Gurson-Tvergaard-Needleman Model Research Articles

Ballistic resistance of 7XXX laminate aluminum alloy plates and base alloys subjected to different projectiles

The ballistic impact of two 7XXX aluminum alloys, 7A52-T6 and 7A62-T6, as well as their combination in a 7B52 laminate plate, was simulated and experimentally tested. Three types of projectiles were utilized hard ogival nosed, hard blunt nosed, and 304 steel core projectiles to investigate the ballistic resistance and failure mechanisms of the aluminum alloy targets. Additionally, an existing modified Gurson-Tvergaard-Needleman (GTN) model incorporating shear, void growth, and spalling failure mechanisms, was employed to simulate the ballistic impact process, utilized to analyze energy dissipation during impact. The results reveal that the 7A52 alloy only experiences ductile hole expansion failure, whereas the 7A62 high-strength aluminum alloy undergoes spalling and fragmentation subsequent to penetration, leading to potential impact hazards. Due to its backing layer being the highly ductile 7A52 alloy, the laminate plate will not produce fragments after penetration. The improved GTN model provided better predictions of the impact failure modes of the aluminum alloys. Concerning impact performance, when subjected to hard ogival projectiles, the laminate alloy did not enhance material impact resistance. However, when impacted by blunt-nosed projectiles, the laminate alloy exhibited a 27 % improvement over the 7A52 plate and an 11.9 % increase over the 7A62 plate. Furthermore, when impacted by 304 steel core ogival projectiles, the laminate alloy demonstrated over a 41.3 % improvement compared to the 7A52 plate and over a 15.5 % increase compared to the 7A62 plate. The laminate plate's high ballistic performance was attributed to the increased plastic deformation energy after spalling failure, while ensuring high energy absorption during ductile hole expansion penetration.

A primal–dual interior point method to implicitly update Gurson–Tvergaard–Needleman model

A primal–dual interior point method to implicitly update Gurson–Tvergaard–Needleman model

Multi-Mode Damage and Fracture Mechanisms of Thin-Walled Tubular Parts with Cross Inner Ribs Manufactured via Flow Forming.

In order to study the multi-mode damage and fracture mechanisms of thin-walled tubular parts with cross inner ribs (longitudinal and transverse inner ribs, LTIRs), the Gurson-Tvergaard-Needleman (GTN) model was modified with a newly proposed stress state function. Thus, tension damage and shear damage were unified by the new stress state function, which was asymmetric with respect to stress triaxiality. Tension damage dominated the modification, which coupled with the shear damage variable, ensured the optimal prediction of fractures of thin-walled tubular parts with LTIRs by the modified GTN model. This included fractures occurring at the non-rib zone (NRZ), the longitudinal rib (LIR) and the interface between the transverse rib (TIR) and the NRZ. Among them, the stripping of material from the outer surface of the tubular part was mainly caused by the shearing of built-up material in front of the rollers under a large wall thickness reduction (ΔT). Shear and tension deformation were the causes of fractures occurring at the NRZ, while axial tension under a large TIR interval (l) mainly resulted in fractures on LIRs. Fractures at the interface between the TIR and NRZ were due to the shearing applied by rib grooves and radial tension during the formation of ribs. This study can provide guidance for the manufacturing of high-performance aluminum alloy thin-walled tubular components with complex inner ribs.

Extended Gurson-Tvergaard-Needleman model considering damage behaviors under reverse loading

Void nucleation, growth, deformation and coalescence are the main microscopic damage mechanisms for plastic deformation of sheet metals. To describe the effect of reverse loading on the microscopic damage accumulation and ductile fracture, the damage evolution equations in regard of void nucleation, void growth, shear void nucleation and shear deformation damage were modified. Through the further introduction of the combined hardening model, an extended Gurson-Tvergaard-Needleman (GTN) model was constructed in this study, to improve the predictive ability of ductile fracture under reverse loading conditions. Two typical reverse loading experiments including compression-tension and shear-reverse shear were performed. The number, size and shape of microscopic voids were qualitatively analyzed and compared through the microscopic observations, it is indicated that the preloading and loading sequence strongly affect the damage accumulation and the final ductile fracture, which is the microscopic damage mechanisms under reverse loading. The proposed GTN model was verified by the load responses and displacements at fracture (DAFs) of the conducted reverse loading experiments. The good agreement between numerical simulations and experimental results proves the rationality of the proposed GTN model and its accuracy to the prediction of ductile fracture under reverse loading conditions.

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.

Numerical simulation of void elimination in the billet during hot shape rolling processes based on the Gurson–Tvergaard–Needleman model

The presence of voids can compromise the strength and continuity of downstream products. The Gurson–Tvergaard–Needleman model was utilized to obtain the relevant parameters. A 3D finite element model was then employed to investigate the elimination of voids in a porous free-cutting steel 1215MS during the hot shape rolling process. The center distribution of voids in the billet was considered in the finite element model, and the relationships between the void elimination and the pressure stress in the billet were analyzed. The influences of rolling reduction, rotation speed, and friction between the work roller and billet on the void elimination were also discussed. The results revealed that the pass reduction has a significant influence on the ultimate value of void volume fraction, which is beneficial for better material self-healing during the shape-rolling process. These findings suggest that accurate predictions of void elimination in the workpiece can be achieved using the finite element method for successful simulation of the hot shape rolling process.

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.

Damage and failure of semi-rigid steel joints during progressive collapse

Ductile metal materials during a ductile failure will suffer from micro-void damage, simulation of which can contribute to the prediction of the macro fracture of steel structure. In this paper, the Gurson-Tvergaard-Needleman (GTN) constitutive model which describes the aggregate failure of metal voids is selected as the constitutive relation to investigating the damage evolution and fracture of semi-rigid joints in steel structures during a progressive collapse. During the process, specific parameters of the GTN model of steel are confirmed based on the combined results of the test and numerical simulation. The progressive collapse of two kinds of semi-rigid joints of steel pipe-to-H shaped steel were simulated by a nonlinear finite element method. A comparison between the simulation and test results verified that the GTN constitutive model can accurately simulate the fracture failure of the steel semi-rigid joints. Besides, a simplified joint failure model based on concentrated plastic hinge theory is proposed. Considering the damage and fracture of semi-rigid joints and the collision contact among different components, the progressive collapse of the semi-rigid steel frame structure is simulated by explicit dynamic analysis based on a finite particle method. Afterwards, the dynamic response of the structural progressive collapse can be predicted more accurately.

Sensitivity analysis of GTN damage parameters: Application to notched plate ductile fracture simulation

The evolution of preexisting voids causes damage to metal structures with large plastic deformation. In the ABAQUS-Explicit computer code, the damage by the Gurson–Tvergaard–Needleman model (GTN model) is included in the porous failure criteria law. The numerical predictions using the GTN model are very sensitive to the calibrations of these parameters of the experimental results. This model describes until the damage, the mechanism of the evolution of the voids, which begins with their growth and their nucleation with the particles until the coalescence of these voids of a critical level, which causes the damage to the structure. This analysis uses Voce’s hardening model and von Mises’ equivalent stress flow theory. After validation with experimental results, this work aims to analyze the sensitivity of these GTN parameters to the response to damage and to the evolution of the gaps. This objective is applied on a plate notch.

A shear modified GTN model based on stress degradation method for predicting ductile fracture

The Gurson–Tvergaard–Needleman (GTN) model has provided a powerful description of the nucleation growth and coalescence of micro voids, but it has limitations in simulating shear fracture due to the absence of a description of shear localization behavior. A shear improvement method is proposed for simulating the ductile fracture of materials under different stress states. The modified model not only allows for strain hardening of the matrix material, but also accounts for the stress degradation caused by shear. The strength equation of the material is described by both the shear stress state function and a decay function, making it easier for materials under shear stress state to experience material softening and further inducing shear fracture. The modified GTN model is developed by incorporating the shear stress degradation factor into the yield function, while taking into account both void growth and shear failure mechanisms. By carefully calibrating the model’s parameters, the deformation and fracture processes of tensile, plane strain, notch tensile, and compression specimens in the 7A52 aluminum alloy are simulated. The damage evolution behavior of the material under different stress states is analyzed. The results indicate that the damage include void growth mechanism and void shear mechanism. The proportions of these two mechanisms vary under different levels of stress triaxiality. Upon localizing material deformation, the shear stress state intensifies, and the shear damage mechanism assumes a critical role in fracture. The modified GTN model accurately predicts the load-displacement response and fracture path of the 7A52 aluminum alloy under a wide range of stress states.

A cyclic GTN model for ultra-low cycle fatigue analysis of structural steels

Ultra-low cycle fatigue (ULCF) is a critical concern in the seismic design of steel structures due to its adverse effects on the ductility and energy dissipation capacity of steel connections. The Gurson-Tvergaard-Needleman (GTN) model, a well-accepted micromechanical fracture model, cannot be applied directly to ULCF analysis, as it requires proper estimation of the effects of cyclic loadings on the ductile fracture of materials. In this paper, a cyclic GTN (C-GTN) model was proposed for the ULCF prediction of materials, in which the evolution of microvoids during ULCF loadings was addressed for tensile and compressive half load cycles, respectively, and the effect of the cumulative plastic strains on the material’s resistance to ductile fracture was considered by the reduction of the critical void volume fraction for void coalescence. Then, a VUMAT subroutine was programmed for the C-GTN model, in which the cyclic hardening behavior of materials was simulated with the Voce-Chaboche model. Finally, the C-GTN model was calibrated for the G20Mn5QT cast steel based on previous tests on notched round bar specimens of the material. The applicability of the C-GTN model and the VUMAT subroutine were validated in the ULCF analysis of double-hole plate specimens of the G20Mn5QT cast steel.

Inter-void shearing effect on damage evolution under plane strain deformation in high-strength aluminum alloy sheet

In this study, the ductile damage responses of high-strength 7000 series aluminum alloy (AA), AA 7075-T6 sheet samples, subjected to the plane strain deformation mode were investigated using finite element (FE) simulations. In the experiments, uniaxial tension (UT) and plane strain tension (PST) tests were conducted to characterize the plasticity and ductile damage behavior of the AA 7075-T6 sheet samples. The limiting dome height (LDH) and V-die air bending tests were conducted to evaluate the ductility of the material subjected to plastic deformation and friction between the tools, and the corresponding fractured samples were qualitatively analyzed in terms of dimples using fractography. FE simulations were performed to predict the ductility of the AA 7075-T6 sheet samples under plane strain deformation using an enhanced Gurson−Tvergaard−Needleman (GTN) model, namely the GTN-shear model. The model was improved by adding the shear dimple effect to the original GTN model. The predicted results in terms of the load–displacement curves and displacements at the onset of failure were in good agreement with experimental data from the aforementioned tests. Furthermore, virtual roll forming simulations were conducted using the GTN-shear model to determine the effect of the prediction on ductile behavior for industrial applications.

A Micro-Macro mixed GTN-MMC model to study plasticity and fracture of AISI 4340 steel

Experimental and numerical studies were conducted to study the plastic and fracture behaviors of AISI 4340 steel (with three different heat treatments) under multiaxial stress loading conditions, including axial symmetric and plane strain loadings. The classical Gurson-Tvergaard-Needleman (GTN) plasticity model was extended and calibrated to consider Lode angle dependence on the material's matrix plastic strength especially needed for plane strain loadings. The 3D fracture loci of AISI 4340 steels were previously calibrated by the Modified Mohr-Coulomb (MMC) model. Considering the microvoid growth and nucleation mechanisms, GTN model is combined with MMC model to derive a new analytical solution of microvoid volume fraction at fracture (ff) under general loading conditions. The ff should NOT be a constant, and it depends on different stress states. The modified GTN-MMC model was implemented using VMAT in Abaqus, and it gives a very good correlation between experimental data and finite element simulations.

Experimental investigations on parameter identification and failure predictions of titanium alloy by Gurson–Tvergaard–Needleman model

This study focused on the experimental investigations on parameter identification and failure prediction of Ti-6Al-4 V by Gurson–Tvergaard–Needleman (GTN) model. Two approaches, i.e., direct (by image processing of SEM observations) and indirect measurements (by the reduction of effective Young’s modulus or FE trail-and-error), were used to determine the GTN parameters. Through digital image processed SEM micrographs of uniaxial tensile specimens at different deformation stages, the developments of void volume fraction (VVF) were obtained and compared with that from indirect measurements. The three nucleation parameters can then be analytically derived from this experimentally obtained VVF developments. The critical VVF at void coalescence was directly measured through a SEM observation of the section surface around the fracture region of uniaxial tensile specimen, and this value is also consistent with that from indirect measurement. However, as the matrix of a fracture surface is characterized with an obvious varying grayscale due to its dimple morphology, the VVF at final fracture is suggested to be determined from FE trial-and-error rather than a direct measurement of the fracture surface to avoid error induced by subjective judgements. Consistency of the determined GTN parameters was verified through failure predictions on notched tension (R = 6, 20, 100), notched Arcan tests (R = 1, 3, 5), and cracked Arcan tests (SECS, DECS, and CCS), which proved that GTN model with parameters from this experimental investigation cannot only predict the macroscopic mechanical behavior of ductile metals, but also well match the entire damage evolution, from void nucleation to final fracture.

Ductile fracture prediction of HPDC aluminum alloy based on a shear-modified GTN damage model

In this paper, we investigate how the shear-modified Gurson-Tvergaard-Needleman (GTN) model can be used to reveal the effect of manufacturing-process-induced porosity on the scatter of ductile fracture properties of a high-pressure die-casting aluminum alloy. The GTN model exhibits great advantages in predicting the variation of failure strain/displacement by altering the initial void volume fraction (f0), compared with uncoupled ductile damage models. For a specific metallic material, one unique set of model parameters is usually determined from experiments, which leads to the fact that only a deterministic failure strain/displacement can be obtained under a fixed porosity. To overcome this shortcoming of the shear-modified GTN model, a novel parameter calibration scheme is proposed and validated in the present study. Following the physical background of the GTN model, the twelve material parameters of the shear-modified GTN model have been determined based on a combination of macroscopic mechanical tests covering a wide range of stress states and micromechanics-based unit cell simulations. Different from the existing calibration strategies, the simulation results of unit cells embedded with a spherical void have revealed a mutual dependence between the f0 and critical void volume fraction (fc). By conducting interrupted shear tests, the evolution of secondary nucleated void volume fraction was identified according to the statistical results of the fractured brittle silicon particles. The remaining parameters have been further iteratively determined. In the end, the effectiveness of the proposed parameter determination approach is confirmed based on the accurate prediction of stochastic ductile failure properties (both the global failure displacements and the local failure patterns) in different fracture tests. Given the proposed parameters identification strategy, the GTN material models have been enriched to predict the ductile failure behavior of metallic materials, which possess relatively high porosities and more pronounced scattering in failure properties.

A gradient-based non-local GTN model: Explicit finite element simulation of ductile damage and fracture

Non-local models have over the years been established as an effective approach to solve the pathological mesh dependency problem observed in finite element simulation of strain-softening materials. This paper presents the formulation, implementation, and application of a gradient-based non-local Gurson–Tvergaard–Needleman (GTN) model for explicit finite element analysis. The porosity is taken as the non-local variable where the increment in porosity is averaged over the volume using an implicit gradient model. The gradient model is implemented in Abaqus/Explicit by utilising the coupled thermal–mechanical solver, which proves to be both a simple and computationally efficient approach. Due to the use of an explicit integration scheme, a transient term is introduced to the partial differential equation of the gradient formulation. The non-local GTN model is compared to the local counterpart for increasing mesh refinements using a plane strain shear band specimen, a plane strain tension specimen, and a plane strain compact tension specimen. The proposed approach can remedy the pathological mesh dependency problem. For the plane strain tension specimen, it is shown that the non-local GTN model will preserve the fracture mode (slant versus cup–cup fracture mode) when the mesh is refined. The non-local GTN model is also able to predict the same fracture mode as observed in ductile tearing experiments. However, non-local averaging can over-smooth the fields and exclude the slant fracture mode from occurring if the material length Lc is too large.

Numerical Study on Ductile Failure Behaviours of Steel Structures under Quasi-Static Punch Loading

A reliable finite element procedure to simulate shear-dominated ductile fractures in large-scale, thin-walled steel structures is still evolving primarily due to the challenges in determining the failure criterion of metal materials under complex stress states. This paper aims to examine the accuracy of the modified Gurson–Tvergaard–Needleman (GTN) model considering the shear failure in simulating the ductile fracture of steel plate structures under quasi-static punch loading. The modified GTN damage models are performed by the ABAQUS user-defined material subroutine (VUMAT). The void-related parameters and shear damage parameters of Xue’s and the N-H modified GTN models are calibrated from test specimens with various geometries corresponding to different stress triaxiality and shearing conditions. The damage evolution associated with shearing of voids in the modified GTN models has strong influences on the stress triaxiality versus plastic strain under complex stress states, especially for the shear-dominated loading conditions. Based on the original GTN model, Xue’s and the N-H modified GTN model with calibrated material parameters, a numerical comparative study examines the ductile fracture of steel non-stiffened plates and stiffened plates under punch loading. Benchmarked against the experimental studies, the numerical simulations demonstrate that the shear-driven void evolution in the modified GTN model imposes significant effects on the load–displacement responses as well as the onset and extension of ductile fractures in steel plates under punch actions. The N-H modified model with calibrated shear damage parameters shows a better correlation with the ductile fractures in steel plates observed in the experiment than the original GTN model and Xue’s modified GTN model. As a result of this study, the modified GTN model considering shear action can be applied for practical applications in the crashworthiness assessment of ship collision and grounding.

The modified GTN model for fracture of nickel-based superalloys considering size effect and healing effect in pulsed current assisted deformation

Gurson-Tvergaard-Needleman (GTN) model is one of the most famous and classical criterions widely used in modelling the ductile fracture process of metal. However, the existence of grain size effect affects the ductile fracture prediction in micro-scaled plastic deformation of nickel-based superalloy ultrathin sheet. In the pulsed current assisted (Pca) forming process, the current has a healing effect on the micro-void of metal due to the existence of local Joule heat, yet the strain has a promotion on the micro-void growth, and the coupled effect between grain size and electrical field is complicated, which makes it difficult to predict the fracture for the traditional GTN model in Pca forming process. To solve this problem, the authors added pulsed current parameters to the GTN model to describe the healing effect of pulsed current on the voids in the material. The parameters of the GTN model were calibrated by the finite element inverse identification method. The modified GTN model was embedded into Abaqus by VUMAT, and the Backward Euler algorithm was employed to integrate the constitutive equation. The validity of the model was verified by comparing the true stress-strain curves with the simulation results and comparing the void volume fraction (VVF) measured by three-dimensional X-ray computerized tomography (3DCT). The model provides a new method for ductile fracture prediction of multiphase alloys under a discontinuous energy field. Meanwhile, it is confirmed that the behaviour of fracture and necking in the Pca forming process is affected by the coupling effect of pulsed current and grain size effect, which provides a new idea for studying the Pca forming process.

Impact Deposition Behavior of Al/B4C Cold-Sprayed Composite Coatings: Understanding the Role of Porosity on Particle Retention

This study explores the role of porosity in the impact deposition of a ceramic-reinforced metal-matrix (i.e., Al/B4C) composite coating fabricated via cold spraying. The Johnson-Holmquist-Beissel constitutive law and the modified Gurson-Tvergaard-Needleman model were used to describe the high strain-rate behavior of the boron carbide and the aluminum metal matrix during impact deposition, respectively. Within a finite element model framework, the Arbitrary Lagrangian-Eulerian technique is implemented to explore the roles of reinforcement particle size and velocity, and pore size and depth in particle retention by examining the post-impact crater morphology, penetration depth, and localized plastic deformation of the aluminum substrate. Results reveal that some degree of matrix porosity may improve particle retention. In particular, porosity near the surface facilitates particle retention at lower impact velocities, while kinetic energy dominates particle retention at higher deposition velocities. Altogether, these results provide insights into the effect of deposition variables (i.e., particle size, impact velocity, pore size, and pore depth) on particle retention that improves coating quality.

A method for determining the ductile damage parameters of high strength steels and weld metal

The microvoid based Gurson-Tvergaard-Needleman (GTN) model is a powerful tool for predicting ductile fracture behavior, and application of such model to steels and welds needs the identification of microvoid related damage parameters. Currently, there is no standard damage parameter identification method available. In this study the previously proposed complete Gurson model (CGM) where a physical void coalescence mechanism is incorporated into the GTN model is revisited. According to the CGM, the void nucleation process dictates ductile fracture. By adopting the cluster nucleation model with an effective initial void volume fraction as the only controlling parameter, a method is proposed to explicitly determine the effective initial void volume fraction from the strain at maximum load and strain at fracture of a specially designed notched tensile specimen. The proposed equation has been experimentally verified by applying to three high strength materials, including a X80 pipeline steel and associated weld metal, and a 15CrMo steel. A general procedure for damage parameter identification is also suggested. It is argued that the obtained effective initial void volume fraction can be treated as a type of material ductility indicator.