GTN Model Research Articles

OS1428 汎用FEAコードによるGTNモデルを用いた延性破壊評価手法の検討

OS1428 汎用FEAコードによるGTNモデルを用いた延性破壊評価手法の検討

Description of shear failure in ductile metals via back stress concept linked to damage-microporosity softening

Starting from experimental observations on hat shape samples of a Titanium alloy of Ti6Al4V family showing that the failure of ductile materials under low triaxiality may result (at least partially) from void growth, the present work develops an approach based on a damage related softening mechanism acting as a kinematic mean stress drop causing a shift of the yield locus centre. For micro-porous viscoplastic material described via micro-mechanics based elliptic potentials (and obeying the normality rule) this ‘back mean stress’ concept allows reproducing the inelastic dilatancy due to void growth, in addition to the isochoric plastic deformation due to dislocation glide, at zero and low negative stress triaxiality. The approach is applied to the well-known GTN model and the 3D constitutive equations are implemented as user material in the engineering finite element computation code Abaqus®. Numerical simulations are conducted considering a single finite element under simple shear loading and a hat shape specimen under shear–compression loading. Numerical results are compared with experimental ones.

Plastic damage of T-shape hydroforming

The Gurson-Tvergaard-Needleman model (GTN model) was employed to analyze bursting behavior in the hydroforming of stainless steel T-shape. A free-bulging test combined with simulation was conducted to determine the critical porosity and the failure porosity in GTN model. The effects of the forming pressure and the axial feeding on damage development were investigated and the influences of stress triaxiality and the plastic strain on porosity variation were also studied. The results show that a higher forming pressure or a less axial feeding will lead to bursting failure. The stresses of the top of protrusion are in bi-axial tension state, while the stresses of the side wall of main tube are in hoop tension state and axial compression state, respectively. The plastic strain has a more significant influence on the porosity than the stress triaxiality under the lower internal pressure; however, the stress triaxiality will govern the growth of porosity under the higher internal pressure. The simulation results give a good agreement with the experimentally determined thickness, and the maximum thickness-thinning rate is about 36%.

Modeling the Transition between Dense Metal and Damaged (Microporous) Metal Viscoplasticity

This article presents a physically motivated approach, which has been developed in order to describe the transition of behavior between dense metal plasticity and microporous metal plasticity in the context of dynamic plasticity and adiabatic conditions. Considering that void germination requires a certain amount of plastic deformation, a ‘primary’ hole nucleation criterion as well as a statistical law governing the ‘secondary’ hole formation kinetics has been proposed. In a consistent way, the hole nucleation criterion accounts for the accelerating effects of stress triaxiality and the delaying effects of temperature and strain rate. In addition, a modification of the GTN model was proposed, allowing for describing cavity growth under shear loading. The 3D constitutive equations were implemented as user material in the engineering finite element computation code Abaqus®. Numerical simulations were conducted considering a single finite element under uniaxial tensile loading and simple shear then notched cylindrical samples under remote uniaxial tensile loading. The numerical results clearly show the influence of the hole nucleation criteria on the ductile damage and failure.

Notched Specimens Fracture Prediction with an Advanced GTN Model

This present contribution consists of implementing an advanced GTN damage model as a "User Material subroutine" in the Abaqus FE code. This damage model is based on specific nucleation and growth laws in order to predict the void coalescence properties of the material. When applied, this implementation predicts the damage evolution and the stress state of notched specimens made from dual phase steel. By comparing numerical predictions with experimental results, the numerical approach was improved and then validated.

Numerical investigation of ductile crack growth behavior in a dissimilar metal welded joint

In this paper, the finite element method (FEM) based on GTN model is used to investigate the ductile crack growth behavior in single edge-notched bend (SENB) specimens of a dissimilar metal welded joint (DMWJ) composed of four materials in the primary systems of nuclear power plants. The J–Δ a resistance curves, crack growth paths and local stress–strain distributions in front of crack tips are calculated for eight initial cracks with different locations in the DMWJ and four cracks in the four homogenous materials. The results show that the initial cracks with different locations in the DMWJ have different crack growth resistances and growth paths. When the initial crack lies in the centers of the weld Alloy182 and buttering Alloy82, the crack-tip plastic and damage zones are symmetrical, and the crack grow path is nearly straight along the initial crack plane. But for the interface cracks between materials and near interface cracks, the crack-tip plastic and damage zones are asymmetric, and the crack growth path has significant deviation phenomenon. The crack growth tends to deviate into the material whose yield stress is lower between the two materials on both sides of the interface. The different initial crack locations and mismatches in yield stress and work hardening between different materials in the DMWJ affect the local stress triaxiality and plastic strain distributions in front of crack tips, and lead to different ductile crack growth resistances and growth paths. For the accurate integrity assessment for the DMWJ, the fracture toughness data and resistance curves for the initial cracks with different locations in the DMWJ need to be obtained.

Numerical simulation of damage evolution in multi-pass wire drawing process and its applications

This paper presents a numerical simulation of damage evolution in multi-pass wire drawing process and its potential relevance to manufacturing design. The Gurson–Tvergaard–Needleman model (GTN model) is introduced to describe damage evolution in the drawn wire. Based on a three-dimensional model of the drawn wire generated through ABAQUS, the numerical analyses on damage behavior in multi-pass wire drawing are undertaken for the purpose of investigating the damage evolution during all phases of the process. Convergence problems in the process of simulation are discussed. The results illustrate the damage evolution of the drawn wire in each of the eight passes and the damage distribution along axial and circular directions. It turns out that the damage values continuously rise up with the increase of drawing passes and the damage evolution in the drawing process shows obvious nonlinear characteristic. The damage distribution along axial and circular directions agrees well with actual drawing situation. Wire breakage is expected to occur in those areas of the drawn wire where fractures most possibly initiate. Furthermore, the numerical analyses contribute a new approach for the optimization of the drawing parameters. Based on the principle of least damage accumulation in the drawing process, the optimal area reduction is chosen and selection of material processes is proposed. The currently standard 8-pass wire drawing process can be potentially optimized by a proposed 7-pass wire drawing process.

A comparison of shear mechanisms for the prediction of ductile failure under low stress triaxiality

PurposeThe purpose of this paper is to perform a numerical assessment of two recently proposed extensions of the Gurson‐Tveegard‐Needleman ductile damage constitutive model under low stress triaxiality.Design/methodology/approachOne of the most widely used ductile damage models is the so‐called Gurson‐Tveegard‐Needleman model, commonly known as GTN model. The GTN model has embedded into its damage formulation the effects of nucleation, growth and coalescence of micro‐voids. However, the GTN model does not include void distortion and inter‐void linking in the damage evolution. To overcome this limitation, some authors have proposed the introduction of different shear mechanisms based on micromechanical grounds or phenomenological assumptions. Two of these constitutive formulations are reviewed in this contribution, numerically implemented within a quasi‐static finite element framework and their results critically appraised.FindingsThrough the analysis of the evolution of internal variables, such as damage and effective plastic strain, obtained by performing a set of numerical tests using a Butterfly specimen, it is possible to conclude that the extended GTN models are in close agreement with experimental evidence.Research limitations/implicationsEven though the results obtained with the modified GTN models have shown improvements, it can also be observed that both shear mechanisms have inherent limitations in the prediction of the location of fracture onset for some specific stress states.Originality/valueFrom the results reported, it is possible to identify some shortcomings in the recently proposed extensions of the GTN model and point out the direction of further improvements.

Micromechanical modelling of weldments using GTN model

Non-transferability of fracture data from specimen level to component level is a serious limitation of conventional fracture mechanics, as fracture resistance data obtained is largely geometry dependant. The difficulty is largely overcome by GTN model which models the drop in load carrying capacity of a material with the increase in plastic strain, considering nucleation, growth and coalescence of micro-voids in the material. However, determination of the model-parameters with experiments is extremely difficult and doubtful. Hence, a parameter-study has been done to find out the effects of different parameters on material behaviour to asses the parameter for best practical result with least metallographic study. The parameters were finally verified by predicting ductile fracture in a real life piping component.

Lengthscale-dependent modelling of ductile failure in metallic microstructures

The purpose of the current work is the application of a recent extension (Reusch et al., 2003a, 2003b) of the Gurson-Needleman-Tvergaard (GTN) model (e.g., Needleman and Tvergaard, 1984) to the simulation of ductile damage and failure processes in metal matrix composites at the microstructural level. The extended model is based on the treatment of void coalescence as a lengthscale-dependent process. In particular, we compare the predictions of the (local) with GTN model with those of the lengthscale-dependent extension for ductile crack initiation in ideal and real Al-SiC metal matrix microstructures. As shown by the current results for metal matrix composites and as expected, the simulation results based on the local GTN model for both the structural response and predicted crack path at the microstructural level in metal matrix composites are strongly mesh-dependent. On the other hand, those based on the current lengthscale-dependent void-coalescence modelling approach are mesh-independent. This correlates with the fact that, in contrast to the local approach, the predictions of the lengthscale-dependent approach for the crack propagation path in the real Al-SiC metal matrix composite microstucture considered here agree well with the experimentally-determined path.

Failure modeling of multiphase steels using representative volume elements based on real microstructures

The current work aims at predicting of damage and failure in multiphase steels (Dual phase and transformation-induced plasticity (TRIP) steels) during production processes. These kinds of steel consist of a ferritic matrix with dispersed second phases like bainite, martensite and retained austenite. A microstructure-based approach by means of representative volume elements (RVE) is used taking into account carbon partitioning for the flow curve description of each individual phases. With the help of the RVE it is possible to establish a link between the microstructure and the macroscopic failure behavior. In the case of DP-steels, the real microstructures were investigated in a two-dimensional approach. A cohesive zone model (CZM) has been used to study the debonding analysis of the martensitic islands from the ferrite parent phase. To describe the ductile damage of the ferritic matrix, the Gurson–Tvergaard–Needleman model (GTN) was applied. The parameter identification for the CZM and GTN models is based on metallographic investigations and fracture surface analysis. The calculated stress-strain distribution in the heterogeneous microstructure was studied. The investigations provide a physically-based correlation between the multiphase microstructures, mechanical properties, and failure behavior of multiphase steels for automotive applications.

Size effects on the ductile/brittle fracture properties of the pressure vessel steel 20 g

Detailed un-standard experiments of fracture toughness in which SENB specimens of five different thicknesses were included were carried out to investigate the size effect on the ductile and brittle fracture. It is found that the ductile fracture toughness parameter-the critical strain energy release rate increases with the size of the specimens which have the similar geometry shape and then decreases gradually to the plane strain fracture toughness. On the upper shelf the critical strain energy release rate increases with the size in the range of 4–16 mm for the increment of the plastic deformation zone size and plastic fracture strain under general yielding conditions, and then drops down from 16 mm to 22 mm for the plastic deformation zone size not changing much which is less than the residual ligament width and the increase of the proportional of the high stress triaxiality zone to the whole specimen. While on the lower shelf the critical strain energy release rate increases with the thickness in the range of 4–8 mm for the plastic deformation zone size increasing under small scale yielding conditions, and then drops down from 8 mm to 22 mm for the increase of the high out-of-plane constraint. Theoretical analysis with the primary definition of the strain energy release rate, the constraint level and the plastic deformation volume was performed to investigate the different size effects for different temperatures. FEA simulations with continuum damage model of GTN models to get the results of the stress triaxiality as an important factor of fracture toughness increasing with the reduction of the thickness.

구조물용 강재의 파단기준에 대한 실험 및 이론 연구

Six smooth flat tensile specimens and eighteen punch specimens with three different thicknesses were machined from steel of JIS G3131 SPHC. In addition to punch tests, incremental tensile tests were conducted to obtain average true flow stress - logarithmic true strain curves. Through parametric FE simulations for the tensile specimens, material parameters related to GTN model were identified. Using indenters with three kinds of radius, punch tests were carried out to obtain fracture characteristics of punch specimens. Numerical analyses using both fracture models, GTN and plasticity model, gave that the former estimated well the fracture of punch specimen but the latter did not. A new concept for critical size of plate elements was introduced based on minimum relative sharpness between contact structures. Consequently, a new criterion for critical element size was proposed to be less than 20% of minimum relative radius of interacting structures.

Nonlocal Modeling and Simulation of Ductile Damage and Failure in Metal Matrix Composites

The purpose of the current work is the application of a recent nonlocal extension (Reusch, F., Svendsen, B., and Klingbeil, D., 2003, “Local and Non-Local Gurson-Based Ductile Damage and Failure Modelling at Large Deformation,” Eur. J. Mech. A∕Solids, 22, pp. 779–792; “A Non-Local Extension of Gurson-Based Ductile Damage Modeling,” Comput. Mater. Sci., 26, pp. 219–229) of the Gurson–Needleman–Tvergaard (GTN) model (Needleman, A., and Tvergaard, V., 1984, “An Analysis of Ductile Rupture in Notched Bars,” J. Mech Phys. Solids, 32, pp. 461–490) to the simulation of ductile damage and failure processes in metal matrix composites at the microstructural level. The extended model is based on the treatment of void coalescence as a nonlocal process. In particular, we compare the predictions of the local with GTN model with those of the nonlocal extension for ductile crack initiation in ideal and real Al–SiC metal matrix microstructures. As shown by the current results for metal matrix composites and as expected, the simulation results based on the local GTN model for both the structural response and predicted crack path at the microstructural level in metal matrix composites are strongly mesh-dependent. On the other hand, those based on the current nonlocal void-coalescence modeling approach are mesh-independent. This correlates with the fact that, in contrast to the local approach, the predictions of the nonlocal approach for the crack propagation path in the real Al–SiC metal matrix composite microstructure considered here agree well with the experimentally determined path.

A complete GTN model for prediction of ductile failure of pipe

The micro mechanical model by Gurson–Tvergaard–Needleman is widely used for the prediction of ductile fracture. Some material properties (Gurson parameters) used as material input in this model for simulation are estimated experimentally from specimen level. In this article an attempt has been made to tune the values of some of these Gurson’s parameters by comparing the simulated results with the experimental results in the specimen level (axisymmetric tensile bar and CT specimens). An elastic–plastic finite element code has been developed together with Gurson–Tvergaard–Needleman model for void nucleation and growth. The initial value of fc is determined from Thomason’s limit load model and then tuned on the basis of best prediction of the failure of one-dimensional tensile bar. Then the load versus load line displacement and J versus \({\Updelta}\)a results for CT specimen are generated with the same code and the value of fn is tuned to match the simulated J versus \(\Updelta\)a results with the experimental results. Lastly the same code and the Gurson’s parameters obtained are used to simulate the load versus load point displacement and crack growth for pipe with circumferential crack under four point bending. The simulated results are compared with the experimental results to assess the applicability of the whole method. In the proposed material modelling, post-yielding phenomena and necking of the tensile bar are simulated accordingly and strain softening due to void nucleation and growth has been taken care of properly and drop in stress is implicitly simulated through a model. Incremental plasticity theory with arc length method is used for the nonlinear displacement control problem.

Multi-Scale Characterization and Modeling of Ductile Failure in Cast Aluminum Alloys

This paper develops three components contributing to the framework of multi-scale modeling of ductile fracture in aluminum alloys. The first module is morphology-based domain partitioning, which delineates regions of statistical inhomogeneity. The second module is micromechanical analysis with particle fragmentation and matrix cracking. A locally enriched VCFEM or LE-VCFEM is developed to incorporate ductile failure through matrix cracking in the form of void growth and coalescence using a non-local Gurson-Tvergaard-Needleman model. The third module develops a homogenized anisotropic plasticity-damage model for macroscopic analysis. Parameters in this GTN model are calibrated from results of homogenization of microstructural variables of microstructural RVE.

Cohesive Zone Model and GTN Model Collation for Ductile Crack Growth

The micromechanical modelling encounters a problem that is different from basic assumptions of continuum mechanics. The material is not uniform on the microscale level and the material within an element has its own complex microstructure. Therefore the concept of a representative volume element (RVE) has been introduced. The general advantage, compared to conventional fracture mechanics, is that, in principle, the parameters of the respective models depend only on the material and not on the geometry. These concepts guarantee transferability from specimen to components over a wide range of dimensions and geometries. The prediction of crack propagation through interface elements based on the fracture mechanics approach (damage) and cohesive zone model is presented. The cohesive model for crack propagation analysis is incorporated into finite element package by interface elements which separations are controlled by the traction-separation law.

Assessment of In-Plane Size Effect for Nuclear Carbon Steels Using Damage Models

The present work deals with an applicability of the local approach to assess in-plane size effects among different sized compact tension (CT) specimens. To characterize ductile crack growth of typical nuclear materials, SA515 Gr.60 and SA516 Gr.70 carbon steels, finite element analyses employing modified GTN and Rousselier models as well as fracture toughness tests were carried out. Material damage parameters were calibrated using standard CT specimens and reflected to predict fracture resistance (J-R) curves of larger CT specimens. Since comparison results between numerically estimated J-R curves and experimentally determined ones corresponded well, it is anticipated that the local approach might be used as a promising tool for ductile fracture evaluation incorporating the in-plane size effect.

Constitutive modeling of void shearing effect in ductile fracture of porous materials

Many solids, including geomaterials and commercially available metallic alloys, can be considered as a porous media. The Gurson-like model has been proposed to describe plastic deformation for such type of materials. It has attracted a great deal of attention and various modifications to this model have been proposed. The constitutive equations of Gurson-like model are governed by the first and second stress invariants and the current void volume fraction of the material. Tvergaard and Needleman included void nucleation, growth and coalescence to Gurson model in a phenomenological way [Tvergaard V, Needleman A. Analysis of the cup-cone fracture in a round tensile bar. Acta Metall 1984;32(1):157–69] – thus suggesting the so called GTN model. Meanwhile, little attention was given to the dependence of the damage evolution on the third stress invariant. McClintock et al. [McClintock FA, Kaplan SM, Berg CA. Ductile fracture by hole growth in shear bands. Int J Fract Mechan 1966;2(4):614–27] proposed damage model based on the void evolution in localized shear banding. In the present paper, a separate internal damage variable which differs from the conventional void volume fraction is introduced. The GTN model is further extended to incorporate the void shearing mechanism of damage, which depends on the third stress invariant. Numerical aspects are addressed concerning the integration of the proposed constitutive relations. A unit cell is studied to illustrate the intrinsic mechanical behavior of the modified model. Computations of the deformation in axisymmetric and transverse plane strain tension are also performed. Realistic crack modes in these simulations are achieved for the modified GTN model.

Modelling of ductile fracture initiation in strength mismatched welded joint

In this paper, the effect of strength mismatch and width of the welded joints on the stress–strain distribution in the crack tip region has been discussed. The single-edge notched bend (SENB) specimens (precrack length a 0/ W = 0.32) were experimentally and numerically analysed. The model of local approach to fracture, proposed by Gurson, Tvergaard and Needleman, was used. High-strength low-alloyed (HSLA) steel was used as a base metal in quenched and tempered condition. The flux-cored arc-welding process in shielding gas was used. Two different fillers were selected to make over- and undermatched weld metal. The experimental analysis of fracture behaviour of the over- and undermatched welded joints was followed by numerical computations of void volume fraction in front of the crack tip. The critical void volume fraction, f c, used in prediction of the crack growth initiation on the SENB specimen had been previously determined on a round smooth specimen. Three widths of weld metal were considered: 6, 12 and 18 mm. A comparison of the crack tip opening displacement (CTOD) values corresponding to crack initiation in the SENB specimens is given, as determined both experimentally and using the GTN model.