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To investigate the microstructural changes that occur in stainless steel (SS) 304 during single point incremental forming (SPIF), experiments and finite element (FE) simulations were conducted for a truncated square pyramid geometry. Results from material characterization experiments for four stress states, i.e., uniaxial tension, equibiaxial tension, shear, and uniaxial compression, were combined to construct a material model based on the constituent phases and transformation kinetics. The material model was implemented into numerical analyses, where a two-step FE approach was utilized to predict martensite transformation in SPIF with increased computational efficiency. Validation experiments showed good agreement with the martensite transformation predictions from the FE simulations. The four locations along the pyramid wall revealed varying martensite volume fractions because of the differing stress states of bending, stretching, and shear that the blank is subjected to during SPIF, which can affect the microstructure. The stress state can be defined in terms of the stress triaxiality and Lode angle parameter. The FE results indicate that stress triaxiality impacted the martensitic transformation kinetics in SS304 more than the Lode angle parameter for SPIF for this particular material and geometry. Thus, distinct stress states in incremental forming can affect the martensitic transformation locally and, when used strategically, achieve functionally graded materials. This is pertinent to industrial applications requiring custom components, e.g., trauma fixation hardware for medical applications. [Display omitted] • SPIF pyramids exhibit heterogeneous microstructures affected by stress states. • A two-step FEA efficiently predicts the phase transformation of SS304 during SPIF. • SS304 models for constituent phases and transformation kinetics are identified. • Stress triaxiality impacted transformation kinetics more than Lode angle parameter. • Controlling microstructure can create functionally graded materials through SPIF. [ABSTRACT FROM AUTHOR]

The fracture behavior of rhombic dodecahedron (DOD) and body-centered cubic (BCC) 3D printed lattice structure considering surface roughness was investigated. Tensile tests on flat specimens with different surface roughness were performed, which indicates surface quality has an important influence on the fracture elongation. Smoothed round and round notched tensile specimens were also tested to calibrate damage constitutive model parameters. Based on the statistical data of the diameter variations of the struts and a progressive damage material model, FEM models were built to simulate the fracture behaviors of lattice structures. The simulation results are consistent with the experimental ones and damage evolution characteristics of the fractured struts are discussed. It's proved that surface roughness is a key factor to affect the strength of the lattice structure and fracture behavior. [ABSTRACT FROM AUTHOR]

• The 6061-T6 rolled aluminum alloy sheets exhibit significant anisotropic ductile fracture both in-plane and out-of-plane. • A linear-transformation-free anisotropic fracture model is proposed based on critical principal direction. • The model accurately predicts anisotropic ductile fracture under various stress states and sampling directions. • The model features a clear physical basis for the anisotropic ductile fracture dependent on the triaxiality, Lode angle, and sampling direction. The linear transformation has been successfully used to characterize the anisotropic ductile fracture, whereas the physical background of the transformed anisotropic stress state or the equivalent plastic strain becomes somewhat vague. This deficiency in the linear-transformation model might overlook the microscopic mechanisms of the anisotropic ductile fracture related to various stress states and loading direction. Therefore, this paper proposes an advanced linear-transformation-free anisotropic ductile fracture modeling framework that is dependent on stress triaxiality and the Lode angle, two state variables intimately related to microscopic fracture mechanisms. Notably, the model introduces the critical principal stress direction to account for the dependency on loading direction. The stress state variables and principal stress direction correspond to the geometry and sampling direction straightforwardly, which significantly facilitates the calibration of fracture parameters. Furthermore, compared to traditional linear-transformation-based anisotropic models, the proposed model is underpinned by a clear physical basis and accurately captures the relationships between triaxiality, Lode angle and material ductility with respect to varying loading directions. This model has been calibrated and validated based on the testing program on aluminum alloy 6061-T6 rolled plates under various stress states, considering both in-plane and out-of-plane anisotropies. The accurate prediction in terms of the softening initiation and failure modes for all testing cases demonstrate the validity of the proposed anisotropic ductile fracture model, as evidenced by the low averaged percentage of damage indicator at softening initiation at 4.6 %. [Display omitted] [ABSTRACT FROM AUTHOR]

• Investigating a coupled damage-plasticity model to characterize the failure behavior of CuZn30 brass. • Conducting various tests to explore the failure characteristics influenced by stress triaxiality and Lode angle. • The simplified approach used to implement the Ganjiani and Lou ductile failure models in numerical simulations. • Simulating the observed softening (necking) phenomenon across all conducted tests. • Verifying fracture strains obtained by numerical methods with experiments through image processing. The investigation of ductile failure in CuZn30 brass under various stress triaxialities and Lode angles is the main subject of this paper. To accomplish this, six different specimen geometries were fabricated, including dog-bone, notched, two types of in-plane shear, torsion, deep drawing, upsetting and central-hole specimens. Only dog-bone, notched, two shears specimens were tested in three orientations: rolling, diagonal, and transverse to explore potential anisotropic properties in plastic deformation. A fully coupled ductile damage-plasticity model, incorporating the effects of stress triaxiality and Lode angle, along with a non-linear damage evolution law, is used to predict material failure. The modified Ganjiani and Lou ductile failure models were employed as failure onset criteria. Despite variations in their mathematical formulations, both models were considered due to their comparable predictions. Experimental results were validated through a combination of experimental and numerical simulations using ABAQUS with VUSDFLD and VUHARD codes. The outcomes of the simulation demonstrated good concordance with the results obtained through experiment, particularly in terms of force and the softening (necking) zone for all specimen types. Both failure models produced nearly identical failure strain values and accurately predicted damage initiation locations. The fracture strains obtained from numerical simulations were also experimentally validated using images of the ruptured cross-sections, processed with Microstructural Image Processing (MIP) software. For the dog-bone, notched, shear-60°, torsion, and central-hole specimens, failure occurs at the maximum force, where the force–displacement curve's slope reaches zero. However, for the shear-45°, deep-drawing, and upsetting specimens, failure is identified at the inflection point, where the curve changes from concave upward to concave downward. [ABSTRACT FROM AUTHOR]

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

In this paper, fracture toughness (K J) was measured for high strength rail steels and AL2024-T351 via chamfered cylindrical flat-end indentation. The indentation loading focused on applying the J-integral approach to curves of load versus indentation depth up to the crack initiation point based on a modified limit load via multiple indenter sizes. To promote single indenter size for practical use, virtual indenter sizes were proposed based on geometrical similarities, where the stress intensity factors according to J-integral approach were extrapolated to minimize the contribution of the plastic component of J-integral (J P). However, when the indentation method for K J is applied to high strength rail steels, a consideration for the modification of the J-integral approach is suggested with the inclusion of stress triaxiality effect to accommodate the pressure sensitivity experienced in compression-based testing for some materials. The K J values were seen to agree well with fracture toughness from conventional testing (K IC) for all materials in the study showing a relative difference below 5% except the JP rail steel, which showed only a relative difference of 16%. This is based on the condition that pressure sensitivity effect is present for the rail steels and not for AL2024-T351. The study also compares different indenter sizes, which show similar pressure and normalized depth profiles consequently offering the potential for a non-destructive means to measure mechanical properties and fracture toughness via micro-sized indenters. This opens an opportunity for further studies in material characterization capabilities across a wide range of industries in the future. [ABSTRACT FROM AUTHOR]

• An innovative compressive fracture characterization method is proposed using bilinear strain paths: pre-tension and compression. • A damage index approach in strain-space is utilized for the calculation of the compressive fracture under linear and bilinear paths. • A ductile fracture model capable of predicting the cut-off region is selected for the ductile fracture loci of the bilinear paths and implemented into the numerical simulation with different pre-tensile strain levels. • The verification of the proposed characterization method is performed by comparing experimental data and simulation results for fractured specimen shapes and load-displacement curves. This study proposes the compressive fracture characterization method using bilinear strain paths: pre-tension and compression. Compressive ductile fracture exhibits extremely large strain, which has been regarded as being difficult to be measured. Large deformation under compressive loading makes the shape of a specimen barreled and changes the stress triaxiality rapidly. Due to these complicated and large strains, compressive fracture strain can be considered to be within the so-called cut-off region where no fracture occurs. In order to enable compression tests to be easier, an approach that can lower the range of fracture strain is needed. Uniaxial tensile deformation is a strain path that induces the growth of voids inside ductile materials and leads to ductility reduction. Ductile materials subjected to pre-tensile loading before compressive loading can show the premature compressive fracture. A ductile fracture model capable of predicting the cut-off region is selected for ductile fracture loci of the bilinear strain paths and implemented into the numerical simulation with different pre-tensile strain levels. The verification of the proposed characterization method is performed by comparing experimental data and simulation results for fractured specimen shapes and load-displacement curves. [ABSTRACT FROM AUTHOR]

• By altering the loading stress states, a transition from shear to tensile failure in MGs is achieved. • The critical stress triaxiality that regulates the failure transition is established by determining the failure criterion under both failure modes. • The shear, tensile, and transition failure zones are distinguished by a nearly elliptical yield surface of MGs. • The microstructural evolution of SRO in MGs is analyzed to determine the failure mechanism when MGs experience a variety of failure modes. As a novel and highly promising metal in the future application of weapons equipment and aerospace fields, metallic glasses (MGs) demonstrate intricate failure modes that encompass both the brittle and plastic characteristics when subjected to varying loading conditions. In this work, a set of Cu 50 Zr 50 models subjected to a combined pure shear and equi-triaxial tension loading are simulated via molecular dynamics to investigate the impact of the stress state on the complex failure modes of MGs. The characteristic and critical moments when failure occurs are established under both the shear-band-induced shear failure and the micro-void-induced tensile fracture. The stress triaxiality is applied as a pivotal stress parameter that governs the transition from the shear failure mode to the tensile failure mode. The critical stress triaxiality of Cu 50 Zr 50 MG is approximately in the range of (2.0, 3.0) when both the shear and tension failures simultaneously occur, resulting in the largest failure strain at various stress states. We subsequently obtain a nearly elliptical yield surface of the Cu 50 Zr 50 MGs, in which the shear failure zone, tensile failure zone, and transition zone are clearly distinguished. The microstructural evolution of MGs during the failure transition is analyzed from the perspective of the specific short-range order. In contrast to the tensile deformation, icosahedral (quasi-icosahedral) clusters demonstrate a high level of shear resistance and remain stable in the shear-dominant deformations, which is confirmed as the structural origin of the stress state impacting the failure transition. [Display omitted] [ABSTRACT FROM AUTHOR]

The phase field model is a promising method for simulating fatigue crack growth (FCG) behavior. However, the conventional phase field (PF) model may not adequately account for constraint effects, where fracture toughness is affected by geometries. Therefore, stress triaxiality is incorporated into the PF model by modifying the fracture energy release rates to consider constraint effects. The model successfully simulates the FCG behavior of different geometries, such as CT, SENB, and MT specimens, as well as the mixed-mode FCG behavior of CTS specimens and other complex geometries. All simulations agree well with experiments, proving that our model is capable to capture the constraint effects in FCG behavior. These findings indicate that stress triaxiality is important to capture the constraint effects. [ABSTRACT FROM AUTHOR]

The local embrittlement of the coarse-grained heat-affected zone (CGHAZ) and intercritically reheated CGHAZ (IC-CGHAZ) in X65 pipeline steel was investigated using an in situ crack-tip opening displacement test in air and H 2 S, combined with microstructure-based simulation. The IC-CGHAZ exhibited significantly lower cracking resistance, with the fracture toughness reduced by 50 % compared to CGHAZ in both environments (0.160 mm in air and 0.017 mm in H₂S for IC-CGHAZ, compared to 0.307 mm in air and 0.034 mm in H₂S for CGHAZ). The martensite/austenite (M/A) constituents showed exceptionally higher intrinsic hardness than the ferrite matrix. The continuous distribution of M/As along the prior austenite grain boundaries resulted in local hardening and the formation of heterogeneous hard zones in IC-CGHAZ. Such microstructure heterogeneity resulted in the unique partitioning of plastic strain localization and stress triaxiality that promotes premature fracture, particularly with the coupled effect of hydrogen. This study provides a novel perspective on the fracture mechanisms and the typical fracture morphology of IC-CGHAZs in pipeline steel under the coupled effect of microstructure heterogeneity and hydrogen. • Fracture toughness of IC-CGHAZ was reduced by 50 % compared to CGHAZ in air and H 2 S. • Increased microstructure heterogeneity led to significant toughness degradation. • Formation of heterogeneous hard zones caused increased microstructure heterogeneity. • Partitioning of plastic strain and stress triaxiality influences fracture behavior. • Hydrogen dominated the cleavage fracture related to microstructure heterogeneity. [ABSTRACT FROM AUTHOR]

[Display omitted] • The effect of He bubble on the mechanical properties of materials is strongly related to the stress triaxiality and Lode parameter. • The underlying mechanism of He bubble fragmentation at low stress triaxiality, mediated by dislocation slip and surface diffusion, is clearly revealed. • T - L phase maps to illustrate regions where He bubble fragmentation, coalescence and neither of the two are possible. • The heuristic applications of coalescence onset criteria for He bubble at the nanoscale are explored. The He bubble is of utmost importance for understanding the dynamics and evaluating the performance of irradiated metals. This work systematically investigates the effect of the stress triaxiality and Lode parameter on the evolution of He bubble in Al via molecular dynamic simulations. Numerical results show that implanting He atoms into the cavity reduces the yield strength but boosts the ductility of the material, with this effect becoming more pronounced as both the stress triaxiality and Lode parameter decrease. One important discovery is the He bubble fragmentation under low stress triaxiality, and the underlying mechanism mediated by dislocation slip and surface diffusion is clearly revealed. Conversely, the He bubble tends to coalesce under high stress triaxiality, and the coalescence strain increases with the increasing He concentration. Additionally, the heuristic applications of coalescence onset criteria for He bubble are explored. The extended Thomason criterion, considering the hardening effect, provides qualitatively acceptable predictions. [ABSTRACT FROM AUTHOR]

In this study, cubic coupons of AlSi10Mg alloy were printed using the laser powder bed fusion (LPBF) technique. The effect of heating/reheating cycles on solute trapping and partitioning of alloying elements was investigated using atom probe tomography and transmission electron microscopy. Nano-hardness analysis and uniaxial tensile tests equipped with digital image correlation were employed to investigate the mechanical properties and Poisson's ratio. X-ray micro-computed tomography was utilized to detect strain localization sites along the building direction. Also, the uniaxial tensile test was simulated using finite element analysis to verify the experimental data and predict stress triaxiality. The results showed that the solute trapping and partitioning during the LPBF process results in remarkable changes in phases, their size and morphology, Poisson's ratio, strengthening factor, and consequently mechanical properties. While the tensile sample from top part of the LPBF coupon mostly shows porosity due to floating and entrapment of gases during layer-by-layer fusion/solidification, the sample from bottom part is exposed to sub-surface microcracking induced by residual stresses. The hardness, elastic, and shear moduli, Peierls stress, and cumulative strain energy of the top-part sample are higher than those of the bottom-part sample even though electron backscatter diffraction analyses report similar grain size and texture. Besides, by distancing from the build plate, the Poisson's ratio decreases. Simulation results of both samples indicate that the middle of the gauge is a high-potential area of failure initiation, where the bottom-part sample shows higher stress localization. • Undeniable role of solute partitioning on strengthening gradient in AM AlSi10Mg. • Variations in prevailing factors of strengthening through building direction of LPBF AlSi10Mg. • A transition in nature of structural defects due to residual stresses and thermocapillary forces. • A transition in type, size, morphology, and volume fraction of precipitates at constant grain size. • Variations in stress triaxiality of tensile samples taken along with building direction. [ABSTRACT FROM AUTHOR]

• Four commonly used shear test specimens were designed and optimized by FEA. • The advantages and disadvantages of each specimen were clarified to provide guidance for shear tests. • The plastic and failure characteristics of different specimens were compared and analyzed. • The underlying causes for the different characteristics and performances were also analyzed. In this paper, the dynamic shear response and failure of Ti-6Al-4V using four different test specimen geometries, viz. Hat-Shaped Specimen (HSS), Flat Hat-Shaped Specimen (FHSS), Chip Hat-Shaped Specimen (CHSS) and Double Shear Specimen (DSS), are critically examined and compared. Through a combination of experiments (using the standard Split-Hopkinson Pressure Bar system), finite-element simulations and metallographic examinations of their fracture morphology, the dynamic shear characteristics (strain hardening, strain rate strengthening effect and failure strain) of Ti-6Al-4V obtained using the different specimen geometries are critically examined, compared and analyzed. It will be shown that differences in the stress/strain uniformity, the plastic deformation zone, and the stress state induced by the different specimen geometries lead to discrepancies in the measured shear response and failure that were observed. The shear stress–strain curve obtained using the DSS will be shown to be more precise than the other specimen geometries. [ABSTRACT FROM AUTHOR]

[Display omitted] • Conduct fracture tests under a continuous wide range of stress states using a single type of butterfly-shaped specimen and corresponding multiaxial loading device. • Utilize full-field strain measurement technology to monitor the strain distribution patterns under continuously varying stress triaxiality in real time. • Investigate the differences and transitions in the fracture behavior of AZ31 magnesium alloy under different ranges of stress triaxiality. • Develop material failure criteria for AZ31 magnesium alloy under continuously changing high, medium, and low stress triaxialities. Understanding the fracture behavior of magnesium alloys under complex stress states is crucial for the development of forming applications for magnesium alloy structural components. However, current fracture tests to obtain fracture model parameters still depend on various complex and inefficient specimen shapes, which may result in errors due to geometrical differences between specimens, and the obtained stress states are limited, scattered, and lack continuity. Therefore, this paper conducted fracture tests on magnesium alloy materials using a single type of butterfly-shaped specimen and a supporting Multiaxis Loading Apparatus (MALA). The digital image correlation (DIC) technology was employed to obtain the strain field distribution during the continuous loading process of the butterfly-shaped specimen in real-time under MALA, which assisted in verifying the accuracy of finite element simulation fracture tests. Subsequently, the average stress triaxiality was calculated based on the temporal and spatial distribution effects of stress triaxiality. The macroscopic fracture morphology, microfracture mechanisms, and stress triaxiality of butterfly-shaped specimens were then correlated, ultimately establishing a failure criterion for AZ31 magnesium alloy material under a continuous wide range of stress triaxiality (−0.608 to 0.594). The results show that the fracture behavior of AZ31 magnesium alloy differs and transitions under varying ranges of stress triaxiality. Specifically, in the mid-to-high stress triaxiality range, cleavage fracture and microvoid coalescence mechanisms coexist and compete, leading to a significant macroscopic transition in fracture mode at a stress triaxiality of about 0.5. Microscopically, the fracture mechanism transitions from microvoid evolution at high stress triaxiality to cleavage fracture at low/negative stress triaxiality. This also causes the established material failure criterion (equivalent fracture strain vs. stress triaxiality) to exhibit a discontinuous piecewise pattern, with segmentation points around stress triaxiality values of 0.037 and 0.564. [ABSTRACT FROM AUTHOR]

• Creep tests on smooth and single-hole plates were conducted to explore the effect of complex stress state on creep life. • A viscoplastic model was developed to simulate creep behavior of single-hole plates and V-notched bars. • A mechanical explanation for significant differences in creep life among differently structured specimens was provided. • New life model accounting for stress triaxiality accurately predicts creep life of single-hole plates and V-notched bars. This study investigates the effects of complex stress states on creep rupture life of nickel-based superalloys. Creep experiments were conducted at 900 °C on both smooth and single-hole plate specimens. A viscoplastic constitutive model was developed to simulate the creep behavior of single-hole plates and V-notched bars. The analysis offered a detailed mechanical explanation for the significant differences in creep rupture life observed among these differently structured specimens. This investigation incorporated the effects of complex stress states into the Monkman-Grant relationship, resulting in a new creep life model that accounts for stress triaxiality. The results indicate that the increased stress triaxiality significantly extends the creep life of V-notched bars. In contrast, the single-hole plates, which approach a uniaxial stress state, exhibit a creep rupture life closely aligning with that of the standard smooth plates. The proposed model accurately predicts the creep rupture life of both single-hole plates and V-notched bars, with all predictions falling within a threefold scatter band. [ABSTRACT FROM AUTHOR]

Under severe seismic action, the local stress concentration region in steel structures is prone to the ultra-low-cycle fatigue (ULCF) under high triaxiality and irregular cyclic deformation with intensively varying strain amplitudes. It emphasizes the necessity of the jointed effects of the stress triaxiality and strain range incorporated in the ULCF life prediction. Given the limited relevant studies in terms of the underlying micro-mechanisms, this paper focuses on experimental and modeling studies of the combined effects of stress triaxiality and strain range on the ULCF failure, based on Gurson-Tvergaard-Needleman (GTN) microvoid evolution theories. Monotonic tensile tests on three types of notched round bars suggest that fracture strain decreases with increasing triaxiality. Cyclic tests on two types of notched bars under various strain ranges confirm the combined effects of stress triaxiality and strain range. Given a specific triaxiality, the ULCF damage accumulation rate increases linearly as the tensile plastic strain range ramps up. For the same tensile plastic strain range, higher triaxiality results in a greater damage accumulation rate. In the modeling studies, the consistency of the GTN and uncoupled damage models has been proven in terms of ULCF failure of structural steel. Based on GTN theories, a new micromechanical cyclic void growth model (GCVGM) is proposed, considering the detailed processes of void nucleation, growth, and coalescence under monotonic and cyclic loadings. Moreover, the joint effects of stress triaxiality and strain range can be explicitly described within a unified framework, without additional empirical assumptions. Based on experimental and simulation results, the proposed GCVGM shows significant advantages over conventional models in accurately predicting ULCF failure under various loading protocols, with low average errors of 2.73 % and −0.91 % for two types of notched bar specimens, respectively. • The joint effect of stress triaxiality and strain range is investigated. • Cyclic tests under various triaxialities and loading protocols are performed. • The rate of ULCF damage accumulation linearly increases with the plastic strain range. • Triaxiality raises the damage rate of ULCF under a specific strain range. • A new micromechanical cyclic void growth model is proposed based on the GTN theory. [ABSTRACT FROM AUTHOR]

• V-notch compression test coupled with AE technique is newly proposed for high negative stress triaxiality. • Ductile fracture initiation is accurately detected using unsupervised learning with AE signal data. • The relationship between the average Lode angle parameter and the average stress triaxiality was established. • Fracture strains of CHQ steel wires under various deformation modes are identified. • Fracture loci for four distinct CHQ steel wires are well established. This study presents a comprehensive approach for constructing the ductile fracture locus of cold-heading quality (CHQ) steel wires across a wide range of stress triaxialities, from −0.58 to 1.31. We introduce a novel V-notch compression test combined with acoustic emission (AE) techniques to characterize ductile fracture under high negative stress triaxiality. Ductile fracture is analyzed via a hybrid experimental–numerical method. In addition to the V-notch compression test, fracture experiments are conducted under various deformation modes, including torsion and tensile tests, to encompass a broad spectrum of stress states. Unsupervised learning is also used to detect the ductile fracture initiation in a V-notch compression test based on AE-signal data. Elastoplastic finite element analysis was conducted to calculate the stress triaxiality, Lode angle parameter and equivalent plastic strain for various deformation modes. Using recently developed ductile fracture models, we constructed 3D fracture loci and established the relationship between average stress triaxiality and the average Lode angle parameter to create 2D fracture loci that appropriately consider the stress state. These fracture loci accurately depict fracture behavior across negative and positive stress triaxialities, thereby enabling a comprehensive understanding of ductile fracture across a variety of stress conditions. The results demonstrate the robustness of the proposed approach in identifying the ductile fracture at high negative stress triaxiality, enabling a comprehensive analysis of material formability under complex stress states. [Display omitted] [ABSTRACT FROM AUTHOR]

• Fracture in open-stretched flanging by SPIF on AA2024-T3 sheet was studied experimentally and numerically. • Corner fracture in open-stretch flanges was analysed and compared with flange edge failure. • A critical formability analysis in the space of average stress triaxiality versus equivalent plastic strain was conducted. • A region of Mode I fracture for plane stress in SPIFed flanges and Nakazima tests was assessed. This study presents a comprehensive investigation of fracture in open-stretched flanges formed using Single Point Incremental Forming (SPIF) on AA2024-T3 aluminium sheets. The work systematically explores the impact of geometric parameters, namely initial width and length, on the occurrence of the two primary failure modes: fracture at the corner and fracture at the edge of the flange. The experimental campaign comprises a series of flanging tests on medium-small radii to examine the deformation process on both the inner and outer surfaces of the flanges. The novelty of the investigation lies in two key aspects. Firstly, it offers, for the first time, an experimental characterisation of the onset of failure at the flange corner, which significantly limits the process's capabilities, and critically compares it with the failure at the flange edge. It is highlighted that the fracture at the corner is strongly influenced by tool-induced friction and the incremental nature of the SPIF process, resulting in a local formability significantly higher than expected with a quasi-proportional deformation process, as characterised by the conventional Fracture Forming Limit (FFL) evaluated through Nakazima tests. Secondly, a detailed formability analysis of the flange in the average stress triaxiality versus equivalent strain space is conducted, identifying a common region of Mode I fracture for plane stress applicable to both open-stretched flanges by SPIF and conventional Nakazima tests. To this end, an explicit numerical model based on the Barlat-89 anisotropic yield criterion is used to assess the non-proportional strain/stress paths, inherent in the incremental process. A numerical-experimental methodology is employed to predict both edge and corner failures of the flanges within the average stress triaxiality - equivalent strain space. The fracture loci for Mode I have been determined for both the incremental flanging tests and the Nakazima tests. A comparison of both fracture loci reveals a noticeably lower average stress triaxiality and larger equivalent strain in the SPIFed flanges than in the Nakazima tests, consistent with the increase in the apparent formability of the material observed experimentally in the incremental processes with respect to the conventional tests. [Display omitted] [ABSTRACT FROM AUTHOR]

The heterogeneous deformation of polycrystalline metals inherently originates from the intergranular deformation incompatibility. This paper proposes physical parameters related to the crystal orientations, the Schmid factor of the most activated slip system, and the misorientation angle to characterize the deformation incompatibility between the adjacent grain couple. A comprehensive multiscale investigation is conducted to reveal the mechanism from intergranular deformation incompatibility to fracture initiation at grain boundaries. At the specimen scale, experimental and numerical uniaxial tensile tests are performed on smooth and pre-notched dog-bone specimens to achieve different loading paths on the materials. The heterogeneous fields of stress triaxiality explains the heterogeneous size of the dimples observed in fractography. At the grain scale, electron backscatter diffraction analysis is conducted to characterize the microstructural properties around the nucleated voids within the materials. Voids are captured at the grain boundaries with directions parallel to the loading direction and intergranular deformation incompatibility is characterized using the proposed parameters. Simulations on the plastic deformation of realistic microstructures are performed to clarify the phenomenon. The results reveal that the fluctuation in stress triaxiality at grain boundaries is ascribed to intergranular deformation incompatibility, leading to fracture initiation at these sites. The relationships between the proposed physical parameters of intergranular deformation incompatibility and fluctuation in stress triaxiality are summarized in all circumstances. Finally, the ductile damage at the grain scale is predicted by the Rice–Tracey model, and the results show that the effects of microstructures on heterogeneous plastic deformation and stress state can be well considered. [Display omitted] • Intergranular deformation incompatibility is characterized by physical parameters. • Heterogeneous distribution of voids at grain boundary is captured. • Intergranular deformation incompatibility causes high triaxiality at grain boundary. • Ductile damage in the microstructure is predicted by Rice–Tracey model. [ABSTRACT FROM AUTHOR]

This paper investigates void growth and coalescence in porous ductile solids under dynamic loading condition. A physical definition for the onset of void coalescence in porous ductile solids under dynamic loading is proposed. The onset is deemed to occur when the third invariant of the tensorial form of the Hill–Mandel condition attains a zero value. The definition allows for systematic investigations on the effects of dimensionless stress rate κ and stress state, defined by the stress triaxiality T and Lode parameter L , on the onset of void coalescence via micromechanical analyses. The analyses reveal that the critical macroscopic effective strain for the onset of void coalescence displays an increasing–decreasing transition trend as the dimensionless stress rate increases, for all levels of T and L considered. The macroscopic effective strain at the transition is identified as the "ductile–brittle" transition strain. The dimensionless stress rate at which the transition strain occurs is found to be relatively constant. A mapping in the κ − T space for L = − 1 , representative of a generalized uniaxial tension typical in spall fracture experiments, is established which depicts regions where coalescence and non-coalescence can take place, as well as the ductile–brittle regions demarcated by a ductile–brittle transition curve. The results also show that the critical void volume fraction and macroscopic effective strain at the onset of void coalescence are insensitive to inertia at high stress triaxialities at L = − 1. • Novel definition for the onset of dynamic void coalescence in porous ductile solids. • Investigated stress rate and stress state effects on void coalescence via cell analyses. • Identified a critical ductile-brittle transition strain under varying stress rates. • Established a κ − T mapping for void coalescence and ductile-brittle transition. [ABSTRACT FROM AUTHOR]

Using load-independent creep constraint parameters Q * and Q m * , the variations of crack front stress field and constraint level are analyzed for various crack sizes of pipelines containing internal surface cracks under high temperature conditions. The results show that the trends of stress changes in the axial and circumferential internal surface crack front for different crack sizes are similar. For axial internal surface cracks, when the crack depth to length ratio a/c is the same, the maximum values of crack front Q * and Q m * are shifted from the deepest part of the crack (2 Φ/π = 1) to the vicinity of the free surface (2 Φ/π = 0.2) as the crack depth a/t increases. As for the circumferential inner surface cracks, when the crack depth a/t exceeds 0.2, the locations where the maximum values of crack fronts Q * and Q m * appear are mainly concentrated in the deepest part of the crack (2 Φ/π = 1). Based on the calculation results of the constraint parameters, the empirical formulas for the engineering calculation of the relationship between the average constraint parameters (Q a v g * and Q m ‐ a v g *) and the crack size are obtained by fitting. • Creep constraints of crack fronts in pipes with different shapes were analyzed. • The constraints of creep crack fronts were characterized using Q m * and Q *. • CCG behaviors were consistent with the constraint parameter results. • Average constraint parameters Q a v g * and Q m ‐ avg * for creep crack fronts had been proposed. [ABSTRACT FROM AUTHOR]

Ultra-low cycle fatigue failure is an important ultimate limit state of the structures. Based on the ductile fracture model proposed by the authors, the Coffin-Manson model, and the Miner law, a new model was proposed in this study. The strategy of the proposed model is intended for the prediction of ultra-low cycle fatigue fracture onset covering a wide range of stress triaxiality and being suitable for the variable amplitude straining. Three kinds of metal alloys, Q345qC steel, G20Mn5QT cast steel, and 2024-T351 aluminum alloy, were used to verify the model. The results showed that the proposed model advanced the original Coffin-Manson model greatly. More importantly, the verification demonstrates that the proposed model can predict the ultra-low cycle fatigue fracture initiation over a wide range of stress triaxiality and under variable amplitude straining. Besides, compared with the ULCF-2021 model, the proposed model has a relatively lower average error. • A new ultra-low cycle fatigue (ULCF) damage model is proposed. • The proposed ULCF model can predict the ULCF fracture initiation more accurately relative to the Coffin-Manson model. • The proposed model has a relatively lower average error than the ULCF-2021 model. [ABSTRACT FROM AUTHOR]

• A micromechanical model was first established to study crack and fibers. • The isotropic, anisotropic and microscopic models were compared. • The impacts of crack size and location, fiber content on stress field were revealed. • The variations of various mechanical properties were discussed. Accurately clarifying the influence of cracks on the mechanical behaviors of unidirectional fiber-reinforced composites (UD FRCs) is of great significance for the structural integrity evaluation of UD FRCs with defects. Although several experiments and numerical analyses have explored the impact of cracks on stress field, satisfactory quantitative characterizations of crack size, a / W and location, Δ , fiber content, V f have not yet been obtained. In this paper, the accurate and detailed microscopic models containing crack were first established and thoroughly validated. Then, a parametric study was conducted using three-dimensional micromechanical analysis to investigate how the crack size and location, fiber content affect the von Mises, stress triaxiality, Lode angle and J -integral of UD FRCs. Results showed that homogeneous models, whether isotropic or anisotropic, cannot accurately describe the mechanical behavior of cracked UD FRCs. The von Mises stress and J -integral are greatly influenced by the crack and fiber content, while stress triaxiality and Lode angle are not sensitive to changes in these factors. Further, the von Mises and J -integral increase with the decrease of V f and the increase of a / W , but show a more complex trend in the variation of Δ. These findings will help clarify the failure mechanism of cracked UD FRCs and can be used for reliability evaluation. [ABSTRACT FROM AUTHOR]

Void growth and morphology evolution in fcc bi-crystals are investigated using crystal plasticity finite element method. For that purpose, representative volume element of bi-crystals with a void at the grain boundary are considered in the analysis. Grain boundary is assumed initially perpendicular/coaxial with the straight sides of the cell. Fully periodic boundary conditions are prescribed in the representative volume element and macroscopic stress triaxiality and Lode parameter are kept constant during the whole deformation process. Three different pairs of crystal orientations characterized as hard-hard, soft-soft and soft-hard have been employed for modelling the mechanical response of the bi-crystal. Simulations are performed to study the implications of triaxiality, Lode parameter and crystallographic orientation on slip mechanism, hardening and hence void evolution. The impact of void presence and its growth on the heterogeneity of lattice rotation and resulting grain fragmentation in neighbouring areas is also analysed and discussed. [ABSTRACT FROM AUTHOR]

A crystal plasticity-based finite element study is performed to understand hydrogen effects on void growth in single crystals of austenitic stainless steel. The model assumes plastic deformation is driven primarily by dislocation motion and captures the influence of hydrogen. Hydrogen effects are incorporated by assuming agreement with the hydrogen enhanced localised plasticity (HELP) mechanism. Despite experimental evidence, hydrogen effect on face centred cubic (FCC) crystals has hitherto not been considered in a numerical void growth model for a wide range of stress states. For the first time, the influence of hydrogen on void growth for different Lode parameters at single crystalline levels is investigated for a range of stress triaxialities in FCC crystals. Hydrogen was found to increase equivalent stresses and hardening responses for various stress triaxialities and Lode parameters. Hydrogen also induces higher void growth response at different stress states, and this was more pronounced at high stress triaxialities. Image 1 • Crystal plasticity study of hydrogen effect on face centred cubic crystals. • Model is based on the hydrogen enhanced localised plasticity theory. • Model accounts for slow diffusion of hydrogen in face centred cubic crystals. • Hydrogen initially inhibits void growth but this changes with void shape. • Hydrogen influence is affected by void shape and strain localisation. [ABSTRACT FROM AUTHOR]

Edge cracks, which are typical formability defects, severely limit the widespread application of Mg/Al composite sheets. Accurate prediction of damage is crucial for understanding the underlying mechanisms behind crack formation. In this study, a continuum damage model that incorporates the stress-state function and effective equivalent plastic strain into the standard Lemaitre model is proposed. This enhanced model effectively addresses the issues of damage-evolution linearization and tension–compression asymmetry in the standard Lemaitre model. Thus, it can be successfully applied to predict the fracture response of ductile composite materials under pressure-forming conditions. Considering AZ31B Mg alloy and 5052 Al alloy as experimental materials, physical experiments and numerical validation are performed under a 50% reduction and 350 °C. The findings show that the proposed model effectively captures crack initiation and propagation during the rolling process, with errors of only 23.1% and 19.9% for average crack quantity and length, respectively. Results of numerical analysis reveals that the high-stress triaxiality at the edge of the sheet contributes significantly to crack formation. Additionally, the strain along the normal direction in the Al alloy significantly affects crack propagation and the formation of serrated cracks on the side of Mg alloy. This study provides important theoretical foundations for the development of Mg-based composite sheets. [ABSTRACT FROM AUTHOR]

Unlike strain-hardening (the increase of flow stress with plastic strain) due to glide of dislocations in conventional crystalline metals, metallic glasses (MGs) usually exhibit strain-softening, which leads to extreme localization of plastic flow in shear bands. In the present study, triaxial stress states are introduced by fabricating annular notches, and molecular dynamics (MD) simulations have been performed on nanoscale notched MGs to systematically investigate the influence of stress triaxiality on their tensile fracture strengths and failure mechanisms. It is found that the triaxial stress states suppress the formation and rapid extensions of shear-banding and lead to strain-hardening of MGs. With the increase of stress triaxiality, the failure mechanisms of MGs transits from shear-banding to cavitation. In the vicinity of the critical stress triaxiality, the failure mechanism of necking occurs and the strain-hardening effect is the strongest. The reasons are the large degree of free volume growth and recovery at the notch and the large degree of recovery of Cu-centered full-icosahedral fraction. Our study systematically investigates the strain-hardening effect and the transition of the failure mechanisms of MGs below the critical stress triaxiality, at the critical stress triaxiality, and above the critical stress triaxiality, which provides significant insights into the effect of the triaxial stress state on the strain-hardening and failure mechanisms of nano-sized MGs. [Display omitted] • Strain-hardening of nano-sized metallic glasses under triaxial stress. • Necking of metallic glasses at critical stress triaxiality. • Large degree recovery of free volume and full-icosahedron by high hy-drostatic stress controlled. [ABSTRACT FROM AUTHOR]

The safety of steel bridge piers is threatened by ultra-low cycle fatigue (ULCF) damage, which dominates the failure mode in those with relatively compact section under strong seismic action. Existing methods for calculating such ULCF damage face the dilemma between accuracy and efficiency. To this end, this paper proposes a simplified evaluation method based on fiber model to expediently evaluate the ULCF damage of unstiffened steel piers, evenly with sound precision. Specifically, the average stress triaxiality is assumed as 0.63 for steel piers, and it is validated by cyclic loading experiments with the modified Coffin-Masson formula and solid element sub-model. The disparity between local plastic strain range in fiber and solid models is compensated by introducing a magnified coefficient. The analyzed results indicate the slenderness ratio, axial compressive ratio, especially the flange thickness and the width-to-thickness ratio, strongly influence the strain concentration effect occurring in the pier bottom. In addition, the proposed close equation for the magnified coefficient fits well with the discrete calculated points. The 3.05% mean absolute error is realized on the predicting half cycles when applying this method in random cyclic loading. Its favorable applicability in practical engineering is also verified with considering different ground motion types. • A method based on fiber model is proposed to evaluate the ULCF of steel piers, evenly with simplicity and precision. • The average stress triaxiality is assumed as 0.63 for steel piers in calculating ULCF. • The magnified coefficient β is obtained by discriminatively weighting the plastic strain range in each half cycle. • The favorable applicability of the method under regular and irregular cyclic loading is verified. [ABSTRACT FROM AUTHOR]

We perform three-dimensional crystal plasticity simulations of smooth and notched bar geometries made of polycrystalline hexagonal close-packed material representing a magnesium alloy. The polycrystalline microstructure is explicitly resolved to investigate the combined effect of initial texture and grain size on the rate-dependent macroscopic responses and their micromechanical underpinnings under uniaxial and multiaxial stress states. The simulations reveal that in addition to the textural effect recently investigated by Ravaji et al. (2021), grain size plays an important role in the anisotropy of macroscopic responses. For a given texture, the lateral deformation anisotropy increases with grain size refinement for all strain rates considered here. The load-deformation responses exhibit a synergistic strengthening effect in microstructures with stronger initial textures and finer grain sizes, which is enhanced with increasing notch acuity. A transition from a conventional power-law type load-deformation response to a sigmoidal load-deformation response may occur, which depends on the imposed strain rate. It is a result of the interaction between textural weakening and grain size refinement that influence extension twinning together with an equitable landscape of the different slip mechanisms. We discuss possible implications of the net material plastic anisotropy due to texture and grain size on macroscopic failure using a micromechanical basis. • 3D polycrystalline Mg notched bar simulations with resolved grain size and texture. • Insights into rate-dependent microstructure–response relations via micromechanics. • Assesses net plastic anisotropy effects on rate-dependent failure of Mg notched bars. [ABSTRACT FROM AUTHOR]

Fracture of an anisotropic rare-earth-containing magnesium alloy (ZEK100) sheet is investigated at different stress states and strain rates. A variety of sample geometries, loading conditions, and loading orientations are used to achieve different stress triaxiality and deformation mechanisms. Digital image correlation (DIC) technique is used to measure the surface strains up to fracture for all the specimens. We show that ZEK100 exhibits larger strain at fracture across the gage section of the test specimens aligned with the transverse direction (TD) than specimens aligned with the rolling direction (RD); however, the opposite is shown for the local strain measurements at fracture. With an increase in the strain rate, the strains at fracture decrease for all loading paths. A crystal plasticity finite element model is used to simulate the local stress state and deformation mechanisms for each loading condition. ZEK100 exhibits an anisotropic fracture behavior that is a function of the stress triaxiality and Lode parameter. We show that extension twinning also plays an important role in the fracture response of ZEK100. Overall, the local effective strain at fracture is lower for the specimens that exhibit the largest volume fraction of extension twinning. A novel anisotropic extension to the Hosford-Coulomb (HC) fracture model is then developed to account for the effect of extension twinning on the anisotropic fracture response of ZEK100. Image 1 • Fracture of ZEK100 is dependent on the stress state, strain rate, and the activity of different deformation mechanisms. • Extension twinning improves the hardening capability of magnesium which improves the macroscopic ductility. • The local strain at fracture was the lowest for the specimens that exhibited large volume fraction of extension twinning. • A novel anisotropic extension to a fracture initiation model was developed to account for the role of twinning on fracture. [ABSTRACT FROM AUTHOR]

In this paper, the block shear fracture behavior of base metal in austenitic stainless steel (STS304, corresponds to ASTM 304 type) fillet-welded connection has been investigated through experimental and numerical methods. Even though the block shear fracture strength of welded connection thanks to stress triaxiality effect differs from those of bolted connection under monotonic tension, block shear strength equations of welded connection with base metal fracture in the design codes are identical to those of bolted connection. Main variables are weld method (TIG and Arc welding) and weld length (transverse and longitudinal to the direction of loading). It is found from study results that welding method did not affect the strength of welded connection. Block shear strengths by current codes (KBC2016, AISC2016 and EC3 1–3) and other researchers' proposed equations were compared with those of experimental results and finite element analysis results. Finite element analysis (FEA) model was developed based on previously test data. Also, parametric study for investigating the weld length effect on strength has been performed with the developed finite element analysis procedures. Consequently, condition of weld length and end distance perpendicular to the direction of applied force for fracture mode transition boundary from tensile fracture to block shear fracture in welded connection was investigated. In addition, block shear strength equation with modified tensile stress and shear stress factors of base metal fracture in austenitic stainless steel (STS304) welded connection is suggested considering stress triaxiality. • Finite element analysis of stainless steel welded connections was conducted. • Strength and fracture mode by analysis agreed with those of test results. • Specimens failed by block shear fracture of base metal. • Condition of fracture transition according to variables were investigated. • Effective tensile and shear stress factors were suggested. [ABSTRACT FROM AUTHOR]

• Water-cooling reduces ductility and increases tensile strength due to formation of martensite phase. • Air-cooling results in a slight increase in ductility and reduction in tensile strength. • High stress triaxiality combined with water-cooling results in significant loss of ductility. The goal of this paper is to understand the post-fire mechanical behavior of ASTM A572 Gr. 50 structural steels cooled from high temperatures using both air-cooling (slow cooling rate) and water-cooling (rapid cooling rate) methods under the influence of high stress triaxiality. In this study, various levels of stress triaxialities in uniaxial tension specimens are achieved by introducing notches in the test specimens. The uniaxial notched test specimens are subjected to temperatures ranging between 500 °C and 1000 °C at 100 °C intervals to simulate fire temperatures. The furnace-heated specimens are then either left outside the furnace for air-cooling or quenched in a water bath in the case of water-cooling method. Uniaxial tension tests are performed on both air and water cooled notched specimens to extract the post-fire mechanical properties. Non-linear finite element analyses are performed to obtain the triaxiality profiles along the critical cross sections of notched specimens by employing hardening curves obtained from post-fire uniaxial tension tests. Moreover, microstructures at selected temperatures are obtained to assess the microstructural changes that caused a significant change in post-fire mechanical properties. It is observed that ASTM A572 steels do no exhibit considerable change in mechanical properties when exposed to temperatures up to 600 °C, for both cooling methods. Beyond 600 °C, air-cooling resulted in a reduction in yield strength and ultimate tensile strength and increase in ductility of ASTM A572 steels. Water-cooling from temperatures beyond 600 °C increased the ultimate tensile strength and decreased the ductility of ASTM A572 steels due to the formation of the martensite phase. High stress triaxiality leads to the reduction in ductility and an increase in yield strength and ultimate tensile strength of ASTM A572 steels in both air-cooled and water-cooled conditions. The combined influence of high stress triaxiality and formation of martensite phase resulted in significant increase of up to 158% in yield strength and up to 172% increase in ultimate tensile strength of ASTM A572 steels that are water-cooled after exposure to temperatures beyond 800 °C. On the other hand, the presence of the high stress triaxiality and water-cooling resulted in up to 89% loss of ductility of ASTM A572 steels specimens that are exposed to temperatures beyond 800 °C. [ABSTRACT FROM AUTHOR]

In addition to the stress triaxiality, the Lode angle has recently been recognized as an important parameter influencing the ductile crack initiation, propagation and final failure of structural steels. In this paper, a modified ductile fracture model is proposed to consider the effects of different stress states on the ductile fracture behavior of steels by introducing the deviatoric state parameter. Different stress states, including the tension, compression, shear, tension-shear, and compression-shear states, can be expressed by the stress triaxiality and deviatoric state parameter relating to the Lode angle. Three flat bar tension specimens and eight flat bar shear specimens were designed to model the different stress states, and ductile fracture tests were carried out on these 11 specimens. The parameters of the modified ductile fracture model in this study were determined based on these ductile fracture tests, and the corresponding finite element analytical results regarding these specimens exhibited strong agreement with the tested results. The proposed model was verified as being suitable for simulating the ductile fracture behavior of steels under different stress states. • A modified ductile fracture model including effect of Lode angle is proposed. • Eight shear specimens were tested to simulate compression-shear and tension-shear stress states. • Different stress states can lead to different ductile fracture behavior of steels. • Six material parameters in the proposed model were determined for SM490 steel. [ABSTRACT FROM AUTHOR]

The initiation of ductile fracture in grade DH36 shipbuilding steel was modeled using the Hosford-Coulomb fracture model. The hardening and ductile fracture characteristics of DH36 were assessed by performing experiments on notched tension, central hole tension, plane strain tension and shear specimens. Detailed finite element analysis of each experiment was performed to evaluate the evolution of local stress and strain fields. The loading paths to ductile fracture initiation were determined in terms of the stress triaxiality and Lode angle parameter histories extracted from finite element analyses with very fine solid element meshes. The Hosford-Coulomb fracture model parameters were identified using the extracted loading paths and adopting a linear damage accumulation law. It has been found that ductile fracture behavior of DH36 is dependent not only on the stress triaxiality but also the Lode angle. • Material specific fracture initiation model for DH36 is presented. • Ductile fracture of DH36 grade steel is sensitive to both stress triaxiality and the Lode angle. • Hosford-Coulomb fracture model is suitable for predicting the fracture initiation in grade DH36 steel. • Increased hardening rate and yield strength decreases Lode angle sensitivity and ductility. [ABSTRACT FROM AUTHOR]

Abstract Due to the texture formed in cold/hot rolled forming process, anisotropy is a key issue not only in modeling of plastic deformation but also in characterization of fracture behavior. In this study, an anisotropic ductile fracture criterion is developed by introducing anisotropic parameters into the weight function of an uncoupled shear ductile fracture criterion. The proposed anisotropic ductile fracture is applied to describe the anisotropic characteristics in the ductile fracture of AA6082-T6. Ductile fracture behavior of AA6082 is experimentally investigated at the different loading conditions: shear by in-plane torsion test, uniaxial tension by specimens with a central hole, plane strain tension by notched specimens, and the balanced biaxial tension by the Nakajima test. In-plane torsion and tension tests with a central hole and notch are conducted along three directions: rolling direction, diagonal direction and transverse direction. Specimen deformations during the tests are recorded and fracture strains are measured by digital image correlation approach. The measured fracture strains are then utilized to calibrate the parameters in the proposed ductile fracture criterion. With the calibrated ductile fracture criterion, the fracture locus and anisotropic ductile fracture in various loading conditions are predicted and compared with experimental measurement and those predicted by linearly transformed anisotropic fracture model to investigate the predictability of the proposed ductile fracture criterion. The comparison demonstrates that the anisotropic fracture of AA6082 is predicted by the proposed criterion with good agreement in the different loading directions of shear, uniaxial tension, plane strain tension, and the balanced biaxial tension. Considering the high accuracy of the proposed ductile fracture criterion, it is expected that the proposed anisotropic ductile fracture criterion can improve the reliability of failure prediction in metal forming for materials with strong directionality in fracture. [ABSTRACT FROM AUTHOR]

• Present different J and K along crack fronts in CCT and CT specimens. • Present different near-tip stresses in CCT and CT specimens. • Determine lower fracture initiation load for CCT than those for CT and PT specimens. • Visualize localized plastic strain between circumferential hydrides in CCT specimens. • Show similar percentage of fracture toughness reduction for all hydrided specimens. The effects of curvature on K, J, plastic zone, near-tip stress and fracture initiation in curved compact tension (CCT) specimens of unhydrided and hydrided irradiated Zr-2.5Nb materials are determined by three-dimensional finite element analyses. Based on a strain-based failure criterion, the fracture initiation load for unhydrided CCT specimens is slightly lower than those for unhydrided compact tension (CT) and pressure tube (PT) specimens. For hydrided specimens, the reductions of fracture initiation loads for CT, CCT and PT specimens are similar. The fractions of fracture initiation loads for hydrided specimens are about 60–70% of those for unhydrided specimens. [ABSTRACT FROM AUTHOR]

A new constitutive model σ eq = 1 - D ‾ f η 〈 l n p - ln p th 〉 ln ε f - ln p th σ y (p) 1 - η - η 0 f η 0.5 1 + α η - η 0 ln p ̇ p ̇ 0 to predict fracture initiation sites, and decay of fracture strain. • Evaluation of a new stress triaxiality-dependent viscoplastic damage model for ductile fracture. • Transferability of model parameters over a large range of positive stress triaxialities. • Consistency viscoplastic regularization method for mesh independency and strain softening. • Prediction for decay of fracture strains and transition of fracture initiation locations in notched tensile specimens. The aim of this paper is to gain insight for the transition of fracture initiation sites in notched tensile specimens. For this purpose, a stress triaxiality-dependent viscoplastic damage model was proposed for various types of notched tensile specimens, where the influence of stress triaxiality on damage, damage-free stress-strain curve and viscoplasticity was considered. Also, in this constitutive model, the consistency viscoplastic regularization method was used to solve the pathological mesh-dependent problem due to strain softening. A hybrid experimental-numerical approach was used to calibrate model parameters by using smooth and one type of round-notched tensile specimens. The same set of model parameters was then applied to predict ductile fracture for three other types of round-notched tensile specimens. Good agreement between experimental data and simulation results confirmed the transferability of model parameters to all types of tensile specimens considered and the ability of the proposed constitutive model to predict ductile fracture over a large range of positive stress triaxialities. This study found that at the onset of fracture critical damage parameters for all five types of tensile specimens were relatively constant, and fracture initiation sites in these specimens were associated with critical damage parameters, shifting from the center to the notch root. Therefore, the critical damage parameter was defined as a ductile fracture criterion and the fracture strain for all the five types of tensile specimens was successfully predicted. [ABSTRACT FROM AUTHOR]

Abstract In this work, the yielding response of high-density polyethylene (HDPE) under different stress states and strain rates was experimentally examined and the ability of classical yield criteria to capture their deformation response assessed. A series of biaxial loading tests (pure shear, combined shear and tension/compression, pure tension/compression) using a designed Arcan testing apparatus were performed. In order to investigate a wider range of stress states, flat and cylindrical notched specimens with different curvature radii were also tested. The predictive ability of the Von Mises and the Drucker-Prager yield criteria are compared against the acquired experimental data. The Drucker-Prager yield model allowed an improved description of the available experimental results, demonstrating the need to account for pressure dependency in the yield model's formulation for semi crystalline polymers. Some differences observed may be attributed to the third invariant stress tensor effects. The evolution of stress triaxiality and Lode angle parameters with equivalent plastic strain were extracted from simulations with Drucker-Prager yield criterion. The results show sensitive stress state dependency of the plastic yielding behaviour, which can be attributed to different combinations of stress triaxiality and Lode angle parameters. Also numerical simulations show that there is variation of the stress triaxiality and equivalent plastic strain along the cross section and the location of the maximum plastic strain and maximum stress triaxiality in the specimens are located at the centre of the specimens. [ABSTRACT FROM AUTHOR]

Highlights • Proposed mini-Nakazima fracture experiment with dihedral punch. • Observed proportional loading path until fracture initiation. • Compared results with notched tension and V-bending. • Validated for aluminum 2024-T351, DP450, DP980. Abstract A new experimental technique is proposed for measuring the strain to fracture for sheet metal after proportional loading under plane strain conditions. The proposed technique makes use of a mini-Nakazima specimen that is clamped onto a 30 mm diameter die and subjected to out-of-plane loading through a dihedral punch. While other techniques for determining the strain to fracture for plane strain tension loading (e.g. notched tension or V-bending) suffer from limitations with regards to the thickness and ductility of the material to be characterized, the mini-Nakazima experiments are more robust and universally applicable. Experiments are performed on mini-Nakazima, notched tension and V-bending specimens extracted from 1.2 mm thick aluminum 2024-T351, 0.8 mm thick DP450 and 1.6 mm thick DP980 steel. In addition, detailed numerical simulations are performed for each experiment. The hybrid experimental-numerical results show the limitations of existing experimental techniques and demonstrate the reliability of the proposed stretch-bending technique. As a by-product, it is shown that the Yld2000-3D yield function with associated flow rule provides a reasonably accurate description of the large deformation response of aluminum 2024-T351. Equally good predictions are obtained for the DP450 and DP980 steels when using a von Mises yield function in conjunction with a non-associated Hill'48 flow rule. Furthermore, to characterize the effects of the stress triaxiality and the Lode angle parameter on the fracture response of the above materials, the strains to fracture are determined for simple shear and equi-biaxial tension. Graphical abstract Image, graphical abstract [ABSTRACT FROM AUTHOR]

Abstract The response surface methodology in the design of experiments (DOE) wizard and Gurson-Tvergaard-Needleman (GTN) model were employed to estimate the optimum GTN damage parameters and to validate their significant effects respectively on the ductile fracture behavior of ECAP deformed AZ61 magnesium alloy. Hollomon's flow stress was applied to identify uniform deformation and non-uniform deformation regions to investigate the void nucleation and coalescence processes separately. The significance of statistical results was evaluated with the analysis of variance (ANOVA) based on P-values and coefficients of determination (R 2). Correspondingly, the contributions of ECAP plastic deformation and the corresponding local plasticity (damage progresses) on the progress of GTN ductile fracture damage parameters were studied. Desirability function was used to show the significance of individual and interaction effects of optimum initial damage parameters on the respective response variables. By using response surface methodology, the optimum GTN damage parameters were determined at the corresponding positions of each critical response variables. Results also showed that varying both stress triaxiality and damage variables simultaneously can greatly affect the curve fitting process of experimental, simulation and GTN model curves. However, at constant stress triaxiality condition, the GTN model curve was observed perfectly fitting with the tensile test curve. [ABSTRACT FROM AUTHOR]

Highlights • A continuum damage mechanics (CDM) and XFEM based methodology is developed for high cycle fatigue crack growth simulations. • A new damage model is proposed for the evaluation of fatigue crack growth life. • A new criterion is proposed based on the damage evolution to identify the appropriate definition of stress triaxiality. • A non-local CDM approach is implemented to reduce the mesh sensitivity. • The present methodology is found quite successful for fatigue crack growth simulations. Abstract In this paper, we have developed a continuum damage mechanics (CDM) based methodology for high cycle fatigue crack growth simulations. A fatigue damage law is proposed and implemented in the framework of extended finite element method (XFEM). A new criterion is proposed based on damage evolution to identify the appropriate definition of stress triaxiality for acquiring the constraint effect on the stress state correctly. Few mesh regularization schemes are also employed for reducing the mesh sensitivity in the results. Simulations are performed on fracture specimens of different materials subjected to constant amplitude fatigue loading. The fatigue life of a turbine disc is also predicted under constant amplitude loading. The results obtained from present methodology (CDM and XFEM) are found in good agreement with the published experimental results. These simulations highlight that the continuum damage mechanics is a simple and effective tool to perform crack growth simulations under high cycle fatigue conditions. [ABSTRACT FROM AUTHOR]

Highlights • The influence of stress triaxiality on the material formability in SPIF tests is discussed and compared with conventional Nakajima tests in the ɛ ¯ − η ¯ space. • The analytical procedure of mapping the FFL from the ε 1 − ε 2 space to the ɛ ¯ − η ¯ space, using the kinked strain path associated to the onset of local necking in Nakajima tests, is presented. • The difference in the average stress triaxiality at fracture exhibited in SPIF and Nakajima tests would allow explaining the enhancement on formability observed in incremental sheet forming. Abstract Traditionally the fracture in sheet metal forming is characterized by the fracture forming limit (FFL) curve typically obtained by using conventional Nakajima tests. This curve is implicitly assumed a material property. Single point incremental forming (SPIF) is a novel and flexible forming process characterized by the ability to suppress local necking and develop stable plastic deformation up to sheet fracture. In many cases, these fracture strains are clearly above the conventional FFL. The current work presents a numerical study of the evolution of stress triaxiality in SPIF in the ɛ ¯ − η ¯ space. The simulations are validated with hole-flanging tests by single-stage SPIF over AA7075-O sheet of 1.6 mm thickness. The difference in the average stress triaxiality at fracture exhibited in SPIF and Nakajima tests would allow explaining the enhancement on formability observed in incremental sheet forming. Graphical abstract Image, graphical abstract [ABSTRACT FROM AUTHOR]

In this paper, the stress corrosion and monotonic tensile test of corroded steel wire were carried out. The effects of different corrosion ages and stress levels on failure modes, stress-strain curve and mechanical properties of corroded steel wire were discussed. Then, a finite element model of steel wire considering real surface morphology was established, and the surface stress distribution and the failure of steel wire under different corrosion degrees were compared. The relationship between stress triaxiality and critical equivalent plastic strain to different corrosion parameters was given. Finally, the degradation model of mechanical properties of corroded steel wires was established. The results showed that the failure patterns of steel wires with different degrees of corrosion were mainly divided into three types: cup cone shape, milling cutter shape and splitting shape. The shear lip zone of fracture section basically disappeared with the increase of stress corrosion, and the location of fiber area was transferred from the inside to the surface of steel wire. The decrease in strength and elastic modulus of the specimen under stress corrosion was four times and three times greater than that under non-stress corrosion, respectively. In addition, the crack position of specimen changed from the inside of section to the location of corrosion pit with the increase of corrosion degree. The fracture equivalent plastic strain decreased gradually, while the stress triaxiality increased. When the degree of corrosion reached 19.53%, the fracture equivalent plastic strain decreased by 55.41% from 0.314 to 0.140, and the stress triaxiality increased by 23.53% from 0.390 to 0.510. The influence of uniform thickness loss on the stress triaxiality was less than that of pit depth-width ratio. The larger the depth-width ratio, the larger the maximum stress triaxiality corresponding to the failure element. The constitutive model proposed in this paper could reflect the degradation law of mechanical properties of corroded steel wires. • The effect of corrosion ages and stress levels on the mechanical properties of corroded steel wire was discussed. • The stress distribution and failure of steel wire under different corrosion degrees were compared. • The degradation model of mechanical properties of corroded steel wires was established. [ABSTRACT FROM AUTHOR]

• The new tensile tests combining with finite element simulations were developed. • Weakening during post-necking deformation was firstly found in 1.5-GPa class steel. • Weakening behavior did not follow the previously developed damage models. • X-ray diffraction analyses detected material damage relating the weakening. • Unobservable vacancies are likely responsible for damage resulting in weakening. The weakening behavior of ultra-high-strength steel(UHSS) remains unknown, even though it is a requirement for the accurate prediction of strain localization and ductile fracture in automobile applications. In this study, we, therefore, revealed the stress–strain curves of UHSSs up to their ductile fracture under different stress triaxialities for the first time. Smooth and notched tiny round-bar specimens cut from UHSSs with 1.6 mm thickness were subjected to tensile tests, during which the forces and neck diameters of the specimens were measured. Notably, the evaluated flow stresses in the 1.5 GPa-class notched UHSS specimens exhibited weakening of up to 3%. This was in contrast to the 980 MPa-class UHSS specimens, which did not exhibit notch-induced weakening. The absence of weakening during stress measurements, as confirmed by synchrotron X-ray diffraction (XRD) analysis, suggested that weakening was caused by material damage. However, the weakening behavior did not follow the previously developed damage models based on microvoid formation. The volume fraction of the microvoids, as observed by X-ray computer tomography, was extremely small (at 0.2%) and cannot account for the 3% material weakening indicated by the flow stress measurement results. A new damage mechanism, associated with unobservable small lattice vacancies, was implied in UHSSs deformation under high stress triaxialities. [Display omitted] [ABSTRACT FROM AUTHOR]

The impact of high stress triaxiality on work hardening in transformation-induced plasticity (TRIP) steel has been widely acknowledged, particularly through measurements of the austenite fraction. Understanding this TRIP behavior is crucial for predicting material fracture in press-forming processes. However, the actual flow stresses under high-stress-triaxiality conditions remain largely undetermined. To address this gap, we developed a new tensile testing method using tiny notched round bars to investigate stress-triaxiality-induced work hardening in TRIP steels. The specimens were analyzed using two-dimensional micrometry to allow finite element analyses to identify the flow stress. Additionally, we conducted in situ tensile tests in which their crystal lattice stresses were monitored using synchrotron X-ray diffraction (XRD) to realize mechanism analyses of the unexpected work-hardening behavior identified by the developed tensile testing method. Our combined approach revealed a mutual, unstable increase in the flow stress and stress triaxiality in the TRIP-aided bainitic ferrite steel, which reduced the hardening exponent coefficients and thus induced a higher stress triaxiality. In contrast, the TRIP-aided martensitic steel exhibited a weakening behavior, characterized by a significant decrease in the hardening exponent coefficients in the case of the sharpest notch. XRD analyses showed that microstructural heterogeneity led to an extraordinarily high hydrostatic stress in the austenite phase, accounting for these contrasting behaviors. This finding challenges the established consensus on TRIP steels and suggests the need for a revised framework for their application in press-forming, taking into account stress-triaxiality conditions. [Display omitted] • New tensile testing method using tiny notched round bars was developed. • Stress-triaxiality-induced hardening (STH) was directly evaluated in TRIP steels. • Instable stress triaxiality increase by STH was newly discovered. • Weakening behavior instead of STH was firstly found in high strength TRIP steel. • Extremely high hydrostatic stresses on the austenite phase caused weakening. [ABSTRACT FROM AUTHOR]

• A generalized plasticity framework for tension‒compression asymmetry (TCA) was developed. • The new framework was applied to various yield functions: Hill48, Yld2k-2d, Poly6, and Min2016. • Accurate TCA capture was achieved in plastic anisotropy under uniaxial and equi-biaxial loads. • Anisotropy-asymmetry in dual-phase steel, Al, and Ti alloys was successful predicted. • The new framework reproduced anisotropic hardening in Q&P steel using analytical calibration. Microstructural characteristics and complex loading conditions in the deformation of metallic materials lead to complexity in mechanical responses. In this study, we propose a generalized constitutive framework that reproduces the plastic anisotropy and asymmetry under various loading conditions. Particularly, the developed model can accurately capture distinctive flow stress, plastic flow and strain hardening between tensile and compressive dominant loadings under a wide range of stress states. The model is based on the stress triaxiality dependence of state variable (or weighting factor) newly incorporated in the existing plasticity theory to keep the computational efficiency and versatility. For example, the new generalized framework can be applied to widely employed Hill48, Yld2k-2d, and Poly6 as a class of associated flow rule-based yield functions, as well as Stoughton-Yoon2009 and Min2016 yield functions for the non-associated flow rule. Also, the model is adaptable when selecting the yield function under tension or compression, which efficiently controls the degree of accuracy in anisotropic modeling under tension and compression. The generalized plasticity framework is validated comprehensively by demonstrating the predictive capability for anisotropy in yield stress and plastic flow of metallic materials with different crystal structures. Moreover, the model can efficiently capture the continuous evolution of asymmetric yield surfaces as functions of strain, temperature, and strain rate. Finally, the identification procedure of the model is discussed by demonstrating the analytical determination of model parameters utilizing the experimental or generic material data obtained from various loading conditions such as tension, compression, plane strain loading, and pure shear. [ABSTRACT FROM AUTHOR]

• Post-fire tension tests were performed on Q690 steel under plane strain state. • Post-fire tension tests were performed on Q690 steel under generalized tension state. • Post-fire stress state-dependent strain to fracture surface for Q690 steel was obtained. • Stress states influence post-fire ultimate strength of Q690 steel. Fire is one of the most dangerous disasters for high-strength steel structures. After a fire event, the deterioration of mechanical properties of high-strength steel together with the complex stress state generated by external loading may lead to an unexpected failure or collapse of high-strength steel structures. Therefore, it is very critical to evaluate the post-fire behavior of high-strength steel considering stress state effects. This study conducted a series of tests on the Q690 steel specimens after being exposed to high temperatures ranging from 200 to 1000°C with different cooling methods including air-cooling and water-cooling methods. The tested specimens including smooth round specimens, notched round specimens, and grooved plate specimens were designed to consider the failure mode in axisymmetric stress state and plane strain state. To validate the accuracy of the test results, the mechanical properties such as yield strength, ultimate strength, elastic modulus, and ultimate strain were first compared with other test results reported in the literature. The post-fire ultimate strength under different stress states was obtained directly from the test results. Then, the post-fire equivalent plastic strain at fracture of different specimens was obtained from test data together with the finite element analysis results and analyzed under different stress triaxialities and Lode angle parameters. According to this study, an increase in stress triaxiality can result in an increase in ultimate strength but a decrease in the equivalent plastic strain at fracture for Q690 steel after fire. When the exposed temperature was not higher than 800°C, the post-fire strength of the plane strain specimen (Grooved Plane Specimen) was higher than that of the axisymmetric tension specimen (Notched Round Specimen) under a similar stress triaxiality; however, for their post-fire equivalent plastic strain at fracture, the results were opposite. [ABSTRACT FROM AUTHOR]