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ABSTRACT Being aimed at the strain path–related ductile fracture characteristic, this research develops a two‐component stress‐based DF2016 fracture model with 10 parameters through combining two single‐component corresponding fracture model with the addition form. This model possesses high flexibility to describe the ductile fracture behavior in various stress states. Stress‐based fracture‐related variables of the specimens with 10 different structures for WE43 alloy are captured, and the hardening behavior is with some strength differential effect. These fracture stresses have a strong sensitiveness to stress triaxiality and Lode parameter. Fracture loci of WE43 alloy are constructed by the proposed model with the smaller prediction error of 0.25683 than the stress‐based DF2016 fracture model (0.527). The reliability and high flexibility of the developed model are further uncovered through the description of ductile fracture behavior of AA2024‐T351 alloy. This research provides a valuable tool for predicting fracture failure of metals in engineering applications. [ABSTRACT FROM AUTHOR]

Abstract Constrained groove pressing (CGP) process is one of the most efficient and novel methods of severe plastic deformation to manufacture ultra-fine sheet metal. The present research work is related to the study of CGP process of 2024-T3 Aluminum alloy sheet. The empirical and numerical simulation of CGPed- specimens have been examined at both room and elevated temperatures. In order to simulate the constrained groove pressing process in Abaqus software, the Johnson–Cook material model has been employed. The geometrical variables of the CGP process include the teeth number, teeth angle, and sheet thickness, and the criterion for the superiority of the numerical test is the maximum reduction of two equivalent strain and equivalent force factors, simultaneously. To determine the weight’s coefficients of the target factors and select the superior test, the Shannon’s Entropy and Simple Additive Weighting (SAW) methods have been used, respectively. After validating the numerical findings, the variation of damage parameter, stress triaxiality and the equivalent plastic strain distribution in the superior practical condition have been evaluated in detail. Based on the Entropy-SAW hybrid technique, the weight’s coefficients of equivalent strain and equivalent force target factors were computed to, in turn, 0.38 and 0.62. Also, the results revealed that the CGP process could not be performed at room temperature based on high damage evolution. But, at elevated temperature, the damage parameter (D) doesn't exceed 0.26. Also, the maximum stress triaxiality and equivalent plastic strain (PEEQ) at this process temperature reached to 0.5 and 0.1, respectively.

Structural steel (E250 grade) is used in several engineering applications involving loadings from quasi-static to high strain rates (blast discs, explosion vents, etc.), which introduce large deformation, strain and strain rate hardening, thermal softening, and damage to the material. The material's dynamic constitutive behaviour can be aptly modelled by a visco-plasticity-based Johnson–Cook (J–C) strength model and damage initiation and complete failure by the J–C's damage model. In the latter, damage initiation is modelled through continuum damage mechanics and propagation by the fracture mechanics. This paper focuses on the determination of 10 different J–C's dynamic constitutive and damage model parameters for E250 structural steel by conducting several experiments involving tensile tests at different strain rates (0.0003–1.0 s-1), stress triaxialities (0.33–0.95), temperatures (30–800 °C), and SHPB experiments (at 3000 and 8000 s-1). It explains the processes and step-by-step procedures for extracting the model parameters from the experimental results. A different approach is followed in arriving at fracture strain for extracting damage model parameters to suit fracture mechanic-based damage evolution available in the existing FEA codes. The constitutive and damage model parameters thus determined are validated through numerical simulations and comparison with three independent experiments viz. i) experiment of a plain tensile specimen, ii) tensile experiment of a notched specimen, and iii) hydrostatic burst experiment of a flat burst disc. The responses and failure patterns from numerical simulations agreed very well in all three experiments, thereby validating the determined model parameters. The determined model parameters can be utilised directly in the commercially available nonlinear explicit FEA codes. [ABSTRACT FROM AUTHOR]

The mechanical properties of local materials subjected to various stress triaxialities were investigated via self-designed small punch tests and corresponding simulations, which were tailored to the geometry and notch forms of the samples. The finite element model was developed on the basis of the actual test method. After verifying the accuracy of the simulation, the stress, strain, and void volume fraction distributions of the Ti6Al4V titanium alloy under different stress states were compared and analyzed. The results indicate that the mechanical properties of the local material significantly differ during downward pressing depending on the geometric shape. A three-dimensional tensile stress state was observed in the center area, where the void volume fraction was greater than the fracture void volume fraction. The fracture morphology of the samples further confirmed the presence of different stress states. Specifically, the fracture morphology of the globular head samples (with or without U-shaped notches) predominantly featured dimples. Modifying the specimen's geometry effectively increased stress triaxiality, facilitating the determination of the material's constitutive relationship under varying stress states. [ABSTRACT FROM AUTHOR]

The ability of wood–plastic composites (WPCs) to withstand various loads and resist plastic failure is attracting more and more interest due to the global increase in demand for WPCs by over 6 million tons per year. Among the most important and innovative research methods are those based on fracture mechanics—their results enable material designers to optimize the structures of these hybrid polymer composites at the nano, micro and macro levels, and they allow engineers to more accurately evaluate and select functional, sustainable, long-lasting and safe product designs. In this study, standard single-edge notched bending (SENB) tests were used to analyze the fracture toughness of two different extruded WPCs along the longitudinal (L) and transverse (T) directions of extrusion. In addition to their resistance to crack propagation, critical fracture criteria, initial contact stiffness, fracture parameters and fracture surfaces, the mechanical properties of these composites were also investigated. The results showed that WPC-A coded composites withstood higher loads until failure in both directions compared to WPC-B. Despite the larger data spread, both types of composites were more resistant to crack propagation in the T direction. Mode II of crack propagation was clearly visible, while mode III was not as pronounced. The experimental results and the numerical finite element (FE) model developed up to 58% of the maximum load correlated well, and the obtained deformation curves were best approximated using cubic equations (R2 > 0.99). The shear stress zone and its location, as well as the distribution of the equivalent stresses, had a major influence on crack propagation in the fracture process zone (FZP). [ABSTRACT FROM AUTHOR]

The Modified Mohr–Coulomb criterion has been demonstrated to exhibit high accuracy in the prediction of fracture in high-strength steels. Taking DP780 as the research object, the undetermined parameters of the Modified Mohr–Coulomb criterion at different temperatures were calibrated by tensile and shear tests combined with simulation. The relationships between the parameters and temperature were investigated. Finally, the relationship between criterion parameters and temperature was verified using the stretch-bending tests of U-shape parts. The fracture of automotive parts can be accurately predicted by simulation during warm stamping, thereby guiding actual production. [ABSTRACT FROM AUTHOR]

Estimates of physical and mechanical characteristics of materials at high strain rates play a key role in enhancing the accuracy of prediction of the stress–strain state of structures operating in extreme conditions. This article presents the results of a combined experimental–numerical study on the mechanical response of a thin-sheet rolled Ti-5Al-2.5Sn alloy to dynamic penetration. A specimen of a titanium alloy plate underwent punching with a hemispherical indenter at loading rates of 10, 5, 1, and 0.5 m/s. The evolution of the rear surface of specimens and crack configuration during deformation were observed by means of high-speed photography. Numerical simulations were performed to evaluate stress distribution in a titanium plate under specified loading conditions. To describe the constitutive behavior and fracture of the Ti-5Al-2.5Sn alloy at moderate strain rates, a physical-based viscoplastic material model and damage nucleation and growth relations were adopted in the computational model. The results of simulations confirm a biaxial stress state in the center of specimens prior to fracture initiation. The crack shapes and plate deflections obtained in the calculations are similar to those observed in experiments during dynamic punching. [ABSTRACT FROM AUTHOR]

Springback, buckling, and cracking are typical problems that take place during the stamping of titanium alloy sheets. Accuracy of material response characterization at moderate strain rates is an important factor for improving the adequacy of predictions of structures subjected to forming processes. In this paper, the deformation and fracture of alpha titanium alloys were studied using numerical simulations and the punch test at strain rates up to several hundred per second. Loading velocities from 0.5 to 10 m/s were realized during the spherical body penetration through a thin titanium plate. A viscoplastic constitutive model and damage model are used to describe the mechanical behavior of alpha titanium alloys at strain rates ranging from 10 to 103 s−1. Estimates of the residual stress of alpha titanium alloys are obtained using inverse simulation technique. It was found that amplitudes of residual stresses in CP-Ti after high speed punching are consistent with the increment of the yield stressas a result of strain hardening. Therefore, a comprehensive understanding of plastic deformation localization is essential for analyzing residual stresses in titanium alloys deformed at moderate strain rates. [ABSTRACT FROM AUTHOR]

Grain boundaries (GBs) serve not only as strong barriers to dislocation motion, but also as important carriers to accommodate plastic deformation in crystalline solids. During deformation, the inherent excess volume associated with loose atomic packing in GBs brings about a microscopic degree of freedom that can initiate GB plasticity, which is beyond the classic geometric description of GBs. However, identification of this atomistic process has long remained elusive due to its transient nature. Here, we use Au polycrystals to unveil a general and inherent route to initiating GB plasticity via a transient topological transition process triggered by the excess volume. This route underscores the general impact of a microscopic degree of freedom which is governed by a stress-triaxiality-based criterion. Our findings provide a missing perspective for developing a more comprehensive understanding of the role of GBs in plastic deformation. [ABSTRACT FROM AUTHOR]

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

In order to predict the ductile fracture failure of different high-strength steel plates, the damage parameters of the ductile fracture criterion were calibrated by designing the tensile, shear and fracture failure tests of four high-strength steel plates. The relation between damage parameters and material properties is established by combining test and numerical simulation, so as to reduce the difficulty of calibrating the damage parameters of ductile fracture criterion. In order to verify the universality and accuracy of the criterion in predicting the fracture failure of high-strength steel under different stress triaxiality, through shear, tension bending, bulging test and numerical simulation. The results show that the ductile fracture criterion can better predict the fracture failure of different advanced high strength steels.

In order to investigate the fracture behavior of the ZK60 Mg alloy rolling under different stress triaxiality, the different nominal stress triaxiality samples were well-designed, and the in-situ DIC tensile tests were carried out. The finite element method (FEM) model was validated by experimental results and the stress triaxiality evolution of samples was determined by modeling. The fracture strain of the ZK60 Mg alloy was non-monotonic with the nominal stress triaxiality increase and the best deformation performance of the central hole sample was indicated via the experimental and modeling results. The low stress triaxiality gradient of the central hole sample led to better deformation performance in terms of the macroscopic mechanical response. The transformation of the fracture mechanism from shear transgranular fracture to intergranular fracture and then to transgranular fracture during the stress triaxiality increased from 0 to 2/3 and was revealed via scanning electron microscope (SEM) characterization and FEM modeling. To further confirm the above fracture mechanism, X-ray computed tomography (XCT) was carried out to characterize the micro damage volume fraction and morphology. Due to the transgranular fracture induced by the high stress triaxiality at the initial fracture position of the central hole sample, the micro damage was smaller, delaying the fracture failure and achieving higher strain.

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ABSTRACTImproved strength-ductility synergy is not uncommon among metallic materials with gradient structures of grains and twins. In this work, we report that the texture gradient innately created in Al-Mn strips by twin-roll casting is also capable of increasing the material’s ductility without sacrificing its strength. Analyses based on crystal plasticity theory demonstrated that the underlying mechanism of this texture-gradient-induced ductility enhancement lies in the orientation-dependent slip and grain rotation, which generate backstress, alter the local stress triaxiality, and delay the fracture process. These results advocate the integration of texture gradient design into the fabrication of high-performance gradient materials.

The aim of this article is to investigate numerically and experimentally the effect of stress triaxiality and anisotropy on the fracture strain for metals. As the aluminum has always been one of the most widely used metals in the industry. This metal has unique properties such as lightness and high resistance to corrosion, hence, 1100 aluminum alloy is used in this article. This metal is malleable and also has high workability so it is suitable for applications including shaping. To achieve the properties of the sheet, it is first necessary that all samples were made according to the ASTM-E8 standard and the specimens were designed to achieve some different stress triaxiality. This samples includes the standard-, notched- and shear-specimens. All samples are loaded in tension state. In order to investigate the anisotropy, the specimens are prepared in rolling direction, 45 and 90 degrees to rolling direction for each samples. The uniaxial tensile test was performed on the specimens until the onset of failure. For measuring the fracture strain experimentally, a new method with lower costs than others have been proposed. For standard and notched specimens, the strain measuring is based on the difference between cross-section areas for shear-specimen, the changes in the notched radius has been proposed for strain measuring criterion. Also, in order to calculate the stress triaxiality in the fracture zone, all experiment tests are simulated in Abaqus. The equivalent plastic strain and stress triaxiality of the elements in fracture zone are reported. The average value of these elements are compared to the corresponding experimental data. At the end comparing the results obtained from experimental and simulations shows that the failure strain is calculated with great accuracy. For more explanation, the maximum error is found to be 12.8% for notched-specimen. Furthermore, the non-linear effect of stress triaxiality on the fracture strain are well shown.

The Modified Mohr–Coulomb criterion has been demonstrated to exhibit high accuracy in the prediction of fracture in high-strength steels. Taking DP780 as the research object, the undetermined parameters of the Modified Mohr–Coulomb criterion at different temperatures were calibrated by tensile and shear tests combined with simulation. The relationships between the parameters and temperature were investigated. Finally, the relationship between criterion parameters and temperature was verified using the stretch-bending tests of U-shape parts. The fracture of automotive parts can be accurately predicted by simulation during warm stamping, thereby guiding actual production.

This work establishes a computational framework for the quantification of the effect of uncertainty of material model parameters on extremal stress triaxiality and Lode angle values in plastically deformed devices, whereby stress triaxiality and Lode angle are accepted as key indicators for damage initiation in metal forming processes. Attention is paid to components, the material response of which can be represented as elasto-plastic with proportional hardening as a prototype model, whereby the finite element method is used as a simulation approach generally suitable for complex geometries and loading conditions. Uncertainty about material parameters is characterized resorting to probability theory. The effects of material parameter uncertainty on stress triaxiality and Lode angle are quantified by means of a variance-based global sensitivity analysis. Such sensitivity analysis is most useful for apportioning the variance of the stress triaxiality and Lode angle to the uncertainty on material properties. The practical implementation of this sensitivity analysis is carried out resorting to a Gaussian process regression, Bayesian probabilistic integration and active learning in order to decrease the associated numerical costs. An example illustrates the proposed framework, revealing that parameters governing plasticity affect stress triaxiality and Lode angle the most.

This paper studies the hydrogen-assisted microdamage (HAMD) in fully-pearlitic steel. A detailed analysis is provided of the HAMD region in axisymmetric round-notched samples of high-strength eutectoid pearlitic steel under hydrogen embrittlement environmental conditions. The microscopic appearance and evolution of the hydrogen affected region is analyzed from the initiation (sub-critical) to the fracture (critical) situations. The use of very distinct notched samples and their associated stress distributions in the vicinity of the notch tip allows for a study of the key role of the triaxial stress state on hydrogen diffusion and micro-cracking (or micro-damage). The microscopic appearance of the hydrogen-affected zone (the so-called tearing topography surface) resembles micro-damage, micro-cracking or micro-tearing at a micro- or nano-scale due to hydrogen degradation, thus affecting the notch tensile strength and producing hydrogen embrittlement. A micromechanical model is proposed to explain these hydrogen effects on the material on the basis of the lamellar micro- and nano-structure of the pearlitic steel. [ABSTRACT FROM AUTHOR]

Hot-stamped steel is currently the most widely used lightweight material in automobiles, and accurately predicting its failure risk during the simulation is a bottleneck problem in the automobile industry. In this study, the fracture failure behavior of the hot-stamped PHS2000 steel manufactured by Ben Gang Group (Benxi, China) is investigated by experiments and simulation. Static tension and high-speed tension tests are conducted to obtain the elastic-plastic stress-strain relations, and a Swift + Hockett–Sherby model is proposed to describe the hardening behavior under static and high-speed loads. Tests under five kinds of stress states, namely static shear, static tensile shear, notched static tension, center-hole static tension, and static punching, are conducted to obtain the ultimate fracture strains under different stress states for establishing a failure model. The finite element method (FEM) is used to inversely achieve the fracture parameters of the material, and the GISSMO model in LS-Dyna is adopted to describe the fracture characteristics of the material. A fracture card is further established for simulation analysis by combining fracture characteristics with high-speed tension curves and simultaneously loading size effect curves of meshes. Finally, the card is applied in the simulation of the three-point bending test. High-precision results of fracture simulation matching the experimental results are obtained. This research proves that the proposed fracture card is accurate and can be widely used in the simulation of fracture behaviors of the hot-stamped PHS2000 steel. [ABSTRACT FROM AUTHOR]

Hydrogen can degrade the mechanical properties of steel components, which is commonly referred to as "hydrogen embrittlement" (HE). Quantifying the effect of HE on the structural integrity of components and structures remains challenging. The authors investigated an X70 pipeline steel through uncharged and hydrogen-charged (notched) tensile tests. This paper presents a combination of experimental results and numerical simulations using a micro-mechanics-inspired damage model. Four specimen geometries and three hydrogen concentrations (including uncharged) were targeted, which allowed for the construction of a fracture locus that depended on the stress triaxiality and hydrogen concentration. The multi-physical finite element model includes hydrogen diffusion and damage on the basis of the complete Gurson model. Hydrogen-Assisted degradation was implemented through an acceleration of the void nucleation process, as supported by experimental observations. The damage parameters were determined through inverse analysis, and the numerical results were in good agreement with the experimental data. The presented model couples micro-mechanical with macro-mechanical results and makes it possible to evaluate the damage evolution during hydrogen-charged mechanical tests. In particular, the well-known ductility loss due to hydrogen was captured well in the form of embrittlement indices for the different geometries and hydrogen concentrations. The limitations of the damage model regarding the stress state are discussed in this paper. [ABSTRACT FROM AUTHOR]

Improved strength-ductility synergy is not uncommon among metallic materials with gradient structures of grains and twins. In this work, we report that the texture gradient innately created in Al-Mn strips by twin-roll casting is also capable of increasing the material's ductility without sacrificing its strength. Analyses based on crystal plasticity theory demonstrated that the underlying mechanism of this texture-gradient-induced ductility enhancement lies in the orientation-dependent slip and grain rotation, which generate backstress, alter the local stress triaxiality, and delay the fracture process. These results advocate the integration of texture gradient design into the fabrication of high-performance gradient materials. This work demonstrates for the first time that gradient texture could ductilize Al strips. It provides a new pathway — texture gradient design — to the fabrication of advanced structural materials. [ABSTRACT FROM AUTHOR]

Tensile tests were conducted for notched round-bar specimens to acquire the limit conditions of local failure, which is ductile failure after large local deformation for three types of steel, SGV480, SPV490 and SGV410, for nuclear containment structures. The notch deformation was monitored using a profile projector. The notch’s cross-section radius and the curvature radius of the notched profile were continuously measured by image analysis in the tensile test. From those measurements, the stress and strain at the notch’s cross-section center were determined by Bridgman’s approximate solution and the elastoplastic FEM analysis. The true stress-true strain curve for the elastoplastic FEM was identified a priori by an optimization program that searches for the good curve in the exponential form applicable to large strain regions. No cracks were observed at the notch bottom surface in all specimens until the final rupture. The failure at the notch’s cross-section center was detected from the inflection point of the load-displacement curve. The limit strain diagrams were compared with those of ASME Sec. VIII-2 and its conservatism were discussed. Further, small-size notched round-bar specimens were sampled from the weld joints of SGV480 and SPV490 to determine the limit strain diagrams and true stress-true strain curves of the base metal, HAZ, and weld metal. The limit strain diagrams at each material of the weld joints were as high as or higher than the base metal, except for the weld metal of SPV490. The authors discussed the optical micrographs for fracture surfaces of specimens, the fracture morphology of weld joints, and the modified expression of a limit failure stress index regarded as the stress indication of the limit strain diagram in the high-stress triaxiality region.

Estimates of physical and mechanical characteristics of materials at high strain rates play a key role in enhancing the accuracy of prediction of the stress–strain state of structures operating in extreme conditions. This article presents the results of a combined experimental–numerical study on the mechanical response of a thin-sheet rolled Ti-5Al-2.5Sn alloy to dynamic penetration. A specimen of a titanium alloy plate underwent punching with a hemispherical indenter at loading rates of 10, 5, 1, and 0.5 m/s. The evolution of the rear surface of specimens and crack configuration during deformation were observed by means of high-speed photography. Numerical simulations were performed to evaluate stress distribution in a titanium plate under specified loading conditions. To describe the constitutive behavior and fracture of the Ti-5Al-2.5Sn alloy at moderate strain rates, a physical-based viscoplastic material model and damage nucleation and growth relations were adopted in the computational model. The results of simulations confirm a biaxial stress state in the center of specimens prior to fracture initiation. The crack shapes and plate deflections obtained in the calculations are similar to those observed in experiments during dynamic punching.

It is significant to study the relationship between the stress triaxiality and the fracture behavior for analyzing the failure process of additive manufactured titanium alloy. This paper combined the tensile test of smooth round bar specimens and notched round bar specimens with the numerical simulation to obtain the stress triaxiality distribution and fracture strain in order to study fracture behavior of additive manufactured titanium under different stress triaxiality. Fracture analysis was proceeded by using scanning electronic microscope to analyze the correlation between the stress triaxiality and the fracture behavior. Results show that the fracture strain decreases while the stress triaxiality increases and the location of the crack initiation moves from the center to the edge of the minimum cross-section while the radius of the notch decrease.

Hydrogen embrittlement (HE) in API 5L X70 steel was investigated by testing notched and unnotched uniaxial tensile specimens and single-edge tension specimen, SE(T). Apparent hydrogen diffusivity (Dapp = 1.4 x 10-10 m2/s) and solubility (Sapp = 4.9 mol H/m3) were determined by electrochemical hydrogen permeation tests. Through mathematical fitting, it was possible to separate the strong traps present at the beginning of the first permeation curve (φ = 0.43 mol H/m3). Uniaxial tensile tests showed a loss of ductility of up to 33% in the hydrogenated condition. Fracture mechanics tests exhibited a toughness decrease of 14% after exposure to hydrogen. The high resistance to HE was presented suggesting that these microalloyed steels can solubilize hydrogen in the matrix with low segregation, reducing the impact on embrittlement. A mix of ductile and quasi-cleavage fracture was observed in the hydrogenated samples with an increased stress triaxiality.

A series of tensile tests were conducted for notched plate specimens whose shapes are similar to the pressure shell to clarify the local failure characteristics for the steel nuclear containment. The specimens included the full or partial-width notched plate specimens of 10 mm thickness, and full-width notched thick plate specimens of 34 mm thickness the same as the actual pressure shell. In the full-width notched plate specimens with a small curvature notch, the cracking occurred on the notch bottom, and the crack propagated and finally ruptured. The plate specimens with a large curvature notch failed in shear suddenly without notch bottom cracking. Those failure modes were very unlike notched round-bar specimens, in which failure always starts at the notch section center. In the case of partial-width notch plate specimens, the notch bottom cracking also occurred for a small curvature notch, and the notch section failure happened before the specimen’s rupture for a large curvature notch. The limit strain diagrams were 40% to 50% lower than those of the notched round-bar specimens. The limit failure stress indexes, which correspond to the stress indications for the limit strain diagrams, could be applied to the shear failure of notched plate specimens. The indexes of the notched plate specimens were approximately 10% lower than those of the round-bar specimens. The crack initiation points for small curvature notch specimens were concentrated in the range of stress triaxiality 0.6 and equivalent plastic strain 0.5 to 0.8. In the full-width notched thick plate specimens, notch bottom cracking occurred for all specimens, and the cracking conditions were almost the same as the full and partial notched plate specimens. However, the maximum nominal stress exceeded 2/3 of the design tensile strength, and it was concluded that local failure occurs at more than twice the design pressure.

Complete understanding of the local stress triaxiality and stress concentration is essential to ensuring structural safety of several structures. A combination of mechanical tests with numerical simulations can be used to obtain this information. One way to study stress triaxiality is by modifying the standard tensile test geometry (ASTM E8) with a notch. Based on previous results from the literature, five notches were chosen: 10, 5, 3, 2, and 1 mm. These geometries were tested, and the results were numerically reproduced using the Abaqus/Explicit 2020 software. The models used were a non-linear model with the Gurson-Tvergaard-Needleman damage model to reproduce the failure. The numerical analyses allowed the assessment of the von Mises stress and stress triaxiality near the notch to compare with the standard smooth specimen. Two instants were considered as crack propagation onset; the instant of the maximum von Mises stress in the element at the center of the specimen, where the failure process begins; and the moment of maximum stress in the true stress x true strain curve. For the von Mises stress analysis, the difference between the curves was small. The stress triaxiality is a better variable to visualize the influences of the notch. When the strain is equal to a 0.07 (instant of the maximum force for the standard specimens), for the smaller notches (1 and 2 mm), there is a region where the effective plastic strain is zero. Consequently, the stress triaxiality is larger in this region than in the center. For the crack propagation onset instant, the plastic strain occurs along the whole transversal section. In this instant, the maximum value of stress triaxiality occurs in the center for all specimens. These results demonstrate that the stress triaxiality changes as the strain increases, i.e., varies with time.

As a flexible sheet metal forming process, incremental sheet forming (ISF) has been extended to fabricate lightweight sheet metal components, and increasing the formability is one of the key topics. In the present work, a novel ISF process integrating an auxiliary sheet (ISF-AS) is proposed for the improvement in formability, and investigated by using commercially pure titanium (CP-Ti) as the target sheet (TS). The experimental results demonstrate that the fracture strain obtained by ISF-AS process is increased by 50.6% compared with conventional ISF (CISF), and the geometric accuracy by ISF-AS is less than that by CISF. To explore the deformation mechanism during ISF-AS process, an analytical model of stress triaxiality based on membrane analysis has been developed, which demonstrates that ISF-AS can further increase the hydrostatic compression stress and reduce the stress triaxiality of TS compared with CISF. The fracture morphologies indicate that the dimples by CISF and ISF-AS processes are both elongated along the circumferential direction, but there are more tiny dimples with uniform distribution on the fractured surface of ISF-AS. In addition, orange peels on the lower surface of the part can be obviously restricted by ISF-AS with the improved surface quality. [ABSTRACT FROM AUTHOR]

Tensile deformation behavior of the heat affected zone (HAZ) of Mod. 9Cr-1Mo weldment has been characterized. Different microstructural regions (coarse grain, fine grain and inter-critical) of the HAZ have been experimentally simulated using weld simulator. Flat tensile specimens, with desired microstructural region in the gage portion, were extracted from simulated bars prior and after post weld heat treatment (PWHT). The tensile tests have been carried out at ambient temperature. Parallelly, the local deformation characteristics of the HAZ have also been assessed using automated ball indentation tests to assess material specific parameters for constitutive model. Further, FEM analyses have been carried out to assess the effect of stress triaxiality on deformation behavior across the HAZ interfaces. The effect of triaxiality on the spread of plastic zone has been discussed. [ABSTRACT FROM AUTHOR]

To study the deformation and fracture mechanism of 6061 aluminum alloy extruded pipe after secondary heat treatment under different stress triaxiality, a Johnson–Cook failure model was developed. Through the FEM method and SEM, the fracture mechanism of different types of aluminum alloy tensile specimens was analyzed. The research results show that the Johnson–Cook failure model could better simulate the tensile deformation of 6061 aluminum alloy specimens of different types, the parameters of the Johnson–Cook failure model were finally obtained D1 = 0.29, D2 = 1.356, and D3 = −2.567. With the increase of the stress triaxiality, the fracture strain showed a decreasing trend as a whole, and the fracture mechanism changed from a shear type to a hole aggregation type. The stress triaxiality gradually decreased with the increase of the notch radius/angles of the aluminum alloy notch specimen, and the stress triaxiality at the center of the notch was higher than the stress triaxiality at the root of the notch. [ABSTRACT FROM AUTHOR]

In this paper, smooth and notched bar tensile tests of austenitic stainless steel 304 are performed, covering four different multi-axial stress states and six different strain rate conditions, to investigate the effect of the stress triaxiality and strain rate on fracture strain. Test data show that the measured true fracture strain tends to decrease with increasing stress triaxiality and strain rate. The test data are then quantified using the Johnson-Cook (J-C) fracture strain model incorporating combined effects of the stress triaxiality and strain rate. The determined J-C model can predict true fracture strain overall conservatively with the difference less than 20%. The conservatism in the strain-based acceptance criteria in ASME B&PV Code, Section III, Appendix FF is also discussed.

• 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]

Different dimensions of tensile test specimen can be used for qualification of welding procedure according to the existing standard. However, they are found to be dissimilar in tensile properties. In this study, the tensile properties of TIG welded 2219-T8 aluminum alloy joints were tested with different tensile specimen sizes. The welding residual stress releasing, specimen size effect, as well as fracture criteria were taken into account by using a sequential “welding - cutting - tensile” finite element simulating method. Results indicated that the degree of welding residual stress releasing decreased with the increasing of specimen width. For specimens with 250 mm width, over 80% of the residual stresses were kept. Tensile testing result showed that the tensile strength and elongation of joint decreased when the specimen width increased. The differences in tensile properties were proved to result from the size distinctions, rather than residual stress releasing, because the stress triaxialities were different in the specimens with different sizes. This phenomenon was precisely simulated by using the Johnson–Cook fracture criterion. Eventually, the constitutive equations of Johnson–Cook model were established based on the experimental tensile strengths to describe the tensile behaviors of 2219 aluminum alloy joints.

• 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]

[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]

Abstract A ductile fracture model is implemented to an elastoplastic constitutive model of steel material for large‐scale finite element analysis of steel frames. The stress modified critical strain model is extended to simulate the structural response after initiation of ductile fracture. The yield stress, Young's modulus, as well as the stress are reduced using the fracture variable. Positive definiteness of the material tangent stiffness matrix is always maintained, and the unbalanced loads are carried over to the succeeding step to analyze the responses in the range of degrading strength using an implicit finite element analysis. It is shown using a notched rod model and a double notched plate that the proposed model can simulate steep stiffness degradation due to strain localization after ductile fracture. Applicability to a large‐scale finite element analysis is investigated using a component frame of moment frame subjected to cyclic forced deformation.

The influence of temperature and strain rate on the deformation behavior of twin-roll casting AZ31 alloy has been examined as a function of stress state using notched and un-notched tensile specimens. Failure behavior during the physical tension was carried out using FEM simulations with different fracture criteria. Using a combined experimental-FEM investigation, the applicability of each fracture criterion was verified to serve the prediction for the crack initiation under multiaxial stress state. Results show that the critical fracture strain presents a clear exponential relationship with stress triaxiality and strain rate, and a linear relationship with temperature. Through the quantitative analysis of the relationship, a mathematical model can be well established. After comparison and verification, the fracture model can accurately predict the forming limit during the plastic deformation of twin-roll casted AZ31 magnesium alloy under complex stress state, and the classical Cockcroft & Latham criterion is the most suitable criterion for predicting the related crack initiation.

For more then half a centre just the same approach to the simulation of the ductile crack formation was developed independently by the scientific communities of foreign and native researchers. The importance at these studies drastically increased. A set of the characteristics, according to which it is recommendly to perform the detail comparison of the existing fracture models is developed. The examples of the analysis of a number of the most popular models by means of obtaining and study their analytical expressions regarding the conditions of the plane state are given. The generalized relations of the know models and a number of separate relations are obtained.

Titanium alloys has high fatigue resistance, high corrosion resistance, high temperature resistance, and other excellent properties, and have been widely used in deep-sea equipment and aviation industries. In this paper, the fracture mechanism and failure strain of TA31 titanium alloy, which has been widely used in deep-sea equipment, were studied experimentally and numerically in different stress states. Considering the pressure sensitivity, the Modified Johnson-Cook (MJC) model and the Bonora damage model were used to study the fracture behavior. In order to obtain the parameters of models, four types of specimens under different stress triaxiality were conducted, and a hybrid experimental-numerical approach was employed in this paper. Then, the coupled constitutive elastic–plastic-damage model was developed and implemented in ABAQUS explicit finite element analysis (FEA) code. Finally, to validate the suggested model, FEA simulation was carried out and compared with the experimental results. The comparison revealed that the Bonora model with constant parameters was not enough to predict the failure strain. The damage parameters were sensitive to the stress triaxiality. In addition, the fracture morphology was observed by scanning electron microscope (SEM), which revealed the micro-mechanism of failure for TA31 titanium alloy. It is concluded that a higher stress triaxiality and shear mechanism lead to lower plastic deformation, and will inhibit the void growth on the damage evolution.

The aim of the article is to examine the workability of sintered powder material of aluminum alloy (Alumix 321) through severe plastic deformations under the conditions of the equal channel angular rolling (ECAR) process. Accordingly, the stress–strain analysis of the ECAR was carried out through a computer simulation using the finite element method (FEM) by Deform 3D software. Additionally, the formability of the ALUMIX 321 was investigated using the diametrical compression (DC) test, which was measured and analyzed by digital image correlation and finite element simulation. The relationship between failure mode and stress state in the ECAR process and the DC test was quantified using stress triaxiality and Lode angle parameter. It is concluded that the sintered powder material during the ECAR processing failure by a shearing fracture because in the fracture location the stress conditions were close to the pure shear (η and θ ¯ ≈ 0). Moreover, the DC test revealed the potential role as the method of calibration of the fracture locus for stress conditions between the pure shear and the axial symmetry compression. [ABSTRACT FROM AUTHOR]

This paper provides a numerical assessment of the ductile fracture of the AA6101 and AISI 4340 alloys using the Lemaitre and Gurson models. The simulations were carried out to verify the evolution of the accumulated plastic strain at fracture, assuming the high range of the triaxiality ratio, applying monotonic tensile loads on smooth and notched cylindrical specimens. The numerical strategy was structured for the Lemaitre and Gurson models, from establishing a non-linear system of equations using an implicit integration algorithm and solving the non-linear equation system using the Newton-Raphson method. When assessing the numerical and experimental results, it was observed that the cumulative plastic strain at the fracture decreases with the increasing levels of the triaxiality ratio for both alloys and models. On the one hand, the Lemaitre model was more optimistic than the experimental results. On the other hand, Gurson's model proved to be more conservative in its prediction of ductile fracture. Regarding determining the fracture onset, in general, both models showed good predictive capacity. However, the numerical results for the aluminum alloy presented more in agreement with experimental data than for the AISI 4340 alloy. In the end, assuming the determination of the level of displacement at fracture, the Gurson's model has the best performance. In this sense, for a high level of triaxiality ratio, the Gurson porous material can be recommended to describe the mechanical behavior of the material at fracture. [ABSTRACT FROM AUTHOR]

Material characterization at moderate strain rates is an important factor for improving the adequacy and accuracy of analysis of structures operating under extreme conditions. In this paper, the deformation and fracture of Ti-5Al-2.5Sn alloys were studied utilizing the punch test at strain rates up to several hundred per second. Loading velocities from 0.0003 to 15 m/s were realized during the spherical body penetration through a thin titanium plate. To describe the plastic flow and fracture of the Ti-5Al-2.5Sn alloy at strain rates ranging from 0.001 to 103 s−1, a micromechanical damage model was coupled with a viscoplastic constitutive model based on the dislocation dynamics. Numerical simulations of the punch test at 15 and 2 m/s were carried out to validate used constitutive relations. It was verified that the simulated fracture shape and deflections were similar to experimental ones. It was found that dynamic punch test is suitable for validation of damage kinetics under complex stress states. [ABSTRACT FROM AUTHOR]