Fracture Energy Density Research Articles

Effect of Aged Binder Distribution on the Fracture Tolerance of Asphalt Mixtures with Reclaimed Asphalt Pavement

Abstract This study investigated the effect of the distribution of aged binder from reclaimed asphalt pavement (RAP) on the fracture tolerance of recycled asphalt mixtures. Two RAP sources (one coarse, one fine), one virgin polymer-modified asphalt binder, and four RAP contents (0 %, 20 %, 30 %, and 40 %) were used to produce a total of seven mixtures. Fracture tolerance was assessed in terms of fracture energy density (FED) at three levels: binder, interstitial component (IC) (composed of effective binder and fine aggregate fraction), and mixture. Binder fracture energy tests were conducted to measure the FED of blends of virgin and recovered RAP binder. IC direct tension tests were employed to determine the IC FED. Finally, Superpave indirect tensile fracture tests were performed to obtain the FED of RAP mixtures. FED decreased with increasing RAP content at the three levels (binder, IC, and mixture). More importantly, IC and mixture exhibited almost identical FED reductions in relative terms, while the reduction was less significant at binder level. This finding indicates that the full blending scenario artificially created at the binder level did not occur at IC and mixture levels. Furthermore, the coarse RAP yielded greater FED than the fine RAP, which substantiates that RAP gradation controls the distribution of RAP binder in recycled mixtures. Consequently, the lower content of aged RAP binder in the IC portion for mixtures with the coarser RAP resulted in better fracture tolerance. The application of a newly developed guideline for determining the maximum allowable RAP content in recycled mixtures confirmed that the coarser RAP used in this study allows for a greater RAP content than the finer RAP despite the stiffer RAP binder.

Volume dependent fracture energy and brittle to quasi-brittle transition in intermetallic alloys

Intermetallic alloys such as titanium aluminide (TiAl) are lightweight with superior specific strength and high temperature oxidation resistance. They have a potential to replace heavier nickel based super alloys in low pressure high temperature sections of an aero engine. To facilitate an industry wide implementation, it is however indispensable to develop physically accurate computational methods which account for key deformation and fracture mechanisms. This assists the virtual prototyping required for the new product development using TiAl alloys. In this work, the quasi-brittle and volume dependent 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 to investigate the volume dependence of fracture properties. In addition, three compact tension tests with identical specimen geometries are performed to analyze brittle to quasi-brittle transition and a switch in failure mechanism. Since the material fracture is observed to be preceded by plasticity, a theoretical and numerical framework of phase field ductile fracture which accounts for both elastic and plastic work densities is applied. The averaged fracture energy density for each test is evaluated numerically which is found to be lower for larger volumes. The work concludes with the proposal of an empirical law relating the fracture energy density with the specimen volume. Data from literature for different classes of materials is used for validation of the proposed empirical law. The mechanisms of transition from brittle to quasi-brittle fracture are investigated on the basis of local stress triaxiality in three-point and compact tension simulations.

High-Temperature Deformation and Low-Temperature Fracture Behavior of Steel Slag Rubber Asphalt Mixture Surface Layer

Steel slag is regarded as one of the most widespread solid by-products of steel smelting with little commercial value. It can play a vital role in the construction industry especially in the field of transportation infrastructure construction. However, there are few evaluation systems established on the high-temperature deformation and low-temperature fracture behavior of steel slag rubber asphalt mixture (SSRAM). This study explores the performance of SSRAM by uniaxial penetration test, Semi-Circular Bending (SCB) test and evaluates test data through regression analysis. The uniaxial penetration test results shows that the failure deformation of SSRAM increases with the increase of steel slag content. According to the minimum allowable permanent deformation (RTS-min), the deformation of SSRAM should be controlled within 3 mm. Meanwhile, the cracking index of the SSRAM surface layer calculated at low temperature can meet the design requirements. The SCB test results show that the stress peak degradation rate (specimens with 10 mm notch are compared with 0 mm) of SSRAM with 40% steel slag content is 20.04%. That means proper steel slag content makes the stress peak degradation rate of SSRAM reaches the lowest value. The calculation results of fracture energy density (J1C) show that the steel slag additive reduced the fracture energy density of SSRAM. However, it is still proved that SSRAM with 40% steel slag has the best low-temperature fracture performance based on critical fracture toughness (K1C) and fracture stress peak. Furthermore, the crack propagation velocity parametric equation of SSRAM is proposed through fracture mechanics theory and the increase of velocity is exponential. Considering the high-temperature deformation resistance and low-temperature fracture property, the SSRAM surface layer with 40% steel slag content showed a batter application potential.

Temperature-dependent bending strength in piezoelectric semiconductive ceramics

By using theoretical analysis and three-point bending experiments, influence of temperature on the bending strength of GaN ceramics is investigated. Based on the critical fracture energy density, a simple and effective temperature-dependent bending strength prediction model is established for piezoelectric semiconductive ceramics. In the model, the bending strength at high temperature depends on the reference temperature, stiffness, polarization and melting point, as well as piezoelectric polarization charges. It is shown that the theoretical predictions are consistent with experimental results. Thus, such a model is instructive to the reliability design of GaN high-temperature devices.

CHANGE OF ENERGY CHARACTERISTICS OF LITHOSPHERE ELEMENTS DURING THEIR DEFORMATION

Purpose. The purpose of this study is to establish analytical patterns for predicting changes in stress and energy density spent on the destruction of rocks according to experimental studies. To solve this purpose in the article were set the following scientific problems: 1) analytical description of the dependence of the stress σij on the main deformation εij; 2) establishment of calculation parameters that are included in the analytical patterns; 3) analytical description and study of fracture energy density curves.
 Methodology. In the course of analytical and experimental researches of full diagrams of deformation of rocks the mathematical model of dependence of the stress on the deformation is developed. Physico-mechanical processes of all characteristic sections of the complete deformation diagram were also analyzed and described. Analysis of the resulting curve showed that the rock mass and elements of the lithosphere are not perfectly elastic or plastic objects. Along with the elastic ones, plastic ones are always present to one degree or another.
 The integration of the obtained analytical expression σ11 = f(ε11) allowed to establish the volumetric energy density spent on the destruction of the rock sample under the action of external load. The maximum activation energy for the considered rock is 0.67 MJ/m3. A comparison of the experimental and calculated values of the energy dependence u(ε1) shows a coincidence over almost the entire range of deformation changes (ε11 = 0..0.04).
 Findings. The study of rock samples at hard stress allowed to obtain a complete deformation characteristics of the rock. The curve that surrounds the deformation cycles (1) combines pre-boundary, boundary, extremal modes of deformation and destruction of rocks. Equation (4) allows us to establish that the destruction can occur at different values of energy density U(ε).
 Originality. An analytical description of the energy diagram of deformation and a complete diagram of stress change in the form of a single dependence, which takes into account the boundary and extremal areas, was developed in the work. In contrast to the method of piecewise linear approximation, this approach corresponds to the physics of the process and reduces errors in calculations.
 Practical implications. Theoretical and experimental analysis of the obtained energy fracture diagrams and complete stress change diagrams in rocks allows to estimate the bearing capacity of a rock mass or other solid body. This allows you to predict critical values of stresses and external loads to prevent failure in a timely manner.

Understanding asphalt binder cracking characterization at intermediate temperatures: Review and evaluation of two approaches

Accurate characterization and proper selection of asphalt binder can prolong the fatigue life of asphalt pavements. The objective of this study was to evaluate the linear amplitude sweep (LAS) test and the binder fracture energy density (BFE) test using a broad range of asphalt binders with a particular emphasis on the identification of appropriate failure definition. Three unmodified binders and three modified binders were investigated. LAS test results revealed that the failure criteria in the existing specification (35% reduction in G*sinδ and peak shear stress) did not capture the improved performance expected from modified binders whereas the peak stored pseudo strain energy (PSE) failure criterion did. This could be attributed to the larger strain levels that binder samples undergo before the instant of failure defined by the peak stored PSE. Fracture energy density measured with the BFE test on fractured specimens clearly distinguished between unmodified and modified binders. It was concluded that binder response can influence the outcome of performance comparison parameters. For comparable binder types, binders with a more ductile behavior may exhibit a more strain tolerant response in the LAS test whereas stiffer binders appeared to show a more fracture tolerant response in the BFE test.

Experimentally validated phase-field fracture modeling of epoxy resins

In recent years the phase-field fracture (PFF) model has attracted much attention on failure problems in fiber-reinforced composite materials and structures. However, the discussion on the determination of input parameters remains unsettled. This work aims to seek a general solution for determining the length scale parameter lc and critical fracture energy density gf, the primary parameters of the PFF model. We design benchmark experiments, including uniaxial tensile and three-point bending tests, for two epoxy resins, PR 520 and LT-5078. The fracture structure responses of these two materials are investigated via the PFF method, emphasizing existing possible estimations for the length scale parameter lc. A calibration method is proposed for brittle fracture of epoxy resins, which combines benchmark experiments and numerical simulation trials. The input parameters of two epoxy resins are obtained using this calibration method. Simulated results are validated with experimental data qualitatively. Numerical predictions and experimental data are compared to show this method’s reliable estimation for the critical fracture energy density and length scale.

Microstructural integrity characterization of cement-based construction materials

In this paper, a new micromechanical framework to characterize the microstructural integrity and predict the effective properties of multi-phase particulate composites is presented. Within the framework, a new scalar micromechanical parameter is identified and used to derive new expressions for the effective elastic properties of particulate composites using the mean-field homogenization technique. The derived equations are then generalized for composites with multiple phase constituents. The generality of the proposed framework is demonstrated by combining the derived equations with the existing homogenization techniques such as the Mori–Tanaka method and the Generalized Maxwell’s Approach (GMA). The results show that the theory delivers consistent estimates of the effective properties of two-phase elastic composite materials. The new scalar micromechanical parameter is also used to characterize the microstructural integrity of both asphalt mixtures and Portland cement concrete. The results show that the new scalar micromechanical parameter correlates well with multiple key fundamental properties of asphalt concrete mixture, including the creep rate, the fracture energy density, the endurance limit, and the damage rate parameters. The results also show that the new micromechanical framework can be used to accurately predict the effective modulus properties of Portland cement concrete mixtures.

Modification mechanism of C9 petroleum resin and its influence on SBS modified asphalt

In this paper, C9 petroleum resin was used as the raw material, and the microstructure of C9/SBS modified asphalt at a different time under different C9 petroleum resin content was studied by fluorescence microscope. The mechanical properties were studied by using the whole section fracture energy, the pavement performance of C9/SBS modified asphalt was tested and analyzed. The results show that C9 petroleum resin is conducive to SBS particles being sheared into smaller particles under the same preparation process. The larger the content of C9 petroleum resin, the smaller the final size of SBS particles, and the smallest SBS particle size can be reduced by about half. When the content of C9 petroleum resin is more than 9%, the decreasing trend is no longer obvious. This phenomenon mainly occurs in the final stage of shearing. C9 petroleum resin can affect the swelling behaviour of SBS in asphalt and its final microstructure by reducing the particle size of SBS. The larger the content of C9 petroleum resin, the larger the area occupied by SBS after swelling, and the longer the skeleton length of SBS, the easier the crosslinking occurs and the denser the crosslinking network structure is formed. The addition of C9 petroleum resin can effectively improve the fracture energy density of SBS modified asphalt, and its mechanism is closely related to the effect of C9 petroleum resin on the shear particle size and final swelling degree of SBS particles. C9 petroleum resin can effectively hinder the floating and aggregation of SBS modifier in asphalt during high-temperature storage, thus improving the storage stability of SBS modified asphalt. The incorporation of C9 petroleum resin can significantly increase the viscosity of SBS modified asphalt, improve the low-temperature performance of SBS modified asphalt, and improve the anti-ageing performance of SBS modified asphalt. The results provide a new way to improve the performances of SBS modified asphalt.

Rheological behavior of high modulus asphalt binder and its indication for fracture performances

High modulus asphalt concrete (HMAC) has been used as a high-quality road construction material to tackle permanent deformation of asphalt mixtures primarily due to its exceedingly high modulus. However, rheological behavior, especially non-linear rheological behavior, and fracture behavior of high modulus asphalt binder (HMAB) are not well studied yet. In this study, linear and non-linear rheological tests, and fracture energy density tests were conducted on three HMABs, one base asphalt binder and one styrene-butadienestyrene (SBS) modified asphalt binder. The results show that HMABs have significantly higher rutting resistance, even after experiencing non-linear viscoelastic deformation. However, low cracking resistance was observed for HMAB due to its low ductility and low stress dissipation at its crack tip. Therefore, cracking resistance of HMACs should be a concern if they’re subjected to tensile loading in application.

Research on the Performance of Regenerant Modified Cold Recycled Mixture with Asphalt Emulsions

In order to study the mechanical properties and effect of a regenerant on a cold recycled mixture with asphalt emulsions (CRMEs), the moisture susceptibility, high-temperature performance, low-temperature performance, dynamic mechanical properties and durability of CRMEs were analyzed and evaluated by immersion splitting strength tests, freeze-thaw splitting strength tests, rutting tests, semi-circle bending tests, uniaxial compression dynamic modulus tests and indirect tensile tests. Scanning electron microscopy (SEM) was used to analyze the micromorphology of CRMEs modified with regenerant. Finally, a comprehensive evaluation system of five different CRMEs was established based on the efficacy coefficient method to quantitatively analyze the comprehensive performance of the CRMEs. The test results showed that the regenerant can significantly improve the water immersion splitting strength, freeze-thaw splitting strength fracture energy density, and fatigue resistance of CRMEs. However, the addition of regenerant affected the high-temperature performance of the cold recycled mixture. The dynamic modulus of the CRMEs first increased and then decreased with regenerant content increasing. When the regenerant content was 8%, the dynamic modulus of the CRMEs was the highest. Adding styrene-butadiene rubber (SBR) latex can improve the high-temperature performance of CRMEs, but the moisture susceptibility, low temperature performance and fatigue resistance of the cold recycled mixture were not significantly improved, and the dynamic modulus of the mixture was reduced. Based on the efficacy coefficient method, the optimal content of regenerant is 8%. Regenerant are potential modifiers for cold recycled mixture that they can significantly improve the dynamic mechanical properties and durability.

The variations of characteristic scale length of friction evolution affect earthquake dynamics

Within a fault governing model the characteristic scale length is one of the most relevant physical parameters because it accounts for the so–called fracture energy (density) of the system, its dynamics, the time during which the accumulated stress is released and the seismic waves are excited, the amount of slip developed during an instability event. Friction laboratory experiments reveal that it is not a material property, but that it changes with the sliding velocity. We propose two rather different analytical models to fit laboratory evidence and we incorporate them into a fault model able to simulate repeated earthquakes in the framework of various formulations of rate and state friction. We demonstrate that temporal variations of the scale length do not prevent the system to reach its limit cycle, but they systematically reduce the magnitude of the expected event (both in term of developed slip, and thus seismic moment, and released stress) and also reduce the inter–event time (recurrence interval). Depending on the friction model, the system can penetrate into the stable regime and can either continue the accelerating phase toward to failure or decelerate and abort instability.

Dynamic measurement of amnion thickness during loading by speckle pattern interferometry

IntroductionIn previous studies on the mechanical parameters of amnions (AM), there is a limitation due to the lack of an accurate thickness measurement, which is an important parameter for determining AM-specific mechanical properties. As a bottleneck, the characterization of the basic mechanical properties of AM are greatly restricted, even with the proposal of fracture criteria. MethodFirst, the initial thickness of the AM is estimated by the interpolated-volume-area method. Second, through combinations of our self-developed mini-biaxial tensile device with speckle pattern interferometry, this is the first time that researchers can accurately obtain the AM thickness at each transient moment in the process of loading. ResultsBased on the experimental results, an accurate stress-strain curve could be obtained. Two important mechanical parameters—the fracture energy density and amnion rupture modulus—could be extracted as 0.184±0.036MPa and 108.57±17.32MPa, respectively. The fracture energy density and amnion rupture modulus provide objective criteria and a scientific basis for the evaluation of AM rupture. DiscussionThe tensile stress-strain curve of a normal human amnion shows a distinct J-shape. This proves that the experimental results are basically reliable. Both important parameters ——the fracture energy density and amnion rupture modulus, can be calculated from the stress-strain curve. Extracting these two parameters is critical for the evaluation and prediction of ROM, PROM and PPROM.

The effect of constraint on fracture properties of Z3CN20.09M after accelerated thermal aging

The main coolant piping material Z3CN20.09 M was heat treated at 400 °C for 18,000 h and then the fracture behavior has been studied. To understand the effect of in-plane constraint on fracture behavior, J-R curves were determined by the pre-cracked specimens with a wide range of crack depth ratios. And the stretch zone width (SZW) values were measured by experimental method and finite element method (FEM) based on fracture energy density. The comparisons of SZW value show that good agreements have been achieved among experimental tests and FEM. Moreover, to reveal and quantify the constraint effect (a/W), three-dimensional FEM was used to obtain the second terms in the Williams’ series expansion. The J-R curves, JIC and JSZW and SZW are higher at lower crack depth ratios a/W, and gradually decrease with increasing crack depth. Then, the constraint dependent fracture properties of Z3CN20.09 M were determined and could be used to predict fracture properties under other constraint conditions.

Simulation of the thermal shock cracking behaviors of ceramics under water quenching for 3-dimension conditions

To overcome the limitations of widely used criteria, maximum principal stress and maximum tension stress, in simulating and evaluating thermal shock resistance of ceramics for 3-dimension (3D) problems, a temperature-dependent critical fracture energy density criterion was proposed based on the force-heat equivalence energy density principle for the 3D thermal shock fracture problems of ceramic materials in this paper. Taking advantage of the criterion and finite element method, the thermal shock behavior of water quenching of cuboid Al2O3 specimens with different temperature differences were simulated. The crack patterns of the simulation results were shown to be approximated in the experiments. Especially the essential features, the longitudinal main crack and crack branches, are embodied well in the simulation results. However, the thermal shock cracks obtained by using the criteria, maximum principal stress and maximum tension stress, failed to meet the experiments. The effects of water entry posture on thermal shock crack features revealed in the results confirm the efficiency of the criterion in 3D conditions of thermal shock fracture in this paper. Finally, the maximum temperature gradient, not maximum temperature difference, was found to be the main controlling factor which caused the fracture energy density to reach a critical value to produce thermal shock crack.

Optimal Regularity and Structure of the Free Boundary for Minimizers in Cohesive Zone Models

We study optimal regularity and free boundary for minimizers of an energy functional arising in cohesive zone models for fracture mechanics. Under smoothness assumptions on the boundary conditions and on the fracture energy density, we show that minimizers are C^{1, 1/2}, and that near non-degenerate points the fracture set is C^{1, alpha }, for some alpha in (0, 1).

Frequency domain analysis of mechanical properties and failure modes of PVDF at high strain rate

Fast Fourier transform (FFT) theory is used to analyze the tensile stress-strain curves of coated fabric membrane materials (PVDF) at high strain rates (350/s, 500/s, 750/s, 900/s and 950/s). The transformation results are extended to characterize the failure and dynamic response of Ferrari 1002S2 in frequency domain. Firstly, the dynamic mechanical properties of the materials are analyzed, which include stress-strain relationship curve, ultimate tensile strength, fracture elongation and fracture energy density. Then, the stress-time, strain-time and voltage-time signals are converted in frequency domain, and the dynamic mechanical properties of materials are analyzed from the point of view of frequency domain. Finally, according to the power-frequency curve obtained from the voltage-time signal, the corresponding relationship between the failure mode and the frequency domain is proposed. Besides, the typical power-frequency curve corresponding to each failure mode is analyzed by combining with the failure mode of the specimens. The results show that the dynamic mechanical properties of Ferrari 1002S2 materials are analyzed well from the point of view of frequency domain. The failure mode is directly related to the frequency domain distribution.

Effect of Reclaimed Asphalt Pavement and Recycled Asphalt Shingles on Fracture Tolerance of Asphalt Binders

Abstract Fracture energy density (FED), which is defined as the energy per unit volume required to initiate fracture, is a key property governing the resistance to fracture of asphalt binders. This study evaluated the effect of reclaimed asphalt pavement (RAP) and recycled asphalt shingles (RAS) on virgin binder FED using the binder fracture energy (BFE) test. The objective was to determine whether RAP and RAS can be used with soft virgin binders to achieve satisfactory fracture tolerance. Experimental factors included two RAP sources, two RAS sources (manufacture waste (MW) shingles and tear-off (TO) shingles), and four virgin binders. BFE tests were conducted on blends of virgin and recovered RAP/RAS binders at two binder replacement rates of 15 % and 30 %. Moreover, the Superpave true grade of RAP/RAS binder blends was determined using the dynamic shear rheometer and bending beam rheometer. Results showed that the use of soft virgin binders effectively compensated for the stiffening effect of RAP/RAS in terms of true grade. The addition of RAP binder and MW shingle binder increased the FED of unmodified binders, whereas the opposite trend was observed for TO shingle binder. Furthermore, great caution should be exercised when using virgin polymer-modified binders because significant reductions in FED were observed when RAP and RAS binder was introduced, possibly because of the dilution of polymer modification in addition to stiffening and embrittlement effects. This study indicated that both RAP and RAS are recyclable, according to the Superpave true grade requirements. However, further research is needed to evaluate the effect of the reduction in binder FED caused by TO shingles on mixture fracture performance before its acceptance in asphalt mixtures.

Fracture behavior of random distributed short tungsten fiber-reinforced tungsten composites

In future fusion reactors, tungsten is considered as the main candidate material for plasma-facing components. However, the intrinsic brittleness of tungsten is of great concern during operation. To overcome this drawback, tungsten fiber-reinforced tungsten composites (Wf/W) are being developed relying on extrinsic toughening principles. Tungsten (W) fibers with extremely high tensile strength and ductility are used to reinforce a tungsten matrix.In this work, field assisted sintering technology (FAST) is used to produce Wf/W material. Mechanical characterizations including Charpy impact and 3-point bending tests are performed. Based on the 3-point bending test results, the Wf/W materials can facilitate a promising pseudo-ductile behavior even at room temperature, similar to fiber reinforced ceramic composites. Fracture energy density and fracture toughness together with the crack-resistance curves (R-curves) are measured. Compared to conventional pure tungsten, Wf/W shows significant improvement in fracture toughness.

Highly compressive and stretchable poly(ethylene glycol) based hydrogels synthesised using pH-responsive nanogels without free-radical chemistry.

Poly(ethylene glycol) (PEG) based hydrogels are amongst the most studied synthetic hydrogels. However, reports on PEG-based hydrogels with high mechanical strength are limited. Herein, a class of novel, well-defined PEG-based nanocomposite hydrogels with tunable mechanical strength are synthesised via ring-opening reactions of diglycidyl ethers with carboxylate ions. The pH responsive crosslinked polyacid nanogels (NG) in the dispersed phase act as high functionality crosslinkers which covalently bond to the poly(ethylene glycol) diglycidyl ethers (PEGDGE) as the continuous matrix. A series of NG-x-PEG-y-z gels are prepared where x, y and z are concentrations of NGs, PEGDGE and the PEGDGE molecular weight, respectively. The hydrogel compositions and nano-structural homogeneity of the NGs have strong impact on the enhancement of mechanical properties which enables property tuning. Based on this design, a highly compressive PEG-based nanocomposite hydrogel (NG-13-PEG-20-6000) exhibits a compressive stress of 24.2 MPa, compressive fracture strain greater than 98% and a fracture energy density as high as 1.88 MJ m-3. The tensile fracture strain is 230%. This is amongst one of the most compressive PEG-based hydrogels reported to-date. Our chemically crosslinked gels are resilient and show highly recoverable dissipative energy. The cytotoxicity test shows that human nucleus pulposus (NP) cells remained viable after 8 days of culture time. The overall results highlight their potential for applications as replacements for intervertebral discs or articular cartilages.