Crack Initiation Load Research Articles

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.

Enhancing concrete beam performance with PVA fibers, coal ash, and graphene fabric: a comprehensive structural analysis

ABSTRACT This study evaluates the structural performance of Polyvinyl Alcohol Cementitious Composites (PVCC)-layered reinforced concrete beams with coal ash under static loading. Experimental investigations included first crack load, ultimate load, load-deflection behavior, ductility, stiffness, and energy absorption. Results highlight the influence of Polyvinyl Alcohol-(PVA) fiber dosage on structural behavior. The control specimen exhibited an initial crack load of 80kN, with subsequent specimens showing varied crack initiation loads influenced by PVA fiber content. Optimal performance was observed at 1.2% PVA fiber dosage, with higher dosages leading to earlier crack initiation. Ultimate load carrying capacity increased with PVA fiber addition, reaching a peak at 1.2% dosage before slight decreases occurred with higher dosages. Load-deflection behavior demonstrated the superior performance of PVCC layered beams, particularly specimen BP3, attributed to optimal fiber content. Ductility, stiffness, and energy absorption increased with PVA fiber reinforcement, with 1.2% dosage yielding optimal results. Excessive fiber content led to diminishing returns. Energy index analysis revealed superior energy dissipation in specimens with higher PVA fiber content, emphasizing the effectiveness of fiber reinforcement in enhancing structural performance. Overall, the study underscores the importance of optimizing PVA fiber dosage to maximize structural resilience and load-bearing capacity in PVCC-layered concrete beams with coal ash.

Temperature dependence of the deformation behavior and mechanical properties of a Fe–Mn–Al–C low-density steel for cryogenic application

The temperature dependence of the deformation behavior and mechanical properties of a Fe–20Mn–6Al-0.6C-0.15Si austenitic low-density steel was studied by tensile test and Charpy impact test at −196 °C, −77 °C and room temperature (RT), followed by microstructure analyses. The results indicate that the decreased tensile temperature, which is corresponding to reduced stacking fault energy (SFE), promotes the planar glide of dislocations. This led to larger fraction of low-angle grain boundaries (LAGBs) at lower tensile temperature. Consequently, both the tensile strength and elongation were improved as temperature decreased. At lower impact test temperature, the load and energy of crack initiation were larger, indicating a higher resistance to crack initiation. However, the transition from stable to unstable crack propagation occurred more rapidly at lower temperature, resulting in lower crack propagation energy and reduced resistance to crack propagation. This is because less region experienced planar glide. Due to the rapid unstable crack propagation, the Charpy absorbed energy at −196 °C was the lowest. The smaller fracture surface area, larger fibrous zone and more obvious ductile fracture characteristics in radial zone suggest that the toughness is better at higher temperature. Additionally, the presence of secondary cracks at RT delayed fracture, therefore benefitting toughness.

Fracture performance of concrete-epoxy mortar interface subjected to bending and shear: Experimental and numerical study

To investigate the fracture performance of concrete-epoxy mortar interfaces, experimental and numerical simulation methods were employed to obtain the failure patterns and applied load P versus opening displacement curves of specimens. A special emphasis is placed on the discussions of crack initiation load (Pini), maximum load (Pmax), corresponding deformation (CTODini and CTODmax, CTSDini and CTSDmax), KR and GR curves of I-Type and stress intensity factors of I-II-Type cracks (KIini and KIIini) and facture energy (GF). Test results show that increasing both concrete compressive strength and interface roughness enhances the load carrying capacity and crack initiation toughness, as well as crack extension resistance. Higher concrete compressive strength improves the moment capacity of the interface and increases the proportion of KIini. An increase in the interface roughness enhances the mechanical interlocking interaction at the concrete-epoxy mortar interface, thereby decreasing the CTSD/CTOD ratio and increasing the proportion of KIIini for the I-II Type crack. As the mode ratio (KIIini/KIini) increases, the proportion of shear and bending moment acting on the interface changes continuously, with the shear effect becoming more dominant. Basically, the increase in both the crack-height ratio (a0/D) and initiated crack offset ratio (C1/C0) decreases the fracture performances of specimen. The observations provide a deeper understanding to the design and practice of concrete-epoxy mortar interface.

Evaluation of crack initiation load of silica glass surfaces formed during subcritical crack growth

AbstractThe crack initiation load of freshly fractured surfaces for silica glass was evaluated with ball indentation. The fracture surfaces were formed during subcritical crack growth in the regions I, II, and III of the stress intensity factor (KI)—crack velocity (V) curve. From the KI–V curve, we linked the obtained fracture surfaces with the ones in the regions I, II, and III. It was found that the crack‐forming probability was the lowest for the fracture surface formed in the region III of the KI–V curve. In order to understand the controlling factors of the crack formation, some properties which are topography, relative nonbridging oxygens (NBO), hydrogen concentrations, and Si–O three‐ or four‐membered ring structures, of the fracture surfaces were measured by atomic force microscopy, X‐ray photoelectron spectroscopy, dynamic secondary ion mass spectroscopy, and Raman spectroscopy, respectively. No distinct difference in NBO and hydrogen concentrations nor the ring structures were found among the fracture surfaces formed in different regions in the KI–V curve. The peak‐to‐valley height of the fracture surface, however, decreased with increasing crack velocity. It is concluded that the roughness or topography of the freshly fractured surface is one of the controlling factors which reduce the intrinsic strength of silica glass.

Parameter analysis and prediction of crack propagation for thermoplastic composite pipes under lateral pressure

ABSTRACT The research investigates the process of crack propagation in thermoplastic composite pipes (TCPs) with initial racks subjected to lateral pressure, through a combination of numerical simulations and experimental studies. In the numerical analysis, a TCP is subjected to lateral pressure, considering parameters such as initial crack length, initial crack angle, and lateral displacement. This analysis employs the extended finite element method (XFEM). The results reveal that crack propagation predominantly occurs perpendicular to the fibre winding angle. Moreover, it is observed that longer initial cracks result in lower crack initiation loads, while the final extent of crack propagation increases with the initial crack length. The experimental study considers three distinct initial crack angles and verifies the conclusions drawn from the numerical simulations. Furthermore, a crack propagation prediction model is developed that combines particle swarm optimization (PSO) with backpropagation (BP) neural networks. The predictive results demonstrate a high level of accuracy.

Experimental and analytical investigation of T-beams retrofitted through the external post-tensioning using steel and various FRP strands

This study aimed to scrutinize the potential benefits of using fiber-reinforced polymer (FRP) materials as unbonded strands in post-tensioning systems for reinforced concrete (RC) flexural members. The research meticulously evaluated the influence of these FRP materials on global and local response levels. To this end, four-point loading tests were performed on T-beam specimens, and the experimental results were compared with numerical predictions. The study also incorporated insights from previous research on external post-tensioning variables. The results of this study, with their practical implications, demonstrate a strengthening technique that significantly enhances the load-carrying capacity at ultimate and yielding points, as well as the crack initiation load of non-strengthened specimens. The strengthening technique also significantly influences deflection during yielding and maximum loads and plays a crucial role in restoring deflection after unloading. However, it is essential to note that strengthening with external post-tensioning does reduce the member’s ductility. The choice of materials also emerges as a significant factor that leads to noticeable differences in crack widths and distribution among the specimens. These practical findings hold considerable importance and offer valuable insights into the potential use of FRP materials in post-tensioning systems for RC flexural members.

Novel sustainable techniques for enhancing shear strength of RC beams mitigating construction failure risk

The aim of this study is to evaluate the effectiveness of various innovative and sustainable methods for improving the shear performance of reinforced concrete (RC) beams. The potential risk of failure for such elements is considered a potential threat, therefore, this study addresses it through experimental tests and numerical analyses to be mitigated carefully in order to enhance the safety and sustainability of buildings. A total of eleven specimens, comprising two control specimens and nine strengthened specimens, underwent three-point testing. Several proposed strengthening techniques, each involving multiple parameters, were examined. In the initial approach, glass fiber-reinforced polymer (GFRP) textile embedded in an external fiber-reinforced cementitious mortar (FRCM) jacket was utilized, with an evaluation of the number of the GFRP textile layers (1, 2, and 3 layers). The second technique incorporated near surface mounted (NSM) GFRP bars along with the FRCM jacketing, where the diameter of the GFRP bars (10, 12, and 16 mm) served as the primary parameter. In the final technique, externally bonded stainless-steel strips (SSSs) of varying thicknesses (1, 1.25, 1.50 mm) were affixed to the beams’ surface. The obtained results revealed that the application of the FRCM jacketing method yielded positive results, showing a significant 30.7 % average increase in the crack initiation load and a 17.1 % improvement in the failure load compared to the defected beam. However, issues of debonding beneath the loading point were observed in the FRCM jacket, particularly with three layers of the GFRP textile, leading to the separation of the concrete cover. Moreover, combining the NSM GFRP bars with an FRCM jacket addressed the absence of shear stirrups. The most remarkable improvement was noted utilizing the NSM GFRP bars and an FRCM jacket, followed by employing SSSs with an FRCM jacket.

Numerical simulation of the crack propagation effect on the hysteretic behavior of CHS-X joints

The circular hollow section (CHS) X-joint hysteresis behavior significantly affects the seismic behavior of the steel tubular structure using this type of joint. The hysteresis behavior of this type of joint considering crack growth is studied by tests and numerical simulation. Two CHS X-joints were fabricated and tested under axial cyclic loading until the joints were cracked. The hysteresis curves of the joints, considering the influence of damage and fracture, were obtained, and the hysteresis performance of the joints was evaluated according to the curves. The VUSDFLD subroutine based on the ductile fracture model CVGM (cyclic void growth model) was embedded into ABAQUS, and the FE simulation of the test joints considering crack occurrence and growth was carried out. The test results are compared with the results of FE analysis, revealing that the proposed method accurately simulates the hysteresis behavior of these joints and the crack propagation behaviors under cyclic loads. The difference between the test and simulated crack initiation loads for the two joints is 10.8 % and 5.7 %, respectively.

Damage-tolerant behavior of structural epoxies with thin PEI and PVDF interlayers

This work examines the crack-arresting capability of PEI and PVDF thermoplastic interlayers in short-glass fiber modified and core–shell rubber toughened epoxy materials under mode-I fracture loading. Experimental results show that the initial crack can be effectively arrested by the thermoplastic-epoxy interface and reinitiation of this crack at the thermoplastic layer requires up to 2.5 times higher load than the crack initiation load of the pristine epoxies. The interlayered designs also exhibit a significant increase in energy absorption by up to 43 times more than their pristine counterparts. Competing damage mechanisms and failure events are captured by microscopy images, digital image correlation and high-speed photography observations. Additionally, elasto-plastic fracture mechanics models based on configurational material forces theory are developed for a preliminary crack-arresting material selection and to elucidate the material inhomogeneity effects.

Epoxy-Printed Circuit Board Interfacial Fracture Reliability Under Three-Point and Four-Point Bend Loading After Sustained Elevated Temperature Exposure

Abstract The survivability and reliability of commercial electronic components under very high thermo-mechanical loads are improved using underfilling and potting methods. Potting protects from operating conditions such as moisture, water, or corrosive agents. Furthermore, potting offers damping against shock and vibrations, heat dissipation, and structural support. Being one of the most cost-efficient methods, potting greatly increases reliability and therefore reduces costs for replacements and repairs. It also addresses trapped hot air issues better than other restraint technologies. In potted electronic assemblies, interfacial delamination at the epoxy and printed circuit board (PCB) interface has been one of the major failure modes. Interfacial delamination happens at the epoxy/PCB interface under dynamic shock loads, which leads to failures at the solder interconnects of the electronic components. Sustained operation and storage at elevated temperatures change the interfacial characteristics at the epoxy/PCB interface. This research is focused on interfacial failure mechanics at epoxy/PCB interfaces with high-temperature isothermal aging. In the selection of the epoxy potting material and the reliability assessments of the supplemental restraint systems, fracture parameters such as steady-state strain energy release rate stress and fracture toughness are critical. Rectangular beam specimens of the epoxy/PCB interface are fabricated for different potting compounds, and the fracture behavior is studied under quasi-static monotonic three-point and four-point bend loads. One of the main differences between three-point and four-point bend loading is that the maximum bending stress occurs at the midpoint under the point of loading of the specimen in three-point bending, whereas the peak stress is distributed over the section of the specimen between the loading points in four-point bending. Four different potting compounds with diverse properties have been studied. The recommended curing schedule from the manufacturer has been chosen and followed for all the potting compounds. The epoxy/PCB interfacial samples are aged at a high temperature of 100 °C for 30–180 days. Damage has been assumed to happen at the epoxy/PCB interface under dynamic loads. The critical load of crack initiation for the epoxy/PCB interface has been determined from the experimental findings, and it is used in the computation of fracture toughness values. The fracture toughness values are compared for the various epoxy/PCB systems based on the number of days of thermal aging and the method of flexure testing. A cohesive zone model has been constructed for predominantly mode-I delamination with four-point bend stress to predict the interfacial delamination behavior at the epoxy/PCB interfaces. It has been assumed that the bulk material is linear elastic during the bending load. The cohesive zone has been modeled at the interface, where the interfacial fracture has been assumed to occur. The fracture behavior in the simulation is predicted based on the fracture parameters determined through the experiment. The computed cohesive zone parameters are unique to the interfaces, and they can be used across various applications with the same epoxy/PCB interface to predict interfacial delamination and to select a more suitable potting material.

Digital Fracture Surface Morphology and Statistical Characteristics of Granite Brazilian Tests after Non-Steady-State Thermal Disturbance

With the widespread advent of digital technologies, traditional perspectives in rock mechanics research are poised for further expansion. This paper presents a Brazilian test conducted on granite after non-steady-state thermal disturbance at 25 °C, 200 °C, 400 °C, and 600 °C, with detailed documentation of the damage process and failure response using an acoustic emission (AE) apparatus and a digital image correlation (DIC) system. Subsequently, utilizing point cloud data captured by a three-dimensional (3D) laser scanning system, a digital reconstruction of the failed specimen’s fracture surface was accomplished. The 3D fractal characteristics and roughness response of the digitized fracture surface were studied using the box-counting method and least squares approach. Furthermore, texture information of the digitized fracture surface was calculated using the Gray Level Co-occurrence Matrix (GLCM), and statistical characteristics describing the elevation distribution were analyzed. The results elucidate the influence of thermal disturbance temperature on the mechanical parameters of the specimen, acoustic emission behavior, surface strain field evolution, and digital fracture morphology characteristics. The findings indicate a non-linear degradation effect of temperature on the specimen’s tensile strength, with a reduction reaching 80.95% at 600 °C, where acoustic emission activity also peaked. The rising thermal disturbance temperature inhibited the crack initiation load at the specimen’s center but expanded the high-strain concentration areas and the growth rate of horizontal displacement. Additionally, varying degrees of linear or non-linear relationships were discovered between thermal disturbance temperature and the 3D fractal dimension of the fracture surface, average roughness (Ra), peak roughness (Rz), and root mean square roughness (Rq), confirming the potential of Rsm in predicting the 3D fractal dimension of Brazilian test fracture surfaces. The study of the GLCM of the digitized 3D fracture surface demonstrated a high dependency of its four second-order statistical measures on thermal disturbance temperature. Finally, the statistical parameters of the fracture surface’s elevation values showed a significant non-linear relationship with thermal disturbance temperature, with a critical temperature point likely existing between 400 and 600 °C that could precipitate a sudden change in the fracture surface’s elevation characteristics.

Rheological and Flexural Strength Characteristics of Cement Mixtures through the Synergistic Effects of Graphene Oxide and PVA Fibers.

This study investigates the synergistic effects of incorporating graphene oxide (GO) and polyvinyl alcohol (PVA) fibers into cement paste mixtures, aiming to modify their rheological properties and flexural behaviors with resistance to crack formation. The relationship between static yield stress and critical shear strain was examined in ten cement paste mixtures with varying concentrations of 6 mm and 12 mm PVA fibers and 0.05% GO. Additionally, viscosity analyses were performed. For the specimens fabricated from these mixtures, flexural strength tests were conducted using the Digital Image Correlation (DIC) technique for precise strain analysis under load history. The results indicated a significant increase in static yield stress, viscosity, and critical shear strain due to the combined addition of GO and PVA fibers, more so than when added individually. Notably, in PVA fiber-reinforced cement mixtures, the integration of GO increased the crack initiation load by up to 23% and enhanced pre-crack strain by 30 to 50%, demonstrating a notable delay in crack initiation and a reduction in crack propagation. Microstructural analyses using Scanning Electron Microscopy (SEM) and Energy Dispersive X-ray Spectroscopy (EDS) revealed a concentrated presence of GO around and on the PVA fibers. This promotes increased C-S-H gel formation, resulting in a denser microstructure. Additionally, GO effectively interacts with PVA fibers, enhancing the adherence of hydration products at their interface.

Crack Propagation Phenomenon in Gangue Concrete Using the Digital Image Correlation (DIC) Method

In order to study the mode I crack propagation mechanism of coal gangue concrete with different contents, the digital image correlation (DIC) method was used to carry out the three-point bending fracture tests on coal gangue concrete with different contents. The results show that the process of the mode I crack propagation of coal gangue concrete with different contents can be divided into three stages as follows: the elastic stage before crack initiation, extended viscoelastic stage, and extended fracture stage. The amount of coal gangue has a significant impact on the crack propagation path. The more the amount of coal gangue, the more the crack penetrates through the coal gangue coarse aggregate, the smaller the bending degree of the failure path, and the faster the crack propagation to the penetration speed. The crack initiation load, ultimate load, external force work, gravity work, and fracture energy all decrease with the increase of the coal gangue content. The data obtained by the DIC method and displacement extensometer are in good agreement, which proves that the DIC method is feasible. Based on the DIC method, before reaching the horizontal displacement on both sides of the crack tip, the horizontal displacement of the horizontal pixel is very small and there is a jump increase after the ultimate load. There are obvious inflection points on the left and right, and the horizontal displacement remains unchanged after the inflection point. After the horizontal displacement field of crack propagation reaches the limit load, there is an obvious limit; the limit gradually extends upward, and the corresponding crack tip strain field is also gradually enhanced. The more the coal gangue is added, the smaller the corresponding horizontal displacement and strain field is at the same limit load moment. The shape of the crack generation area of coal gangue concrete takes the crack tip as the axis of symmetry and is “gourd shaped.” The more the content of the crack, the larger the crack generation area.

Evaluation of the Fracture Toughness of Short Carbon Fiber Reinforced Thermoplastic Composites

Abstract Short carbon fiber (SCF) reinforced thermoplastic composites (SCFRTCs) are attracting broad attention in various fields for their excellent mechanical properties. The fracture toughness, an essential characteristic of the resistance of materials to crack propagation, is considered a critical aspect of the long-term performance of SCFRTCs structures. The fracture toughness of SCFRTCs depends on two competing mechanisms: the interface between SCFs and polymer matrix may promote crack initiation, while the SCFs hinder the crack propagation. In this study, the fracture toughness of SCFRTCs with varying SCFs volume fractions is first determined by a three-point bending test. The results show that adding SCFs effectively improves the fracture toughness of SCFRTCs, and an increase of up to 73.7% at the SCFs volume fraction of 5.45 vol%. In addition, it is found that heat treatment and its temperature have no effect on the fracture toughness of SCFRTCs. Subsequently, the full-field strain around the crack tip is analyzed by digital image correlation (DIC), and the strain level significantly decreases after adding SCFs. The fracture surface of the SCFRTCs specimen is much rougher compared with HDPE, and obvious bridging SCFs are observed, which make it to absorb more energy for fracture, thus explaining the toughening mechanism of SCFs on SCFRTCs.

Design of an innovative self-compacting material modified with recycled steel fibers and spent equilibrium catalyst for ultra-high performance applications

The main aim of the present study is to design an innovative self-compacting material modified with recycled steel fibers (RSF) from waste tires and spent equilibrium catalyst (Ecat) from the petrochemical industry for ultra-high performance application. For this purpose, 17 different mixtures were developed and analysed using different percentages of RSF (0%-3%) and replacement of cement by different percentages of Ecat (0%-15%).
 The developed mortars' self-compatibility was evaluated in a fresh stage using mini-cone tests. Regarding the hardened stage, the mortars were characterized at the ages of 7 days and 28 days using compression and unnotched flexural tests. The abilities of RSF to increase the post-cracking behavior of the specimens and to use Ecat to increase the bond performance between RSF and the cement matrix were assessed by performing notched three-point bending tests. The results of notched flexural tests were used to obtain the residual flexural strength in service limit state (SLS), ultimate limit state (ULS), and two equivalent flexural strengths.
 The experimental results for the fresh stage demonstrated that inclusion of RSF and Ecat significantly reduced the workability of mortars. The beneficial use of RSF and Ecat was observed to increase compressive strength and flexural strength for 7 days and 28 days of tested specimens. Notched flexural tested specimens showed that the addition of RSF and Ecat can significantly decrease the brittle behavior of cement-based materials by improving its toughness and post-cracking resistance. Middle-span deflection, crack initiation load, and ultimate flexural load were also increased with the addition of RSF and Ecat. In this sense, the results of this research showed that RSF and Ecat seem to have the potential to constitute a sustainable material for structural and nonstructural applications.

Effect of different loading rates on the fracture behavior of FRP‐reinforced concrete

AbstractIn order to study the effect of different loading rates on the fracture behavior of fiber‐reinforced polymer (FRP) reinforced concrete, the fracture experiments of FRP‐reinforced concrete beams under different loading rates were carried out. The calculation method of fracture toughness was given by analytic deduction, and the effects of different loading rates on the fracture parameters were analyzed. The experimental results show that there are three critical points in the fracture process of FRP‐reinforced concrete beam, which are the crack initiation load, crack resistance load, and ultimate load points. The effective crack length at the crack resistance load point increases with the increase of loading rate, and the effective crack length at the ultimate load point does not vary as the loading rate. With the increase of loading rate, the elastic modulus and fracture toughness increase gradually, and there is a logarithmic relationship with the loading rate, which has obvious rate correlation. The fracture process zone (FPZ) length of FRP‐reinforced concrete beams gradually decreases with the increase of loading rate.

A study on the bond strength of interface between post-fire concrete and different epoxy resin adhesives

In order to investigate the influences of temperature that concrete has undergone on the resin/concrete interface bonding performance for different epoxy resin adhesives, 40 tensile specimens and 24 three-point bending specimens were heated to 200, 300, and 600 ℃, respectively. After natural cooling, resin was injected to form tensile specimens and sandwich specimens, which were subjected to pull-out tests and three-point bending tests, respectively. The interface bond-separation constitutive relationship was obtained to study the influence of fire temperature and different epoxy resin adhesives on the properties of the resin/concrete interface bonding. The results showed that the reinforcement of high-temperature concrete with different permeable epoxy resin adhesives caused the crack initiation load, interface strength, and fracture energy of the concrete/resin interface to increase slightly and then decrease sharply as the temperature of the concrete in the fire increased. When the fire temperature was 200 ℃, the peak value of the bonding performance of high-temperature concrete/resin interface was higher than that at room temperature.

Heating-path dependency of fracture behavior of sandstone subjected to thermal treatment

The thermal effect has a negative impact on the strength and fracture properties of rocks, and much related research has been carried out around heat treatment methods such as temperature levels, heating rates and cyclic thermal shocks. In fact, the temperature history to which rocks are subjected is often complex, and the effects of this accumulation of thermal damage on the rock cannot be ignored. In this work, we have carried out three-point bending tests on sandstone subjected to thermal treatments under conventional and complex heating paths based on digital image correlation (DIC) method. The results show that the P-wave velocity, peak load and fracture toughness all tend to decrease with increasing temperature under conventional heating paths, and that 600 °C is the sandstone threshold temperature for strong and weak transformation. Under complex heating paths, a constant temperature of 200 °C for two hours and further heating to the target temperature does not weaken the mechanical properties of the sandstone, whereas a constant temperature of 400 °C for two hours and further heating results in a significant reduction. The variation trend of crack opening displacement (COD) with axial load shows that the cracks transition from slow opening in the early loading stage to rapid propagation near the peak load and develop into decelerated extension in the later stage. Finally, the crack propagation process was refined by determining the jump points of the maximum principal strain at different positions on the crack propagation path. At room temperature, the sandstone cracks at approximately 0.8Pm and propagates at a higher rate, exhibiting clear brittle characteristics. Both the crack initiation load and propagation rate show a significant decrease with increasing temperature after 200 °C, with ductile characteristics gradually becoming apparent.

Initial and unstable fracture toughness of quartz-diorite rock under mixed mode I/II loading: Experimental and numerical investigation

The initiation and propagation of crack in rock bodies is a complex process because the rock is a typical quasi-brittle material. In this study, the fracture process of the specimens under four angles of crack inclination (α = 0°, 15°, 30°, and 46°) was examined using the digital image correlation technique, and, based on the double-K fracture model and linear superposition principle, the initial fracture toughness and unstable fracture toughness of the specimens under different fracture modes were obtained. The crack is in the elastic state when the load is less than the crack initiation load; when the load exceeds the crack initiation load, the crack propagates stably; and when the load reaches the peak load, the crack propagation becomes unstable and uncontrollable, which coincides the principle of the double-K fracture model. The initial fracture toughness (KI,IIini) and crack propagation angle (θ0) of the specimens are consistent with the predictions of the MTS criterion. Furthermore, the fracture of the specimens will transform into pure mode I with the extension of crack though they are initially loaded in the mixed mode I/II or pure mode II conditions. Accordingly, the rock fracture toughness at the peak load, i.e., the unstable fracture toughness (KI,IIun), is controlled by the mode I component (KIun) and shows less dependence on the fracture mode. Finally, it was shown that the MTS criterion coupled with the initial fracture toughness is applicable for simulating the fracture of rock specimens under mixed mode I/II loading.