Johnson Cook Constitutive Relation Research Articles

Ballistic analysis of high-performance armor steel by numerical simulation

In order to establish a connection between the ballistic performance and mechanical properties of armor steel, a ballistic simulation model was developed and subsequently validated for accuracy and reliability. The mechanical properties of the target plate were described using the Johnson–Cook constitutive relation. An analysis was conducted to investigate the impact of the J–C parameters of the target plate on its ballistic performance, revealing a strong linear relationship between them. Subsequently, a mathematical model represented as H = 14.82 − 0.0048A − 0.0023B + 5.95n − 81.3C was derived, and its accuracy was demonstrated to exceed 90%. This mathematical model can effectively predict the ballistic performance of the armor steel, even when its mechanical properties undergo variations during the production process. This prediction capability significantly contributes to reducing research costs and time.

DETERMINATION OF DYNAMIC PROPERTIES OF 3D PRINTED G3SI1 STEEL

Taylor anvil test is one of the dynamic test method used to determine the dependences of strain rate, strain and temperature on flow stress. This method can be used to determine the stress and strain at any point in the specimen at different temperatures and strain rates. The paper deals with the description of the Taylor anvil test experiment for G3Si1 welding wire. The experiment was carried out in the laboratory of high strain rates at the Faculty of Mechanical Engineering of Brno University of Technology. ANSYS Explicit dynamics software was used to simulate the material behaviour during the test. The Johnson-Cook constitutive relation was used to describe the material behaviour. The simulation results were compared with the experiment.

Finite-element study of residual stress distribution in Ti-6Al-4V alloy treated by laser shock peening with varying parameters

Laser shock peening (LSP) is used to enhance surface quality of the metallic structures by the generation of compressive residual stresses on it. This work studies the effect of the main LSP parameters on residual stress fields by the finite-element method. The specimen under investigation is a square plate with a thickness of 3 mm made of Ti-6Al-4V. The performed analysis enhances understanding of LSP application to structures manufactured from this material and this information can be useful for a choice of optimal peening parameters. The effect of the spot size and shape, the pulse energy, the number of peen layers, overlapping of spots and temporal variation of the mechanical pressure induced by plasma is considered and analyzed. A 3D finite-element model based on the Johnson-Cook constitutive relation is developed and verified by the results of residual stress measurements performed for the LSP-treated samples under different conditions. From the obtained results the following main conclusions can be drawn: pulse energy provides the more significant effect although the resulting residual stresses profile tends to some saturation curve; temporal pressure pulse shape and its total duration also substantially alter the residual stress field; the least significant parameter is the spot shape.

Ballistic Impact of Structural Steels at Low Temperatures

Abstract Steels are usually stronger at low temperatures than at high temperatures. But low temperatures are, particularly in combination with high strain rates and high stress triaxiality ratios, known to cause embrittlement. The common understanding is that the ductility of steels decreases dramatically below a threshold temperature known as the ductile-to-brittle transition temperature. This study explores the ballistic performance of Strenx 960 Plus steel plates at both low temperatures and room temperature. We describe a ballistic setup where target plates were cooled down to as low as −60 °C before we present results from ballistic impact tests with three different projectile types. The ballistic limit velocities from tests at low temperatures were higher than the ballistic limit velocities from tests at room temperature, indicating that brittle fracture does not take place. An analytical approach based on the Johnson–Cook constitutive relation, the Cockcroft–Latham ductile failure criterion, and a simple brittle fracture criterion is presented. The model suggests that ductile fracture prevails for most realistic material state histories, both in the ballistic impact tests as well as for quasi-static and dynamic tensile tests. This supports previous observations that brittle fracture is unlikely to occur in modern steels even when subjected to rapid loading and low temperatures.

Predictive Computational Model for Damage Behavior of Metal-Matrix Composites Emphasizing the Effect of Particle Size and Volume Fraction.

In this paper, an integrated numerical model is proposed to investigate the effects of particulate size and volume fraction on the deformation, damage, and failure behaviors of particulate-reinforced metal matrix composites (PRMMCs). In the framework of a random microstructure-based finite element modelling, the plastic deformation and ductile cracking of the matrix are, respectively, modelled using Johnson–Cook constitutive relation and Johnson–Cook ductile fracture model. The matrix-particle interface decohesion is simulated by employing the surface-based-cohesive zone method, while the particulate fracture is manipulated by the elastic–brittle cracking model, in which the damage evolution criterion depends on the fracture energy cracking criterion. A 2D nonlinear finite element model was developed using ABAQUS/Explicit commercial program for modelling and analyzing damage mechanisms of silicon carbide reinforced aluminum matrix composites. The predicted results have shown a good agreement with the experimental data in the forms of true stress–strain curves and failure shape. Unlike the existing models, the influence of the volume fraction and size of SiC particles on the deformation, damage mechanism, failure consequences, and stress–strain curve of A359/SiC particulate composites is investigated accounting for the different possible modes of failure simultaneously.

Mechanical Properties of Brass under Impact and Perforation Tests for a Wide Range of Temperatures: Experimental and Numerical Approach.

The originally performed perforation experiments were extended by compression and tensile dynamic tests reported in this work in order to fully characterize the material tested. Then a numerical model was presented to carry out numerical simulations. The tested material was the common brass alloy. The aim of this numerical study was to observe the behavior of the sample material and to define failure modes under dynamic conditions of impact loading in comparison with the experimental findings. The specimens were rectangular plates perforated within a large range of initial impact velocities V0 from 40 to 120 m/s and in different initial temperatures T0. The temperature range for experiments was T0 = 293 K to 533 K, whereas the numerical analysis covered a wider range of temperatures reaching 923 K. The thermoelasto-viscoplastic behavior of brass alloy was described using the Johnson–Cook constitutive relation. The ductile damage initiation criterion was used with plastic equivalent strain. Both experimental and numerical studies allowed to conclude that the ballistic properties of the structure and the ballistic strength of the sheet plates change with the initial temperature. The results in terms of the ballistic curve VR (residual velocity) versus V0 (initial velocity) showed the temperature effect on the residual kinetic energy and thus on the energy absorbed by the plate. Concerning the failure pattern, the number of petals N was varied depending on the initial impact velocity V0 and initial temperature T0. Preliminary results with regard to temperature increase were recorded. They were obtained using an infrared high-speed camera and were subsequently compared with numerical results.

Modeling and Simulation of Void Closure during Steckel Mill Rolling for Steel Plate

Internal void defects as shrinkage porosity, gas bubble, and thermo‐mechanical cracks are usually formed during steel casting processes. These defects have critical impact on the quality and service life of hot‐rolled products. Study of the possibility of self‐healing of existing internal defects during hot‐rolling process has been of interest to industry and researchers. Prediction of void closure is extremely useful in relation to better product design and manufacturing process optimization. Herein, a 3D finite element model of the slab hot‐rolling process is developed to simulate and analyze the healing of internal voids in hot‐rolled steel plate. The material model for the steel plate is developed based on Johnson–Cook constitutive relation to accurately represent its viscoplastic behavior at high temperatures as well as account for strain rate sensitivity. The study evaluates the thermal and mechanical response of low‐carbon steel slabs having pre‐existing voids during multi‐pass strands reverse hot‐rolling process. Through thickness plastic strains within the slab are found to influence void closure. Results show that variation in void size and locations also affect the healing possibilities. Finally, the effect of thermal history and thermo‐mechanical stresses on void closure is studied.

A random microstructure-based model to study the effect of the shape of reinforcement particles on the damage of elastoplastic particulate metal matrix composites

The mechanical properties of materials are greatly affected by the occurrence of the first damage during the loading process. This study presents a comprehensive investigation of the effect of particulate shape and combination of two shapes or more, as a design parameter, on the damage mechanism of particulate-reinforced metal matrix composites (PRMMCs). In the context of a random microstructure-based finite element modelling, the proposed model accounts for all possible failure modes; plastic deformation and ductile cracking of the matrix, matrix-particle interface decohesion, and brittle fracture of the reinforcement particles. The matrix plastic deformation and cracking are, respectively, modeled via Johnson-Cook constitutive relation and Johnson-Cook ductile fracture model. The cohesive zone method is adopted to simulate the particle-matrix interfacial debonding. The particle fracture is simulated using an elastic-brittle cracking model, in which the damage evolution criterion depends on the crack opening energy. An extensive parametric study is carried out to explore the effect of different shapes of SiC particles; circular, hexagons, squares, triangles, and their combinations, on the damage mechanism and consequences of failure of A359/SiC particulate composites.

Finite element simulation and experimental research on microcutting mechanism of single crystal silicon

Microcutting technology, which has been proven to be an indispensable means for investigating the material removal mechanism, is able to realize the high efficiency processing of brittle materials with an ultrasmooth surface and a low-damage subsurface. In this study, a series of simulations were performed by finite element (FE) method to investigate the microcutting mechanism of the typical semiconductor material, single crystal silicon. The FE cutting models were established in terms of the Johnson–Cook constitutive relation. First, the material removal behavior during the microcutting process was studied. The results indicated that the chip formation was dominated by extrusion rather than shearing action, and both sides of the chips were smooth without any wrinkle or shear band. Then, the cutting force and cutting heat during the microcutting process were analyzed in deep. It was determined that when the cutting characteristic size reduced to less than the tool edge radius, much energy was needed to remove the materials per unit volume. Besides, microcutting experiments were conducted using a specially designed cutting platform in a scanning electron microscope, and the experimental results were observed to be in agreement with the FE simulation results.

Effect of Lode angle in predicting the ballistic resistance of Weldox 700 E steel plates struck by blunt projectiles

The necessity of incorporating the Lode angle into a fracture criterion in predicting ballistic resistance of ductile metal plates has not been well elucidated so far although the ductility of a metal may be Lode dependent. In this paper, 4.0 mm thick Weldox 700 E steel plates were fired by 5.95 mm diameter blunt rigid projectiles in a one-stage gas gun in the impact velocity range of 141.2 m/s∼275.7 m/s. A failure mode of shear plugging was observed in the test and the ballistic limit was obtained by fitting the initial-residual velocity data. An axisymmetric finite element (FE) model corresponding to the test was built in ABAQUS and then was utilized to predict the ballistic resistance and fracture behavior of the targets. In the FE model, a slightly modified Johnson-Cook constitutive relation was companied by either a Lode independent modified Johnson-Cook (MJC) or the Lode dependent modified Mohr–Coulomb (MMC) fracture criterion. The plasticity and fracture of the metal were fully calibrated by a series of mechanical tests under varying stress states, strain rates and temperatures. According to the tests and parallel FE simulations, it was found that the fracture of Weldox 700 E is obviously Lode dependent. However, ballistic simulations using the MMC and MJC fracture criterion predicted very close ballistic limit velocity and similar shear plugging failure mode when compared with the test results. The dominant stress state of the material failed in the process of shear plugging was revealed by detailed FE analysis and it was found that the ductility of the metal is quite different on the dominant stress state according to the two fracture criteria. To interpret the current simulation results, further FE simulations were carried out on fictitious metals and it was found that for less ductile metallic plates the MMC fracture criterion predicts a much lower ballistic limit velocity (as much as 22%) when compared with the simulation result from the MJC fracture criterion. In contrast, for metal plates with high ductility, the simulations from the two different fracture criteria would produce quite close ballistic limit velocity predictions.

Application of the modified Mohr–Coulomb fracture criterion in predicting the ballistic resistance of 2024-T351 aluminum alloy plates impacted by blunt projectiles

The majority of current finite element (FE) simulations on shear plugging adopted Lode independent fracture criteria, and the value of utilizing a Lode dependent fracture criterion in predicting the ballistic resistance of metallic plates undergoing shear plugging has not been well understood. A group of 12.65 mm diameter blunt rigid projectiles were fired against 9.94 mm thick 2024-T351 aluminum alloy plates by using a one-stage gas gun in the impact velocity range of 133.4 m/s∼363.8 m/s. A failure mode of Shear plugging was observed in the test and the ballistic limit was obtained by fitting the initial and residual velocity data. A 3D FE model corresponding to the test was built in ABAQUS and then was adopted to predict the ballistic resistance and fracture behavior of the target. In the simulations, a slightly modified Johnson–Cook constitutive relation was companied with either the Lode dependent Modified Mohr–Coulomb (MMC) fracture criterion or the Lode independent original Johnson-Cook fracture criterion. It was found that the FE model using the MMC fracture criterion predict the ballistic limit and shear plugging behavior in good accordance with that obtained in the tests. In contrast, the simulations using the Johnson–Cook fracture criterion over-predicted the ballistic limit by 28.5% although the shear plugging failure pattern was reasonably predicted. Detailed analysis shows that the dominant stress state of the material in the shear plugging band is nearly shear, where the Lode angle has an obvious influence to reduce the fracture strain of the metal comparing with axial symmetric conditions. FE simulations by using fictitious metals with the same fracture data at axial symmetry tension but different fracture stain at shear also confirm that the ballistic resistance of a metal plate is much dependent on the effect of the Lode angle on a material's ductility.

Adiabatic shear fracture prediction in high-speed cutting at various negative rake angles and feeds

The critical characteristics of adiabatic shear fracture (ASF) that induce the formation of isolated segment chip in high-speed machining was further investigated. Based on the saturation limit theory, combining with the stress and deformation conditions and the modified Johnson-Cook constitutive relation, the theoretical prediction model of ASF was established. The predicted critical cutting speeds of ASF in high-speed machining of a hardened carbon steel and a stainless steel were verified through the chip morphology observations at various negative rake angles and feeds. The influences of the cutting parameters and thermal–mechanical variables on the occurrence of ASF were discussed. It was concluded that the critical cutting speed of ASF in the hardened carbon steel was higher than that in the stainless steel under a larger feed and a lower negative rake angle. The proposed prediction model of ASF could predict reasonable results in a wide cutting speed range, facilitating the engineering applications in high-speed cutting operations.

Numerical study of fillet welds subjected to quasi-static and impact loading

Fillet welding is widely used in connections in civil engineering and marine structures. Thus, understanding the behavior of fillet welds under various types of loading is important, and numerical simulations can provide increased insight into this topic. This paper concerns finite element simulations of previous quasi-static and dynamic (impact) tests on fillet welds. The test specimens employed were structural steel components joined by either longitudinally or transversely oriented fillet welds. In the simulations, the material of the fillet welds was modeled using a shear-modified Gurson model, which accounts for material softening in both low and high stress triaxiality regimes. Additionally, strain rate and temperature dependencies were incorporated in the material model with a modified Johnson–Cook constitutive relation for the matrix material. Several types of material tests were conducted to identify the parameters entering the material model. For the quasi-static component tests and simulations, a good agreement was observed in terms of both force–deformation curves and failure mechanisms. The simulations of the dynamic tests predicted appreciably higher force levels and weld deformations at failure than those obtained in the corresponding experiments. A parameter study showed that these discrepancies may partly be due to inaccurate values used for the material parameters related to strain-rate hardening and thermal softening. Finally, a comparison was made between simulations with the shear-modified Gurson model and a simpler material model that does not account for void-induced softening. The simpler model employed the Cockcroft–Latham failure criterion, uncoupled from the constitutive relations. This model was unable to capture the response of the fillet welds to the same extent as the shear-modified Gurson model.

Investigation on high-velocity impact performance of multi-layered alumina ceramic armors with polymeric interlayers

In this study, ballistic behavior of multi-layered ceramic armors under high velocity impact is studied numerically. The model consists of 2D-axisymmetric Lagrangian approach with Johnson–Holmquist constitutive model for alumina ceramic tiles, Mie–Gruneisen equation of state for polymeric interlayers, and Johnson–Cook constitutive relation for Armor Piercing (AP) projectile. The finite element results obtained from various armor layups show the potentiality of multi-layered ceramic armor in extending conoid fracture through the ceramic layers, thus leading to the increase in the armor performance. It is illustrated that besides ceramic armor layup, interlayers of ceramic tiles have a significant role in increasing the armor performance. Finally, the effect of different polymeric interlayers on ballistic performance of multi-layered ceramic armors against AP projectile is investigated. In order to measure the ballistic performance of the armors, various criteria are introduced. Depth of penetration of the projectile in the armor, residual velocity of the projectile, time duration in which the projectile is engaged inside the armor, projectile tip erosion during impact, and interaction volume ratio are some of these criteria. The study indicates that armor layup with thin front ceramic tiles backed by thicker tiles shows better conoid fracture extension and often better ballistic performance. Furthermore, among the polymeric interlayers used between the ceramic tiles, polystyrene causes the best and nylon causes the worst ballistic performance in the armor.

Development of an experimental set-up for dynamic force measurements during impact and perforation, coupling to numerical simulations

Quasi-static tension and dynamic compression experiments on S235JR mild steel were performed using a screw-driven machine and a split Hopkinson pressure bar (SHPB) device. A wide range of strain rates from 10−4 to 2500 s−1 has been covered during experiments. The Johnson–Cook constitutive relation was adopted to describe the material visco-plastic behaviour. Ballistic impact experiments on S235JR plates with conical-nose shaped projectile were carried out using pneumatic gas gun having different impact velocities varying from 49 to 181 m/s. A new experimental set-up allowing resistance force measurement during impact and perforation was developed. Different impact velocities and thicknesses were evaluated during ballistic experiments. All the projectiles are 12.8 mm in diameter and 28g in weight. The ballistic impact device is equipped with laser sensors for velocities measurements and piezoelectric sensors for dynamic force measurement. Based on numerical and experimental investigations, the ballistic properties and failure modes of the material have been studied. The finite element code ABAQUS/Explicit was used to simulate the perforation process but also to have a better understanding of the measurement. A good agreement between experiments and numerical results has been observed in terms of ballistic curves, failure patterns, resistance force as well as the energy balance.

An Experimental Determination of Johnson Cook Material and Failure Model Constants for Armour Steel

An experimental programme for determination of the Johnson Cook material and failure model constants for a typical armour steel material is reported. Tensile tests on specimens made from the armour material have been conducted at quasi-static and dynamic strain rates and at ambient and elevated temperatures. The analysis of the experimental data generates the model constants that are required as inputs during numerical simulation of dynamic events like armour impact using Johnson Cook constitutive relation and failure model implemented in most of the commercially available Finite Element codes.

Ballistic Resistance of AA5083-H116 Aluminum Plates against Conical-Nose Steel Projectiles Impact

This paper evaluates the ballistic resistance of AA5083-H116 aluminum plates against conical-nose steel projectiles impact using Arbitrary Lagrange-Euler (ALE) finite element methods. The target material was modeled with the Johnson-Cook constitutive relation using 2D axisymmetric elements with ALE rezoning. Impact vs. residual velocity curves were constructed and the ballistic limit velocity was determined. It is found that the ballistic limits increase almost linearly with increasing plate thicknesses. The numerical results have been compared to available experimental results, and good agreement was in general obtained. The study shows that the ALE formulation works well for large deformation in ballistic penetration.

Numerical Simulations of the Perforation in Metal Plates with Different Conical-Nosed Projectiles

Numerical simulations with ABAQUS/Explicit into which Johnson-Cook constitutive relation is incorporated, are performed to study the perforation of Weldox 460E steel plates struck normally by conical-nosed projectiles with different cone angles. Different failure modes and perforation process are obtained. Numerical results are found to be in good agreement with available test data. It is revealed that with increasing cone angle, the failure modes of metal plates become to shear plugging from ductile hole enlargement, and the ballistic limits decrease with that. The conclusions are helpful for the design of protective structures.

Validation of Johnson-Cook plasticity and damage model using impact experiment

The validity of the Johnson–Cook constitutive relation and failure criterion at high strain rates, up to ∼106 s−1, was assessed by predicting the dynamic response of Ti–6Al–4V under high-speed ball impact at various velocities and angles. White-light scanning was performed to characterize impact craters formed on target surfaces. The measured crater was compared with that predicted by the corresponding finite element model developed using the finite element code Abaqus/Explicit. The target material behavior was modeled by the Johnson–Cook material model that induced both plastic deformation and damage mechanism. Good agreement was obtained between the experimental measurements and numerical predictions for all testing conditions.

Transient pressure loading of clamped metallic plates with pre-formed holes

The combined effect of blast and impact loading against protective structures is still not fully understood. In this paper, the motivation is to investigate the combined effect of pressure and fragment loading on steel plates. To simplify the approach, it is assumed that the fragments strike and perforate the flexible target before the pressure load arrives. These perforations are idealized as pre-formed holes of generalized shapes in thin, ductile Docol 600DL steel plates, which are then subjected to controlled pressure pulses in the laboratory. The tests were carried out in a Pulse Pressure Loading Rig, and two different pressure levels were applied for each plate design. After the tests, the deflections caused by the pressure pulses were measured. Even though the plates were much deformed in some of the tests, no sign of failure was observed. Based on a number of material tests, the parameters in the modified Johnson–Cook constitutive relation were identified. Several sets of non-linear finite element simulations of the pressure loading process were then conducted. The agreement between standard Lagrangian simulations and the experimental results was in general good, but the simulations failed to give an accurate description of the deflection around the pre-formed holes. Fully coupled FSI simulations of the experimental tests were then carried out and these simulations demonstrate significant spatial variation of the pressure load. The FSI simulations also showed that this spatial variation of the pressure load influence the deflection profile, especially in the vicinity of the holes.