Anisotropic Ductile Fracture Research Articles

Numerical investigation on bending characteristic and ductile fracture of AA7075 thin-walled beam using advanced orthotropic plasticity and fracture models

Thin-walled structures manufactured from the 7075 aluminum alloy are gaining tremendous attention in the automotive industry for their potential to reduce vehicle weight. However, the bending characteristics and rupture behavior of the AA7075 thin-walled beams under unexpected collision events have not been extensively studied. This study aims to fill that gap through a detailed numerical investigation of the bending deformation and failure mechanism of AA7075 thin-walled beams under quasi-static three-point bending at room temperature. Full-size, three-dimensional numerical simulations of laboratory-scale AA7075-T6 hat-shaped beam were conducted using the ABAQUS/Explicit solver. The material elastic–plastic response is described by a rate-independent constitutive description, incorporating advanced non-quadratic orthotropic plasticity and anisotropic ductile fracture criteria via VUMAT subroutines. Results indicate that the simulations accurately reproduced experimental observations, including the loading-displacement curves and deformation patterns. The bending behavior of the AA7075-T6 thin-walled beams aligns with typical bending collapse mechanisms, consistent with Kecman’s theory. The rupture process exhibits ductile fracture characteristics, with heterogeneous stress distribution across the material thickness affecting crack initiation rates between the upper and lower surfaces. Notably, the stress state at the fracture’s half-thickness section approximates an equi-biaxial tension condition. These findings provide essential insights into the bending deformation and failure mechanisms of AA7075 thin-walled structures under unexpected impact loading.

Anisotropic ductile fracture of a stainless steel under biaxial loading: Experiments and predictions

The anisotropic ductile fracture behavior of a stainless steel is investigated using a combination of experiments and analysis. The material is SS-304L, an austenitic, low-carbon stainless steel, received in the form of tubes of 2.38 mm dia. and 0.15 mm thickness. The tubes are inflated under volume control in a custom apparatus. At the same time, the axial force on the tubes is kept proportional to the pressure induced by the inflation. This leads to quasi-proportional stress paths in the meridional-hoop engineering stress space. A total of 15 discrete paths are successfully tested. Stereo-type Digital Image Correlation is used to measure the strains. In every case, the tubes develop a series of instabilities before bursting. The failure is oriented along the meridional or the hoop direction of the tube, depending on which stress is greater. A mild plastic anisotropy is detected in these experiments. Hence these results are then used for calibrating the anisotropic yield criterion Yld2004-3D. This is introduced in a finite element model of the experiments, which includes a thickness imperfection designed to capture the two failure orientations observed in the experiments. The numerical model using the Yld2004-3D criterion reproduces the experiments well, e.g., it captures the experimental stress-strain and induced strain paths better than von Mises. It is then used to probe the conditions at the onset of fracture (hybrid method). It is found that most paths lead to essentially proportional loading during deformation. A significant anisotropy in the fracture behavior is detected, with the meridional-stress-dominated paths being able to develop much higher strains than the hoop-dominated ones. These results are then captured by the DF2016 ductile fracture criterion, modified to use the anisotropic yield criterion Yld91. The proposed criterion is flexible enough to represent the fracture anisotropy very well, without being unnecessarily complex. The fracture forming limit curve (i.e., the fracture envelope in strain space) predicted by the DF2016/Yld91 model is also found to be very close to the experiments. The results and findings of this work help establish a framework to reliably design components and processes when significant fracture anisotropy is expected.

Evaluation of anisotropic fracture in AA1050-O sheet using uncoupled ductile fracture models with Hill48 plasticity

Uncoupled ductile fracture models have gained popularity for accurate prediction of fracture in ductile metallic sheets due to their ease of implementation. Accurate description of anisotropic fracture behavior is an active research field for sheet metal forming. In the present study, two isotropic ductile fracture models, i.e., modified Mohr-Coulomb and Hosford-Coulomb are evaluated for an O-tempered aluminum alloy (AA1050-O) sheet. The plastic anisotropy is modeled with a non-associated Hill48 plasticity model. In order to verify the models, experiments are conducted for a 1.2 mm thick AA1050-O sheet under various loading conditions, such as uniaxial tension, in-plane shear, and plane strain tension at room temperature. For evaluating the anisotropic ductile fracture, tensile tests are carried out in 15° intervals to the rolling direction using digital image correlation technique. The predicted fracture limit strains by the two uncoupled fracture models are compared with experimental results to evaluate the accuracy of these models.

Anisotropic Gurson–Tvergaard–Needleman model considering the anisotropic void behaviors

Anisotropic ductile fracture resulting from different microscopic void behaviors has a significant effect on material formability. To accurately predict the anisotropic ductile fracture, an anisotropic Gurson-Tvergarrd-Needleman (GTN) model considering the anisotropic void behaviors was proposed. The effect of high stress triaxiality on void nucleation was considered and remodeled through an additional stress dependent factor in the modeling formulation. Meanwhile, the anisotropic stress triaxiality was adopted. To describe the difference in damage accumulations along different material orientations, a new formulation related to anisotropic critical damage was proposed. Various uniaxial tensions including round bars and plate-shaped specimens were performed along 30° and 60° with respect to the rolling direction for 2024-T35 aluminum alloy. These experimental results, along with previously-published data, were used to validate the proposed model by comparing numerical predictions and experimental results in terms of the load responses and displacements at fracture (DAFs) along different loading directions. Remarkable improvement can be achieved when the contribution of high stress triaxiality, anisotropic void nucleation and critical damage are considered in the modeling of anisotropic ductile fracture. The proposed modeling formulations provide new ideas for the construction of anisotropic GTN series model.

Modeling anisotropic ductile fracture of AA7075-T6 sheet for sheet metal forming considering anisotropic stress state

Anisotropic ductile fracture is one of the critical issues in the precision plastic forming of lightweight sheet metals. In this work, a new anisotropic ductile fracture model is developed by introducing the anisotropic stress triaxiality into the weight equation of the shear-controlled ductile fracture criterion. In an attempt to consider the effect of material anisotropy on stress state, the proposed fracture model is constructed in the anisotropic stress state form. The proposed anisotropic fracture model is used to characterize the anisotropic ductile fracture behavior of the AA7075-T6 sheet with a thickness of 2.0 mm under various stress states at room temperature. A series of uniaxial tensile tests are conducted using the in-plane shear specimen, the specimen with a central hole, and the plane strain grooved specimen to experimentally investigate the ductile fracture of AA7075-T6 along rolling, diagonal, and transverse directions. The proposed fracture model is calibrated by fracture strains determined from the hybrid experimental–numerical approach. With the calibrated fracture model, the anisotropic ductile fracture behaviors of AA7075-T6 over a wide range of stress states are predicted and compared with experimental measurements. The results show that the proposed fracture model successfully captures the anisotropic ductile fracture behavior of AA7075-T6 under various stress states at room temperature. Furthermore, to further illustrate the fracture predictive capability of the proposed fracture model, the predicted anisotropic fracture forming limit diagram is compared with the experimental forming limit strains obtained from the literature. Reasonable agreement is shown between literature data points and predicted fracture forming limit diagram. Accordingly, the proposed model has a great advantage in quantitative characterizing the anisotropic ductile fracture of high-strength aluminum alloy sheets under various loading conditions.

Anisotropic ductile fracture: experiments, modeling, and numerical simulations

The continuous hot rolling process induces anisotropy in the plastic yield and flow and results in an anisotropic ductile fracture. In this study, experiments, including uniaxial in-plane tension tests and shear tests of butterfly specimens along different material orientations, were performed, and microscopic observations were used to determine the differences in damage mechanisms. The Yld91 anisotropic yield stress was introduced into the extended isotropic Gurson-Tvergaard-Needleman (GTN) model, and the associated flow rule (AFR) and non-associated flow rule (NAFR) were adopted to formulate two anisotropic GTN models. Anisotropic GTN models were implemented in finite element software via user subroutines, and were used to predict the fracture initiation of Al2024-T351. For different plastic flow rules, the anisotropic parameters were calibrated using the anisotropic stress and Lankford coefficients. An inverse analysis with a two-stage optimization algorithm was adopted to calibrate the damage-related parameters. Moreover, an extended isotropic GTN model was adopted for comparison. The prediction accuracy of the proposed anisotropic GTN models was evaluated by analyzing the load responses and displacements at fracture for various specimens and material orientations. The good conformation between the experimental results and numerical predictions verifies the predictive ability of the proposed models to a certain degree. In addition, some suggestions and conclusions are provided for the formulation of an advanced anisotropic GTN model with enhanced accuracy.

Bayesian inversion for unified ductile phase-field fracture

The prediction of crack initiation and propagation in ductile failure processes are challenging tasks for the design and fabrication of metallic materials and structures on a large scale. Numerical aspects of ductile failure dictate a sub-optimal calibration of plasticity- and fracture-related parameters for a large number of material properties. These parameters enter the system of partial differential equations as a forward model. Thus, an accurate estimation of the material parameters enables the precise determination of the material response in different stages, particularly for the post-yielding regime, where crack initiation and propagation take place. In this work, we develop a Bayesian inversion framework for ductile fracture to provide accurate knowledge regarding the effective mechanical parameters. To this end, synthetic and experimental observations are used to estimate the posterior density of the unknowns. To model the ductile failure behavior of solid materials, we rely on the phase-field approach to fracture, for which we present a unified formulation that allows recovering different models on a variational basis. In the variational framework, incremental minimization principles for a class of gradient-type dissipative materials are used to derive the governing equations. The overall formulation is revisited and extended to the case of anisotropic ductile fracture. Three different models are subsequently recovered by certain choices of parameters and constitutive functions, which are later assessed through Bayesian inversion techniques. A step-wise Bayesian inversion method is proposed to determine the posterior density of the material unknowns for a ductile phase-field fracture process. To estimate the posterior density function of ductile material parameters, three common Markov chain Monte Carlo (MCMC) techniques are employed: (i) the Metropolis–Hastings algorithm, (ii) delayed-rejection adaptive Metropolis, and (iii) ensemble Kalman filter combined with MCMC. To examine the computational efficiency of the MCMC methods, we employ the hat{R}{-}convergence tool. The resulting framework is algorithmically described in detail and substantiated with numerical examples.

Phase-field modeling of coupled anisotropic plasticity–ductile fracture in rate-dependent solids

In this paper, an anisotropic ductile fracture is studied using a phase-field model. This model is on the basis of the energy principle in which a scalar field is added as a phase-field variable to determine the probability paths of cracks. Therefore, the system of equations, included for the displacement and phase field, is obtained and solved in a nonlinear finite element procedure through a user element subroutine in ABAQUS commercial software. The effect of anisotropy on cracks’ paths for an anisotropic fracture is assessed according to the Hill criterion for ductile materials. Moreover, an implicit integration algorithm for an anisotropy model combined with a phase field is shown for the plane strain state. The proposed model can also be used for the combination of various constitutive models along with an anisotropy such as the anisotropic rate-dependent (visco-Hill) and the anisotropic rate-independent (elasto-Hill). Furthermore, the threshold parameter is introduced to examine the plastic deformation influence on cracks initiation and propagation in this study. Finally, the influence of the anisotropy on the responses of different specimens in various fracture processes is interrogated. The accuracy of the suggested model is demonstrated by juxtaposing the achieved and given experimental and numerical results in the way that it can be able to simulate the anisotropy effects on the gradual evolution of cracks from ductile to brittle.

A user-friendly anisotropic ductile fracture criterion for sheet metal under proportional loading

Anisotropic ductile fracture is of special importance for accurate modeling of failure in plastic forming of lightweight sheet metals. This research introduces a user-friendly approach to model loading direction effect on fracture limits of sheet metals. The approach is combined with a newly developed fracture criterion (DF2016) to illustrate anisotropic fracture in shear, uniaxial tension and plane strain tension as well as fracture under balanced biaxial tension. The anisotropic DF2016 criterion is applied to describe loading direction effect on the fracture limits of two sheet metals: 6k21 aluminum alloy and a steel sheet of DP980. The predicted loading direction effect is observed to agree with the experimental results with high accuracy. The applications demonstrate that there are three advantages of the proposed approach: high accuracy, good flexibility and being very user-friendly in the calibration of anisotropic parameters. Therefore, we recommend the proposed anisotropic DF2016 criterion for numerical failure prediction in stamping of strong anisotropic metals.

Application of Anisotropic Ductile Fracture Model for Prediction of Diagonal Cracks in Outer Rim of Flange-Shaped Parts

Inclined rotary forming (IRF) combines bending and axial compression with rotation and is employed for forming flange shaft-structured parts from round rod billets. Although the forming load is smaller than that in conventional processes, cracks may develop during this process. However, it is difficult to predict the onset of cracks using conventional ductile fracture prediction equations. In this paper, the ductile fractures were predicted using the anisotropic ductile damage equations that the present authors previously developed. The proposed equation was expressed as a second-rank tensor resulting from the product of the stress tensor and the strain increment tensor. Referring to previously published results on the compression of cylindrical specimens, the difference between diagonal and longitudinal sidewall cracks was assumed by considering the anisotropy of ductile damage. The proposed equation was then applied to the IRF process, where diagonal cracks developed at the outer rim of the flange. Consequently, it was found that the proposed anisotropic damage model can predict the onset of diagonal cracks on the outer rim and the effect of the lubrication condition on the onset of these cracks.

Effect of non-associated flow rule on fracture prediction of metal sheets using a novel anisotropic ductile fracture criterion

The ductile fracture behavior of anisotropic materials was investigated and modeled by the uncoupled ductile fracture criterion for aluminum alloys 6016-AC200. The ductile fracture model takes into account micro-mechanisms of void nucleation, void growth, and evolution of void coalescence. The anisotropic yield function and non-associated flow rule were applied to increase the accuracy of the ductile fracture prediction. Series of uniaxial tensile tests, equi-biaxial tension test, and hydraulic bulge test were utilized to identify coefficients of the plasticity model. Various standard fracture tests covering a wide range of stress triaxiality from negative to moderate and high-stress triaxiality were used in order to calibrate the ductile fracture parameters for AA6016-AC200. The strain field on the surface of specimens was captured by the non-contact measurement DIC system for all tests. The fracture surface, fracture locus, and fracture forming limit diagram constructed by the proposed ductile fracture criterion were plotted. These basic fracture tests and a square cup drawing test were simulated by the ABAQUS/Explicit commercial software to verify the efficiency of the proposed fracture criterion and the advanced plastic model in predicting the onset of ductile fracture behavior. The results indicated that the proposed ductile fracture criterion can be utilized for predicting the onset of the anisotropic ductile fracture behavior in sheet metal forming.

Modeling anisotropic ductile fracture behavior of Ti-6Al-4V titanium alloy for sheet forming applications at room temperature

An anisotropic modified Mohr–Coulomb (MMC) ductile fracture criterion was developed to characterize the ductile fracture behavior of the Ti-6Al-4V titanium alloy at room temperature. The stress triaxiality is inherently coupled within the ductile fracture criterion and shows an exponential effect on the material ductility decay. The effect of the Lode angle is considered as well, considering a parabolic trend. The fracture criterion was developed based on the direction-independent plastic strain-rate increment called isotropic equivalent plastic strain-rate increment. To incorporate the influence of directionality on the ductile fracture behavior, the fourth order linear transformation tensor was successfully introduced. The Ti-6Al-4V fracture behavior under uniaxial tension, in-plane shear, plane strain along various loading orientations, and equi-biaxial tension states of stress was successfully predicted using the newly developed fracture criterion. Furthermore, the theoretical Fracture Forming Limit Curve (FFLC) predicted by the anisotropic ductile fracture criterion was compared with experimental forming limit curves from literature. The results show that the developed phenomenological anisotropic MMC ductile fracture criterion has a great advantage to predict the ductile failure of sheet metals characterized by strong anisotropy.

Anisotropic fracture modeling of sheet metals: From in-plane to out-of-plane

Sheet metals usually exhibit varying degrees of anisotropy due to formation of texture during rolling process. The grain structures and distributions in sheet normal direction may also be different from that within the sheet plane. For example, martensite banding structures are usually observed in the middle of thickness for advanced high strength steels. The particular martensite morphology and inhomogeneous distribution will greatly affect the deformation and fracture behavior under out-of-plane direction. It is necessary to model the anisotropic fracture of sheet metals from in-plane to out-of-plane. In this work, a new stress invariant based ductile fracture criterion was developed by introducing a stress triaxiality and normalized third invariant dependent function h(η, ξ) and further extended to an anisotropic form through the linear transformation of stress tensor. Parametric study showed that the new anisotropic criterion can describe the direction dependency of ductile fracture in both strain and stress spaces. A series of in-plane fracture tests including tension with a central hole, notched tension, V-bending test, Nakajima test and in-plane shear as well as a new out-of-plane shear test were conducted to study the anisotropic fracture behavior of DP980 sheet metals over a variety of stress states. Hybrid experimental-numerical method is used to determine the fracture strains and the loading paths to fracture. The results show that slight in-plane anisotropy of fracture responses exists for this DP980 sheet, while the out-of-plane shear fracture stress is approximately 11% lower than that under the in-plane shear condition. The new anisotropic ductile fracture criterion is able to predict the anisotropic fracture behaviors of this DP980 sheet with high accuracy.

Alternative approach to model ductile fracture by incorporating anisotropic yield function

Due to the texture formed in cold/hot rolled forming process, anisotropy is a key issue not only in modeling of plastic deformation but also in characterization of fracture behavior. In this study, an anisotropic ductile fracture criterion is developed by introducing anisotropic parameters into the weight function of an uncoupled shear ductile fracture criterion. The proposed anisotropic ductile fracture is applied to describe the anisotropic characteristics in the ductile fracture of AA6082-T6. Ductile fracture behavior of AA6082 is experimentally investigated at the different loading conditions: shear by in-plane torsion test, uniaxial tension by specimens with a central hole, plane strain tension by notched specimens, and the balanced biaxial tension by the Nakajima test. In-plane torsion and tension tests with a central hole and notch are conducted along three directions: rolling direction, diagonal direction and transverse direction. Specimen deformations during the tests are recorded and fracture strains are measured by digital image correlation approach. The measured fracture strains are then utilized to calibrate the parameters in the proposed ductile fracture criterion. With the calibrated ductile fracture criterion, the fracture locus and anisotropic ductile fracture in various loading conditions are predicted and compared with experimental measurement and those predicted by linearly transformed anisotropic fracture model to investigate the predictability of the proposed ductile fracture criterion. The comparison demonstrates that the anisotropic fracture of AA6082 is predicted by the proposed criterion with good agreement in the different loading directions of shear, uniaxial tension, plane strain tension, and the balanced biaxial tension. Considering the high accuracy of the proposed ductile fracture criterion, it is expected that the proposed anisotropic ductile fracture criterion can improve the reliability of failure prediction in metal forming for materials with strong directionality in fracture.

The numerical method for predicting failure in single point incremental forming using a new anisotropic ductile fracture model

Abstract Although single point incremental forming (SPIF) possesses various advantages such as great simplicity and high flexibility, the major limitation is failure and fracture that result from extreme thinning along the thickness direction for complex sheet metal parts. So it is necessary and important on investigating the deformation modes and predicting failure and fracture. In this study, the Hu-Chen ductile fracture criterion (DFC) is modified by tensor transformation, then a new anisotropic ductile fracture criterion is proposed. And the new anisotropic ductile fracture criterion is implemented into Abaqus/Explicit by a user subroutine VUSDFLD. Based on the fracture strain measured from experiments, the parameters of anisotropic DFC can be determined by minimizing the system of nonlinear functions using the nonlinear least-square method, so that the calibrated anisotropic ductile fracture model can be applied into finite element simulations of SPIF. The stress and strain states of the deformation field in FE simulations of SPIF are comprehensively analysed. The new anisotropic ductile fracture model on predicting failure behaviours in SPIF is assessed by the comparisons between simulations and experiments for the parts.

Extension of the DF2016 isotropic model into an anisotropic ductile fracture criterion

The paper extends the recently proposed ductile fracture criterion of DF2016 (Lou, Chen, Clausmeyer, Tekkaya and Yoon, 2017. Modeling of ductile fracture from shear to balanced biaxial tension for sheet metals. International Journal of Solids and Structures 112, 169-184) to consider the anisotropic ductile fracture behaviour of sheet metals. The DF2016 criterion is coupled with the Hill48 yield function to model the anisotropy in ductile fracture. For the verification purpose, experiments are conducted for AA6082-T6 sheet with a thickness of 1.0 mm in various loading conditions: in-plane shear, uniaxial tension, plane strain tension, and the balanced biaxial tension. Tests are carried out in the rolling direction, diagonal direction and transverse direction. Fracture strains are measured by digital image correlation along different loading directions. The anisotropic fracture of the sheet is modelled by the DF2016 criterion by incorporating an anisotropic yield function. The predicted anisotropic fracture loci are compared with experimental results in shear, uniaxial tension, plane strain tension and balanced biaxial tension. The comparison demonstrates that the anisotropic DF2016 criterion accurately models the anisotropic fracture behaviour of AA6082-T6 sheet in wide loading conditions from shear to balanced biaxial tension.

Effect of the As-Forged and Heat-Treated Microstructure on the Room Temperature Anisotropic Ductile Fracture of Inconel 718

The purpose of the present work was to investigate the effect of primary carbides and the δ-phase on the anisotropic ductile fracture of Inconel 718 in the forging process. Inconel 718 alloys were prepared by VIM + VAR processes with various carbon contents (0.009 and 0.027 wt.%). Then, the alloys were forged and annealed at temperatures of 980 and 1030 °C. The room temperature mechanical anisotropy of the alloys was evaluated at the longitudinal direction (LD) and transverse direction (TD). Tensile and impact tests were used to characterize the mechanical properties of the specimens. The microstructural characterization and the fractography of the alloys were carried out by FE-SEM. The obtained results showed that the fracture strain and the impact energy in the TD were 30-50% lower than the LD. The fracture was accelerated by the δ-phase, leading to the reduction of impact energy in the longitudinal and the lateral directions up to 50%. The low-carbon alloy indicated similar characteristics in both the LD and the TD. Aligned carbides changed the fracture path from a zigzag path in the LD to a fibrous path in the TD, while the δ-phase created a flat fracture path. The shear lip area ratio in the tensile fracture cross section was decreased by reducing ductility.

Anisotropic fracture of advanced high strength steel sheets: Experiment and theory

Sheet metals such as advanced high strength steels often exhibit varying degrees of anisotropy due to the existence of preferred orientation of their grain structures from the rolling process. While extensive research has been devoted to characterize and model anisotropic plasticity behavior over the past decades, only recently people began to tackle their anisotropic fracture behavior. The focus of these studies is almost always on the in-plane anisotropy, and ignores out-of-plane fracture behavior. The reasons are two-folds: (1). Sheet metal deformation during a stamping or crash application is mostly thought as in a plane stress state and modeled as such, so there is no need to consider out-of-plane fracture behavior; and (2). It is very challenging to develop experimental techniques to reliably measure out-of-plane fracture strengths for sheet metals with a thickness only about 1 mm. In this paper, we theorize, based on strong empirical evidence, that the fracture strength of a thin sheet metal in out-of-plane shear is inherently weaker than that under in-plane shear, analogous to the interlaminar properties of composite laminates. This weakness is responsible for the so-called “shear fracture” behavior, often observed during the stamping operations of advanced high strength steels when the sheet metal flows around a tight radius. A new double-notched shear specimen with shear plane perpendicular to the thickness direction is carefully designed and tested to accurately measure the out-of-plane shear fracture strength. Simulations are executed to validate the rationality of the out-of-plane shear specimen design. Test results of a DP980 sheet show that the out-of-plane shear fracture strength is indeed about 15% lower than that measured under the in-plane shear condition. A new anisotropic ductile fracture model based on linear transformation of stresses is proposed to account for the out-of-plane fracture strength for AHSS sheets. The model is calibrated with experimental data, and the fracture surface is compared to the isotropic Mohr-Coulomb (M-C) fracture model to illustrate its effectiveness.

Anisotropic fracture forming limit diagram considering non-directionality of the equi-biaxial fracture strain

This paper is concerned with modeling of anisotropic fracture forming limit diagram considering non-directionality of the equi-biaxial fracture strain. A new anisotropic ductile fracture criterion is developed based on the Lou–Huh ductile fracture criterion (Lou et al., 2012). In an attempt to predict the forming severity of advanced high-strength steel (AHSS) sheets, the proposed fracture criterion is converted into a Fracture Forming Limit Diagram (FFLD) and anisotropic fracture locus considering the sheet metal orientation. Tensile tests of the DP980 steel sheet with the thickness of 1.2 mm are conducted using various specimen geometries including pure shear, dog-bone, and flat grooved specimens. With Digital Image Correlation (DIC) method, equivalent plastic strain distribution on the specimen surface is computed until surface crack initiates. The fracture predictability of the proposed fracture criterion is evaluated with the experimental results which cover a wide range of stress states in various loading directions. By comparing fracture strains obtained from the experiments with the ones predicted from the proposed fracture criterion, it is clearly confirmed that the fracture criterion proposed is capable of predicting the equivalent plastic strain at the onset of fracture with great accuracy over a wide range of stress states while keeping non-directionality of the equi-biaxial fracture strain.

Prediction of fracture initiation in square cup drawing of DP980 using an anisotropic ductile fracture criterion

This paper deals with the prediction of fracture initiation in square cup drawing of DP980 steel sheet with the thickness of 1.2 mm. In an attempt to consider the influence of material anisotropy on the fracture initiation, an uncoupled anisotropic ductile fracture criterion is developed based on the Lou—Huh ductile fracture criterion. Tensile tests are carried out at different loading directions of 0°, 45°, and 90° to the rolling direction of the sheet using various specimen geometries including pure shear, dog-bone, and flat grooved specimens so as to calibrate the parameters of the proposed fracture criterion. Equivalent plastic strain distribution on the specimen surface is computed using Digital Image Correlation (DIC) method until surface crack initiates. The proposed fracture criterion is implemented into the commercial finite element code ABAQUS/Explicit by developing the Vectorized User-defined MATerial (VUMAT) subroutine which features the non-associated flow rule. Simulation results of the square cup drawing test clearly show that the proposed fracture criterion is capable of predicting the fracture initiation with sufficient accuracy considering the material anisotropy.