Wide Range Of Stress Triaxiality Research Articles

New ultra-low cycle fatigue model for metal alloys

Ultra-low cycle fatigue failure is an important ultimate limit state of the structures. Based on the ductile fracture model proposed by the authors, the Coffin-Manson model, and the Miner law, a new model was proposed in this study. The strategy of the proposed model is intended for the prediction of ultra-low cycle fatigue fracture onset covering a wide range of stress triaxiality and being suitable for the variable amplitude straining. Three kinds of metal alloys, Q345qC steel, G20Mn5QT cast steel, and 2024-T351 aluminum alloy, were used to verify the model. The results showed that the proposed model advanced the original Coffin-Manson model greatly. More importantly, the verification demonstrates that the proposed model can predict the ultra-low cycle fatigue fracture initiation over a wide range of stress triaxiality and under variable amplitude straining. Besides, compared with the ULCF-2021 model, the proposed model has a relatively lower average error.

Ductile fracture prediction of additively manufactured Ti-6Al-4 V alloy based on void growth and coalescence of a unit-cell model

In this work, we have studied the fracture mechanism and proposed a micromechanical method with a unit cell model to predict the ductile fracture of additively manufactured (AMed) Ti-6Al-4 V alloy. The tensile experiments with smooth round bars and notched round bars were conducted to investigate the mechanical properties and ductile fracture behavior of materials. The proposed unit-cell model was validated by quasi-static tensile fracture tests to predict the ductile failure of titanium alloy manufactured by laser power bed fusion (L-PBF) under different stress states, which include a wide range of stress triaxialities. An equivalent initial void fraction was introduced to evaluate the ductile behavior of the titanium alloy. Our investigation shows that the stress states significantly influence the void coalescence behavior of AMed Ti-6Al-4 V alloy, and the fracture locus of L-PBF fabricated Ti-6Al-4 V alloy under different stress states was successfully predicted by the proposed unit-cell model under proportional loading. Our study provides useful guidance for the future design and application of metal materials for additive manufacturing.

Damage and fracture behavior under non-proportional biaxial reverse loading in ductile metals: Experiments and material modeling

This paper deals with a modified anisotropic stress-state-dependent plastic-damage continuum model incorporating combined hardening and softening rules to predict the plastic, damage, and fracture behavior of ductile metals under monotonic and reverse loading conditions. In the experimental part, a newly designed biaxially loaded cruciform flat HC-specimen of aluminum alloy EN AW 6082-T6 was subjected to biaxial non-proportional loading to generate a wide range of stress triaxialities during experiments. Thus, it is enabled to perform shear monotonic and reverse loading superimposed by various preloads without unloading processes. The experimental data reveal the Bauschinger effect, the strength-differential (SD) effect, and the change in the hardening ratio after shear reverse loading. This is captured by a Drucker–Prager-type yield criterion with an extended Voce isotropic hardening and modified Chaboche’s kinematic hardening rule. In addition, the damage surface is assumed to be translated in the direction of the rate of the damage strain. The numerically predicted global force–displacement curves and local strain fields are verified in terms of the digital image correlation (DIC) technique. Moreover, the scanning electron microscopy (SEM) is used to examine the fracture surfaces and to validate the proposed damage constitutive model.

A triaxiality‐dependent fracture model for hot‐rolled sections made of S355 steel

AbstractFracture at net areas of steel sections often leads to premature failures of steel members, especially in the region of joints (bolted connections). This study develops a fracture model for hot rolled S355 steel for enabling a better understanding of the ultimate behaviour of steel sections through numerical simulations using the general‐purpose finite element software ABAQUS. Monotonic tensile tests are conducted on traditional dog‐bone plate specimens with a uniform cross‐section and notched plate specimens extracted from hot‐rolled I‐beams. Two material thicknesses and three notch radii per thickness are considered thus obtaining equivalent plastic strains at fracture over a wide range of stress triaxialities. The experimental fracture displacement is used as a threshold for the determination of the average stress triaxiality – equivalent strain history at the critical location (fracture initiation) of each plate model. Using regression analysis, an exponential approximation of the fracture locus is proposed to correlate the average stress triaxiality for a given equivalent plastic strain at fracture. The proposed model is then used to predict fracture initiation of unnotched tensile coupons and steel plates with a bolt hole in their centre extracted from the same steel sections. The test results are in good agreement with the numerical predictions thus demonstrating the efficiency of the proposed method.

Ductile fracture of X80 pipeline steel over a wide range of stress triaxialities and Lode angles

This study pays attention to the ductile fracture of X80 pipeline steel using both experimental and numerical approaches. First, nineteen experimental cases are tested, consisting of the normalized uniaxial tension, the plain strain tension, pure shear, and shear plus tension/compression. Three fracture modes are observed throughout the experiments. A hybrid testing-FE method is applied to determine the post-necking strain hardening curve of the X80 pipeline steel. Then, parallel computations are conducted in the Abaqus to obtain ductile fracture parameters. The simulated results indicate that the determined strain hardening curve has applicability for all experiments. According to the ductile fracture parameters, three models, viz. the Hosford-Coulomb model, the DF2016 model, and a newly proposed model, are calibrated based on the hold-out strategy. Fracture prediction of the X80 pipeline steel is conducted by the three calibrated models. The results show that the newly proposed model outperforms the other two in terms of stability and accuracy.

A non-local GTN model with two length scales – Application to ductile failure in a wide range of stress triaxiality

A non-local extension of the shear-modified Gurson model for porous plasticity is proposed, which is capable of preventing spurious strain localization and suitable for predicting crack initiation and growth under general loading conditions. In the extended model, the progression of shear failure is separated from flat dimple rupture by the assumption that these failure mechanisms are characterized by a deviatoric and a dilatational material length parameter, respectively. The two length parameters are introduced through a delocalization process based on the non-local integral approach evaluated on the current configuration. A comprehensive numerical investigation is conducted to disclose the influence of these length parameters. For this purpose, five different specimen geometries are considered covering a wide range of stress triaxiality including pure shear. It is observed that separation of the length parameters is essential for predicting crack branching driven by shear localization, e.g., the flat dimple-to-shear failure transition of a crack that approaches and penetrates a free surface.

Influence of the stress history and of the Lode angle on the determination of the ductile fracture locus for two steel alloys

The fracture locus of ductile materials is primarily related to the stress triaxiality. Recently, the Lode angle was also found to be relevant in the fracture locus determination. In order to characterize a material in terms of fracture locus, usually several tests, spanning a wide range of stress triaxiality and Lode angle values, have to be performed using different specimen geometries, obtained both from round bars and sheets.In this paper the fracture loci of two steel alloys (S500MC and 22MnB4) are obtained using a simplified procedure, based on the Bai–Wierzbicki model. The procedure considers, for experimental tests, only flat specimens, avoiding the use of round specimen of the same material which were not available. Experimental tests were performed on differently shaped specimens and the results were used to train finite element (FE) models. The triaxiality and Lode angle histories, computed for each test by the FE model, were used to obtain the fracture loci following two different approaches: the proportional loading approach and the non-proportional loading approach. The former does not consider how the stress triaxiality and Lode angle vary during the test, while the latter considers their history in the computation of the fracture locus.The results show how the Lode angle influences the fracture locus, especially for 22MnB4, and how non-proportional loading approach is more accurate to compute the damage for the different specimen geometries.

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.

Influence of stress triaxiality on the fracture behaviour of Ti6Al4V alloy manufactured by electron beam melting

This paper aims to investigate the influence of stress triaxiality on the fracture behaviour of Ti6Al4V fabricated by Electron Beam Melting (EBM). Here, specimens with seven configurations were manufactured and tested to obtain a wide range of stress triaxialities. A combined approach using Digital Image Correlation (DIC) and finite element (FE) modelling was used to evaluate the current stress triaxiality levels of the various specimens. The material fracture envelope was defined with the triaxiality in a range from -0.28 to 0.71, noting that the fracture was strongly dependent on the stress triaxiality. The characterisations were then carried out by testing an ad-hoc specimen to evaluate failure criteria at low and high stress triaxialities. It was shown that the FE model using the failure criterion based on triaxiality offers more accurate predictions of the material's failure response than that based on the effective plastic strain. The modelling approach based on anisotropic elasto-plasticity contributes to better predictions of the alloy's response. Thus, the failure models based on the stress triaxiality are highly recommended for producing accurate numerical predictions of the fracture response of Ti6Al4V-EBM.

Fracture prediction in spin forming of anisotropic metal sheets

Fracture often occurs in the spin forming process of thin-walled metal sheets, due to the limited fracture strain and local large plastic deformation of the sheets during the process. However, the accurate fracture prediction is a huge challenge due to the combinations of material anisotropy, complex deformation history and contact boundary conditions in the process. Though there are scattered uncoupled ductile fracture criteria proposed with various deformation mechanisms, reasons for their different fracture prediction abilities remain unclear. Thus in this study, eight popular uncoupled ductile fracture criteria i.e., Freudenthal, C-L, R-T, Brozzo, Oh, Oyane, MMC4 and DF2016, are embedded into an anisotropic constitutive model through VUMAT interface in the ABAQUS simulation software and then realized their fracture prediction in the spin forming process of an anisotropic metal sheet. The results show that the damage accumulation in the spin forming process occurs in a wide range of stress triaxiality, and the most damage accumulation occurs in the stress triaxiality range of 0–1/2. Furthermore, the eight fracture criteria have different prediction abilities in the process and a new deformation history related equivalent fracture strain is proposed to explain these differences. In addition, there exists the abnormal phenomenon that some simple damage models, as Oyane, Oh, etc. provide the more accurate fracture prediction ability than the complex and advanced MMC4 and DF2016 models in the process, and reasons for this phenomenon are explained.

Finite Element Modeling for Orthogonal Machining of AA2024-T351 Alloy With an Advanced Fracture Criterion

Abstract Numerical modeling of the plastic deformation and fracture during the high-speed machining is highly challengeable. Consequently, there is a need for an advanced constitutive model and fracture criterion to make the numerical models more reliable. The aim of the present study is to extend the recent advanced static Lou-Yoon-Huh (LYH) ductile fracture creation to high strain rate and temperature applications such as machining. In the present work, the LYH static fracture creation was extended to machining conditions by introducing strain rate and temperature dependency terms. This extended LYH fracture criterion was calibrated over the wide range of stress triaxialities and different temperatures. Modified Khan- Huang-Liang (KHL) constitutive model along with the variable friction model was employed to predict the flow behavior of work material during the machining simulation. Damage evolution method was coupled to identify the element deletion point during the machining simulation. Orthogonal machining experiments were carried out for an aerospace-grade AA2024-T351 at cutting speeds varying between 100 and 400 m/min with the feed rates varying between 0.1 and 0.3 mm/rev. To assess the prediction capabilities of extended LYH fracture criterion, numerical simulations were also carried out using Johnson-Cook (JC) fracture criterion under all experimental conditions. Specific cutting energy, chip morphology, and compression ratio predictions were compared with the experimental data. Numerical predictions with coupled extended LYH criterion showed good agreement with experimental results compared to coupled JC fracture criterion.

Characterization of ductile fracture criterion for API X80 pipeline steel based on a phenomenological approach

Steel pipelines for oil/gas transportation might be subjected to large plastic strain under extreme loading conditions, which will lead to localized fracture. The damage mechanics model is a promising tool to perform most of the assessment analysis and evaluation at the simulation level. In this paper, a micro-based Gurson-Tvergarrd-Needleman (GTN) model and two recently proposed uncoupled fracture criteria, modified Mohr-Coulomb (MMC) criterion and extended Rice-Tracey (ERT) criterion are evaluated using API X80 steel. A comprehensive experimental study including five different notched specimens covering a wide range of stress triaxiality and lode dependence is conducted. Corresponding finite element models are established. A phenomenon-based hybrid numerical-experimental calibration method is used to determine the fracture parameter for these three models. Then the calibrated parameters are validated through notched tensile tests and compact tension (CT) tests. It is shown that the presented fracture criteria are in a good capability to characterize the ductile fracture behaviors of API X80 pipeline steel.

Comparison of Modified Mohr\u2013Coulomb Model and Bai\u2013Wierzbicki Model for Constructing 3D Ductile Fracture Envelope of AA6063

Ductile fracture of metal often occurs in the plastic forming process of parts. The establishment of ductile fracture criterion can effectively guide the selection of process parameters and avoid ductile fracture of parts during machining. The 3D ductile fracture envelope of AA6063-T6 was developed to predict and prevent its fracture. Smooth round bar tension tests were performed to characterize the flow stress, and a series of experiments were conducted to characterize the ductile fracture firstly, such as notched round bar tension tests, compression tests and torsion tests. These tests cover a wide range of stress triaxiality (ST) and Lode parameter (LP) to calibrate the ductile fracture criterion. Plasticity modeling was performed, and the predicted results were compared with corresponding experimental data to verify the plasticity model after these experiments. Then the relationship between ductile fracture strain and ST with LP was constructed using the modified Mohr–Coulomb (MMC) model and Bai-Wierzbicki (BW) model to develop the 3D ductile fracture envelope. Finally, two ductile damage models were proposed based on the 3D fracture envelope of AA6063. Through the comparison of the two models, it was found that BW model had better fitting effect, and the sum of squares of residual error of BW model was 0.9901. The two models had relatively large errors in predicting the fracture strain of SRB tensile test and torsion test, but both of the predicting error of both two models were within the acceptable range of 15%. In the process of finite element simulation, the evolution process of ductile fracture can be well simulated by the two models. However, BW model can predict the location of fracture more accurately than MMC model.

A closed-form yield criterion for porous materials with Mises–Schleicher–Burzyński matrix containing cylindrical voids

This work develops a closed-form yield criterion applicable to porous materials with pressure-dependent matrix presenting tension–compression asymmetry (Mises–Schleicher–Burzynski material) containing parallel cylindrical voids. To develop the strength criterion, the stress-based variational homogenization approach due to Cheng et al. (Int J Plast 55:133–151, 2014) is extended to the case of a hollow cylinder under generalized plane strain conditions subjected to axisymmetric loading. Adopting a strictly statically admissible trial stress field, the homogenization procedure results in an approximate yield locus depending on the current material porosity, tension–compression material asymmetry, the mean lateral stress, and an equivalent shear stress. The analytical criterion provides exact solutions for purely hydrostatic loading. Theoretical results are compared with finite element (FE) simulations considering cylindrical unit-cells with distinct porosity levels, different values of the tension–compression asymmetry, and a wide range of stress triaxialities. Based on comparisons, the theoretical results are found to be in good agreement with FE simulations for most of the loading conditions and material features considered in this study. More accurate theoretical predictions are provided when higher material porosities and/or lower tension–compression asymmetries are considered. Overall, the main outcome of this work is a closed-form yield function proving fairly accurate predictions to engineering applications, in which pressure-dependent and tension–compression asymmetric porous materials with cylindrical voids are dealt with. This can be the case of honeycomb structures or additively manufactured materials, in which metal matrix composites are employed.

Effect of non-associated flow rule on fracture prediction of metal sheets using a novel anisotropic ductile fracture criterion

The ductile fracture behavior of anisotropic materials was investigated and modeled by the uncoupled ductile fracture criterion for aluminum alloys 6016-AC200. The ductile fracture model takes into account micro-mechanisms of void nucleation, void growth, and evolution of void coalescence. The anisotropic yield function and non-associated flow rule were applied to increase the accuracy of the ductile fracture prediction. Series of uniaxial tensile tests, equi-biaxial tension test, and hydraulic bulge test were utilized to identify coefficients of the plasticity model. Various standard fracture tests covering a wide range of stress triaxiality from negative to moderate and high-stress triaxiality were used in order to calibrate the ductile fracture parameters for AA6016-AC200. The strain field on the surface of specimens was captured by the non-contact measurement DIC system for all tests. The fracture surface, fracture locus, and fracture forming limit diagram constructed by the proposed ductile fracture criterion were plotted. These basic fracture tests and a square cup drawing test were simulated by the ABAQUS/Explicit commercial software to verify the efficiency of the proposed fracture criterion and the advanced plastic model in predicting the onset of ductile fracture behavior. The results indicated that the proposed ductile fracture criterion can be utilized for predicting the onset of the anisotropic ductile fracture behavior in sheet metal forming.

A new ductile fracture criterion considering both shear and tension mechanisms on void coalescence

A new ductile fracture criterion is proposed based on three stages of ductile fracture: void nucleation, growth and coalescence from the microscopic viewpoint. Based on the observation of SEM fracture surfaces of AA2024-T351 aluminum alloy sheet and bar samples under different stress states, it is assumed that the void aggregation is controlled by shear or shear-tension fracture mechanism according to the stress state. And the stress triaxiality is deemed as the only influence factor for controlling the void growth. The new ductile fracture criterion applied to a wide range of stress triaxiality is built. By fitting the available testing data of AA2024-T351 aluminum alloy and AISI 1045 steel, the fracture loci in the stress triaxiality, Lode parameter and equivalent fracture strain space ([Formula: see text]) built by the new criterion are compared with those by DF2014, Hu criterion, modified Mohr-Coulomb criterion (MMC) and Hosford- Coulomb (H-C) criterion. The fitting results prove better prediction accuracy for the new criterion. To further compare the stability of these criteria, the fracture loci in the space of ([Formula: see text]) for AA2024-T351 alloy are established by only fitting five tests. The new criterion can still well predict the equivalent fracture strain ([Formula: see text]). Compared with DF2014, Hu criterion, MMC and H-C criterion, the average errors of the new criterion are reduced by 26.72%, 20.07%, 31.78% and 34.62%, respectively. Furthermore, the maximum errors are reduced by 49.62%, 27.31%, 33.76% and 29.91%, separately. Therefore, the new fracture criterion has higher prediction accuracy and better prediction stability. Last but certainly not least, the new criterion can predict more accurately under high stress triaxiality conditions.

Analysis of API S-135 steel drill pipe cutting process by blowout preventer

In offshore oil exploration, the use of a Dynamic Positioning System (DPS) to maintain the platform at a fixed point regardless of the influence of the environment has become common practice. In the event of failure, however, the drill string inside BOP (BlowOut Preventer) must be cut and safely disconnected from the platform. Therefore, it is evident the need for an accurate and realistic virtual model of this failure process. Numerical model analysis, in addition to avoiding expensive and complex experimental tests, allows, through post-processing tools, a detailed understanding of all phases of the failure process. The present work aims to characterize the API S-135 steel, as material commonly used to manufacturing drill strings. The material parameters for the Johnson-Cook model (J-C) are obtained from experimental tensile tests on dog bone and 3-point bending beams specimens with different notch radii, covering a wide range of stress triaxialities. Experimental tests and numerical simulations were compared by means of stress-strain curves, Digital Image Correlation (DIC) and Surface Electron Microscopy (SEM) to validate the model. The material model is applied to simulate the pipe cutting process and to predict the required force for the BOP to cut drill pipes with different geometries, which in comparison to experimental tests permitted to determine BOP internal frictions. Additionally, the numerical simulation also allowed a better understanding of the cutting process here presented as well, coherent to J-C model and SEM imaging of a similar cut tube in BOP.

A damage model for predicting ductile fracture with considering the dependency on stress triaxiality and Lode angle

This paper aims to present a Continuum Damage Mechanics based fracture model. Two yield surfaces, plastic and damage, are utilized to develop the model. A modified ductile fracture model coupling both stress triaxiality and Lode angle parameter is then proposed. The proposed model is applied to construct the fracture loci of four types of metal alloys: steel HY100, steel PCrNi3MoVA, aluminum 2024-T351, steel TRIP690 and steel A533B. The prediction is also involved investigation of the dependency of damage evolution on stress triaxialities for steel HY100 and steel A533B. The new model is also utilized to construct the Fracture Forming Limit Diagram (FFLD) of steel TRIP690 to validate the performance of the model. The predicted results are in good agreement with the experimental data over a wide range of stress triaxialities. Comparison between the proposed model and some fracture criteria is also provided, and the results indicate that the proposed model has significant potential to predict ductile fracture as well as FFLD at both low and high triaxialities. In order to validate the capability of the model in structural response, the proposed model has been implemented into user-defined subroutines VUMAT in the finite element program ABAQUS/Explicit. For this purpose, the explicit stress integration algorithms of the model have been explained. The model has been validated by comparing the predicted results with experimental data of steel A533B. The results show the excellent correlation between experiments and simulation for the force and damage results as well as the fracture shape.

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.

Ductile fracture of high strength steel under multi-axial loading

The high strength steel (HSS) with a nominal yield stress not less than 460 N/mm2 has been increasingly used in engineering structures. Compared with mild steels, HSSs have higher strength but lower ductility. This paper is concerned with the ductile fracture prediction of the HSS in a wide range of stress triaxiality and Lode angle. Experimental investigation is conducted to study the influence of stress triaxiality and Lode angle on fracture ductility of three different HSSs (Q550, Q690 and Q890). The experimental results are used to calibrate three typical fracture criteria: Void Growth Model (VGM), Combined Fracture Model (CFM) and Bai-Wierzbicki Model (BWM). It is found that without of consideration of Lode angle, the VGM fails to give an accurate prediction of fracture responses of all types of experiments. Compared with VGM, the CFM gives better fitting results. However, because the stress triaxiality dependence and Lode angle dependence are separated in CFM, there still exists discrepancy between prediction and real responses. The BWM gives the most accurate fitting results and prediction for all tests on three different HSSs. Moreover, it is found that elongation at fracture fails to describe the fracture ductility of HSS in a wide range of stress states. Based on parametric study results, it is found that with increasing Lode angle dependence of plasticity, the Lode angle dependence of fracture ductility of HSSs tend to decrease.