the fatigue life prediction models showed that both indirect tensile strength and fracture energy significantly influence the fatigue life of asphalt mixtures subjected to aging and moisture conditioning.