Predict Fracture Initiation Research Articles

A Crystal Plasticity-Based Simulation to Predict Fracture Initiation Toughness of Reactor-Grade Aluminium: Experimental Verification and Study of Effect of Crystal Orientation

A Crystal Plasticity-Based Simulation to Predict Fracture Initiation Toughness of Reactor-Grade Aluminium: Experimental Verification and Study of Effect of Crystal Orientation

Prediction of fracture initiation in cohesive soils based on data mining modelling and large-scale laboratory verification

Many empirical and analytical methods have been proposed to predict fracturing pressure in cohesive soils. Most of them take into account three to four specific influencing factors and rely on the assumption of a failure mode. In this study, a novel data-mining approach based on the XGBoost algorithm is investigated for predicting fracture initiation in cohesive soils. This has the advantage of handling multiple influencing factors simultaneously, without pre-determining a failure mode. A dataset of 416 samples consisting of 14 distinct features was herein collected from past studies, and used for developing a regressor and a classifier model for fracturing pressure prediction and failure mode classification respectively. The results show that the intrinsic characteristics of the soil govern the failure mode while the fracturing pressure is more sensitive to the stress state. The XGBoost-based model was also tested against conventional approaches, as well as a similar machine learning algorithm namely random forest model. Additionally, several large-scale triaxial fracturing tests and an in-situ case study were carried out to further verify the generalization ability and applicability of the proposed data mining approach, and the results indicate a superior performance of the XGBoost model.

Patient-specific finite element analysis for assessing hip fracture risk in aging populations

The femur is one of the most important bone in the human body, as it supports the body’s weight and helps with movement. The aging global population presents a significant challenge, leading to an increasing demand for artificial joints, particularly in knee and hip replacements, which are among the most prevalent surgical procedures worldwide. This study focuses on hip fractures, a common consequence of osteoporotic fractures in the elderly population. To accurately predict individual bone properties and assess fracture risk, patient-specific finite element models (FEM) were developed using CT data from healthy male individuals. The study employed ANSYS 2023 R2 software to estimate fracture loads under simulated single stance loading conditions, considering strain-based failure criteria. The FEM bone models underwent meticulous reconstruction, incorporating geometrical and mechanical properties crucial for fracture risk assessment. Results revealed an underestimation of the ultimate bearing capacity of bones, indicating potential fractures even during routine activities. The study explored variations in bone density, failure loads, and density/load ratios among different specimens, emphasizing the complexity of bone strength determination. Discussion of findings highlighted discrepancies between simulation results and previous studies, suggesting the need for optimization in modelling approaches. The strain-based yield criterion proved accurate in predicting fracture initiation but required adjustments for better load predictions. The study underscores the importance of refining density-elasticity relationships, investigating boundary conditions, and optimizing models through in vitro testing for enhanced clinical applicability in assessing hip fracture risk. In conclusion, this research contributes valuable insights into developing patient-specific FEM bone models for clinical hip fracture risk assessment, emphasizing the need for further refinement and optimization for accurate predictions and enhanced clinical utility.

New Method for Detecting Flange Fracture Initiation in Incremental Radial Extrusion.

This study investigates flange fracture formation in unconventional incremental radial extrusion. This manufacturing technique involves using rings with a gradually increasing inside diameter for constraining the free flow of material in the radial direction. As a result, the shaped flange has a constant thickness and a significantly larger diameter than that formed using the standard extrusion process conducted without the use of rings. EN AW 6060 aluminum alloy tube sections were used as the billet material, and the extrusion process was conducted under cold forming conditions at ambient temperature. For the determination of material fracture initiation, a new method was proposed involving the analysis of strain, strain rate and values of the normalized Cockcroft-Latham fracture criterion integral. The main advantage of the new method is that it allows for the prediction of fracture initiation via only FEM results analysis, i.e., it is not necessary to carry out additional experiments aimed at calibrating or determining limit parameters of a given material. It was shown that the occurrence of differences in the distribution of the above-mentioned parameters coincided with flange fracture initiation.

Fracture initiation pressure prediction of hydraulic fracturing for layered reservoirs considering borehole deformation

Accurately predicting fracture initiation pressure is crucial for successfully applying hydraulic fracturing technology in layered reservoirs. However, existing models overlook the effects of rock anisotropy and borehole deformation. In this study, we simplified the layered reservoir to a transversely isotropic medium and developed a model to estimate borehole deformation precisely. Based on this estimated deformation, we created a model to predict fracture initiation pressure in hydraulic fracturing. By comparing previous models and experimental data, we validated the effectiveness of these proposed models. We examined the impacts of various factors on borehole deformation, fracture initiation pressure, and initiation angle. The results revealed that circular boreholes in layered reservoirs deform into elliptical boreholes under in situ stress, with the major axis not aligning with the principal stress direction, which highlights the significant impact of rock anisotropy on borehole deformation. Furthermore, the fracture initiation pressure of hydraulic fracturing either increases or decreases following borehole deformation, depending on specific geological parameters. The calculated initiation angle after borehole deformation is within 10°, closer to previous experimental results, underscoring the notable effect of borehole deformation on hydraulic fracturing. Our research indicates that the impact of borehole deformation on hydraulic fracturing is significant and should not be overlooked. This finding will offer fresh avenues for further study in the field of hydraulic fracturing.

Numerical Study on a Ductile Fracture Model in Pre-Cracked Tension Tests of SUS304L.

The effectiveness of a ductile fracture model in accurately predicting fracture initiation has been demonstrated. In this study, we concentrate on applying the ductile fracture model to pre-cracked structures constructed from SUS304L stainless steel with experimental and numerical analyses. The Swift hardening law was employed to extend the plastic behavior beyond the onset of necking. Additionally, the Hosford-Coulomb model, integrated with a damaged framework, was utilized to predict ductile fracture behavior, particularly under non-proportional loading conditions. Tension tests were conducted on various specimens designed to illustrate various fracture modes resulting from geometric effects. Numerical analyses were conducted to explore the loading histories, utilizing an optimization process to calibrate fracture model parameters. The proposed fracture model is validated against pre-cracked structures detailed in a reference paper. The results convincingly demonstrate that the fracture model effectively predicts both fracture initiation and propagation in pre-cracked structures.

A triaxiality‐dependent fracture model for hot‐rolled sections made of S355 steel

AbstractFracture at net areas of steel sections often leads to premature failures of steel members, especially in the region of joints (bolted connections). This study develops a fracture model for hot rolled S355 steel for enabling a better understanding of the ultimate behaviour of steel sections through numerical simulations using the general‐purpose finite element software ABAQUS. Monotonic tensile tests are conducted on traditional dog‐bone plate specimens with a uniform cross‐section and notched plate specimens extracted from hot‐rolled I‐beams. Two material thicknesses and three notch radii per thickness are considered thus obtaining equivalent plastic strains at fracture over a wide range of stress triaxialities. The experimental fracture displacement is used as a threshold for the determination of the average stress triaxiality – equivalent strain history at the critical location (fracture initiation) of each plate model. Using regression analysis, an exponential approximation of the fracture locus is proposed to correlate the average stress triaxiality for a given equivalent plastic strain at fracture. The proposed model is then used to predict fracture initiation of unnotched tensile coupons and steel plates with a bolt hole in their centre extracted from the same steel sections. The test results are in good agreement with the numerical predictions thus demonstrating the efficiency of the proposed method.

Application of ductile fracture model for the prediction of low cycle fatigue in structural steel

The complexity of the loading conditions makes it challenging to accurately predict the damage evolution and resulting ductile fracture in materials and structures. This paper presents an application method to predict fracture initiation for low cycle fatigue of 4-point bending in structural steel SS275. The swift isotropic hardening law was used in the numerical simulation to account for large strain deformation. The damage indicator framework with the Hosford-Coulomb (HC) model was adopted to characterize the damage accumulation and fracture behavior. Uniaxial tension tests on specimens with various fracture modes were conducted to determine the material properties required for calibration of the plasticity model and fracture model param1eters. Non-linear finite element analyses were performed to identify fracture model parameters based on the loading path of fracture initiation. The presented HC model was applied to an extremely low fatigue test (less than 100 cycles) and demonstrated good accuracy in predicting fracture initiation for complex loading scenarios.

A new ductile fracture model for Q460C high-strength structural steel under monotonic loading: Experimental and numerical investigation

Tensile fracture static tests on nine specimens covering different stress states were performed to investigate the ductile fracture behavior of Chinese Q460C high-strength structural steel (HSS). Based on combining the Rice-Tracey model and Xue model, the new model considering the effect of stress triaxiality and Lode angle was proposed to predict ductile fracture of Q460C HSS. Furthermore, the stress softening criterion was incorporated into the new fracture model to simulate the fracture propagation of Q460C HSS better. The material parameters of the proposed fracture model for Q460C HSS were identified using MATLAB optimization code. The VUMAT subroutine was developed to perform ductile fracture simulations for each specimen, and the fracture simulation results show satisfactory agreement with the experimental results. In addition, the five existing ductile fracture models were also selected to compare the prediction accuracy of the new model. The comparative results show that the new model has better accuracy and is more suitable for predicting fracture initiation and propagation of Q460C HSS. Finally, the applicability of the new model in predicting the fracture of Q460 HSS was furtherly verified by successfully simulating the existing fracture tests of the notched round bar specimens and the bolted connections.

Study on the Accuracy of Fracture Criteria in Predicting Fracture Characteristics of Granite with Different Occurrence Depths

The fracture network of a deep geothermal reservoir forms the place for heat exchange between injected fluid and rock mass with high temperature. The fracture resistance ability of reservoir rocks will affect the formation of fracture-network structure, heat exchange and transmission characteristics, and reservoir mechanical stability. However, there are few reports on the fracture toughness and trajectory prediction of geothermal reservoirs with different depths. In this paper, the modified maximum tangential stress criterion (MMTS) is analyzed. The results show that the experimental data are significantly different from the theoretical estimate of MMTS under the influence of different occurrence depths. It is found that the fracture process zone (FPZ) seriously affects the accuracy of predicting fracture initiation angle and mixed-mode (I+II) fracture toughness by MMTS. The FPZ value, considering the influence of different occurrence depths, is modified, and the accuracy of MMTS in predicting the fracture mechanical characteristics of granite is improved. In addition, the mechanical test results show that the Brazilian splitting strength (σt) of granite fluctuates increase with the increase in temperature. With the increase in deviatoric stress, the Brazilian splitting strength and the Brazilian splitting modulus of rock show a trend of first increasing, then decreasing, and then increasing.

Cortical bone continuum damage mechanics constitutive model with stress triaxiality criterion to predict fracture initiation and pattern.

A primary objective of finite element human body models (HBMs) is to predict response and injury risk in impact scenarios, including cortical bone fracture initiation, fracture pattern, and the potential to simulate post-fracture injury to underlying soft tissues. Current HBMs have been challenged to predict the onset of failure and bone fracture patterns owing to the use of simplified failure criteria. In the present study, a continuum damage mechanics (CDM) model, incorporating observed mechanical response (orthotropy, asymmetry, damage), was coupled to a novel phenomenological effective strain fracture criterion based on stress triaxiality and investigated to predict cortical bone response under different modes of loading. Three loading cases were assessed: a coupon level notched shear test, whole bone femur three-point bending, and whole bone femur axial torsion. The proposed material model and fracture criterion were able to predict both the fracture initiation and location, and the fracture pattern for whole bone and specimen level tests, within the variability of the reported experiments. There was a dependence of fracture threshold on finite element mesh size, where higher mesh density produced similar but more refined fracture patterns compared to coarser meshes. Importantly, the model was functional, accurate, and numerically stable even for relatively coarse mesh sizes used in contemporary HBMs. The proposed model and novel fracture criterion enable prediction of fracture initiation and resulting fracture pattern in cortical bone such that post-fracture response can be investigated in HBMs.

A stress-based shear fracture criterion considering the effect of stress triaxiality and Lode parameter

Failure in lightweight metal forming is a big challenge currently and prevents their widely application in weight reduction of automobile and aerospace structures. A stress-based shear ductile fracture criterion is introduced in this study to improve the prediction accuracy of failure for lightweight metals. The criterion (sDF2016) is developed based on the DF2016 criterion thereby endowing the criterion with the precise fracture predictability under wide stress states of shear, uniaxial tension, plane strain tension and equibiaxial tension. Besides, the criterion takes into account the stress state effect on fracture in a form of the stress triaxiality, the maximum shear stress and the Lode parameter. The sDF2016 criterion is also expected to be less sensitive to strain path changing effect because sDF2016 describe the onset of fracture in stress space. For the verification of the proposed sDF2016 criterion, the experiments are carried out for AA5182-O sheet with central hole, notched, in-plane shear and bulging specimens. Plastic deformation is accurately modeled by the Swift-Voce hardening law and the Drucker yield function. The sDF2016 criterion is then calibrated both by the direct and inverse engineering approaches, which is applied to predict fracture initiation under distinct stress states. The modeled result indicates that the calibrated sDF2016 criterion based on the inverse engineering method predicts the fracture stroke with a higher accuracy than the direct approach. The sDF2016 criterion is also used to depict fracture limits of AA2024-T351 alloy from compression to tension. The application shows that the proposed ductile fracture criterion is capable of modeling the fracture limits for sheet metals under various loading conditions from shear to plane strain tension.

A New Semi-Analytical Solution for an Arbitrary Hardening Law and Its Application to Tube Hydroforming.

The present study consists of two parts. The first part supplies an exact semi-analytical solution for a general model of rigid plastic strain hardening material at large strains. The second part applies this solution to tube hydroforming design. The solution provides stress and velocity fields in a hollow cylinder subject to simultaneous expansion and elongation/contraction. No restriction is imposed on the hardening law. A numerical method is only required to evaluate ordinary integrals. The solution is facilitated using Lagrangian coordinates. The second part of the paper is regarded as an alternative to the finite element design of tube hydroforming processes, restricted to rather simple final shapes. An advantage of this approach is that the hardening law is not required for calculating many process parameters. Therefore, the corresponding design is universally valid for all strain hardening materials if these parameters are of concern. In particular, the prediction of fracture initiation at the outer surface is independent of the hardening law for widely used ductile fracture criteria. The inner pressure is the only essential process parameter whose value is controlled by the hardening law.

Experimental Investigation of Shale Tensile Failure under Thermally Conditioned Linear Fracturing Fluid (LFF) System and Reservoir Temperature Controlled Conditions.

Linear fracturing fluid (LFF) provides viscosity driven benefits of proppant suspensibility and fluid loss control, and with the use of a breaker agent, flowback recovery can be greatly enhanced. Shale tensile strength is critical in the prediction of fracture initiation and propagation, but its behavior under the interaction with LFF at reservoir temperature conditions remains poorly understood. This necessitated an in-depth investigation into the tensile strengths of Eagle Ford and Wolfcamp shales under thermally conditioned LFF and reservoir temperature controlled conditions. Brazilian Indirect Tensile Strength (BITS) testing was carried out for the quantitative evaluation of shale tensile strength, followed by extensive failure pattern classifications and surface crack length analysis. The thermally conditioned LFF saturation of shale samples led to average tensile strength (ATS) increases ranging from 26.33–51.33% for Wolfcamp. Then, for the Eagle Ford samples, ATS increases of 3.94 and 6.79% and decreases of 3.13 and 15.35% were recorded. The exposure of the samples to the temperature condition of 90 °C resulted in ATS increases of 24.46 and 33.78% for Eagle Ford and Wolfcamp shales, respectively. Then, for samples exposed to 220 °C, ATS decreases of 6.11 and 5.32% were respectively recorded for Eagle Ford and Wolfcamp shales. The experimental results of this research will facilitate models’ development towards tensile strength predictions and failure pattern analysis and quantifications in the LFF driven hydraulic fracturing of shale gas reservoirs.

Quantitative analysis of fracture evolution in fold: Insights from FDEM modelling

Fractures associated with buckle folds play a vital role in hydrocarbon migration and accumulation in reservoirs. However, the prediction of fracture initiation and propagation during buckle folding is technically challenging. In this study, a series of buckle folds with different initial geometries, which represent different deformation stages of folds, are simulated to study the fracturing mechanism during buckling. To obtain a better understanding of the progressive fracturing process, a 2D modelling approach using an improved combined finite-discrete element method (FDEM) is utilized. The influence of fold geometries with significant influence on fracture development are considered, including layer thickness and wavelength. The results show that the development of fractures can be directly observed through the improved FDEM modelling. It is concluded that the development and distribution of major fracture sets are different at various periods during the evolution history of the fold. Tensile fractures initiate more easily in tighter folds, while shear fractures develop more easily in gentle folds. The pressure from the overburden or the constrains of the surrounding rock is critical for the developments of fractures at hinges. As the fold becomes tight, the density of fractures decreases, whereas the length of single fractures increases. The results further show that the layer thickness and wavelength are vital for the initiation and propagation of major fracture sets. In summary, the FDEM modelling approach can well explain most of the fracture sets occurring in the buckle fold. This study has provided a deeper insight into the fracture evolution in fold.

Prediction of fracture initiation and propagation in pelvic bones

The objective is developing an XFEM model that is capable of predicting different types of fracture in the pelvic bone under various loading conditions. Previously published mechanical and failure characteristics of cortical and cancellous tissues were implemented and assigned to an intact pelvic bone with specified cortical and cancellous tissues. Various loading conditions, including combined load directions, were applied to the acetabulum to model different types of fracture (e.g., anterior/posterior wall fracture and transverse fracture) in the pelvic bone. The predicated types of fracture and the maximum force at fracture were compared to those acquired from previously published experimental tests. Anterior/posterior wall fracture and transverse fracture were the most common types of fractures determined in the simulations. The XFEM simulations were able to predict similar fractures to those reported in the experimental tests. The maximum fracture force in the XFEM model was found to be 18.6 kN compared to 8.85 kN reported in the previous experimental tests. The results revealed that different types of fracture in the pelvic bones can be caused by the various loading conditions in unstable high-rate impact loads. Using proper mechanical and failure behaviors of cortical and cancellous tissues, XFEM modeling of pelvic bone is capable of predicting bone fracture. In future work, the XFEM models of cancellous and cortical tissues can be assigned to other bones in human body skeleton so that the failure mechanism in such bones can be investigated.

Energy based fracture initiation criterion for strain-crystallizing rubber-like materials with pre-existing cracks

Fracture prediction is indispensable for polymers, like rubbers, which have a broad range of applications mainly due to their high extensibility. The phenomenon known as strain-induced crystallization further contributes to the fracture toughness of certain rubbers. In this study, a criterion based on internal bond energy, incorporating the effects of crystallization, is proposed to predict fracture initiation in rubber-like materials with pre-existing cracks. First, a multi-scale mechanical model is developed for characterizing the behavior of rubber when subjected to both uniaxial and biaxial deformation states. At the microscale, both the amorphous and crystalline chain segments are modeled as elastic in order to consider the energy contribution by the molecular bond distortions. This internal energy is considered along with the entropic and crystalline free energy for each chain. In the chain model, the effects of loading condition and the relative orientation of a chain on its crystallinity are taken into account. At the macroscopic scale, an existing crystallinity distribution function is adapted and a mixed finite element formulation with an augmented Lagrangian multiplier is utilized to impose the incompressibility constraint. A non-affine maximal advance path constraint based homogenization model is utilized for bridging the two scales. Its potential to account for anisotropy in the stretched network compels the model to be preferable due to its physical significance, for the purpose of fracture modeling. The rigidity of the crystallites is accounted for by proposing a crystallite distortion energy in addition to the critical bond dissociation energy, for fracture initiation to occur. The model is validated by comparison with existing experimental results for both crystallizing and non-crystallizing rubbers. In addition to its potential to predict the material behavior when subjected to uniaxial and biaxial loading, the capability of the model to quantitatively estimate the effect of crystallization on fracture initiation is also verified.

Initiation mechanisms of radial drilling‐fracturing considering shale hydration and reservoir dip

AbstractRadial drilling‐fracturing is an innovative fracturing technology that achieves superior stimulation effects. This paper develops a model for radial drilling‐fracturing in shale reservoirs, which can predict fracture initiation pressure and failure mode of shale. Compared with published models, this model additionally considers shale hydration and inclinations of boreholes and reservoir. Then, the influences of 7 factors are studied and main conclusions are as follows. First, with the angle between radial borehole and formation strike increasing, matrix failure pressure declines only around 90° and 270°. Bedding tensile failure pressure ascends and then falls back. Bedding shear failure pressure rapidly descends, then reaches a plateau, and finally rebounds. A small or large angle is favorable for bedding tensile failure. Shale tends to crack with bedding shear failure under a moderate angle and with matrix failure only at 90° and 270°. Second, with the enlargement of azimuth difference between the radial borehole and main wellbore, matrix failure pressure periodically fluctuates, forming an inverted W‐shape curve. Bedding tensile failure pressure and bedding shear failure pressure both ascend, then slide downward, and finally rise again. Besides, a small azimuth difference inclines shale to bedding shear failure, and the other failure modes tend to occur when azimuth difference is around 90°. Third, pressures required for all failure modes descend as the dip of shale formation increases. However, the difference in descending rate leads to that the increase of dip angle can incline shale to bedding shear failure. Besides, pressures required for bedding tensile failure and matrix failure decline linearly with the increasing reservoir temperature. Temperature has no impact on bedding shear failure. Hence, matrix failure and bedding tensile failure are more prone to occur in the high‐temperature reservoir. The research provides a reference for field applications of radial drilling‐fracturing in the shale reservoir.

An Analytical Model for Fracture Initiation of Radial Drilling-Fracturing in Shale Formations

Abstract Radial drilling-fracturing, the combination of radial drilling and hydraulic fracturing, can guide fractures toward the target area and effectively enhance the recovery of the low permeable reservoir. In this paper, based on the stress superposition principle, we establish an analytical model to predict fracture initiation pressure (FIP) and the shale failure mode for radial drilling-fracturing applied in shale formations. In contrast with the former studies, this model can additionally consider the failure from shale beddings and is more applicable in the shale reservoir. The model classifies the shale failure into three modes and, respectively, gives the criterion for each failure mode. Then, a series of sensitivity analyses is conducted by examining effects of various parameters. By analyzing the variation characteristic of the initiation pressures required for three failure modes, the main conclusions are as follows. Firstly, matrix failure and shear failure along bedding tend to take place when the azimuth of radial borehole is moderate. Small and large azimuths are favorable for the occurrence of tensile failure along bedding. Secondly, a high ratio of horizontal in situ stress predisposes shale to generate matrix failure, and bedding tensile failure and bedding shear failure are apt to occur when the ratio of horizontal in situ stress is low. Thirdly, with the increasing intersection angle of the radial borehole wall and bedding plane, the failure mode apt to occur changes from bedding tensile failure to bedding shear failure and then to matrix failure. Fourthly, shale prefers to yield bedding shear failure under a small Biot coefficient and generate the other two failure modes when Biot coefficient is large. Fifthly, permeability coefficient virtually has no influence on the failure mode of shale. The research clarifies the fracture initiation characteristics of radial drilling-fracturing in shale formations and provides a reference for the field application of radial drilling-fracturing.

Fracture initiation in a single crystal copper edge-crack specimen for various crystallographic orientations

The motivation of the present study entails the determination of fracture initiation of a single crystal copper edge-crack specimen subjected to tensile load by considering the influence of crystallographic anisotropy, strain hardening and damage accumulation. To accomplish the purpose of this study, a damage criterion coupled with crystal plasticity finite element method was used to determine material softening after the peak load. Damage evolution was chosen as the function of maximum shear strain within the crystal plasticity framework. Coupled with a damage criterion, the crystal plasticity model was used to reproduce the stress-strain responses of copper single crystals until failure. The model was then applied to assess damage evaluation near crack-tip of a single crystal copper edge-crack specimen along two crystallographic orientations of tensile loading directions. The analysis abetted to predict fracture initiation (J-initiation) of a crack lying along various crystallographic orientations, while keeping the loading direction orientation identical in all the cases. The methodology presented here has the scope to analyze single crystal complex structures with cracks subjected to loading along various crystallographic orientations.