Gurson-Tvergaard-Needleman Research Articles

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.

Effect of process parameters on porosity defects in Al-Si alloy hot rolling

Hot-rolled Al-Si alloy sheets are used to be formed Al alloy welding additions and cladding materials that are widely used in the aviation, automotive, and air conditioning industries. However, if parameters of hot-rolling process are not properly selected, porosity defects during casting will lead to cracks or fractures in Al-Si alloy sheets. This study based on meso-damage theory and established a damage equation describing porosity defects in the hot rolling process. The parameters of GTN (Gurson-Tvergaard-Needleman) void defect evolution, including the volume fraction of voids in different periods, the plastic equivalent variation of void nucleation, the standard variance of equivalent variation of void nucleation, and the correction coefficient of the material, are determined in this study. A finite element model of the porosity defects is developed based on the determined parameters. The finite element method is used to analyze the effect of different process parameters on the porosity defects and cracks in Al-Si alloy sheets during hot rolling, then we performed the hot rolling test to validate the results. The results show that the void stress and diameter are reduced and the quality of porosity defects is improved by decreasing rolling reductions and increasing the temperature. The optimized process parameters were a 20% depression and a temperature of 550°C.

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.

Gradient strengthening effects in mode I tearing of ductile plate at the engineering scale

The present study aims to quantify the influence of void size effect on crack initiation and growth in mode I tearing of large ductile plates. Specifically, the aim is to demonstrate how size effects influence the transition from crack initiation to steady-state tearing and reveal the evolution in both the traction-separation relation and the fracture energy dissipated in the tearing process when related to large-scale cohesive modeling. The study investigates mode I tearing by adopting the gradient enriched Gurson–Tvergaard–Needleman (GTN) model by Niordson and Tvergaard (2019), where the novelty lies in accounting for strain gradient hardening near growing micro-voids in relation to large-scale plate tearing. The steady-state crack growth conditions are compared to a 2D plane strain model setup, while the transition from crack initiation to steady-state is analyzed using full 3D plate tearing calculations. A discussion about the 2D versus 3D models’ capability, their differences, and agreement is presented. The results are related to the traction-separation relations fit for efficient large-scale simulations, e.g., using cohesive zone modeling. The present study shows that the material length parameter incorporated into the constitutive model has a negligible impact on the onset of plate thinning (or necking) but delays the onset of shear localization and, thus, increases the total cohesive fracture energy.

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.

Numerical simulation of fracture behavior for the pipeline with girth weld under axial load

The failure accidents of the pipeline caused by girth weld problems occur frequently in recent years. However, the fracture mechanism and behavior of girth weld in pipeline are not clear at present. Accordingly, based on Gurson-Tvergaard-Needleman (GTN) damage model, a three-dimensional full-scale model of the X80 pipeline with girth weld was established in this paper, in which the differences of material properties in base, weld, and heat-affected zone (HAZ) were considered. Subsequently, the fracture process of the pipeline with girth weld under uniaxial tensile load was obtained. On this basis, the fracture behavior and the causes of failure of the pipeline were analyzed. The elongation and fracture strain were respectively defined to quantitatively describe the fracture toughness of the pipeline. The results showed that the crack initiated at the junction of the weld and HAZ in the inner wall of the pipeline due to material softening of HAZ, and then the crack propagated from the inner wall to the outer wall until forming a penetrated crack. Lastly, the crack grew rapidly along the circumferential direction, resulting in the overall failure of the pipe. Compared to the pipeline without weld, there was a smaller value of the elongation and fracture strain in the pipeline with girth weld. The elongation and fracture strain of the pipeline without weld was 26.49% and 0.78, and that of the pipeline with girth weld was 4.73% and 0.18, which was reduced by 82% and 77% respectively.

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.

Development of a damaged viscoplasticity model with preliminary application in Zircaloy cladding material

Structural integrity of nuclear fuel cladding is the most important factor limiting the life and the safety of nuclear fuels. However, a rigorous evaluation of the damage and fracture behavior of the cladding is hindered by the absence of a constitutive model which can reasonably describe the complex mechanical behavior of the metallic cladding material. In this paper, a damaged viscoplasticity model is proposed by combing the damaged plasticity model, i.e., the classical Gurson-Tvergaard-Needleman (GTN) model, and a general viscoplasticity model. After instantiating the general viscoplasticity model by the thermal creep, the irradiation creep and the irradiation growth models, the damaged viscoplasticity model can thus describe the damaged viscoplastic behavior of Zircaloy cladding material. In addition, the model can describe the hydrogen embrittlement by correlating the damage parameters with the hydride content. A stress updating algorithm is proposed to implement the model within the general finite element software, i.e., ABAQUS. Then the model is evaluated by parametric studies. The typical failure behavior of the Zircaloy cladding is also investigated by using the developed constitutive model.

Damage Analysis of Third-Generation Advanced High-Strength Steel Based on the Gurson–Tvergaard–Needleman (GTN) Model

The third generation of advanced high-strength steels (AHSS) brought attention to the steel and automotive industries due to its good compromise between formability and production costs. This work evaluated a third-generation AHSS (USS CR980XG3TM) through microstructural and X-ray diffraction (XRD) analyses, uniaxial tensile and plane-strain tension testing, and numerical simulations. The damage behavior of this steel is described with the Gurson–Tvergaard–Needleman (GTN) model using an identification procedure based on the uniaxial tensile and initial microvoids data. The microstructure of the CR980XG3TM steel is composed of ferrite, martensite–austenite islands, and retained austenite with a volume fraction of 12.2%. The global formability of the CR980XG3TM steel, namely the product of the uniaxial tensile strength and total elongation values, is 24.3 GPa%. The Lankford coefficient shows a weak initial plastic anisotropy of the CR980XG3TM steel with the in-plane anisotropy close to zero (−0.079) and the normal anisotropy close to unity (0.917). The identified GTN parameters for the CR980XG3TM steel provided a good forecast for the limit strains defined according to ISO 12004-2 standard from the uniaxial tensile and plane-strain tension data.

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.

GTN Damage Modelling of the AA6063 Using Image Processing

In this paper, an innovative way of calculating the Gurson–Tvergaard–Needleman parameter has been developed for AA 6063. AA 6063 is an aluminum alloy comprising the alloying ingredients magnesium and silicon. The Aluminum Association maintains the standard that governs its composition. It has strong mechanical properties and may be heat treated and welded. Image processing technique has been used to calculate the damage constant for the AA 6063. The image of the sample has been taken under a microscope of undeformed and fractured material. Then the images are analyzed using the Open CV tool in a python open-source environment. The initial and final void fraction of the sheet has been calculated. Damage models, particularly the Gurson–Tvergaard–Needleman (GTN) model, are widely used in numerical simulation of material deformations. Each damage model has some constants which must be identified for each material. The direct identification methods are costly and time-consuming. A combination of experimental, numerical simulation and optimization have been used to determine the constants in the current work. Numerical simulation of the dynamic test was performed utilizing the constants obtained from quasi-static experiments. The results showed a high precision in predicting the specimen's profile in the dynamic testing.

Damage evolution of 7075 aluminum alloy basing the Gurson Tvergaard Needleman model under high temperature conditions

Based on the Gurson-Tvergaard-Needleman (GTN) damage model, the damage evolution and ductile fracture of 7075 aluminum alloy sheets during the tensile process were predicted. First, the true stress–strain curve and micro morphology of 7075 aluminum alloy at 310 °C∼460 °C were obtained using ultra-high temperature confocal microscope with tensile and compression functions, and the damage characteristics of the fracture position of the tensile specimen were observed by Scanning Electron Microscope (SEM). Then, using the finite element reverse calibration method, the identification method of GTN damage parameters under high temperature was systematically explained and the damage characteristic parameters of 7075 aluminum alloy under high temperature (310 °C∼460 °C) were obtained. The influence of fluctuations in damage parameters on the macroscopic mechanical behavior of materials and the influence of temperature on the value of material damage variables were analyzed. Finally, the void volume fraction of 7075 aluminum alloy at 360 °C was obtained by microscopic observation and compared with the void volume fraction obtained by the finite element reverse calibration method. The results show that the effect of temperature on void volume fraction is basically the same as that of plasticity. The change of void volume fraction has a greater impact on the mechanical properties of the material. There is a small gap between the void volume fraction obtained using the microscopic observation method and the void volume fraction obtained using the finite element reverse calibration method, which verifies the accuracy of the finite element reverse calibration method.