Gurson-Tvergaard-Needleman Research Articles

Cohesive traction-separation relations for plate tearing under mixed mode loading

Abstract The present study investigates a sequence of failure events related to steady-state tearing of large-scale ductile plates by employing the micro-mechanics based Gurson-Tvergaard-Needleman (GTN) model. The fracture process in front of an advancing crack is approximated by a series of 2D plane strain finite element models to facilitate a comprehensive study of mixed mode fracture behavior as well as a parameter study of the cohesive energy and tractions involved in the process. The results from the conducted GTN model simulations are used to define cohesive zone models suitable for plate tearing simulations at large scale. It is found that mixed mode loading conditions can have a significant effect on the cohesive energy as well as relative displacement (in reference to pure mode I loading), while peak traction is practically unaffected. Specifically, increasing mode II contribution leads to monotonic increase of the cohesive energy. In contrast, the effect of mode III is more complicated as it leads to reduction of the mixed mode cohesive energy (in reference to pure mode I loading) at low to medium levels of mode mixity ratios (0–0.3). However, increasing mode III contribution beyond the mode mixity ratio of 0.3, reverses this trend with cohesive energy potentially exceeding the pure mode I level when at mode mixity ratio of 0.6 or higher. This behavior cannot be captured by the interactive cohesive zone models that rely on a simple rotational sweep of mode I traction-separation relation. Depending on the shear mode contribution, i.e., mode II or mode III, these models can lead to overly conservative (mode II) or unconservative (mode III) prediction of the crack growth resistance.

A digital image correlation analysis on a sheet AA6061-T6 bi-failure specimen to predict static failure

Abstract The failure prediction on the mechanism of fracture in fine grained sheets is an unsolved problem in the framework of non-linear plastic damage and fracture mechanics. Several engineering ductile materials exhibit inelastic behaviour with corresponding large deformations. This work hence focuses on a bi-failure specimen made of an Aluminium alloy AA6061-T6 under a tensile loading circumstance with a geometry adapted to determine the failure phenomenon at high and low stress triaxiality states. A 3D non-contact full-field optical technique, Digital Image Correlation, DIC, is employed to process the experimental data in which the force/displacement response in addition to the internal fields are thereby documented. One of the purposes of the specimen's geometry is to test the robustness of proposed DIC procedure. So, to further pursue the failure phenomenon, an uncoupled model, Gurson–Tvergaard–Needleman (GTN), is computationally implemented using an explicit finite element analysis. Encouraging numerical results were achieved from Finite Element Method (FEM), validating the proposed model. Besides, the failure evolution analysed by the experimental data clearly elucidate failure modes. Considering all successful results, it can be concluded that the objectives of the present study were prosperously fulfilled revealing that the proposed procedure is feasible and efficient to predict the damage and failure phenomena on sheet AA6061 bi-failure specimens.

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.

Finite Element Analysis of the Void Growth and Interface Failure of Ductile Adhesive Joints

Progressive failure of ductile porous adhesive joint generally includes two competitive failure modes: the void growth of ductile adhesive layer and the interface debonding between the adhesive layer and bonding plates. The damage evolution behavior and ultimate strength of ductile adhesive joint are largely dominated by their evolving interactions. However, most of the existing research failed to predict the damage evolution of these two failure modes simultaneously. After the variational weak form of dynamic equilibrium for two adhesive solids with a finite-thickness adhesive layer and two discontinuous cohesive interfaces is given, this paper studies theoretically the competition between these two failure modes using explicit finite element analysis (FEA). The finite-deformation Gurson–Tvergaard–Needleman (GTN) model is used to predict the void growth of adhesive layer, and the bilinear cohesive model as a ABAQUS module is used to simulate the interface debonding. For single-lap joint under tensile loads, effects of the cohesive strengths, the initial void volume fraction, and the thickness of adhesive layer on their interactions are explored. Besides, the ultimate strengths by FEA are also compared with analytical solutions. Numerical results show that dominating failure mode changes from the interface debonding to the failure of adhesive layer at about the cohesive strength 40 MPa and the thickness of adhesive layer 0.5 mm for FM-73 ductile adhesive joint.

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.

Numerical analysis of damage during hot forming

The main aim of the presented research is the analysis of damage evolution in 16MnCrS5 steelduring hot formingbased on results obtained from finite element modelling. Particular attention is put on the interaction between dynamic recrystallization (DRX) and damage initiation at the matrix-inclusion interface. Moreover, a modified Gurson-Tvergaard-Needleman (GTN) model is proposed with the nucleation criterion taken from an extended Horstemeyer model, which predicts damage nucleation based on material softening due to the DRX and stress state in the material.

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.

Determination of the Constants of GTN Damage Model Using Experiment, Polynomial Regression and Kriging Methods

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. In the current work, a combination of experimental, numerical simulation and optimization were used to determine the constants. Quasi-static and dynamic tests were carried out on notched specimens. The experimental profiles of the specimens were used to determine the constants. The constants of GTN damage model were identified through the proposed method and using the results of quasi-static tests. 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. The sensitivity analysis was performed on the constants of GTN model to validate the proposed method. Finally, the experiments were simulated using the Johnson–Cook (J–C) damage model and the results were compared to those obtained from GTN damage model.

Formability Prediction for Tube Hydroforming of Stainless Steel 304 Using Damage Mechanics Model

Tube hydroforming (THF) is an important manufacturing technology for producing tube components by means of fluid pressure. In comparison to other basic forming processes like deep drawing, forming steps can be reduced and more complex shape is allowed. In this work, it was aimed to establish the forming limit curve (FLC) of stainless steel tube grade 304 for the THF process by using finite element (FE) simulations coupled with the Gurson–Tvergaard–Needleman (GTN) damage model as failure criterion. The parameters of the GTN model were obtained by metallography analysis, tensile test, plane strain test of the examined steel in combination with the direct current potential drop (DCPD) and digital image correlation (DIC) techniques. These parameters were well verified by comparing the predicted FLC of steel sheet with the experimental FLC gathered from the Nakazima test. Then, the FLC of steel tube 304 was established by FE simulations coupled with the damage model of tube bulging tests. During the bulge tests, pressure and axial feed were properly controlled in order to generate the left-hand FLC, while pressure and external force needed to be simultaneously incorporated for the right-hand FLC. Finally, the FLC was applied to evaluate material formability in an industrial THF process of the steel tube.

Numerical Evaluation of Compressive Strain Capacity for API X100 Line Pipe

In the strain-based design, pipeline steels are required to satisfy not only the stress capacity but also the strain capacity. Thus, considerable efforts have been made to meet the various requirements of the pipe-material properties that might undergo large deformation during the installation stage in various hostile environments. An adequate compressive strain capacity can help effectively avoid local buckling. Hence, highly deformable steel becomes crucial in achieving the required strain capacity. This study proposes a nonlinear finite element procedure based on the commercial software ABAQUS combined with the User-defined Material Module (UMAT), which is created using Fortran language. The Gurson–Tvergaard–Needleman (GTN) model is implemented in UMAT to fully consider the nonlinear behavior of an API X100 pipe subjected to compressive loading. The numerical simulation results of the full-scale bending test were compared with the experimental results to verify the nonlinear finite element procedure equipped with the GTN model. The simulation results are in good agreement with the experimental results. The parametric studies reveal the effects of geometric imperfections and material properties on the compressive strain limit.

Parameter Calibration of GTN Damage Model and Formability Analysis of 22MnB5 in Hot Forming Process

Hot forming of high strength steel at elevated temperatures is an attractive technology to achieve the lightweight of vehicle body. The mechanical behavior of boron steel 22MnB5 strongly depends on the variation of temperature which makes the process design more difficult. In this paper, the Gurson–Tvergaard–Needleman (GTN) model is used to study the formability of 22MnB5 sheet at different temperatures. Firstly, the rheological behavior of 22MnB5 is analyzed through a series of hot tensile tests at a temperature range of 600-800 °C. Then, a detailed process to calibrate the damage parameters is given based on the response surface methodology and genetic algorithm method. The GTN model together with the damage parameters calibrated is then implemented to simulate the deformation and damage evolution of 22MnB5 in the process of high-temperature Nakazima test. The capability of the GTN model as a suitable tool to evaluate the sheet formability is confirmed by comparing experimental and calculated results. Finally, as a practical application, the forming limit diagram of 22MnB5 at 700 °C is constructed using the Nakazima simulation and Marciniak–Kuczynski (M–K) model, respectively. And the simulation integrated GTN model shows a higher reliability by comparing the predicted results of these two approaches with the experimental ones.

Modelling of ductile fracture in single point incremental forming using a modified GTN model

Understanding the deformation and failure mechanisms in single point incremental forming (SPIF) is of great importance for achieving improved formability. Furthermore, there will be added benefits for more in depth evaluation of the effect of localised deformation to the fracture mechanism in SPIF. Although extensive research has been carried out in recent years, questions still remain on the shear and particularly its effect to the formability in SPIF processes. In this work, a modified Gurson–Tvergaard-Needleman (GTN) damage model was developed with the consideration of shear to predict ductile fracture in the SPIF process due to void nucleation and coalescence with results compared with original GTN model in SPIF. A combined approach of experimental testing and SPIF processing was used to validate finite element results of the shear modified Gurson–Tvergaard-Needleman damage model. The results showed that the shear modified GTN model improved the modelling accuracy of fracture over the original GTN model under shear loading conditions. Furthermore, the shear plays a role under meridional tensile stress to accelerate fracture propagation in SPIF processes.

Tearing failure of ultra-thin sheet-metal involving size effect in blanking process: Analysis based on modified GTN model

In this account, the ductile tearing behavior of a 0.08 mm thick ultra-thin martensitic stainless steel sheet was probed during the blanking process. The experiments suggested that void growth was suppressed around the narrow region due to the relatively low-stress triaxiality. The typical failure phenomena were exhibited in the form of tearing, which may imply that the conventional Gurson–Tvergaard–Needleman (GTN) model failed to predict such shearing domination failure. Therefore, a modified GTN model based on Lode parameter was tested to describe the failure mechanism. Furthermore, to reflect the remarkable material strengthening behavior at the micrometer scale, the Mechanism-based Strain Gradient (MSG) plasticity was implemented in the User MATerial (UMAT) subroutine of ABAQUS, and a finite element model of three-dimensional blanking processing was then built. The cohesive elements were inserted into the finite element mesh so that the tearing process could be visualized. The numerical results generated by the proposed model were compared with the experimental observations, as well as data from conventional plasticity model. The analysis revealed that shear damage rather than microvoids was the primary cause of tearing failure. The effects of strain gradient on distributions of stress level, void volume fraction and shear damage evolution were examined. It was concluded that size effect played a significant role in inducing the tearing failure, and the modified GTN model was able to capture shear damage evolution inside the shear region.

Effective yield surface of porous media with random overlapping identical spherical voids

The present paper concerns a computational study of a three-dimensional (3D) unit cells with identical spherical voids in a von Mises matrix. The objective is to estimate the effective plastic flow surface of 3D microstructures. The work originality is to deal with identical spherical overlapping voids, covering a wide range of stress triaxiality ratios. The effective plastic flow surface is computed for nine distinct loadings on four distinct microstructures. The result indicates that the classical Gurson–Tvergaard–Needleman (GTN) model obtained using the Fritzen et al. [40] parameters, matches with our numerical simulations.

Assessment of Fracture Toughness Using Small Punch Tests of Prenotched Specimens

In this paper, line- and ring-notched small punch test (SPT) specimens were studied; a three-dimensional (3D) model of a ring-notched SPT specimen was established using the contour integral method, and the validity of the model was verified using ring-notched specimens. The stress and strain fields were analyzed using numerical simulations of a ring-notched SPT specimen, and the change in the stress gradient during deformation was considered. To verify the finite element model, the results of the numerical simulations were compared with those of three-point bending tests and a Gurson–Tvergaard–Needleman (GTN) model. Compared with the line-notched specimen, the ring-notched specimen was more suitable for notch propagation analysis and fracture toughness evaluation. The results of the numerical simulations were in good agreement with those of the experiments, which showed that the numerical model used in this study was correct. For a notch that initiated when the load reached its maximum value, the value of the J integral was 335 × 10−6 kJ/mm2, and at time 0.85Pmax, the value of the J integral was 201 × 10−6 kJ/mm2, and the difference from the result of the three-point bending test was 14.4%. For a notch that initiated during the stretching deformation stage, the relevant fracture toughness was 225 × 10−6 kJ/mm2, and the difference from the result of the three-point bending test was 3%.

Study of the influence of cold working on mechanical behavior and ductile fracture of 5754 aluminum alloy: experimental and numerical simulations

The ductile damage of automotive aluminum sheet alloy AA5754-H111 is investigated by experiments and numerical simulation using the Gurson-Tvergaard-Needleman (GTN) mo- del. The GTN parameters were determined by a uni-axial tensile test and the inverse finite element method. The same parameters were employed to provide the ductile damage beha- vior of central cracked panel (CCP) specimens. A good prediction can be established among the numerical simulation and experimental data in from of the force opening displacement. As an application, the identified GTN model is used to predict the influence of cold wor- king on deformation and ductile damage. The numerical simulation results obtained are assimilated with experimental data.

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.

Size effects in micro-tensile testing of high purity polycrystalline nickel

Tensile properties and fracture characteristics of high purity polycrystalline nickel were investigated using micro-tensile specimens. The material response to the applied load was found to be sensitive to both geometry and sample size. The post-tests examination of the fracture surfaces revealed that the mechanisms leading to failure were associated with the nucleation, growth and coalescence of voids. These mechanisms were studied using finite element implementation of the Gurson–Tvergaard–Needleman (GTN) model. A physical meaning of the model parameters was proposed and validated against experimental data. The model provided good predictions of the failure mode, but did not capture the variability observed for the micro-tensile specimens. The factors such as machining process, surface roughness, and local variations in the microstructure were most likely responsible for these differences.

Micromechanical Analysis of In-Plane Constraint Effect on Local Fracture Behavior of Cracks in the Weakest Locations of Dissimilar Metal Welded Joint

In this work, a set of GTN (Gurson–Tvergaard–Needleman) parameters of the Alloy52M dissimilar metal welded joint (DMWJ) have been calibrated, and a micromechanical analysis of in-plane constraint effects on the local fracture behavior of two cracks, which located in the weakest regions of the DMWJ, has been investigated by the local approach based on the GTN damage model. The results show that the partition of the material and the variation of the q 2 parameter make the J-resistance curves obtained by numerical simulations close to the experimental values. The numerical J-resistance curves and crack growth paths are consistent with the experiment results, which show that the GTN damage model can incorporate the in-plane constraint effect. Furthermore, after the stress, strain and damage fields at the crack tip during the crack propagation process have been calculated, and the change of the J-resistance curves, crack growth paths and fracture mechanism with in-plane constraint have been analyzed.

Numerical simulations and modeling of the effective plastic flow surface of a biporous material with pressurizedintergranular voids

This study is devoted to the effective plastic flow surface of a biporous polycrystalline material, with an intragranular porosity due to spherical voids, and an intergranular porosity due to larger elongated voids along the grain boundaries. These two populations of voids (or bubbles) with well separated scales and shapes are saturated by a fluid and therefore are subjected to internal pressures. The effect of the intragranular voids is modeled through a GTN (Gurson–Tvergaard–Needleman) criterion in the matrix. Numerical simulations are performed with a FFT-based (Fast Fourier Transforms) method. Particular attention is paid to the effect of the distribution of the intergranular bubbles on the effective plastic flow surface. Different microstructures with different volume fractions and sizes for the intergranular bubbles are tested under three loading conditions (the mean size of the grains being fixed). Two main results are exhibited. First, it is shown that the effect of the relative size of the intergranular bubbles on the effective plastic flow surface depends on the loading direction. Secondly, a comparison is made with the analytical model of (Vincent et al., 2014) and a correction of the porosity relative to the intergranular bubbles is introduced in this analytical model in order to take into account the specific distribution of the intergranular bubbles along the grain boundaries. This correction is expressed as a sum of two power law functions, each of them being significant either for low or for large values of the porosity of intergranular bubbles.