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• 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]

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]

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]

• 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]

Highlights • Mechanisms of ductile fracture is investigated experimentally in the wide range of loading conditions from compressive upsetting to the tension of notched specimens for two lightweight metals of DP980 (t1.2) steel sheets and a bulk aluminum alloy of AA7075. • All the specimens tend to fail along the direction of the maximum shear stress in various loading states of plane strain compression, uniaxial compression, shear, uniaxial tension and plane strain tension. • Fractured voids elongate along the direction of the maximum shear stress for all specimens with the stress triaxiality ranging from negative in compression to 0.57 in the plane strain tension. • The experiments of DP980 and AA7075 reveal that ductile fracture takes place along the direction of the maximum shear stress in the wide loading conditions of compressive upsetting, shear, uniaxial tension, and plane strain tension with stress triaxiality below 0.6. • Effect of the maximum shear stress must be correctly coupled in modeling of ductile fracture in these loading conditions. Abstract Mechanisms of ductile fracture are investigated experimentally in a wide range of loading conditions from compressive upsetting to the balanced biaxial tension for two metals with high strength-to-density ratio of DP980 (t1.2) steel sheets and a bulk aluminum alloy of AA7075. Specimens are carefully designed to achieve various loading conditions from shear at low stress triaxiality to the balanced biaxial tension at high stress triaxiality for DP980, while both tensile and compressive tests are conducted for AA7075. Fractured specimen surfaces are analyzed macroscopically focusing on their relations with the maximum shear stress. It is observed that all the specimens tend to fail along the direction of the maximum shear stress in various loading states of plane strain compression, uniaxial compression, shear, uniaxial tension, plane strain tension and the balanced biaxial tension. Scanning electron microscope analyses of fracture surfaces are also conducted to explore the underlying mechanism of void coalescence since coalescence of voids is viewed as the last step of ductile fracture after nucleation and growth of voids. It is noted that fractured voids elongate along the direction of the maximum shear stress for all specimens with the stress triaxiality ranging from about −0.57 in compression to 0.67 in the balanced biaxial tension. The experiments of DP980 and AA7075 reveal that ductile fracture takes place along the direction of the maximum shear stress in the wide loading conditions of compressive upsetting, shear, uniaxial tension, plane strain tension and the balanced biaxial tension with stress triaxiality below 0.67. Thus, ductile fracture is expected to be governed by the maximum shear stress in these wide loading conditions of compression, shear and tension. It is suggested that effect of the maximum shear stress must be correctly coupled in modeling of ductile fracture in these loading conditions with uncoupled and coupled ductile fracture criteria. Graphical abstract Shear fracture takes place in wide loading conditions of tension, shear and compression. Image, graphical abstract [ABSTRACT FROM AUTHOR]

In this paper, by separately characterizing the influence of stress triaxiality (ratio of hydrostatic stress to von Mises stress) on the stress response to plastic deformation and to damage evolution, the constitutive equation of the pressure-insensitive metal under axisymmetric tensile loading is defined as a new stress triaxiality-dependent plasticity damage model. For this purpose, experimental testing and finite element modelling are performed based on smooth and notched round bars, machined from a high-strength rail steel. The test results show that mechanical behaviour of both types of tensile specimens can be closely simulated based on the same constitutive equation calibrated following the classical J 2 flow theory; even though stress triaxiality and damage evolution generated in these two types of specimens are very different. Such an issue is investigated by implementing the new constitutive model to finite element modelling of smooth and notched specimens using the ABAQUS user subroutine VUMAT. It is found that the rates of both damage-free stress response to deformation and damage evolution increase with increasing stress triaxiality. Also, the increase of damage-free stress response to deformation, caused by the increase of stress triaxiality, is offset by the decrease of stress due to the increase of damage evolution. This results in the constitutive equation insensitive to the change of stress triaxiality. [ABSTRACT FROM AUTHOR]

• Intermediate principal stress effect and strain rate effect were investigated by true triaxial dynamic test system. • The constitutive model was modified by introducing the lode angle and strain rate. • The lateral inertia effect of concrete was further revealed by introducing the Weibull-type modification. • The relative equivalent stress was proposed to evaluate the size effect and strain rate effect. The strain rate sensitivity and stress state are two important factors affecting the mechanical behavior of concrete under dynamic load. However, few studies involved high strain rates and different stress states. Herein, the strain rate effect and intermediate principal stress effect of concrete are studied by using the true triaxial Hopkinson test system, and the influence of heterogeneity under dynamic load is also discussed. A series of experiments, including the static biaxial and static triaxial confinements, are conducted to investigate the intermediate principal stress effects by a dynamic testing system for cubic concrete specimens under static triaxial confinements. The results show that the triaxial experimental data show good consistency with the dynamic M-C strength, but the biaxial experimental data deviate greatly from the dynamic M-C strength, which indicates evident the intermediate principal stress effect. The Drucker-Prager (D-P) model is then modified to describe the intermediate principal stress dependence and loading rate effect by introducing the Lode angle (θ) and the strain rate, and better simulation results are obtained. The meso finite element model (meso‑FEM) is employed to further explain the effects of non-uniformity in concrete specimens, and a Weibull-type modification is introduced to describe the transversal inertia effect due to concrete heterogeneity. Although the relative dynamic stress (η = (σ x − σ e) / σ x) in the x-axis is rate-dependent, hydrostatic pressure-dependent, and size-dependent, the relation of η to the stress triaxiality is insensitive to these effects. This work would provide experimental and theoretical guidance for the effect of stress state on the mechanical behavior of concrete under dynamic load. [Display omitted] [ABSTRACT FROM AUTHOR]

A plastic instability model is extended to predict evolution of a bounded deformation in necking phenomenon. There are several studies to predict the plastic instability such as the vertex model proposed by Stören and Rice, which considers strain and stress rate discontinuities in the necking band. Here, the model is established on the J 2 deformation theory of classical plasticity. Effect of stress triaxiality is investigated on the localization in bifurcation analysis. Also, a modified maximum force criterion is applied to predict diffuse necking considering loading conditions. Although considering the effect of strain rate hardening plays an important role to give accurate results, usually imposing it leads to emerging relatively the main complex constitutive equations. Therefore, a delicate bridge between the diffuse and localized models is made using the maximum force assumption to overcome on the complexity of the problem. Also, by investigating the strain rate behavior on the plastic instability, the forming limit diagrams are obtained illustrating more accurate results than other existing models. The anisotropy effect is studied by application of a quadratic Hill's criteria. The necking band angle will be investigated per different conditions through extending the vertex model coupled with the angle-dependent yield criterion. [ABSTRACT FROM AUTHOR]

A constitutive model considering the composition of surface grain, grain boundary and grain interior and their contributions to the flow stress or strength of materials in micro-scale plastic deformation is developed and termed as a combined surface layer and grain boundary strengthening model in this research. To determine the composition of the three interior microstructural parts of materials, optical microscope and digital image processing technologies are employed. A series of micro-tensile experiments using the specimens with three different geometrical shapes and microstructural grain sizes are conducted for study of deformation and ductile fracture behaviors of material. The model is implemented in finite element analysis and validated via physical experiments. The relationship among fracture strain, grain size and stress triaxiality of the deforming material is thus established. It is found both fracture strain and stress triaxiality increase with the decrease of grain size, while the high stress triaxiality leads to small fracture strain for the given grain size. Through observation of the fractographs, it is revealed that the domination of shear fracture in the ‘cup-cone’ fracture increases with grain size. The research thus helps understand the ductile fracture in micro-scale deformation and facilitates deformation based working process determination and application. [ABSTRACT FROM AUTHOR]

In automotive engineering, sheet metal components are subject to a 20–30 min heat treatment at 180 C during paint baking. This process may significantly alter the mechanical properties of 6000-series aluminum alloys through artificial ageing. Here, a comprehensive experimental program is carried out to characterize the anisotropic plasticity and the fracture initiation in pre-strained artificially-aged aluminum 6451 sheets. It is found that the combination of pre-straining up to 5% strain and heat treatment mainly changes the material's strain hardening behavior and the stress-state sensitivity of its fracture response. The material parameters of the Yld2000-2d plasticity model with combined Swift-Voce hardening are identified for four distinct materials from uniaxial tension and shear experiments. The corresponding Hosford-Coulomb fracture model parameters are determined from smiley shear, V-bending and punch experiments. As an important byproduct of the research, the Yld2000-2d and Hosford-Coulomb models are successfully validated for all four materials through notched and central hole tension experiments. Simple empirical expressions are also provided to estimate the material properties as a function of the pre-strain in engineering practice. [ABSTRACT FROM AUTHOR]

• A series of specimens are designed to control stress states over wide range. • Different failure mechanisms are found for various stress states. • A new stress-state-incorporated ductile fracture model is proposed. • This model can capture the non-monotonic feature of fracture strain. • This model can predict fracture strain more precisely in wide stress-state range. To understand comprehensively the relationship between material ductility and stress state, the new shear, shear-compression, and shear-tension specimens were specially designed, and seven types of specimens were used in total to achieve precise control of stress states over wide ranges of stress triaxialities and Lode angle parameters. A hybrid experimental-numerical method was employed to determine the equivalent plastic strain, stress triaxiality, and Lode angle parameter, and hence to construct the 3D fracture locus of the Ti-6Al-4V alloy. Different micromechanisms were found to dominate the failure process under various stress states. Based on the experimental results, a new ductile fracture model coupling both stress triaxiality and Lode angle parameter was proposed and implemented into the commercial finite element program ABAQUS/Explicit via the user material subroutine VUMAT. Comparative studies with some other fracture criteria indicate that the proposed fracture model can capture the non-monotonic feature of fracture strain, and predict the fracture strain with better accuracy in a wide range of stress states. A verification test was performed to check the predictive capability of the present model. The results show the excellent agreement between experiment and simulation with respect to the fracture displacement and fracture morphology. This study paves the way for characterizing and predicting the ductile behavior of metallic materials under complex stress states, and provides a fundamental databank for the analysis and design of Ti-6Al-4V alloy structures. [Display omitted] [ABSTRACT FROM AUTHOR]

• A modified GTN damage model is proposed by improving the sensitivity of shear damage to negative stress triaxiality. • The rolling edge crack morphology and location of AZ31B magnesium alloy are accurately predicted. • High-stress triaxiality at the edge is an important factor for magnesium alloy rolling edge cracks. • A novel process called edge-constraint rolling is proposed to inhibit the edge crack of AZ31B magnesium alloy. Edge cracks are a type of damage that critically affect the quality and properties of rolled Mg alloys sheet. Accurate damage prediction plays a key role in root cause analysis and process optimization. Although the phenomenological prediction of edge damage in Mg alloy rolling has made some progress so far, the prediction of edge crack behavior and analysis of the mechanisms of crack formation and evolution during rolling have not yet been well reported. In this research, a modified Gurson-Tvergarrd-Needleman (GTN) model was proposed by modifying the growth mode of shear damage. The three-dimensional single-unit finite element (FE) model test results indicated that the proposed model improved the accuracy of the fracture response under negative stress triaxiality. Using AZ31B Mg alloy as the case study material, physical experiments and FE analysis of the rolling process were conducted. The simulations showed that the proposed model can accurately reflect the morphology and location of cracks during the rolling process, and revealed that the high-stress triaxiality at the Mg alloy edge was a significant cause of edge cracking. On this basis, an edge-constraint rolling process was proposed to inhibit edge cracking by embedding the billet into a U-shaped sheet. The numerical results showed that the minimum value of edge stress triaxiality could be reduced from -0.8 to -2.05 during edge-constraint rolling, and the accumulation of damage could be limited. The sheet forming quality was verified with different reduction rates of 30, 35, and 40%, and the results showed that the edge cracks could be effectively avoided during edge-constraint rolling, which provides an important basis for optimizing the rolling deformation process of Mg alloys. [Display omitted] [ABSTRACT FROM AUTHOR]

For general stress states the fracture locus, under strictly proportional loadings, may be viewed as a two dimensional surface. Deviations from that locus under non-proportional loadings have received limited attention in the literature. The general problem is quite complex because of unavoidably intertwined history effects on both damage-free plasticity and plasticity-induced damage . This work first reports on a systematic attempt at quantifying deviations from the proportional fracture locus given a fracture theory. Two generic types of nonproportional loading are considered, which are believed to represent a heuristic integrity basis for an infinity of possible loading histories. In doing so, emphasis is laid on that component of the deviation associated with damage, thus reducing the representation of plastic flow to its simplest form. The predictive capability of the simple theory is then employed to rationalize experimental trends from the literature. [ABSTRACT FROM AUTHOR]

The aluminium alloy 2024-T351 and AISI 1045 carbon steel was examined in scope of uncoupled ductile fracture criteria calibration using newly designed specimen. Its novel geometry allowed to reach extremely low stress triaxialities. The analysis of fracture envelopes was carried out with comparison of each criteria cut-off regions after the calibration where one novel criterion, KHPS, has been introduced. Ductile fracture criteria implemented into the commercial finite element code Abaqus through user subroutine VUMAT were applied to simulation of compression of newly designed cylinder with specific recess to show the crack prediction ability using the element deletion technique. Crack initiation loci together with force responses were compared to experimental observations. [ABSTRACT FROM AUTHOR]

Abstract: The aim of the present paper is to study the influences of the clearance and the notch-sensitivity on a new type of metal-bar non-chip fine-cropping system by combining the ductile damage initiation criterion, the fatigue crack propagation path analysis and the micrograph fractography observation. The single factor test method and the orthogonal test method are both applied to the numerical simulations and the corresponding non-chip fine-cropping experiments. The comparative numerical results show that the ductile damage initiation criterion is obviously influenced by the clearance and the notch geometric parameters. The corresponding cropping experiments are carried out and achieve a good agreement with the simulation results. And some other interesting results, which are useful for practical fine-cropping, are also obtained. [Copyright &y& Elsevier]

Abstract: Developments in computational mechanics have given engineers tools to predict the evolution of damage in complex structures. Damage models have been developed that relate failure strain to stress triaxiality and Lode angle. Calibration of these models has traditionally relied on specimens that exhibit high triaxiality and limited Lode angle. This paper presents a specimen that can be tested in combined tension and torsion to achieve low triaxiality over a range of Lode angle. Numerical analysis of the specimen shows that it exhibits uniformity of stress–strain and stable values of triaxiality and Lode angle as plastic strain develops, both of which are desirable characteristics for calibration of ductile failure models. The design of a new displacement and rotation gage is presented that allows non-contact measurement at the gage section. Experimental results are used to develop the failure surface for 5083 aluminum. [Copyright &y& Elsevier]

Abstract: In this study, we investigate deformation behavior of f.c.c. single crystals containing microvoids by using three-dimensional finite element methods. The unit cell analysis has been conducted to study the effect of stress triaxialities, crystallographic orientations and initial void volume fractions on the growth and coalescence of voids in f.c.c. single crystals. The locally homogeneous constitutive model for the rate-dependent single crystal plasticity is implemented into a finite element program (ABAQUS) by means of the user-defined subroutine (UMAT). To identify the effect of stress triaxiality and the crystallographic orientation on the void evolution, the stress triaxiality was kept constant during deformation. The numerical results showed that the stress triaxiality and the deformation mode specified by the crystallographic orientation have a competitive effect on the evolution of voids. For the low level of stress triaxiality, the deformation mode is mainly determined by the crystallographic orientation. For high stress triaxiality, however, the deviation from the specific deformation mode is large even for incipient void growth and the void growth rate is mainly determined by stress triaxiality and the initial void volume fraction. For the small initial void volume fraction, the growth rate of a void is rapid compared with the large one and the effect of the initial crystallographic orientation is significant. [Copyright &y& Elsevier]

The response of thin clamped plates subjected to static punch indentation is investigated experimentally, analytically and numerically to determine the onset of fracture. The accumulated equivalent plastic strain with stress triaxiality as a weighing function is introduced as ductile fracture criterion in the finite-element simulation and analytical prediction. The fracture criterion was calibrated by finite-element simulations of uniaxial tensile tests. Based on the calibration, and calculated distributions and histories of stress and strain, the critical location, and penetration to fracture were predicted within 5–10% accuracy for three punch radii.The plots of force–penetration and locations of fracture initiation in the static punch indentation tests were compared with finite-element simulations and analytical approximations showing good agreement. The transverse deflection profiles of the plates at the point of fracture obtained numerically were shown to agree well with the closed-form solution derived by taking into account a variable stress ratio and varying stress triaxiality. The strain distribution along the plate radius is influenced by the friction between the interfaces of punch and plate. By changing the friction coefficient, the fracture-forming limit diagram was constructed numerically. The present procedure can replace the time-consuming experimental technique in which the strain path is controlled by changing the radius of a cut off. [Copyright &y& Elsevier]

The stress triaxiality is, besides the strain intensity, the most important factor that controls initiation of ductile fracture. In this study, a series of tests including upsetting tests, shear tests and tensile tests on 2024-T351 aluminum alloy providing clues to fracture ductility for a wide range of stress triaxiality was carried out. Numerical simulations of each test was performed using commercial finite element code ABAQUS. Good correlation of experiments and numerical simulations was achieved. Based on the experimental and numerical results, the relation between the equivalent strain to fracture versus the stress triaxiality was quantified and it was shown that there are three distinct branches of this function with possible slope discontinuities in the transition regime. For negative stress triaxialities, fracture is governed by shear mode. For large triaxialities void growth is the dominant failure mode, while at low stress triaxialities between above two regimes, fracture may develop as a combination of shear and void growth modes. [Copyright &y& Elsevier]

• Temperature and triaxiality effects on AA7075-T6 mechanical behaviour were studied. • Necking locus as a function of the temperature and stress triaxiality was modelled. • Higher uniform elongations were obtained when deforming at sub-zero temperatures. • Coarsened intermetallic particles characterized samples deformed in warm range. Age-hardenable aluminium 7XXX alloy sheets represents a very attractive material for the aerospace field; however, their limited formability at room temperature restricts their adoption in the industrial context. In the present study, deformation of AA7075 sheets at temperatures lower than the room one is presented as a possible strategy to overcome this limitation. To this aim, a comprehensive experimental campaign was carried out on AA7075 sheets in peak aged condition at varying temperature and triaxiality states. Specifically, the temperature was changed from −100 °C to 300 °C whereas different stress triaxialities states were achieved by adopting different specimen configurations, namely smooth, notched and shear. A necking locus curve was presented and modelled. Results show that, regardless of the stress state, the uniform elongation monotonically increased as the testing temperature was reduced, favouring material formability. Microstructural and mechanical investigations carried out on the deformed samples revealed that deforming at temperatures higher than the room one drastically increased the number of coarse intermetallic particles. On the contrary, sub-zero deforming temperatures favoured the intermetallic particle fragmentation and the formation of high density of precipitates and dislocations. Image, graphical abstract [ABSTRACT FROM AUTHOR]

• A new phenomenological ductile fracture criterion considering micro mechanisms of void nucleation, void growth, and evolution of void coalescence is presented in this paper. • The secondary voids band and rotation of voids effect are considered in the new ductile fracture criterion. • The new ductile fracture criterion can be utilized for predicting initial fracture in sheet metal forming with lager range of stress triaxiality. A new phenomenological ductile fracture criterion that is proposed. The proposed model is associated with the micro mechanisms of void nucleation, void growth, and evolution of void coalescence. The secondary voids band and rotation of voids effect are considered in the new ductile fracture criterion. A series of upsetting test results of aluminum 2024-T351 and TRIP RA-K40/70 steel are used to construct and compare the accuracy of fracture locus proposed by new ductile fracture criterion, Modified Mohr-Coulomb criterion and extend Lou-Huh criterion. The fracture locus constructed using the proposed criterion is close to the experimental data points over a wide stress state range from uniaxial compression to balanced biaxial tension. Then, a series of upsetting tests and square cup drawing tests are conducted with Al6014-T4 to evaluate the accuracy of the proposed criterion. All results indicate that the proposed ductile fracture criterion can be utilized for predicting initial fracture in sheet metal forming. Image, graphical abstract [ABSTRACT FROM AUTHOR]

• The effect of Lode parameter on void volume evolution rate was studied. • An analytical model accounting for the effect of stress triaxiality, Lode parameter, effective strain and Norton exponent on void evolution was presented to predict the relative volume of void. • Paired screw threads were used to investigate the distribution of strain around void and the evolution of true void in radial forging process. • The model validated by comparison of model results with those of RVE simulation and experiments. Large numbers of voids inevitably exist in the metal ingot due to non-equilibrium solidification. Forging is an important technique to eliminate such internal defects and obtain sound products. However, the research regarding void evolution mechanisms are currently not sufficient to direct the technological design in practical engineering because of the lack of suitable void evolution model, especially in terms of complex stress states. On the basis of a large number of numerical computations, the effect of Lode parameter on the void volume evolution rate is firstly investigated, and then incorporated together with the stress triaxiality T , effective strain E e and Norton exponent n into a newly proposed void evolution model. At the scale of representative volume element (RVE), the prediction of void evolution calculated from the new model has achieved better accuracy than other analytical models comparing with the simulation results. Radial forging test for rectangular cross-section billet is carried out to verify the accuracy of the proposed void evolution model. Paired screw threads are used to introduce pre-fabricated voids and then embedded into the billet for measuring void volume variation and the distribution of strain around void during forging. The comparison of void evolution between the experimental and analytical solutions also shows that the prediction of void relative volume change by the proposed model is more accurate than those by other models. [ABSTRACT FROM AUTHOR]