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This study employs a hybrid numerical-experimental calibration method based on phenomena to determine the fracture parameters of the Modified Mohr–Coulomb (MMC) model. Using a self-developed VUMAT subroutine and the element deletion technique, the fracture process of a wide plate pipeline is thoroughly analyzed. This study investigates the impact of various crack shapes on the fracture response under tensile loading and the influence of surface crack size on the initiation location of a wide plate. These results demonstrate the calibrated MMC fracture model's accurate prediction of the toughness fracture behavior of X80 pipeline steel. Under equal area conditions of the dangerous section, circular cracks exhibit lower bearing capacity compared to elliptical cracks. Elliptical cracks predominantly propagate in the thickness direction, whereas circular cracks show nearly uniform growth in all directions. Furthermore, when the crack depth is less than half of the wall thickness, the damage accumulation value at the midpoint of the crack front is maximized; conversely, when the crack front is closer to the internal measurement point of the wide plate, the damage accumulation value is maximized. [ABSTRACT FROM AUTHOR]

A coupled thermomechanical non-ordinary state-based peridynamics (NOSB-PD) model is developed to simulate the dynamic response arising from temperature and to predict the crack propagation with thermal shocks in brittle and ductile solids. A unified multiaxial constitutive model with damage growth is proposed to simultaneously describe the ductile and brittle fracture mechanisms. The main idea is the use of Lemaitre's model to describe ductile damage behavior and the use of tensile strength instead of yield stress in Lemaitre's model to describe brittle damage behavior. A damage-related fracture criterion is presented in the PD framework to predict crack propagation, which avoids numerical oscillations when using the traditional bond stretch criterion. To capture the dynamic plastic response induced by thermal shocks, the time and stress integration are achieved by an alternating solving strategy and implicit return-mapping algorithm. Several numerical examples are presented to show the performance of the proposed model. Firstly, a thermomechanical problem simulation based on both the proposed model and the FEM illustrate the accuracy of the proposed model in studying the thermal deformation. Moreover, a benchmark brittle fracture example of the Kalthoff–Winkler impact test is simulated, and the crack path and angle are similar to the experimental observations. In addition, the simulation of ductile fracture under different loads illustrates the effect of temperature on crack propagation. Finally, the simulation of the 2D quenching test shows the ability of the proposed model in predicting crack propagation under thermal shocks. [ABSTRACT FROM AUTHOR]

(1) Modeling and characterization of ductile fracture in metals is still a challenging task in the field of computational mechanics. Experimental testing offers specific responses in the form of crack-mouth (CMOD) and crack-tip (CTOD) opening displacement related to applied force or crack growth. The main aim of this paper is to develop a phase-field-based Finite Element Method (FEM) implementation for modeling of ductile fracture in stainless steel. (2) A Phase-Field Damage Model (PFDM) was coupled with von Mises plasticity and a work-densities-based criterion was employed, with a threshold to propose a new relationship between critical fracture energy and critical total strain value. In addition, the threshold value of potential internal energy—which controls damage evolution—is defined from the critical fracture energy. (3) The material properties of AISI 316L steel are determined by a uniaxial tensile test and the Compact Tension (CT) specimen crack growth test. The PFDM model is validated against the experimental results obtained in the fracture toughness characterization test, with the simulation results being within 8% of the experimental measurements. (4) The novel implementation offers the possibility for better control of the ductile behavior of metallic materials and damage initiation, evolution, and propagation. [ABSTRACT FROM AUTHOR]

Metal parts undergo a blanking test that involves experimentation with different process parameters across multiple levels. The presence of uncontrolled burrs (measured as Hbv) significantly affects the precise geometry of the blanked parts, making it a primary concern in precision blanking. Moreover, the maximum blanking force (Fmax) holds considerable significance, as it aids in forecasting fracture mechanisms and plays a pivotal role in the design of blanking tools. The aim of this study is to assess the predictive capabilities of an elasto-plastic model coupled with damage in capturing the behavior of sheet material during the blanking process. Additionally, integrating the rate-dependent aspect into the model is crucial for accurately modeling the mechanical behavior of sheet metal. Our focus remains on demonstrating the efficacy of the model in predicting blanking force and burr formation. The numerical model incorporates modified plasticity and damage Johnson–Cook models to achieve this objective, considering the combined effect of strain and strain rate fields in the sheet blanking process. Experimental validation proves the efficacy of the proposed model in accurately predicting blanking outcomes. The experimental results confirm the model's capability to provide a consistent prediction of the blanking force and burr dimensions. In addition, it was proved experimentally that the sheet thickness has the most influence on Hbv and Fmax. [ABSTRACT FROM AUTHOR]

This study introduces a modified DF2016 criterion to model a ductile fracture of sheet metals from shear to equibiaxial tension. The DF2016 criterion is modified so that a material constant is equal to the fracture strain at equibiaxial tension, which can be easily measured by the bulging experiments. To evaluate the performance of the modified DF2016 criterion, experiments are conducted for QP980 with five different specimens with stress states from shear to equibiaxial tension. The plasticity of the steel is characterized by the Swift–Voce hardening law and the pDrucker function, which is calibrated with the inverse engineering approach. A fracture strain is measured by the XTOP digital image correlation system for all the specimens, including the bulging test. The modified DF2016 criterion is also calibrated with the inverse engineering approach. The predicted force–stroke curves are compared with experimental results to evaluate the performance of the modified DF2016 criterion on the fracture prediction from shear to equibiaxial tension. The comparison shows that the modified DF2016 criterion can model the onset of the ductile fracture with high accuracy in wide stress states from shear to plane strain tension. Moreover, the calibration of the modified DF2016 criterion is comparatively easier than the original DF2016 criterion. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Fracture initiation in plastic metals is attributed to the development of voids. Analyzing the nucleation and growth processes of voids facilitates the study of plastic deformation and fracture mechanisms in metal materials. Uniaxial tensile tests were conducted on two high-quality carbon structural steels, and the microfracture surface morphology of the tensile specimens was observed by using a scanning electron microscope (SEM). From the perspective of vacancy condensation, the nucleation mechanism of voids in the absence of inclusions or particles was analyzed. Based on the continuum damage mechanics theory and the Rice–Tracy (R-T) model, a damage parameter considering the void volume fraction was derived, and a plastic potential function, hardening curve, and constitutive model for the plastic deformation process of the plastic metal material were established. Based on the uniaxial tensile test data of the two sheets of high-quality carbon steel, the strain range data in the hardening stage were converted into true stress–plastic strain data, and the established hardening curve was used to fit the true stress–plastic strain data. The results showed good agreement between the established hardening curve and the experimental results, which effectively reflected the deformation process of ductile fractures in plastic metal materials. [ABSTRACT FROM AUTHOR]

A reliable finite element procedure to simulate shear-dominated ductile fractures in large-scale, thin-walled steel structures is still evolving primarily due to the challenges in determining the failure criterion of metal materials under complex stress states. This paper aims to examine the accuracy of the modified Gurson–Tvergaard–Needleman (GTN) model considering the shear failure in simulating the ductile fracture of steel plate structures under quasi-static punch loading. The modified GTN damage models are performed by the ABAQUS user-defined material subroutine (VUMAT). The void-related parameters and shear damage parameters of Xue's and the N-H modified GTN models are calibrated from test specimens with various geometries corresponding to different stress triaxiality and shearing conditions. The damage evolution associated with shearing of voids in the modified GTN models has strong influences on the stress triaxiality versus plastic strain under complex stress states, especially for the shear-dominated loading conditions. Based on the original GTN model, Xue's and the N-H modified GTN model with calibrated material parameters, a numerical comparative study examines the ductile fracture of steel non-stiffened plates and stiffened plates under punch loading. Benchmarked against the experimental studies, the numerical simulations demonstrate that the shear-driven void evolution in the modified GTN model imposes significant effects on the load–displacement responses as well as the onset and extension of ductile fractures in steel plates under punch actions. The N-H modified model with calibrated shear damage parameters shows a better correlation with the ductile fractures in steel plates observed in the experiment than the original GTN model and Xue's modified GTN model. As a result of this study, the modified GTN model considering shear action can be applied for practical applications in the crashworthiness assessment of ship collision and grounding. [ABSTRACT FROM AUTHOR]

Recent research has focused on sheet shear cutting operations. However, little research has been conducted on bar shear cutting. The main objective of the present investigation is to study bar shear cutting with numerical and experimental analysis. Bar shear cutting is an important operation because it precedes bulk metalworking processes for instance machining, extrusion and hot forging. In comparison to sheet shear cutting, bar shear cutting needs thermomechanical modelling. The variational formulation of the model is presented to predict damage mechanics in the bar shear cutting of aluminium alloys. Coupled thermomechanical modelling is required to analyse the mechanical behaviour of bulk workpieces, in which the combined effect of strain and temperature fields is considered in the shear cutting process. For this purpose, modified hardening and damage Johnson–Cook laws are developed. Numerical results for sheet and bar shear cutting operations are presented. The comparison between numerical and experimental results of shearing force/tool displacement during sheet and bar shear cutting operations proves that the use of a thermomechanical model in the case of the bar shear cutting process is crucial to accurately predict the mechanical behaviour of aluminium alloys. The analysis of the temperature field in the metal bar shows that the temperature can reach T = 388 °C on the sheared surface. The current model accurately predicts the shear cutting process and shows a strong correlation with experimental tests. Two values of clearance (c1 = 0.2 mm) and (c2 = 1.2 mm) are assumed for modeling the bar shear cutting operation. It is observed that for the low shear clearance, the burr is small, the quality of the sheared surface is better, and the fractured zone is negligible. [ABSTRACT FROM AUTHOR]

The mechanical behavior of bolted connections in high-strength (HS) steel structures is a matter of concern, since the less ductility compared to mild steels may affect the load transfer and stress distribution of bolted connections. Conducting advanced finite element (FE) analysis incorporating validated material plasticity and ductile fracture criterion allows for a deeper understanding for the load transfer mechanism of HS steel joints. This paper focused on the plasticity and ductile fracture behaviors of HS (S700MC and S960Q) center-holed (CH) plates under tension, which are the essential component in bolted connections. Firstly, a combined linear and power law was used to calibrate and describe the post-necking stress–strain relations of the investigated HS steels. Then, a void-growth-model based on Rice–Tracey criterion was used to simulate the ductile fracture of five groups of CH plates with different hole diameters. The tensile strength and deformation capacity of the CH plates were discussed. The results showed that S700MC had a strain-hardening plasticity until the tensile fracture, while S960Q had a strain-hardening plasticity with a strain-softening behavior followed near the tensile fracture. Incorporating the calibrated plasticity and ductile fracture criterion in FE analyses generated close force-displacement curves as the experimental results. The equation specified in Eurocode produced conservative predictions for the net cross-sectional tensile strength of the investigated HS steels. [ABSTRACT FROM AUTHOR]

In this paper, a validation study of a recently proposed rate-dependent shell element fracture model using quasi-static and dynamic impact tests on square hollow sections (SHS) made from offshore high-tensile strength steel was presented. A rate-dependent forming limit curve was used to predict the membrane loading-dominated failure, while a rate-dependent ductile fracture locus was applied for predicting failure governed by bend loading. The predicted peak force and fracture initiation using the adopted material and fracture model agreed well with the experimental results. The fracture mode was also captured accurately. Further simulations were performed to discuss the importance of the inclusion of dynamic effects and the separate treatment of failure modes. Finally, the shortcomings of the common practice of treatment of rate-effects in low-velocity impact simulations involving fracture were highlighted. [ABSTRACT FROM AUTHOR]

The purpose of this study is to predict the load-bearing capacity (LBC) of fracture specimens containing V-notched friction-stir welded (FSWed) joints of AA7075-Cu and AA7075-AA6061 materials and subjected to mode I loading conditions. Due to the resulting elastic-plastic behavior and the corresponding development of significant plastic deformations, the fracture analysis of the FSWed alloys requires elastic-plastic fracture criteria, which are complex and time-consuming. Thus, in this study, the equivalent material concept (EMC) is applied, equating the actual AA7075-AA6061 and AA7075-Cu materials to equivalent virtual brittle materials. Then, two brittle fracture criteria, the maximum tangential stress (MTS) and mean stress (MS), are utilized to estimate the LBC of the V-notched FSWed parts. The comparison between the experimental results and the theoretical predictions reveals that both fracture criteria, in combination with EMC, can accurately predict the LBC in the analyzed components. [ABSTRACT FROM AUTHOR]

Welding is the main method for oil/gas steel pipeline connection, and a large number of girth welds are a weak part of the pipeline. Under extremely complex loads, a steel pipeline undergoes significant plastic deformations and eventually leads to pipeline fracture. A damage mechanics model is a promising approach, capable of describing material fracture problems according to the stress states of the materials. In this study, an uncoupled fracture 2D model with a function of fracture strain and stress triaxiality, two uncoupled 3D fracture models, a consider the effect of Lode parameter stress-modified critical strain (LSMCS) model, and an extended Rice–Tracey (ERT) criterion were applied to X80 pipeline girth welds. Comprehensive experimental research was conducted on different notched specimens, covering a wide range of stress states, and the corresponding finite element models were established. A phenomenon-based hybrid numerical–experimental calibration method was also applied to determine the fracture parameter for these three models, and the stress triaxiality of the influence law of the tensile strength was analyzed. The results showed that the proposed fracture criterion could better characterize the ductile fracture behaviors of the girth welds of the X80 pipeline; however, the prediction accuracy of the 3D fracture model was higher than that of the 2D fracture model. The functional relationship between the tensile strength and stress triaxiality of the X80 pipeline girth welds satisfied the distribution form of the quadratic function and increased monotonically. The research results can be used to predict the fracture of X80 pipeline girth welds under various complex loads. [ABSTRACT FROM AUTHOR]

In this paper, the fracture behavior of ML15 cold heading steel was investigated based on the ductile fracture theory. Smooth and notched bar, flat grooved and tensile–shear mixed flat plate specimens were designed, and tensile tests were carried out to examine the fracture mechanism of ML15. The micromechanical characteristics of the fracture surfaces of different specimens were studied by performing scanning electron microscopy. The results showed that the specimens under different stress states showed different micro fracture morphologies. The Rice–Tracey model and Bai–Wierzbicki model were calibrated using test results. Based on the calibrated fracture locus, a finite element model is developed and compared to the test results, which confirms the feasibility of the calibrated fracture locus for metal failure analysis. [ABSTRACT FROM AUTHOR]

Because of its geometry dependence and loss of physical meaning, the incremental crack resistance curve cannot characterize ductile fractures with large crack extensions and plastic deformations. Therefore, the energy dissipation rate R is employed to overcome these deficiencies, even though specimen size effects still exist. In the study, considering the fractal crack path and concomitant plastic dissipation in the fractal domain, a scale-invariant energy dissipation rate, γp*, is proposed in the context of renormalization group theory. Some experiments in the literature have validated this approach. The fitted fractal energy dissipation rate is independent of the specimen size and initial crack length; moreover, as the specimen size increases, progressive fractality vanishing is found consistently with geometrical multifractality. [ABSTRACT FROM AUTHOR]

The main purpose of this study is to develop a variational formulation for predicting structure behavior and accounting for damage mechanics in metallic materials. Mechanical and coupled thermomechanical models are used to predict failure in manufacturing processes. Ductile failure is accompanied by a significant amount of plastic deformation in metallic structural components. Finite element simulation of damage evolution in ductile solids is presented in this paper. Uncoupled models are implemented in a finite element model simulating deep drawing as well as cutting processes. Based on the Johnson–Cook model, the effect of deformation on the evolution of flow stress is described. The combined effect of strain, strain rate, and temperature on plasticity and damage behavior in cutting processes is considered. The accuracy of these models is verified when predicting ductile damage in forming and cutting processes. [ABSTRACT FROM AUTHOR]

The paper presents a literature review on the development of microvoids in metals, leading to ductile fracture associated with plastic deformation, without taking into account the cleavage mechanism. Particular emphasis was placed on the results of observations and experimental studies of the characteristics of the phenomenon itself, without in-depth analysis in the field of widely used FEM modelling. The mechanism of void development as a fracture mechanism is presented. Observations of the nucleation of voids in metals from the turn of the 1950s and 1960s to the present day were described. The nucleation mechanisms related to the defects of the crystal lattice as well as those resulting from the presence of second-phase particles were characterised. Observations of the growth and coalescence of voids were presented, along with the basic models of both phenomena. The modern research methods used to analyse changes in the microstructure of the material during plastic deformation are discussed. In summary, it was indicated that understanding the microstructural phenomena occurring in deformed material enables the engineering of the modelling of plastic fracture in metals. [ABSTRACT FROM AUTHOR]

Austenitic stainless steel is useful for storing and transporting liquefied natural gas (LNG) at temperatures below −163 °C due to its superior low-temperature applications. This study develops a computational method for the failure prediction of 304L stainless steel sheet to utilize its usability as a design code for industrial purposes. To consider material degradation in a phenomenological way during the numerical calculation, the combined Swift–Voce equation was adopted to describe the nonlinear constitutive behavior beyond ultimate tensile strength. Due to the stress state-dependent fracture characteristics of ductile metal, a modified Mohr–Coulomb fracture criterion was adopted using stress triaxiality and Lode angle parameter. The numerical formulation of the elastoplastic-damage coupled constitutive model with fracture locus was implemented in the ABAQUS user-defined subroutine UMAT. To identify the material and damage parameters of constitutive models, a series of material tests were conducted considering various stress states. It has been verified that the numerical simulation results obtained by the proposed failure prediction methodology show good agreement with the experimental results for plastic behavior and fractured configuration. [ABSTRACT FROM AUTHOR]

Governing void growth, stress triaxiality (η) is a crucial parameter in ductile damage prediction. η is defined as the ratio of mean stress to equivalent stress and represents loading conditions. Attempts at introducing material anisotropy in ductile damage models have started only recently, rendering necessary in-depth investigation into the role of η here. η is commonly derived via finite elemnt (FE) simulation. An alternative is presented here: based on analytical expressions, η is obtained directly from the strains in the critical zone. For anisotropic materials, η associated with a specimen varies with yield criterion and material (anisotropy). To investigate the meaning of triaxiality for anisotropic materials, metal sheets made of dual phase steel DP780, and zirconium alloy Zirlo are chosen. Analytical expressions for η are derived for three popular yield criteria: von Mises, Hill48 and Barlat89. Tensile tests are performed with uniaxial tension, notch, and shear specimens, and the local principal strains, measured via digital image correlation (DIC), are converted to h. The uniaxial tension case reveals that only the anisotropic yield criteria can predict the expected η = 1/3. The ramifications associated with anisotropy become apparent for notched specimens, where η differences are highest; for shear specimens, the yield criterion and material-dependence is relatively moderate. This necessitates η and, consequently, the triaxiality failure diagram (TFD) being accompanied by the underlying yield criterion and anisotropy parameters. As the TFD becomes difficult to interpret, it seems more advantageous to provide pairs of principal strain ratio β and failure strain. Suggestions for deriving representative β and η are made. [ABSTRACT FROM AUTHOR]

In this study, Ti-30Mo-nTiC (0, 0.5 wt.%) and Ti-30Mo-0.5TiC-xZr (0, 4, 8, 12 wt.%) alloys were prepared using the powder metallurgy process with the addition of Zr at different rates. The effect of TiC and Zr additions on the microstructure and mechanical properties of the Ti-30Mo alloys were investigated, respectively. The results demonstrated that the addition of 0.5 wt.% TiC significantly improved the density, tensile strength and elastic modulus. The ultimate tensile strength, elongation and elastic modulus of the Ti-30Mo-0.5TiC alloy were determined to be 825 MPa, 7.3% and 112 GPa, respectively. For Ti-30Mo-0.5TiC-xZr alloys, the addition of Zr (8 wt.% or less) results in alloys having a high relative density (>98%), with the density of the alloy decreasing significantly when the Zr content is 12 wt.%. As the Zr content increases, the β phase lattice constant also increases along with the amount of carbide aggregation. This leads to a decrease in the alloy strength, with an increase in the alloy hardness. During high temperature tensile testing at 600 °C, the Ti-30Mo-0.5TiC alloy still had suitable mechanical properties, with its ultimate tensile strength and elongation being 472 MPa and 12.8%, respectively. [ABSTRACT FROM AUTHOR]

In this study, the Void Growth Model (VGM) is employed to predict the ductile fracture of X80 pipeline steel. The X80 pipeline tends to be applied in challenging scenarios, such as extremely deep water and long-distance pipelines, which might cause a ductile fracture; however, the study of ductile fractures for pipeline steel is rare, especially for X80 pipeline steel. To understand ductile fractures of X80 pipeline steel, a hybrid numerical–experimental calibration method is used to determine the fracture parameter for the VGM model. The toughness capacity defined by the critical void growth index (VGI) in this study is determined to be 4.304. A shear-tension specimen is applied to verify the calibrated VGM. The results show that the calibrated VGM can predict the fracture initiation of the shear-tension specimen. In addition, the fracture of the shear-tension specimen initiates at the center of the section and propagates to the edge of the groove of the specimen. The initiation of fracture is identical to the testing observation. [ABSTRACT FROM AUTHOR]

The evaluation of tube burring formability is a crucial task for finding a suitable material for tube-based automobile parts. The local strain at the ductile fracture site (fracture strain) should be evaluated for this purpose. Moreover, a cold-drawn steel tube has a strong anisotropic shaped microstructure and possibly causes anisotropic fracture strain behavior. Based on this background, the study evaluated the axial and hoop directional fracture strains of cold-drawn steel tubes using the small round-bar tensile specimen. The burnished surface ratio on the pierced surface was also investigated for possibility estimation of in-line formability inspection. As a result, three tubes are presented with inferior, nearly the same, and superior hoop directional fracture strains compared with the axial strains, where exceeding 40% deterioration in the hoop direction occurs by a combination of grain elongation and carbide aggregation. The scanning electron micrographs suggest that the microvoid growth and linkage percolated thorough carbides on the elongated grain boundaries. For the piercing test, the 30% fracture strain deterioration resulted in a 4% decrease in the burnished surface ratio on the pierced surface. This result suggested that the estimation of the pierced surface can detect material defects before the actual tube-burring process. [ABSTRACT FROM AUTHOR]

The wide application of advanced high strength steels with high specific strength in the automotive industry can significantly reduce energy consumption and contribute to carbon neutrality. Accurate prediction of the ductile fracture behavior of advanced high strength steels under complex stress states is of great significance for its application in automobile industry. In this study, the ductile fracture behavior of QP980 under complex stress states, covering shear, uniaxial tension, and plane strain tension, is investigated by conducting the hybrid experiment and simulation. The pressure-coupled Drucker yield function is chosen to characterize the effect of stress states on yielding for QP980, considering its high accuracy compared with the von Mises yield function. Failure limit of the stress states is modelled by five uncoupled ductile fracture criteria (Brozzo, Oh, Rice-Tracey, Ko-Huh, and DF2012). To improve the numerical prediction accuracy, the parameters of the constitutive model are optimized by using the inverse engineering approach. The numerical predicted results are compared with the experimental load-stroke curves with the onset of fracture. The comparison indicates that the prediction error of the DF2012 criterion is significantly lower than those of the other four criteria. In addition, the prediction accuracy is greatly improved with the parameters of the constitutive model optimized by the inverse engineering. [ABSTRACT FROM AUTHOR]

A series of earthquake events give impetus to research on the ductile fracture behavior of steel materials. In the last decades, many fracture models have been developed and utilized in the mechanical or aerospace engineering. Nevertheless, very little application to structural members used in the construction industry has been made due to the lack of a suitable model for the fracture behavior of constructional steel. This paper presents the experimental and finite element (FE) technique to predict ductile fracture in mild carbon structural steel (SS275) sheets, which has been widely used in building structures. The post-necking true stress–strain responses were successfully estimated using the weighted-average method. The Bao and Wierzbicki (BW) model, which requires only two model parameters, was selected for the identification of fracture locus. Each model parameter was calibrated from uniaxial tension and in-plane shear specimens with the aid of digital image correlation (DIC) and finite element analysis. Fracture simulation was then performed and validated based on the experimental results of the specimens under combined tension and shear stress state. [ABSTRACT FROM AUTHOR]

The ductile fracture of thin-shell structures was studied here using a localized necking model. The punching experiments for unstiffened and stiffened panels were compared with numerical predictions using a combined ductile fracture and localized necking model using shell elements. The plasticity and fracture model parameters of JIS G3131 SPHC steel were identified by performing calibration experiments on standard flat bars, notched tension, central hole tension, plane strain tension, and shear specimens. The plasticity beyond the onset of necking was modeled using the Swift hardening law. The damage indicator framework with a combined Hosford–Coulomb fracture model and the domain of shell-to-solid equivalence (DSSE) were adopted to characterize the fracture initiation. The model parameters were calibrated based on the loading paths to fracture initiation, which were extracted from a non-linear finite element (FE) analysis. The presented HC–DSSE model was validated using punch tests and was able to predict fracture initiation with good accuracy. [ABSTRACT FROM AUTHOR]

Featured Application: The paper allows the fracture behavior of biopolymers containing notches to be better understood. This paper analyzes the notch effect on the fracture behavior of two biomaterials (a brittle bone cement and a ductile dental material) under mode I loading. U-notched Brazilian disk (UNBD) specimens of both materials were tested under remote compression, determining the corresponding fracture loads and load-displacement curves. Additionally, cracked rectangular and semicircular bend (SCB) specimens were tested under symmetric three-point bending in order to determine the fracture toughness of the two materials. Then, fracture loads were derived theoretically by applying the maximum tangential stress (MTS) and the mean stress (MS) criteria. Due to the brittle linear elastic behavior of the bone cement material, the MTS and MS criteria were directly applied to this material; however, given the significant nonlinear behavior of the dental material, the two fracture criteria were combined with the Equivalent Material Concept (EMC) for the fracture analyses of the dental material specimens. The results reveal a very good accuracy of both the MTS and the MS criteria for the fracture analysis of bone cement notched specimens. In the case of the dental material, very good results are also obtained when combining the MTS and the MS criteria with the EMC. The proposed approach can be useful for the fracture analysis of a wide range of biopolymers, from brittle to ductile behavior. [ABSTRACT FROM AUTHOR]

A comparison is made of the ductility limits of one mild (normal) and two high-tensile strength shipbuilding steels with an emphasis on stress state and loading path dependency. To describe the ductile fracture behavior of the considered steels accurately, an alternative form of ductile fracture prediction model is presented and calibrated. The present fracture model combines the normalized Cockcroft–Latham and maximum shear stress criterion, and is dependent on both stress triaxiality and Lode angle parameter. The calibrations indicate that, depending on the hardening characteristics of the steels, ductile fracture behavior differs considerably with stress state. It is demonstrated that the adopted fracture model is able to predict the ductile fracture initiation in various test specimens with good accuracy and is flexible in addressing the observed differences in the ductile fracture behavior of the considered steel grades. [ABSTRACT FROM AUTHOR]

Perforated steel plates with regularly shaped holes are already widely employed as steel dampers, which dissipate seismic energy through plastic deformation of steel. As a typical auxetic structure, two-dimensional (2D) re-entrant honeycomb configurations have characteristics of large deformation and good energy absorption. However, research on the effects of these configurations on the mechanical performance of steel is limited. This paper investigated the auxetic properties of perforated steel plates with re-entrant hexagon holes. Repetitive units are controlled by three parameters, hole ratio, re-entrant angle, and chamfer radius. Elastoplastic behavior and damage under large deformation were studied via tension tests and finite element (FE) analysis based on a micromechanics-based ductile fracture model. The effects of different parameters on mechanical properties of configurations were analyzed and discussed. The static performance of the perforated steel plates obtained in this study provides a good basis for its further dynamic study under large deformation. [ABSTRACT FROM AUTHOR]

The intergranular crack propagation of the lamellar structure β titanium alloys is investigated by using a modified Gurson-type damage model. The representative microstructure of the lamellar alloy, which consists of the soft α phase layer surrounding the hard grain interiors, is generated based on an advanced Voronoi algorithm. Both the normal fracture due to void growth and the shear fracture associated with void shearing are considered for the grain boundary α layer. The individual phase properties are determined according to the experimental nanoindentation result and the macroscopic stress-strain curve from a uni-axial tensile test. The effects of the strain hardening exponent of the grain interiors and the void shearing mechanism of the grain boundary α layer on fracture toughness and the intergranular crack growth behavior are emphatically studied. The computational predictions indicate that fracture toughness can be increased with increasing the strain hardening ability of the grain interiors and void shearing can be deleterious to fracture toughness. Based on the current simulation technique, qualitative understanding of relationships between the individual phase features and the fracture toughness of the lamellar alloys can be obtained, which provides useful suggestions to the heat treatment process of the β titanium alloys. [ABSTRACT FROM AUTHOR]

A unified experimental-computational study on ductile fracture initiation and propagation during small punch testing is presented. Tests are carried out at room temperature with unnotched disks of different thicknesses where large-scale yielding prevails. In thinner specimens, the fracture occurs with severe necking under membrane tension, whereas for thicker ones a through thickness shearing mode prevails changing the crack orientation relative to the loading direction. Computational studies involve finite element simulations using a shear modified Gurson-Tvergaard-Needleman porous plasticity model with an integral-type nonlocal formulation. The predicted punch load-displacement curves and deformed profiles are in good agreement with the experimental results. [ABSTRACT FROM AUTHOR]

In this study, a phase field viscoplastic model is proposed to model the influence of the loading rate on the ductile fracture, as one of the main causes of metallic alloys' failure. To this aim, the effects of the phase field are incorporated in the Peric's viscoplastic model; the model can efficiently be converted to a standard rate-independent model. The novel aspects of this work include: Describing a coupling between rate-dependent plasticity and phase field formulation by defining an energy function that contains the energy dissipation caused by plastic deformation as well as the fracture process and elastic energy. In addition, the equations required to develop the numerical solution are presented. The governing equations are determined by a minimization principle that results in balance laws for the coupled displacement-phase field problem. Furthermore, an implicit integration algorithm for a viscoplasticity model coupled with a phase field is presented for a three-dimensional stress state. The proposed algorithm can be utilized for different constitutive models of rate-dependent and rate-independent plasticity models coupled with fracture by changing the definition of the plastic multiplier. In addition, to control the influence of the plastic deformation and its work on the crack propagation, a threshold variable is defined in the model. Finally, using the proposed model, the influence of the loading rate on the responses of the different specimens in one-dimensional and multi-dimensional cases is investigated and the accuracy of the results was verified by comparing them with existing experimental and numerical results. The obtained result proves that the model can simulate the impact of the loading rate on the material response, and the gradual change of the fracture phase from ductile to brittle, caused by increasing the loading rate. [ABSTRACT FROM AUTHOR]

Tensile and compression tests were carried out on a ductile cast iron for temperatures up to 1073 K. The damage caused inside and around graphite nodules was evaluated as a function of the local equivalent plastic strain by using microstructural quantifications. The mechanical properties are strongly dependent on a temperature above 773 K. Concerning tensile behavior, an evolutional law issued from the Gurson model representing the void growth as a function of the deformation and temperature was successfully employed. It is demonstrated that the strain state and the temperature have a strong influence on the void growth function. In the case of compression tests, the temperature has a weak influence on the nodule deformation for temperatures lower than 773 K, and the mechanical behavior is driven by the viscoplastic properties of the ferrite. For higher temperatures, the mechanical properties in compression are progressively modified, since graphite nodules tend to remain spherical, and ferrite grains are severely deformed. A synthesis of the damage mechanisms is proposed in the studied range of temperature and plastic strain. It appears that the graphite nodule aspect ratio can be used as an indicator of the deformation under compression loading for temperatures ranging from room temperature to 673 K. [ABSTRACT FROM AUTHOR]

The use of a stress-strain constitutive relation for the undamaged material and a traction-separation cohesive crack model with softening for cracking has been demonstrated to be an effective strategy to predict and explain the size-scale effects on the mechanical response of quasi-brittle materials. In metals, where ductile fracture takes place, the situation is more complex due to the interplay between plasticity and fracture. In the present study, we propose a multi-scale numerical method where the shape of a global constitutive relation used at the macro-scale, the so-called hardening cohesive zone model, can be deduced from meso-scale numerical simulations of polycrystalline metals in tension. The shape of this constitutive relation, characterized by an almost linear initial branch followed by a plastic plateau with hardening and finally by softening, is in fact the result of the interplay between two basic forms of nonlinearities: elasto-plasticity inside the grains and classic cohesive cracking for the grain boundaries. [ABSTRACT FROM AUTHOR]

Hot stamping components with tailored mechanical properties have excellent safety-related performance in the field of lightweight manufacturing. In this paper, the constitutive relation and damage evolution of bainite, martensite, and mixed bainite/martensite (B/M) phase were studied. Two-dimensional representative volume element (RVE) models were constructed according to microstructure characteristics. The constitutive relations of individual phases were defined based on the dislocation strengthening theory. Results showed that the damage initiation and evolution of martensite and bainite phases can well described by the Lou-Huh damage criterion (DF2015) determined by the hybrid experimental–numerical method. The calibrated damage parameters of each phase were applied to the numerical simulation, followed by the 2D RVE simulations of B/M phase under different stress states. To study the influence of martensite volume fraction (Vm) and distribution of damage evolution, the void nucleation and growth were evaluated by RVEs and verified by scanning electron microscope (SEM). Three types of void nucleation modes under different stress states were experimentally and numerically studied. The results showed that with the increase of Vm and varying martensite distribution, the nucleation location of voids move from bainite to martensite. [ABSTRACT FROM AUTHOR]

The article aims to investigate the effect of different austenitization temperatures on the hot ductility of C-Mn-Al High-Strength Low-Alloy (HSLA) steel. The thermo-mechanical simulator of physical processes Gleeble 1500D was used for steel hot ductility study. Hot ductility was estimated by measuring the reduction of area after static tensile testing carried out at temperatures in the range 600 °C to 1200 °C with the step of 50 °C. Evaluation of fracture surfaces after austenitization at 1250 °C and 1350 °C with a holding time of the 30 s showed significant differences in the character of the fracture as well as in the ductility. The fracture surfaces and the microstructure near the fracture surfaces of samples at a test temperature of 1000 °C for both austenitization temperatures were analyzed by Scanning Electron Microscopy (SEM), Light Optical Microscopy (LOM), and AZtec Feature analysis (particle analysis of SEM). AlN and AlN-MnS precipitates at grain boundaries detected by the detailed metallographic analysis were identified as the main causes of plasticity trough in the evaluated steel. Moreover, using Thermo-Calc software, it was found that AlN particles precipitate from solid solution below the temperature of 1425 °C. [ABSTRACT FROM AUTHOR]

The precise identification of micro-features on 2.25Cr1Mo0.25V steel is of great significance for understanding the mechanism of hydrogen embrittlement (HE) and evaluating the alloy's properties of HE resistance. Presently, the convolution neural network (CNN) of deep learning is widely applied in the micro-features identification of alloy. However, with the development of the transformer in image recognition, the transformer-based neural network performs better on the learning of global and long-range semantic information than CNN and achieves higher prediction accuracy. In this work, a new transformer-based neural network model Swin–UNet++ was proposed. Specifically, the architecture of the decoder was redesigned to more precisely detect and identify the micro-feature with complex morphology (i.e., dimples) of 2.25Cr1Mo0.25V steel fracture surface. Swin–UNet++ and other segmentation models performed state-of-the-art (SOTA) were compared on the dimple dataset constructed in this work, which consists of 830 dimple scanning electron microscopy (SEM) images on 2.25Cr1Mo0.25V steel fracture surface. The segmentation results show Swin–UNet++ not only realizes the accurate identification of dimples but displays a much higher prediction accuracy and stronger robustness than Swin–Unet and UNet. Moreover, efforts from this work will also provide an important reference value to the identification of other micro-features with complex morphologies. [ABSTRACT FROM AUTHOR]

The aluminum alloys (AA) are among the most utilized materials in engineering structures, which induces the need for careful investigation, testing, and possibilities for accurate simulation of the structure's response. AA 5083-H111 specimens were used to investigate the possibility of employing a Phase-Field Damage Model (PFDM) for the simulation of AA structures' behavior. The specimens were mechanically tested by uniaxial tensile loading tests. Based on the obtained results, the PFDM was employed with a von Mises plasticity model, implemented in the Finite Element Method software. The plasticity model was extended by modification of the hardening function defined in two-intervals: a linear hardening and a Simo-type hardening. An excellent superposition of the simulation and experimental force-displacement response was recorded. These findings suggest that the AA structures' response can be successfully simulated in the elastic-plastic domain, as well as its failure by damage being controlled. [ABSTRACT FROM AUTHOR]

This paper aims to develop a method for determining the workability diagram by varying frictional conditions in the cylinder upsetting test. The method is based on a known theoretical relationship between the average stress triaxiality ratio and in-surface strains if the initiation of fracture occurs at a traction-free surface. This relationship is valid for any rigid/plastic strain hardening material obeying the Mises-type yield criterion and its associated flow rule, which shows the wide applicability of the method. The experimental input to the method is the strain path at the site of fracture initiation. Neither experimental nor numerical determination of stress components is required at this site, though the general ductile fracture criterion involves the linear and quadratic invariants of the stress tensor. The friction law's formulation is neither required, though the friction stress is the agent for varying the state of stress and strain at the site of ductile fracture initiation. The upsetting tests are carried out on normalized medium-carbon steel C45E, for which the workability diagram is available from the literature. Comparison of the latter and the diagram found using the new method shows that the new method is reliable for determining a certain portion of the workability diagram. [ABSTRACT FROM AUTHOR]

The aim of this work was to include a local variation in material properties to simulate the fracture behaviour in a multi-pass mis-matched X-weld joint. The base material was welded with an over and under-match strength material. The local variation was represented in a finite element model with five material groups in the weld and three layers in the heat-affected zone. The groups were assigned randomly to the elements within a region. A three-point single edge notch bending (SENB) fracture mechanics specimen was analysed for two different configurations where either the initial crack is in the over or under-matched material side to simulate experimentally obtained results. The used modelling approach shows comparable crack propagation and stiffness behaviour, as well as the expected, scatter and instabilities of measured fracture behaviour in inhomogeneous welds. [ABSTRACT FROM AUTHOR]

In this work, a small-strain phase-field model is presented, which is able to predict crack propagation in systems with anisotropic brittle and ductile constituents. To model the anisotropic brittle crack propagation, an anisotropic critical energy release rate is used. The brittle constituents behave linear-elastically in a transversely isotropic manner. Ductile crack growth is realised by a special crack degradation function, depending on the accumulated plastic strain, which is calculated by following the J 2 -plasticity theory. The mechanical jump conditions are applied in solid-solid phase transition regions. The influence of the relevant model parameters on a crack propagating through a planar brittle-ductile interface, and furthermore a crack developing in a domain with a single anisotropic brittle ellipsoid, embedded in a ductile matrix, is investigated. We demonstrate that important properties concerning the mechanical behaviour of grey cast iron, such as the favoured growth of cracks along the graphite lamellae and the tension–compression load asymmetry of the stress–strain response, are covered by the model. The behaviour is analysed on the basis of a simulation domain consisting of three differently oriented elliptical inclusions, embedded in a ductile matrix, which is subjected to tensile and compressive load. The material parameters used correspond to graphite lamellae and pearlite. [ABSTRACT FROM AUTHOR]

This study examined the effects of the strain rate and thermal softening on large-scale ductile fracture in ship collisions using a rate-dependent combined localized necking and fracture model. A Johnson–Cook type-hardening model, consisting of strain hardening, rate-sensitivity, and thermal softening terms, was adopted together with an associated flow rule. The temperature was treated as an internal state variable and was calculated from the plastic strain energy using a strain-rate-dependent weighting function under fully isothermal and adiabatic conditions. At every time increment, the fracture locus was updated based on the temporal strain rate, whereas the necking locus was coupled with the hardening law, which was dependent on both the strain rate and temperature. The damage indicator framework was used to consider the non-proportional loading paths. The dynamic shell-element failure model was verified through plate-panel penetration tests and applied to a large-scale ship collision analysis involving a struck ship/ship-shaped offshore installation and a supply vessel. The effects of the loading rate and impact energy were assessed in terms of the global behavior of the structure and observed failure modes. [ABSTRACT FROM AUTHOR]

The paper discusses the basic issues of the local approach to ductile fracture of structural metals, with particular emphasis on the failure due to microvoid development. The mechanisms of nucleation of voids around inclusions and precipitates are characterized. The criteria for the nucleation of voids resulting from cracking of the existing particles or their separation from the material matrix are presented. Selected results of experimental studies and Finite Element Method (FEM) simulations on nucleation of voids are discussed. The analytical and numerical models of growth and coalescence of voids are described, indicating the effect of the stress state components on the morphology of voids and the course of the cracking on a microscopic scale. [ABSTRACT FROM AUTHOR]

This study investigates the disparate impact of internal pores on the fracture behavior of two metal alloys fabricated via laser powder bed fusion (L-PBF) additive manufacturing (AM)—316L stainless steel and Ti-6Al-4V. Data from mechanical tests over a range of stress states for dense samples and those with intentionally introduced penny-shaped pores of various diameters were used to contrast the combined impact of pore size and stress state on the fracture behavior of these two materials. The fracture data were used to calibrate and compare multiple fracture models (Mohr-Coulomb, Hosford-Coulomb, and maximum stress criteria), with results compared in equivalent stress (versus stress triaxiality and Lode angle) space, as well as in their conversions to equivalent strain space. For L-PBF 316L, the strain-based fracture models captured the stress state dependent failure behavior up to the largest pore size studied (2400 µm diameter, 16% cross-sectional area of gauge region), while for L-PBF Ti-6Al-4V, the stress-based fracture models better captured the change in failure behavior with pore size up to the largest pore size studied. This difference can be attributed to the relatively high ductility of 316L stainless steel, for which all samples underwent significant plastic deformation prior to failure, contrasted with the relatively low ductility of Ti-6Al-4V, for which, with increasing pore size, the displacement to failure was dominated by elastic deformation. [ABSTRACT FROM AUTHOR]

In molten carbonate fuel cell (MCFC) systems, it is known that the shape of corrugated plates has a significant influence on performance, durability, and cost. A corrugated plate with a repeating open trapezoidal-shaped slot supports membrane electrode assembly and provides a gas flow channel. To increase the efficiency of the MCFC, the slot between the corrugated and center plates has a relatively large contact length. However, increasing the contact length of the slot increases the risk of necking or fracture generation at the corner of the slot. Therefore, we focus on the development of forming technology of corrugated plate which has large contact length of slots without any necking or fracture. To this end, numerical simulation was conducted to determine the appropriate process and tool design. In the simulation, to capture shear fracture during the forming process of slots, the normalized Cockroft–Latham ductile fracture model was used. The critical value for slitting and fracture was evaluated by comparing the deformed shapes in the slitting plane obtained from experimental and simulation results. Based on simulation results, a reasonable design concept of the two-stage forming process was suggested to increase the contact length of the slot without necking or fracture. In addition, the experiment results confirmed the validity of the proposed forming process and tool design. [ABSTRACT FROM AUTHOR]

The main purpose of this study is to investigate the feasibility of the seismic fragility analysis (FA) with the strain-based failure modes for the nuclear metal components retaining pressure boundary. Through this study, it is expected that we can find analytical ways to enhance the high confidence of low probability of failure (HCLPF) capacity potentially contained in the conservative seismic design criteria required for the nuclear metal components. Another goal is to investigate the feasibility of the seismic FA to be used as an alternative seismic design rule for beyond-design-basis earthquakes. To do this, the general procedures of the seismic FA using the inelastic seismic analysis for the nuclear metal components are investigated. Their procedures are described in detail by the exampled calculations for the surge line nozzles connecting hot leg piping and the pressurizer, known as one of the seismic fragile components in NSSS (Nuclear Steam Supply System). To define the seismic failure modes for the seismic FA, the seismic strain-based design criteria, with two seismic acceptance criteria against the ductile fracture failure mode and fatigue-induced failure mode, are used in order to reduce the conservatism contained in the conventional stress-based seismic design criteria. In the exampled calculation of the inelastic seismic strain response beyond an elastic regime, precise inelastic seismic analyses with Chaboche's kinematic and Voce isotropic hardening material models are used. From the results of the seismic FA by the probabilistic approach for the exampled target component, it is confirmed that the approach of the strain-based seismic FA can extract the maximum seismic capacity of the nuclear metal components with more accurate inelastic seismic analysis minimizing the number of variables for the components. [ABSTRACT FROM AUTHOR]

This paper aims to (1) study ductile fracture behavior, and (2) provide a computational tool for predicting fracture initiation in ASTM A572 Gr. 50 structural steels under axisymmetric tension loading are heated to elevated temperatures and cooled down in air and in water. Employing the post-fire test results reported in the literature for A572 Gr. 50 steels, this paper carries out coupon-level finite element (FE) simulations to capture the stress and strain fields and explore the micro-mechanism of post-fire fracture in ASTM A572 Gr. 50 steels, respectively. Numerical results show that the effects of the experienced temperature and cooling method on fracture parameters are more significant for the steels cooled after being heated to temperatures from 800 °C to 1000 °C than those from 500 °C to 700 °C, due to microstructural changes during the cooling process. Air-cooled and water-cooled specimens show an improvement and a significant reduction in ductility, respectively. A modified void growth model (VGM) is proposed by introducing two additional temperature-dependent functions, through which the effects of elevated temperature and cooling method on fracture behavior are quantitatively analyzed. Limitations of this study are also discussed. [ABSTRACT FROM AUTHOR]

Advanced high strength dual-phase steels are one of the most widely sought-after structural materials for automotive applications. These high strength steels, however, are prone to fracture under bending-dominated manufacturing processes. Experimental observations suggest that the bendability of these steels is sensitive to the presence of subsurface non-metallic inclusions and the inclusions exhibit a rather discrete size effect on the bendability of these steels. Following this, we have carried out a series of microstructure-based finite element calculations of ductile fracture in an advanced high strength dual-phase steel under bending. In the calculations, both the dual-phase microstructure and inclusion are discretely modeled. To gain additional insight, we have also analyzed the effect of an inclusion on the bendability of a single-phase material. In line with the experimental observations, strong inclusion size effect on the bendability of the dual-phase steel naturally emerge in the calculations. Furthermore, supervised machine learning is used to quantify the effects of the multivariable input space associated with the dual-phase microstructure and inclusion on the bendability of the steel. The results of the supervised machine learning are then used to identify the contributions of individual features and isolate critical features that control the bendability of dual-phase steels. [ABSTRACT FROM AUTHOR]

This study compared the experimental test results on punch-loaded unstiffened and stiffened panels with numerical predictions using different localized necking modeling approaches with shell elements. The analytical models that were derived by Bressan–Williams–Hill (BWH) were used in their original form and extended version, which considers non-proportional loading paths while using the forming-severity concept and bending-induced suppression of through-thickness necking. The results suggest that the mesh size sensitivity depends on the punch geometry. Moreover, the inclusion of bending effects and the use of the forming-severity concept in the BWH criterion yielded improved estimations of fracture initiation with shell elements. [ABSTRACT FROM AUTHOR]

Steel structures are designed to operate in an elastic domain, but sometimes plastic strains induce damage and fracture. Besides experimental investigation, a phase-field damage model (PFDM) emerged as a cutting-edge simulation technique for predicting damage evolution. In this paper, a von Mises metal plasticity model is modified and a coupling with PFDM is improved to simulate ductile behavior of metallic materials with or without constant stress plateau after yielding occurs. The proposed improvements are: (1) new coupling variable activated after the critical equivalent plastic strain is reached; (2) two-stage yield function consisting of perfect plasticity and extended Simo-type hardening functions. The uniaxial tension tests are conducted for verification purposes and identifying the material parameters. The staggered iterative scheme, multiplicative decomposition of the deformation gradient, and logarithmic natural strain measure are employed for the implementation into finite element method (FEM) software. The coupling is verified by the 'one element' example. The excellent qualitative and quantitative overlapping of the force-displacement response of experimental and simulation results is recorded. The practical significances of the proposed PFDM are a better insight into the simulation of damage evolution in steel structures, and an easy extension of existing the von Mises plasticity model coupled to damage phase-field. [ABSTRACT FROM AUTHOR]