Gurson-Tvergaard-Needleman Model Research Articles

Ductile Failure Under Combined Tension and Shear: Simulation Using A Gurson-Type Porous Plasticity Model

A modification of the Gurson–Tvergaard’s yield function based on the micromechanics analysis of the plastic deformation of the porous materials containing spherical empty voids arranged in cubic arrays was proposed by Sean McElwain et al. [2006a, Yield criterion for porous materials subjected to complex stress states, Acta Materialia, 54, 1995–2002; 2006b, Yield functions for porous materials with cubic symmetry using different definitions of yield, Advanced Engineering Materials, 8, 870–876]. The derived yield function possesses in particular the distinctiveness to explicitly depend upon the third stress invariant. On another note, a phenomenological modification of the well-known Gurson–Tvergaard–Needleman (GTN) isotropic hardening model that incorporates damage accumulation under shearing was proposed by Nahshon and Hutchinson, [2008, Modification of the Gurson model for shear failure, European Journal of Mechanics A/Solids, 27, 1–17]. This model incorporates only one extra parameter to account for damage under shear-dominated loadings. In this work, the quasi-static ductile damage and failure behavior of a butterfly specimen is numerically studied using a further extension of this model based on both of the above modifications. To this end, a stress integration algorithm based on the general backwards-Euler return algorithm has been implemented into a finite element code. The simulations show that the proposed extended damage evolution model can capture both the tension and shear failure mechanisms. As long as the softening initiation of the considered specimen is not reached, the computational fracture results highlight the similarities and almost have perfect agreement with those provided by the use of the GTN model. This observation holds for tension-dominated deformation and shear-dominated deformation as well. However, for the later loading, discrepancy shows up at the onset of softening and especially as soon as the failure of material is triggered.

Anisotropic ductile fracture: experiments, modeling, and numerical simulations

The continuous hot rolling process induces anisotropy in the plastic yield and flow and results in an anisotropic ductile fracture. In this study, experiments, including uniaxial in-plane tension tests and shear tests of butterfly specimens along different material orientations, were performed, and microscopic observations were used to determine the differences in damage mechanisms. The Yld91 anisotropic yield stress was introduced into the extended isotropic Gurson-Tvergaard-Needleman (GTN) model, and the associated flow rule (AFR) and non-associated flow rule (NAFR) were adopted to formulate two anisotropic GTN models. Anisotropic GTN models were implemented in finite element software via user subroutines, and were used to predict the fracture initiation of Al2024-T351. For different plastic flow rules, the anisotropic parameters were calibrated using the anisotropic stress and Lankford coefficients. An inverse analysis with a two-stage optimization algorithm was adopted to calibrate the damage-related parameters. Moreover, an extended isotropic GTN model was adopted for comparison. The prediction accuracy of the proposed anisotropic GTN models was evaluated by analyzing the load responses and displacements at fracture for various specimens and material orientations. The good conformation between the experimental results and numerical predictions verifies the predictive ability of the proposed models to a certain degree. In addition, some suggestions and conclusions are provided for the formulation of an advanced anisotropic GTN model with enhanced accuracy.

Improvement of the return mapping algorithm based on the implicit function theorem with application to ductile fracture analysis using the GTN model

Elastic-plastic analyses based on finite element method are widely applied to simulate the nonlinear behavior of materials. When an analysis is conducted by implicit method, the stress values are generally updated with a time increment by using the so-called return mapping algorithm. This algorithm requires solving simultaneous nonlinear equations related to a constitutive model by an iterative solution scheme. In this study, we proposed a general method to reduce the number of unknowns in the return mapping algorithm based on the implicit function theorem. In addition, the proposed method was applied to the Gurson-Tvergaard-Needleman (GTN) model that considers the influence of damage due to nucleation and growth of microscopic void in materials in the simulation of the nonlinear behavior. After the GTN model with the proposed method was verified, elastic-plastic analysis was performed by the implicit method for a 4-point bending test of pipe with a through-wall crack. The numerical solution agreed well with the experimental result. In addition, the number of iterations to obtain converged solution was reduced. Thus, we concluded that the proposed method is useful for simulating nonlinear behavior, including void nucleation and growth in materials.

A two characteristic length nonlocal GTN model: Application to cup–cone and slant fracture

Ductile failure prediction is essential to avoid loss of structural integrity or to control crack propagation during forming processes. One of the main difficulties is the prediction of complex crack paths. This study proposes a nonlocal extension of a local Gurson–Tvergaard–Needleman (GTN) ductile damage model at finite strains able to capture cup–cone or slant fracture. The proposed model is based on an implicit gradient formulation which enables to solve the problem of spurious strain and damage localization. The model integrates two different material characteristic lengths, which are used to separately regularize damage by void growth and damage by damage nucleation. After parameter fitting using data for a line pipe steel, conditions to obtain converged solutions are studied, which can be used to select the mesh size in the localization band. With the appropriate mesh design, it was possible to study the effect of the characteristic lengths on the formation of cup–cone fracture and slant fracture. It is observed that, for a given specimen size, larger characteristic lengths favor flat crack advance. Similarly, for given material lengths, size effects can be predicted with small specimens being more prone to flat fracture. This paves the way to a more direct determination of material lengths by using homothetic specimens so as to obtain different crack paths.

Homogenized constitutive equations for porous single crystals plasticity

Ductile fracture through void growth to coalescence occurs at the grain scale in numerous metallic alloys encountered in engineering applications. Classical models used to perform numerical simulations of ductile fracture, as the Gurson–Tvergaard–Needleman model and its extensions, are relevant for the case of large voids compared to the grain size, in which a homogenization of the material behavior over a large number of grains is used. Such modeling prevents assessing the effects of microstructure on both crack path and crack propagation resistance. Therefore, homogenized constitutive equations for porous single crystals plasticity are proposed, featuring void growth and void coalescence stages, hardening and void shape evolution. An original numerical implementation based on the coupling of Newton–Raphson and fixed point algorithms is described. In order to assess the accuracy of the proposed model as well as another one described recently in the literature, an extended database of porous unit-cell simulation results is gathered, investigating the effect of crystallographic orientations and hardening behavior for a FCC material. Strengths and weaknesses of both models are detailed with respect to the reference simulations, leading to the definition of the validity domain of the current model and to pinpoint necessary refinements.

Less damage accumulation of aluminum alloy sheet during electromagnetic forming based on Gurson-Tvergaard-Needleman model

The formability of aluminum alloy sheet is usually improved during electromagnetic forming (EMF). Here, the ductility enhancement mechanism was investigated on the basis of Gurson-Tvergaard-Needleman (GTN) model. The parameters of GTN models under quasi-static tension and EMF conditions were respectively determined by inverse identification. For AA2024-O aluminum alloy sheet under quasi-static tension, the initial void volume fraction is identified as 0.006, the critical void volume fraction where voids begin to aggregate is 0.075, the void volume fraction of nucleating particles is 0.131 and the mean nucleation strain is 0.44. With the similar initial void volume fraction, the other parameters under EMF condition are determined as 0.045, 0.055 and 0.58. The evolution curve of void volume fraction with strain were compared under EMF condition and quasi-static tension. The results show that the total growth of void volume fraction is less under EMF condition than that under quasi-static tension. A box part with inclined flange was preliminary achieved by electromagnetic forming process. The GTN model was finally verified by comparing the numerical and experimental results.

Prediction of Fracture Behavior of 6061 Aluminum Alloy Based on GTN Model.

To determine the Gurson-Tvergaard-Needleman (GTN)damage model parameters of 6061 aluminum alloy after secondary heat treatment, the uniaxial tensile test was carried out on the aluminum alloy circular arc specimen, and the mechanical properties parameters and the load-displacement curve of aluminum alloy tube were obtained. With the help of the finite element reverse method, scanning electron microscope and a orthogonal test method, the GTN damage model parameters (f0, fN, fC, and fF) were calibrated, and their values were 0.004535, 0.04, 0.1, and 0.2135, respectively. Then the shear specimen and notch specimen were designed to verify the damage model, the results show that the obtained GTN damage model parameters can effectively predict the fracture failure of 6061 aluminum alloy after secondary heat treatment during the tensile process.

Gurson–Tvergaard–Needleman model guided fracture‐resistant structural designs under finite deformations

AbstractA finite strain shear modified Gurson–Tvergaard–Needleman (GTN) model based on multiplicative elastoplasticity, together with its implementation details, is presented. This GTN model which can simulate the loss of load‐carrying capacity of porous metals through nucleation, growth, shearing, and coalescence of voids is incorporated in an optimization framework for designing structures with optimal plastic energy dissipation capacity while satisfying prescribed constraints on material usage and damage. An adjoint method‐based analytical path‐dependent sensitivity analysis is presented that can be used with gradient‐based optimization algorithms. Using the proposed topology optimization formulations, the optimized designs exhibit well‐constrained fracture at the design displacements. Ultimate performance analyses of the optimized designs demonstrate that the fracture‐resistant designs can have higher ductility, ultimate strength as well as improved energy dissipation, as compared to the designs guided by von Mises plasticity where no fracture mechanisms are modeled. Moreover, due to finite deformations, a fracture can initiate at multiple locations and critical fracture locations can change during the loading process. In addition, different failure modes are revealed from different optimized designs under large deformations.

GTN 모델을 이용한 Hastelloy-X의 성형성 예측을 위한 수치해석 및 실험적 파손 기준 연구

Hastelloy-X material is widely used in aircraft engines, furnaces, and chemical process components due to its excellent oxidation resistance and high-temperature strength. In the case of making plate-shaped parts, its quality can be improved by forming limit diagram (FLD), which can predict crack and failure of a product. However, experimental-based FLD can be costly and time-consuming. In this paper, we tried to predict the formability of Hastelloy-X through FE simulations using the GTN (Gurson-Tvergaard- Needleman) model. First, appropriate values for GTN model parameters were derived from RSM using tensile test. FLD based on GTN model was then obtained by applying derived parameters to FLD simulations. These obtained parameters can be used to predict the formability of sheet metal undergoing severe deformation processes in aircraft and gas turbine engine manufacturing.

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.

Simulation of ductile tearing during a full size test using a non local Gurson–Tvergaard–Needleman (GTN) model

Ductile tearing of a full size precracked pipe is experimentally investigated. In order to model and interpret the test, the pipe material is characterized using smooth and notched tensile bars and precracked C(T) specimens. This experimental database is used to fit the parameters of the non local Gurson–Tvergaard–Needleman (GTN) proposed in Zhang et al. (2018) and Chen et al. (2020). The model is used in finite element simulations using specific elements allowing for the control of strain/damage localization as well as volumetric locking. Mesh size independence is checked on notched tensile bars. The model is then able to represent the early stages of crack propagation in the pipe. In particular, experimentally observed crack branching is reproduced, whereas this appeared much more difficult to obtain using a local GTN model.

Modeling the anchoring and performance of downhole equipment using an extended Gurson model

In oil and gas (O&G) exploration the well casing, in the form of a long steel tube, maintains the opening of the drilled well hole. Mechanical equipment is often inserted into the well for the purpose of well monitoring, pressure control and various operations. This downhole equipment may be mechanically connected to the pipe casing by the outward radial motion of anchoring teeth such that the inner wall casing is indented. The connection between the tool and the casing must support significant mechanical loads in the longitudinal (axial) direction of the casing, i.e. transverse to the direction of indentation, while minimizing the indentation depth in order to preserve the stiffness and strength of the casing. Consequently, a determination of the ultimate strength of the connection is of critical importance. Failure of this connection involves intense shear of the inner wall of the casing, akin to a machining operation. The critical load for axial slip can be determined experimentally or numerically (or by combination of both). In this study, detailed simulations are performed using the shear-extended GTN (Gurson-Tvergaard-Needleman) model. The choice of model is motivated by the need to accurately the extensive plastic deformation associated with indentation as well as shear-dominated ductile failure on a sub-millimeter scale.The shear-extended GTN model requires a careful calibration of the model parameters by an accurate measurement of the material response. Accordingly, the casing steel was characterized by appropriate measurements under a range of stress states. The calibrated model was used to investigate an idealized two-dimensional representation of the anchoring problem, with a focus on the effect of indentation depth upon connection strength. Both the indentation of the casing inner wall by the anchoring teeth and the subsequent shear of the casing wall were simulated in detail to determine the load required to initiate and progress slip of the anchoring teeth. The results of these analyses show that the connection strength increases linearly with increasing indentation depth.

Micromechanics-based modeling of plastic and ductile fracture of aluminum alloy 2024-O

In this study, the plastic deformation behavior at a large strain range, as well as the ductile damage and fracture of aluminum alloy 2024-O materials, were investigated under quasi-static conditions. The plasticity of the material, including a large deformation, was characterized by conducting uniaxial tension and balanced-biaxial bulging tension tests. This condition was reproduced using the Hershey–Hosford nonquadratic isotropic plastic yielding criterion and combined Hollomon/Voce strain-hardening model. The ductile damage and fracture were analyzed using notched plane strain and in-plane shear experiments by incorporating a wide range of stress states. Finally, multiaxial Nakajima tests with a round sphere punch were conducted to assess the material formability. Simultaneously, finite element predictions of the ductile fracture behavior were performed using micromechanics-based material models, such as modified Gurson–Tvergaard–Needleman (GTN) and Hosford − Coulomb models. The force–displacement characteristics and surface strain distributions measured using the experimental approach were compared with the simulated results. The results indicated that the modified GTN model provided better prediction of plasticity and ductile damage behavior of aluminum alloy 2024-O materials.

Study on Fracture Assessment for BWR Reactor Pressure Vessel Steel by GTN model

In the JSME fitness-for service code, fracture evaluation methodology based on linear elastic fracture mechanics is provided for reactor pressure vessel (RPV) components by considering brittle fracture due to neutron irradiation in the RPV beltline region. However, in order to make a rational fracture evaluation for the RPV component such as bottom head component of boiling water reactor (BWR), where irradiation embrittlement is not concerned, it is necessary to consider the applicability of the ductile fracture evaluation methodology consistent with material fracture behavior. In this study, the applicability of the damage mechanics analysis method using Gurson-Tvergaard-Needleman (GTN) model, which is a numerical analysis method for ductile failure, was investigated for RPV bottom head component. Mechanical properties tests and fracture tests with plate specimens were performed using RPV law alloy steel (LAS) material. GTN model parameters of RPV LAS material that can reproduce stress-strain curve and load-displacement curve were determined. Fracture analyses of the plate specimens were performed using determined parameters as well. The load-Crack Mouth Opening Displacement (CMOD) curves and fracture behavior of the fracture tests were compared with the analyses results. The analyses predicted the maximum loads of the tests within an error of 4% and the fracture behavior between the tests and analyses was consistent. The results in this study clearly supported the applicability of the GTN model to RPV bottom head ring component.

Void-growth computational analysis in elastic-plastic porous materials

This study aims to model the effective mechanical response of highly porous materials using computational homogenisation. A two-phase material is considered here in the form of a von Mises elastic-plastic matrix that includes spherical identical voids. A wide range of void volume fractions from 0.1% to 24% is investigated. The representative volume element principle is adopted to determine the effective yield surface of each case. Its representativeness is checked from a statistical point of view and the mechanical response is set for each porosity rate considering a wide range of stress triaxiality ratios. The relation between void volume fraction and stress triaxiality is discussed and an analysis based on the unit cell computation is proposed to examine the void shape evolution according to these parameters. Therefore, an improvement of the Gurson–Tvergaard–Needleman (GTN) model considering a wide range of void volume fractions is presented. The computational data are subsequently used to enhance the original GTN model. The parameter q1 is translated as a linear function of the porosity while q2 is kept equal to 1. This makes the model simpler and more suitable for a wide range of porous materials.

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.

Hot damage evolution in a high strength aluminum alloy during hot forming: a study using the Gurson–Tvergaard–Needleman model

The investigation on the formability of 7075-T6 aluminum alloy at elevated temperatures is significant due to its low plasticity at room temperature. Meso-Damage mechanics suggests that the growth and accumulation of micro-voids is an important factor that leads to material damage, fracture, and affects its formability. In this work, the Gurson–Tvergaard–Needleman (GTN) model was used to investigate the damage evolution of the 7075-T6 aluminum alloy during the hot forming process. The effects of different temperatures and strain rates on the formability were investigated through uniaxial hot tensile tests. The parameters of the Gurson–Tvergaard–Needleman (GTN) model were inverse-calibrated using the Central Composite Design (CCD)-Response Surface Method (RSM)-Genetic Algorithm (GA). Control variable method was used to explore the effect of each damage parameter on the fracture initiation and evolution. The results showed that the calibrated Gurson–Tvergaard–Needleman (GTN) model well predicted the high-temperature damage of the 7075-T6 aluminum alloy at 300–450 °C. Predicted necking and fracture volume fractions of voids were less than 3% error from experimental results. Initial void volume fraction (f0) had little effect on damage. Increasing void nucleation volume fraction (fN) significantly advanced the necking and fracture of the material. An increase in the critical void volume fraction (fC) and fracture void volume fraction (fF) resulted in higher peak stresses and fracture strains.

A novel method to uniquely determine the parameters in Gurson–Tvergaard–Needleman model

AbstractThe Gurson–Tvergaard–Needleman (GTN) model is promising in failure prediction as it takes the micromechanical behavior of ductile metals into consideration. However, its engineering applications have scarcely progressed due to the difficulty in determining its eight strongly coupled parameters. Taking the physical background of GTN model into consideration, a set of methods was established to determine all parameters in the GTN model. The knowledge of continuum damage mechanics was introduced to experimentally determine the development of void volume fraction through an interrupted uniaxial tensile test, by which the three parameters regarding void nucleation were analytically derived. Other parameters in the GTN model were also uniquely determined through a joint use of the chemical composition analysis, the cell model analyses, and the inverse finite element method. Reliability of this novel parameter determination method was verified through failure predictions on both cracked and un‐cracked specimens of STPT410.

FCG Modelling Considering the Combined Effects of Cyclic Plastic Deformation and Growth of Micro-Voids.

Fatigue is one of the most prevalent mechanisms of failure. Thus, the evaluation of the fatigue crack growth process is fundamental in engineering applications subjected to cyclic loads. The fatigue crack growth rate is usually accessed through the da/dN-ΔK curves, which have some well-known limitations. In this study a numerical model that uses the cyclic plastic strain at the crack tip to predict da/dN was coupled with the Gurson–Tvergaard–Needleman (GTN) damage model. The crack propagation process occurs, by node release, when the cumulative plastic strain reaches a critical value. The GTN model is used to account for the material degradation due to the growth of micro-voids process, which affects fatigue crack growth. Predictions with GTN are compared with the ones obtained without this ductile fracture model. Crack closure was studied in order to justify the lower values of da/dN obtained in the model with GTN, when compared with the results without GTN, for lower ΔK values. Finally, the accuracy of both variants of the numerical model is accessed through the comparison with experimental results.

Numerical Study about the Influence of Superimposed Hydrostatic Pressure on Shear Damage Mechanism in Sheet Metals

It is generally accepted that the superimposed hydrostatic pressure increases fracture strain in sheet metal and mode of fracture changes with applying pressure. Void growth is delayed or completely eliminated under pressure and the shear damage mechanism becomes the dominant mode of fracture. In this study, the effect of superimposed hydrostatic pressure on the ductility of sheet metal under tension is investigated using the finite element (FE) method employing the modified Gurson–Tvergaard–Needleman (GTN) model. The shear damage mechanism is considered as an increment in the total void volume fraction and the model is implemented using the VUMAT subroutine in the ABAQUS/Explicit. It is shown that ductility and fracture strain increase significantly by imposing hydrostatic pressure as it suppresses the damage mechanisms of microvoid growth and shear damage. When hydrostatic pressure is applied, it is observed that although the shear damage mechanism is delayed, the shear damage mechanism is dominant over the growth of microvoids. These numerical findings are consistent with those experimental results published in the previous studies about the effect of superimposed hydrostatic pressure on fracture strain. The numerical results clearly show that the dominant mode of failure changes from microvoid growth to shear damage under pressure. Numerical studies in the literature explain the effect of pressure on fracture strain using the conventional GTN model available in the ABAQUS material behavior library when the mode of fracture does not change. However, in this study, the shear modified GTN model is used to understand the effect of pressure on the shear damage mechanism as one of the individual void volume fraction increments and change in mode of fracture is explained numerically.