Static Fracture Research Articles

Fatigue behavior and reliability of pressed lithium disilicate ceramics compared to 5Y-TZP zirconia under different loading protocols

ObjectiveTo compare the fatigue behavior and reliability of 5 pressed lithium disilicate ceramics and a 5 mol% yttria-stabilized zirconia (5Y-TZP) when 3 dynamic loading protocols were used. MethodsBar-shaped specimens (30 × 4 × 3 mm) were fabricated from 5 pressed lithium disilicate ceramics (AMB, CEL, INI, IPS, and LIV) and a 5Y-TZP (ZR) (N = 324). Six specimens from each material were subjected to a static 4-point fracture load test, while the remaining specimens were subjected dynamic loading by increasing the starting load (30 % of the static fracture load) in every 5000 cycles by 50 N (loading protocol 1), in every 5000 cycles by 5 % (loading protocol 2) or in every 1000 cycles by 10 N (loading protocol 3) until fracture (n = 16). The fracture load, flexural strength, and number of cycles until failure were analyzed with 2-way analysis of variance and Scheffé tests. The survival rate was evaluated with Kaplan-Meier analysis and further compared with Mantel-Cox test, while the correlation between the fracture load and flexural strength was analyzed with Pearson’s correlation test (α = 0.05). Fractographic analysis was also performed. ResultsThe interaction between the materials and the loading protocol affected the number of cycles until failure, while the material type affected fracture load and flexural strength values (P < 0.001). ZR had the highest and LIV mostly had lower fracture load and flexural strength (P ≤ 0.034). A positive correlation was found between the fracture load and flexural strength (r = 0.997, P < 0.001). For lithium disilicate ceramics, loading protocol 2 and for ZR, loading protocols 1 and 3 led to the highest number of cycles and survival rate (P ≤ 0.041). Regardless of the loading protocol, all lithium disilicate ceramics had a similar fragmentation pattern with single compression curls and 2-piece fractures were observed. SignificanceTested materials are suitable for adhesively luted monolithic single-unit prosthesis as they had mean flexural strength values higher than 100 MPa. Measuring the fracture load with loading protocol 3 can be considered time-efficient to evaluate the fatigue behavior of pressed lithium disilicate ceramics.

Effects of micron-sized Si particles on the static and dynamic mechanical properties and fracture behavior of Al-xSi alloy sheets

In this paper, a comprehensive analysis was conducted on the effects of micron-sized Si particles on the microstructure, static and dynamic mechanical properties, and fracture behavior of wrought Al-xSi alloy sheets. The investigation employed techniques such as optical microscope, scanning electron microscope, laser scanning confocal microscope, transmission electron microscope, tensile testing and fatigue testing. The results show that when the Si content is below 12 wt%, the size of the Si particles in the alloy sheets does not exceed 3 μm, and their quantity gradually increases with higher Si content. As the Si content increases, the grain size of the alloy sheets is refined from 63 μm to 8 μm. The alloy strength initially increases and then slightly decreases with further Si addition. while elongation exhibits a general downward trend. The tensile fracture modes of Al-(1–12 wt%) Si alloy sheets are all ductile fractures. The fatigue life of Al-xSi alloy sheets first extends and then shortens as the Si content increases. With the increase of Si content, the yield strength of the alloy sheets gradually increases from 47.6 MPa to 85.7 MPa. When the Si content is 12 wt%, the tensile strength reaches the maximum value of 185.4 MPa. With the increase of Si content, the elongation of the alloy sheet first increases slightly, reaching 35.0 %, when the Si content increases to 15 wt%, the elongation gradually decreases to 17.5 %. As the Si content increases, the fatigue life of the alloy sheets gradually extends. When the Si content reaches 12 wt%, the alloy sheet achieves its maximum fatigue life, reaching 9.97 × 105–1.97 × 10⁶ cycles, approximately 11–14 times longer than that of the Al-1 wt% Si alloy sheet. However, with a further increase in Si content to 15 wt%, the fatigue life significantly decreases to 4.08 × 10⁵–4.70 × 10⁵ cycles, shortening by approximately 59–76 %. The fatigue crack source of Al-xSi alloy sheets gradually changes from the persistent slip bands on the surface of the sheet to the large-sized Si particles on the surface of the sheet. The functional relationship between the fatigue life of Al-xSi alloy sheets as the Si content changes is established, and the fatigue life influencing factor ISi is introduced to quantitatively describe the influence of the number of micron-sized eutectic Si particles on the fatigue life or fatigue properties of the alloy sheets. This study provides important scientific insights for optimizing alloy property and meeting diverse industrial demands, thereby promoting the application and development of wrought Al-Si alloy in broader fields.

Does selective root canal retreatment preserve the tooth’s fracture resistance? An ex-vivo study

ObjectivesTo assess the tooth’s fracture resistance when submitted to a selective root canal retreatment compared to the conventional approach.Methods33 intact permanent mandibular first molars were selected according to specific criteria. After teeth mounting, the primary root canal treatment was conducted and followed by thermo-mechanical aging procedures to mimic a few clinical conditions. The specimens were randomly divided into three groups (n = 11); a control group in which intact teeth were used and two experimental groups according to the retreatment approach: conventional non-surgical retreatment (Conventional-NSR), and selective non-surgical retreatment (Selective-NSR). Later, the teeth were submitted to a final thermo-mechanical aging procedure and tested regarding their fracture resistance (static fracture test). The maximum load to fracture was recorded as were the types of failure modes (repairable or non-repairable fracture). A proper statistical analysis was conducted, considering a significance level of 5%.ResultsThe Conventional-NSR group showed a mean failure load of 867.7 ± 108.9 N while the Selective-NSR group had 1106.8 ± 159.8 N (P = 0.012). Both retreatment groups showed significantly lower results when compared to the control group. Additionally, the Conventional-NSR group showed higher proportions of non-repairable fractures (54.5%) when compared to both the Selective-NSR (36.4%) and control (18.2%) groups.ConclusionsSelective root canal retreatment preserved the tooth’s fracture resistance compared to the conventional retreatment approach.Clinical trial numberNon-applicable. Conducting the current experiment was limited to obtaining approval from the local Research Ethics Committee at the Faculty of Dentistry, Minia University (Committee No. 105, Registration No. 902, Date: 26/3/2024).

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.

Characterization and differences of acoustic signals response of semi-circular red sandstone under combined monotonous and cyclic loadings

After underground coal mining, rocks are often subjected to tensile damage by the interaction of dynamic and static loadings. The process of rock fracture development under dynamic and static loadings will be released in the form of acoustic energy to form an acoustic signal. In addition, the acoustic signals in dynamic loading differ from that in static loading. Therefore, this study conducted three-point bending experiments with continuous dynamic loading and dynamic–static coupling loading on semi-circular red sandstone specimens. The acoustic signals during red sandstone specimens’ tensile damage were monitored in real-time. The results show that red sandstone’s tensile strength and deformation are enhanced under dynamic–static coupling loading. The red sandstone has a more effective acoustic emission hit rate, energy rate, and r during tensile damage under continuous dynamic loading. In dynamic loading, macroscopic fractures are developed in red sandstone, which has few acoustic emission events but releases strong acoustic signals. In static loading, the pores inside the red sandstone are compacted, the rock particles are rearranged, and the tiny fractures are closed, and its acoustic emission events are many but low in energy. In addition, the rock particles in the front area of the static loading fracture are tightly cemented, which increases the difficulty of separating the rock particles in the front area of the fracture under dynamic loading. Then weakening the red sandstone fracture development process and suppressing its acoustic signals. The research results provide more insight into the differences in tensile damage processes in red sandstone under the interaction of dynamic and static loadings.

Comparative analysis of mechanical properties and fracture characteristics between sodium silicate modified polyurethane and polyurethane materials

Sodium silicate modified polyurethane (SS/PU) and polyurethane (PU) have become the most widely used grouting materials at present, but their differences in mechanical properties and fracture characteristics remain unclear. In this study, uniaxial compression, digital image correlation (DIC), split Hopkinson pressure bar (SHPB), and scanning electron microscopy were used to compare the dynamic and static mechanical properties and fracture characteristics of the two materials at different aging times. In terms of static mechanics, the stress-strain curve evolution, compression strength characteristics, and crack evolution fracture of SS/PU and PU were compared and analyzed. In dynamic mechanics, the impact compression stress-strain curve, peak strength, strength evolution characteristics, and micro-damage fracture characteristics of the materials were explored. Based on static compression measurements, both materials belong to viscoelastic bodies, with SS/PU being more rigid and PU being more elastic. SS/PU exhibits higher early strength (6 h, 36.9 MPa), while PU shows higher later strength (36 h, 48.9 MPa). Cracks appear instantaneously before or after the peak strength in both materials, with vertical cleavage fracture predominating. Under dynamic impact compression, both materials exhibit an increase with increasing impact velocity, showing a significant strain rate strengthening effect. At different aging times (6 h, 12 h, 24 h, 36 h), the dynamic compression strength of PU is greater than that of SS/PU. The fracture of SS/PU mainly involved continuous fracture, while the fracture of PU mainly involved polymer tearing. In general, when grouting reinforcement projects require materials with higher early strength and better rigidity, SS/PU is more suitable. If the area to be reinforced is in a dynamic impact environment and requires higher final strength, PU is preferable.

Relationship between fatigue crack threshold K max,th and K 1SCC

Abstract This article describes the relationship that relates the static threshold parameter of K 1SCC (at ∼10−10 m/s) to ΔK th and K max,th (at ∼10−10 m/cycle) under fatigue load at high R-ratio like R = 0.85. At these high R-ratios (&gt;0.75), applied K max &gt; K 1SCC and the fracture path has a larger component of static fracture. 5083 Al alloy is adapted as an example to demonstrate this relationship at room temperature their relationship with and without GB-β anodic precipitates in inert and a 3.5 % NaCl solution environments. We are interested in the mechanical cyclic ΔK th and K max,th and quasi-static K ISCC driving forces affecting the damage in the presence of a chemical environment due to anodic dissolution of the GB-β precipitates. Detailed discussions involve how these parameters are interrelated.

Fracture energy of concrete after sustained loading

The fracture energy of concrete after sustained loading is a necessary parameter to calculate the residual carrying capacity of concrete structures in service. This study investigated the fracture energy of concrete after sustained loading by combining experimental observations and theoretical analyses. Firstly, a series of creep fracture tests were conducted on 100 three-point bending beams under various sustained loads, i.e., 75 %, 80 %, 85 %, and 90 % of peak loads. After different loading time, i.e., 10 %, 30 %, 50 %, 70 %, and 90 % of creep fracture lifetimes, the static fracture tests were performed until failure. Then, based on the relationship between the work done by external forces and the energy consumed by the crack propagation of specimens, an analytical model for the fracture energy of concrete after sustained loading was developed, describing the quantitative relationship between the fracture energy of concrete and the crack opening displacement, and the loading time. Finally, the impact of the loading time and sustained load levels on the fracture energy was investigated. The results indicated that the fracture energy of concrete after sustained loading decayed rapidly, with the decay rate gradually decreasing until stability over the loading time. Additionally, specimens subjected to lower sustained load levels experienced a longer loading time for the same crack opening displacement, indicating a greater decay degree of the fracture energy. The analytical model proposed in this study can be employed for predicting and evaluating the crack propagation process and residual carrying capacity of concrete structures during their service life.

Influence of remaining coronal tooth morphology with resin abutment and fiber post on static and dynamic fracture resistances.

This study aimed to clarify the fracture resistance of resin abutments built on endodontically treated roots with the remaining coronal teeth via static and cyclic loading tests. Endodontically treated bovine roots, which had a remaining coronal tooth covered with an occupied area for a quarter and half of the circumference at the tensile side or covered the circumference at both the tensile and compressive sides, were fabricated to build up to the resin abutment. Fracture resistance was evaluated via static and cyclic loading tests by applying a load of 30° to the tooth axis. Half of the circumference of the remaining coronal tooth showed a significantly higher static fracture load and survival rate. The remaining coronal tooth on the compressive side improved the dynamic fracture resistance associated with severe fractures. The occupied area and location of the remaining coronal tooth affected the static and dynamic fracture resistances.

A Two-Phase Flowback Type Curve with Fracture Damage Effects for Hydraulically Fractured Reservoirs

Summary Type curves are a powerful tool in characterizing hydraulic fracture (HF) and reservoir properties based on flowback and production data. We propose a type-curve method to evaluate HF characteristics and their dynamics for multifractured horizontal wells (MFHWs) in hydrocarbon reservoirs using flowback production data. The type curve incorporates the HF damage effect of choked-fracture skin factor in the two-phase flow in HF and matrix domains. The type-curve method can be applied to inversely estimate choked-fracture skin factor, s, HF pore volume (PV), Vfi, and HF initial permeability, kfi, by analyzing two-phase flowback production data. By introducing the new dimensionless parameters, the nonuniqueness problem of the type-curve analysis for two-phase flow is significantly reduced by incorporating the complexity of fracture dynamics into one set of curves. The accuracy of the type curve is examined against the results obtained from numerical simulations of shale gas and oil reservoirs. The validation results demonstrate a good match of analytical type curves and numerical data plots and confirm the accuracy of the proposed method in estimating the static and dynamic fracture properties. The results show that the relative errors in Vfi, kfi, and s estimations are all &amp;lt;10% for the simulated cases that are presented in this work. The flexibility and robustness of the proposed method are illustrated using the field example from a shale oil MFHW. The accuracy and applicability of the proposed type curve are also validated by comparing the calculated fracture properties from the field example using straightline analysis with Vfi and kfi of 705.3 Mcf and 245.2 md, type-curve analysis method (without skin effect) with Vfi and kfi of 751.9 Mcf and 249.8 md, and the type-curve method (with the choked fracture skin considered) with Vfi and kfi of 708.7 Mcf and 252.9 md, which showed that the results of each case are very close to one another. The interpreted results from the flowback analysis of the field example offer quantitative insight into HF properties and dynamics.

Simulation method of asphalt mixture based on fracturable digital aggregate model

This study proposed an approach to construct a fracturable aggregate model to make the fracture patterns consistent with the real situation. Firstly, this study utilized three-dimensional structured light technology to obtain the geometric shell of aggregate and divide them into four categories of spherical, angular, elongated and flaky aggregates according to the minimum bounding box algorithm. Secondly, this study proposed a discrete-spheres filling algorithm based on the Bubble Pack Filling algorithm to fill the shell accurately. Thirdly, this study established the conversion equations between the macro and micro parameters of aggregate by using the linear parallel bonding model, and used it to establish the fracturable aggregate model. Through the indoor and virtual static fracture tests, this study found that the fracture patterns of the fracturable aggregate models are similar to the real situation and characterized the fracture patterns of four types of aggregates. Further analyzing the virtual static fracture tests, this study found that the bearing capacity of aggregates is determined by the compressive strength of host rocks and the shape of aggregate. Through the indoor and virtual uniaxial compression creep tests, this study investigated the behavior of the mixture specimens consisted by the fracturable aggregate model. The stress-strain curves of the fracturable and unfracturable aggregate model in this test were plotted in this study, and the results showed that the relative error between the results obtained by the fracturable model and those of the indoor test is much smaller than that of the unfracturable model. Considering that existing simulation tests on asphalt mixture often ignore aggregate deformation and fracture, so this study used the method mentioned above to obtain the fracturable aggregate model, which can improve the confidence of asphalt mixture simulation results.

Study of physical and mechanical properties of plant fruits on the example of walnut

Perennial plantations that are zoned in Ukraine allow to obtain high-quality fruits (nuts), which are widely used in the perfumery, pharmaceutical, oil, confectionery and other industries, as well as in the production of feed and feed additives. The known technologies of mass processing of walnut kernels mostly work well with crops that have a spherical or close to spherical external shape. The simplest, but least productive, are primitive manual devices for peeling walnut shells. Despite the simplicity of their design, these devices are inefficient and unsuitable for adjusting their operation to different varieties and physical and mechanical properties of biological fruits. The analysis of the known designs of walnut shell destruction machines and mechanisms showed the need to study the physical and mechanical properties of biological fruits (walnuts), to develop technical recommendations for the design of impact mechanisms to improve the quality of shell destruction and the possibility of their application in mass production technologies. A research methodology was developed, a laboratory setup was manufactured, and experiments were conducted. To determine the strength characteristics, the author designed and manufactured a device. It consists of a lever mechanism and a deforming device. The dimensions and load measurements were carried out according to well-known methods of physical mechanics. The statistical analysis of the results showed the need for in-depth scientific research of the geometric parameters of the design of the working bodies of machines for destroying the walnut shell in the mechanisms of fruit peeling machines, taking into account the quality indicators performance of works with certain conditions of their implementation. We conclude that according to the results of the experiments, there is a fairly high dependence between the geometric dimensions of the walnut fruit at the level of 0.72, 0.57 and 0.49, respectively. The weight of the fruit also depends on its dimensional characteristics, which is logical at the level of 0.6–0.75. The force of critical static fracture has a weak correlation with the dimensional characteristics at the level of 0.3. And it depends little on the plane of its application.

Experimental study on the design method of lost circulation materials for induced fractures

Owing to the influence of fluctuating wellbore pressure, the fracture width in formations with induced fractures changes dynamically. However, the traditional design method for fracture plugging materials is based on a static fracture width, which leads to the easy destruction of the plugging layer established underground and a high risk of secondary loss. Until now, the treatment of lost circulation in formations with induced fractures still faces significant challenges. Therefore, a dynamic fracture plugging experimental device was developed in this study to investigate the bridging–plugging process of lost circulation materials (LCMs) within induced fractures, as well as the design criteria for LCMs for induced fractures. Experimental results show that through adjusting the mass ratio and total concentration of the three-level bridging material, the plugging position of the bridging material can be changed, and the fracture reopen pressure can be increased. When the mass ratio of the three-level bridging material satisfies primary bridge particle: secondary bridge particle: tertiary bridge particle = 1:1:2 and the total concentration is greater than 5%, the plugging material compounded with the three-level bridging material is prone to retention in the induced fractures, exhibiting short bridging time, low permeability of the formed plugging layer, and high fracture initiation pressure. It can effectively prevent the opening of fractures or the generation of new induced fractures, thereby reducing the risk of secondary loss. The research results can provide a scientific theoretical basis for the loss control of induced fractures.

Static and dynamic fracture toughness of graphite materials with varying grain sizes

Graphite materials play critical roles as moderators, reflectors, and core structural components in high-temperature gas-cooled nuclear reactors. During the reactor operation, graphite materials may experience a variety of loads, including thermal, radiation, fatigue, and dynamic loads, potentially leading to crack initiation and propagation. Therefore, it is imperative to investigate their fracture properties. Despite this, there remains a paucity of comprehensive studies on the fracture toughness of graphite materials with varying grain sizes, particularly concerning dynamic fracture toughness. This study addresses this gap by employing a digital-image-correlation-based virtual extensometer to analyze crack propagation in graphite materials of different grain sizes, enabling precise measurement of crack propagation length and fracture toughness. Findings reveal that static fracture toughness increases with larger grain sizes, while under dynamic loading, smaller grain sizes exhibit greater fracture toughness. Additionally, dynamic fracture toughness shows a near-linear increase with impact speed. Scanning electron microscopy analysis of fracture surface morphology highlights the impact of grain size and impact speed on fracture toughness. Nuclear graphite specimens with larger grain sizes have more irregular grain and pore distributions, enhancing crack deflection and propagation resistance, thereby increasing fracture toughness. The observed loading rate dependence of dynamic fracture toughness is attributed to a gradual transition from intergranular to transgranular fracture modes with increasing impact speed.

Fracture Resistance of Direct versus Indirect Restorations on Posterior Teeth: A Systematic Review and Meta-Analysis.

The aim of this systematic review and meta-analysis was to compare static compression forces between direct composite resin restorations and indirect restorations for posterior teeth. All studies comparing mechanical properties of direct versus indirect restorations of posterior teeth were included from 2007 up to February 2024. A meta-analysis was conducted for static compression fracture resistance. Medline, Central, and Embase databases were screened. Twenty-four articles were included in the qualitative synthesis, and sixteen studies were finally included in the quantitative synthesis. There was no difference in terms of fracture resistance between direct and indirect restorations for posterior teeth (p = 0.16 for direct and indirect composite resin restorations and p = 0.87 for direct composite resin restorations and indirect ceramic restorations). Also, sub-group analysis with or without cusp coverage in each group revealed no discernable difference. Based on this study, it can be concluded that the choice between direct and indirect restoration approaches may not significantly impact fracture resistance outcomes. There was no statically significant difference between direct and indirect restorations for posterior teeth in all cases of restorations with or without cusp coverage and no matter the used materials. However, to better evaluate these materials, further studies are warranted.

A coupling method between phase field model and classical linear elastic theory model for static and dynamic fracture

Although phase field model has demonstrated excellent performance in dealing with complex fracture, its development and application are hindered by computational costs. In order to reduce the computational time, a novel method is proposed in this paper that couples the phase field model with the classical linear elastic theory model. The solution domain is divided into different subdomains, and corresponding solution scheme is used for each region. The phase field model is solved only in the subdomain where the crack is about to propagate to determine the crack path, while the rest of the solution domain is solved using a linear elastic theory model, allowing for coarser discretization to improve computational efficiency and reduce computational costs. A transition subdomain is included between the two models to ensure that the results from the different models are harmonized at the boundary and to improve convergence. The coupling model is implemented in ABAQUS using user defined element and built-in features, and the model is applied to both static and dynamic fracture analysis. The coupling model is validated through representative examples, and the results show that the presented model can not only effectively portray the static and dynamic fracture processes and accurately describe the crack propagation, but also reduce the computational costs.

Two scale models for fracture behaviours of cementitious materials subjected to static and cyclic loadings

This study employs a lattice fracture model to simulate static and fatigue fracture behaviour of Interfacial Transition Zone (ITZ) at microscale and mortar at mesoscale. The heterogeneous microstructure of ITZ and mesostructure of mortar are explicitly considered in the models. The initial step involves calibrating and validating the microscopic model of the ITZ through micro-cantilever bending tests. Subsequently, this validated ITZ model serves as a constitutive law to simulate the fracture behavior of mortar at the mesoscale using an uncoupled upscaling method. The influence of microstructural features, such as w/c ratio and microscopic roughness, on the fracture behaviour of ITZ is investigated. Moreover, the effect of ITZ properties and stress level on the fracture performance and fatigue damage evolution of mortar is also studied. The simulation results for both the ITZ and mortar demonstrate good agreement with experimental results. The proposed two models provide insights into the fracture mechanisms and fatigue damage evolution in cementitious materials subjected to static and cyclic loadings.

A Generalized Method for Dynamic Fracture Characterization Using Two-Phase Rate Transient Analysis of Flowback and Production Data

Summary This study presents a comprehensive method for characterizing reservoir properties and hydraulic fracture (HF) closure dynamics using the rate transient analysis of flowback and production data. The proposed method includes straightline analysis (SLA), type-curve analysis (TCA), and model history matching (MHM), which are developed for scenarios of two-phase flow in fracture, stimulated reservoir volume (SRV), and nonstimulated reservoir volume (NSRV) domains. HF closure dynamics are characterized by two key parameters, which are pressure-dependent permeability and porosity controlled by fracture permeability modulus and compressibility. The above techniques are combined into a generalized workflow to estimate iteratively the five parameters (including four optional parameters and one fixed parameter) by reconciling data in different domains of time (single-phase water flow, two-phase flow, and hydrocarbon-dominated flow), analysis methods (SLA, TCA, and MHM), and phases (water and hydrocarbon phase). We used flowback and production data from a shale gas well in the US and a shale oil well in China to verify the practicability of the method. The analysis results of the field cases confirm the good performance of the newly developed comprehensive method and verify the accuracy in estimating the static fracture properties [initial fracture pore volume (PV) and permeability] and the HF dynamic parameters using the proposed generalized workflow. The accurate prediction of the decreasing fracture permeability and porosity, fracture permeability modulus, and compressibility demonstrates the applicability of the comprehensive method in quantifying HF dynamics. The field application results suggest a reduction of the fracture PV by 15% and 20%, and a reduction of the fracture permeability by 80% and 90% for shale gas and shale oil wells, respectively.

The Effect of Die Material on the Crown Fracture Strength of Zirconia Crowns.

Determination of the eligibility of several tooth analog materials for use in crown fracture testing. A standardized premolar crown preparation was replicated into three types of resin dies (C&B, low modulus 3D printed resin; OnX, high modulus 3D printed resin composite; and highest modulus milled resin composite). 0.8 mm zirconia crowns were bonded to the dies and the maximum fracture load of the crowns was tested. Twelve extracted human premolars were prepared to a standardized crown preparation, and duplicate dies of the prepared teeth were 3D printed out of C&B. Zirconia crowns were bonded to both the dies and natural teeth, and their fracture load was tested. There was no statistical difference between the fracture load of zirconia crowns bonded to standardized dies of C&B (1084.5 ± 134.2 N), OnX (1112.7 ± 109.8 N) or Lava Ultimate (1137.5 ± 88.7 N) (p = 0.580). There was no statistical difference between the fracture load of crowns bonded to dentin dies (1313 ± 240 N) and a 3D-printed resin die (C&B, 1156 ± 163 N) (p = 0.618). There was no difference in the static fracture load of zirconia crowns bonded to standardized resin dies with different moduli or between a low modulus resin die and natural dentin die.

A unified bond–based peridynamic model without limitation of Poisson's ratio

The issue of fixed Poisson's ratio is a critical problem plaguing bond–based peridynamic (BB–PD) models. The popular approach of introducing the bond's tangential stiffness cannot completely remove Poisson's ratio limitation, but instead leads to some additional troubles, such as negative tangential stiffness and bond force density misalignment in finite rigid body rotation problems. To address the issue of fixed Poisson's ratio thoroughly, a unified bond–based peridynamics (UPD) was originally proposed. In the proposed model, a novelty pairwise force density function has been developed, in which dilatation and distortion are distinguished, and the model assigns different stiffnesses to the two deformation components. Arbitrary and reasonable values of Poisson's ratio can be achieved by adjusting the PD parameters that control the bulk and shear moduli of the material. The theoretical range of Poisson's ratio in the proposed model is (-1, 0.5], which is consistent with those in continuum mechanics. In addition, the absence of tangential stiffness prevents the proposed model from misalignment of bond force density due to rigid body rotation. Several numerical examples, including four two–dimensional and three–dimensional deformation analyses and three quasi–static fracture analyses, were implemented to verify the accuracy and reliability of the proposed model. The results show that the proposed model can accurately simulate the elastic properties of the material and obtain the deformation with high accuracy. The numerical examples also demonstrate the fracture prediction capability of the proposed model.