Ductile Failure In Metals Research Articles

Analysis of effects of material anisotropy on ductile damage using microscopic unit‐cell model

AbstractIt is experimentally observed that the failure in ductile metals is mainly due to the nucleation, growth, and coalescence of micro‐voids as well as micro‐shear‐cracks. Furthermore, plastic anisotropy has significant role in damage and failure behavior of ductile metals. Finite element simulations of unit cell provide a basis to understand different mechanisms on micro‐scale, for example, changes in shape and size of single voids and defects as well as localization of plastic strains. This contribution deals with the numerical analysis of unit cell containing spherical void subjected to symmetrical boundary conditions taking material anisotropy into account. Elastic isotropic behavior is described by Hooke's law while Hoffman yield criterion considering the strength‐differential effect is used to model the anisotropic plastic behavior. Generalized anisotropic stress invariants, generalized stress triaxiality, and generalized Lode parameter are introduced to characterize the stress state in the anisotropic ductile metal. The effect of plastic anisotropy on the damage behavior of the aluminum alloy EN AW‐2017A is studied in detail by performing a series of numerical simulations covering a wide range of stress triaxialites and Lode parameters. Stress triaxility and Lode parameter are controlled and kept constant during the entire loading process. The numerical results are then used to discuss general mechanisms of damage and failure process in ductile metals.

Simulations of complex crack paths using a robust and cost-efficient continuous–discontinuous approach

Prediction of complex crack propagation is necessary to guarantee performance in service of critical parts of transport vehicles despite the presence of a crack. In cases where linear fracture mechanics assumptions are not valid, e.g. for ductile rupture, this prediction may require continuous–discontinuous strategies to insert a strong discontinuity (i.e. a crack) into a continuous model based on a scalar variable related to material degradation. These strategies still face difficult challenges regarding robustness and cost-efficiency, in particular for 3D problems. To overcome these challenges, it is useful to consider the different ingredients that constitute a continuous–discontinuous strategy and try to optimize each of them. With this perspective, this work addresses the simulation of crack initiation and propagation in ductile metals and proposes new contributions to some rarely addressed points: (i) a simple geometrical approach to initiate realistic crack shapes in 3D meshes, (ii) a new 3D insertion criterion to minimize the number of transfer operations, (iii) a pragmatic remeshing procedure to refine only Active Process Zones, and (iv) an equilibrium recovery method meant to improve the convergence rate after the insertion of a discontinuity.The effectiveness of these new ingredients is demonstrated in 2D axisymmetric, 2D plane strain, and 3D cases in the case of test specimens used to characterize ductile failure in metals. This includes axisymmetric specimens exhibiting cup-cone fracture, plane strain specimens with slant fracture, and pre-cracked CT-like specimens with crack blunting and large crack propagation.

Microstructural, multilevel simulation of notch effect in ferritic ductile cast iron under low cycle fatigue

Triaxiality of stress affects damage and failure of ductile metals. In mechanical components, triaxiality increases in the proximity of a notch, or, at the microstructural level, due to inclusions or voids. In this work,the effect of triaxiality on the LCF ofductile cast iron is investigated by a multilevel approach, homogenizing the response of a microstructural model which feeds a notched specimen. Moving from micro- to macro-scale, results indicate that triaxiality shorten the fatigue life. Thus, the notch effect on fatigue life of cast iron can be explained in terms of the combined effects of microstructure and applied triaxiality.

Modelling stress‐state dependent nonlocal damage and failure of ductile metals

AbstractDamage and failure of ductile metals is highly influenced by the stress state. In fact, void growth takes place under hydrostatic tensile loading and void coalescence leads eventually to ductile failure. A completely different damage mechanism occurs for shear dominated loading that results in void elongation within a narrow shear band. In order to account for both failure mechanisms, a stress state dependent damage model is proposed. The model is based on a continuum damage mechanics approach, whereby nonlinear damage evolution is taken into account. The influence of the stress triaxiality and the LODE parameter on damage initiation and failure is considered by the Hosford‐Coulomb model. Pathological mesh sensitivity is prevented by an integral type nonlocal formulation. Finally, the proposed stress‐state dependent nonlocal damage model is verified by test data for the microalloyed high strength steel HX340LAD for a wide range of stress states.

Representative volume element (RVE) based crystal plasticity study of void growth on phase boundary in titanium alloys

Crystal plasticity based finite element method (CPFEM) studies have been successfully used to model different material behaviour and phenomenon, including but not limited to; fatigue, creep and texture evolution. This capability can be extended to include the ductile damage and failure in the model. Ductile failure in metals is governed by void nucleation, growth, and coalescence. High strength titanium alloys can be formed from sheets and components and are prone to ductile failure. α – β Titanium alloys are in widespread use, ranging from aerospace, automotive, energy to oil and gas. They have multiple phases present in the microstructure but α and β phases are dominant and are present in various morphologies. This study focuses on the 3D representative volume element (RVE) simulations of spherical void of known initial porosity at the interface of α and β phase single crystals. The effect of initial porosity, applied triaxiality and orientation of RVE with respect to the loading direction is investigated. Slip based crystal plasticity formulation implemented as a user subroutine in commercially available software was used to simulate the void growth and the results of the same are presented. Lastly, a generalised correlation among loading type, loading direction, crystal orientation, phase interface orientation, and void growth is presented.

Damage evolution on dynamic tensile fracture of ductile metals

Dynamic tensile failure, e.g. spallation, of ductile metals is a complex phenomenon, due to its multiple tempo-spatial scales and structural levels involved on one hand, and due to its irreversible and nonlinear features as a non-equilibrium process on the other. Activated/Stimulated by tensile stress, non-uniform mesoscopic structures of materials evolve, leading to internal damage nucleation, growth, coalescence and final fracture, which consist the basic physical processes of dynamic tensile failure of ductile metals. Damage evolution on dynamic tensile fracture of ductile metals has been reported elsewhere, however, our ability to understand the mechanism of damage evolution in micro-scale and to accurately predict fracture in macro-scale is still limited. In this paper, we present investigations on macroscopic response, microscopic mechanism and physical models of dynamic tensile failure, based on our previous works. Current difficulties and challenges encountered when studying such a complex, multi-scale phenomenon are also discussed.

Quantitative In Situ Analysis of Deformation in Sliding Metals: Effect of Initial Strain State

Using in situ, high-speed imaging of a hard wedge sliding against pure aluminum, and image analysis by particle image velocimetry, the deformation field in sliding is mapped at high resolution. This model system is representative of asperity contacts on engineered surfaces and die-workpiece contacts in deformation and machining processes. It is shown that large, uniform plastic strains of 1-5 can be imposed at the Al surface, up to depths of 500 mu m, under suitable sliding conditions. The spatial strain and strain rate distributions are significantly influenced by the initial deformation state of the Al, e.g., extent of work hardening, and sliding incidence angle. Uniform straining occurs only under conditions of steady laminar flow in the metal. Large pre-strains and higher sliding angles promote breakdown in laminar flow due to surface fold formation or flow localization in the form of shear bands, thus imposing limits on uniform straining by sliding. Avoidance of unsteady sliding conditions, and selection of parameters like sliding angle, thus provides a way to control the deformation field. Key characteristics of the sliding deformation such as strain and strain rate, laminar flow, folding and prow formation are well predicted by finite element simulation. The deformation field provides a quantitative basis for interpreting wear particle formation. Implications for engineering functionally graded surfaces, sliding wear and ductile failure in metals are discussed.

Ductile failure with gradient plasticity coupled to the phase‐field fracture at finite strains

AbstractMost metals fail in a ductile fashion, i.e, fracture is preceded by significant plastic deformation. The modeling of failure in ductile metals must account for complex phenomena at micro‐scale, such as nucleation, growth and coalescence of micro‐voids. In this work, we start with von‐Mises plasticity model without considering void generation. The modeling of macroscopic cracks can be achieved in a convenient way by the continuum phase field approaches to fracture, which are based on the regularization of sharp crack discontinuities [1]. This avoids the use of complex discretization methods for crack discontinuities and can account for complex crack patterns. The key aspect of this work is the extension of the energetic and the stress‐based phase field driving force function in brittle fracture to account for a coupled elasto‐plastic response in line with our recent work [3]. We develop a new theoretical and computational framework for the phase field modeling of ductile fracture in elastic‐plastic solids. To account for large strains, the constitutive model is constructed in the logarithmic strain space, which simplify the model equations and results in a formulation similar to small strains. We demonstrate the modeling capabilities and algorithmic performance of the proposed formulation by representative simulations of ductile failure mechanisms in metals. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

New Model for Ductile Fracture of Metal Alloys. II: Reverse Loading

AbstractDuctile fracture of metals resulting from large amplitude inelastic reverse straining has been the predominant reason for the failure of structural components under extreme loadings. This kind of fracture, characterized by only a few reverse cycles with large precrack plastic strain, is often termed ultra-low cycle fatigue (ULCF). Ductile failure of metals has recently been recognized to be a function of stress triaxiality and Lode angle parameter. In this paper, a new fracture model with full consideration of stress triaxiality and Lode angle parameter as well as the cutoff regions is proposed from the extension of its equivalence for monotonic loading in the parallel paper. The underlying mechanism and determination of the cutoff region boundary is well-defined and discussed. Additionally, the effect of load excursion on shifting the boundary of the cutoff region and the subsequent damage evolution is assessed. The nonlinearity of damage evolution is also studied and well-characterized. The deve...

Modeling of Stress-State-Dependent Damage and Failure of Ductile Metals

The paper discusses an anisotropic continuum damage model. It takes into account the effect of stress state on damage and failure conditions as well as on evolution equations of damage strains. To validate the proposed framework experiments with biaxially loaded specimens and corresponding numerical simulations are performed covering a wide range of stress states. In addition, scanning electron microscope images of the fracture surfaces show different fracture modes corresponding to stress states revealed by numerical analyses.

Towards Phase Field Modeling of Ductile Fracture in Gradient‐Extended Elastic‐Plastic Solids

AbstractThe modeling of failure in ductile metals must account for complex phenomena at a micro‐scale as well as the final rupture at the macro‐scale. Within a top‐down viewpoint, this can be achieved by the combination of a micro‐structure‐informed elastic‐plastic model with a concept for the modeling of macroscopic crack discontinuities. In this context, it is important to account for material length scales and thermo‐mechanical coupling effects due to dissipative heating. This can be achieved by the construction of non‐standard, gradient‐enhanced models of plasticity with a full embedding into continuum thermodynamics [1,2]. The modeling of macroscopic cracks can be achieved in a convenient way by recently developed continuum phase field approaches to fracture based on regularized crack discontinuities. This avoids the use of complex discretization methods for crack discontinuities, and can account for complex crack patterns within a pure continuum formulation. Moreover, the phase field modeling of fracture is related to gradient theories of continuum damage mechanics, and fits nicely the structure of constitutive models for gradient plasticity. The main focus of this work is the extensions to gradient thermoplasticity and phase field formulation of ductile fracture, conceptually in line with the work [3]. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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.

Ductile tensile failure in metals through initiation and growth of nanosized voids

We here reveal the initiation of ductile failure in metals at the nanometer scale by molecular dynamics simulations coupled with a novel analytical model. This proceeds by the emission of a special type of dislocation shear loop, which can expand as a partial or perfect dislocation, evolve into a prismatic loop through reaction, or develop into twins. Molecular dynamics (MD) simulations predict a strong dependence of the stress required for the initiation of plastic flow at the surface of the void for both Cu (a model fcc metal) and Ta (a model bcc metal). The decrease in stress with increasing void size is also analyzed in terms of a new analytical approach based on the energetics of dislocation loop emission. For both fcc (copper) and bcc (tantalum) metals initiation of plastic flow in MD simulations takes place at voids as small as a tri-vacancy (radius R≈0.1nm). Extensive calculations for tantalum combined with the analytical model, which tracks the simulations, enable extrapolation to R≈300nm, in the realm of second phase particles and inclusions. Thus we conclude that this is a general mechanism of tensile failure in pure monocrystalline metals where other initiation sites are absent.

Identification of GTN model parameters by application of response surface methodology

A reliable prediction of ductile failure in metals is still a wide-open matter of research. Among different models, Gurson-Tvergaard-Needleman (GTN) has been used extensively. One major issue is the accurate identification of GTN model parameters, which it is not possible to perform experiments for their evaluation. In the present paper a novel inverse procedure aimed to estimate the material parameters of the GTN porosity-based plastic damage model by means of RSM method is represented. The results showed good agreement between experimental and predicted forming limit diagrams when determined GTN parameters were utilized. FE-simulation by means of Abaqus software used to predict FLDs. © 2011 Published by Elsevier Ltd. Selection and peer-review under responsibility of ICM11

A damage accumulation model for complex strain paths: Prediction of ductile failure in metals

The characterisation of strain path with respect to the directionality of defect formation is discussed. The criterion of non-monotonic strain path is used in the scalar and tensor models for damage accumulation and recovery. Comparable analysis of models and their verification has been obtained by simulation of crack initiation in a two-stage metal forming operation consisting of wire drawing followed by constrained upsetting.

The role of dislocations in the growth of nanosized voids in ductile failure of metals

Dislocations are the most important element in our understanding of the mechanical response of metals. Their postulation in 1934 led to revolutionary advances in our ability to predict the mechanical behavior of materials. The authors recently advanced a dislocation mechanism for void growth in ductile metals. This paper reviews the analytical and atomistic calculations carried out in support of this model. The emission of shear dislocation loops, nucleated at the surface of nanosized voids, is responsible for the outward flux of matter, promoting void growth. This is a new paradigm in the initiation of void growth, which was attributed to convergent vacancy diffusion or to prismatic loops by others. The analytical treatment is based on the emission of a dislocation from a void in the plane along which the shear stresses are maximum. Molecular dynamics calculations performed for different orientations of the tensile axis show how the loops generate and expand outward. These loops involve the emission of partial dislocations and are the counterpart for voids of the Ashby geometrically necessary shear loops postulated for rigid particles. This process is demonstrated for bicrystalline and nanocrystalline copper.

Predicting failure modes and ductility of dual phase steels using plastic strain localization

Ductile failure of metals is often treated as the result of void nucleation, growth and coalescence. Various criteria have been proposed to capture this failure mechanism for various materials. In this study, ductile failure of dual phase steels is predicted in the form of plastic strain localization resulting from the incompatible deformation between the harder martensite phase and the softer ferrite matrix. Microstructure-level inhomogeneity serves as the initial imperfection triggering the instability in the form of plastic strain localization during the deformation process. Failure modes and ultimate ductility of two dual phase steels are analyzed using finite element analyses based on the actual steel microstructures. The plastic work hardening properties for the constituent phases are determined by the in-situ synchrotron-based high-energy X-ray diffraction technique. Under different loading conditions, different failure modes and ultimate ductility are predicted in the form of plastic strain localization. It is found that the local failure mode and ultimate ductility of dual phase steels are closely related to the stress state in the material. Under plane stress condition with free lateral boundary, one dominant shear band develops and leads to final failure of the material. However, if the lateral boundary is constrained, splitting failure perpendicular to the loading direction is predicted with much reduced ductility. On the other hand, under plane strain loading condition, commonly observed necking phenomenon is predicted which leads to the final failure of the material. These predictions are in reasonably good agreement with experimental observations.

Identification of Material Damage Model Parameters: an Inverse Approach Using Digital Image Processing

A reliable prediction of ductile failure in metals is still a wide-open matter of research. Several models are available in the literature, ranging from empirical criteria, porosity-based models and continuum damage mechanics (CDM). One major issue is the accurate identification of parameters which describe material behavior. For some damage models, parameter identification is more or less straightforward, being possible to perform experiments for their evaluation. For the others, direct calibration from laboratory tests is not possible, so that the approach of inverse methods is required for a proper identification. In material model calibration, the inverse approach consists in a non-linear iterative fitting of a parameter-dependent load–displacement curve (coming from a FEM simulation) on the experimental specimen response. The test is usually a tensile test on a round-notched cylindrical bar. The present paper shows a novel inverse procedure aimed to estimate the material parameters of the Gurson–Tvergaard–Needleman (GTN) porosity-based plastic damage model by means of experimental data collected using image analysis. The use of digital image processing allows to substitute the load–displacement curve with other global quantities resulting from the measuring of specimen profile during loading. The advantage of this analysis is that more data are available for calibration thus allowing a greater level of confidence and accuracy in model parameter evaluation.

A damage model for orthotropic metals

The paper describes a ductile damage model for orthotropic metals. The ductile failure of metals is an important phenomena in crashworthiness, impact and shock problems, and therefore must be considered in structural simulations. The model is based on an orthotropic damage matrix which is incorporated in the constitutive equations for stress update and provides degradation of material properties. The evolution of the damage matrix assumes the growth and coalescence of voids. The implementation of the model for both continuum and shell elements is discussed. Finally the model is demonstrated on test problems.

A physically-based and fully coupled model of elasto-plasticity and damage for dynamic failure in ductile metals

It is well established that spall fracture and other rapid failures in ductile materials are oftenominated by nucleation and growth of micro-voids. In the present work, a mechanistic model for failureby cumulative nucleation and growth of voids is fully coupled with the thermo-elastoplastic constitutiveequations of theMechanical Threshold Stress (MTS) which is used to model the evolution of the flow stress.The damage modeling includes both ductile and brittle mechanisms. It accounts for the effects of inertia, ratesensitivity, fracture surface energy, and nucleation frequency. The MTS model used for plasticity includesthe superposition of different thermal activation barriers for dislocation motion. Results obtained in thecase of uncoupled and coupled model of plasticity and damage from the simulations of the planar impactwith cylindrical target, are presented and compared with the experimental results for OFHC copper. Thiscomparison shows the model capabilities in predicting the experimentally measured free surface velocityprofile as well as the observed spall and other damage patterns in the material under impact loading. Theseresults are obtained using the finite element code Abaqus/Explicit.