Fracture Model Research Articles

Biomechanical comparison of Gofried positive support reduction of Pauwels type III femoral neck fractures: A finite elements analysis

ObjectiveThis study aims to investigate the biomechanical characteristics of non-anatomical reduction and different screw positions on the stability of Pauwels type III femoral neck fractures. MethodsThree-dimensional finite element models of femoral neck fractures were constructed using CT images. Four types of internal fixation methods were simulated, including biplane double-supported screw fixation (BDSF), three inverted triangular parallel cannulated screws (3CS), new parallel cannulated screws with posterior screws moving down (New 3CS), and two parallel cannulated screws (2CS). von Mises stress and total displacement were compared between the fracture models after the femoral head was subjected to an axial load of 2100 N. Stress and displacement data for the implants and the femur were recorded for each fixation method and compared. ResultsThe results demonstrated that positive reduction of a Pauwels type III femoral neck fracture provided greater stability than neutral or negative reduction. Specifically, the BDSF group showed the lowest maximum von Mises stress in the femur (17.66 MPa) in positive reduction, compared to 3CS (21.08 MPa), New 3CS (22.14 MPa), and 2CS (36.57 MPa). The total displacement of positive reduction in the BDSF group was 0.3143 mm, which was lower than in the 3CS (0.3498 mm), New 3CS (0.3343 mm), and 2CS (0.4533 mm) groups. The stress distribution in the positive support reduction group was lower than that of the other groups, indicating better load distribution. Among the three-screw fixation methods, the New 3CS system exhibited the highest stress in the screws (with a peak of 28.62 MPa), while the 2CS group displayed the highest stresses overall, both in the femur and the screws. ConclusionFor Pauwels type III femoral neck fractures, a positive support reduction with BDSF fixation exhibited superior biomechanical performance than negative reduction. Based on the finite element analysis conducted in this study, the positive support reduction with BDSF fixation can enhance fixation stability, suggesting that non-anatomical reduction is recommended.

An enhanced Hosford–Coulomb fracture model for predicting ductile fracture under a wide range of stress states

In this study, an Enhanced Hosford–Coulomb (EHC) fracture model is proposed, which suits a wide range of stress states. The model is validated by quantitatively investigating the ductile fracture behaviors of Ti-6Al-3Nb-2Zr-1Mo titanium alloy through experiments and numerical simulations, and the fracture morphologies are characterized using scanning electron microscopy. The results show that the EHC model has higher accuracy in predicting ductile fracture strain for Ti-6Al-3Nb-2Zr-1Mo alloy compared to the original Hosford–Coulomb (HC) model. Finally, the accuracy and material applicability of the EHC model are further verified with X80 pipeline steel and AA2024-T351 aluminum alloy, demonstrating its advantages.

Study on the characteristics of CO2 fracturing rock damage based on fractal theory

CO2 fracturing is emerging as a carbon–neutral technology for underground excavation. Traditional studies on structural stability during excavation have largely focused on the vibration characteristics of rocks. However, the inherent damage in rock layers during CO2 fracturing poses significant challenges for understanding damage mechanisms under complex multi-field coupling. This study introduces a novel approach for calculating rock damage induced by CO2 fracturing.We developed a physical model of CO2 fracturing and applied a “two-stage effect” division method, creating a staged damage calculation model based on fractal damage mechanics theory. Experiments were conducted under combined dynamic and static loads to evaluate rock damage. A two-factor Analysis of Variance (ANOVA) was used to assess the significance of dynamic and static effects on the extent of rock damage.The findings revealed that static loads guide crack propagation direction, reducing the angle between the crack and vertical axis, while initial CO2 dynamic load pressure strongly influences crack patterns, with higher pressures resulting in more fractures. The extent of rock damage observed ranged from 0.680 to 0.845. Although dynamic loads showed no significant impact, static loads exhibited a notable effect, as indicated by a P-value approaching 0.01. This study’s fractal-damage calculation model provides a valuable tool for addressing stability concerns in structures affected by CO2 fracturing.

Improved fracture toughness evaluation for fiber-reinforced asphalt concrete through double-parameter theory

Fracture toughness serves as a key parameter in the design and durability assessment of asphalt concrete. Quantifying the fracture toughness for fiber-reinforced asphalt concrete (FRAC), remains challenging due to the incorporation of fibers. This study proposes an improved method for evaluating the fracture toughness of FRAC, based on the double-parameter theory derived from the theoretical concepts of stress intensity factor K and energy release rate (double-K and double-G fracture models). Using Digital Image Correlation (DIC) technology, crack propagation during three-point bending beam tests on FRAC beams was measured, refining the calculation of critical crack length ac in the double-K fracture parameters. Additionally, a method is introduced to calculate the improved solution of double-G fracture parameters by monitoring crack propagation in real-time to determine the effective crack length a, and simultaneously computing the energy absorbed per unit crack extension, thereby constructing the J-R curve during stable crack growth phases. The fracture toughness of FRAC is evaluated by the improved method obtained double-G fracture parameters were used in Virtual Crack Closure Technique (VCCT) simulations to achieve virtual modeling of FRAC. The results demonstrate that the improved method provides accurate fracture performance indicators for FRAC. Moreover, the study establishes modified calculation formulas for (GICu) and (KICu) at unstable fracture toughness for FRAC at different temperatures, considering various fiber types and contents, thereby enhancing computational efficiency for practical applications. This research contributes to more accurate and effective methods for testing and evaluating the fracture performance of FRAC

Characterization of compressive fracture strain based on bilinear strain paths

This study proposes the compressive fracture characterization method using bilinear strain paths: pre-tension and compression. Compressive ductile fracture exhibits extremely large strain, which has been regarded as being difficult to be measured. Large deformation under compressive loading makes the shape of a specimen barreled and changes the stress triaxiality rapidly. Due to these complicated and large strains, compressive fracture strain can be considered to be within the so-called cut-off region where no fracture occurs. In order to enable compression tests to be easier, an approach that can lower the range of fracture strain is needed. Uniaxial tensile deformation is a strain path that induces the growth of voids inside ductile materials and leads to ductility reduction. Ductile materials subjected to pre-tensile loading before compressive loading can show the premature compressive fracture. A ductile fracture model capable of predicting the cut-off region is selected for ductile fracture loci of the bilinear paths and implemented into the numerical simulation with different pre-tensile strain levels. The verification of the proposed characterization method is performed by comparing experimental data and simulation results for fractured specimen shapes and load-displacement curves.

Uncoupled Ductile Fracture Models for Grade 8.8S Steel Bolts Considering Different Stress States and Elevated Temperatures

Uncoupled Ductile Fracture Models for Grade 8.8S Steel Bolts Considering Different Stress States and Elevated Temperatures

Machining Characteristics During Short Hole Drilling of Titanium Alloy Ti10V2Fe3Al

The single-phase titanium ß-alloy Ti10V2Fe3Al (Ti-1023) has been widely used in the aerospace industry due to its unique mechanical properties, which include high fatigue strength and fracture toughness, as well as high corrosion resistance. On the other hand, these unique properties significantly hinder the cutting processes of this material, especially those characterized by a closed machining process area, such as drilling. This paper is devoted to the study of the short hole drilling process of the above-mentioned titanium alloy using direct measurements and numerical modeling. Measurements of the cutting force components in the drilling process and determination of the resultant cutting force and total cutting power were performed. The macro- and microstructure of chips generated during drilling were analyzed, and the dependence of the chip compression ratio and the distance between neighboring segments of serrated chips on cutting speed and drill feed was determined. Experimental studies were supplemented by determining the temperature on the lateral clearance face of the drill’s outer cutting insert in dependence on the cutting modes. For the modeling of the drilling process using the finite element model, the parameters of the triad of component submodels of the numerical model were determined: the machined material model, the model of contact interaction between the tool and the machined material, and the fracture model of the machined material. The determination of these parameters was performed through the DOE sensitivity analysis. The target values for performing this analysis were the total cutting power and the distance between neighboring chip segments. The maximum deviation between the simulated and experimentally determined values of the resulting cutting force is no more than 25%. At the same time, the maximum deviation between the measured values of the temperature on the lateral clearance face of the drill’s outer cutting insert and the corresponding simulated values is 26.1%.

Simulation Study of Gas Seepage in Goaf Based on Fracture–Seepage Coupling Field

In order to solve the problem of gas overrun in the fully mechanized caving face and the upper corner of high gas and extra-thick coal seam, the fracture and caving process of the roof in the goaf is analyzed and studied by using the relevant theories of fracture mechanics and seepage mechanics. The mathematical model of fracture and caving of the immediate roof and main roof in the goaf is established. Combined with ANSYS Fluent 6.3.26, the seepage process of gas in coal and rock accumulation in the goaf under different ventilation modes is simulated. The distribution law of gas concentration in the goaf is obtained, and the application scope of different ventilation modes is determined. In addition, the influence of the tail roadway application and the wind speed size on the gas concentration in the goaf and the upper corner of the fully mechanized caving face is also explored. The results show that, affected by wind speed and rock porosity, along the strike of the goaf, about 30 m near the working face, the gas concentration is low and growth is slow. In the range of 30~160 m, the gas concentration increases rapidly and reaches a higher value. After 160 m, the gas concentration tends to be stable. Along with the tendency of the working face, the gas concentration in the goaf increases gradually from the inlet side to the return side, and the gas concentration increases noticeably near the return air roadway. Along the vertical direction of the goaf, the gas concentration gradually increases, and the concentration of the fracture zone basically reaches 100%. Different ventilation modes have different application scopes. The U-type ventilation mode is suitable for the scenario of less desorption gas in the coal seam, while U + I and U + L-type ventilation modes are suitable for the scenario of more desorption gas in coal seam or higher mining intensity. The application of the tail roadway can reduce the gas concentration in the upper corner to a certain extent, but it has limited influence on the overall gas concentration distribution in the goaf. In addition, when the wind speed of the working face should be controlled at 2.0~3.5 m/s, it is more conducive to the discharge of gas, the method of reducing the gas concentration in the upper corner by increasing the wind speed of the working face is more suitable for the case where the absolute gas emission of the fully mechanized caving face is low, and the effect is limited when the absolute gas emission is high. The above conclusions provide a reference for solving the problem of gas overrun in the goaf and the upper corner of a fully mechanized caving face.

A Prediction Method for Calculating Fracturing Initiation Pressure Considering the Modification of Rock Mechanical Parameters After CO2 Treatment

The establishment of a more realistic CO2 fracturing model serves to elucidate the intricate mechanisms underlying CO2 fracturing transformation. Additionally, it furnishes a foundational framework for devising comprehensive fracturing construction plans. However, current research has neglected to consider the influence of CO2 on rock properties during CO2 fracturing, resulting in an inability to precisely replicate the alterations in the reservoir post-CO2 injection into the formation. This disparity from the actual conditions poses a substantial limitation to the application and advancement of CO2 fracturing technology. This work integrates variations in the physical parameters of rocks after complete contact and reaction with CO2 into the numerical model of crack propagation. This comprehensive approach fully acknowledges the impact of pre-CO2 exposure on the mechanical parameters of reservoir rocks. Consequently, it authentically restores the reservoir state following CO2 injection, ensuring a more accurate representation of the post-fracturing conditions. In comparison with conventional numerical simulation methods, the approach outlined in this paper yields a reduction in the error associated with predicting fracturing pressure by 9.8%.

Simple model for the fracture of a polymer chain: Single-bond potential of mean force and tension-based rate constants for chain rupture.

A linear chain of N particles connected by Morse bonds with periodic boundaries in a Brownian bath is considered as a model for polymer fracture. The potential of mean force (pomf) with respect to the length of a bond and its energy and entropic components are computed via Langevin Dynamics simulations at various chain elongations λ > 1. A narrow range of λ values is identified over which equilibrium is established between an intact (i) and a fractured (f) state over a pomf barrier. While the barrier and (f) regions of the pomf are well described by a well-known (N - 1)-bond adiabatic approximation, the shape of the (i) region departs from it, exhibiting a bimodal character. A new, 1-bond adiabatic approximation is proposed to explain this. The lower envelope of the two adiabatic approximations provides an excellent description of the pomf. The relationship between (f) states for individual bonds and for the entire chain is elucidated. A new approach, based on analysis of equilibrium tension autocorrelation functions, is developed to extract rate constants for the fracture and reformation of the chain in dependence of λ. Results from it agree with tension relaxation during nonequilibrium simulations initiated at equispaced configurations of the particles. Rate constants for chain fracture conform to a Boltzmann-Arrhenius-Zhurkov dependence on the tension averaged over the intact state of the chain, the activation length being higher than estimated from pomf extrema. These findings constitute a step toward a predictive multiscale simulation scheme for fracture in polymeric materials.

Modeling Hydraulic Fracture Entering Stress Barrier: Theory and Practical Recommendations

Numerical modeling of hydraulic fracturing is complicated when a fracture reaches a stress barrier. For high barriers, it may require changing the computational scheme. In view of the strong influence of stress barriers on the final footprint and opening of a hydraulic fracture, for decades, their modeling has been the subject of special investigations. Actually, classical models of propagation within a pay layer with impenetrable boundaries referred to the case of extremely high-stress contrast in neighbor layers. Further improvements tended to account for the fracture growth in these layers by including stress contrasts as input parameters of a model. This tendency resulted in the suggestion and successive enhancements of pseudo-three-dimensional models. All of them have used stress intensity factors (SIFs) to characterize the combined resistance caused by stress contrasts, material strength, and fluid viscosity. Specifically, the SIFs served to formulate the conditions that control the front penetration into a neighbor layer. This key concept presents the background of our research. Despite examples of modeling propagation through barriers, there is no general theory clarifying when and why conventional schemes may become inefficient and how to overcome computational difficulties. This paper presents the theory and practical recommendations following it. We start with the definition of the barrier intensity, which exposes that the barrier strength may change from zero for contrast-free propagation to infinity for channelized propagation. The analysis reveals two types of computational difficulties caused by spatial discretization as follows: (i) general, arising for fine grids and aggravated by a barrier, and (ii) specific, caused entirely by a strong barrier. The asymptotic approach, which avoids spatial discretization, is suggested. It is illustrated by solving benchmark problems for barriers of arbitrary intensity. The analysis distinguishes three typical stages of the fracture penetration into a barrier and provides theoretical values of the Nolte–Smith slope parameter and arrest time as functions of the barrier intensity. Special analysis establishes the accuracy and bounds of the asymptotic approach. It appears that the approach provides physically significant and accurate results for fracture penetration into high, intermediate, and even weak stress barriers. On this basis, simple practical recommendations are given for modeling hydraulic fractures in rocks with stress barriers. The recommendations may be promptly implemented in any program using spatial discretization to model fracture propagation.

Shale Fracture Static Stability Evaluation Method Based on 3D Discrete Fracture Model: A Case Study on the Luzhou Area in Southern Sichuan Basin, SW China

Abstract The stress interference in deep shale may lead to shale fracturing and instability and consequently results in engineering risks such as casing deformation in horizontal wells. Therefore, in the early stages of shale gas exploration and development, it is of great significance to evaluate the stability of shale fractures in advance. The stability evaluation of shale reservoir faults can be mainly divided into two categories at present: quantitative evaluation of single faults and qualitative evaluation of wide-range faults. The quantitative evaluation of single faults primarily relies on numerical simulation techniques, while the qualitative evaluation of wide-range faults primarily employs geophysical methods. Both methods are difficult to meet the needs of shale gas exploration and development. The shale fracture stability evaluation method based on 3D discrete fracture model which is developed in this article can quantitatively evaluate the static stability of wide-range shale fractures in the early stage of exploration and development. In this article, seismic geometric attributes were calculated, and fracture seismic facies was established by means of the Bayesian probabilistic cluster analysis method. Then, 3D discrete fracture modeling under the constraint of fracture seismic facies was performed to establish a discrete fracture model. Finally, according to the Mohr–Coulomb criterion, the shear stress and effective normal stress of discrete fracture were calculated by using the formation pressure data in other exploration and development results and the regional in situ stress obtained through seismic prestack inversion. And thus, the stability evaluation of the fractures in shale reservoirs was eventually completed. In addition, this method was verified by using the casing deformation points in some actual shale-gas horizontal wells, the actual small fault points, and microseismic data. It indicates that the method has higher accuracy and is better applicable to the early shale gas exploration and development.

Production Simulation of Stimulated Reservoir Volume in Gas Hydrate Formation with Three-Dimensional Embedded Discrete Fracture Model

Natural gas hydrates (NGHs) in the Shenhu area of the South China Sea are deposited in low-permeability clayey silt sediments. As a renewable energy source with such a low carbon emission, the exploitation and recovery rate of NGH make it difficult to meet industrial requirements using existing development strategies. Research into an economically rewarding method of gas hydrate development is important for sustainable energy development. Hydraulic fracturing is an effective stimulation technique to improve the fluid conductivity. In this paper, an efficient three-dimensional embedded discrete fracture model is developed to investigate the production simulation of hydraulically fractured gas hydrate reservoirs considering the stimulated reservoir volume (SRV). The proposed model is applied to a hydraulically fractured production evaluation of vertical wells, horizontal wells, and complex structural wells. To verify the feasibility of the method, three test cases are established for different well types as well as different fractures. The effects of fracture position, fracture conductivity, fracture half-length, and stimulated reservoir volume size on gas production are presented. The results show that the production enhancement in multi-stage fractured horizontal wells is obvious compared to that of vertical wells, while spiral multilateral wells are less sensitive to fractures due to the distribution of wellbore branches and perforation points. Appropriate stimulated reservoir volume size can obtain high gas production and production efficiency.

Cigarette Smoke Exposure Impairs Fracture Healing in a Rat Model: Preferential Impairment of Endochondral over Membranous Healing.

Cigarette smoking affects fracture repair, leading to delayed healing or nonunion. We sought to investigate if cigarette smoke differentially affects intramembranous and endochondral ossification in healing fractures, focusing on whether endochondral ossification is particularly impaired. This study utilized a bilateral femur fracture model in Sprague Dawley rats to examine the impact of cigarette smoke exposure on healing of femur fractures, treated with either a custom-locked intramedullary nail or compression plating to induce endochondral and membranous ossification, respectively. Animals were exposed to tobacco smoke 30 days before and after surgery, with evaluations including radiographs, histomorphometry, and microCT at 10 days, 1, 3, and 6-months post-operation, and biomechanical testing at 3, 6 months. Sixty-eight animals were randomized to control or exposure groups (two died perioperatively), and 89% of the femora achieved union when harvested at 3 and 6 months. Smoke exposure delayed cartilaginous callus formation and bone maturation in nailed fractures compared to plated fractures and controls in same animals. Plated fractures in exposed animals exhibited little cartilage callus and healed like control animals. At 3 months, plated fractures were stiffer and stronger than nailed fractures in both groups, but these differences vanished by 6 months. Plated fractures healed more rapidly and more completely than nailed fractures under both control and smoke-exposed conditions. Using compression plating instead of IM nailing for closed long bone fractures may lead to better outcomes in patients who smoke compared to current results with nailing.

Progranulin-dependent repair function of Regulatory T cells drive bone fracture healing.

Local immunoinflammatory events instruct skeletal stem cells (SSCs) to repair/regenerate bone after injury, but mechanisms are incompletely understood. We hypothesized that specialized Regulatory T (Treg) cells are necessary for bone repair and interact directly with SSCs through organ-specific messages. Both in human patients with bone fracture and mouse model of bone injury, we identified a bone injury-responding Treg subpopulation with bone-repair capacity marked by CCR8. Local production of CCL1 induced a massive migration of CCR8+ Treg cells from periphery to the injury site. Depending on secretion of progranulin (PGRN), a protein encoded by the granulin (Grn) gene, CCR8+ Treg cells supported the accumulation and osteogenic differentiation of SSCs, and thereby bone repair. Mechanistically, we revealed that CCL1 enhanced expression level of basic leucine zipper ATF-like transcription factor (BATF) in CCR8+ Treg cells, which bound to Grn promoter and increased Grn translational output and then PGRN secretion. Together, our work provides a new perspective in osteoimmunology and highlights possible ways of manipulating Treg cell signaling to enhance bone repair and regeneration.

Progress of fracture mapping technology based on CT three-dimensional reconstruction

Fracture Mapping is a new technology developed in recent years. This technology visually representing the morphology of fractures by overlaying fracture lines from multiple fracture models onto a standard model through three-dimensional reconstruction. Fracture mapping has been widely used in acetabular fracture, proximal humerus fractures, Pilon fracture, tibial plateau fractures, and so on. This technology provides a new research method for the diagnosis, classification, treatment selection, internal fixation design, and statistical analysis of common fracture sites. In addition, the fracture map can also provide a theoretical basis for the establishment of a biomechanical standardized fracture model. Herein, we reviewed various methods and the most advanced techniques for fracture mapping, and to discuss the issues existing in fracture mapping techniques, which will help in designing future studies that are closer to the ideal. Moreover, we outlined the fracture morphology features of fractures in various parts of the body, and discuss the implications of these fracture mapping studies for fracture treatment, thereby providing reference for research and clinical decision-making on bone and joint injuries to improve patient prognosis.

Fourth-order phase field modelling of brittle fracture with strong form meshless method

This study aims to find a solution for crack propagation in 2D brittle elastic material using the local radial basis function collocation method. The staggered solution of the fourth-order phase field and mechanical model is structured with polyharmonic spline shape functions augmented with polynomials. Two benchmark tests are carried out to assess the performance of the method. First, a non-cracked square plate problem is solved under tensile loading to validate the implementation by comparing the numerical and analytical solutions. The analysis shows that the iterative process converges even with a large loading step, whereas the non-iterative process requires smaller steps for convergence to the analytical solution. In the second case, a single-edge cracked square plate subjected to tensile loading is solved, and the results show a good agreement with the reference solution. The effects of the incremental loading, length scale parameter, and mesh convergence for regular and scattered nodes are demonstrated. This study presents a pioneering attempt to solve the phase field crack propagation using a strong-form meshless method. The results underline the essential role of the represented method for an accurate and efficient solution to crack propagation. It also provides valuable insights for future research towards more sophisticated material models.

Initial construct stability of long cephalomedullary nails with superior locking for a complex trochanteric fracture model AO31A2.2– a biomechanical study

BackgroundComplex fractures of the trochanteric region, as well as fractures located in the directly subtrochanteric region, are controversially discussed around the world regarding the nail type to be used. A long nail is recommended by manufacturers but requires longer surgical and fluoroscopy times. A possible solution could be a nail with an appropriate length which can be locked in a minimally invasive manner by the main aiming device. We aimed to determine if such a nail model (DCN SL nail, SWEMAC, Linköping, Sweden) offers similar structural stability on biomechanical testing on artificial bone as a standard long nail when used to treat complex trochanteric fractures and compared it to long nails usually used in this setting.MethodsAn osteoporotic bone model was chosen. The Swemac Hansson DCN Nail System was used as osteosynthesis material. Two types of nails were chosen: a superior lock nail which can be implanted with a singular targeting device, and a long nail with distal locking using free-hand technique. AO31A2.2 fractures were simulated in a standardised manner. Axial height of the construct, varus collapse, and rotational deformity directly after nail insertion were simulated. A Universal Testing Machine was used. Measurements were made with a stereo-optic tracking system.FindingsThere was a detectable difference in the axial fracture movement resulting in narrowing of the fracture gap. There was no difference in varus collapse or rotational deformity between the nail variantsConclusionWe conclude that there are small differences which are clinically insignificant and that a superior locking nail can safely be used to manage complex trochanteric fractures.

Most AOTL type A and type B thoracolumbar primary fracture line follow the mechanism of an imaging-based injury model.

Based on the phenomenon that most thoracolumbar primary fracture line passes the center of the pedicle, we proposed an injury mechanism model to evaluate. Consecutive patients with thoracolumbar fractures treated operatively between October 2019, and December 2020 were analyzed retrospectively. Demographic and spinal radiographical parameters were measured and recorded. Pedicle hyperintensity on T2-weighted sagittal MR images was labeled. We examined the relationship between the course of the line (Radius) connecting the center of the pedicle of the injured vertebra and the IAR and orientation of the thoracolumbar primary fracture line. A partial correlation test was calculated to find correlations between demographic and spinal radiographical parameters. Nonlinear regression analysis was run with the Radius as the dependent variable and the other spinal kyphosis parameters as the independent variables to verify this model. Ninety-seven patients with 104 thoracolumbar fractures were included in this study. Ninety-four (90.4%) thoracolumbar fractures showed a high signal on MRI T2 through the pedicle. Involvement of the center of the pedicle was distributed among most AOTL Type A and Type B thoracolumbar fractures. In total, 92.3% of primary vertebral fracture lines followed the Radius of the model (r2 = 0.940). We provide a simple and quantifiable spinal instantaneous injury mechanism model for thoracolumbar fractures. Specifically, most AOTL type A and B thoracolumbar primary fracture line conforms to this model.

Fracture Toughness of Ordinary Plain Concrete Under Three-Point Bending Based on Double-K and Boundary Effect Fracture Models.

Fracture tests are a necessary means to obtain the fracture properties of concrete, which are crucial material parameters for the fracture analysis of concrete structures. This study aims to fill the gap of insufficient test results on the fracture toughness of widely used ordinary C40~C60 concrete. A three-point bending fracture test was conducted on 28 plain concrete and 6 reinforced concrete single-edge notched beam specimens with various depths of prefabricated notches. The results are reported, including the failure pattern, crack initiation load, peak load, and complete load versus crack mouth opening displacement curves. The cracking load showed significant variation due to differences in notch prefabrication and aggregate distribution, while the peak load decreased nonlinearly with an increase in the notch-to-height ratio. The reinforced concrete beams showed a significantly higher peak load than the plain concrete beams, attributed to the restraint of steel reinforcement, but the measured cracking load was comparable. A compliance versus notch-to-height ratio curve was derived for future applications, such as estimating crack length in crack growth rate tests. Finally, fracture toughness was determined based on the double-K fracture model and the boundary effect model. The average fracture toughness value for C50 concrete from this study was 2.0 MPa·m, slightly smaller than that of lower-strength concrete, indicating the strength and ductility dependency of concrete fracture toughness. The fracture toughness calculated from the two models is consistent, and both methods employ a closed-form solution and are practical to use. The derived fracture toughness was insensitive to the discrete parameters in the boundary effect model. The insights gained from this study significantly contribute to our understanding of the fracture toughness properties of ordinary structural concrete, highlighting its potential to shape future studies and applications in the field.