Johnson-Cook Fracture Research Articles

Effect of Lode angle in predicting the behaviour of stiffened 921A steel target plates in ballistic impact by truncated ogive projectiles

Two sets of penetration experiments with truncated ogive projectiles were carried out on large unstiffened and stiffened target plates made of 921A steel; the residual velocity of the projectile was recorded, and the failure mode of the target was analysed. The experimental results show that the unstiffened target plate exhibited obvious petaling failure, whereas the stiffened plate exhibited a coupled complex failure mode because of its spatial structure. Many recent studies have shown that the failure strain of metals can be affected by the Lode angle in addition to the stress triaxiality, so this study introduced the Lode angle into the fracture criterion to investigate whether it affects the ballistic behaviour of the target plate. A numerical model was established in the Ansys LS-DYNA finite-element software, with the mechanical properties of 921A steel characterized by the Johnson–Cook (JC) constitutive equation and the failure strain controlled by either the JC fracture criterion independent of the Lode angle or the modified Mohr–Coulomb (MMC) fracture criterion dependent on the Lode angle. The numerical and experimental results shows that both fracture criteria predict well the residual velocity after penetration. However, the failure mode of the target plate obtained with the JC fracture criterion exhibits a reaming process, as reflected in the local upward dish deformation, and although the target plate also forms multiple petals, they are all connected and gathered inward, acting as a whole. The results calculated with the MMC fracture criterion predict the experimental ones well, with the unstiffened plate exhibiting obvious petaling failure. Finally, the MMC fracture criterion is added to the numerical model of the stiffened plate, and the calculation results show that the ballistic impact behaviour of the target plate can still be predicted effectively.

Ballistic response of additively manufactured AA6061/AA7075 multistack plate for armor-piercing projectile

The current ballistics research study focuses heavily on substituting heavy metals with lightweight materials to make mobility more accessible and effective for all armor applications. To do so, the researchers found that aluminum alloys are the better alternative to substitute steel armor due to their high strength-to-weight ratio. Therefore, this research conducted ballistic studies on aluminum alloys using the Finite Element Analysis (FEM) methodologies and associated mathematical analysis. This Research primarily focuses on the damage factor, ballistic limit, and residual velocity of the bullet following penetration of target plates. In this investigation, the Johnson-Cook fracture and Recht-Ipson models were implemented on materials AA6061-T6 and AA7075-T6. The main objective of these models is to establish the damage factor and verify whether it is less than unity; if the factor is less than unity, it is eligible to study the residual velocity of the bullet after penetration into the target armor plate. The target plate was impacted with a 7.62 mm armor-piercing projectile with an impact velocity of 500 m/s. Monolithic plates of 18 mm thickness were evaluated initially. After that, the multilayered stack of each 3 mm thick plate was analyzed, and studied the effectiveness of using a multilayered stack armor plate.

A Study of the Dynamic Mechanical Properties of Q460D Steel

The dynamic mechanical properties of Q460D steel were studied to facilitate an assessment of the impact resistance of building structures. In the present work, material performance tests of Q460D steel at different temperatures, strain rates, and stress states were conducted. Using a hybrid experimental–numerical approach, a modified Johnson–Cook (JC) constitutive relation, a modified Johnson–Cook (JC) fracture criterion, and a lode-dependent fracture criterion were calibrated. To validate the calibration, Taylor impact tests of Q460D steel rods onto rigid target plates were carried out in a one-stage light-gas gun system. Mushrooming, tensile splitting, and petalling failure modes were obtained as the impact velocity was increased from 191.6 to 422.1 m/s. A three-dimensional finite element model was built for the Taylor impact tests, and FE simulations were run using the material models calibrated. It was found that the FE simulations using the lode-dependent fracture criterion were reasonable in terms of the failure modes of the Taylor rods. In contrast, the fracture behavior of the Taylor rods was significantly underestimated using the lode-independent JC fracture criterion. Finally, the effect of anisotropy, strain rate sensitivity and yield plateau on the Taylor impact FE predictions were explored and discussed.

Research on dynamic constitutive model and fracture criterion of 6082-T6 aluminium alloy

In this study, the mechanical properties of materials under different stress states, strain rates, and temperatures were tested, and a variety of material mechanical properties were obtained. The modified Johnson-Cook (JC) constitutive model and ASCE-MJC fracture criterion with Lode angle correction were calibrated. A 6082-T6 aluminium alloy projectile with a diameter of 5.95 mm was used in performing the Taylor impact test with an impact velocity ranging from 156.548 to −417.216 m/s. Mushrooming and shear cracking were observed during the test. A finite element model (FEM) corresponding to the test was established using the finite element software ABAQUS, and the model was used to predict the ductile fracture behaviour of the projectile. Through a comparison of experiments and parallel simulations, the ASCE-MJC fracture criterion was used to predict a very close fracture mode of the projectile. This proves the validity of the calibrated dynamic constitutive model and the fracture criterion. After comparing the finite element simulation results based on the classic JC fracture criterion prediction, it was found that the ASCE-MJC fracture criterion can better predict the ductility of 6082-T6 aluminium alloy, indicating that the fracture behaviour of the material has a significant Lode correlation. This improvement was verified. The validity of the modified JC constitutive model and ASCE-MJC fracture criterion in predicting the dynamic mechanical properties and fracture behaviour of the 6082-T6 aluminium alloy was also verified.

Experimental and Numerical Study on the Protective Behavior of Weldox 900 E Steel Plates Impacted by Blunt-Nosed Projectiles

To demonstrate the importance of incorporating Lode angle into fracture criterion in predicting the penetration resistance of high-strength steel plates, ballistic tests of blunt-nosed projectiles with a diameter of 5.95 mm impacted 4 mm thick Weldox 900 E steel plates were conducted. Impacting velocity range was 136.63~381.42 m/s. The fracture behavior and the ballistic limit velocities (BLVs) were obtained by fitting the initial-residual velocities of the projectiles. Subsequently, axisymmetric finite element (FE) models parallel to the tests were built by using Abaqus/Explicit software, and the Lode-independent Johnson–Cook (JC) and the Lode-dependent ASCE fracture criterion were incorporated into the finite element model for numerical simulation. Meanwhile, to verify the sensitivity of the mesh size in the numerical simulation, different mesh sizes were used in the shear plug area of the target. It can be found that Weldox 900 E steel has obvious mesh size sensitivity by comparing the experimental results and numerical simulation, and the JC fracture criterion and the ASCE fracture criterion predicted similar BLV for the same mesh size.

Effect of incorporating Lode angle parameter into a fracture criterion in predicting ballistic impact behavior of double-layered 2024-T351 aluminum alloy plates against blunt projectiles

Recent studies showed that the ductility of some metals was affected by not only stress triaxiality but also Lode angle parameter. However, the majority of impact-related simulations used Lode independent fracture criteria. The necessity of incorporating Lode angle parameter into a fracture criterion in predicting ballistic impact behavior of monolithic 2024-T351 aluminum alloy (AA2024-T351) plates has been previously addressed in the work of Xiao et al. [1]. This paper serves as an extension by considering plates with double-layered configuration and the same total thickness. Ballistic impact tests were performed on 4.82 + 4.82 mm thick double-layered plates. Blunt projectiles with dimensions of Φ 12.66×50.56 mm3 and a nominal mass of 50 g were used, and the impact velocities ranged from 133.4 to 363.8 m/s. According to the experimentally obtained data, ballistic limit velocities (BLVs) were calculated and fracture patterns of post-test plates were analyzed. It was found that for double-layered configurations, the first plate failed by shear plugging and the second plate failed by tensile stretching and global deformation. By replacing monolithic plates with double-layered ones, the BLV increased from 138.4 to 180.1 m/s, a 30% improvement in ballistic resistance. Subsequently, numerical simulations of ballistic impact tests were performed by software ABAQUS/Explicit. Mechanical property of AA2024-T351 was described by Johnson-Cook (JC) plasticity model accompanied with either the Lode independent JC fracture criterion or the Lode dependent modified Mohr-Coulomb (MMC) fracture criterion. The numerical results were compared with those obtained from experiments. It was found that MMC criterion predicted BLVs more accurately than JC criterion. The prediction errors for MMC and JC criteria were respectively 3.3% and 11.4%, with the former being merely one-third of the latter. The overall failure modes of double-layered plates were correctly predicted by both JC and MMC fracture criteria. However, details of the fracture patterns, such as the formation of fragments, the shape and number of ejected plugs, and the initiation and propagation of cracks, were better captured by MMC criterion than by JC criterion. Detailed analysis shows that the stress state governing ballistic impact tests locates in the range where Lode angle parameter is strong enough to induce a significant difference between JC and MMC criteria. Under such stress state, the ductility of AA2024-T351 is correctly predicted by the Lode dependent MMC criterion but is overestimated by the Lode independent JC criterion.

Finite Element Modeling for Orthogonal Machining of AA2024-T351 Alloy With an Advanced Fracture Criterion

Abstract Numerical modeling of the plastic deformation and fracture during the high-speed machining is highly challengeable. Consequently, there is a need for an advanced constitutive model and fracture criterion to make the numerical models more reliable. The aim of the present study is to extend the recent advanced static Lou-Yoon-Huh (LYH) ductile fracture creation to high strain rate and temperature applications such as machining. In the present work, the LYH static fracture creation was extended to machining conditions by introducing strain rate and temperature dependency terms. This extended LYH fracture criterion was calibrated over the wide range of stress triaxialities and different temperatures. Modified Khan- Huang-Liang (KHL) constitutive model along with the variable friction model was employed to predict the flow behavior of work material during the machining simulation. Damage evolution method was coupled to identify the element deletion point during the machining simulation. Orthogonal machining experiments were carried out for an aerospace-grade AA2024-T351 at cutting speeds varying between 100 and 400 m/min with the feed rates varying between 0.1 and 0.3 mm/rev. To assess the prediction capabilities of extended LYH fracture criterion, numerical simulations were also carried out using Johnson-Cook (JC) fracture criterion under all experimental conditions. Specific cutting energy, chip morphology, and compression ratio predictions were compared with the experimental data. Numerical predictions with coupled extended LYH criterion showed good agreement with experimental results compared to coupled JC fracture criterion.

Analysis of two parameter identification methods for original and modified Johnson-Cook fracture strains, including numerical comparison and validation of a new blue-brittle dependent fracture model for free-cutting steel 50SiB8

A non-linear relation between fracture strain and temperature is observed in Split Hopkinson Tension Bar (SHTB) tests for free-cutting steel 50SiB8 at high strains and high temperatures, due to blue-brittleness. A fourth-degree polynomial function for the thermal parts of the original and modified Johnson-Cook (JC) fracture strain constitutive equation is suggested and the corresponding parameters are identified. Fracture modelling of 50SiB8 is not reported in literature. 50SiB8 is characterized under quasi-static, isothermal, high temperature and high strain rate conditions using smooth and notched tension specimens. For the calculation of the original and modified JC fracture parameters, two different parameter identification procedures, so-called forward and backward parameter identification methods are performed, compared with each other and explained in detail. For the stress triaxiality factor of the original and modified JC fracture model, the forward parameter identification method is suggested for the original JC fracture model, while backward parameter identification method is proposed for the modified JC fracture model. The effect of blue-brittleness in the temperature factor and the corresponding parameters are presented. Furthermore, FEM simulations of the original and the blue-brittleness based JC fracture model are compared with experiments. In the blue-brittle temperature range, the new adjusted JC model shows more accurate results, regarding fracture diameter and strain. Additionally, this work introduces a fracture model combining the Bai-Wierzbicki stress triaxiality dependent model, JC fracture models and the nonlinear temperature factor with blue-brittleness effect, while further experiments are required in order to determine its parameters.

Temperature-dependent Charpy impact property of 3D printed 15-5 PH stainless steel

In this study, the impact property of 3D printed 15-5 PH stainless steel was investigated at low (77 K), room (298 K), and high temperatures (723 K) using integrated experimental and modelling studies. The finite element model was based on the Johnson-Cook phenomenological material model and fracture parameters. The experimentally measured impact energies are 0.01, 6.78 ± 4.07, and 50.84 ± 3.39 J cm−2, at the low, room, and high temperatures, respectively. The experimental and modelling predicted impact energies are in good agreement. The microstructures show that the steel exhibits a brittle behaviour at low and room temperatures as indicated by a transgranular fracture, but changes to a more ductile behaviour at high temperatures as illustrated by microvoid coalescence induced facture morphology.

Effect of Lode angle incorporation into a fracture criterion in predicting the ballistic resistance of 2024-T351 aluminum alloy plates struck by cylindrical projectiles with different nose shapes

The aim of the present paper is to evaluate the effect of Lode angle incorporation into a fracture criterion when predicting the ballistic resistance of 2024-T351 aluminum alloy plates struck by cylindrical projectiles with different nose shapes through finite element (FE) simulations. To this end ballistic tests in the sub-ordnance impact velocity range were firstly conducted on 9.94 mm thick 2024-T351 aluminum alloy plates using cylindrical projectiles with blunt, hemispherical and ogival nose shapes, a nominal diameter of 12.66 mm, and a nominal mass of 50 g. Ballistic limit velocities (BLVs) for different projectile-target pairs considered were calculated using initial vs. residual velocity data obtained in the experiments. Subsequently FE simulations of the conducted experiments were performed with SIMULIA Abaqus software. In those simulations Johnson–Cook yield criterion with a modified strain hardening law was accompanied with either the Lode-independent Johnson–Cook (JC) fracture criterion or the Lode-dependent modified Mohr–Coulomb (MMC) fracture criterion to describe target material properties. Finally, the predicted ballistic resistance and fracture patterns of the targets were compared with those observed in the experiments. It was found that in the simulations with the Lode-independent JC fracture criterion the BLVs of the targets were overestimated by 18.0–35.1% depending on the projectile nose shape. In the simulations with MMC fracture criterion the BLVs predictions were substantially improved, so that the difference with the experimental results did not exceed 9.0%. Targets failure mechanisms obtained in the simulations with MMC fracture criterion also better match the experiments than those predicted with JC fracture criterion. In the simulations with MMC fracture criterion the targets impacted by the projectiles with blunt and hemispherical noses failed through shear plugging, whereas ogive-nosed projectiles caused ductile hole enlargement and target fragmentation due to its rear side radial fracture and bending of formed short petals with their eventual shear fracture. At the same time the simulations with JC fracture criterion predicted shear plugging for the blunt-nosed projectiles, very small conical plug ejection and target fragmentation due to discing for the hemispherical-nosed projectiles, and ductile hole enlargement for the ogive-nosed projectiles. A detailed analysis of the failure process revealed that in the case of the ogive-nosed and hemispherical-nosed projectiles, respectively, the ductile hole enlargement occurs during the initial stage of the impact and subsequent through-thickness fracture develops causing either fragmentation of the target or its shear plugging failure. The Lode-independent JC fracture criterion overestimates a material fracture strain under shear, thus leading to poor prediction of 2024-T351 aluminum alloy targets ballistic performance in the numerical simulations.

Constitutive Modeling of High-Strength Steel Designed for Ballistic Protection

Constitutive behaviour of a high-strength nanostructured bainitic steel NANOS-BA® was investigated in the article. A few types of mechanical tests under varying strain rates were carried out to determine the values of constants of Johnson-Cook flow and fracture models for the analysed material. In quasi-static conditions (8×10-3 s-1) the material samples were subjected to uniaxial tension and compression tests. In a high strain rates conditions (2,7×103 s-1) the Taylor impact test was carried out. On the basis of the data obtained from mechanical tests the constitutive model of the NANOS-BA® steel was built. It was then validated to determine the extent and degree of compliance between the numerical and experimental observations. The examples of combined numerical-experimental analyses of protective structures containing investigated material were shown. Small differences between the both types of results testifies that determined constants of Johnson-Cook equation may properly reproduce actual behaviour of the material, and the numerical model allows the preliminary evaluation of the effectiveness of armours containing layers of analysed grade of steel.

Shear localization sensitivity analysis for Johnson–Cook constitutive parameters on serrated chips in high speed machining of Ti6Al4V

This research aims to investigate the influence of material constitutive parameters on the serrated chip formation during high speed machining (HSM) of Ti6Al4V alloys with finite element simulations and cutting experiments. The Johnson–Cook (JC) constitutive model and JC fracture model with an energy-based ductile failure criterion are adopted to simulate the HSM process. Five JC constitutive model parameters such as initial yield stress, hardening modulus, strain hardening coefficient, strain rate dependency coefficient, and thermal softening coefficient are included in this research. Shear localization sensitivity is novelly proposed to describe variations of serrated chips under different JC constitutive model parameters. Shear localization sensitivity is subdivided into chip serration sensitivity and chip bending sensitivity. The research finds that the influences of initial yield stress and thermal softening coefficient parameters on the chip serration and bending are much more prominent than those of the rest three JC constitutive model parameters. With initial yield stress or hardening modulus in JC constitutive model increasing, the chip serration sensitivity increases and the chip bending sensitivity decreases. However, the influences of the rest three parameters on chip serration sensitivity are opposite. High speed orthogonal cutting experiments of Ti6Al4V are carried out to validate the simulation results under different cutting speeds ranging from 50m/min to 3000m/min and fixed uncut chip thickness with 0.1mm. The results show that the serrated degree of chips increases with the cutting speed increasing until the chips become completely fragmented. The cutting speed break point of chip morphology from serrated to fragmented ones for Ti6Al4V is about 2500m/min. The average cutting force decreases with the cutting speed increasing, which is a prominent advantage for HSM. This paper can help to get deeper insights into the serrated chip formation mechanism in HSM.

Investigations on the chip formation mechanism and shear localization sensitivity of high-speed machining Ti6Al4V

This study develops a combined numerical and experimental approach to get deeper insights into chip formation mechanism for high-speed machining of titanium alloy Ti6Al4V. The numerical investigation of high-speed machining is implemented with the aid of finite element analysis software Abaqus/Explicit, in which the Johnson-Cook (JC) fracture model with an energy-based ductile failure criterion is adopted. Meanwhile, the experiments of high-speed orthogonal cutting are carried out to validate the numerical results. The cutting speeds are selected ranging from 50 to 3,000 m/min, and the uncut chip thickness is fixed at 0.1 mm. The variables investigated include the serrated degree and serrated frequency of chips in addition to the cutting force. The results show that both the serrated degree and serrated frequency have positive correlations with the cutting speed. An important regularity for the transformation of chip morphology from serrated to unit at a critical cutting speed has been achieved, and the critical value for Ti6Al4V is about 2,500 m/min. The research also finds that the cutting force decreases with the increasing cutting speed, while its fluctuant frequency and amplitude increase sharply. Furthermore, the influences of JC fracture constants (the five constants in JC fracture model) on chip formation are investigated based on the finite element method, which is the main original and innovative highlight of this study. The shear localization sensitivity is firstly proposed to describe the influences of JC fracture constants on the chip formation process. When the JC fracture constants decrease, the shear localization sensitivity is positive which means that the serrated degree increases and vice versa. The sensitivity analyses indicate that the influences of initial failure strain D 1 and exponential factor of stress triaxiality D 2 on chip formation process are more conspicuous than the rest three ones. This paper is enticing from both the engineering and the analytical perspectives aimed at predicting the evolution of serrated chip formation and chip morphology transformation in metal cutting process.

Computational comparisons of homogeneous and statistical descriptions of AerMet100 steel subjected to high strain rate loading

In order to simulate the effect of material microstructure a statistically compensated Johnson-Cook (JC) fracture model has been implemented into the Eulerian shock physics code, CTH. This model uses a Weibull function to produce a distribution of initial failure strains within the JC fracture model. A parametric analysis where the Weibull modulus was systematically varied was conducted on two sets of experimental fragmentation data. The first experiment consisted of an explosively loaded cylinder of AerMet100. The second was an expanding tube experiment which used a plastic cylinder to load the AerMet100 and provided a problem at a lower strain rate. In both sets of experiments, the fragments were soft captured for later examination. While CTH does not explicitly track fragments, a post processor written at the Naval Surface Warfare Center Dahlgren Division was used to calculate the mass of each of the fragments in the expanding debris cloud. The results were analyzed and compared back to baseline homogeneous calculations. The use of a statistically compensated JC fracture model substantially improved the fragment mass distribution for the explosively loaded cylinder. However, the lower strain rate expanding tube showed only minimal improvement. A probable reason for this limitation and future analysis are discussed.

Behaviour of Thin Aluminium Plates Subjected to Impact by Ogive-nosed Projectiles

A pneumatic gas gun has been used to fire ogive-nosed projectiles on aluminium plates (1mm) at varying impact velocities above the ballistic limit. Impact and residual velocities have been measured. Deformation of the target plate was studied. Experimental results formed the basis of a subsequent finite element analysis of the problem using the ABAQUS 6.3 code. The Johnson-Cook plastic flow and fracture model available in the code were utilised. Explicit finite element analysis has been performed to model the perforation phenomenon. Numerical results were significantly improved by reducing the element size up to a certain level beyond which no significant variation in the results was observed. Adaptive meshing has been found to be useful in obtaining the accurate results and avoiding the problem of premature termination of the program due to excessive element distortion. Experimental and numerical results are compared and a good agreement between the two has been found.