Fracture Curves Research Articles

A nonlinear elastic-plastic model describing the bending and fracture behavior of Caragana korshinskii Kom. branch wood

ABSTRACT Caragana korshinskii Kom. branch (CKB), a vital biomass source in northwest China, has not been thoroughly studied in terms of its bending fracture mechanics. This research aims to establish a nonlinear constitutive model that clarifies the fracture behavior of CKB when subjected to bending loads. The nonlinear bending fracture process of CKB was characterized through a three-point bending test, revealing stages of elastic deformation, elastic-plastic transition, and plastic fracture. A power-enhanced elastic-plastic model combined with continuous damage mechanics theory was used to develop an intrinsic bending fracture model, from which the equations governing bending damage evolution were derived. The model's accuracy was validated with simulations in Abaqus/Explicit, showing that CKB from various growth sites demonstrated distinct nonlinear bending behaviors. At the critical damage strain, cumulative damage led to a reduction in the effective elastic modulus, with the bending fracture curve exhibiting a power function trend. The parameters of the nonlinear elastic-plastic constitutive model were derived through curve fitting, yielding coefficients of determination (R²) exceeding 0.99. The consistency between the trends observed in actual tests and simulations, along with a peak bending force error of 7.7%, validated the finite element model's reliability and confirmed the intrinsic model's accuracy.

Green syntheses of silk fibroin/wool keratin-protected Au[sbnd]Ag nanoclusters with enhanced fluorescence for multicolor and patterned anti-counterfeiting

Counterfeiting is a serious worldwide issue that threatens human health and economic security. How to apply anti-counterfeiting techniques to textile materials remains a great challenge. Herein, we report bimetallic AuAg nanoclusters (NCs) synthesized by one-step reduction of chloroauric acid (HAuCl4) and silver nitrate (AgNO3) with wool keratin (WK) as reducer and silk fibroin (SF) as stabilizer. The strongest orange-red fluorescence under ultraviolet light as well as the highest zeta potential absolute values of −27.97 mV were simultaneously realized in the optimal proportion Au-AgNCs2 (WK/SF is 3/2), which was further processed to a series of anti-counterfeiting films by blending with SF, silk sericin (SS), and polyvinyl alcohol (PVA). After successfully being numbered into fifteen colors, a dark blue-orange-dark red-dark blue cyclic fluorescent anti-counterfeiting color chart was designed. In addition, a two-Maxwell-unit model was constructed to assist with the microstructure analysis, which found that the formation of hydrogen bonds and the secondary structure transition from α-helices to β-sheets during stretching were responsible for improving the mechanical properties and the two-staged fracture curves of films, respectively. Finally, a patterned and multicolor fluorescence anti-counterfeiting fabric application was demonstrated by combining the color chart and screen printing, indicating the great potential in textile anti-counterfeiting.

The influence of recycled asphalt pavement materials on low and intermediate fracture behavior of asphalt concrete (AC) after exposing to different thawing and freezing periods

The effects of compaction process, mixture type and environmental conditions on mode I cracking resistance of asphalt concrete (AC) materials was investigated experimentally. To do that, a large number of edge notched disc bend specimens containing 0, 25 and 50% recycled asphalt mixture (RAP) material and exposed to different numbers of thawing and freezing cycles (0 to 10 cycles) were fractured. The critical values of stress intensity factor and fracture energy indexes were obtained for the AC mixtures at three test temperatures of −25, 0 and + 25 °C. Based on the results, the fracture resistance capacity of the AC mixture was decreased by increasing the RAP content, number of thawing/freezing cycles and decreasing the test temperature. The effect of thawing/freezing cycles on decreasing the cracking resistance was more pronounced for the first cycles and the variations of fracture toughness and fracture energy values with the numbers of thawing/freezing cycles showed a plateau form for higher numbers of cycles. The fracture curves of the tested samples manufactured using the Gyratory compaction method was upper than the related curves of samples made by Marshall compaction method. The sensitivity of fracture results (i.e., gradient of reduction in the fracture resistance versus freeze/thaw cycles) became low by increasing the test temperature.

DFNMesh: Finite element meshing for discrete fracture matrix models

This paper presents a novel methodology for robust Finite Element (FE) mesh generation of Discrete Fracture Matrix (DFM) models. The method can handle the complete multi-dimensional domain from the tridimensional porous rock matrix, through fracture surfaces, down to open curves for fracture–fracture intersections. The accompanying open-source code is written in modern C++ with a JSON interface and largely relies on two state-of-the-art FE libraries: NeoPZ and Gmsh. Starting from a user-defined coarse mesh, fractures are sequentially read as convex polygons and introduced without distortions to the coarse geometry. The main steps involve: intersect edges by checking for nodes on opposite sides of the fracture plane, extend intersections from edges to faces, coalesce intersections to closest existing nodes (given a tolerance), refine interface elements to conform to the fracture, identify subsets of fracture surface, mesh the surface, and locate boundaries and intersections where they arise. Finally, the space around fractures is filled with the fine-scale unstructured mesh, which is kept conformal. The robustness of the implementation is derived from the consistent background of well-defined and simple premises like convexity and side-specific element neighborhood. Results show that the proposed technique can construct adequate 3D DFM grids, while still giving users freedom to adjust between geometrical fidelity and mesh quality through more aggressive feature rejection.

Influence of Horizontal Multi-Bedding on Hydraulic Fracture Propagation in Shale Reservoirs

Artificial fractures can easily occur and propagate in shale reservoir bedding. Their height restricts the volume of fracturing modification. A physical simulation of true triaxial hydraulic fracturing was used to analyze the characteristics of fracture morphology and the fracturing curve, as well as explore the influence of horizontal multi-bedding on the hydraulic fracture propagation of shale reservoirs. The results showed that a weaker bedding strength increased bedding fracture activation and reduced the fracture height. A higher bedding density increased the fracture complexity and reduced the main fracture height. A high injection flow can easily cause morphologically complex multi-bedding fractures. A higher injected fracturing-fluid viscosity increased the layer-penetration ability of the main hydraulic fracture when it expanded and reduced the opening degree of the bedding plane. This study provides technical support for the hydraulic fracturing design of shale reservoirs.

Adjusting FRAX Estimates of Fracture Probability Based on a Positive Vertebral Fracture Assessment

FRAX is the most widely used and validated fracture risk prediction tool worldwide. Vertebral fractures, which are an indicator of subsequent osteoporotic fractures, can be identified using dual-energy x-ray absorptiometry (DXA) vertebral fracture assessment (VFA). To assess the calibration of FRAX and develop a simple method for improving FRAX-predicted fracture probability in the presence of VFA-identified fracture. This prognostic study analyzed the DXA and VFA results of all individuals who underwent a VFA between March 31, 2010, and March 31, 2018, who were included in the Manitoba Bone Mineral Density Registry. These individuals were randomly assigned to either the development cohort or validation cohort. A modified algorithm-based qualitative approach was used by expert readers to code VFAs as positive (≥1 vertebral fractures detected) or negative (0 vertebral fracture detected). Statistical analysis was conducted from August 7, 2022, to May 22, 2023. FRAX scores for major osteoporotic fracture (MOF) and hip fracture were calculated with or without VFA results. Incident fractures and death were ascertained using linked population-based health care provincial data. Cumulative incidence curves for MOF and hip fracture were constructed, including competing mortality, to predict the 10-year observed risk of fracture. The observed probability was compared with FRAX-predicted fracture probability with and without VFA results and recalibrated FRAX from derived multipliers. The full cohort of 11 766 individuals was randomly allocated to the development cohort (n = 7854; 7349 females [93.6%]; mean [SD] age, 75.7 [6.8] years) or the validation cohort (n = 3912; 3713 females [94.9%]; mean [SD] age, 75.5 [6.9] years). Over a mean (SD) observation time of 3.8 (2.3) years, with the longest observation at 7.5 years, FRAX was well calibrated in subgroups with negative VFA results. For individuals without a prior clinical fracture but with a positive VFA result, the 10-year FRAX-predicted MOF probability was 16.3% (95% CI, 15.7%-16.8%) without VFA information and 23.4% (95% CI, 22.7%-24.1%) with VFA information. The observed 10-year probabilities were 26.9% (95% CI, 26.0%-27.8%) and 11.2% (95% CI, 10.3%-12.1%), respectively, resulting in recalibration multipliers of 1.15 (95% CI, 0.87-1.43) for MOF and 1.31 (95% CI, 0.75-1.87) for hip fracture. For individuals with a prior clinical fracture and a positive VFA result, the 10-year FRAX-predicted probabilities were 25.0% (95% CI, 24.2%-25.7%) for MOF and 9.3% (95% CI, 8.7%-10.0%) for hip fracture. The observed 10-year probabilities were 38.1% (95% CI, 37.0%-39.1%) for MOF and 16.4% (95% CI, 15.4%-17.4%) for hip fracture, resulting in a recalibration multiplier of 1.53 (95% CI, 1.10-1.96) for MOF and 1.76 (95% CI, 1.17-2.35) for hip fracture. Good calibration (>0.90) was confirmed using the derived multipliers in the validation cohort. Results of this prognostic study suggest that FRAX underestimated fracture risk in patients with VFA-identified fractures. Simple multipliers could recover FRAX calibration in individuals with VFA-identified fractures.

Effect of Thermal Aging on the Interfacial Reaction Behavior and Failure Mechanism of Ni-xCu/Sn Soldering Joints under Shear Loading.

Ni-xCu/Sn soldering joints were aged at 200 °C, and the microstructure evolution and mechanical properties during the solid-state reaction were studied under shear loading. Results showed that the intermetallic compounds (IMCs) exhibited a Cu content-dependent transformation from the (Ni,Cu)3Sn4 phase to the (Cu,Ni)6Sn5 phase at the Ni-xCu/Sn interface. Furthermore, a Cu3Sn layer was observed exclusively at the Cu/Sn interface. The shear strength of the soldering joints after thermal aging exhibited an initial decrease followed by an increase, except for a significant enhancement at the Cu content of 60 wt.%. In addition, the evolution law of mechanical properties and failure mechanism of the thermal aging joints were elucidated based on the fracture microstructure and the fracture curve of the joints.

Experimental study of hydraulic fracturing initiation and propagation from perforated wellbore in oil shale formation

Perforation hydraulic fracturing is essential in developing unconventional oil and gas resources. This study scales the critical parameters to simulate operations at the field scale, using a true triaxial hydraulic fracturing experimental system to mimic actual far-field stress conditions. The research simulates various scenarios of perforation and fracturing fluid parameters, which significantly influence fracture propagation behaviour and fracture network morphology. The results showed that the initiation pressure required for fracturing with perforation is 20.91% lower than that of open-hole fracturing. Multiple fractures, including bedding and branch fractures, exhibit cross-propagation behaviour, forming barrier-type morphology. Induced by perforation, hydraulic fracture initiation and propagation occur along the direction of maximum geo-stress, but unreasonable orientation and reduction in perforation length can also increase initiation pressure. The flow rate and viscosity of fracturing fluid are positively proportional to the initiation pressure. A high flow rate of 100 mL/min facilitates the generation of bedding fractures, enhances the bedding fractures connectivity and increases fracture network complexity. However, the increase in viscosity forces hydraulic fracture to penetrate the bedding plane directly and diminishes the complexity of the fracture network. Compared to the pressure build-up phase, fluctuations in the fracturing curve during the propagation phase are significantly related to the complexity of the fracture network. Small-scale structural surfaces developed within the strata can become part of the hydraulic fractures and increase the fracture network complexity. Additionally, the hydraulic fractures are captured and hindered by large-scale structural surfaces, forming a single fracture morphology. The findings significantly aid in predicting fracture propagation and fracture network morphology in oil shale exploitation.

Corrosion Behavior and Simulation Analysis of Silicate Adhesive under High Temperature and Abrasion-Acid Environment

For studying the corrosion behavior and simulation analysis of silicate adhesive under high temperature and abrasion-acid environment, the corrosion behavior of silicate adhesive was tested with mechanical compression, scanning electron microscopic and X-ray diffraction (XRD), and analyzed under high temperature with finite element modeling. The results showed: under high temperatures and the abrasion-acid environment, the solid filler in the adhesive network structure will be exposed with the effect of particle wear. This will lead to a corrosion reaction between some fillers and hydrochloric acid, making dissolution loss. Large hollow holes will be formed at the loss part with the deepening of corrosion, the internal interconnection will occur, and the compression fracture curve characteristics of porous materials will appear, which will greatly reduce the compression strength of the materials. In special environments (temperature 200°C, flow rate 2m/s, and 31% concentration acid solution), hydrochloric acid corrosion is the control factor of silicate adhesive degradation.

Deep ensemble learning for quantitative geological fracture analysis using borehole televiewer images

In the geological survey of hydraulic engineering projects, the Borehole televiewer (BHTV) technique is applied widely. The BHTV images are usually interpreted by engineers. To improve the automatic level of geological images analysis and decrease the subjective influence of the engineers, a fracture quantitative approach based on deep ensemble learning is proposed. In the research, the BHTV images' segmentation using the ensemble model is the basis of the fracture quantitative analysis. Therefore, the accuracy of segmentation can not be ignored. In the experimental study, the different deep learning architectures, UNet, SegNet, and FRRN based on VGG and ResNet, are employed. The evaluation result shows that the IoU values of the single models are in the range of 83.96%–84.36%, while the ensemble model outperforms all of them with a mean IoU of 86.36% and ranks top-3 for the all testing images. Through comparison of the segmentation for the single image, it is evident that the ensemble model is effective for noises removal, which improves the accuracy and efficiency of fracture parameter quantitative analysis. Finally, the thinning method and sine function based on Hough Transform (HT) and the generalized least squares (GLS) are adopted to fit the fracture curve. The calculation result of the dip azimuth, dip angle, and mean thickness also validates the effectiveness of the ensemble model.

Combining machine learning and physics modelling to determine the natural cave property with fracturing curves

Currently, it is still challenging to determine the geological parameters of natural caves in deep reservoirs accurately. By inheriting the advantages of Machine Learning (ML) method and physics modelling, a novel ML-Physics method is developed to determine the geological parameters of natural caves based on the data mining of fracturing curves obtained during Hydraulic Fracturing (HF) operation. The computational time of ML-Physics method is divided into two stages, preparation-stage and operation-stage. The preparation-stage happens before HF operation, therefore there is no limitation to the computational time. During this preparation-stage, the implicit relationship between cave property and fracturing curve is generated using ML, which usually fails to ensure the accuracy under different geological and operational conditions. The operation-stage happens during HF operation, in which the computational time is limited because the geological parameters of natural caves are required to be determined in real time. During this operation-stage, the physical modelling based inverse analysis method is carried out, in which the initial value is chosen based on the ML results obtained in preparation-stage. Results show that, with the same target error, the iteration step of ML-Physics method (1 iteration) is much less than that of traditional inverse analysis method (5 iterations). After the same iterations, the error of fracturing curve using the traditional inverse analysis method is 0.40%, while the error using ML-Physics method is 0.02%. Meanwhile, the error of permeability using the traditional ML is up to 10.33%, while the error of ML-Physics method is 0.29%. The present ML-Physics method is potentially useful to optimize the HF design based on the data mining of fracturing curves in real time.

Investigation into the Time-Dependent Crack Propagation Rate of Concrete.

Mass concrete structures under long-term loads are susceptible to time-dependent fractures, which pose a threat to their structural integrity and safety. In order to study the crack growth rate of concrete materials under long-term constant load, the data were processed according to the calculation method of fatigue crack growth rate. The relationship between the crack growth rate and strength factor in the stable growth stage was obtained using the Paris formula. The experimental data and theoretical analysis show that the time-dependent fracture curve CMOR(t)-t of the standard three-point bending beam specimens could be divided into three stages. The relationship between the crack propagation rate da/dt(t) in the second stage and the intensity factor K(t) could be well described by the Paris formula. The life of crack growth of a standard three-point curved beam is inversely proportional to the level of constant load. These conclusions can provide data support for further studies on crack extension life under long-term constant load.

Viscoelastic tensile model of core/wrapped composite yarn with double filament

Viscoelastic models are typically employed to investigate the mechanical properties of yarn. In this study, a viscoelastic model was developed to predict the tensile stress–strain relationship of a core/wrapped composite yarn with double filaments. The tensile properties of the yarn were tested, and various stages of the tensile curve were analyzed. Moreover, based on the tensile fracture characteristics, a five-element nonlinear viscoelastic model comprising Kelvin element, Maxwell element, and linear springs was established. Furthermore, the tensile properties of the composite yarns were simulated and calculated using the developed model. Additionally, the stress–strain relationship was fitted using a polynomial on the basis of the established model. The results reveal that the tensile fracture curve of the composite yarn comprises three stages. They are a small strain linear stage, a large strain stage, and a strength fluctuation stage. The viscoelastic tensile model can decently explain the three-stage stress–strain characteristics of the composite yarn tensile curve. The theoretical results were consistent with the experimental results, and the correlation coefficient was greater than 0.999. Based on the results, the proposed model can be employed with high accuracy to predict the tensile properties of a core/wrapped composite yarn with a double filament.

Assessment Effect of Nanometer-Sized Al2O3 Fillers in Polylactide on Fracture Probability of Filament and 3D Printed Samples by FDM

In this paper, a mathematical model for the description of the failure probability of filament and fused deposition modeling (FDM)-printed products is considered. The model is based on the results of tensile tests of filament samples made of polyacrylonitrile butadiene styrene (ABS), polylactide (PLA), and composite PLA filled with alumina (Al2O3) as well after FDM-printed products of "spatula" type. The application of probabilistic methods of fracture analysis revealed that the main contribution to the reduction of fracture probability is made by the elastic and plastic stages of the fracture curve under static loading. Particle distribution analysis of Al2O3 combined with fracture probability analysis shows that particle size distributions on the order of 10-5 and 10-6 mm decrease the fracture probability of the sample, whereas uniform particle size distributions on the order of 10-1 and 10-2 mm do not change the distribution probability. The paper shows that uneven distribution of Al2O3 fillers in composite samples made using FDM printing technology leads to brittle fracture of the samples.

Fracture characteristics of various concrete composites containing polypropylene fibers through five fracture mechanics methods

Abstract This paper investigates and compares the experimental results of fracture characteristics in various polypropylene fiber-reinforced concretes (high strength concrete, lightweight concrete, and engineered cementitious composite) on 90 three-point bend (notched and un-notched) beams. Five widely used fracture mechanics testing methods, such as work of fracture method, stress-displacement curve method, size effect method, J integral method, and ASTM E399, were used to investigate the fracture behavior. Results have demonstrated that fracture energy and fracture toughness improved as the dosage of polypropylene fibers increased in concretes. However, this improvement was different in concretes owing to various results of fracture mechanics testing methods and different properties of each concrete. Aggregates played significant role in the performance of polypropylene fibers on the fracture behavior of concretes. Among testing methods, the ASTM E399 showed the lowest values for the fracture toughness of concretes. Both work of fracture and stress-displacement curve methods exhibited appropriate results for the fracture energy of polypropylene fiber-reinforced concrete composites. The accuracy of size effect method was acceptable for determining size-independent fracture parameters of plain high strength and lightweight concretes. Furthermore, the J integral method showed more relevant results for the fracture toughness of polypropylene fiber-reinforced engineered cementitious composite.

REFINED ENGINEERING THEORY OF FRACTURE WITH A TWO-PARAMETER STRENGTH CRITERION

We present a refined engineering theory of cracks, based on a two-parameter strength criterion. Unlike the basic theory, the refined approach utilizes an improved algorithm for the regular stress component computation. This improvement allows extending the applicability range of the engineering theory to longer cracks. The two-parameter Leonov-Panasyuk-Dagdale fracture criterion serves as a basis. A coupled fracture criterion includes a strain-based criterion, which is formulated at the tip of the true crack, as well as a stress-based criterion, formulated at the tip of a fictitious crack. Based on the refined criterion, quasi-brittle fracture curves are constructed for a compact specimen, a strip with an edge crack, and a beam under four-point bending. To validate the new refined fracture criterion, we present simulation results of quasi-brittle fracture for structures made from various virtual materials. The corresponding virtual materials are modeled using a nonlocal damage accumulation theory accounting for the average size of the aggregate state of the material. Additionally, various classes of damage accumulation hypotheses are considered. Analysis of various types of virtual materials provides insights into the impact of hypotheses behind the engineering theory. For each type of material, the influence of the microstructural length scale on the overall structural strength is investigated. The analysis shows that the refined engineering theory has a wider range of applicability as compared to the basic theory based on two-parameter strength criteria.

Empirical mode decomposition approach to simplify the fracture roughness for numerical models

The shear strength of natural, unfilled rock fractures is influenced by surface roughness. The surface curve of a fracture can be viewed as a waveform graph, and in general, it is of the characteristic that high-frequency represents the low amplitude (local variation) and low-frequency represents the high amplitude (general trend). In this work, the signal processing method, Empirical Mode Decomposition (EMD) was employed to decompose the original fracture surface scanned by photogrammetry to several frequency-dependent curves. Low-frequency curves were selected and composed as the element geometry while high-frequency curves were ignored and replaced by parameters related to the roughness in each surface element in Abaqus. The process of push-shear test is simulated using the simplified fracture curve, showing the geometry simplification by EMD can help model the shear failure of rock fractures.

Mixed Mode Fracture Investigation of Rock Specimens Containing Sharp V-Notches.

This work aims to assess both experimentally and analytically the fracture behavior of rock specimens containing sharp V-notches (SV-notches) subjected to mixed mode I/II loading. To this end, firstly, several mixed mode fracture tests were conducted on Brazilian disk specimens weakened by an SV-notch (SVNBD sample), performed in their corresponding center and with various notch opening angles. Secondly, the fracture resistance of the tested samples was predicted using a criterion named MTS-FEM. This approach is based on the maximum tangential stress (MTS) criterion, in which the tangential stress is determined from the finite element method (FEM). Additionally, in the present research, the required critical distance is calculated directly from finite element analyses performed on cracked samples. Comparing the experimental results and the analytical predictions, it is shown that the fracture curves obtained from the MTS-FEM criterion are in agreement with the experimental results. These results are achieved without the need for the calculation of stress series expansion coefficients, as an additional advantage of the proposed approach.

Statistical determination of fracture parameters of concrete with wide variation of water-cement ratio

The size effect and boundary effect fracture models were used to determine the fracture parameters of quasi-brittle materials through geometrically similar and non-geometrically similar specimens. Combining the characteristics of size effect and boundary effect, the concept of relative size was proposed. The simplified calculation method for quantitatively determining the fictitious crack growth length of concrete specimens with wide variation range of water-cement ratio under peak load. Based on the fracture test results of actual concrete, the tensile strength and fracture toughness of concrete with different water-cement ratios can be determined simultaneously. Using the normal distribution function, fracture curves with upper and lower limits covering all test data was established. According to the fracture failure curve, the minimum theoretical size of concrete specimens with different water-cement ratios satisfying linear elastic fracture mechanic was obtained. Furthermore, an analytical formula was established to directly determine the fracture parameters of concrete with different water-cement ratios from the peak load, and based on the analytical formula, the peak state of a large size structure meeting linear elastic fracture mechanic was predicted • The fracture toughness and tensile strength of concrete with different water-cement ratios can be determined by the proposed model in this paper. • The simplified calculation method of fictitious crack expansion Δafic for concrete samples with different water-cement ratio by determining peak load was quantitatively studied. • The relationship between the peak load and the fracture parameters is established, and the prediction of the peak state of the large-size specimen met LEFM was realized.

Damage accumulation and limit states under the low-cycle loading of structural softening steel

Determination and study of patterns of deformation and fracture of structural materials under cyclic loading is an important fundamental scientific problem. The kinetics of damage accumulation in softening TC (12Kh2MFA) structural steel under low-cycle loading is investigated in the paper based on the unified strain-kinetic criterion of fatigue fracture developed by the author. The damaging role of plastic and elastic strain depending on the loading (durability) is shown. Limit states and peculiarities of their occurrence during static, quasi-static, and fatigue failure are described. The force and deformation parameters determining the load-bearing capacity of the material and the nature of its exhaustion under static and cyclic loading have been established. The critical values of deformation and strength characteristics of steel under soft and hard loading are obtained. It is noted that it is reasonable to use these characteristics when modeling the stress–strain states. A method for determining the cyclic behavior of the material (hardening, softening, stabilization) by static fracture curves is proposed. The possibility of describing the kinetics of damage accumulation and limit states of softening materials by the strain-kinetic criterion of fatigue fracture is confirmed.