Hosford Coulomb Research Articles

The third Sandia Fracture Challenge: deterministic and probabilistic modeling of ductile fracture of additively-manufactured material

Within the scope of the third Sandia Fracture Challenge the plasticity and ductile fracture behavior of an additively manufactured 316L stainless steel tensile specimen containing through holes and internal cavities is predicted in a blind round robin format. Only a limited number of experimental results, including flat dogbone-shaped and double-notch tension specimens, as well as EBSD maps of the Challenge geometry are provided by Sandia National Laboratory. A non-associated Hill’48 plasticity model with Swift-Voce strain hardening and Johnson–Cook strain rate hardening is used to accurately describe the large deformation response of the material. A special case of the recently developed Hosford–Coulomb model is used to predict fracture initiation and propagation by crack re-initiation. Very good qualitative and quantitative agreement of the blind prediction with the experimental results is obtained for both global force-displacement responses as well as the local surface strain evolution throughout the test. In a post challenge follow-up study, the role of the plasticity model is evaluated, focusing on the effect of the anisotropy and the strain-rate on the material response. Aside from considering the deterministic model, the statistical material properties of the additively manufactured structure are analyzed by defining a heterogeneous random media model. Probabilistic material properties for both plasticity and fracture are assigned to each element of the Challenge specimen. As an alternative, the role of intrinsic porosities is analyzed by randomly deleting 1% of the pristine geometry. The results of both approaches show that the presence of homogeneities follows a more realistic description of the material behavior, especially in the crack propagation regime post maximum force and when looking at local strains.

Plasticity and ductile fracture modeling of an Al–Si–Mg die-cast alloy

The plastic anisotropy and ductile fracture behavior of an Al–Si–Mg die-cast alloy (AA365-T7, or Aural-2) is probed using a combination of experiments and analysis. The plastic anisotropy is assessed using uniaxial tension, plane-strain tension and disc compression experiments, which are then used to calibrate the Yld2004-3D anisotropic yield criterion. The fracture behavior is investigated using notched tension, central hole and shear specimens, with the latter employing a geometry that was custom-designed for this material. Digital image correlation is used to assess the full strain fields for these experiments. However, fracture is expected to initiate at the through-thickness mid-plane of the specimens and thus it cannot be measured directly from experiments. Instead, the stresses and strains at the onset of fracture are estimated using finite element modeling. The loading path and the resulting fracture locus were found to be sensitive to the yield criterion employed, which underscores the importance of an adequate modeling of plastic anisotropy in ductile fracture studies. Based on the finite element modeling, the fracture locus is represented with three common criteria (Oyane, Johnson–Cook and Hosford–Coulomb), as well as a newly proposed one as the linear combination of the first two. However, beyond that, it is still questionable if all of these experiments are probing the same fracture locus, since the predicted loading paths of notched tension specimens are highly evolving compared to those of central hole and shear ones.

Ductile fracture prediction of EH36 grade steel based on Hosford–Coulomb model

ABSTRACTTo predict ductile fracture initiation of EH36 grade high tensile strength steels, the Hosford–Coulomb ductile fracture model was employed. The ductile fracture tests were carried out on different specimen geometries: central-hole, shear specimen, and notched tensile specimens with three different notch radii. Finite element analysis was carried out for each experiment to identify hardening curve and fracture model parameters. Notched tension specimens were utilised to calibrate Swift-Voce type strain hardening function for equivalent plastic strains beyond the onset of diffuse necking. The location of the fracture initiation and corresponding loading path were investigated using finite element analysis and the test results. The Hosford–Coulomb fracture model parameters were identified using the loading paths extracted from finite element analysis results. Validation of the presented loading path dependent Hosford–Coulomb model was conducted by simulating the tests with a user-defined material subroutine implemented in the finite element analysis software package Abaqus/Explicit.

Hosford-Coulomb ductile failure model for shell elements: Experimental identification and validation for DP980 steel and aluminum 6016-T4

When using shell elements, the Domain of Shell-to-Solid Equivalence (DSSE) needs to be defined in addition to the Hosford-Coulomb (HC) fracture initiation model to guarantee the convergence of the initiation of ductile fracture with respect to the mesh size. A comprehensive plasticity and fracture testing program is performed on 0.8 mm thick DP980 steel sheets. It includes uniaxial tension experiments along different material directions to characterize the plastic response, as well as simple shear, V-bending, and punch experiments to characterize the HC model parameters. Nakazima, tension, and bending experiments are performed on flat specimens with different notch radii to validate the predictions obtained with the combined DSSE-HC model. Aside from calibrating and validating the model for DP980 steel sheets, the model parameters are also identified from experiments on 1 mm thick aluminum 6016-T4 sheets and validated through numerical simulations of the deep drawing of a triangularly-shaped cup. The good agreement of the shell element simulations with all experiments demonstrates that the DSSE-HC model is capable of providing reasonable predictions of the onset of ductile failure for both membrane- and bending-dominated loading conditions.

Plastic anisotropy and ductile fracture of bake-hardened AA6013 aluminum sheet

The anisotropic plastic flow and ductile fracture of AA6013 aluminum sheet is investigated under quasistatic conditions. The plasticity of the material is probed through uniaxial tension, plane-strain tension and disk-compression experiments, from which the Yld2004-18p non-quadratic 3D anisotropic yield criterion and the combined Swift-Voce hardening model are calibrated. The ductile fracture is characterized with two notched-tension (different notch radii), one center-hole tension and one shear experiment. These experiments cover a wide range of stress triaxialities, while requiring only a universal testing machine to be conducted. Digital Image Correlation is used throughout the experiments to assess the surface strain fields. The predictions of three plasticity models, i.e., von-Mises and Yld2004-18p with constant and with evolving exponents and the corresponding Swift-Voce curves, are compared to the measured force–displacement curves and surface strain histories. These models are then used to probe the stresses, strains, stress triaxiality and Lode angle parameter throughout the loading to fracture. It was found that this hybrid experimental-numerical approach for the fracture strain determination is very sensitive to the constitutive model adopted. As an independent assessment, a microstructure-based estimation of the fracture strains is described. This verified that the von–Mises yield criterion for this AA6013 aluminum sheet provides erroneous estimates of the fracture strains. The most suitable constitutive model is the Yld2004-18p with evolving exponent. Based on these results, the fracture loci are represented by the Oyane, Johnson–Cook and Hosford–Coulomb models.

Predicting shear fracture of aluminum 6016-T4 during deep drawing: Combining Yld-2000 plasticity with Hosford–Coulomb fracture model

Shear fracture cannot be predicted with conventional forming limit curves even though it often limits the formability of modern engineering materials. To circumvent the need of a special set of ductile fracture experiments in addition to standard forming experiments, a hybrid experimental–numerical procedure is proposed to identify the three material parameters of the Hosford–Coulomb fracture initiation model from the same experiments that are used to identify the forming limit curve. To increase the reliability of the model identification, a cup drawing experiment is proposed to characterize the fracture response of out-of-plane shear loading. Uniaxial tension, bulge, Nakazima and drawing experiments are performed on specimens extracted from 1 mm thick aluminum 6016-T4 sheets. The anisotropic Yld2000 plasticity model with self-similar Swift-Voce hardening is identified to describe the large deformation response. The loading paths to fracture for stress states ranging from pure shear to equi-biaxial tension are obtained from detailed numerical simulations of all forming experiments. The identified material parameters of the Hosford–Coulomb model reveal that the fracture response of the aluminum 6016-T4 alloy is highly Lode angle dependent. Aside from identifying the anisotropic plasticity, the forming limit curve and the stress-state dependent fracture model, the deep drawing of a complex three-dimensional part with a triangular-shaped die is performed experimentally and simulated to validate the models at the structural level.

Influence of manufacturing processes on material characterization with the grooved in-plane torsion test

In-plane torsion tests offer advantages such as a proportional loading path and a homogeneous stress and strain distribution when characterizing the material behavior in the state of in-plane shear. The use of a grooved specimen is mandatory for the characterization of the damage behavior. The manufacturing of the groove by turning, milling, and electrical discharge machining for a DP600, DP1000, and CP1000 showed a strong influence on the experimentally measurable strain values at failure. Fine machining by milling displayed good results for all tested materials. The notch-effect in turned grooves led to an early fracture initiation. A straightforward parameter identification scheme for the Hosford–Coulomb fracture criterion as proposed by [16] was used to show the sensitivity of fracture curves on the experimental database.

Benefits of Using Lode Angle Dependent Fracture Models to Predict Ballistic Limits of Armor Steel

Ductile fracture experiments are carried out at different stress states, strain rates and temperatures on a range of flat Mars 300 steel specimens to calibrate both a plasticity and a fracture model. To predict the onset of fracture a stress state and strain rate-dependent Hosford–Coulomb fracture initiation model is used. Single material impact experiments are performed on targets of homogenous and perforated Mars 300 plates by accelerating cylindrical Mars 300 impactors in a single-stage gas gun. It is shown that the chosen modeling approach allows accurate modeling of the plastic response as well as the fracture patterns.

Lode dependent plasticity coupled with nonlinear damage accumulation for ductile fracture of aluminium alloy

The experimental program was designed and proportional tests carried out at a room temperature on aluminium alloy 2024-T351. These concerned tension, torsion and compression, in order to investigate the damage accumulation nonlinearity and to reliably calibrate new phenomenological ductile fracture criterion. This fracture model, KHPS2, expressed through the fracture strain, was dependent on the stress triaxiality and normalized third invariant of deviatoric stress tensor. The ductile fracture model was then coupled with the yield criterion, as in the continuum damage mechanics, using the material softening. The plasticity model was considered in the form of taking into account the Lode dependence for investigated material, through normalized third invariant of deviatoric stress tensor. The whole approach, fully applicable to multiaxial ductile fracture related problems, was implemented using the user subroutine into the commercial software, based on the explicit finite element method. In the end, the proposed approach was verified using chosen realized fracture tests, which were used in the calibration, and newly designed KHPS2 criterion along with an existing one—modified Hosford–Coulomb model. The latter model showed better performance in simulations despite worse approximation ability, which can be attributed to its micromechanically-motivated formulation.

Fracture of high-strength armor steel under impact loading

Mars® 300 is an ultrahigh hard armor (UHHA) martensitic steel designed for ballistic protection. It is available in sheets of different thicknesses and also as perforated plates with a periodic pattern of cylindrical holes. Installed as an add-on layer in front of a main armor, its aim is to cause deflection or fragmentation of small-caliber projectiles. In the present study, the impact process is investigated with a hybrid experimental-numerical approach. Ductile fracture experiments are carried out at different stress states, strain rates and temperatures on a range of flat Mars® 300 steel specimens to identify the plasticity and fracture response. The plasticity model is composed of von Mises yield surface, a non-associated anisotropic flow rule, a combined Swift–Voce strain hardening law and a Johnson–Cook type of rate and temperature-dependency. To predict the onset of fracture, a stress state and strain rate-dependent Hosford–Coulomb fracture initiation model is used. Impact experiments are performed on targets of homogenous and perforated Mars® 300 plates by accelerating cylindrical Mars® 300 projectiles in a single-stage gas gun. Depending on the impact location, three different failure mechanisms are identified for the perforated plate. Subsequently, finite element simulations using the calibrated material model are carried out to thoroughly analyze the impact experiments. A very good prediction of the different impact cases and their fracture patterns is obtained, validating the applicability of the plasticity and the fracture model for impact loadings.

A new shear and tension based ductile fracture criterion: Modeling and validation

Abstract A new ductile fracture criterion (DFC) is developed based on two typical fracture mechanisms - tension fracture and shear fracture by analyzing the morphologies of the fractured surfaces, and is discussed through void nucleation, void growth and void coalescence. The parameters in the proposed DFC are determined by analytical and numerical methods, and the influences of these parameters on the surface of equivalent plastic strain to fracture (EPSF) and the curve of EPSF to stress triaxiality in plane stress condition are discussed. Besides, the total Lode dependence of the proposed DFC about the influences of these parameters is also illustrated. The curves of EPSFs for Al 6061-T6 and Al 2024-T351 sheet are established and compared with the curves of CrashFEM criterion, modified Mohr-Coulomb criterion (MMC), extended Lou criterion and Hosford–Coulomb criterion and the absolute relative errors of these DFCs are also compared with the experimental data of Al 6061-T6 and Al 2024-T351, demonstrating the better accuracy of the proposed DFC. Comparative studies also show that the proposed DFC can accurately predict the ductile fractures with stress triaxiality less than −1/3, in round bar and notched bar tension.

Stress-state and strain-rate dependent ductile fracture of dual and complex phase steel

A comprehensive combined hybrid numerical-experimental program is executed on three advanced high strength steels (DP980, CP980 and CP1180) with the objective of validating (1) the hypothesis of a positive strain rate effect on the ductility under biaxial tension, as well as (2) the Hosford–Coulomb model assumptions with regards to the Lode parameter and stress triaxiality dependency of fracture initiation. The basic low strain rate testing program included punch, notched tension, central hole tension and smiley shear experiments. In addition, intermediate and high strain rate SHPB experiments are carried out to characterize the effect of strain rate. A non-associated quadratic plasticity model with Swift-Voce hardening and Johnson–Cook type of strain rate and temperature dependency is employed to model the large deformation response. The fracture model parameters are identified based on the loading paths to fracture extracted from numerical simulations with fine solid element meshes up to the point of fracture initiation in the experiments. It is found that the simple three-parameter Hosford–Coulomb model can describe the pronounced stress state effect on the strain to fracture for all materials. The results for notched tension also confirm that the ductility increases as function of the loading velocity for biaxial loading.

Combined necking & fracture model to predict ductile failure with shell finite elements

The implementation of recent progress on stress state dependent ductile fracture models is inhibited by the break-down of shell element solutions whenever through-thickness necking occurs. The concept of the Domain of Shell-to-Solid Equivalence (DSSE) is therefore introduced to capture the onset of localized necking with shell element meshes. As long as the elasto-plastic loading paths lie inside the DSSE, ductile fracture may be predicted with shell elements using exactly the same models as for solid elements. A simple criterion describing the boundary of the DSSE is proposed based on the results from Marciniak-Kuczynski type of localization analysis. It is combined with the stress triaxiality and Lode angle dependent Hosford-Coulomb (HC) fracture initiation model and implemented as a user material subroutine for explicit finite element analysis. The combined DSSE-HC model is validated for a DP780 steel for notched tension, hemispherical punch loading, stretch bending, and V-bending of strips.

Critical hardening rate model for predicting path-dependent ductile fracture

A new phenomenological framework for predicting ductile fracture after non-proportional loading paths is proposed, implemented into FE software and validated experimentally for a limited set of monotonic and reverse loading conditions. Assuming that ductile fracture initiation is imminent with the formation of a shear band, a shear localization criterion in terms of the elastoplastic tangent matrix is sufficient from a theoretical point of view to predict ductile fracture after proportional and non-proportional loading. As a computationally efficient alternative to analyzing the acoustic tensor, a phenomenological criterion is proposed which expresses the equivalent hardening rate at the onset of fracture as a function of the stress triaxiality and the Lode angle parameter. The mathematical form of the criterion is chosen such that it reduces to the Hosford–Coulomb criterion for proportional loading. The proposed framework implies that the plasticity model is responsible for the effect of loading history on ductile fracture. Important non-isotropic hardening features such as the Bauschinger effect, transient softening and hardening stagnation must be taken into account by the plasticity model formulation to obtain reasonable fracture predictions after non-proportional loading histories. A new comprehensive plasticity model taking the above effects into account is thus an important byproduct of this work. In addition, compression–tension and reverse-shear experiments are performed on specimens extracted from dual-phase steel sheets to validate the proposed plasticity and fracture model.

On the Dependency of Ductile Damage Evolution to Stress State with Shock Loading Pre-Mechanical Working in 7075-T6 Aluminum Alloy

In this paper, the evolution of a ductile damage in the 7075-T6 aluminum alloy is considered based on stress state parameters with a special focus on pre-mechanical working dependency. Uniaxial stress–strain curves are investigated experimentally for two conditions; specimens with shock loaded pre-mechanical working and without it. This kind of loading is applied in order to find out impulsive pressure effects of damage variation procedure. Some experiments are done to take different stress states. Applying two fracture initiations criteria, i.e., Hosford–Coulomb and Xue models, two types of fracture locus of Al-7075-T6 are predicted in terms of plastic strains and stress state parameters under above conditions. By considering experimental data, a new ductile damage evolution model is proposed among plastic behavior. It is introduced by explicating an uncoupled plasticity and related to initial rate dependent stress state. By using both fracture models, our damage evolution model is implemented, phenomenologically as well as the Xue damage model, to compare results.

The second Sandia Fracture Challenge: blind prediction of dynamic shear localization and full fracture characterization

In the context of the second Sandia Fracture Challenge, dynamic tensile experiments performed on a Ti–6Al–4V alloy with a complex fracture specimen geometry are modeled numerically. Sandia National Laboratories provided the participants with limited experimental data, comprising of uniaxial tensile test and V-notched rail shear test results. To model the material behavior up to large plastic strains, the flow stress is described with a linear combination of Swift and Voce strain hardening laws in conjunction with the inverse method. The effect of the strain rate and temperature is incorporated through the Johnson–Cook strain rate hardening and temperature softening functions. A strain rate dependent weighting function is used to compute the fraction of incremental plastic work converted to heat. The Hill’48 anisotropic yield function is adopted to capture weak deformation resistance under in-plane pure shear stress. Fracture initiation is predicted by the recently developed strain rate dependent Hosford–Coulomb fracture criterion. The calibration procedure is described in detail, and a good agreement between the blind prediction and the experiments at two different speeds is obtained for both the crack path and the force–crack opening displacement (COD) curve. A comprehensive experimental and numerical follow-up study on leftover material is conducted, and plasticity and fracture parameters are carefully re-calibrated. A more elaborate modeling approach using a non-associated flow rule is pursued, and the fracture locus of the Ti–6Al–4V is clearly identified by means of four different fracture specimens covering a wide range of stress states and strain rates. With the full characterization, a noticeable improvement in the force–COD curve is obtained. In addition, the effect of friction is studied numerically.

Numerical failure analysis of three-point bending on martensitic hat assembly using advanced plasticity and fracture models for complex loading

A variety of phenomenological models have been developed and validated at a specimen level to simulate plasticity and fracture of metallic materials using finite element analysis. It is both scientifically challenging and crucial for the industry to confirm their applicability at a structural level for the engineering practice. An outwardly simple three-point bending on a hot-stamped martensitic (22MnB5) hat assembly yields complex local loading histories, which eventually creates two symmetric macro-cracks under a semicircular punch. Attempts are made to numerically reproduce the deformed configuration with cracks using the Hosford–Coulomb fracture criterion, recently proposed by Mohr and Marcadet (2015). Two constitutive models of different complexity are compared: pure isotropic hardening with linear damage accumulation and combined isotropic–kinematic hardening with non-linear damage accumulation (Marcadet and Mohr, 2015). The model parameters are identified based on comprehensive mechanical tests. The latter model turns out to predict the location and shape of cracks with great accuracy by considering the dominance of kinematic hardening and enhanced ductility upon loading reversal. The force-punch stroke curves are compared with the experiment. Parametric studies are performed on the friction coefficient and possible anisotropic fracture properties. The deformation sequence is also analyzed.

Probabilistic fracture of Ti–6Al–4V made through additive layer manufacturing

The large deformation response of Ti–6Al–4V parts made through additive layer manufacturing is investigated. A wire-feed process is chosen instead of a powder process in an attempt to reduce the oxide contaminations of the final part. The experimental program includes uniaxial tension experiments along different part directions and fracture experiments on flat specimens with cut-outs covering stress states ranging from pure shear to equi-biaxial tension. More than 100 experiments are performed in total to characterize the randomness in the material's fracture response. It is found that the stress-strain response of the ALM material is comparable to that of Ti–6Al–4V sheet stock, while its average ductility is substantially lower. For example, for pure shear loading, the average strain to fracture for the ALM material is 0.47, while the mill product of the same alloy failed at a strain of 0.65. A probabilistic extension of the stress state dependent Hosford–Coulomb fracture initiation model is proposed to account for the significant standard deviation in the identified strains to fracture. Microscopic and surface strain field analysis demonstrate that the initiation and propagation of ductile fracture in the ALM material is strongly affected by the presence of prior-beta grains.

Anisotropic Hosford–Coulomb fracture initiation model: Theory and application

An anisotropic extension of the Hosford–Coulomb localization criterion is obtained through the linear transformation of the stress tensor argument. Unlike for isotropic materials where the stress state is characterized through the stress triaxiality and Lode parameter, the normalized Cauchy stress tensor is used to describe the stress state in an anisotropic solid. Based on experiments on extruded aluminum 6260-T6 covering stress states from pure shear to equi-biaxial tension for different material orientations, it is shown that this phenomenological and uncoupled model is capable to provide reasonable engineering approximations of the strains and displacements to fracture for thirteen different loading conditions.

Ductile fracture of aluminum 2024-T351 under proportional and non-proportional multi-axial loading: Bao–Wierzbicki results revisited

The effect of stress state and loading path on the ductile fracture of aluminum 2024-T351 is characterized through tension–torsion experiments on tubular specimens. The experimental program includes proportional and non-proportional loading paths leading to the onset of fracture at nearly plane stress conditions at stress triaxialities between 0 and 0.6. Stereo digital image correlation is used to measure the displacements and rotations applied to the specimen shoulders. An isotropic non-quadratic Hosford plasticity model with combined Voce–Swift hardening is used to obtain estimates of the local stress and strain fields within the specimen gage section. The hybrid experimental–numerical results indicate a higher strain to fracture for pure shear than for uniaxial tension. The calibration of a Hosford–Coulomb fracture initiation model suggests that the ductility of aluminum 2024-T351 decreases monotonically as a function of the stress triaxiality, whereas it is a non-symmetric convex function of the Lode angle parameter. It is shown that a simple non-linear damage accumulation rule can describe the effect of non-proportional loading on the strain to fracture.