Gurson-Tvergaard-Needleman Research Articles

Ductile Damage in Tension and Bending for DP980 Steel Sheets

The mechanical behavior of DP980 steel sheets of 1.7 mm thickness has been investigated with both tensile and bending tests. Free bending tests were performed on square samples of 60mm side. The bending tool has a sharp radius of around 0.4 mm and the sample simply lies on two rollers. Scanning electron micrography observations were performed in order to check the occurrence of cracks, that indicate the onset of rupture in bending. Moreover, X-ray microtomography observations were performed on smooth and notched tensile specimen, with a specific small-size geometry, and bending specimen. Maximum void volume fractions of 1.5 10-3 were recorded and the influence of the triaxiality ratio was investigated, by changing the notch radius. In the case of bending, samples were cut in the bent area and void volume fraction distribution was analyzed along the sheet thickness. Material parameters for Gurson-Tvergaard-Needleman (GTN) model, associated with isotropic hardening and von Mises yield criterion, were identified from the tensile tests. Inverse identification was performed over the different sample geometries, showing that GTN model can not capture the triaxiality ratio influence. Finite element simulations of the bending test were then carried out, in order to compare experimental and predicted void volume fractions in the sheet thickness.

Forming Limit Diagram Determination of Al 3105 Sheets and Al 3105/Polypropylene/Al 3105 Sandwich Sheets Using Numerical Calculations and Experimental Investigations

Sandwich sheet structures are gaining a wide array of applications in the aeronautical, marine, automotive, and civil engineering fields. Since such sheets can be subjected to forming/stamping processes, it is crucial to characterize their limiting amount of deformation before trying out any forming/stamping process. To achieve this goal, sandwich sheets of Al 3105/polymer/Al 3105 were prepared using thin film hot melt adheres. Through an experimental effort, forming limit diagrams (FLDs) of the prepared sandwich sheets were evaluated. In addition, simulation efforts were conducted to predict the FLDs of the sandwich sheets using finite element analysis (FEA) by considering the Gurson–Tvergaard–Needleman (GTN) damage model. The agreement among the experimental results and simulated predictions was promising. The effects of different parameters such as polymer core thickness, aluminum face sheet thickness, and shape constraints were investigated on the FLDs.

Numerical Modeling of Tube Hydropiercing Using Phenomenological and Micro-Mechanical Damage Criteria

Hydropiercing is an efficient way of piercing holes in mass produced hydroformed parts with complex geometries. By driving piercing punches radially into a hydroformed and fully pressurized tube, holes will be pierced and extruded into the tube-wall. Recent experimental studies have shown that the formability of advanced high strength steel (AHSS) tubes can be increased with the application of internal pressure. In this study, three-dimensional finite element simulations of a tube hydropiercing process of a dual phase steel (DP600) were performed in LS-DYNA, using phenomenological, micromechanical and combined damage criteria. Damage was included in the numerical analysis by applying constant equivalent plastic strain (CEPS), the Gurson-Tvergaard-Needleman (GTN), and the Extended GTN (GTN+JC) model. In order to calibrate the parameters in each model, a specialized hole-piercing fixture was designed and piercing tests were carried out on non-pressurized tube specimens. Of the various ductile fracture criteria, the results predicted with the GTN+JC model, such as the punch load-displacement, the roll-over depth, and the quality of the clearance zone correlated the best with the experimental data.

A consistent use of the Gurson-Tvergaard-Needleman damage model for the R-curve calculation

The scope of the present work is to point out a consistent simulation procedure for the quasi-static fracture processes, starting from the micro-structural characteristics of the material. To this aim, a local nineparameters Gurson-Tvergaard-Needleman (GTN) damage law has been used. The damage parameters depend on the micro-structural characteristics and must be calculated, measured or opportunely tuned. This can be done, as proposed by the author, by using an opportunely tuned GTN model for the representative volume element simulations, in order to enrich the original damage model by considering also the defect size distribution. Once determined all the material parameters, an MT fracture test has been simulated by a FE code, to calculate the R-curve in an aeronautical Al-based alloy. The simulation procedure produced results in a very good agreement with the experimental data.

Micromechanical modelling of damage behaviour of Ti–6Al–4V

The effort of this study is to develop a simulation method to predict the effect of microstructural morphology in mechanical properties and failure mechanism of Ti–6Al–4V with 55% α and 45% β. Finite element models were then created based on a clarification of a damage mechanism to control the ductile cracking with focusing on the heterogeneity in strength of microstructure. By the way, Simulation for the dimple failure of the material, using the Gurson–Tvergaard–Needleman (GTN) model, will be presented. The large number of micro-voids nucleation at lower strength side near two phase boundary associated with the localisation of stress/strain is found to control ductile cracking. Numerical simulations, which were carried out using the scanning electron micrograph, are able to predict the void initiation in the material. During fractography of the material, some evidence is observable which can validate the results obtained by the simulation. The good correlation between the numerical and experimental observations from fractographic and tensile test results shows the efficiency of the proposed models in predicting the failure mechanism of Ti–6Al–4V.

Failure analysis based on microvoid growth for sheet metal during uniaxial and biaxial tensile tests

The aim of the presented investigations is to perform an analysis of fracture and instability during simple and complex load testing by addressing the influence of ductile damage evolution in necking processes. In this context, an improved experimental methodology was developed and successfully used to evaluate localization of deformation during uniaxial and biaxial tensile tests. The biaxial tensile tests are carried out using cruciform specimen loaded using a biaxial testing machine. In this experimental investigation, Stereo-Image Correlation technique has is used to produce the heterogeneous deformations map within the specimen surface. Scanning electron microscope is used to evaluate the fracture mechanism and the micro-voids growth. A finite element model of uniaxial and biaxial tensile tests are developed, where a ductile damage model Gurson–Tvergaard–Needleman (GTN) is used to describe material deformation involving damage evolution. Comparison between the experimental and the simulation results show the accuracy of the finite element model to predict the instability phenomenon. The advanced measurement techniques contribute to understand better the ductile fracture mechanism.

FEA Simulation of Clinching Process Based on GTN Damage Model

In this work, the Gurson-Tvergaard-Needleman (GTN) damage model is adopted to depict the material damage during the clinch joining process in a simulation-based theoretical model. The parameters of the GTN model which influence the void nucleation, growth and coalescence are identified. Their values of a specific material, C45E4 (ISO) steel, have been determined after carefully comparing the simulation results with the real sheet material tensile test. The established GTN damage model parameters are then imported into the simulation model to investigate the material damage during the mechanical clinch joining process. The Finite Element Analysis (FEA) simulation results show promising, because the material’s initial damage position can be located and analyzed. For a given design, the initial fracture point was predicted which is located on the inner side of the clinched joint neck of the upper sheet, which matches with the results of the experimental test very well. It can be concluded that the incorporation of GTN damage model has extend the capability of the simulation model.

Numerical investigation and experimental validation of physically based advanced GTN model for DP steels

This numerical investigation of an advanced Gurson–Tvergaard–Needleman (GTN) model is an extension of the original work of Ben Bettaiebet al. (2011 [18]). The model has been implemented as a user-defined material model subroutine (VUMAT) in the Abaqus/explicit FE code. The current damage model extends the previous version by integrating the three damage mechanisms: nucleation, growth and coalescence of voids. Physically based void nucleation and growth laws are considered, including an effect of the kinematic hardening. These new contributions are based and validated on experimental results provided by high-resolution X-ray absorption tomography measurements. The current damage model is applied to predict the damage evolution and the stress state in a tensile notched specimen experiment.

Application of Gurson–Tvergaard–Needleman Constitutive Model to the Tensile Behavior of Reinforcing Bars with Corrosion Pits

Based on meso-damage mechanics and finite element analysis, the aim of this paper is to describe the feasibility of the Gurson–Tvergaard–Needleman (GTN) constitutive model in describing the tensile behavior of corroded reinforcing bars. The orthogonal test results showed that different fracture pattern and the related damage evolution process can be simulated by choosing different material parameters of GTN constitutive model. Compared with failure parameters, the two constitutive parameters are significant factors affecting the tensile strength. Both the nominal yield and ultimate tensile strength decrease markedly with the increase of constitutive parameters. Combining with the latest data and trial-and-error method, the suitable material parameters of GTN constitutive model were adopted to simulate the tensile behavior of corroded reinforcing bars in concrete under carbonation environment attack. The numerical predictions can not only agree very well with experimental measurements, but also simplify the finite element modeling process.

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.

Effect of Initial Porosity on Material Response Under Multi-Axial Stress State for S235JR Steel

AbstractThe effect of the initial porosity on the material response under multi-axial stress state for S235JR steel using the Gurson-Tvergaard-Needleman (GTN) material model was examined. Three levels of initial porosity, defined by the void volume fraction f0, were considered: zero porosity for fully dense material without pores, average and maximum porosity according to the metallurgical requirements for S235JR steel. The effect of the initial porosity on the material response was noticed for tensile elements under multi-axial stress state defined by high stress triaxiality σm/σe = 1.345. This effect was especially noticeable at the range of the material failure. In terms of the load-bearing capacity of the elements, the conservative results were obtained when maximum value of f0 = 0.0024 was used for S235JR steel under multi-axial stress state, and this value is recommended to use in the calculations in order to preserve the highest safety level of the structure. In usual engineering calculations, the average porosity defined by f0 = 0.001 may be applied for S235JR.

Unified characterisation of in‐plane and out‐of‐plane constraint based on crack‐tip equivalent plastic strain

ABSTRACTConstraint can be divided into two conditions of in‐plane and out‐of‐plane, and each of them has its own parameter to characterize. However, in most cases, there exists a compound change of both in‐plane and out‐of‐plane constraint in structures, a unified measure that can reflect both of them is needed. In this paper, the finite element method (FEM) was used to calculate the equivalent plastic strain (ɛp) distribution ahead of crack tips for specimens with different in‐plane and out‐of‐plane constraints, and the FEM simulations based on Gurson–Tvergaard–Needleman (GTN) damage model and a small number of tests were used to obtain fracture toughness for the specimens with different constraints. Unified measure and characterisation parameter of in‐plane and out‐of‐plane constraints based on crack‐tip equivalent plastic strain has been investigated. The results show that the area APEEQ surrounded by the ɛp isoline ahead of crack tips can characterize both in‐plane and out‐of‐plane constraints. Based on the area APEEQ, a unified constraint characterisation parameter Ap was defined. It was found that there exists a sole linear relation between the normalised fracture toughness JIC/Jref and regardless of the in‐plane constraint, out‐of‐plane constraint and the selection of the ɛp isolines. The unified JIC/Jref−reference line can be used to determine constraint‐dependent fracture toughness of materials. The FEM simulations with the GTN damage model (local approach) can be used in obtaining the unified JIC/Jref−reference line for materials with ductile fracture.

Numerical modeling of multi-stage tube hydropiercing

Hydropiercing is a cost-effective method for piercing holes in a hydroformed tubular structure. When the tube wall around a pierced hole is also extruded toward the inside of the tube, brackets or other connecting parts can be fastened to the hydroformed structure by inserting a self-tapping screw into the extruded hole. In this study, three-dimensional finite element simulations of the hydroforming, hydropiercing and wall extrusion of a DP600 steel tube were performed using different damage criteria. The constant equivalent plastic strain, with and without cut-off stress-triaxiality values (CEPS+C and CEPS, respectively) and the Johnson–Cook (JC) damage criterion were considered as phenomenological damage models, and the Gurson–Tvergaard–Needleman (GTN) criterion was used as a micro-mechanical damage model. In order to calibrate the parameters in each model, tube-piercing tests were conducted and the punch load versus displacement response was determined. The damage parameters were then calibrated by correlating the predicted punch load versus displacement behavior to the experimental data, considering particularly the load reduction behavior when the slug breaks through. The calibrated damage parameters were then used in simulations of the multi-stage hydropiercing and tube-wall extrusion process and the accuracy of each damage criterion was evaluated in terms of the predicted deformation and damage behavior. The damage accumulation direction during the hydropiercing, depth of roll-over, and tube extruded length were the main parameters in the evaluation of each damage criteria. JC and CEPS+C criteria showed the best agreement with the experimental observations.

Forming limit diagram prediction of AA5052/polyethylene/AA5052 sandwich sheets

Metal–plastic sandwich sheet has received increasing attention in aeronautical, automotive, marine and civil engineering industries due to its lower density, higher specific flexural stiffness, better dent resistance, better sound and vibration damping characteristics. In the present study, an AA5052/polyethylene/AA5052 sandwich sheet is developed and its formabilities are investigated. A numerical simulation method based on the Gurson–Tvergaard–Needleman (GTN) damage model is used for simulating the forming process of sandwich sheet, in which the interface conditions between skin sheet and core materials are considered by using the cohesive zone model (CZM). The rigid punch dome tests and the Nakazima forming tests are carried out to build the forming limit diagrams (FLDs) of sandwich sheet. A strain history method is applied to determine the limited strain. Comparisons between predictions and experimental results validate the used numerical simulation method. Finally, the influences of polyethylene’s thickness on the formabilities of sandwich sheet are analyzed. Research results show that: AA5052/polyethylene/AA5052 sandwich sheet has a better formability than monolithic AA5052 sheet and the formability of AA5052/polyethylene/AA5052 sandwich sheet increases with increasing the thickness of polyethylene core layer.

Parameter identification of a mechanical ductile damage using Artificial Neural Networks in sheet metal forming

In this paper, we report on the developed and used of finite element methods, have been developed and used for sheet forming simulations since the 1970s, and have immensely contributed to ensure the success of concurrent design in the manufacturing process of sheets metal. During the forming operation, the Gurson–Tvergaard–Needleman (GTN) model was often employed to evaluate the ductile damage and fracture phenomena. GTN represents one of the most widely used ductile damage model. In this investigation, many experimental tests and finite element model computation are performed to predict the damage evolution in notched tensile specimen of sheet metal using the GTN model. The parameters in the GTN model are calibrated using an Artificial Neural Networks system and the results of the tensile test. In the experimental part, we used an optical measurement instruments in two phases: firstly during the tensile test, a digital image correlation method is applied to determinate the full-field displacements in the specimen surface. Secondly a profile projector is employed to evaluate the localization of deformation (formation of shear band) just before the specimen’s fracture. In the validation parts of this investigation, the experimental results of hydroforming part and Erichsen test are compared with their numerical finite element model taking into account the GTN model. A good correlation was observed between the two approaches.

Prediction of anisotropic material behavior based on multiresolution continuum mechanics in consideration of a characteristic length scale

New advanced materials have received more attention from many scientists and engineers because of their outstanding chemical, electrical, thermal, optical, and mechanical properties. Since the design of advanced material by experiments requires high cost and time, numerical approaches have always been of great interest. In this paper, finite element analysis of anisotropic material behavior has been carried out based on a multiresolution continuum theory. Gurson-Tvergaard-Needleman (GTN) damage model has been applied as a constitutive model at macroscale. Effects of plastic anisotropy on deformation behavior are assessed using Hill’s 48 yield function for anisotropic material and von Mises yield function for isotropic material, respectively. The material parameters for both isotropic and anisotropic damage models have systematically been determined from microstructure through unit cell modeling. The newly proposed linear approximation of local velocity gradient resolved the underdetermined problem of the previous homogenization process. Anisotropic material behaviors of a tensile specimen have been investigated by the proposed multiresolution continuum theory.

Influence of Initial Porosity on Strength Properties of S235JR Steel at Low Stress Triaxiality

Abstract The paper discusses the influence of the initial parameters on the strength parameters of S235JR steel at low stress triaxiality. The analysis was performed using the Gurson-Tvergaard-Needleman (GTN) material model, which takes into consideration the material structure. The initial material porosity was defined as the void volume fraction f0. The fully dense material without pores was assumed and the typical and maximum values of porosity were considered for S235JR steel in order to analyse the porosity effect. The strength analysis of S235JR steel was performed basing on the force-elongation curves obtained experimentally and during numerical simulations. Taking into consideration the results obtained, the average values of the initial void volume fraction f0 = 0.001 for S235JR steel is recommended to use in a common engineering calculations for elements operating at low stress triaxiality. In order to obtain more conservative results, the maximum values of f0 = 0.0024 may be used.

Numerical study of electron beam welded butt joints with the GTN model

The fracture behavior of S355NL electron beam welded steel joints is investigated experimentally and numerically. The simulation of crack propagation in an electron beam welded steel joint was performed with the Gurson–Tvergaard–Needleman (GTN) damage model. A parameter study of the GTN model was adopted which reveals the influence of parameters on the material behavior of notched round and compact tension specimens. Based on the combined method of metallographic investigations and numerical calibration, the GTN parameters were fixed. The same parameters were used to predict the ductile fracture of compact tension specimens with the initial crack located at different locations. Good match can be found between the numerical and experimental results in the form of force versus Crack Opening Displacement as well as fracture resistance curves.

Effect of geometric factors and processing parameters on plastic damage of SUS304 stainless steel by small punch test

The effects of friction coefficient, specimen thickness, punching rate and the diameter of center hole in lower die on the plastic damage of SUS304 stainless steel have been studied by small punch test (SPT). The finite element model (FEM) was established based upon Gurson–Tvergaard–Needleman (GTN) ductile damage constitutive equations. The results showed that the load–displacement (L–D) curves and final fracture locations of the broken specimens produced by experiment and FEM had a good agreement. The growth of plastic damage had a stage from the constant speed to the accelerated speed. The initial crack and necking region were away from the center when the friction coefficient increased. The initial crack occurred at 0.74mm away from the center with the friction coefficient of 0.3. The increase of specimen thickness retarded the fracture time and it made the position of the crack initiation moving toward the center of specimen. When the punching rate changed from 0.5mm/min to 10mm/min, the size of dimples reduced and the number of dimples increased. There were some brittle fracture features in the final fracture surface, and the fracture time will delay with increasing the diameter of center hole in lower die.

A rate-dependent homogenization based continuum plasticity-damage (HCPD) model for dendritic cast aluminum alloys

This paper develops a rate-dependent homogenization based continuum plasticity damage model (HCPD) model for computationally efficient analysis of ductile failure in porous ductile materials containing brittle inclusions. The HCPD model developed has the overall structure of the anisotropic Gurson–Tvergaard–Needleman (GTN) model for porous ductile materials. The material is assumed to remain orthotropic in an evolving principal material coordinate system throughout the deformation history. The rate-dependency of plastic deformation is captured through an over-stress viscoplastic model. The anisotropic viscoplasticity parameters in the HCPD model depend on morphological features of the microstructure as well as on the plastic deformation. They are calibrated from homogenization of evolving micro-variables in a representative volume element (RVE) of the microstructure. Micromechanical analyses of the RVE are performed using the rate-dependent locally enhanced Voronoi cell finite element model (LE-VCFEM) [8,26]. This work also introduces a novel rate-dependent void nucleation criterion due to inclusion and matrix cracking in the underlying microstrucure. Predictions of the rate-dependent HCPD model for a cast aluminum alloy are compared with the homogenized response obtained with LE-VCFEM micromechanical analyses of the actual microstructure with excellent agreement.