Recent work on ductile failure under shear-dominant stress states has challenged the long-accepted premise that the strain at failure monotonically decreases with increasing triaxiality. This paper ...presents results from experiments in which custom Al-6061-T6 tubular specimens are loaded to failure under radial paths of shear and tension, spanning a range of triaxiality from 0.07 to 0.58. A long, thin-walled test section machined into the specimens has nearly uniform stress and deformation until a load maximum is reached and provides minimum constraint to the localized deformation that follows. Localization takes the form of a circumferential band with width the order of the wall thickness. Stereo digital image correlation (DIC) is used to monitor the deformation inside these localization zones up to failure. The specimen geometry, experimental setup, and use of DIC allow the true stresses and strains to be established directly from experimental measurements. The measured strains at failure are found to monotonically decrease as the triaxiality increases, a trend that is in concert with long accepted theory. However, the failure strains are significantly larger than previously reported values, approaching measurements based on statistical grain-level measurements. The results highlight the important role of localization in ductile failure, and the need for a diagnostic technique with sufficient resolution to accurately establish the strain at failure. In incorporating the reported failure strains in the modeling of ductile failure, the observation that this alloy deforms to rather large strains free of damage must be taken into account. In other words, plasticity governs this behavior until very close to the end of life of the material.
•The cut-off value for stress triaxiality is discussed based on experimental observation.•A shear-controlled ductile fracture criterion is proposed with a changeable cut-off value for stress ...triaxiality.•A cut-off value function for stress triaxiality is suggested as the zero maximum principal stress with a constant offset.•The proposed criterion accurately predicts ductile fracture behavior of 2024-T351 from compression to tension.
A macroscopic ductile fracture criterion is proposed based on micro-mechanism analysis of nucleation, growth and shear coalescence of voids from experimental observation of fracture surfaces. The proposed ductile fracture model endows a changeable cut-off value for the stress triaxiality to represent effect of micro-structures, the Lode parameter, temperature, and strain rate on ductility of metals. The proposed model is used to construct fracture loci of AA 2024-T351. The constructed fracture loci are compared with experimental data covering wide stress triaxiality ranging between −0.5 and 1.0. The fracture loci are constructed in full stress spaces and plane stress conditions to analyze characteristics of the proposed fracture loci. Errors of the equivalent stress to fracture are calculated and compared with those predicted by the MSV model (Khan and Liu, 2012a) and series of the modified Mohr–Coulomb criteria. The comparison suggests that the proposed model can provide a satisfactory prediction of ductile fracture for metals from compressive upsetting tests to plane strain tension with slanted fracture surfaces. Moreover, it is expected that the proposed model reasonably describes ductile fracture behavior in high velocity perforation simulation since a reasonable cut-off value for the stress triaxiality is coupled with the proposed ductile fracture criterion.
The heterogeneous deformation of polycrystalline metals inherently originates from the intergranular deformation incompatibility. This paper proposes physical parameters related to the crystal ...orientations, the Schmid factor of the most activated slip system, and the misorientation angle to characterize the deformation incompatibility between the adjacent grains couple. A comprehensive multiscale investigation is conducted to reveal the mechanism from intergranular deformation incompatibility to fracture initiation at grain boundaries. At the specimen scale, experimental and numerical uniaxial tensile tests are performed on smooth and pre-notched dog-bone specimens to achieve different loading paths on the materials. The heterogeneous fields of stress triaxiality explains the heterogeneous size of the dimples observed in fractography. At the grain scale, electron backscatter diffraction analysis is conducted to characterize the microstructural properties around the nucleated voids within the materials. Voids are captured at the grain boundaries with directions parallel to the loading direction and intergranular deformation incompatibility is characterized using the proposed parameters. Simulations on the plastic deformation of realistic microstructures are performed to clarify the phenomenon. The results reveal that the fluctuation in stress triaxiality at grain boundaries is ascribed to intergranular deformation incompatibility, leading to fracture initiation at these sites. The relationships between the proposed physical parameters of intergranular deformation incompatibility and fluctuation in stress triaxiality are summarized in all circumstances. Finally, the ductile damage at the grain scale is predicted by the Rice-Tracey model, and the results show that the effects of microstructures on heterogeneous plastic deformation and stress state can be well considered.
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•Intergranular deformation incompatibility is characterized by physical parameters.•Heterogeneous distribution of voids at grain boundary is captured.•Intergranular deformation incompatibility causes high triaxiality at grain boundary.•Ductile damage in the microstructure is predicted by Rice-Tracey model.
A micromechanics-based yield criterion is developed to model void coalescence of three-dimensional voids under combined tension and shear. The analysis treats a cylindrical cell containing a coaxial ...cylindrical cavity, both having an elliptic cross section. Limit analysis is employed to first derive a criterion for homothetic cells. The model is then generalized to incorporate independent void spacing ratios (non-homothetic cells) The model predictions are assessed against finite-element based limit analysis on similar geometries. The effects of relative void spacing and void shape on effective yielding are investigated. In tension, the results indicate an increase in the coalescence stress with increasing in-plane anisotropy for both homothetic and non-homothetic cells. The new criterion is chiefly motivated by modeling shear failure. The extent to which the shear limit load reduces when shearing perpendicular to the largest transverse void dimension, as compared with shearing parallel to it, is discussed.
•A yield criterion is developed for a material in a state of void coalescence under tension or shear.•The criterion is obtained using an elliptic cylindrical cell and a concentric elliptical void.•Finite-element based limit analysis is used to assess the new criterion.•The coalescence stress is found to increase with increasing cell distortion in tension.•It is found to decrease with increasing distortion in shear along the minor transverse void axis.
•Unit cell calculations have been performed covering a wide range of stress triaxialities and Lode parameters.•Stress state dependent damage criterion is proposed.•Stress state dependent damage rule ...is proposed.•Functions depending on stress triaxiality and Lode parameter are proposed and parameters are identified.•Numerical results from unit cell calculations and from the continuum damage model show good agreement.
The paper deals with the effect of stress state on the damage behavior of ductile metals. The continuum damage model has been generalized to take into account the effect of stress state on damage criteria as well as on evolution equations of damage strains. Different branches are considered corresponding to various damage mechanisms depending on stress intensity, stress triaxiality and the Lode parameter. Basic material parameters are identified using experiments with differently notched tension and shear specimens. To be able to get more insight in the complex damage and failure behavior additional series of three-dimensional micro-mechanical numerical analyses of void containing unit cells have been performed. These calculations cover a wide range of stress triaxialities and Lode parameters in the tension, shear and compression domains. The numerical results are used to show general trends, to develop equations for the damage criteria, to propose evolution equations of damage strains, and to identify parameters of the continuum model.
•A network alteration theory for the Mullins effect, the permanent set and the stress-softening.•Reconciliation between physical and phenomenological approaches.•Normalized network parameter depends ...only on the normalized cycle number.
This contribution provides an improvement on GTN model upon the prediction of fracture location within low level of stress triaxiality. In the proposition, two distinct damage parameters are introduced as internal variables of the degradation process and an effective damage is calculated as a sum of both contributions in the post-processed step. In the beginning, the volume void fraction, based on conservation mass law, is assumed as the first damage parameter, similar to Gurson’s original model. This volumetric damage contribution is able to capture spherical void growth, which plays the main role in tensile loading condition. The second damage parameter is proposed as a new shear mechanism, based on geometrical and phenomenological aspects and is also a function of the equivalent plastic strain, Lode angle and stress triaxiality. The shear damage parameter is formulated independent of the volume void fraction and requires a new nucleation of micro-defects mechanism to trigger the shear growth contribution, and hence is able to capture elongated (and rotation) void growth which is present in simple shear and combined shear/tensile or shear/compression loading conditions. Furthermore, the first and the second damage parameters are coupled in the yield function in order to affect the hydrostatic stress and deviatoric stress contributions, separately. In the first part of this paper, a review of Gurson’s model and its most famous version as GTN’s model is done. After that, the new contribution is presented and an implicit numerical integration algorithm is determined, based on the operator split methodology. The calibration strategy is discussed for determination of material parameters. Numerical tests are performed for a butterfly specimen using two types of materials (aluminum alloy 2024-T351 and steel 1045) under ranges of stress triaxiality between-1/3<η<1/3 (shear/compression or shear/tensile). At the end, the behavior of internal variables is analyzed, such as: evolution of both damage parameters, evolution of the equivalent plastic strain, the reaction curve and the contour of the effective damage parameter. The results obtained are compared with experimental data and have shown that the present formulation performs well in the prediction of the fracture location and determination of the correct level of equivalent plastic strain at fracture under predominant shear loading condition.
•Two damage parameters representing the volumetric damage and the shear damage are considered.•The GTN model is extended by coupling the two damage parameters into the yield function and flow ...potential.•The effectiveness of the new model is illustrated through a series of numerical tests.•The modified GTN model is applied to predict the ductile fracture behavior of a Zircaloy-4.•The calibrated model predicts failure initiation and propagation in various specimens.
One of the major drawbacks of the Gurson-type of porous plasticity models is the inability of these models to predict material failure under low stress triaxiality, shear dominated conditions. This study addresses this issue by combining the damage mechanics concept with the porous plasticity model that accounts for void nucleation, growth and coalescence. In particular, the widely adopted Gurson–Tvergaard–Needleman (GTN) model is extended by coupling two damage parameters, representing the volumetric damage (void volume fraction) and the shear damage, respectively, into the yield function and flow potential. The effectiveness of the new model is illustrated through a series of numerical tests comparing its performance with existing models. The current model not only is capable of predicting damage and fracture under low (even negative) triaxiality conditions but also suppresses spurious damage that has been shown to develop in earlier modifications of the GTN model for moderate to high triaxiality regimes. Finally the modified GTN model is applied to predict the ductile fracture behavior of a beta-treated Zircaloy-4 by coupling the proposed damage modeling framework with a recently developed J2–J3 plasticity model for the matrix material. Model parameters are calibrated using experimental data, and the calibrated model predicts failure initiation and propagation in various specimens experiencing a wide range of triaxiality and Lode parameter combinations.
The ductile fracture characteristics of Chinese Q460 high strength structural steel under quasi-static condition were studied by using mechanical tests of four types of notched specimens. The ...influence of stress state on fracture mechanism of the material was investigated by observing the fracture surfaces of all test specimens using the Scanning Electron Microscope. Meanwhile, corresponding numerical simulations were conducted to collect the critical stress and strain at notch for all test specimens. The effects of stress triaxiality and Lode angle parameter, which were found to be the key parameters governing the ductile fracture of metallic material in many studies, on fracture strain of the Q460 structural steel were investigated. The analysis results show that different fracture mechanisms were observed in different stress triaxiality regions. At high stress triaxialities, Q460 steel exhibits a typical mechanism of “void nucleation, growth and coalescence”. When stress triaxiality equals to zero, a shear fracture mechanism was observed. At low stress triaxiality values, fracture develops as a combination of shear and void growth modes. In addition, the ductility of Q460 structural steel under pure shear or plane strain is lower than that under axisymmetric tension, especially at low stress triaxiality.
•The notch has an “embrittling and strengthening” effect on Q460 structural steel.•The stress triaxiality controls the ductility and fracture mechanism of the steel.•The ductility of Q460 steel is different under different Lode angle parameter.•The results can be used to calibrate micromechanical fracture models for Q460 steel.
Stress triaxiality has attracted wide attention in the research of material deformation and fracture behavior. This paper aims at exploring the effects of stress triaxiality on serrated chip fracture ...during high speed machining (HSM) of titanium alloy Ti6Al4V. Firstly, the models of normal stress and stress triaxiality distributions are presented to describe the stress state along the adiabatic shear band (ASB) of serrated chips generated in HSM of Ti6Al4V. The material fracture in ASB is extracted as the material failure problem under the combined loads of constant shear stress with gradient tensile/compressive stress. Secondly, a modified Bao-Wierzbicki fracture strain model is developed to predict the serrated chip fracture which considers the effects of strain rate and temperature. The equivalent fracture strain predicted with the modified Bao-Wierzbicki model is found to be more accurate than the original Bao-Wierzbicki model. At last, the fracture loci of ASBs in serrated chips for Ti6Al4V under different cutting speeds have been determined and validated by HSM experiments. The influences of stain rate and temperature on the material fracture strain have also been discussed. The research proves that the stress triaxiality plays a vital role in serrated chip formation during HSM.
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•Serrated chip fracture is influenced by stress triaxiality distributed along primary deformation zone.•The distributions of normal stress and stress triaxiality along primary deformation zone are modeled.•Bao-Wierzbicki model is modified with the consideration of strain rate and temperature to predict serrated chip fracture.•Extension of tensile stress zone under higher cutting speeds leads to increases of chip serrated degree and crack length.
In this contribution, it is suggested a damage evolution law which is based on Continuum Damage Mechanics (CDM) and dependent on the hydrostatic pressure, by the stress triaxiality, and the third ...invariant of deviatoric stress tensor, by the so-called normalized third invariant. The contribution has been motivated meanly by the reason that the accuracy in describe the mechanical behavior of materials and the predictive fracture onset ability of damage constitutive models are strongly dependent on the loading condition used to procedure the calibration of material parameters. Regarding classical damage models as Lemaitre and Gurson, the level of material degradation can be optimist or conservative for loading conditions far from the calibration point. In the first part of this paper, the suggested damage evolution law is presented and the new state and dissipation potential are determined. The plastic flow rules for associative and non-associative plasticity are derived and an implicit numerical integration algorithm is suggested, based on the operator split methodology. The numerical algorithm is also implemented in an "in house" finite element framework and its robustness is tested for a set of numerical simulations upon wide range of stress triaxiality. Numerical results are compared with experimental data presented in literature and parameters as reaction curve, evolution of the equivalent plastic strain and damage variable at fracture are analyzed. In a critical situation, the numerical results have shown that the original damage models as Lemaitre's model has a prediction of 68% in disagreement with experimental data and the proposed damage evolution law has around 1%, regarding the determinations of the displacement at fracture initiation.
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