Stress Triaxiality Values Research Articles

Experimental and numerical investigation of the damage state of Ti-6Al-4V alloy sheet in the tensile test, hydraulic bulging, and hydroforming processes

There has not been any damage prediction using Johnson-Cook’s (JC) hardening and damage model in the hydraulic bulging (HB) and hydroforming (HF), which are the advanced manufacturing processes, of the Ti-6Al-4V (Ti64) alloy. In the presented study, the damage behavior of the Ti64 alloy sheet in the HB and HF processes was investigated both experimentally and numerically for the first time to address the existing research gap. In this context, firstly, tensile tests (TT) were carried out on samples with different stress triaxiality values at three different tensile speeds, and the fracture morphologies of the samples were examined to evaluate whether it was appropriate to use the JC hardening and damage model. Since the fracture surfaces generally exhibit a ductile fracture morphology and are affected by stress triaxiality and strain rate, it was determined that it would be appropriate to use the JC hardening model and damage criterion to predict the damage of the Ti64 alloy in finite element analysis (FEA). Then, JC model parameters were determined by fitting the stress-strain curve obtained from the FEA and experimental tensile tests. In the HB experiments, bulging height and thickness thinning were predicted by FEA with an accuracy of 97% and 96.85%, respectively. In the HF experiments, the experimental burst pressure, die inlet radius, and base radius were predicted correctly at a rate of 92.5%, 95.5%, and 97.8%, respectively. Also, the thickness of the sample showed good agreement with the FEA results. The fracture zones in each process exhibited good agreement with the experimental results. Thus, it has been demonstrated that the JC damage criterion can be successfully applied in FEA if the Ti64 titanium alloy is damaged in various processes.

Prediction of fretting fatigue lifetime of aluminium alloy treated with Friction Stir Processing using continuum damage mechanics

In the aviation industry, fretting fatigue represents a significantly hazardous form of fatigue failure, thus warranting substantial research attention. A key area of focus lies in enhancing the fretting fatigue resistance of aluminium alloys. This study investigates the feasibility of using Friction Stir Processing (FSP) to enhance fretting fatigue lifetime. After FSP, large-size inclusions in the Base Material (BM) are shattered, clustered inclusions are dispersed, and the preferred orientation of inclusions is disrupted. Consequently, areas of stress concentration, damage concentration and merging of hazardous zones become less, and the peak values of stress, stress triaxiality, and damage are decreased with 6–10 %. Compared to BM, the results show that the fretting fatigue lifetime of Friction Stir Processed (FSPed) material is increased by 50.1 %. Hence, FSP could emerges as a highly promising surface treatment technique for enhancing fretting fatigue performance.

The damage mechanism of the metastable β-titanium alloy Ti5321 with specific microtexture using synchrotron X-ray microtomography

In order to investigate damage mechanism of metastable β-titanium alloy Ti5321 with bimodal microstructure and specific microtexture, in situ tensile test was performed facilitating with synchrotron X-ray microtomography. The damage evolution of metastable β-titanium alloy Ti5321 can be predicted in three dimensions by proper micromechanics-based modelling methods, the Rice and Tracey model and Huang model. Through comparisons of the Rice and Tracey model and Huang model validated using the values of stress triaxiality calculated from experimental data and Finite Element (FE) simulations, the prediction accuracy of growth rates of voids can be enhanced. The results also show that the void growth is strongly related to microtexture of α plates. It is found that the growth path of largest voids is along α plates which have their c-axes with similar inclination angle of ∼45° from rolling direction (RD). Electron backscatter diffraction (EBSD) was also used to reveal the damage mechanism. This result is important enlightenment for study of damage mechanism of metastable β-titanium alloys.

A novel calibration procedure of Johnson-Cook damage model parameters for simulation of scratch abrasion

Numerical simulation of scratch abrasion requires the use of a material damage model to simulate material degradation and removal. From our previous research, the stress state during scratch was found to show negative values of stress triaxiality and Lode angle parameter. However, models are “classically” calibrated using experiments with positive triaxiality and Lode angle parameter. In this work, a novel “scratch-based” calibration procedure is developed to acquire Johnson-Cook (JC) damage model parameters, using experimental scratch tests showing negative stress triaxiality and Lode angle parameter. An optimization procedure is used to obtain the parameters by minimizing the error between the experimental and numerical wear rates. Fracture loci obtained from both calibration procedures vary significantly, thus estimating different material losses. This highlights the importance of the calibration process of the damage model. The validity of the exponential Johnson-Cook fracture locus is questioned since it cannot account for accurate predictions under the entire range of stress triaxiality values covered in the paper. Hence, it may not be feasible for any calibration approach to obtain a single set of JC model parameters to accurately estimate the material loss for different cases of abrasion.

A shear modified enhanced Gurson constitutive relation and implications for localization

The most widely used phenomenological constitutive relation to model ductile failure of structural metals at room temperature is based on the work of Gurson (1977) and has the advantage of having both a micromechanics basis and sufficient simplicity to enable complex engineering calculations to be carried out. The predictions of this framework have been most successful in circumstances where the stress triaxiality, the ratio of mean normal stress to Mises effective stress, is relatively large. For stress states with smaller values of stress triaxiality, the predictive capability has typically been much reduced. We present a shear modified enhanced Gurson constitutive relation that combines the shear modification of Nahshon and Hutchinson (2008) with the second porosity concept of Gologanu et al. (1994). This maintains both the connection with micromechanics and the computational simplicity. The predictive capability of the framework is illustrated by the good agreement with cell model calculations for localization of deformation over a wide range of stress states. Strain localization analyses with an initial porosity imperfection predict that for axisymmetric stress states with a superposed hydrostatic tension, the minimum critical strain for the onset of localization follows the onset of coalescence, as defined within the context of the constitutive model here, if the value of the stress triaxiality is sufficiently small. For an imposed shear stress state with a superposed hydrostatic tension, the minimum critical strain for the onset of localization is predicted to precede the onset of coalescence. A strong sensitivity of the critical strain for localization of deformation to the strain or stress range over which void nucleation occurs is also predicted, with void nucleation and localization of deformation essentially coinciding for sufficiently abrupt nucleation.

Prediction of magnesium alloy edge crack in edge-constraint rolling process by using a modified GTN model

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.

Numerical Analysis of the Damage Evolution of DP600 Steel Using Gurson–Tvergaard–Needleman Model

This research models the ductile fracture in DP600 steel sheets by using Gurson–Tvergaard–Needleman (GTN) damage model with experimentally obtained parameters. Uniaxial tensile tests are carried out to determine the deformation behavior of the material and obtain GTN model parameters. Further, SEM investigations on the fractured surface of the material display a dimpled surface, which indicates ductile fracture. Also, density measurements are carried out to define the critical and final volume fractions. A finite element model (FEM) of the tensile testing is developed. Then, the experimental parameters of the GTN model are verified by comparing load–displacement curves and porosity values for different zones. The results put forth that the experimental parameters can be used to model the deformation behavior of the DP 600 steel. Further, the growth of total void volume fraction increases exponentially, attributed to the increasing value of stress triaxiality. Also, the shift in the void volume fraction after the critical void volume fraction is explained with the void coalescence. Finally, the thickness of the sheet has a power‐law relationship and the porosity level of the material can be predicted for a known thickness value.

Experimental investigation of the effect of Lode angle on fracture initiation of steels

In this paper, the effect of Lode angle on the fracture strain of steels is discussed based on experimental evidence. To isolate the effect of the Lode angle, fracture strains corresponding to stress states with constant stress triaxiality but variable Lode angle parameters are obtained from both the literature and tests performed in this study of newly designed rectangular notched specimens. From investigations of currently available experimental data, it is demonstrated that the fracture strain is significantly affected by the Lode angle, and the influence can be modeled by an exponential function of the Lode angle parameter. This implies that the fracture locus is asymmetric with respect to the Lode angle parameter, whereas many existing fracture models assume it is symmetric. Moreover, the data indicate that the effect of the Lode angle increases with a decreasing value of stress triaxiality and is more pronounced for high strength steels. Having comprehensively evaluated the effect of the Lode angle, a new fracture model termed the Lode angle Modified Void Growth Model (LMVGM) is proposed, which combines the effects of stress triaxiality T, through the Void Growth Exponential Function (VGEF), and the Lode angle parameter ξ, using exponential functions for both. The LMVGM has only three free parameters, α, β and γ, and predicts fracture strain as εf = α∙exp(-β∙T + γ∙ξ), in which β is always positive while γ can be either positive or negative depending on the material. The proposed model is compared to other published models and validated against experimental data, showing good accuracy.

Fracture behavior of prestressed ductile target subjected to high velocity impact - Numerical study

Impact studies are performed to evaluate the ballistic performance of material subjected to a high strain rate. At high velocities, the projectile penetrates through the material which leads to a fracture of the target body. The fracture behavior depends upon the condition of the target body. It is anticipated that the fracture behavior should depend upon the prestress condition of the target. Considering the aforementioned concern, the thermo-elastic-plastic finite element model is formulated using MSC Marc Mentat to analyze the effect of the prestress condition of the target body on fracture behavior. A detailed comparison has been presented considering four different prestress states subjected to impact by a blunt-shaped projectile. The continuum damage mechanics using a stress triaxiality-based damage model is used to simulate damage evolution and fracture. It is found that the presence of prestress alters the overall fracture response of the structure subjected to high strain rate deformation. In the presence of tensile prestress, the material resists the accumulation of damage which is due to the lower values of stress triaxiality and equivalent plastic strain. It is also found that the presence of tensile prestress inside the target body increases the ballistic performance, whereas the presence of compressive prestress inside the target body degrades the performance.

The effect of material orientation on void growth

In this work, we have brought to light the effect of material orientation on void growth. For that purpose, we have performed finite element calculations using a cubic unit-cell model with a spherical void at its center and subjected to periodic boundary conditions. The behavior of the material is described with an elastic isotropic, plastic orthotropic constitutive model with yielding defined by Yld2004-18p criterion (Barlat et al., 2005). We have used the multi-point constraint subroutine developed by Dakshinamurthy et al. (2021) to enforce constant values of macroscopic stress triaxiality T and Lode parameter L in calculations that have been carried out for different stress states resulting from the combination of T=0.33, 1 and 2, with L=−1, 0 and 1 (axisymmetric tension, generalized shear and axisymmetric compression, respectively). Firstly, we have performed numerical simulations in which the loading directions are collinear with the orthotropy axes of the material, so that the principal directions of macroscopic stress and strain are parallel. Investigation of the cases for which the minor loading axis coincides either with the rolling, the transverse or the normal direction, has shown that the initially spherical void turns into an ellipsoid whose rate of growth and eccentricity depend on both stress state and material orientation. A key result is that for specific material orientations the anisotropy switches the effect of Lode parameter on void growth, reversing the trends obtained for isotropic von Mises materials. Secondly, we have carried out calculations using a novel strategy which consists of including angular misalignments within the range 0∘≤θ≤90∘, so that one loading direction is parallel to one of the symmetry axes of the material, and θ is the angle formed between the other two loading directions and the second and third orthotropy axes. In fact, to the authors’ knowledge, these are the first unit-cell calculations ever reported in which the material is modeled using a macroscopic anisotropic yield function with prescribed misalignment between loading and material axes and, at the same time, the macroscopic stress triaxiality and the Lode parameter are controlled to be constant during loading. The finite element calculations have shown that the misalignment between loading and material axes makes the void and the faces of the unit-cell to rotate and twist during loading. Moreover, the main contribution of this work is the identification of an intermediate value of the angle θ for which the growth rate of the void reaches an extreme value (minimum or maximum), so that the numerical results indicate that material orientation and angular misalignment can be strategically exploited to control void growth, and thus promote or delay localization and fracture of anisotropic metal products. The conclusions of this research have been shown to be valid for three different materials (aluminum alloys 2090-T3, 6111-T4 and 6013) and selected comparisons have also been performed using two additional yield criteria (CPB06ex2 and Yld2011-27p).

Damage evolution and failure in a titanium alloy: Revealed by 3D in situ X-ray tomography

In this work, damage/fracture development of Ti-6Al-4V alloy was analyzed with the help of in situ tensile test by synchrotron X-ray tomography. The result shows that during the whole damage/fracture procedure for Ti-6Al-4V alloy, the value of stress triaxiality (T) seems to maintain as a constant (T = 0.472–0.510) and to be adjacent with the critical value (Tc=0.49). This can result in the fracture of the alloy in the way of Mix mode (component induced by cleavage component and ductile component). With the help of X-CT scanning, voids evolution were clearly realized and characterized during damage development. On the basis of void tracking results, Rice-Tracey damage model and Huang damage model were adapted to depict and predict the voids growing behavior by calibrating the material parameter. Finally, the micro-mechanism of the mix damage mode was revealed, which can be attributed to local internal shear stress. The significant act of microstructure morphology on the component from mix damage mode was also determined and discussed.

On fracture locus of corroded steel plates with nominal fracture strain and corrosion morphology

In order to study the fracture ductility of corroded steel plates under tension load, a series of tensile tests and numerical calculations on corroded steel plates were conducted. The results showed that corrosion damage would increase the speed of equivalent plastic strain growing at critical point, and decrease the equivalent plastic strain to fracture, thus degrade the nominal strain at fracture. The weakened and uneven cross-section along longitudinal direction caused by corrosion damage led to the strain concentration and accelerated growth of equivalent plastic strain. The corrosion pits increased the values of stress triaxiality and Lode stress parameter, thus degenerated the equivalent plastic strain to fracture. Based on the above results, the fracture locus of corroded steel plates in the nominal strain to fracture-corroded morphology space was established.

Experimental and numerical investigation of the ductile fracture of structural steel at elevated temperatures

Fracture of steel at ambient temperature has been extensively studied. Such studies developed efficient micromechanical fracture models, which can be used to predict the behaviour of steel structures and components up to failure under extreme monotonic or cyclic loading, e.g. extreme deformations due to loss of column scenarios or large earthquakes. Considerable research has been also carried out on the high-temperature fracture of steel under creep conditions but its findings have not yet been applied to structural fire engineering practice, though ductile fracture has been reported as a common mode of failure for steel structural elements under fire conditions. This paper reports results of an experimental program carried out to investigate fracture of the S275 structural steel grade at temperatures ranging from 20 °C to 450 °C. A series of tests, including tensile and shear tests, are executed to extract information on fracture of structural steel for a wide range of stress triaxiality values. Moreover, numerical simulations of the tests are carried out using MSC Marc to get further insight for the role of stress triaxiality, Lode angle parameter, and temperature. Based on both the experimental and numerical results, a fracture model proposed in the literature is calibrated to predict fracture of structural steel for the temperature range 20 °C - 450 °C.

Investigation on void growth and coalescence in single crystal copper under high-strain-rate tensile loading by atomistic simulation

The failure mechanism of ductile metals is dominated by the nucleation, growth and coalescence of voids, and it is important to capture the evolution of voids on nanoscale. More than ten atomic models, each containing about 10 million atoms, are simulated under tensile loading at strain rate 5×108s−1. The influences of two parameters, the initial radius and the initial spacing of two voids, are also investigated in detail. The increment in void fraction increases linearly with strain at the last stage of void evolution, and the increment has little relation with initial radius and spacing of voids in this stage. The peak value of stress triaxiality increases first with the initial intervoid ligament distance until it reaches the critical point of void coalescence, and then decreases. It suggests that stress triaxiality may be an important indicator to characterize whether the void coalescence will occur. Dislocation analysis shows that the dislocation emissions from void surface is an important behavior in the initial stage of void evolution, but it has little effect on the void volume in the cases studied.

On mechanical response of Zircaloy-4 under a wider range of stress states: From uniaxial tension to uniaxial compression

The present work summarizes the experimental campaign and computational effort performed on Zircaloy-4 material commonly used in nuclear applications. The Zircaloy-4 exhibits a mild strength differential response under compression as compared with tension. Because of the well-known twinning-slip mechanism usually activated in compression after yielding in HCP metals, distortional hardening is required to define plastic flow throughout fracture. A general asymmetric yield function with the first invariant to the Cauchy stress tensor and the third invariant to the deviator stress tensor are considered to model the pressure-sensitive response and the Strength Differential (SD) effect in HCP polycrystal materials. The proposed macroscopic yield function provides results that are in good agreement with experiments. The onset of fracture and subsequent crack propagation in upsetting tests is also investigated. The results show that failure is not only controlled by material properties but also by friction between contact surfaces of specimens and experimental setup. In addition, the concept of a fixed cutoff value for negative stress triaxiality (η=-1/3) condition is analyzed. It turns out that the specimen fails differently of what is observed experimentally when a constant cutoff value is set. However, a cutoff stress triaxiality function, yields a more realistic fracture pattern consistent with tests.

Spherical indentation creep characteristics and local deformation analysis of 310S stainless steel

To estimate the creep properties of 310S stainless steel reasonably, its spherical indentation creep characteristics and local deformation behaviour during vacuum indentation creep tests are analysed in this study. The influence of creep load, temperature, and indenter diameter on the indentation depth – time curve is discussed. The results indicate that the spherical indentation depth rate decelerates before becoming approximately constant. With an increase in creep load and temperature, there is an apparent increase in the creep depth rate. Along with the increase of creep deformation, the hardness value increases. Compression deformation can be observed at the specimen center under the indenter. With an increase in the distance from the specimen centre, the value of stress triaxiality on the upper surface of the specimen increases gradually. Unlike that at the specimen centre, a pile-up phenomenon along with tensile deformation feature is observed at the contact boundary. When the indentation creep depth is small, changes in the microstructure of the specimen are not obvious. Overall, the local deformation has an apparent influence within a distance of approximately twice the indenter radius from the contact boundary.

Micromechanical modeling of the effect of stress triaxiality on the strain to failure of ductile cast iron

This paper presents modeling of the tensile and failure behavior of different nodular cast iron microstructures under variable stress triaxialities. The model is based on a Representative Volume Element (RVE) approach, which reproduces periodic stochastic distributions of nodules within a 3-D cell. Three cast iron matrices, from fully ferritic to fully pearlitic, are considered as representing the various nodular cast iron classes in relation to strength and ductility. Ductile damage and shear damage models are used for ferrite and pearlite, respectively. Several values of stress triaxiality are applied within the RVE. It is found that numerical results support experimental findings in relation to the local strain distribution and damage initiation and accumulation, reproducing macroscopic tensile responses with good approximation. As highlighted by experiments, triaxiality is found to have a strong effect on material ductility and void volume fraction growth.

Evaluations of residual stresses in repair welding of Ni-based IN939 superalloy

The residual stresses (RSs) generated from partial penetration repair welding of a specimen extracted from the 4th stage vane of a gas turbine replace studied. The RSs are maximum in the heat-affected zone, beneath the weld along the weld center at the specimen mid-section. The RS field tends to exhibit over a large volume beneath the weld bead where severe restraint conditions exist in the repair welding. The stress triaxiality field was presented as an assessment tool to find the critical areas of welding RSs. The maximum value of stress triaxiality occurs beneath the weld bead in somewhere different from maximum residual stress locations. This indicates the role of a through-thickness component of RSs in the integrity of repair welds.

On the ductile rupture of 13% Cr-4% Ni martensitic stainless steels

Ductile rupture of 13% Cr-4% Ni martensitic stainless steels was examined during tension testing in order to better understand the role of second phase particles in these materials. SEM fracture surface examinations revealed that micro-voids were initiated from inclusions, and these inclusions were characterized from metallographic polished sections. Effect of stress triaxiality on the growth and impingement of the micro-voids were examined using a modified model of Rice and Tracey. In the case of the cast and wrought versions, the true fracture strains predicted for the measured stress triaxiality values were in a good agreement with the measured ones. For the weld metals, only the contribution of the micro-void growth cannot explain the experimental results, and it shows that the matrix properties such as austenite content and hardness of martensite play a significant contribution. The magnitude of the final stress triaxiality ratio measured after rupture was also related to the inclusion characteristics.

A quantitative analysis of the transition of fracture mechanisms of Ti6Al4V over a wide range of stress triaxiality and strain rate

The material fracture behavior and associated mechanism is known to be affected by the stress state and strain rate. Using a recently developed rectangular hat-shaped specimen, the fracture behavior of Ti6Al4V was investigated with a stress triaxiality varying from −0.31 to 0.50 at strain rates ranging from quasi-static to 104 /s. The fracture mechanisms of Ti6Al4V under these conditions were studied at micro-scale through observations of cross-sectional microstructure and quantitative analysis of fracture surface morphology. It was found that λ, a parameter defining the percentage of equiaxed dimples on the fracture surface, shows a close correlation with the observed fracture mechanism. Therefore, a λ based criterion based has been introduced in this work to quantitatively describe the transition of fracture mechanisms. It was observed that the embrittlement of Ti6Al4V was promoted by a higher strain rate or a larger positive stress triaxiality, as expected. However, the stress triaxiality appeared to play a more dominant role. At sufficiently high negative or positive stress triaxiality values, the effect of strain rate on fracture mechanism became negligible.