Three-point Bend Specimens Research Articles

Investigating the influence of geometric configurations and loading modes on mixed mode I/II fracture characteristics of rocks: Part I-Numerical simulation

The influence of geometric configurations and loading modes is a bottleneck that restricts the accurate determination of rock fracture parameters and the precise understanding of fracture mechanisms. Therefore, the phase field method is employed to analyze the influences of specimen geometry and loading modes on the dimensionless stress intensity factors, peak load, fracture toughness, and crack initiation angle during the rock mixed mode I/II fracture process. Three new configurations of specimens are proposed to test rock mixed mode I/II fracture. The research results indicate that as the prefabricated crack inclination angle increases, the peak load of three-point bending type specimen increases, while the peak load of diametric-compression type specimen decreases. Moreover, the influence of geometric configurations on the fracture parameters of three-point bending specimens is greater than that of diametric-compression disk specimens. The research findings of this work can provide basic supporting data for the establishment of mixed mode I/II fracture testing standards.

Characterization of the stress-state dependent ductile fracture behavior for Q960 ultra-high-strength structural steel

Ultra-high-strength structural steels are gaining popularity in civil engineering due to their exceptional strength-to-weight ratio. However, their inherent lower ductility compared to normal strength structural steel warrants particular attention and further investigation for safety assessment. In this study, a total of 24 specimens made of Q960 ultra-high-strength steel (UHSS), including 21 tensile specimens with various stress states and 3 three-point bending specimens, were tested to assess its mechanical behavior undergoing large deformation. Subsequently, the impact of stress state on plasticity, damage evolution and fracture initiation was analyzed and characterized. The Bai-Wierzbicki yield surface with a deviatoric associated flow rule was identified to characterize the complex plasticity behavior of Q960 UHSS. With respect to damage evolution, the stress-state dependent fracture energy Gf was proposed in this study to describe the damage softening behavior. The uncoupled Hosford-Coulomb locus with a non-linear weight function was utilized to predict the fracture initiation behavior. Finally, the utilized stress-state dependent constitutive models for Q960 UHSS, with the calibrated parameters and user-defined material subroutine VUMAT, were successfully verified through the three-point bending test with good agreement. Moreover, based on a parametric analysis of radius-to-thickness ratio, the bendability design regarding the minimum radius-to-thickness ratio of Q960 UHSS was proposed.

Effect of sintering temperature on feature resolution and flexural strength of ceramics fabricated through vat photopolymerization additive manufacturing

PurposeAlthough ceramic additive manufacturing (AM) could be used to fabricate complex, high-resolution parts for diverse, functional applications, one ongoing challenge is optimizing the post-process, particularly sintering, conditions to consistently produce geometrically accurate and mechanically robust parts. This study aims to investigate how sintering temperature affects feature resolution and flexural properties of silica-based parts formed by vat photopolymerization (VPP) AM.Design/methodology/approachTest artifacts were designed to evaluate features of different sizes, shapes and orientations, and three-point bend specimens printed in multiple orientations were used to evaluate mechanical properties. Sintering temperatures were varied between 1000°C and 1300°C.FindingsDeviations from designed dimensions often increased with higher sintering temperatures and/or larger features. Higher sintering temperatures yielded parts with higher strength and lower strain at break. Many features exhibited defects, often dependent on geometry and sintering temperature, highlighting the need for further analysis of debinding and sintering parameters.Originality/valueTo the best of the authors’ knowledge, this is the first time test artifacts have been designed for ceramic VPP. This work also offers insights into the effect of sintering temperature and print orientation on flexural properties. These results provide design guidelines for a particular material, while the methodology outlined for assessing feature resolution and flexural strength is broadly applicable to other ceramics, enabling more predictable part performance when considering the future design and manufacture of complex ceramic parts.

Evolution of fracture process zone and variation of crack propagation velocity in sandstone

To solve the safe containment and recovery efficiencies of gas in rock masses, a study on fracture process zone (FPZ) and crack propagation is conducted. By using digital image correlation technology, the displacement of three-point bending specimens was measured. By analyzing the distributions of displacement at different loading stages, a specific region between the pre-crack tip and the loading point was divided into three zones: the intact zone, the crack propagation zone, and the FPZ. The length and the migration velocity of FPZ were determined, and the crack propagation velocity was also measured. The microstructures in FPZ were investigated through optical microscopy, x-ray diffraction analysis, and x-ray photoelectron spectroscopy. The results show that (1) FPZ length slightly varies during crack propagation and the FPZ is fully formed at the peak load; (2) the average value of the bond energy (446.7 eV) in the grains is greater than that (296.7 eV) in the matrix, thus the microdamage appears in the matrix around grain boundaries in FPZ; (3) the mean FPZ length varies from 4.09 to 8.42 mm for all tested specimens during crack propagation; (4) the propagation of the crack and the migration of FPZ proceed simultaneously in the loading process, and both velocities of crack propagation and FPZ migration are almost the same and with the same trend; (5) the peak velocity of crack propagation appears after the peak load, and the crack propagation progress was intermittent due to fracture energy accumulation, fracture energy release, and FPZ's shielding effect.

Blind prediction of fracture in an additively manufactured geomaterial using the finite discrete element method

Modeling fracture and damage processes is a challenging, yet critical capability for promoting safe and sustainable design in geotechnical, energy, and hydrological applications. Numerical methods capable of modeling fracture processes are rarely asked to make blind predictions against experimental observations. Here, we report results from a numerical study of blind fracture prediction in an additively manufactured, three-point bend specimen. We record a number of physical mechanisms associated with the fracture of the specimen and make a blind prediction against experimental results that were unknown when the numerical study was performed. We then compare results from our model to the blind data set. We find that the combined finite discrete element method performs exceptionally well in the simulation and prediction of fracture processes.

Numerical simulations on the structural heterogeneity and fracture bias effect of three-point bending specimen

Granite is a common surrounding rock in tunnels, nuclear waste repositories, and other underground engineering. It is essential to investigate granite’s mechanical behavior and fracture mechanism at the mesoscale. In this paper, the three-point bending model considering granite meso-heterogeneity was constructed, and the three-point bending test and acoustic emission (AE) simulation were carried out under different crack sizes and porosities, different prefabricated fracture offset distances, and bedding conditions. The results show that large-size mineral particles and intrinsic fractures mainly determine the sample’s crack propagation pattern. As the prefabricated crack’s deviation distance increases, the sample’s peak load, fracture energy, number of AE events, and internal damage range all gradually rise. The sample’s crack propagation path has a distinct step shape due to bedding, and tensile fractures primarily occur in the through-layer crack, whereas shear fractures mainly occur at the bedding plane. The specimen’s surface crack’s fractal dimension is positively associated with the cumulative acoustic emission energy during the fracture process. The conclusion of the research can offer a theoretical foundation for analyzing the stability of the surrounding rock.

Investigating the influence of various three-point bending specimen configurations on rock fracture parameters testing: an experimental study

The fracture parameters of rocks, including fracture toughness and fracture energy, represent their resistance to crack propagation under external stress. These parameters play a critical role in engineering design, construction safety, geological mechanics research, and rock material assessment. This study determined the fracture parameters of granite under Mode I loading conditions using notched semicircular bend (NSCB) and single-edge notched beam (SENB) specimens. Although there was little difference between the initial and unstable fracture toughness values of the two specimen configurations, significant differences were observed in the fracture process and other fracture parameters. For example, the NSCB specimen exhibits a higher elastic modulus, and it witnessed rapid failure after reaching the peak load, whereas the SENB specimen displayed a more gradual failure process with a distinct post-peak stage. This may be one of the reasons for the higher fracture energy in the NSCB specimen than in the SENB specimen. Based on finite element analysis and the extraction of the tangential stress at the crack tip region, the application of the maximum tangential stress fracture criterion provided a robust explanation for the coherence observed in the unstable fracture toughness test results between the two specimen configurations.

Experimental and numerical insights into fatigue crack propagation of railway component with gradient residual stress

As a representative structure with an acute radial gradient in terms of residual stress (RS) and grains, the induction-hardened railway S38C axle exhibits excellent mechanical properties and fatigue resistance. To investigate the effect of gradient features on fatigue crack growth (FCG) behaviors, we designed three-point bending (TPB) tests with different gradient features, including the negative-gradient, positive-gradient, and matrix specimens. Finite element modeling was introduced to simulate the FCG of the TPB specimens in terms of the cyclic J-integral (ΔJ) and equivalent plastic strain at the growing crack tip. The results reveal that the FCG rates in both negative- and positive-gradient structures decrease and a more pronounced tendency of decline is achieved in the positive-gradient ones. The substantial compressive residual stress (CRS) within the negative-gradient structure directly influences the crack tip area, while the CRS in the positive-gradient structure indirectly mitigates the crack driving force by impeding the overall structural deformation. Coarser grains aid in enhancing energy absorption along the zigzag crack path, thereby diminishing the crack driving force. ΔJ and the equivalent plastic zone surrounding the crack tip indicate significant reductions in the presence of CRS.

Development of a Novel Lightweight Utility Pole Using a New Hybrid Reinforced Composite—Part 1: Fabrication and Experimental Investigation

This paper is the first part of a two-part paper that discusses the development of a novel lightweight and cost-effective hybrid 3D composite material and its and utilization for constructing utility poles. The main objective was to generate a material/pole with a comparable performance to the commercially available poles made of 2D fiber-reinforced polymer (FRP) and examine its feasibility. The novel hybrid composite was configured using a recently developed and marketed 3D E-glass fabric–epoxy composite reinforced with wood dowels, referred to as 3D dowel-reinforced FRPs (3D-drFRPs) hereafter. Firstly, the compressive and flexural properties of the 3D-drFRPs are evaluated. Then, the development of the 3D pole is discussed followed by the fabrication details of two 3D-drFRPs using the standard test method, and their responses are compared. For the second part, robust finite element (FE) models were developed in an LS-DYNA environment and calibrated based on the experimental results. A sophisticated nonlinear FE model was used to simulate the performances of ASTM standard-size compression and three-point bending specimens and tapered 2D and prismatic 3D poles. Moreover, the responses of equivalent 2D and 3D poles were simulated numerically, as the task could not be accommodated experimentally due to our laboratory’s deficiencies. The integrity of the numerical simulation results was validated against experimental results, confirming the accuracy of the developed model. As an example, the stiffness values for the 3-pt bending specimens and the 3D poles obtained through the simulations were very close to the experimentally obtained results, with small margins of errors of 3.2% and 0.89%, respectively. Finally, a simplified analytical calculation method was developed so practicing engineers can determine the stiffnesses of 3D-DrFRP poles very accurately and quickly.

Fatigue Life Prediction for Injection-Molded Carbon Fiber-Reinforced Polyamide-6 Considering Anisotropy and Temperature Effects.

The effects of anisotropy and temperature of short carbon fiber-reinforced polyamide-6 (CF-PA6) by the injection molding process were investigated to obtain the static and fatigue characteristics. Static and fatigue tests were conducted with uniaxial tensile and three-point bending specimens with various fiber orientations at temperatures of 40, 60, and 100 °C. The anisotropy caused by the fiber orientations along a polymer flow was calculated using three software connecting analysis sequences. The characteristics of tensile strength and fatigue life can be changed by temperature and anisotropy variations. A semi-empirical strain-stress fatigue life prediction model was proposed, considering cyclic and thermodynamic properties based on the Arrhenius equation. The developed model had a good agreement with an R2 = 0.9457 correlation coefficient. The present fatigue life prediction of CF-PA6 can be adopted when designers make suitable decisions considering the effects of temperature and anisotropy.

Structural size effect in the mode I and mixed mode I/II fracture of strain-hardening cementitious composites (SHCC)

The size effect in the fracture of solids represents a highly critical issue with a prolonged history of research. The size effect of traditional quasi-brittle materials can already be well described through the size effect model. However, there is still a lack of research on the size effect of strain-hardening cementitious composites (SHCC), a special type of fibre-reinforced concrete with macro-scale strain-hardening behaviour after first cracking. Being distinct from traditional quasi-brittle materials with softening nature, SHCC is thus expected to behave differently in terms of size effect. In this research, the structural size effect problem of SHCC is comprehensively studied by experimental investigation and theoretical analysis. Geometrically similar notched three-point bending specimens were tested in mode I and mixed mode I/II fracture condition. The whole-process of failure and matrix cracking zone around the main crack was captured with high resolution by digital image correlation technology. Experimental results showed that apparent fracture energy, nominal strength, structural ductility and fracture resistance curve are all structural size-dependent. The apparent fracture energy was shown to arise with specimen size within the tested range. This is related to large-scale pseudo yielding, i.e., enlargement of matrix cracking zone (like the yielding zone in metals) with increasing structural size. It thus provides an indirect method for the estimation of cohesive fracture energy of single crack with constitutive nature. Due to the scaled matrix cracking zone, an intermediate asymptote exists in the size effect curve of nominal strength, in addition to the plastic and LEFM asymptotes in the Bažant original size effect law. This resembles the recent finding of intermediate asymptote in plastic-hardening metal. The size-dependence of R-curve was also examined. Though size-dependent, the equivalent LEFM-based R-curves are shown to have three common stages reflecting different cracking processes. Based on experimental results, the size effect of fracture energy and nominal strength are finally modelled theoretically in the Bažant’s framework of equivalence between energy release and fracture resistance.

Influence of specimen geometry on the energy release rate in concrete

The energy release rate during the crack propagation in concrete was studied using three-point bending (TPB) beams with different geometries. Expressions for determining the energy release rate were established. A total of 44 beams, i.e., TPB specimens with the height of 150 mm and various spans and the same span of 800 m but different heights, named as Series-T and Series-TH, respectively, were tested. The obtained results reveal that (1) with the crack propagation, the energy release rate curves (GR-curves) monotonically increased and convergence to the fracture energy of each specimen, and the average values were 161.136 N/m and 112.343 N/m for Series-T and Series-TH. (2) For Series-T, with increasing the specimen span from 300 mm to 900 mm, the maximum fracture process zone (FPZ) length kept constant of 68.317 mm, and for Series-TH, the result increased by 187.6 % with increasing the specimen height from 100 mm to 300 mm. Moreover, the relative FPZ length was not affected by the spans and depths of the specimens. (3) The evolution of crack tip opening displacement was only affected by the specimen ligament length, i.e. for the same crack extension length, a larger value was noticed for longer ligament length. (4) The stability during crack propagation can be analyzed using GR-curves.

Enhanced flexural strength-to-weight ratio of Inconel718 lattice structure parts made of powder bed fusion process

The present work investigates the enhancement of the flexural strength-to-weight ratio on the lattice structure of additively manufactured Inconel-718 parts made using the powder bed fusion (PBF) process. ASTM-E290 standard three-point bending experiments and finite element modeling were conducted on solid and lattice structure parts. Four novel lattice structure unit cells with positive Maxwell’s number for stretch-dominant mechanical behavior were designed and used in the three-point bending specimens. The different lattice structure types investigated are strengthened-cubic (named Model_1), strengthened-cubic + kagome (named Model_2), strengthened-cubic + octet truss (named Model_3), and strengthened-cubic + kagome+octet truss (named as Model_4). Results obtained for the lattice structure specimens were compared with those obtained for solid specimens. The study revealed significant differences in strength-to-weight ratio among them, proving the tremendous potential of lattice structures in flexural loading applications by giving higher strength-to-weight ratios than solid specimens. Out of the four lattice structures and one solid structure investigated, Model_2 with only angular beams and Model_3 with only interior beams gave a better strength-to-weight ratio than solid specimens. Model_2 and Model_3 have beams along the unit cell’s body diagonal, leading to better performance. Out of all the lattice-structured specimens, Model_2 showed the highest strength-to-weight ratio. In the finite element model, the maximum equivalent strain was used as the criterion for failure. The failure sites found by finite element simulation coincided with those in the experiments.

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.

Three-dimensional discrete element model of crack evolution on the crack tip with consideration of random aggregate shape

In this paper, a method for concrete three-dimensional random polyhedral aggregate mesostructure is proposed. Moreover, a concrete discrete element fracture mesoscopic analysis model is established. The mesoscopic destruction mechanism of three-dimensional fracture of concrete three-point bending specimens is investigated. Three-dimensional evolutionary extension morphology of crack tip and fracture process zone (FPZ) of small-size concrete specimens in an indoor laboratory is simulated and analyzed. Furthermore, the entire fracture process of concrete specimens is investigated. The three-dimensional morphology of the crack tip and fracture process zone is analyzed via normal distribution statistics. Consequently, the size effect law of crack extension and fracture process zone evolution is derived. The fracture process of actual large-scale concrete specimens is predicted based on deficiencies of small-scale specimens in indoor tests. The results show that the proposed model is an effective method to characterize the three-dimensional fracture process of concrete and predict mechanical properties of large-scale specimens in actual structures.

Pressure reduction strategy based on a new CTOD model considering room temperature creep for X80 pipeline steel

The growing demand for energy consumption has led to the rapid development of high strength and high toughness pipeline steel technology, with fracture toughness being a crucial factor in evaluating the mechanical properties of pipeline steel. Despite experimental studies demonstrating that metallic materials, including pipeline steel, undergo creep at room temperature, the effects of room temperature creep (RTC) on pipeline steel fracture properties are still relatively unexplained. This study analyzes the impact of RTC on the fracture toughness of X80pipeline steel, using the X80pipeline steel base material as the research object. Firstly, the time-dependent change in crack notch opening displacement is added to the calculation formula for fracture toughness of three-point bending specimens, considering the effect of RTC. The test data is fitted to a power-law equation of the form, where k=0.01423 and m=-0.89651, with the improved formula indicating an incremental CTOD of approximately 0.0098 mm after 36 h of RTC for X80 pipeline steel. Secondly, a time-dependent CTOD model is proposed based on the ductile defect growth model, with the plastic part derived from the D-B model and the creep part obtained by fitting the test data. The study proposes a CTOD criterion for RTC and a pressure reduction strategy based on this criterion, providing a reference for quantitatively assessing the fracture toughness of pipeline steel under RTC conditions.

Influence of chopped basalt fibers on the fracture performance of concrete subjected to calcium leaching

Calcium leaching is one of the major causes of concrete structure failure in soft water environments. In this study, acceleration leaching and three-point bending (TPB) tests were conducted on single-notched TPB specimens to investigate the influence of chopped basalt fibers (CBF) on the fracture performance of concrete subjected to calcium leaching. The fracture-related parameters such as crack initiation and maximum loads, fracture toughness, elastic modulus, tensile strength, and fracture energy of CBF concrete (with ten different fiber length and volume dosage addition combination schemes) under calcium leaching effect were determined and compared based on the test results. Furthermore, the mechanism of CBF for improving the crack and leaching resistance of concrete were analyzed based on the stress intensity factor superposition method and microscopic test results. The results show that a suitable combination of CBF length and volume dosage can effectively improve concrete fracture resistance when subjected to calcium leaching. Too long and excessive fiber additions can result in increased concrete weaknesses, as well as fiber agglomeration and crossover, making CBF less effective in enhancing concrete resistance to calcium leaching and fracture. The addition of CBF to concrete with a length of 6 mm (i.e., aspect ratio is 400) and a volume dose of about 0.35% was determined to be the optimal scheme for improving concrete’s resistance to calcium leaching and fracture, and the comprehensive performance of concrete was improved by approximately 17.68% with this scheme.

Experimental and numerical investigation of mechanical behavior of plain woven CFRP composites subjected to three-point bending

The mechanical behavior of plain woven Carbon Fiber-Reinforced Polymer (CFRP) composites under Three-Point Bending (TPB) is investigated via experimental and numerical approaches. Multiscale models, including microscale, mesoscale and macroscale models, have been developed to characterize the TPB strength and damages. Thereinto, Representative Volume Elements (RVEs) of the microscale and mesoscale structures are established to determine the effective properties of carbon-fiber yarn and CFRP composites, respectively. Aimed at accurately and efficiently predicting the TPB behavior, an Equivalent Cross-Ply Laminate (ECPL) cell is proposed to simplify the inherent woven architecture, and the effective properties of the subcell are computed using a local homogenization approach. The macroscale model of the TPB specimen is constructed by a topology structure of ECPL cells to predict the mechanical behavior. The TPB experiments have been performed to validate the multiscale models. Both the experimental and numerical results reveal that delamination mainly appears in the top and bottom interfaces of the CFRP laminates. And matrix cracking and delamination are identified as the significant damage modes during the TPB process. Finally, the quasi-static and dynamic behaviors of plain woven composites are discussed by comparing the results of Low-Velocity Impact (LVI) and TPB simulations.

Study on mode I dynamic fracture characteristics with a mini three-point bending specimen for the split Hopkinson bar technique

In recent years, dynamic fracture experimental techniques have been developed rapidly in the field of engineering and scientific research. However, there still exist some difficulties in dynamic fracture tests, such as the limitation of loading rate, the accuracy of transmitted wave, the difficulty of crack initiation, and etc. To solve such problems, a novel mode I dynamic fracture experimental technique is proposed in this work, with a mini three-point bending(3PB) specimen and two kinds of fixtures specially designed for the split Hopkinson pressure bar (SHPB) system. In this method, the dynamic stress intensity factor curve (DSIF) is obtained by the experimental-numerical method, and the crack initiation time is determined by the strain gauge method. To verify the feasibility and reliability of the proposed method, the dynamic fracture toughness (DFT) of two kinds of ultra-high-strength steel (UHSS) is determined by this new method and then compared with the results of other methods. Meanwhile, the loading rate effect of fracture toughness, the size effect of crack initiation time and the failure mechanisms of the two materials under mode I fracture are also studied. The results show that fracture toughness depends on the energy consumed to form two types of fracture regions within the fracture initiation time. This work provides a new method for studies of the dynamic fracture behaviors of brittle solids.

Preparation and Thermo-Mechanical Characteristics of Composites Based on Epoxy Resin with Kaolinite and Clinoptilolite.

Herein the synthesis, characterization, and study of spectroscopic, thermal, and thermo-mechanical properties of polymeric composites are presented. The composites were obtained in special molds (8 × 10 cm) based on the commercially available epoxy resin Epidian® 601 cross-linked by 10% w/w triethylenetetramine (TETA). To improve the thermal and mechanical properties of the synthetic epoxy resins, natural fillers in the form of minerals from the silicate cluster kaolinite (KA) or clinoptilolite (CL) were added to the composites. The structures of the materials obtained were confirmed by attenuated total reflectance-Fourier transform infrared spectroscopy (ATR/FTIR). The thermal properties of the resins were investigated by differential scanning calorimetry (DSC) and dynamic-mechanical analysis (DMA) in an inert atmosphere. The hardness of the crosslinked products was determined using the Shore D method. Moreover, strength tests were performed on the 3PB (three-point bending) specimen, with the analysis of tensile strains conducted using the Digital Image Correlation (DIC) technique.