Hosford-Coulomb Model Research Articles

Effect of the loading-rate and stress state on the constitutive modelling and fracture of 2205 Duplex stainless steel

Shear cutting is a high-speed forming process where material separation is involved. The nature of the process leads to high strain rates and temperatures on the sheared zone of the material subjected to the operation. In this work, the mechanical behavior in terms of flow stress, plastic deformation and fracture of a 2205 Duplex stainless steel sheet is determined. Uniaxial tension, uniaxial compression, stack compression, plane strain tension and simple shear tests at different angles with respect to the rolling direction of the metal sheet are performed to determine the anisotropic behavior of the material. Strain rate and temperature dependence of the flow stress and the plastic behavior of the material is determined through notched tensile tests performed under various temperatures (20°C, 100°C, 300°C and 500°C) and strain rates (0.001 s-1, 10 s-1 and >100 s-1). Finally, fracture behavior under various stress states is determined through notched tensile, central hole, in-plane shear and plane strain tests. The temperature and strain rate dependence of the fracture behavior is determined through notched tensile, in-plane shear and plane strain tests performed under various temperatures (20°C, 100°C, 300°C and 500°C) and strain rates (0.001 s-1, 10 s-1 and >100 s-1). The anisotropic behavior and work hardening of the material are modelled by the Hill48 yield function and Swift-Hockett-Sherby hardening law, respectively. Among the two ductile fracture models tested, Hosford-Coulomb model showed the best agreement and is therefore used to account for the temperature and strain rate effects on the fracture behavior. By combining these three models, an accurate reproduction of the mechanical behavior of the 2205 Duplex stainless steel sheet is achieved.

Study on ductile fracture behavior of hydrogen-charged API pipeline steel

With the increasing focus on reducing carbon emissions, hydrogen has emerged as a promising alternative energy source. However, the safe transportation of hydrogen poses challenges due to its potential impact on the integrity of pipeline materials. This study aims to investigate the effect of hydrogen charging time on the plastic behavior and ductile fracture characteristics of API 5L X42 pipelines, which are commonly used for transporting hydrocarbons. Tensile tests were conducted on various types of hydrogen-charged specimens at room temperature to assess different fracture modes. Hydrogen was introduced into the specimens using a cathodic electrolytic method, and 24-h charging time durations were considered. Finite element analyses were performed on standard dog-bone and notched tension specimens to evaluate the plastic behavior, employing the Swift hardening law to model the flow stress. Numerical analyses were conducted to determine the loading path leading to fracture initiation. A damage framework based on the Hosford–Coulomb model was utilized to predict ductile fracture under non-proportional loading conditions. The findings of this study provide insights into the fracture behavior of pipelines under hydrogen exposure, aiding in the design and assessment of safe and reliable hydrogen transport systems.

Numerical Study on a Ductile Fracture Model in Pre-Cracked Tension Tests of SUS304L.

The effectiveness of a ductile fracture model in accurately predicting fracture initiation has been demonstrated. In this study, we concentrate on applying the ductile fracture model to pre-cracked structures constructed from SUS304L stainless steel with experimental and numerical analyses. The Swift hardening law was employed to extend the plastic behavior beyond the onset of necking. Additionally, the Hosford-Coulomb model, integrated with a damaged framework, was utilized to predict ductile fracture behavior, particularly under non-proportional loading conditions. Tension tests were conducted on various specimens designed to illustrate various fracture modes resulting from geometric effects. Numerical analyses were conducted to explore the loading histories, utilizing an optimization process to calibrate fracture model parameters. The proposed fracture model is validated against pre-cracked structures detailed in a reference paper. The results convincingly demonstrate that the fracture model effectively predicts both fracture initiation and propagation in pre-cracked structures.

Ductile fracture of X80 pipeline steel over a wide range of stress triaxialities and Lode angles

This study pays attention to the ductile fracture of X80 pipeline steel using both experimental and numerical approaches. First, nineteen experimental cases are tested, consisting of the normalized uniaxial tension, the plain strain tension, pure shear, and shear plus tension/compression. Three fracture modes are observed throughout the experiments. A hybrid testing-FE method is applied to determine the post-necking strain hardening curve of the X80 pipeline steel. Then, parallel computations are conducted in the Abaqus to obtain ductile fracture parameters. The simulated results indicate that the determined strain hardening curve has applicability for all experiments. According to the ductile fracture parameters, three models, viz. the Hosford-Coulomb model, the DF2016 model, and a newly proposed model, are calibrated based on the hold-out strategy. Fracture prediction of the X80 pipeline steel is conducted by the three calibrated models. The results show that the newly proposed model outperforms the other two in terms of stability and accuracy.

Plastic deformation and ductile fracture of L907A ship steel at increasing strain rate and temperature

A combined theoretical, numerical, and experimental approach is adopted to systematically characterize the plastic deformation and ductile fracture behaviors of L907A low-alloy ship steel widely used in ship construction, with the effects of strain rate and thermal softening duly accounted for. A mixed Swift-Voce hardening model coupled with strain rate and temperature-dependent terms is proposed, while the Hosford-Coulomb model of ductile fracture is modified by introducing temperature-dependent term to account for the effect of thermal softening. To calibrate the parameters appearing in the constitutive models, dynamic uniaxial tensile tests at varying strain rates (0.001 ∼ 5200 s−1) and quasi-static uniaxial tensile tests at varying temperatures (20 ∼ 800 °C) are separately performed, with the coupling between strain rate and temperature effects ignored. The calibrated plasticity and ductile fracture models are numerically implemented with the method of finite elements (FE), and their applicability to practical applications is validated against experimental results of ballistic impacts. Normal and oblique impacts on L907A target plates with conical, hemispherical, and blunt projectiles are considered. Good agreement between FE simulation results of plastic deformation and ductile fracture modes and those measured experimentally is achieved, thus demonstrating the viability of the established plasticity and fracture models of L907A steel for applications in complex ballistic impact scenarios.

A new ductile fracture model for structural metals considering effects of stress state, strain hardening and micro-void shape

In this study, a new micromechanically-motivated phenomenological uncoupled fracture model is proposed for predicting the ductile fracture of structural metals considering the combinative effects of stress state, strain hardening and micro-void shape. The Lee–Mearvoid growth theory, which is used for characterizing the growth of ellipsoidal voids in a hardening matrix, is modified to derive the influence function of stress triaxiality, void shape and strain hardening on material’s ductility. Meanwhile, a J2-J3 based Bai–Wierzbicki’s yield function is used as a failure criterion and incorporated into the power-law hardening function to derive the Lode dependence of fracture strain. Further, a detailed parametric study is performed to demonstrate the influence of the material parameters on the 3D fracture envelope and 2D fracture locus of the new model. It is shown that the unique feature of the new fracture model is that it constructs an explicit and quantitative relationship between the ductility, strength and microstructure of metals. All parameters in the new model have intuitive physical meanings which correspond to specific material property indies controlling the material strength and evolution of micro-void defects. In the meantime, these model parameters can be easily calibrated via conventional tests, which greatly reduces the difficulty of the calibration work and makes the model being more friendly for engineering applications. Finally, test data of three structural metals, i.e. 2024-T351, 6061-T6 aluminum alloys and Q460 high strength structural steel, obtained under two loading conditions, i.e. proportional and non-proportional loading conditions, are used to calibrate and validate the proposed model. The accuracy of the new fracture model is then investigated by comparing its prediction result with that obtained from the modified Mohr–Coulomb and Hosford–Coulomb model. It is shown that the proposed new fracture model can predict the ductility limit of the investigated structural metals accurately under a wide range of stress states and provides the same good prediction accuracy as the other two typical models, which confirms the promising prospect of the new model in practical applications.

Characterization and prediction of fracture in 6000- and 7000-series aluminum alloy sheet under various stress states

This study investigates the stress state dependentfracture of several high strength aluminum sheet alloys, AA6013-T6, AA7075-T6 and a developmental AA7xxx-T76 alloy. These alloys are targeted for use in automotive structural applications for which accurate knowledge of the fracture loci are required to support crash safety simulations. A generalized Drucker–Prager (GDP) model to describe the fracture locus was proposed and calibrated to the measured fracture strains under simple shear, uniaxial, plane strain and biaxial tension. Calibration of the fracture loci was undertaken directly using measured fracture strains and direct integration of stress based on the measured strain histories. The calibrated fracture loci using the GDP function exhibited good agreement with the measured data across the range of the stress state conditions. An advantage of the GDP model is the admission of fracture asymmetry in uniaxial and biaxial tension which is not captured using the Hosford–Coulomb model. The experimental fracture loci were then paired with a damage model for non-linear strain paths and used to simulate three-point bend experiments on structural hat channel sections. For each material, the load response and onset of fracture were well predicted.

Stress state sensitivity for plastic flow and ductile fracture of L907A low-alloy marine steel: From tension to shear

High-performance marine steel is essential for the marine industry worldwide. L907A low-alloy marine steel was developed by China independently and is now widely used in ship construction. In this study, the plasticity and ductile fracture behavior of L907A steel under various stress states are systematically investigated by experiments, mechanical modeling, and numerical simulations. Through the use of different microscopic methods, the initial microstructure of the material is well characterized. The constituent phases and grain morphologies of L907A introduce a good combination of strength and ductility and exhibit isotropic in-plane features. Specimens with various geometries are designed and tested to characterize the mechanical response of the L907A steel under various stress states ranging from tension to shear. The isotropic von Mises yield function with mixed Swift-Voce hardening law is used to characterize large deformation, while fracture initiation under various stress states is described by the Hosford-Coulomb model. A new parameter identification method, which combines hybrid numerical-experimental approach with simulated annealing optimization algorithm, is proposed to obtain the globally optimal model parameters. It is demonstrated that the calibrated model can predict the plasticity and fracture behavior of L907A with great accuracy. Finally, the mechanical performance of L907A is compared with competing marine steels (e.g., DH36 steel and EH36 steel). Results indicate that the yield stress of L907A is close to DH36 and higher than EH36, but its average strain hardening rate is lower than DH36 and close to EH36; the ductility of L907A is close to DH36 but worse than EH36. The fracture locus of L907A exhibits minimal stress state dependence compared to both DH36 and EH36.

Orientation and stress state dependent plasticity and damage initiation behavior of stainless steel 304L manufactured by laser powder bed fusion additive manufacturing

The plasticity and ductile fracture behavior of stainless steel 304L fabricated by laser powder bed fusion additive manufacturing was investigated under both uniaxial and multiaxial loading conditions through the use of specialized geometry mechanical test specimens. Material anisotropy was probed through the extraction of samples in two orthogonal material directions. The experimentally measured plasticity behavior was found to be anisotropic and stress state dependent. An anisotropic Hill48 plasticity model, calibrated using experimental data, was able to accurately capture this behavior. A combined experimental–computational approach was used to quantify the ductile fracture behavior, considering both damage initiation and final fracture. An anisotropic Hosford–Coulomb model was used to capture the anisotropic and stress state dependent fracture behavior.

Dynamic perforation of lightweight armor: Temperature-dependent plasticity and fracture of aluminum 7020-T6

The design of armored vehicles requires reliable constitutive models that are valid over a wide range of strain rates and temperatures. A comprehensive experimental program is executed to characterize the stress-strain response of high strength aluminum 7020-T6 at temperatures ranging from 20°C to 320°C. It includes tensile experiments on uniaxial, notched, central hole and shear specimens. Aside from low and intermediate strain rate experiments, high strain rate experiments are performed on a Split Hopkinson Pressure Bar (SHPB) system equipped with a load inversion device. Furthermore, hemispherical punch and V-bending experiments are performed to achieve equi-biaxial tension and transverse plane strain conditions. It is found that a Yld2000–3d plasticity model with isotropic strain hardening and thermal softening is suitable to describe the large deformation response, while a rate- and temperature-independent Hosford-Coulomb model is used to predict fracture. Impact experiments are performed on 4 mm thick targets with blunt, hemispherical and conical steel projectiles of 8 mm diameter and a mass of 13.8 g. The impact velocity is varied such that the full spectrum from the ballistic limit to complete penetration can be characterized. In addition, perpendicular and oblique configurations are considered. Numerical simulations are performed for all experiments confirming the validity of the identified constitutive model and providing unmatched insight into the dynamic penetration failure mechanism.

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.

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.

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.

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.

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.

Micromechanically-motivated phenomenological Hosford–Coulomb model for predicting ductile fracture initiation at low stress triaxialities

A phenomenological ductile fracture initiation model for metals is developed for predicting ductile fracture in industrial practice. Its formulation is based on the assumption that the onset of fracture is imminent with the formation of a primary or secondary band of localization. The results from a unit cell analysis on a Levy–von Mises material with spherical defects revealed that a Mohr–Coulomb type of model is suitable for predicting the onset of shear and normal localization. To improve the agreement of the model predictions with experimental results, an extended Mohr–Coulomb criterion is proposed which makes use of the Hosford equivalent stress in combination with the normal stress acting on the plane of maximum shear. A fracture initiation model is obtained by transforming the localization criterion from stress space to the space of equivalent plastic strain, stress triaxiality and Lode angle parameter using the material’s isotropic hardening law. Experimental results are presented for three different advanced high strength steels. For each material, the onset of fracture is characterized for five distinct stress states including butterfly shear, notched tension, tension with a central hole and punch experiments. The comparison of model predictions with the experimental results demonstrates that the proposed Hosford–Coulomb model can predict the instant of ductile fracture initiation in advanced high strength steels with good accuracy.

A rate-dependent Hosford-Coulomb model for predicting ductile fracture at high strain rates

The Hosford-Coulomb model incorporates the important effect of the Lode angle parameter in addition to the stress triaxiality to predict the initiation of ductile fracture. A strain-rate dependent extension of the Hosford-Coulomb model is presented to describe the results from low, intermediate and high strain rate fracture experiments on advanced high strength steels (DP590 and TRIP780). The model predictions agree well with the experimental observation of an increase in ductility as function of strain rate for stress states ranging from uniaxial to equi-biaxial tension.