Fourth-order phase-field modeling for brittle fracture in piezoelectric materials

Failure analyses of piezoelectric structures and devices are of engineering and scientific significance.In this paper,a fourth-order phase-field fracture model for piezoelectric solids is developed based on the Hamilton principle.Three typical electric boundary conditions are involved in the present model to characterize the fracture behaviors in various physical situations.A staggered algorithm is used to simulate the crack propagation.The polynomial splines over hierarchical T-meshes(PHT-splines)are adopted as the basis function,which owns the C1continuity.Systematic numerical simulations are performed to study the influence of the electric boundary conditions and the applied electric field on the fracture behaviors of piezoelectric materials.The electric boundary conditions may influence crack paths and fracture loads significantly.The present research may be helpful for the reliability evaluation of the piezoelectric structure in the future applications.

A phase-field model for simulating the propagation behavior of mixed-mode cracks during the hydraulic fracturing process in fractured reservoirs

A novel phase-field model for the propagation of mixed-mode hydraulic fractures,characterized by the formation of mixed-mode fractures due to the interactions between fluids and solids,is proposed.In this model,the driving force for the phase field consists of both tensile and shear components,with the fluid contribution primarily manifesting in the tension driving force.The displacement and pressure are solved simultaneously by an implicit method.The numerical solution's iterative format is established by the finite element discretization and Newton-Raphson(NR)iterative methods.The correctness of the model is verified through the uniaxial compression physical experiments on fluid-pressurized rocks,and the limitations of the hydraulic fracture expansion phase-field model,which only considers mode I fractures,are revealed.In addition,the influence of matrix mode II fracture toughness value,natural fracture mode II toughness value,and fracturing fluid injection rate on the hydraulic fracture propagation in porous media with natural fractures is studied.

Discontinuity development patterns and the challenges for 3D discrete fracture network modeling on complicated exposed rock surfaces

Natural slopes usually display complicated exposed rock surfaces that are characterized by complex and substantial terrain undulation and ubiquitous undesirable phenomena such as vegetation cover and rockfalls.This study presents a systematic outcrop research of fracture pattern variations in a complicated rock slope,and the qualitative and quantitative study of the complex phenomena impact on threedimensional(3D)discrete fracture network(DFN)modeling.As the studies of the outcrop fracture pattern have been so far focused on local variations,thus,we put forward a statistical analysis of global variations.The entire outcrop is partitioned into several subzones,and the subzone-scale variability of fracture geometric properties is analyzed(including the orientation,the density,and the trace length).The results reveal significant variations in fracture characteristics(such as the concentrative degree,the average orientation,the density,and the trace length)among different subzones.Moreover,the density of fracture sets,which is approximately parallel to the slope surface,exhibits a notably higher value compared to other fracture sets across all subzones.To improve the accuracy of the DFN modeling,the effects of three common phenomena resulting from vegetation and rockfalls are qualitatively analyzed and the corresponding quantitative data processing solutions are proposed.Subsequently,the 3D fracture geometric parameters are determined for different areas of the high-steep rock slope in terms of the subzone dimensions.The results show significant variations in the same set of 3D fracture parameters across different regions with density differing by up to tenfold and mean trace length exhibiting differences of 3e4 times.The study results present precise geological structural information,improve modeling accuracy,and provide practical solutions for addressing complex outcrop issues.

Using fracture-based continuum modeling of coupled geomechanical-hydrological processes for numerical simulation of hydraulic fracturing

This paper describes numerical simulation of hydraulic fracturing using fracture-based continuum modeling(FBCM)of coupled geomechanical-hydrological processes to evaluate a technique for high-density fracturing and fracture caging.The simulations are innovative because of modeling discrete fractures explicitly in continuum analysis.A key advantage of FBCM is that fracture initiation and propagation are modeled explicitly without changing the domain grid(i.e.no re-meshing).Further,multiple realizations of a preexisting fracture distribution can be analyzed using the same domain grid.The simulated hydraulic fracturing technique consists of pressurizing multiple wells simultaneously:initially without permeating fluids into the rock,to seed fractures uniformly and at high density in the wall rock of the wells;followed by fluid injection to propagate the seeded fracture density hydraulically.FBCM combines the ease of continuum modeling with the potential accuracy of modeling discrete fractures and fracturing explicitly.Fractures are modeled as piecewise planar based on intersections with domain elements;fracture geometry stored as continuum properties is used to calculate parameters needed to model individual fractures;and rock behavior is modeled through tensorial aggregation of the behavior of discrete fractures and unfractured rock.Simulations are presented for previously unfractured rock and for rock with preexisting fractures of horizontal,shallow-dipping,steeply dipping,or vertical orientation.Simulations of a single-well model are used to determine the pattern and spacing for a multiple-well design.The results illustrate high-density fracturing and fracture caging through simultaneous fluid injection in multiple wells:for previously unfractured rock or rock with preexisting shallow-dipping or horizontal fractures,and in situ vertical compressive stress greater than horizontal.If preexisting fractures are steeply dipping or vertical,and considering the same in situ stress condition,well pressurization without fluid permeation appears to be the only practical way to induce new fractures and contain fracturing within the target domain.

Algorithmic approach to discrete fracture network flow modeling in consideration of realistic connections in large-scale fracture networks

Analyzing rock mass seepage using the discrete fracture network(DFN)flow model poses challenges when dealing with complex fracture networks.This paper presents a novel DFN flow model that incorporates the actual connections of large-scale fractures.Notably,this model efficiently manages over 20,000 fractures without necessitating adjustments to the DFN geometry.All geometric analyses,such as identifying connected fractures,dividing the two-dimensional domain into closed loops,triangulating arbitrary loops,and refining triangular elements,are fully automated.The analysis processes are comprehensively introduced,and core algorithms,along with their pseudo-codes,are outlined and explained to assist readers in their programming endeavors.The accuracy of geometric analyses is validated through topological graphs representing the connection relationships between fractures.In practical application,the proposed model is employed to assess the water-sealing effectiveness of an underground storage cavern project.The analysis results indicate that the existing design scheme can effectively prevent the stored oil from leaking in the presence of both dense and sparse fractures.Furthermore,following extensive modification and optimization,the scale and precision of model computation suggest that the proposed model and developed codes can meet the requirements of engineering applications.

A new elastoplastic model for bolt-grouted fractured rock

Complexities in mechanical behaviours of rock masses mainly stem from inherent discontinuities,which calls for advanced bolt-grouting techniques for stability enhancement.Understanding the mechanical properties of bolt-grouted fractured rock mass(BGFR)and developing accurate prediction methods are crucial to optimize the BGFR support strategies.This paper establishes a new elastoplastic(E-P)model based on the orthotropic and the Mohr-Coulomb(M-C)plastic-yielding criteria.The elastic parameters of the model were derived through a meso-mechanical analysis of composite materials mechanics(CMM).Laboratory BGFR specimens were prepared and uniaxial compression test and variable-angle shear test considering different bolt arrangements were carried out to obtain the mechanical parameters of the specimens.Results showed that the anisotropy of BGFR mainly depends on the relative volume content of each component material in a certain direction.Moreover,the mechanical parameters deduced from the theory of composite materials which consider the short fibre effect are shown to be in good agreement with those determined by laboratory experiments,and the variation rules maintained good consistency.Last,a case study of a real tunnel project is provided to highlight the effectiveness,validity and robustness of the developed E-P model in prediction of stresses and deformations.

A multi-mechanism numerical simulation model for CO_(2)-EOR and storage in fractured shale oil reservoirs

Under the policy background and advocacy of carbon capture,utilization,and storage(CCUS),CO_(2)-EOR has become a promising direction in the shale oil reservoir industry.The multi-scale pore structure distribution and fracture structure lead to complex multiphase flow,comprehensively considering multiple mechanisms is crucial for development and CO_(2) storage in fractured shale reservoirs.In this paper,a multi-mechanism coupled model is developed by MATLAB.Compared to the traditional Eclipse300 and MATLAB Reservoir Simulation Toolbox(MRST),this model considers the impact of pore structure on fluid phase behavior by the modified Peng—Robinson equation of state(PR-EOS),and the effect simultaneously radiate to Maxwell—Stefan(M—S)diffusion,stress sensitivity,the nano-confinement(NC)effect.Moreover,a modified embedded discrete fracture model(EDFM)is used to model the complex fractures,which optimizes connection types and half-transmissibility calculation approaches between non-neighboring connections(NNCs).The full implicit equation adopts the finite volume method(FVM)and Newton—Raphson iteration for discretization and solution.The model verification with the Eclipse300 and MRST is satisfactory.The results show that the interaction between the mechanisms significantly affects the production performance and storage characteristics.The effect of molecular diffusion may be overestimated in oil-dominated(liquid-dominated)shale reservoirs.The well spacing and injection gas rate are the most crucial factors affecting the production by sensitivity analysis.Moreover,the potential gas invasion risk is mentioned.This model provides a reliable theoretical basis for CO_(2)-EOR and sequestration in shale oil reservoirs.

A fracture model for assessing tensile mode crack growth resistance of rocks

Evaluating the fracture resistance of rocks is essential for predicting and preventing catastrophic failure of cracked structures in rock engineering.This investigation developed a brittle fracture model to predict tensile mode(mode I)failure loads of cracked rocks.The basic principle of the model is to estimate the reference crack corresponding to the fracture process zone(FPZ)based on the maximum normal strain(MNSN)ahead of the crack tip,and then use the effective crack to calculate the fracture toughness.We emphasize that the non-singular stress/strain terms should be considered in the description of the MNSN.In this way,the FPZ,non-singular terms and the biaxial stress state at the crack tip are simul-taneously considered.The principle of the model is explicit and easy to apply.To verify the proposed model,laboratory experiments were performed on a rock material using six groups of specimens.The model predicted the specimen geometry dependence of the measured fracture toughness well.More-over,the potential of the model in analyzing the size effect of apparent fracture toughness was discussed and validated through experimental data reported in the literature.The model was demonstrated su-perior to some commonly used fracture models and is an excellent tool for the safety assessment of cracked rock structures.

Development of an experimental method for well-controlled blast induced traumatic limb fracture in rats

Heterotopic ossification(HO)is a consequence of traumatic bone and tissue damage,which occurs in 65%of military casualties with blast-associated amputations.However,the mechanisms behind blast-induced HO remain unclear.Animal models are used to study blast-induced HO,but developing such models is challenging,particularly in how to use a pure blast wave(primary blast)to induce limb fracture that then requires an amputation.Several studies,including our recent study,have developed platforms to induce limb fractures in rats with blast loading or a mixture of blast and impact loading.However,these models are limited by the survivability of the animal and repeatability of the model.In this study,we developed an improved platform,aiming to improve the animal's survivability and injury repeatability as well as focusing on primary blast only.The platform exposed only one limb of the rat to a blast wave while providing proper protection to the rest of the rat's body.We obtained very consistent fracture outcome in the tibia(location and pattern)in cadaveric rats with a large range of size and weight.Importantly,the rats did not obviously move during the test,where movement is a potential cause of uncontrolled injury.We further conducted parametric studies by varying the features of the design of the platform.These factors,such as how the limb is fixed and how the cavity through which the limb is placed is sealed,significantly affect the resulting injury.This platform and test setups enable well-controlled limb fracture induced directly by pure blast wave,which is the fundamental step towards a complete in vivo animal model for blast-induced HO induced by primary blast alone,excluding secondary and tertiary blast injury.In addition,the platform design and the findings presented here,particularly regarding the proper protection of the animal,have implications for future studies investigating localized blast injuries,such as blast induced brain and lung injuries.

Improved Staggered Algorithm for Phase-Field Brittle Fracture with the Local Arc-Length Method

The local arc-length method is employed to control the incremental loading procedure for phase-field brittle fracture modeling.An improved staggered algorithm with energy and damage iterative tolerance convergence criteria is developed based on the residuals of displacement and phase-field.The improved staggered solution scheme is implemented in the commercial software ABAQUS with user-defined element subroutines.The layered system of finite elements is utilized to solve the coupled elastic displacement and phase-field fracture problem.A one-element benchmark test compared with the analytical solution was conducted to validate the feasibility and accuracy of the developed method.Our study shows that the result calculated with the developed method does not depend on the selected size of loading increments.The results of several numerical experiments show that the improved staggered algorithm is efficient for solving the more complex brittle fracture problems.

Factors influencing the continuity of evidence-based practice in perioperative airway management for elderly patients with fractures:A qualitative study

BACKGROUND More and more evidence-based practices are emerging,but researchers mostly focus on short-term effects,resulting in evidence-based practices not being applied in the clinic in the long term.In this study,we took the evidence-based practice of perioperative airway management in elderly fracture patients as an example and adopted a descriptive phenomenological approach to understand the influencing factors of its sustainability to provide a reference basis for promoting the continuity of evidence-based practice in the clinic.AIM To explore factors influencing the persistence of evidence-based practice in perioperative airway management in elderly patients with fractures.METHODS This study was qualitative research.Nine nurses who implemented evidencebased practice in the orthopedic ward of a tertiary comprehensive hospital in Shanghai from September 2023 to October 2023 were selected using purposive sampling as research subjects.Semi-structured interviews were conducted with them,and the data were analyzed using the Colaizzi phenomenological analysis method based on the three dimensions and ten factors of the NHS sustainability model.RESULTS Three main themes and ten subthemes were identified:Process aspects(benefits to patients,benefits to nurses,lack of follow-up,complex processes);staff aspects(insufficient human resources,inadequate training and education,lack of leadership support);and organizational environment aspects(inadequate infrastructure,poor patient compliance,poor doctor cooperation).CONCLUSION Human resources,training and education,leadership support,infrastructure,and patient-physician collaboration are important factors influencing the sustainability of evidence-based practice for perioperative airway management in older patients with fractures.

Simulation of Fracture Process of Lightweight Aggregate Concrete Based on Digital Image Processing Technology

The mechanical properties and failure mechanism of lightweight aggregate concrete(LWAC)is a hot topic in the engineering field,and the relationship between its microstructure and macroscopic mechanical properties is also a frontier research topic in the academic field.In this study,the image processing technology is used to establish a micro-structure model of lightweight aggregate concrete.Through the information extraction and processing of the section image of actual light aggregate concrete specimens,the mesostructural model of light aggregate concrete with real aggregate characteristics is established.The numerical simulation of uniaxial tensile test,uniaxial compression test and three-point bending test of lightweight aggregate concrete are carried out using a new finite element method-the base force element method respectively.Firstly,the image processing technology is used to produce beam specimens,uniaxial compression specimens and uniaxial tensile specimens of light aggregate concrete,which can better simulate the aggregate shape and random distribution of real light aggregate concrete.Secondly,the three-point bending test is numerically simulated.Thirdly,the uniaxial compression specimen generated by image processing technology is numerically simulated.Fourth,the uniaxial tensile specimen generated by image processing technology is numerically simulated.The mechanical behavior and damage mode of the specimen during loading were analyzed.The results of numerical simulation are compared and analyzed with those of relevant experiments.The feasibility and correctness of the micromodel established in this study for analyzing the micromechanics of lightweight aggregate concrete materials are verified.Image processing technology has a broad application prospect in the field of concrete mesoscopic damage analysis.

Three predictive scores compared in a retrospective multicenter study of nonunion tibial shaft fracture

BACKGROUND Delayed union,malunion,and nonunion are serious complications in the healing of fractures.Predicting the risk of nonunion before or after surgery is challenging.AIM To compare the most prevalent predictive scores of nonunion used in clinical practice to determine the most accurate score for predicting nonunion.METHODS We collected data from patients with tibial shaft fractures undergoing surgery from January 2016 to December 2020 in three different trauma hospitals.In this retrospective multicenter study,we considered only fractures treated with intramedullary nailing.We calculated the tibia FRACTure prediction healING days(FRACTING)score,Nonunion Risk Determination score,and Leeds-Genoa Nonunion Index(LEG-NUI)score at the time of definitive fixation.RESULTS Of the 130 patients enrolled,89(68.4%)healed within 9 months and were classified as union.The remaining patients(n=41,31.5%)healed after more than 9 months or underwent other surgical procedures and were classified as nonunion.After calculation of the three scores,LEG-NUI and FRACTING were the most accurate at predicting healing.CONCLUSION LEG-NUI and FRACTING showed the best performances by accurately predicting union and nonunion.

Estimation of fracture size and azimuth in the universal elliptical disc model based on trace information

The geometric characteristics of fractures within a rock mass can be inferred by the data sampling from boreholes or exposed surfaces.Recently,the universal elliptical disc(UED)model was developed to represent natural fractures,where the fracture is assumed to be an elliptical disc and the fracture orientation,rotation angle,length of the long axis and ratio of short-long axis lengths are considered as variables.This paper aims to estimate the fracture size-and azimuth-related parameters in the UED model based on the trace information from sampling windows.The stereological relationship between the trace length,size-and azimuth-related parameters of the UED model was established,and the formulae of the mean value and standard deviation of trace length were proposed.The proposed formulae were validated via the Monte Carlo simulations with less than 5%of error rate between the calculated and true values.With respect to the estimation of the size-and azimuth-related parameters using the trace length,an optimization method was developed based on the pre-assumed size and azimuth distribution forms.A hypothetical case study was designed to illustrate and verify the parameter estimation method,where three combinations of the sampling windows were used to estimate the parameters,and the results showed that the estimated values could agree well with the true values.Furthermore,a hypothetical three-dimensional(3D)elliptical fracture network was constructed,and the circular disc,non-UED and UED models were used to represent it.The simulated trace information from different models was compared,and the results clearly illustrated the superiority of the proposed UED model over the existing circular disc and non-UED models。

Fracture propagation laws of staged hydraulic fracture in fractured geothermal reservoir based on phase field model

Hydraulic fracturing is widely used in geothermal resource exploitation, and many natural fractures exist in hot dry rock reservoirs due to in-situ stress and faults. However, the infuence of natural fractures on hydraulic fracture propagation is not considered in the current study. In this paper, based on the phase feld model, a thermo-hydro-mechanical coupled hydraulic fracture propagation model was established to reveal the infuence of injection time, fracturing method, injection fow rate, and natural fracture distribution on the fracture propagation mechanism. The results show that fracture complexity increases with an increase in injection time. The stress disturbance causes the fracture initiation pressure of the second cluster signifcantly higher than that of the frst and third clusters. The zipper-type fracturing method can reduce the degree of stress disturbance and increase fracture complexity by 7.2% compared to simultaneous hydraulic fracturing. Both low and high injection fow rate lead to a decrease in fracture propagation time, which is not conducive to an increase in fracture complexity. An increase in the natural fracture angle leads to hydraulic fracture crossing natural fracture, but has a lesser efect on fracture complexity. In this paper, we analyzed the infuence of diferent factors on initiation pressure and fracture complexity, providing valuable guidance for the exploitation of geothermal resources.

Geological characteristics and models of fault-foldfracture body in deep tight sandstone of the second member of Upper Triassic Xujiahe Formation in Xinchang structural belt of Sichuan Basin,SW China

In the second member of the Upper Triassic Xujiahe Formation(T_(3)x_(2))in the Xinchang area,western Sichuan Basin,only a low percent of reserves has been recovered,and the geological model of gas reservoir sweet spot remains unclear.Based on a large number of core,field outcrop,test and logging-seismic data,the T_(3)x_(2) gas reservoir in the Xinchang area is examined.The concept of fault-fold-fracture body(FFFB)is proposed,and its types are recognized.The main factors controlling fracture development are identified,and the geological models of FFFB are established.FFFB refers to faults,folds and associated fractures reservoirs.According to the characteristics and genesis,FFFBs can be divided into three types:fault-fracture body,fold-fracture body,and fault-fold body.In the hanging wall of the fault,the closer to the fault,the more developed the effective fractures;the greater the fold amplitude and the closer to the fold hinge plane,the more developed the effective fractures.Two types of geological models of FFFB are established:fault-fold fracture,and matrix storage and permeability.The former can be divided into two subtypes:network fracture,and single structural fracture,and the later can be divided into three subtypes:bedding fracture,low permeability pore,and extremely low permeability pore.The process for evaluating favorable FFFB zones was formed to define favorable development targets and support the well deployment for purpose of high production.The study results provide a reference for the exploration and development of deep tight sandstone oil and gas reservoirs in China.

Analytical model of 2D leakoff in waterflood-induced fractures

Waterflood-induced fractures,also known as self-induced fractures,spontaneously form at injection wells during waterflooding.These fractures propagate long distances through rock,allowing injected fluids to travel far away from a well,both within and outside the flooding layer.Essentially,the me-chanics of waterflood-induced fracture propagation is similar to that of hydraulic fractures,which are intentionally created for reservoir stimulation.Fracturing models developed for hydraulic fractures can also be applied to waterflood-induced fractures.However,waterflood-induced fractures are typically pumped with much larger volumes of water or brine and grow much longer in time.As a result,fluid leakoff from waterflood fractures into the formation is more extensive and two-dimensional(2D),a characteristic that is often ignored in a majority of modern fracturing simulators,making their appli-cation to waterflood fractures unreliable.In this work,we revisit the problem of leakoff for long-growing waterflood-induced fractures and develop a new analytical model for fluid leakoff that provides improved predictions of fracture geometry and can be easily implemented in fracturing simulators.We incorporate the developed solution into the classical Perkins-Kern-Nordgren(PKN)model of fracture growth,which shows that the choice of the Carter or a 2D leakoff model greatly impacts fracture ge-ometry at large time.The conducted parametric study shows while a toughness-dominated regime af-fects fracture evolution,most of fracture lifetime occurs in a viscosity-and-leakoff-dominated regime.We also develop an asymptotic solution for a leakoff profile in the limiting case of 2D leakoff domination(~~M and~~K).Finally,we study 3D fracture growth and out-of-zone injection with three layers and a complex structure of zones.The study shows that ignoring the 2D leakoff during simulation results in a significant overestimation of fracture geometry predictions.The present work,thus,plays an important role in improving waterflood fracture modelling,as it highlights the significance of 2D leakoff in waterflood-induced fractures and provides a reliable analytical model for fluid leakoff that can be incorporated into modern fracture simulators.

Development of an improved three-dimensional rough discrete fracture network model:Method and application

Structure plane is one of the important factors affecting the stability and failure mode of rock mass engineering.Rock mass structure characterization is the basic work of rock mechanics research and the important content of numerical simulation.A new 3-dimensional rough discrete fracture network(RDFN3D)model and its modeling method based on the Weierstrass-Mandelbrot(W-M)function were presented in this paper.The RDFN3D model,which improves and unifies the modelling methods for the complex structural planes,has been realized.The influence of fractal dimension,amplitude,and surface precision on the modeling parameters of RDFN3D was discussed.The reasonable W-M parameters suitable for the roughness coefficient of JRC were proposed,and the relationship between the mathematical model and the joint characterization was established.The RDFN3D together with the smooth 3-dimensional discrete fracture network(DFN3D)models were successfully exported to the drawing exchange format,which will provide a wide application in numerous numerical simulation codes including both the continuous and discontinuous methods.The numerical models were discussed using the COMSOL Multiphysics code and the 3-dimensional particle flow code,respectively.The reliability of the RDFN3D model was preliminarily discussed and analyzed.The roughness and spatial connectivity of the fracture networks have a dominant effect on the fluid flow patterns.The research results can provide a new geological model and analysis model for numerical simulation and engineering analysis of jointed rock mass.

Revolutionizing Tight Reservoir Production: A Novel Dual-Medium Unsteady Seepage Model for Optimizing Volumetrically Fractured Horizontal Wells

This study presents an avant-garde approach for predicting and optimizing production in tight reservoirs,employing a dual-medium unsteady seepage model specifically fashioned for volumetrically fractured horizontal wells.Traditional models often fail to fully capture the complex dynamics associated with these unconventional reservoirs.In a significant departure from these models,our approach incorporates an initiation pressure gradient and a discrete fracture seepage network,providing a more realistic representation of the seepage process.The model also integrates an enhanced fluid-solid interaction,which allows for a more comprehensive understanding of the fluid-structure interactions in the reservoir.This is achieved through the incorporation of improved permeability and stress coupling,leading to more precise predictions of reservoir behavior.The numerical solutions derived from the model are obtained through the sophisticated finite element method,ensuring high accuracy and computational efficiency.To ensure the model’s reliability and accuracy,the outcomes were tested against a real-world case,with results demonstrating strong alignment.A key revelation from the study is the significant difference between uncoupled and fully coupled volumetrically fractured horizontal wells,challenging conventional wisdom in the field.Additionally,the study delves into the effects of stress,fracture length,and fracture number on reservoir production,contributing valuable insights for the design and optimization of tight reservoirs.The findings from this study have the potential to revolutionize the field of tight reservoir prediction and management,offering significant advancements in petroleum engineering.The proposed approach brings forth a more nuanced understanding of tight reservoir systems and opens up new avenues for optimizing reservoir management and production.

Modified MK model combined with ductile fracture criterion and its application in warm hydroforming

A modified MK model combined with ductile fracture criterion（DFC-MK model） is proposed to compute the forming limit diagrams（FLDs） of 5A06-O aluminum alloy sheet at different temperatures.The material constant（C） of ductile fracture criterion and initial thickness imperfection parameter（f0） at various temperatures are determined by using a new computing method based on wide sheet bending test.The FLDs at 20 and 200 °C are calculated through the DFC-MK model.The DFC-MK model,which includes the influence of through-thickness normal stress,is written into the subroutine VUMAT embedded in Abaqus/ Explicit.The cylindrical cup hydroforming tests are carried out to verify the model.The results show that compared with experimental observations,the predicted FLDs based on DFC-MK model are more accurate than the conventional MK model;the errors between the simulations and experiments in warm hydroforming are 8.23% at 20 °C and 9.24% at 200 °C,which verify the effectiveness of the proposed model.