GTN Damage Model Research Articles

Study on the damage behaviour of titanium alloy laser-welded blank during hot gas pressure forming

The damage behaviour of titanium alloy laser-welded seam during hot gas pressure forming was studied by experiment and simulation. The GTN damage model was used to simulate the hot gas pressure forming process of the welded blank. The evolution of the void volume fraction during the forming process was obtained. Hot gas pressure forming experiments of cup-shaped parts were carried out. The microstructure at different positions of the cup-shaped part was observed by scanning electron microscope. Results show that the damage to the weld seam during hot gas pressure forming was mainly related to the strain. The damage of the inside fillet near the flange develops most rapidly, and it easily cracks due to the large deformation during the free bulging stage. The damage on the bottom centre develops slowly at the free bulging stage. After the bottom of the cup-shaped part contacted the die, the volume fraction of damage on the bottom center continued to increase firstly and then reached to a stable value gradually. Various micro cracks were observed during the hot gas pressure forming. The volume fraction of cracks increased with the increasing strain, and the small cracks gradually grew, expanded, and merged to form larger cracks. It is important to control the maximum strain of the weld seam during the forming to avoid possible harmful damage.

Investigation into the anisotropic damage behavior of LA103Z Mg‐Li alloy rolling sheet using X‐ray computed tomography and numerical modeling

AbstractThe anisotropic damage behavior has a great influence on the formability of rolling sheets. This work aimed to investigate the anisotropic damage mechanism of the LA103Z Mg‐Li alloy rolling sheet by combining mesoscale detection and modeling. The X‐ray computed tomography (XCT) and scanning electron microscope (SEM) were applied to characterize the evolution of damage morphology and volume fraction in RD, DD, and TD directions of the rolling sheet. The GTN damage model was calibrated by the experimental results with the representative volume element (RVE) method. The anisotropic damage mechanism was revealed via experimental and modeling results. The micro void nucleation strain εN was critical to determine the initiation moment of the anisotropic damage. The continuous nucleation in RD direction, the severe growth in DD direction, and the massive coalescence in TD direction were the micro void evolution competition results that caused the anisotropy for damage mechanism and fracture strain.

Damage evolution of titanium alloy laser-welded joint during hot deformation: Experiment and modeling

The damage evolution of TA15 titanium alloy laser-welded joint during hot deformation was studied by tensile tests and the GTN model. Tensile tests of the welded joint at 900 °C with different strain rates were carried out, and the evolution of cracks and voids in the welded joint during the tensile deformation was characterized. The response surface method combined with genetic algorithm was used to calibrate the GTN model at high temperature. The GTN parameters of titanium alloy welded joint under different strain rates at 900 °C were obtained. Results show that the voids first germinate at the grain boundary and gradually expand along the grain boundary during the tensile deformation. The inner wall of the welding porosity is easy to become the source of crack damage during the deformation, and the shape of porosity changes from round to oval gradually with the increase of strain. The true stress-strain curves obtained by simulation agree well with the experimental results, and the error between the predicted fracture strain and the experimental result is less than 5%. The developed GTN damage model was used in the simulation of hot gas free bulging, which demonstrates that it can predict the damage evolution and fracture behavior of the weld seam accurately under different conditions.

Fatigue crack growth: Validation of the Kmax-ΔK approach using the GTN damage model

Considering cyclic plastic deformation as the single damage mechanism behind the fatigue crack growth (FCG), the effect of the mean stress is null in the absence of crack closure. In this study, an additional damage mechanism was introduced, predicting the effects of the growth, nucleation and coalescence of micro-voids. Using a non-local damage model, the reverse plastic zone was identified as the fatigue process zone, allowing to establish a relation to calculate its size. Considering aluminium alloy 2024-T351, the predictions are in close agreement with the experimental da/dN-ΔK curves, for distinct stress ratios. The results highlight that the effect of Kmax on the FCG rate is small in the absence of crack closure. On the other hand, modelling the contact between the crack flanks, the effect of Kmax on the FCG rate is amplified, i.e. the ΔK-Kmax plots for a given da/dN presented a Kmax dominance zone. The developed model suggests a three-parameter approach: ΔKeff -ΔK-Kmax.

Geometry independent J-Tz domination of three-dimensional steady growing crack-tip fields in ductile materials

The crack-tip in-plane (Q and A2) and out-of-plane constraint (Tz) parameters have been extensively studied for ductile fracture problems on the basis of the pioneering HRR and J-Tz solutions. However, these analytic solutions rarely focus on the steady growing cracks, which play a vital role in J-R curve and integrity assessments of complicated structures. In this work, three-dimensional finite element method and GTN damage model are adopted to simulate quasi-static ductile crack growth under different plastic exponents, geometries and load levels. With the follow-up coordinate system, the J-Tz solution is extended to describe the crack-tip stress distributions of the quasi-static elastic–plastic growing cracks. It is found that in front of steady growth cracks, Tz strongly depends on specimen geometry. In the range of small-scale yielding, tensile stress and Tz gradually increase with increasing load J/JC. When the large-scale yielding stage is approaching, tensile stress and Tz tend towards a stable state. The maximum relative errors between the J-Tz solution and three-dimensional finite element results are 4.16% and 9.28% with J/JC smaller than 1 and 2, respectively. Such dominance and geometry independence of the leading order J-Tz solution make it more simply and effectively to assess the ductile fracture problems.

Prediction of Damage and Cracking of Magnesium Alloy Upsetting and Forming Based on Improved GTN Damage Model

Prediction of Damage and Cracking of Magnesium Alloy Upsetting and Forming Based on Improved GTN Damage Model

Tensile low-cycle fatigue performance and life prediction of high-strength bolts

Monotonic tensile tests and tensile low-cycle fatigue tests have been conducted to explore the low-cycle fatigue life of high-strength bolts, which is an important property to guarantee the connections do not occur low-cycle fatigue failure before their connected members under earthquakes. Large-deformation performance and failure modes of bolts were numerically simulated based on the damage constitutive relation which was investigated by the tensile tests of smooth and notched specimens. The results show that complete uniaxial constitutive relation of the bolt material, namely 20MnTiB steel, and the displacement from tensile load response of smooth specimens in the numerical simulation can be better described by the Swift flow stress model. The GTN damage model of the steel was calibrated by tensile tests and finite element models of notched specimens. With the decrease of the notch radius, the tensile capacity of the notched specimen increases while the ductility gets worse. The calibration parameters of GTN damage model can be applied to simulate the load-displacement response and fracture behavior of notched specimens accurately. In order to obtain a more targeted GTN model under different stress states, the quantitative relation between equivalent plastic strain during nucleation and stress triaxiality was proposed, which provided an important reference for establishing fatigue damage models of various bolted joints in the numerical simulation. Both the fatigue failure modes of the bolts under cyclic displacement with constant amplitude and the fatigue life based on the tensile capacity degradation were obtained from the fatigue tests. The fatigue brittle fracture and plastic elongation of the shank are the two fatigue failure modes of the bolt. Typical regional characteristics are presented in the bolt fatigue fracture, with beach-like fatigue bands in the expansion area. Under different failure modes, the capacity degradation can better determine the fatigue life of bolts. The methods for predicting fatigue life were proposed based on cyclic displacement amplitude, equivalent stress amplitude and local plastic strain. A good prediction result was proved by the phenomena that the predicted fatigue life based on the cyclic displacement amplitude and local plastic strain was basically within the scatter band of 1.5. Moreover, the fatigue design parameters of bolts given by the equivalent stress amplitude method provide a reference for establishing a unified fatigue design theory.

Edge tracing technique to study post‐necking behavior and failure in Al alloys and anisotropic plasticity in line pipe steels

AbstractThe recently developed edge tracing (ET) method allows to estimate the radial deformation in axisymmetric tensile specimens via analysis of digital images recorded during the experiments. Images are processed to detect the sample's contours and therefore estimate the minimal cross‐section diameter. This technique was mainly developed to characterize the plastic behavior well beyond the necking strain. The aim of this work is to apply the ET method to two novel case studies. Firstly, the post‐necking behavior and failure of a low ductility Al alloy are investigated. Low ductility alloys tend to fail brutally after reaching the maximum load. The major result is the capture of the sharp load drop which allowed to calibrate parameters of a GTN damage model. Secondly, the anisotropic elastic–plastic behavior of a “vintage” line pipe steel is characterized by a direct measurement of the Lankford coefficient. Assembled experimental data allowed to model the anisotropic plasticity beyond necking in different loading directions.

Experimental crack identification of API X70 steel pipeline using improved Artificial Neural Networks based on Whale Optimization Algorithm

Intelligent systems have recently received recognition for their ability to solve extremely complicated and multidimensional problems. Artificial Neural Networks (ANN) has quite a lot of success in overcoming such issues, but some limitation can be found. The present study discusses in detail the application of the WOA-ANN hybrid model for predicting the crack length based on different input values, i.e. strains, stresses, and displacements, to test the accuracy of the presented technique. The proposed technique is compared with GA-ANN, AOA-ANN, and WOABAT-ANN. Coupled metaheuristic optimization algorithms with ANN aim to increase its effeciency. The connectivity between neurons carries some weight. Neurons are also connected to some biases. Connection weights and biases are modified to give the smallest possible error function based on the input values, and corresponding target output values supplied. Back Propagation (BP) is the usual name for this approach. The investigated approach is related to real engineering applications and controls the structures’ state. Standard ASTM test specimens are chosen to study the evolution of fracture mechanics parameters. Next, an analytical model is developed by simulating the tests using the Finite Element Method (FEM) and validated with experimental results. FEM is used to analyse the tensile failure process of the one-sided notch samples with the mesoscopic GTN damage model and extract the data required for WOA-ANN. After collecting the database, our model is ready for predicting different scenarios. The obtained results using WOA-ANN are efficient compared to other techniques.

A new void coalescence mechanism during incremental sheet forming: Ductile fracture modeling and experimental validation

• Investigated a new void coalescence mechanism and its effect on ductile fracture of ISF. • Improved formability of ISF is attributed to closely-packed void cluster. • Proposed extended GTN model for ISF by considering oriented void cluster. • Validated proposed model with various process conditions and deformation states. The forming limit of sheet metal can be significantly improved by incremental sheet metal forming(ISF) process, however lacks of relevant fundamental researches. Besides, accurate prediction of formability based on deeper understanding of deformation mechanism is beneficial for the evaluation of ductile failure behavior in ISF process. In the present work, a new void coalescence approach, that voids coalesce closely along meridianal direction rather than conventional thickness direction, is proposed and its influence on formability is investigated. The improved formability is attributed to the formation of closely-packed void clusters along meridianal direction, and these void clusters can stably exist inside the sheet metal even after void coalescence. By introducing two independent parameters into classic GTN model, an extended GTN damage model is developed to describe this new void coalescence mechanism in ISF process, and is validated through a series of experiments. Through investigations in this work, the fundamental understanding of improved formability in ISF is revealed, and the extended GTN model shows its comprehensive capability in predicting ductile fracture behavior with a satisfactory accuracy.

Influence of heat treatments on the formability of the 6061 Al alloy sheets: experiments and GTN damage model

The research mainly focused on the forming limit curves (FLC) of the 6061 Al alloy subjected to heat treatments with various (1 mm, 1.6 mm, 2 mm, and 2.5 mm) sheet metal thicknesses. Five peculiar heat treatments, including natural aging temper (T4) and highest-strength (T6) temper, were devised to study the influence of heat treatments on the formability of 6061 Al alloy sheets. Tensile tests were executed to determine the plastic behavior of the alloy under specific heat treatments. Laser marked FLC specimens were deep-drawn with the proposed spring-attached Nakajima deep drawing test setup. A finite element model (FEM) of the deep drawing experiment was constructed to investigate the nucleation and growth mechanism of the voids. The developed model was compared and verified with the experimental FLC, fracture locations, and dome height. The FEM results were differed from the experimental FLC by less than 5% considering all heat treatments and sheet thicknesses. The results declared that sheet metal thickness has a positive effect on the effective strain up to failure. On the other hand, the duration of artificial aging time reduced effective strain to failure controlled by nucleation and growth of voids.

Size effect on the damage evolution of a modified GTN model under high/low stress triaxiality in meso-scaled plastic deformation

Micro-forming is a micro-manufacturing method with broad application prospects, in which the size effect on damage development under different stress states is an allimportant problem, but has not been systematically explained. This study established a coupled model by the combination of mechanism-based strain gradient plasticity (MSG) and a shear modified GTN damage model. The proposed model is implemented in UMAT subroutine of ABAQUS and validated by experimental observation and numerical simulation of notched specimens with different shapes. Fracture photographs suggested that the failure mechanism of materials under high/low stress triaxiality is nucleation, growth and coalescence of voids and shear-induced slip respectively. The fracture displacement and loading force obtained by the numerical simulation considering the coupling model are basically consistent with the tensile test results. Furthermore, the size effect on two damage parameters is qualitatively described, that the MSG theory can promote the evolution of shear damage and inhibit the development of microvoids. In addition, the influence mechanism of the strain gradient is discussed in detail, and the relationship among the equivalent stress, stress triaxiality and damage parameters is revealed. The present work thus facilitates the in-depth understanding of the size effect on damage evolution and fracture formation in meso-scale of metallic materials.

Formability prediction using bifurcation criteria and GTN damage model

In this paper, four plastic instability criteria, which are based on the bifurcation theory, are coupled with the GTN damage model for the prediction of diffuse and localized necking. General bifurcation (GB) criterion and limit-point bifurcation (LPB) criterion are used to predict diffuse necking, while loss of ellipticity (LOE) criterion and loss of strong ellipticity (LOSE) criterion are used to predict localized necking. The resulting constitutive equations and instability criteria are implemented into the finite element code ABAQUS/Standard. The constitutive equations are formulated within the framework of large deformations and fully three-dimensional approach. Since the developed numerical tools have intended applications mainly for thin sheet metals; therefore, the plane-stress conditions are considered within the instability criteria. The present contribution focuses on the effect of destabilizing mechanisms, due to non-associative plasticity and non-normal plastic flow rule, on the prediction of forming limit diagrams (FLDs). Theoretical classification of the bifurcation criteria, in terms of their order of prediction of critical necking strains, is first presented. Then, several variants of the GTN model are combined with the bifurcation criteria for the prediction of FLDs for fictitious materials. It is shown that the hierarchical prediction order of the different instability criteria is consistent with the theoretical classification, for all the considered variants of the GTN model. More specifically, it is shown that the GB criterion provides a lower bound to all bifurcation criteria, in terms of necking prediction, while the LOE criterion represents an upper bound.

Identification of material parameters of a shear modified GTN damage model by small punch test

A new approach was put forward to identify the damage parameters of the shear modified GTN damage model proposed by Nahshon and Hutchinson (Eur J Mech Solid 27:10–17, 2008) by combining the artificial neural networks algorithm and small punch test. The factorial design method was used to analyze the influence of the parameters on the shape of load-displacement curve of small punch test. The less important parameters were set as empirical value and the significant factors were determined by an artificial neural networks model which was build up based on large amount of simulations of small punch tests with different levels of damage parameters values. The identified parameters were validated by small punch test simulations with different specimen thickness. The results show that the identified parameters of the shear modified GTN damage model are effective to characterize the mechanical behavior as well as the damage evolution and ductile failure of material during the process of small punch test. In addition, the applicability of the identified parameters in the tests with different stress condition were verified.

Experimental and numerical investigation of ductile fracture using GTN damage model on in-situ tensile tests

The present work is devoted to experimental and numerical investigation of in situ tensile tests to recognize the mechanisms of ductile fracture under different stress states. The GTN model, which is a micromechanical based damage model, was used for numerical simulations. The void related parameters of GTN model for SAE 1010 plain carbon steel were identified by response surface method (RSM) through minimizing the difference between numerical and experimental results of tensile test on a standard specimen. The void related parameters of GTN model were determined 0.00107, 0.00716, 0.01 and 0.15 for f0, fN, fc and ff respectively. After calibrating the damage model for the studied material, the tensile tests were carried out on the in-situ specimens with different geometries. The fractographic analysis was performed to identify the ductile fracture under wide range of stress states and two failure mechanisms were observed. The calibrated damage model was applied to FE simulations of in-situ tensile tests for numerical study of the experimentally observed fracture phenomenon. The extracted numerical results showed a good agreement with experimental observations comparing load-displacement plots with a margin of error within 5%. A better ductile fracture predictions were captured in 90° specimens. The location of fracture initiation, crack growth orientation and the displacement at fracture zone in numerical studies also showed close correspondence with experiments.

Identification strategy influence of elastoplastic behavior law parameters on Gurson–Tvergaard–Needleman damage parameters: Application to DP980 steel

This work adopts elastic–plastic/damage coupling in order to describe tensile behavior with validation on the deep-drawing test of a DP980 Dual Phase steel sheet. The damage model used is the Gurson–Tvergaard–Needleman (GTN model). The hardening laws used are those of Swift (non-saturating law), Voce (saturating law), Hockett-Sherby (saturating law) and the two combined laws Swift/Hockett-Sherby and Swift/Voce. An identifying method for elastic–plastic parameters and GTN damage model parameters is presented using the software modeFRONTIER. This method based on the inverse analysis is also proposed for the identification of weighting coefficient α of the Swift/Hockett-Sherby combined hardening law. Finally, a parametric study was carried out to show that the plastic modulus can be considered as another criterion for the choice of a hardening law. Dependence of the damage model parameters to the hardening law is clearly established. The different behavior laws are introduced via a VUHARD type subroutine in the calculation code Abaqus.

Ductile fracture prediction in aluminium alloy 5A06 sheet forming based on GTN damage model

The Gurson-Tvergaard-Needleman model (GTN model) was employed to predict the ductile fracture behaviour in the forming of aluminium alloy 5A06 sheet. The in-situ tensile test with scanning electron microscope (SEM) was conducted to determine the original void volume fraction, the critical void volume fraction, and the failure void volume fraction in GTN model. The other parameters in GTN model were determined by an inverse approach. Eleven types of uniaxial tension tests including shear specimen, dog-bone specimen, notched specimens with different root radius, and V-notched specimens, were carried out to investigate the influence of stress triaxiality on predictability for fracture. The results show that the GTN fracture criterion can give a good prediction under high stress triaxiality. The ductile fracture behaviour in hydro-bulging aluminium alloy semi-ellipsoidal shell was researched by experiments and simulation based on the GTN model. Four kinds of semi-ellipsoidal shell with aspect ratio 1, 1.5, 2.0, and 2.5 were studied. The predicted results show good agreements with the experimentally determined bursting position, bursting pressure, and the maximum dome height.

On the numerical implementation of a shear modified GTN damage model and its application to small punch test

Gurson-type models have been widely used to predict failure during sheet metal forming process. However, a significant limitation of the original GTN model is that it is unable to capture fracture under relatively low stress triaxiality. This paper focused on the fracture prediction under this circumstance, which means shear-dominated stress state. Recently, a phenomenological modification to the Gurson model that incorporates damage accumulation under shearing has been proposed by Nahshon and Hutchinson. We further calibrated new parameters based on this model in 22MnB5 tensile process and developed the corresponding numerical implementation method. Lower stress triaxiality were realized by new-designed specimens. Subsequently, the related shear parameters were calibrated by means of reverse finite element method and the influences of new introduced parameters were also discussed. Finally, this shear modified model was utilized to model the small punch test (SPT) on 22MnB5 high strength steel. It is shown that the shear modification of GTN model is able to predict failure of sheet metal forming under wide range of stress state.

Establishment of Unified Correlation of In-Plane and Out-of-Plane Constraints with Ductile Fracture Toughness of Steel

In this paper, the finite element method (FEM) based on GTN damage model was used to obtain ductile fracture toughness and investigate the establishment method of unified correlation of in-plane and out-of-plane constraints with ductile fracture toughness of steels. The unified constraint parameter Ap at different equivalent plastic strain (εp) isolines has been calculated and analyzed for SEN(B) specimens with a wide range of in-plane and out-of-plane constraints. The results show that the average Ap along the specimen thickness (Apave) can well characterize a wide range of in-plane and out-of-plane constraints. The suitable εpisolines range for establishing the unified correlation between Apave and ductile fracture toughness of the steel has been obtained. For the specimens with lower constraint, the higher εp values should be used. The results also show that the correlation line of JC/Jref-Apave1/2is independent of the selections of the suitable εp isolines and the reference specimen. This may bring convenience for the establishment and application of the JC/Jref-Apave1/2correlation lines. Using ductile fracture toughness data of a small number of specimens with different constraints (such as three specimens with different a/W) together with FEM calculations of the parameter Ap, the correlation line of JC/Jref-Apave1/2can be established. The correlation line may be used in structural integrity assessments incorporating both in-plane and out-of-plane constraints.

Modeling the ductile fracture and the plastic anisotropy of DC01 steel at room temperature and low strain rates

This paper presents different extensions of the classical GTN damage model implemented in a finite element code. The goal of this study is to assess these extensions for the numerical prediction of failure of a DC01 steel sheet during a single point incremental forming process, after a proper identification of the material parameters. It is shown that the prediction of failure appears too early compared to experimental results. Though, the use of the Thomason criterion permitted to delay the onset of coalescence and consequently the final failure.