Fracture Surface Energy Research Articles

Modeling of temperature-dependent first matrix cracking stress in ceramic matrix composites considering fracture surface energy and residual thermal stress

Ceramic matrix composites have shown excellent performance in fields such as hypersonic vehicles, and their matrix cracking stress is an important criterion for determining whether damage has occurred in composites, but obtaining the first matrix cracking stress at elevated temperatures is very difficult. In this study, a temperature-dependent theoretical model of first matrix cracking stress considering fracture surface energy and residual thermal stress for ceramic matrix composites was developed based on the Force-Heat Equivalence Energy Density Principle. The model successfully captures the quantitative relationship between the first matrix cracking stress and parameters such as temperature and Young's modulus. Without the need to carry out any high-temperature destructive experiments, the developed model can easily predict the temperature-dependent first matrix cracking stresses of the material. The validation shows that the model predictions achieve good agreement with the experimental data at different temperatures (from 293K to 1673K), and the predictions of the developed model have higher accuracy compared to the two commonly used theoretical models. In addition, the effect of fracture surface energy on matrix cracking stress at different temperatures was quantitatively analyzed. The research results provide a non-destructive method for obtaining the first matrix cracking stress of materials at elevated temperatures.

Fracture behavior of brittle particulate composites consisting of a glass matrix and glass or ceramic particles with elastic property mismatch

The aim of this work is two-fold: i) elaborating dense and transparent inorganic glass composites with improved fracture properties, and ii) testing the theoretical analysis proposed in [1] and based on Poisson's ratio mismatch. Particulate composites, consisting of glass or ceramic particles embedded in a soda-lime-silica glass matrix, were synthesized and their fracture behavior was studied by means of the Single Edge Precraked Beam (SEPB) and Double Cantilever Drilled (DCDC) methods, using in situ experiments with X-ray tomography where possible. An important effect of the T-stress on the fracture toughness (KIc) was observed in the case of DCDC exdperiments. KIc is increased by about 40 % by incorporating 7 vol. % amorphous silica beads or SrAl2O4:Eu,Dy ceramic particles (SAED) with a 40 μm mean particle size. It is suggested that toughening results from the crack front trapping and pinning at particle sites and from the tortuous crack path in the case of a-SiO2 particles, and from the contribution of the intrinsic fracture surface energy of the ceramic particles, which are cleaved by the propagating crack, in the case of the SAED particles. The thermally induced stress field is believed to play a major role in the case of a-SiO2 particles. Two glass grades possessing Young's moduli similar to the one of the matrix but much larger Poisson's ratios were used to produce glass beads. However, the incorporation of these latter beads in the matrix was found to have a minor incidence on the fracture behavior.

Mechanical and Thermal Behavior of Semiconducting Cadmium Oxide at High-Pressure

Abstract The effect of high pressures on the mechanical and thermal properties up to phase transition pressure for cubic rock-salt cadmium oxide (CdO) semiconducting compound is presented in this research. The calculations are based on the equation of state (EOS) parameters measured at ambient conditions reported in the literature. The approach used here was previously applied successfully for other materials. Our study shows that the parameters reflect the rigidity of the semiconductor and the melting temperature increases with increasing pressure, while some other parameters decrease gradually for our material of interest. A comparative analysis of some quantities for CdO compound under high pressure was done. Similar behaviors were observed in the literature for particular materials with particular structures. Furthermore, we calculated both the fracture toughness and the fracture surface energy, which are at around 1.23 MPa.m1/2 and 5.14 J.m−2, respectively.

Experimental study on rock-breaking characteristics of advanced premixed abrasive water jet

ABSTRACT To investigate the rock-breaking characteristics of the advanced premixed abrasive water jet, experiments of abrasive water jet eroding granite were carried out. The micro-failure morphology of erosion pits was observed and analyzed by CT (Computerized Tomography) and SEM (Scanning Electron Microscope). The results show that the difference in erosion effect caused by different rock breaking pressures is due to the difference in impact kinetic energy. The higher the jet pressure, the higher the impact kinetic energy of abrasive particles, and the erosion effect is enhanced. The difference in erosion effect caused by abrasive types is that the harder abrasives produce greater cutting force on the rock and consume less fracture surface energy. The CT scanning results show that the conical crack at the bottom is caused by the stamping action of abrasive particles and expands rapidly under the action of a water wedge, the action of reflective particles makes the erosion holes appear spindle-shaped. The results of SEM show that the sidewalls of the erosion pit are dominated by the cutting and fatigue-crushing effects of reflected abrasives. The bottom of the erosion pit is mainly driven by the punching action of the incident abrasive.

Some strange things about the mechanical properties of glass

Glasses and crystals from the same chemical system mostly share the same interatomic bond strength. Nevertheless, they differ by the arrangement of bonds in space, which gives birth to different atomic packing efficiencies. We show in this review that as far as the elastic moduli and hardness are concerned, the atomic packing density predominates over the bond strength. The shear modulus of crystalline phases is usually much larger than the one of glasses with the same stoichiometric composition, thanks to a more efficient packing of atoms in the former. In contrast, the increase in hardness is quite limited, likely because of the additional contribution of dislocation activity to the deformation processes beneath the indenter in the case of crystals (shear plasticity). We also show that the occurrence of chemical heterogeneities (weak channels) at the mesoscopic scale in glasses, which is often associated with the lack of long range atomic ordering, promotes easy fracture paths and is responsible for the low toughness and fracture surface energy.

A 3D multi-phase-field model for orientation-dependent complex crack interaction in fiber-reinforced composite laminates

We formulate a 3D multi-phase field model to simulate bulk and interfacial fracture in fiber-reinforced composites. The purpose of this study is to predict the complex crack interaction between the interlaminar and intralaminar fracture in FRPCs. For that, the discrete crack and the sharp interface are both smeared using the phase-field approach. A second-order anisotropic tensor is incorporated in the elastic as well as the fracture surface energy to promote direction-dependent crack growth. The interface constitutive behavior is represented by the uncoupled 3D traction–separation laws—in exponential and bi-linear form. The proposed model captures the complicated failure phenomena in FRPCs such as matrix damage, interfacial delamination, and their interactions for different configurations of lamina with different fiber orientations and fracture energies. This model’s capability is further illustrated to study the three common modes of fracture i.e. modes I, II, and III, in 3D FRPC laminates where the crack impinges on the interface. Finally, the obtained framework is validated by two benchmark problems including the mode I and mode II delamination test, and is compared against experimental data reported in the literature.

Characterization and Simulation of the Interface between a Continuous and Discontinuous Carbon Fiber Reinforced Thermoplastic by Using the Climbing Drum Peel Test Considering Humidity.

The objective of this paper is to investigate the debonding behavior of the interface between continuously and discontinuously fiber reinforced thermoplastics using the climbing drum peel test. The study emphasizes on the importance of considering different climatic boundary conditions on the properties of thermoplastics. Specimens with varying moisture contents, from 0m.% up to above 6m.% are prepared and tested. It is observed that an increase in moisture content from 0m.% to 2m.% results in an increase of the fracture surface energy from 1.07·103J/m2 to 2.40·103J/m2 required to separate the two materials, but a further increase in moisture to 6.35m.% conversely results in a subsequent decrease of the required energy to 1.91·103J/m2. The study presents an explanatory model of increasing plasticization of the polymer due to increased polymer chain mobility, which results in more deformation energy being required to propagate the crack, which is corroborated in SEM investigations of the fracture surface. A further increase in humidity leads to polymer degradation due to hydrolysis, which explains the subsequent reduction of the fracture energy. The experimental set up is modeled numerically for the first time with cohesive surfaces, which could successfully reproduce the effective force-displacement curve in the experiment by varying the interface parameters in the model over an influence length, allowing the conclusion of a process induced variation in the interface properties over a specific consolidation length.

Size effects on the fracture behavior of amorphous silica from molecular dynamics simulations

In this work, the role of structure size and interaction potential on the ductility and mechanical properties of bulk glasses are extensively analyzed using molecular dynamics (MD) simulations. Elastic moduli and mechanical properties for bulk silica structures were calculated from the MD trajectories using three different force fields - diffusive charge reactive potential (DCRP), Teter and Vashishta potentials. These results from MD simulations were compared to experimental measurements and the overall results reassert that, while the elastic moduli show a neglectable variation with structure size, the fracture behavior is considerably affected. Specifically, it is found that the length along the deformation axis is the driver for the brittle to ductile transition. The fracture results, combined with an energy analysis, reveal that the energetic condition for brittle fracture, where elastic strain energy should overcome the fracture surface energy, remains valid for the three potentials.

Micro‐scale mechanical properties of surface layer in ion‐exchanged glass

AbstractToday, ion‐exchanged or chemically strengthened glass is ubiquitously used all over the world, typically for scratch‐free display cover of personal mobile phones. It has been known that the strengthening is due to developments of high compressive stress in the surface layer by its internally constrained dilation . We investigated micro‐scale mechanical properties of the surface layer itself of a Na+‐to‐K+ ion‐exchanged soda lime silicate glass, revealing that the strength of the layer increased nearly 40% by the ion‐exchange with little compression effect from the interior. The fracture toughness, however, was comparable before and after the ion‐exchange, indicating that the ion‐exchange reduces the crack size of the fracture origin. Theoretical estimates of fracture surface energies verified the measured fracture toughness. It was presumed that the observed crack‐size reduction is due to crack healing effects enhanced by the ion‐exchange.

Barrier-Induced Rupture Front Disturbances during the 2023 Morocco Earthquake

Abstract Seismic waveforms, including teleseismic body waves, contain information about the irregular behavior of rupture propagation, which is essential for understanding the evolution process of large earthquakes. Here, a high-degree-of-freedom source inversion is applied to the teleseismic P waves of the 2023 moment magnitude 6.8 Morocco earthquake to reveal the irregular rupture behavior during earthquake growth. The resulting total moment tensor solution is an oblique focal mechanism that exhibits reverse faulting with a strike-slip component. There are two distinct peaks at 2 and 4 s in the moment rate function. The reverse fault component dominates at the beginning of the rupture, but then the strike-slip component increases to the second peak and then decreases. The main rupture propagates first in an east-northeast direction, then both up- and down-dip. The down-dip propagating rupture diminishes shortly, whereas the up-dip propagating rupture becomes dominant. The main rupture propagating in the up-dip direction is temporarily suppressed around a point located at 19 km depth and 10 km east-northeast of the hypocenter (region B). After the rupture propagates surrounding region B, the rupture propagates into region B, where a relatively fast slip rate is observed. It is confirmed that the irregular rupture propagation associated with region B is reproduced even when the model settings and the data sampling interval are slightly changed. The irregular rupture propagation obtained in this study suggests that a barrier with high apparent strength (e.g., high fracture surface energy) can cause the rupture to be initially suppressed within the barrier region, followed by delayed rupture propagation through the apparent barrier. The high-frequency seismic motions caused by such an irregular rupture propagation may have contributed to the increase in earthquake-related damage.

Theoretical characterization of the temperature‐dependent mode I fracture toughness of rocks

AbstractMode I fracture toughness, as a key index to reflect rocks' resistance to crack propagation and failure, which is significantly affected by temperature, plays an important role in accident prevention in underground engineering. In this work, a temperature‐damage‐dependent fracture surface energy model of rocks was developed first. Then, the theoretical characterization model of the temperature‐dependent mode I fracture toughness of rocks was proposed according to the relationship between the fracture surface energy and fracture toughness. All obtained experimental results are used for verification, and the predicted values are in good agreement with the experimental results. The temperature‐dependent mode I fracture toughness model of rocks established in this study not only provides a new method to predict the fracture toughness of rocks at different temperatures conveniently but also provides the theoretical basis to the research on stability analysis, monitoring, warning, and disaster control of underground rock engineering.

Characterizing the flexural/damage behavior of Aluminosilicate glass at low/high loading rates: Application of SHPB for mode-1 loading of laminated glass

Understanding the flexural response of monolithic and laminated glass is essential for making informed choices while selecting glass for varying applications. That is because the behavior of monolithic and laminated glass may not necessarily be the same under certain loading conditions and assessing their performance differences helps in determining their suitability for specific applications. The presented work is aimed at quantifying the flexural/damage behavior of monolithic and laminated glass. Quasi-static and dynamic flexural tests were conducted on monolithic and laminated glass in mode-1 loading while maintaining identical loading and support interfaces. In the first phase, quasi-static flexural tests were performed, and results were quantitatively compared by two approaches: Effective Thickness Approximation (ETA) and the theory of Thick Sandwiched Beams (TSB). Experimentally observed deflection corroborated with both the analytical methods; the absolute error remained less than 2.5% and 0.5% for ETA and TSB, respectively. Importantly, failure of the laminate was witnessed at approximately 50% lower force compared to its monolithic counterpart, which was attributed to the span length of the specimen and the interlayer’s shear stiffness. Fractography was performed to elicit Aluminosilicate glass’s mirror constant and fracture surface energy, as 1.86 MN/m3/2 and 3.95 J/m2, respectively. In Phase-2, Dynamic flexural tests were conducted on a novel Electromagnetic Split Hopkinson Pressure Bar (ESHPB), and an experimental-numerical coupled approach was introduced to analyze the results. The results established that the adverse effects of shorter span length on the flexural strength of laminated glass are mitigated, primarily due to the viscoelastic response of the interlayer. The reprographic images attributed the fracture of monolithic and laminated glass specimens solely to the bending-induced stresses.

Silicate glass fracture surface energy calculated from crystal structure and bond-energy data

We present a novel method to predict the fracture surface energy, γ, of isochemically crystallizing silicate glasses using readily available crystallographic structure data of their crystalline counterpart and tabled diatomic chemical bond energies, D0. The method assumes that γ equals the fracture surface energy of the most likely cleavage plane of the crystal. Calculated values were in excellent agreement with those calculated from glass density, network connectivity and D0 data in earlier work. This finding demonstrates a remarkable equivalence between crystal cleavage planes and glass fracture surfaces.

The effect of bedding planes on the bending strength of rock-like material and evaluation of the crack propagation mechanism

Bedding planes affects various material properties, including the bending strength and the crack propagation mechanism of rocks. In this paper, laboratory studies on rock-like material specimens were conducted to investigate the effect of bedding planes on the failure and crack propagation mechanism and to reduce the effect of secondary factors on the results. To this end, semi-circular bend (SCB) specimens were prepared with two concrete mixing designs using aggregate and geopolymer concretes as materials. Next, they were subjected to compressive and three-point bending tests. The crack propagation mechanism, changes in the bending strength, maximum fracture load, relative midspan displacement, fracture energy, and fracture toughness were analyzed for the anisotropic and isotropic specimens. Also, different bedding angles were examined for the anisotropic specimens. The results revealed that bedding planes generally affected the crack propagation mechanism and changed the fracture mode from pure opening mode for the isotropic specimens to mixed modes for different bedding angles. Hence, the strength and fracture parameters were generally smaller in the anisotropic specimens than in the isotropic ones. With an increase in the bedding angle in the specimens, the maximum fracture load and the fracture surface energy increased, and the midspan displacement behaved differently. Moreover, the fracture toughness displayed an increasing trend with increasing the bedding angle in the anisotropic specimens. The rate of changes in the parameters were different for different bedding angles. This may be attributed to the changes in the stress distribution and to the fracture and crack propagation modes in the anisotropic specimens compared to the isotropic ones.

Mechano-electrochemical modeling of lithium dendrite penetration in a solid-state electrolyte: Mechanism and suppression

The mechanism of lithium dendrite penetration in solid-state electrolyte (SE) and its suppression strategies are studied based on a new phase field (PF) model involving fracture mechanics, electrodeposition processes, and mechano-electrochemical coupling (MEC) effects. Numerical results reveal the high stress-intensity factor is caused by high hydrostatic pressure in lithium, and the high stiffness of SE does not inhibit dendrite penetration. It is because the increase in Young's module of SE, ESE, makes the stress-intensity factor even more significant. That is why a stiff SE is “pierced” by the much softer lithium dendrites. Considering MEC, the increase in ESE has a competing effect on dendrite penetration causing a nonmonotonic change in dendrite length, which provides a window to mitigate dendrite penetration. Dendrite suppression by toughening SE is quantitatively evaluated. A critical fracture surface energy density of SE (γ = 3.5 J m−2) is determined. When γ > 3.5 J m−2, facture toughness becomes larger than stress-intensity factor and dendrite penetration is suppressed with ESE. However, toughening is difficult. Engineering compressive traction, Fa, in SE surfaces is a more realistic strategy, that cause a significantly inhibition in dendrite penetration with Fa from 0 to 100 MPa.

Structural, mechanical and thermal properties of cubic bixbyite-structured high-entropy oxides

Cubic bixbyite-structured high-entropy oxides (HEOs) are regarded as potential candidates in high temperature thermal insulation field in recent years. However, their relevant properties are still needed to be explored for possible applications. In this work, twelve new high-entropy oxides (HEO1-12) of (5Re0.2)2O3 (Re represents five elements selected from Ce, Nd, Sm, Eu, Gd, Dy, Ho, Er, Tm, Yb) are prepared by solution combustion synthesis method combined with conventional sintering. Except HEO10 with a single monoclinic phase, other samples have a single bixbyite phase. The average grain size of bixbyite-structured samples is within 0.76 ∼ 4.96 μm. Then, the samples of HEO4, 5, 7–9 are chosen to study their mechanical and thermal properties. Their nano-modulus, nano-hardness, fracture toughness KIC, brittleness M and surface fracture energy are in the range of 152.42 ∼ 237.33 GPa, 9.22 ∼ 12.65 GPa, 1.77 ∼ 2.51 MPa·m1/2, 2.35 ∼ 3.09 μm−1/2 and 9.00 ∼ 22.49 J m−2, respectively. HEO4, i.e., (Ce0.2Nd0.2Sm0.2Dy0.2Gd0.2)2O3, exhibits higher KIC (1.92 MPa·m1/2) and lower M (2.71 μm−1/2) than another reported cubic bixbyite-structured HEO of (Eu0.2Er0.2Lu0.2Y0.2Yb0.2)2O3. Among the five samples, HEO4 has the lowest thermal conductivity κ (1.88 ∼ 2.55 W·m−1·K−1 in 25 ∼ 500 °C), which is much lower than bixbyite-structured Y2O3. In addition, HEO4 possesses a lower oxygen diffusion compared with 8YSZ in 600 ∼ 700 °C, which endows it the better oxygen barrier property. To sum up, HEO4 could be a promising candidate for high temperature thermal insulation applications due to its excellent comprehensive properties.

Preparation and properties of porous MgO based ceramics from magnesite tailings and fused magnesia

Porous MgO based ceramics have been widely used in some key industries due to their excellent performance. To investigate the feasibility of preparing porous magnesia ceramics using magnesite tailings as a magnesium source. Porous MgO based ceramics were prepared using magnesite tailings, fused magnesia as main raw materials and soluble starch as pore-forming agent. The starting materials were mixed in different ratios and sintered at 1500 °C for 2 h to obtain good mechanical and thermophysical properties. The Mg2SiO4 plays a fixing role, inhibiting the growth of MgO grains and further promoting the discharge of pores. This fixation can prevent the linear expansion of cracks, thus increasing the fracture surface energy of the specimen. In addition, the scattering effect of pores on gas molecules decreases as the magnesite tailings content increase, so that the thermal conductivity increases. The results showed that when the mass ratio of magnesite tailings to fused magnesia was increased from 1:1 to 1:0 with 4 wt% soluble starch as the pore-forming agent, the apparent porosity decreased from 35.59% to 11.8%; the bulk density increased from 2.37 to 2.82 g∙cm−3; the linear shrinkage ratio increased from 9.28 to 24.23%; the cold compressive strength increased from 47.75 to 226.52 MPa; the residual strength retention rate after one thermal shock cycles at 1100 °C was between 64.05 and 87.76%; and the thermal conductivity increased from 7.44 to 12.23 W∙m−1 K−1.

Numerical Simulation for Hydrogen-Assisted Cracking: An Explicit Phase-Field Formulation

Hydrogen-assisted cracking is one of the most dominant failure modes in metal hydrogen-facing materials. Therefore, the hydrogen-assisted cracking mechanism has been a hot topic for a long time. To date, there is very little published research on numerical methods to describe hydrogen-assisted cracking. This paper presents a new method for the description of hydrogen embrittlement crack growth: an explicit phase-field formulation, which is based on the phase-field description of cracks, Fick's mass diffusion law, and the relationship between hydrogen content and fracture surface energy. A novel computational framework is then developed using the self-developed FEM software DYNA-WD. We numerically calculate several typical conditions in the 3-D coordinates to validate the effectiveness of the proposed computational framework. Specifically, we discuss (i) the failure of a square plate in a hydrogenous environment, (ii) the CT specimen failed with the inner hydrogen, (iii) the plate/failed with the corrosives, and (iv) the failure of the disk test. Finally, the relationship between Mises stress, the concentration of hydrogen, the thickness of the disc, and the loading rate is investigated.

Irregular rupture process of the 2022 Taitung, Taiwan, earthquake sequence

In September 2022, two destructive earthquakes of moment magnitude (Mw) 6.6 (foreshock) and 7.1 (mainshock) occurred in Taitung County, south-eastern Taiwan. To understand their complex rupture processes, we analysed these earthquakes using the Potency Density Tensor Inversion method, which can stably estimate the rupture propagation process, including fault geometry, without overfitting the data. The analyses revealed that the major rupture of the foreshock propagated towards shallow depth, in a south–southwest direction, following an initial rupture that propagated towards the deeper part of the fault. The mainshock, with its epicentre on the north–northeast side of that of the foreshock, consists of two distinct episodes. During the first episode (0–10 s), the initial rupture propagated north–northeast, through a deep path, followed by the main rupture that propagated bilaterally in a north–northeast and south–southwest direction. The second rupture episode (10–16 s) started near the hypocentre of the mainshock, and the rupture propagated towards the shallow side of the fault. The results suggest that the stress concentration from both the foreshock and mainshock’s first rupture episode may have caused the second rupture episode in the high fracture surface energy area between the foreshock and the first rupture episode of the mainshock. The irregular rupture process of the foreshock and mainshock may reflect the heterogeneity of stress and structure in the source region.

Brittle–ductile transition and toughening of silica glass via Ni nanoparticle incorporation at a small volume fraction

The brittleness of glass significantly limits its application, and an effective solution is to impart ductility to it. In this study, Ni nanoparticles of different sizes were dispersed in SiO2 glass to investigate the effect of the particle size on the ductility of glass. Ni nanoparticles (0.5 vol. %) of two sizes (average particle sizes: 119 and 30 nm) were precipitated in the SiO2 glass by sintering on Ni nanoparticle-dispersed SiO2 glass powder. The fracture toughness obtained by microcantilever beam tests was significantly enhanced from 0.71 MPam1/2 for unmodified glass to 1.02 and 2.03 MPa m1/2, respectively, for the glass samples incorporated with small (30 nm) and larger Ni nanoparticles (119 nm). The fracture surface energy increased significantly with the dispersion of the Ni nanoparticles in the glass matrix, despite their small volume fraction (0.5 vol. %). Moreover, a cup–cone structure indicative of ductile fracture was formed in the glass containing large Ni nanoparticles, whereas the glass dispersed with smaller Ni nanoparticles exhibited brittle fracture. These results indicate large stress dissipation in the former owing to its ductility. A theoretical approach based on the generation and movement of dislocations was employed to rationalize the particle-size-dependent fracture characteristics of the metal-particle-incorporated glass. Thus, we developed a cost-effective method to significantly enhance the fracture toughness of glass by imparting ductility via the dispersion of a small amount of metallic nanoparticles.