Negative Stress Triaxiality Research Articles

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.

Fracture prediction of high-strength steel sheet during in-plane compression-shear forming under negative stress triaxiality

Fracture prediction of high-strength steel sheet during in-plane compression-shear forming under negative stress triaxiality

New insights into the anisotropic ductility of additively manufactured Inconel 718

Anisotropic ductility in additively manufactured (AM) alloys, namely better ductility along the building direction (BD) has been extensively studied and traditionally attributed to the crystallographic texture. However, recent studies have shown significant ductility anisotropy in weakly or non-textured AM alloys, indicating that other factors may also play critical roles. To explore this, AM Inconel 718 with weak crystallographic texture was selected as the model material, and the in-situ high-energy X-ray diffraction tests together with multiscale microstructural characterization techniques were performed to explore the deformation micromechanisms. The results of this study, for the first time, revealed that the better ductility in the vertical specimen (loading parallel to BD) was partially due to the negative stress triaxiality factor (TF) of the {220} grains during plastic deformation, which results in the shrinkage or even healing of the microvoids. Furthermore, the δ-phase alignment in conjunction with grain boundary orientation were also proved to have a pronounced impact on the anisotropic ductility of AM alloys. On the other hand, though in the overall weak-textured microstructure, the proportion of 〈101〉 grains were marginally over other grains. Thus, the positive effect of {220} grains on ductility was stronger than the negative effect of {200} and {311} grains, contributing to the excellent failure elongation exceeding 12% for both samples. The findings of this study shed new light on the mechanisms underlying the anisotropic ductility of AM alloys and provide insight into strategies for enhancing their performance.

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 unified ductile fracture criterion suitable for sheet and bulk metals considering multiple void deformation modes

In engineering practice, it is critical to accurately forecast the fracture initiation of ductile metals. Currently, various uncoupled ductile fracture criteria (DFCs) have been constructed to forecast the ductile fracture initiation of sheet metals, and several uncoupled DFCs have been presented to predict the fracture incipience of bulk metals from high to negative stress triaxiality (HNST). However, there is still lack a unified uncoupled DFC that is capable of predicting the fracture initiation of both sheet and bulk metals, efficiently. To deal with the problem and fill the gap above, a simple general uncoupled DFC is proposed in this paper via taking into account multiple void deformation modes and the effects of accelerated void growth and coalescence under high stress triaxiality based on the theoretical analyses of void nucleation, growth and coalescence. Then, the effects of material parameters on the asymmetry of fracture loci, the predictive ability of the new model for the coupling effect of the Lode parameter and stress triaxiality on the ductility of different materials, the number of material constants, and the flexibility of the new model are investigated to fully comprehend the new DFC. In addition, the experimental results of four different metal materials are utilized to verify the effectiveness of the new DFC, and comparative studies with two representative uncoupled DFCs are conducted using the four different metal materials to demonstrate the advantage of the new DFC. Research findings show that the new DFC can accurately forecast both the fracture initiation of sheet metals from equi-biaxial tension (EBT) to shear and bulk metals from HNST, superior to the other uncoupled DFCs. Due to the high prediction accuracy and flexibility of the proposed new DFC, its use in engineering applications and integration with finite element analysis software is recommended.

Modeling ductile fracture in third stress invariant sensitive materials: Application to Al 2024-T351

Triaxiality alone is not sufficient to account for the role of stress state on ductility in materials that exhibit shear effects on fracture strain. For these materials, it has been proposed that ductility also depends on the third invariant of the stress deviator. Recently, Bonora and Testa [N. Bonora, G. Testa, Plasticity damage self-consistent model incorporating stress triaxiality and shear-controlled fracture mechanisms – model formulation, Eng. Frac. Mech. 271, 108634 (2022).] derived a plasticity damage self-consistent (PDSC) model considering damage contributions due to intervoid necking, shearing, and sheeting for an arbitrary stress state. In this work, the PDSC model has been applied to Al 2024-T351 considering the experimental results reported in the literature obtained on several different sample geometries and material batches. Specifically, the model was verified by predicting the load-displacement conditions for which fracture occurs in 9 specimen geometries loaded in tension, compression, and torsion over a wide range of triaxiality, from positive to negative, and of the third stress invariant related parameter. The ability of the model to predict the transition from cup-cone to slant fracture for different stress states is shown. Finally, the simulation of non-proportional bi-axial compression test confirmed the possibility for ductile fracture to occur at negative stress triaxiality lower than −0.5 as long as the deformation state is shear dominated.

めっき鋼板の端面耐食性を向上させる切断技術の開発

The Keisha-Tanmen (KT) method was developed to improve the corrosion resistance of the cut-edge surface of Zn-alloy-coated steel sheets. The dies used in the KT method have a triangular convex blade. Using the upper and lower blades, a Zn-alloy-coated steel sheet was pinched and broken off. The cut-edge surface resulting from the KT method consists of three areas: roll over, inclined plane, and fracture surface. After using the KT method, a coating could be spread effectively over the inclined plane, and the fracture surface area was decreased compared with that obtained after a conventional cutting operation, namely, shearing. The cutting behavior in the KT method was simulated by the finite element method (FEM). The reason behind the decreased fracture surface area was that the negative stress triaxiality around blade edges prevented crack generation and delayed breakage. The rate of red rust formation on the cut-edge surface after the KT method was approximately 20 % and that after shearing was approximately 60-80 % after 10-200 days of atmospheric corrosion tests. The KT method was confirmed to yield excellent corrosion resistance on the cut-edge surface of a Zn-alloy-coated steel sheet compared with that observed after a shearing operation.

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.

Plasticity damage self-consistent model incorporating stress triaxiality and shear controlled fracture mechanisms – Model formulation

A model for plasticity and damage, developed in the context of continuum damage mechanics and consistent with micromechanisms of void nucleation, growth, and coalescence, is presented. The damage dissipation potential has been formulated specifically to account for different damage contributions due to intervoid necking, shearing, and sheeting under arbitrary stress states. The existence of a cut-off for the negative stress triaxiality was questioned and unilateral conditions for ductile damage have been reformulated accordingly, considering the combination of stress triaxiality and Lode parameter. The model allows the derivation, although in implicit form, of the fracture locus for the whole range of stress triaxiality. An example application to Al2024-T351 and Al6061-T6 is presented. The proposed formulation represents an attempt to reconcile CDM theoretical framework with the ductile fracture specific mechanisms and their sequential progression under general loading conditions, making advantages of micromechanical modeling to establish correlations between void evolution and continuum scale physical quantities. Finite element model implementation and plasticity model formulation will be discussed in a forthcoming companion paper.

Stress-state dependency of ductile fracture in an extruded magnesium alloy and its underlying mechanisms

A comprehensive investigation into the ductile fracture of an extruded magnesium alloy at various stress states is conducted. Tension tests of the smooth and differently notched round specimens, plane strain tension as well as shear tests are carried out to obtain the medium to high stress triaxialities. Additionally, new types of notched round specimens are proposed for compression tests, by which the negative stress triaxialities are realized. In all notched round specimens of the magnesium alloy, ductile fracture is found to initiate from the notch root rather than the inner center of specimen, which is different from some relevant reports on aluminum alloy and steel. Based on a hybrid experimental-numerical procedure, fracture strains and the corresponding loading paths in all tests are obtained. It is found that the fracture strain of magnesium alloy decreases monotonically with increasing stress triaxiality in the range covered by the smooth round and plane strain specimens, while it is less sensitive to the stress states covered by the notched compressive specimens. Besides, the fracture occurring at various compressive states is dominated by shear mode, and the ductility is slightly better than that at the shear state. Despite that the fracture strain of magnesium alloy varies unconventionally in a wide range of stress triaxialities, it is accurately described by the two-component DF2014 fracture model. Furthermore, the fracture mechanisms of magnesium alloy in various deformations are explored by fractographic analysis, and the important roles played by second phase particles and deformation twins in the variation of fracture strain are revealed.

Extended GTN model for predicting ductile fracture under a broad range of stress states

Continuous damage accumulation resulting from void nucleation, growth, and coalescence leads to the final ductile fracture. The Gurson–Tvergaard–Needleman (GTN) model and its extensions, which model these mechanisms, are famous coupled constitutive models for predicting material failure. In this study, the GTN model was extended by incorporating two different damage variables: void volume fraction and shear damage; this was done to describe damage accumulation and ductile fracture under a wide range of stress states from compression-dominated to tension-dominated ones. The shear damage was composed of the shear void nucleation related to secondary voids and shear deformation damage. In addition, the shear void nucleation and void closure effect resulting from compression deformation were introduced to model the change in void volume under different loading conditions. The Lode angle dependence function was updated to express the various stress states and competition mechanism between two damage variables. Furthermore, the effective damage and its incremental form was used to define the extent of damage accumulation and fracture initiation. Subsequently, the proposed model was implemented in finite element software through user subroutines, and three distinct experiments related to high, low, and negative stress triaxiality were performed to calibrate the model parameters by the inverse analysis method for 1045 steel and 2024-T351 aluminum alloy. The experimental results under proportional and path-changing loading conditions were used to analyze the damage evolution and validate the proposed model. The good agreement between the numerical prediction and experimental results for the displacement and location at fracture, indicates good predictive ability of formulated model under arbitrary loading conditions.

Failure Behavior of Laser Metal Deposited Additive Manufacturing Ti-6Al-4V: Effects of Stress State and Initial Defects.

To investigate the mechanical property and failure behavior of laser metal deposited additive manufacturing Ti-6Al-4V (LMD Ti64) in a wide range of stress states and strain rates, different types of specimens were tested at strain rates of 0.001-5000/s. Numerical simulations were conducted to collect the local fracture strain at the critical position where the failure happened for all specimens. By comparing with Ti64 alloy manufactured by different techniques, the failure behavior of LMD Ti64 alloy shows a stronger sensitivity to Lode angle parameter and strain rate. The role of initial defects in failure was discussed. It is found that high laser power and overlap ratio can improve the failure behavior by reducing the number of initial defects. The initial defects on the fracture surface at much higher strain rates were observed, indicating that the initial crack rather than initial void acts as the crack growth point leading to the final fracture at higher strain rates. The scanning electron microscope observation of the fracture surface shows that the failure mechanism of LMD Ti64 alloy varies from different stress states and strain rates. The failure mechanism is characterized by the shear fracture at the negative stress triaxiality, whereas the void growth fracture plays a dominant role in the failure mechanism of LMD Ti64 alloy at a high stress triaxiality on the quasi-static loading condition.

Ductile fracture prediction of additive manufactured Ti6Al4V alloy based on an extended GTN damage model

Selective Laser Melting (SLM) is one of the revolutionary additive manufacturing (AM) technologies to produce metallic mechanical parts. To thoroughly understand the damage and fracture behavior of SLM-fabricated Ti6Al4V alloy under complex stress states, a number of tensile, compressive and torsional experiments covering various stress states were conducted with different types of the specimens. A modified GTN (Gurson-Tvergaard-Needleman) model with dual damage variables characterizing the void growth mechanism and void shear mechanism was adopted to describe and predict the ductile fracture behavior of the SLM-fabricated Ti6Al4V alloy under complex stress states. A new stress state-dependent function was introduced to extend the application of the model to negative stress triaxiality state. A finite element (FE) based inverse analysis strategy was proposed to calibrate the model parameters. The simulation results showed that the damage and fracture behavior of SLM-fabricated Ti6Al4V alloy can be well described by the modified GTN model. The morphologies of the fracture surfaces were successfully predicted by using the developed damage constitutive model, in which the variable of void fraction dominates fibrous zone failure based on the void growth mechanism, and the shear damage variable facilitates shear fracture based on the void shear mechanism.

A stress-weighted ductile fracture model for steel subjected to Ultra Low Cycle Fatigue

A new criterion is proposed to simulate the initiation of ductile fracture due to Ultra-Low Cycle Fatigue (ULCF). Building on previous research, the new fracture criterion broadens the scope of ULCF models to account for a broader range of multi-axial stress and strain states that may be encountered in steel structures. The model formulation, supported by observations from finite element plasticity simulations of void growth and fractographic analyses of fracture surfaces, describes damage accumulation as a function of plastic strain, stress triaxiality, and the Lode stress parameter. The damage rate model is integrated over arbitrary cyclic loading histories of local strains and stresses to predict ULCF fracture. The proposed criterion (termed the Stress Weighted Ductile Fracture Model – SWDFM) is supported by a series of 66 coupon scale experiments on two grades of low-carbon structural steel (A572 and A36). These tests interrogate a range of positive and negative stress triaxiality with absolute values between 0.1 and 1.6, Lode stress parameters between 0 and 1, and monotonic and cyclic loading histories. The SWDFM criterion, which requires the calibration of only two material parameters for the materials investigated in this study, is evaluated against the experimental test data using an average-error assessment as well as a cross-validation analysis. Three other ULCF rupture criteria are similarly assessed and compared. The SWDFM is shown to accurately predict ULCF initiation over a wide range of stress states and loading histories, suggesting that the model represents well the micro-mechanical mechanisms of ULCF.

On ductile fracture of 30CrMnSiNi2A steel considering effects of stress triaxiality

30CrMnSiNi2A steel is a high-strength low-alloy steel and it is widely used in the defense industry. Its ductile fracture properties were investigated by using a combined experimental-numerical approach to address the need for assessment of structural integrity. The parameters of the Johnson-Cook constitutive model were obtained through quasi-static and dynamic tensile tests on round bar specimens at different temperatures and relevant finite element method iterations. The effects of strain rate and temperature on fracture were studied. The tensile tests on notched round bar specimens were performed to calibrate the fracture strain in the range of high positive stress triaxiality. The tensile tests on butterfly plates and compression tests on short cylindrical specimens covered the fracture properties in the range of low and negative stress triaxiality. The finite element models were computed and the fracture loci in the space of the effective plastic strain to fracture and the stress triaxiality in a wide range from −1/3 to 1.5 were constructed. The parameters of the Johnson-Cook fracture model and Bao-Wierzbicki fracture model were calibrated. It is shown that stress triaxiality has a significant effect on the fracture of 30CrMnSiNi2A steel and the monotonicity of the fracture loci varies in different stress triaxiality range. The Bao-Wierzbicki model is capable of predicting the fracture patterns of the 30CrMnSiNi2A steel in different stress states.

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.

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.

Mechanical characterization of the AlSi9Cu3 cast alloy under distinct stress states and thermal conditions

This paper presents the results of several mechanical tests aiming at characterizing the constitutive behaviour of the AlSi9Cu3 cast alloy, covering different temperatures and stress fields, including tensile and compressive tests of smooth and notched specimens as well as combined shear/tension and shear/compression with special designed specimens. The Johnson-Cook model was able to correlate the flow stress under quasi-static uniaxial compression, including thermal effects. However, under tension the yield stress does not reduces monotonically and gradually with temperature, which impedes the application of Johnson-Cook model for positive triaxialities. At room temperature, the AlSi9Cu3 alloy shows significant asymmetrical tensile and compressive behaviours requiring a plasticity model sensitive to the stress triaxiality such as the Drucker-Prager. As regards the ductility limits of the material, different data was analysed to generate fracture loci for the material where equivalent fracture strains were plotted against the stress triaxialities. The calibrated Drucker-Prager constitutive model together with a damage approach based on the fracture loci generated was successfully verified using test data from specimens loaded under combined shear/tension or shear/compression. The AlSi9Cu3 cast alloy exhibits a sharp reduction in ductility between the negative stress triaxiality cut-off and −0.1, keeping at low levels above this triaxiality value.

Numerical and Experimental Analyses of the Effect of Negative Stress Triaxialities on Ductile Damage and Failure

AbstractThe paper deals with an experimental and corresponding numerical series of the biaxial Z‐specimen, which is made of an aluminum alloy, to investigate the effect of negative stress triaxialities on ductile damage and failure, which are stress‐state‐dependent. Therefore, the continuum model contains a stress‐state‐dependent damage condition and a stress‐state‐dependent damage rule to describe the damage and failure mechanisms. In the experimental evaluation, in addition to force‐displacement curves, optical investigations such as digital image correlation (DIC) and scanning electron microscopy (SEM) were used. The results showed that with compression‐shear load fracture occurs at greater negative triaxialities than previously known. Therefore a new function for the cut‐off value of stress triaxiality is proposed.

Experimental and numerical analyses of formability improvement of AA5182-O sheet during electro-hydraulic forming

The formability of electro-hydraulically formed AA5182-O aluminium sheet was investigated by means of experimental testing and numerical modelling. The experimental results were compared with quasi-static, as-received forming limit curve (FLC) and were used to calibrate a finite element model of EHF. It is found that the formability improvement of AA5182-O sheets was insignificant when electro-hydraulically formed without a die. However, when specimens were electro-hydraulically formed with sufficient energy into 34 or 40° conical dies, the effective strain measured in safe grids increased by 40 and 70% respectively when compared with a conservative quasi-static FLC. Finite element simulation results suggested that a combination of different mechanical parameters contributed to the formability improvement. The increased strain rate in areas close to the apex of the speimen, the negative stress triaxiality just before specimens contact the die, and significant compressive through-thickness stress generated by high-velocity impact all contributed to the improvement of formability in electro-hydraulic die forming.