Low Stress Triaxiality Research Articles

Atomistic analysis of nano He bubble evolution in Al: considering stress triaxiality and Lode parameter effects

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.

Measurement of strengths and fracture initiation strains of weld metal and HAZ in steel joints using miniature coupons

This paper investigates the strengths (fy, fu) and fracture initiation strains (εf) of the weld and heat affected zone (HAZ) of welded joints. Miniature coupons were extracted and tested using a custom-built jig. The weld metal was generally isotropic with the highest and lowest εf in the longitudinal and transverse directions, respectively. The HAZ had higher fy and fu than the base metal but smaller εf in the transverse direction under low stress triaxiality, indicating possible fracture through the weld and HAZ when loaded transversely. The strengths of the weld metal and HAZ can be approximated to within 7%-10% using empirical hardness-strength correlation functions.

Ductile fracture prediction of 7A62 high-strength aluminum alloy under a wide range of stress states

The modified Gurson-Tvergaard-Needleman (GTN) model is employed to predict the ductile fracture of 7A62 high-strength aluminum alloy under a wide range of stress states. Mechanical tests were conducted on specimens with different stress states within the range of −0.33 to 1.35 stress triaxiality, including tension, notched tension, compression, and shear. The results indicate that at high stress triaxialities (0.8 ∼ 1.35), the fracture mechanism is intergranular ductile fracture. Under moderate stress triaxialities (0.33 ∼ 0.8), the fracture mechanism involves a combination of intergranular ductile fracture, void growth, and shear fracture. At low and negative stress triaxialities (−0.33 ∼ 0.33), plastic instability occurs due to uneven stress distribution, leading to shear fracture. Fractography analysis reveals that the fractures occurring under tensile stress are associated with enriched Mn particles of approximately 200 nm. The modified GTN model accurately predicts the load-displacement response, and the fracture paths under various stress states exhibit good consistency with experimental results. This study provides reference for failure prediction in the engineering application of high-strength aluminum alloys.

Calibration of micromechanical fracture model parameters for Q355B steel and ER50–6 welds

To calibrate the micromechanical fracture model of Q355B steel and ER50–6 welds, 46 specimens of five types were subjected to monotonic tensile tests. The material constitutive model employed for finite element analysis (FEA) is determined by the Swift-Voce model, which leads to FEA results that closely align with the experimental test results. The parameters of the void growth model (VGM) and the stress-weighted damage model (SWDM) were calibrated, and the VUSDFLD user subroutine was written based on the two models to predict the fracture of each specimen. The prediction results show that the VGM model has good accuracy in the case of high-stress triaxiality. However, the prediction error of the VGM model is relatively large for shear specimens with low-stress triaxiality and significant changes in the Lode angle parameters. In contrast, the SWDM model with Lode angle parameters can predict the fracture of specimens under different stress states more accurately.

Characterization and Simulation of Shear-Induced Damage in Selective-Laser-Sintered Polyamide 12.

This paper presents the characterisation of selective-laser-sintered (SLS) samples of polyamide 12 (PA12) under shear loading. PA12 is a semi-crystalline thermoplastic and is used in various industries. Its behaviour under shear stress, which is particularly important for product reliability, has not yet been sufficiently investigated. This research focuses on understanding the material and damage behaviour of PA12 under shear-induced stress conditions. The study included quasi-static experiments and numerical simulations. Samples were prepared via SLS and tested according to ASTM standards. Digital image correlation (DIC) was used for precise deformation measurements. The Chaboche material model was used for the viscoplastic behaviour in the numerical simulations. Due to existing material discontinuities in the form of voids, the material model was coupled with the Gurson-Tvergaard-Needleman (GTN) damage model. A modified approach of the GTN model was used to account for low stress triaxiality under shear loading. These models were implemented in MATLAB and integrated into Abaqus via a User Material (UMAT) subroutine. The results of the experiments and simulations showed a high degree of accuracy. An important finding was the significant influence of the shear factor kw on the damage behaviour, especially during failure. This factor proved to be essential for the accurate prediction of material behaviour under shear-induced stress conditions. The integration of the modified GTN model with the Chaboche material model in UMAT enables an accurate prediction of the material and damage behaviour and thus makes an important contribution to the understanding of the mechanical material behaviour of SLS PA12 specimens.

Investigation of ductile damage in dual phase steel during tensile deformation by in situ X-ray computed tomography

In situ synchrotron radiation X-ray computed tomography (CT) is used to understand the void nucleation and growth behaviour of dual phase (DP) steel, DP800, during uniaxial tensile deformation. The voids were identified post mortem as having nucleated primarily in the (41 vol%) martensite phase. The behaviour of individual voids was found to be broadly in line with a Rice and Tracey style growth model (their volume increasing by a factor of 10), while the mean void size was broadly in line with a model that included the continuous nucleation of new voids, as well as the growth of existing voids, throughout straining. Voids tended to elongate during uniaxial (low stress triaxiality) straining, but then to dilate more isotropically as necking led to increased triaxiality. One large pre-existing void was found to elongate quicky at first, but then for growth to slow, presumably because it was not located in the highest triaxial stress (necked) region. Perhaps surprisingly the average size of the void population grows only slowly (by a factor of 2) during straining; this is because while the size of each void grows, new small voids are always being nucleated. Finally, the changes of stress triaxiality and shear stress state during tensile deformation of the square cross-section smooth tensile specimen are investigated via finite element modelling, to qualitatively assess the impact of sample geometry on void nucleation behaviour and fracture strain in the current study.

Investigation into the fracture behavior of ZK60 Mg alloy rolling sheet under different stress triaxiality

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.

Effects of Stress State, Crack—γ/γ′ Phase Interface Relative Locations and Orientations on the Deformation and Crack Propagation Behaviors of the Ni-Based Superalloy—A Molecular Dynamics Study

In this study, we systematically investigate the influence of stress states, relative locations, and orientations of crack—γ/γ′ phase interfaces on the deformation and crack propagation behaviors of the Ni-based superalloy through molecular dynamics simulations. The stress state with high stress triaxiality will impede the plastic deformation process of the system, thereby promoting brittle crack propagation within the system. But the stress state of low stress triaxiality results in obvious plastic deformation and plastic crack propagation behaviors of the system. The deformation system with cracks located in both the γ and γ′ phase exhibits the slowest growth rate, regardless of applied stress states. Additionally, the deformation process demonstrates prominent plastic behavior. For the deformation system with cracks perpendicular to the γ/γ′ phase interface, the γ/γ′ phase interface will hinder the crack propagation. Our research provides interesting observations on deformation and crack propagation behaviors at an atomic level and at a nano-scale which are important for understanding deformation and fracture behaviors at a macroscopic scale for the Ni-based superalloy.

Effect of incorporating Lode angle into fracture criterion on predicting ballistic resistance of 6061-T651 aluminum alloy plates with different thicknesses struck by blunt projectiles

According to existing research, in addition to the second deviatoric stress invariant, Lode angle parameter (hereinafter abbreviated as Lode angle), which is related to the third deviatoric stress invariant, is also required to be taken into account when studying plastic flow and failure of metal materials. In order to study the effect of incorporating Lode angle into fracture criterion on predicting ballistic resistance of 6061-T651 aluminum alloy plates, a one-stage gas gun system was used to conduct ballistic tests of 6061-T651 aluminum alloy plates with different thicknesses when struck by the blunt projectile with a diameter of 12.66 mm and a mass of 34.0 g. Meanwhile, Abaqus/Explicit finite element software with user-defined material subroutine (VUMAT) was used to establish corresponding finite element models. Under the same constitutive model, numerical simulations were carried out by using Lode independent MJC fracture criterion and Lode dependent WMJC fracture criterion. It is found that when using MJC fracture criterion, not only the ductility of material is overestimated in low stress triaxiality state, resulting in significantly higher predicted ballistic limits; but also the predicted material fracture strain in high stress triaxiality state is negative, sometimes causing irrational predictions. Therefore, some modifications to MJC fracture criterion are needed to reasonably predict the impact process. By contrast, the predicted results of Lode dependent WMJC fracture criterion are more consistent with experiments. Besides, as the thickness of the target increases, the ballistic limit shows an “S” shaped growth trend. Overall, for ballistic tests of targets with different thicknesses, WMJC criterion has a better predictive effect than MJC criterion, indicating the importance of incorporating Lode angle into fracture criteria.

A Gurson-type layer model for ductile porous solids containing ellipsoidal voids with isotropic and kinematic hardening

The aim of this work is to extend Gurson’s model for plastic porous materials by considering the effects of void shape and heterogeneous hardening, which are both important for cyclic ductile failure at low stress triaxiality. The derivation is based on a sequential limit-analysis of an ellipsoidal cell made of a rigid-hardenable material and containing an ellipsoidal confocal cavity. The heterogeneous distribution of hardening is accounted for by considering a finite number of ellipsoidal layers in which the parameters related to isotropic and kinematic hardening are considered as homogeneous. Several approximations of the macroscopic plastic dissipation lead to an approximate yield criterion based on Madou and Leblond (2012a) solution. Evolution equations of the internal parameters (hardening and geometric parameters) are then derived to complement the yield criterion. Finally, the yield locus is assessed using numerical limit-analysis in a typical case of an ellipsoidal cavity with several distributions of pre-hardening.

Ductile fracture behavior of in situ TiB2 particle reinforced 7075 aluminum matrix composite in various stress states

The fracture behavior of an in situ TiB2 particle reinforced 7075 aluminum matrix composite in various stress states was investigated by mechanical tests, microscopic characterization, and numerical simulations. Four sets of tensile specimens, one group of shear specimens, and one group of compression specimens were designed, and mechanical experiments were conducted on these six groups of specimens. The strain distributions of the six groups of specimens during deformation were investigated by in situ strain testing and finite element simulation. The fracture morphology of the specimens was characterized to analyze the damage mechanism in different stress states. It was found that the fracture mechanism of the material is mainly interfacial debonding and particle fracture, manifested as tensile fracture under high stress triaxiality and shear fracture under low stress triaxiality. For the tensile fracture, the nucleated voids grew with the maximum principal stress; for the shear fracture, they showed significant shape change with the maximum shear stress but little volume change. Based on the fracture mechanisms uncovered by the experiments, a modified ductile fracture criterion, considering the influence of both the maximum principal stress and maximum shear stress, was developed for the composite. Comparison with the modified Mohr–Coulomb, Lou–Yoon–Huh, Hu, and Mu models shows that the proposed model can predict the ductile fracture behavior of the aluminum matrix composites more accurately.

A polycrystalline damage model applied to an anisotropic aluminum alloy 2198 under non-proportional load path changes

A ductile damage model, which fully couples classical void growth at high stress triaxiality and Coulomb ductile model at the slip system scale at low stress triaxiality, was applied for the sheet specimens in an anisotropic aluminum alloy under non-proportional load path changes. The Coulomb model combines the resolved normal and shear stresses for each slip plane and directions. A Reduced Texture Methodology (RTM) was used to provide computational efficiency and this approach involved a significant reduction in the number of representative crystallographic orientations. The 12-grain model using 12 crystallographic orientations was validated for non-proportional load path change experiments. The model was calibrated in plasticity using single element calculations under proportional tension, shear and non-proportional ‘shear to tension’ (ST) loadings. Next, the damage parameters were calibrated against the proportional loading shear and tension experimental results using 3D mesh full-size calculations. The calibrated model successfully predicted non-proportional failure. Locally, the damage indicator maxima coincided with the damage location where the damage features were observed via experimental 3D imaging (computed tomography).

Modified plasticity constitutive model for extruded aluminum alloys

Aluminum alloys have been increasingly used in a wide range of construction applications, especially in important public buildings. A plasticity constitutive model that can accurately describe the elastoplastic behavior of aluminum alloys under complicated stress states is of great importance in precisely simulating aluminum alloy structures under complicated working conditions. Also, a precise plasticity model serves as the foundation for studying the ductile fracture of metals, and is therefore crucial for structural analysis involving large deformation, such as progressive collapse analysis. The classic J2 plasticity model based on the von Mises yield criterion is the most commonly utilized model for ductile metal materials. However, it ignores the effect of stress state on metal plasticity behavior, making it inapplicable to aluminum alloy materials under various complicated stress states. This study experimentally demonstrated that stress triaxiality and Lode angle have a noticeable effect on the plasticity behavior of extruded aluminum alloys (6061-T6, 6082-T6, and 6063-T5). Accordingly, a plasticity constitutive model suitable for extruded aluminum alloys under complicated stress states was proposed and validated, including a full-range hardening law and a new yield criterion. In addition, the parameter calibration method for this new model was detailed. Finally, comparisons between the experimental and numerical results proved the high accuracy of the proposed model in predicting the actual response of a structural extruded aluminum alloy under complicated stress states. Compared with previous studies, the proposed model can not only consider the effects of stress triaxiality and Lode angle, but it can also provide a more reasonable description of yield surface under considerably high or low stress triaxiality.

Study of the slant fracture in solid and hollow cylinders: Experimental analysis and numerical prediction

This paper is devoted to the numerical and experimental study of ductile fracture in bulk metal forming of the 2017A-T4 aluminum alloy. From an experimental standpoint, the ductile fracture of the 2017A-T4 aluminum alloy is investigated under compressive load. Two cross-sections of solid and hollow specimens are considered. The mechanical behavior and the microstructure of the 2017A-T4 aluminum alloy were characterized. It is found that the well-known barrel shape is obtained when a compressive load is applied. Analyses of fracture topographies show a ductile fracture with dimples under tension and coexistence of ductile fracture with dimples and slant under compression. The classical physically-based Gurson-Tvergaard-Needleman (GTN) model and its extension to incorporate shear mechanisms to predict failure at low-stress triaxiality are considered. These two models have been extended to take into account the thermal heating effect induced by the mechanical dissipation within the material during the metal forming process. The two models have been implemented into the finite element code Abaqus/Explicit using a Vectorized User MATerial (VUMAT) subroutine. Numerical simulations of the forging process made for hollow and solid cylindrical specimens show good agreement with experimental results. In contrast with the GTN model, the modified GTN model incorporating shear mechanisms can capture the final material failure.

Simulation of edge cracking using shear GTN damage model during hot plate rolling of magnesium alloys

Edge cracks are a more prominent problem during the rolling process of magnesium alloy sheets. The hexagonal structure of magnesium alloys and the product defects caused by the second phase impurities mixed in the sheets are the main causes of edge cracking. Conventional hot-rolled edge cracking simulations can only characterize the edge damage of the sheets numerically, however, the actual crack morphology is ignored. In this paper, the Gurson-Tvergaard-Needleman (GTN) damage model coupled with a continuous medium shear damage model was developed for improving the applicability of the model at low-stress triaxiality. Powell’s “Dogleg” method was used in the numerical solution of the damage model instead of the traditional Newton-Raphson method and the Vumat subroutine was written for the finite element simulation by the stress return algorithm. The damage model parameters were calibrated by a shear specimen. The results showed a good agreement between the simulated crack morphology and the experiment.

Use of modified Madou–Leblond model to predict crack initiation in low alloy steel specimens with different stress states

This paper aims to predict the ductile fracture in low alloy steel specimens with pure tension, pure shear and combined shear–tension type loading using modified Madou–Leblond (MML) porous plasticity model, proposed by the present authors in a recent work. This model includes the effect of localised mode of plastic deformation in a narrow band through the definition of localised porosity level under shear dominated loading conditions. The damage parameter includes contributions due to void growth process under high stress triaxiality level as well as that due to shear localisation process under low stress triaxiality conditions. Experiments have been performed on the round tensile specimen, flat type shear specimen and combined shear–tension specimen. The numerical simulations results obtained using MML model has been compared with those of experiments. It has been shown that the MML model performs well in the prediction of the material softening behaviour and critical fracture location along with the fracture profile in all three types of specimens.

Deformation mechanisms and fracture in tension under cyclic bending plus compression, single point and double-sided incremental sheet forming processes

This study investigates the deformation and fracture mechanisms of two testing methods, tension under cyclic bending (TCB) and tension under cyclic bending plus compression (TCBC) and their relationship to single point (SPIF) and double-sided (DSIF) incremental sheet forming processes. Experimental tests were carried out by using a bespoke TCBC test rig and a DSIF machine with grade 1 pure Ti samples. The results show the elongation-to-fracture has a high relevance to the bending depth and compression, which leads to detailed investigation to the stress and strain evolutions in the local bending region using finite element (FE) method. A new Gurson-Tvergaard-Needleman (GTN) model is proposed with a modified shear damage mechanism utilising experimental fracture strain loci to calibrate the Lode angle effect under low stress triaxiality. It is found the bending and reverse-bending stages correspond to different stress states and significantly affect the fracture occurrence in TCB, TCBC and SPIF, DSIF processes. For the first time, the stress paths in the plane of stress triaxiality and Lode parameter are used to reveal the transition of deformation modes from equi-biaxial to plane strain tension in SPIF and DSIF, as compared to the plane stress tension in TCB and TCBC. Using the new GTN model, the simulation gives accurate predictions to the elongation-to-fracture in TCB and TCBC, and the fracture depth in SPIF and DSIF with an error of less than 8% in comparison to the experimental results. Although there is a distinction between the equi-biaxial and uniaxial tension deformations, the study concludes that the TCB and TCBC tests provide an insight into the formability improvement and represent intrinsic deformation mechanisms of SPIF and DSIF processes, an ongoing research question, which has drawn considerable attention in recent years.

Fracture prediction of AA6061-T6 sheet in bending process using Gurson–Tvergaard–Needleman model

Fracture is one of the limiting factors of sheet metal forming processes. For this reason, finite element simulations are widely used for providing suitable forming approaches. However, the success of these approaches depends on the correct modeling of fracture in the simulations. In this paper, the fracture behavior of the Aluminum 6061-T6 sheet in the U-bending process is investigated by applying the Gurson–Tvergaard–Needleman model. For this purpose, the Gurson–Tvergaard–Needleman model is defined in the ABAQUS software by means of a proper subroutine. The Gurson–Tvergaard–Needleman model is also modified to take into account the anisotropy effect on the yield surface and the damage evolution due to shear stresses. Then, the proposed models are calibrated using the inverse analysis method based on tension tests with different stress states. The deformation mechanics analysis reveals that considering the normalized Lode angle parameter in the damage function increases the accuracy of fracture prediction, especially in low-stress triaxiality. Comparing the predicted fracture displacements with the experimental value in the U-bending process shows that the modified Gurson–Tvergaard–Needleman model calibrated by the uniaxial tension and in-plane shear tension tests can predict the onset of fracture with acceptable accuracy in the bending process while the original Gurson–Tvergaard–Needleman should be calibrated by a test with stress state close to that in the bending area to have such a result.

Ductile Fracture Investigation of High-Strength Steel SM570 under Low Stress Triaxiality

A comprehensive understanding of the fracture behavior of high-strength steel is of great significance for its structural application. In this study, experiments were conducted to investigate the ductile fracture mechanism of high-strength steel SM570, one type of conventional structural steel. Two types of shear specimens, one with symmetrical notches and the other with asymmetrical notches, were designed, and by changing the notch angles, a wide range of low-stress triaxiality could be obtained. Based on the discussion of the experimental results, crack initiation, and its propagation up to fracture failure were clarified. Compared with the fracture behavior of SM490 (one type of conventional normal-strength structural steel), the SM570 with higher yield stress has relatively severe stress concentration, the crack initiation appears earlier, and the brittle fracture is more likely to occur. Numerical simulations based on the finite element method (FEM) were performed with ABAQUS to obtain the stress triaxialities and equivalent plastic strain of the symmetrical and asymmetrical specimens. A modified N-VG model with a fracture criterion at a negative and low-stress triaxiality range from −0.6 to 1/3 was proposed for evaluating the fracture behavior of steel SM570.

Shear Fracture Criterion of Advanced High-Strength Steel Based on Stress Triaxiality and Equivalent Strain

Abstract Advanced high-strength steel (AHSS) is increasingly used in the automotive industry due to its higher strength and lower weight. The traditional forming limit criterion cannot accurately predict the unique shear fracture of AHSS, so great efforts have been made to develop failure criteria that can predict shear fracture. In this paper, a series of tensile and shear tests for four steel sheets of AHSS are designed, the stress triaxiality and equivalent strain to fracture are solved, and the correlation between them and the performance parameters of steel sheets K and n is studied. In order to study the relationship between stress triaxiality and equivalent strain to fracture in the range of low-stress triaxiality, the Hill'48 orthotropic model and modified Mohr–Coulomb (MMC) fracture model were used to establish tensile and shear fracture models of four dual-phase sheets of steel, simulating and studying the plastic fracture of AHSS. Solving the relevant parameters enriches the stress triaxiality of the four steel types, establishes the relationship between the stress triaxiality and the equivalent strain to fracture, and verifies its correctness through tensile and bending tests and simulations. The results show MMC can accurately predict the fracture of these four dual-phase steels, and the quantitative relationship between stress triaxiality and equivalent strain to fracture of the four dual-phase steels in the low-stress triaxiality range 0–0.3 is similar, which can be established and expressed by the performance parameters of each steel type.