Parameters Of Gurson-Tvergaard-Needleman Model Research Articles

Numerical Analysis of the Damage Evolution of DP600 Steel Using Gurson–Tvergaard–Needleman Model

This research models the ductile fracture in DP600 steel sheets by using Gurson–Tvergaard–Needleman (GTN) damage model with experimentally obtained parameters. Uniaxial tensile tests are carried out to determine the deformation behavior of the material and obtain GTN model parameters. Further, SEM investigations on the fractured surface of the material display a dimpled surface, which indicates ductile fracture. Also, density measurements are carried out to define the critical and final volume fractions. A finite element model (FEM) of the tensile testing is developed. Then, the experimental parameters of the GTN model are verified by comparing load–displacement curves and porosity values for different zones. The results put forth that the experimental parameters can be used to model the deformation behavior of the DP 600 steel. Further, the growth of total void volume fraction increases exponentially, attributed to the increasing value of stress triaxiality. Also, the shift in the void volume fraction after the critical void volume fraction is explained with the void coalescence. Finally, the thickness of the sheet has a power‐law relationship and the porosity level of the material can be predicted for a known thickness value.

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.

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.

Determination of GTN Model Parameters Based on Artificial Neutral Network for a Ductile Failure

The Gurson – Tvergaard – Needleman (GTN) mechanical model is widely used to predict the failure of materials based on laboratory specimens, direct identification of Gurson – Tvergaard – Needleman parameters is not easy and time-consuming, and the most used method to determine them is the combination between the experimental results and those of the finite elements, the process consists of repeating the simulations several times until the simulation data matches the experimental data obtained at the specimen level.This article aims to find GTN parameters for the Compact Tension (CT) and Single Edge Tensile Test (SENT) specimen based on the Notch Specimen (NT) using the Artificial Neural Network (ANN) approach. . This work presents how the ANN could help us determine the parameters of GTN in a very short period of time. The results obtained show that ANN is an excellent tool for determining GTN parameters.

Evaluation of impact ductile fracture behaviour of low carbon austenitic stainless steel SUS304L using damage mechanics model

To clarify the applicability of the Gurson-Tvergaard-Needleman (GTN) model for impact ductile fracture behaviour, SHB test was reproduced by finite element analysis (FEA). The strain-rate dependence of the strength for austenitic stainless steel JIS SUS304L was obtained by tensile tests at quasi-static strain rate and impact strain rate. The CowperSymonds power law, which takes into the strain-rate dependence of strength, and the GTN model implemented in the commercial FEA code were used to simulate for impact ductile-fracture behaviour. GTN model parameters were determined by minimizing the difference between the simulated and measured stress-strain curve using response surface method. SHB test was simulated using GTN model obtained from quasi-static tensile test result. Simulation results did not occur the necking and fracture on the specimen. The fracture surfaces were observed by SEM micrograph. The appearance of ductile fracture since dimples are observed, regardless of the strain rate. It is necessary to adjust the parameter to accelerate the nucleation of the void. By identifying the GTN parameters in consideration of the strain rate dependence including impact strain rate. It would be possible to improve the simulation accuracy of impact ductile fracture behaviour.

A machine learning based sensitivity analysis of the GTN damage parameters for dynamic fracture propagation in X70 pipeline steel

The Gurson–Tvergaard–Needleman (GTN) damage model is widely used to predict ductile failure initiation and propagation. However, the material-dependent parameters can show a significant spread when determined for the same steel grade material. Different calibration procedures and optimisation processes cause a significant variation in the obtained parameter values. Furthermore, there is no clear consensus on which parameters require calibration. In this study, the influence of the material-dependent parameters used to model the dynamic ductile fracture behaviour of X70 grade pipeline steel is investigated. A sensitivity analysis is performed on a finite element model of a Charpy V-Notch (CVN) specimen. Seven GTN model parameters are considered in a total of 70 simulations. A feedforward back-propagating artificial neural network (ANN) is constructed and trained using data obtained through the numerical simulations. A connected weights (CW) algorithm allows to determine the relative influence of each parameter on the fracture energy. It was observed that the void growth acceleration factor plays an important role with respect to the parameter influences. Remarkably, the mean nucleation strain, \( \varepsilon_{N} \) has the highest relative importance whilst the critical void volume fraction, \( f_{c} \)—which is considered as a crucial damage parameter—showed the smallest influence when the acceleration factor is low. On the contrary, when considering a high acceleration factor, \( f_{c} \) becomes the most influential parameter. Based on the obtained importance for each parameter, it is suggested that parameters \( f_{0} \), \( f_{c} \), \( f_{F} \), and \( f_{N} \) should be selected for calibration in each individual application. Finally, the applied machine learning approach is used to predict the fracture energy for a given set of damage parameters for X70 grade steel. It is observed that the trained neural network is able to provide a satisfactory approximation of the CVN fracture energy.

Determination of the tensile and fracture properties of ductile materials by small punch testing

ABSTRACT The uniaxial tensile and fracture properties are the basic data for the structural integrity assessment of ductile material. In this study, the stress-strain relations of ductile materials are predicted by the SPT-related stress-strain relation (SPT-SR) model directly through SPT experiment, which agree with the relations determined by the finite-element-analysis aided testing (FAT) method. Further, the experimental procedures of SPT are simulated by combining the Gurson-Tvergaard-Needleman (GTN) model and the predicted stress-strain relations. The parameters of GTN model can be determined when the simulated load-displacement curves of SPT specimens coincide with the experimental results. Finally, the ductile crack propagation behaviors of the single edge-notched bending (SEB) specimens are simulated utilizing the calibrated GTN model, and the corresponding J resistance curves are successfully predicted via the normalization method.

Experimental Investigation of GTN model parameters of 6061 Al alloy

This research experimentally determines the Gurson-Tvergaard-Needleman (GTN) model damage mechanics parameters for 6061 Al alloys. Five different heat treatment conditions including T4 (natural aging) and T6 (peak strength) conditions of 6061 Al alloy were investigated. The GTN parameters considering different heat treatment conditions of the alloy were obtained by tensile tests. Scanning electron microscope (SEM) micrographs were used as inputs to determine initial and nucleated volume fractions. SEM and energy dispersive X-ray spectrography (EDX) analyses also revealed that the second-phase precipitates are the origin of the incipient voids. SEM analyses enabled the fractographic investigations where the primary and secondary voids were exhibited and thus showing nucleation strain. Density measurements clarify the critical and final void volume fractions and the standard deviation of the nucleated void volume fraction distribution. The results show that the void volume fraction increases exponentially along with increasing effective tensile plastic strain. Hence, a total of six different GTN parameters have been identified experimentally. Finite element method simulations based on GTN damage model were performed to verify the GTN model parameters. The results show that the experimentally obtained GTN model parameters could be used when performing tensile deformation simulations of 6061 Al alloys fabricated with different heat treatment conditions.

Constitutive Modeling of Porous Shape Memory Alloys Using Gurson–Tvergaard–Needleman Model Under Isothermal Conditions

Based on the Gurson–Tvergaard–Needleman (GTN) model, a constitutive relationship considering both the effects of strain hardening and hydrostatic stress for porous shape memory alloys (SMAs) is proposed. To capture the relationship between microscopic and mesoscopic behaviors, a representative volume element (RVE) containing an array of spherical voids is presented. In this paper, an approximate solution including strain hardening exponent [Formula: see text] is deduced by considering the porous SMA as a two phase composite with the SMA matrix and the second phase representing voids. The model parameters, [Formula: see text] and [Formula: see text], accounting for interactions between voids are investigated to take into account their influences on strain hardening, critical phase transformation stress and yield surface. In addition, the evolution equations of phase transformation are derived and then applied to the simulation of porous Ni–Ti SMAs with a porosity of 13%. Using the calibrated GTN model parameters, the critical phase transformation stress closer to experimental data is obtained. The predictions of stress–strain curve by the proposed constitutive model are found to be in excellent agreement with published experimental data and finite element results. The results prove that the model is capable of reproducing the features of porous SMAs such as superelasticity, tensile-compressive asymmetry and internal loops under uniaxial even combined loading conditions. A conclusion is drawn that the present constitutive relationship is powerful and useful for the analysis of porous SMAs.

Ductile crack growth behaviors at different locations of a weld joint for an X80 pipeline steel: A numerical investigation using GTN models

The finite element method (FEM) based on the Gurson–Tvergaard–Needleman (GTN) model was used to investigate the ductile crack growth behaviors at different weld joint locations of X80 pipeline steel. As the result of the welding process, the X80 weld joints are inhomogeneous and can be divided into different zones (base metal, weld metal and heat affected zones), with different material properties and ductile crack growth resistance characteristics. By fitting the experimental results of uniaxial tension and single-edge notched bending (SENB) tests for specific zones, the GTN model parameters were calibrated in consideration of the inhomogeneity of the weld joint. The calibrated GTN models were then used to analyze the ductile crack growth behaviors in single-edge notched tension (SENT) tests at different locations of the weld joint. In addition, the effect of T-stress on the crack propagation at different locations was also studied using the small-scale yield model. It is demonstrated the calibrated GTN models are capable of predicting crack growth resistance curves at different weld joint locations, under different constraint conditions.

Application of a GTN Damage Model Predicting the Fracture of 5052-O Aluminum Alloy High-Speed Electromagnetic Impaction

An increasing demand exists within the automotive industry to utilize aluminum alloy sheets because of their excellent strength-weight ratio and low emissions, which can improve fuel economy and reduce environmental pollution. High-speed automobile impactions are complicated and highly nonlinear deformation processes. Thus, in this paper, a Gurson-Tvergaard-Needleman (GTN) damage model is used to describe the damage behavior of high-speed electromagnetic impaction to predict the fracture behavior of 5052-O aluminum alloy under high-speed impaction. The parameters of the GTN damage model are obtained based on high-speed electromagnetic forming experiments via scanning electron microscopy. The high-speed electromagnetic impaction behavior process is analyzed according to the obtained GTN model parameters. The shape of the high-speed electromagnetic impaction in the numerical simulations agrees with the experimental results. The analysis of the plastic strain and void volume fraction distributions are analyzed during the process of high-speed impact, which indicates the validity of using the GTN damage model to describe or predict the fracture behavior of high-speed electromagnetic impaction.

Damage identification parameters of dual-phase 600–800 steels based on experimental void analysis and finite element simulations

In this work, the damage behavior of cold-rolled zinc-coated dual-phase steel sheets 600 and 800 grades was evaluated by means of standard uniaxial tensile testing, microstructural characterization and finite element modeling. The void formation in both steels was investigated as a function of the plastic strain level from digital image processing of scanning electron micrographs to quantify the average void size and to determine the corresponding measures of void density, void area fraction and void aspect ratio. Based on the void analysis and the experimental uniaxial tensile test data, a four-step procedure is proposed to identify the parameters of the Gurson–Tvergaard–Needleman (GTN) damage model. Bearing in mind the non-uniqueness of the GTN model parameters, 3D finite element simulations using a single element and an 1/8 symmetry uniaxial tensile specimen model were performed in a systematic manner to investigate the role of both nucleation and failure parameters on the uniaxial behavior. At low straining levels, most of the void initiated by debonding of globular aluminum-oxide inclusions identified by EDS in both dual-phase steels. At higher straining levels, the void density evolution is found to be more pronounced in DP600 steel owing to the faster void nucleation rate at the ferrite grain boundaries. A good agreement between predictions and experimental load-elongation is achieved allowing for the identification of the full set of GTN damage model parameters of both DP600 and DP800 steels. The proposed damage calibration of dual-phase steels can be very helpful in simulations of practical sheet metal forming processes.

Plastic deformation and fracture behavior of X65 pipeline steel: Experiments and modeling

In order to respond to the increasing demand of oil and gas, pipeline steel has been noticeably developed to enhance both efficiency and performance of fuel transportation. Hereby, metallurgical and mechanical properties of such steel have been continuously improved. Due to the complex microstructure of advanced pipelines more accurate failure prediction is thus necessary. In this work, the plastic deformation and damage behavior of pipeline steel grade X65 were investigated experimentally and numerically by means of the Gurson-Tvergaard-Needleman (GTN) damage mechanics approach. The differences between observed microstructure characteristics of the center and skin region of examined pipe were taken into account. Initially, FE simulations of tensile test for materials in both pipe regions were conducted using representative volume element (RVE) models, in which the characteristics of existing phases could be incorporated. It was seen that the effective true stress-strain responses calculated by the RVE simulations agreed well with the experimental results. Subsequently, the GTN model parameters were determined by metallographic considerations and RVE simulations. The engineering stress-strain curves until fracture of the steel were fairly predicted by the macroscopic simulations coupled with the damage model. Furthermore, the obtained GTN parameters were verified by a quasi-static fracture mechanics test, in which the single edge notch tension (SENT) specimens taken from both longitudinal and transverse direction of pipe were investigated. Experimental and predicted local stress and strain distributions of SENT specimens for different pipe regions were compared and analyzed.

Forming limit diagram prediction of 6061 aluminum by GTN damage model

Forming limit diagram (FLD) is one of the formability criteria which is a plot of major strain versus minor strain. In the present study, Gurson-Tvergaard-Needleman (GTN) model is used for FLD prediction of aluminum alloy 6061. Whereas correct selection of GTN parameters’ is effective in the accuracy of this model, anti-inference method and numerical simulation of the uniaxial tensile test is used for identification of GTN parameters. Proper parameters of GTN model is imported to the finite element analysis of Nakazima test for FLD prediction. Whereas FLD is dependent on forming history and strain path, forming limit stress diagram (FLSD) based on the GTN damage model is also used for forming limit prediction in the numerical method. Numerical results for FLD, FLSD and punch’s load-displacement are compared with experimental results. Results show that there is a good agreement between the numerical and experimental results. The main drawback of numerical results for prediction of the right-hand side of FLD which was concluded in other researchers’ studies was solved in the present study by using GTN damage model.

Application of the GTN model to ductile crack growth simulation in through-wall cracked pipes

This paper presents ductile fracture simulation using the GTN (Gurson-Tvergaard-Needleman) model of through-wall cracked STPT410 carbon steel pipe test under pure bending. Three issues related to practical application are addressed; (i) how to determine the parameters in the GTN model from fracture toughness data, (ii) how to incorporate the element-size effect to the GTN model and (iii) the effect of the crack-tip mesh design on determination of the GTN model parameters. It is found that determined values of the parameters depend on the crack-tip mesh design and the finite element size used in simulation. The split of the crack tip element into two makes parameter determination easier and gives better simulation results, but is difficult to apply to three-dimensional surface crack problems.

Parameter Identification of GTN Model Using Response Surface Methodology for High-Strength Steel BR1500HS

In order to investigate the damage evolution of ultra-high-strength steels at different temperatures, a series of the uniaxial tensile tests were carried out at different temperatures (20-800 °C) with a constant true strain rate (1 s−1). And then, two different deformation mechanisms were employed to describe the flow behaviors of BR1500HS. It is found that dynamic recrystallization (DRX) occurs during the deformation process at high temperatures (600-800 °C), while the tensile flow behaviors exhibit a very long work hardening period before a short flow softening stages without DRX at lower temperatures of 20-400 °C Furthermore, the Gurson-Tvergaard-Needleman (GTN) damage model was employed in this work to evaluate the ductile damage phenomena of BR1500HS. To determine the four vital parameters in GTN model, several numerical simulations were designed by central composite design and conducted by finite element simulation, and then the error evaluation functions (R) were established using four GTN parameters. Thereafter, the four parameters of GTN model were determined along with four minimum values of R by use of response surface methodology (RSM) and least square method. The results show that temperature affects the microvoid volume fraction significantly. Additionally, the parameters of GTN model were applied in the finite element simulation model and a comparison between the simulation results and the scanning electron microscopic observations was conducted.

Ductile fracture in thin sheet metals: a FEM study of the Sandia fracture challenge problem based on the Gurson–Tvergaard–Needleman fracture model

In this paper, the Gurson–Tvergaard–Needleman (GTN) fracture model has been implemented in a 3D nonlinear finite element framework to investigate ductile failure. The simulation consists of both model parameter calibrations and predictions based on the experimental configurations that were described in the Sandia fracture challenge in 2012. The goal is to test the robustness of the GTN model in predicting crack initiation and propagation in a ductile structural stainless steel (15-5 PH). It has been observed that the predicted load drops at crack initiation agree well with the experimental data. Both the simulation and experiments reveal that cracks always initiate in the subsurface. The observed crack path in the experiments, however, is not unique and is strongly influenced by the geometric variations in the specimen introduced in the fabrication process. The crack path is quite sensitive to the relative location of pre-existing features (notch and holes) in this challenge problem, and a very small variation can potentially lead to different path, hence affecting the ductile failure pattern significantly. Variations in the crack path are also observed in the simulation with different choices of GTN model parameters that control the void nucleation and growth behavior.

Gurson model parameters for ductile fracture simulation in ASTM A992 steels

ABSTRACTThis study is concerned with the modelling the ductile fracture in ASTM A992 steels using the Gurson‐Tvergaard‐Needleman (GTN) model for high stress triaxiality regime. The GTN model for ASTM A992 structural steels is calibrated from the experiments performed on axisymmetrically notched tensile specimens. The experiments are designed to obtain a range of stress triaxiality and different fracture initiation locations. The non‐uniqueness in the constitutive parameters of the GTN model is illustrated in this study. The choice of a unique set of GTN constitutive parameters is made by choosing the nucleation strain (ɛN) as a material constant. The process of estimating this material specific nucleation strain is provided. All the other GTN model parameters corresponding to the material specific nucleation strain (ɛN) are evaluated to best fit the experimental results. The calibrated GTN model is shown to predict the load displacement behaviour, ductility and fracture initiation locations in the notched specimens. The calibrated GTN parameters are used to successfully predict the ductility of structural components: (a) bars with a hole; (b) plate with reduced section and (c) plate with holes; that are typically found in structural engineering applications.

Comparison of Experimental and Numerical Failure Criterion for Formability Prediction of Automotive Part

The ability to predict the forming severity with respect to crack and failure is essential to analysis of sheet metal forming process. The forming limit diagram (FLD) is commonly used to gauge the formability of sheet metal. In this article, forming limit diagrams of cold rolled carbon steel (JIS-SPCC), which widely used to produce the parts of automobile, are obtained by performing experiment and FE simulation with the Nakajima-test. By using the GTN (Gurson-Tvergaard -Needleman) damage mechanical model, a failure criterion based on void evolution was examined in this FE simulation. The parameters of GTN model are determined through comparison of experimental and numerical result with Nakajima-test. These parameters acceptably can be used in GTN model using given material. In application case, the reliability of the GTN model for failure criterion in simulation with automotive part was confirmed.

Failure analysis of DP600 steel during the cross-die test

Dual-phase (DP) steels are suitable candidates for automotive application due to their high strength and high initial work hardening rate. The forming characteristics and failure behaviour of DP steels, which show ductile behaviour with a dimpled fracture surface, have been the point of focus of different researchers. In the current work, the Gurson–Tvergaard–Needleman (GTN) model is utilised to predict the failure behaviour of DP600 steel during the cross-die test, which has been used extensively in the automotive industry to assess the formability of sheet metals. GTN model parameters were identified through the response surface methodology (RSM), and were verified by the comparison of predicted and experimental forming limit curves (FLCs). The good agreement between the simulation and experimental results concerning failure behaviour during the cross-die test indicates that the GTN model can be applied to predict the forming characteristics of DP600 steel. It was also concluded that RSM is a proper method of predicting GTN model parameters.