The effect of target strength on the perforation of steel plates using three different projectile nose shapes

The effect of target strength on the perforation of steel plates is studied. Three structural steels are considered: Weldox 460 E, Weldox 700 E and Weldox 900 E. The effects of strain hardening, strain rate hardening, temperature softening and stress triaxiality on material strength and ductility are determined for these steel alloys by conducting three types of tensile tests: quasi-static tests with smooth and notched specimens, quasi-static tests at elevated temperatures and dynamic tests over a wide range of strain rates. The test data are used to determine material constants for the three different steels in a slightly modified version of the Johnson–Cook constitutive equation and fracture criterion.Using these three steel alloys, perforation tests are carried out on 12 mm-thick plates with blunt-, conical- and ogival-nosed projectiles. A compressed gas gun was used to launch projectiles within the velocity range from 150 to 350 m/s. The initial and residual velocities of the projectile were measured, while the perforation process was captured using a digital high-speed camera system. Based on the test data the ballistic limit velocity was obtained for the three steels for the different nose shapes. The experimental results indicate that for perforation with blunt projectiles the ballistic limit velocity decreases for increasing strength, while the opposite trend is found in tests with conical and ogival projectiles. The tests on Weldox 700 E and Weldox 900 E targets with conical-nosed projectiles resulted in shattering of the projectile nose tip during penetration.Finally, numerical simulations of some of the experimental tests are carried out using the non-linear finite element code LS-DYNA. It is found that the numerical code is able to describe the physical mechanisms in the perforation events with good accuracy. However, the experimental trend of a decrease in ballistic limit with an increase in target strength for blunt projectiles is not obtained with the numerical models used in this study.     

Influence of conical projectile diameter on perpendicular impact of thin steel plate

A numerical study of conical projectiles for perpendicular impact on a thin steel plate is reported. The target material considered, Weldox 460 E steel, is frequently used for this kind of application and several results of experiments are available in the international literature to verify numerical simulations. The Johnson-Cook constitutive relation coupled with the Johnson-Cook failure criterion have been applied to analyse penetration of the target and also the failure process. The analysis has been focussed on the influence of the projectile diameter on the perforation process, assuming the same projectile mass. The aim was to preserve the same initial kinetic energy and identical nose angle. The goal is to estimate the ballistic limit, the residual velocity, the plastic work, and the temperature levels produced during the penetration process. The analysis has shown a linear increase of the ballistic limit with the projectile diameter.     

Strength and ductility of Weldox 460 E steel at high strain rates, elevated temperatures and various stress triaxialities

Strength and ductility data at high strain rates for Weldox 460 E steel was obtained from tensile tests with axisymmetric specimens. The tests were performed in a Split Hopkinson Tension Bar and the initial temperature was varied between 100 and 500 °C. The combined effect of high strain rate, elevated temperature and stress triaxiality on the behaviour was studied by testing both smooth and pre-notched specimens. It was found that the influence of temperature on the stress-strain behaviour differs at high strain rates compared with quasi-static loading conditions. The true fracture strain depends considerably on the stress triaxiality, which is governed by the notch geometry, while the influence of strain rate and temperature is less clear. Numerical simulations with the explicit finite element code LS-DYNA were performed using a model of elasto-viscoplasticity and ductile damage, which is based on the constitutive relation and fracture criterion of Johnson and Cook. The numerical simulations compare reasonably well with the experiments with respect to strength and ductility for both smooth and notched specimens at elevated temperatures.     

Perforation resistance of five different high-strength steel plates subjected to small-arms projectiles

Thin plates of high-strength steel are frequently being used both in civil and military ballistic protection systems. The choice of alloy is then a function of application, ballistic performance, weight and price. In this study the perforation resistance of five different high-strength steels has been determined and compared against each other. The considered alloys are Weldox 500E, Weldox 700E, Hardox 400, Domex Protect 500 and Armox 560T. The yield stress for Armox 560T is about three times the yield stress for Weldox 500E, while the opposite yields for the ductility. To certify the perforation resistance of the various targets, two different ballistic protection classes according to the European norm EN1063 have been considered. These are BR6 (7.62 mm Ball ammunition) and BR7 (7.62 mm AP ammunition), where the impact velocity of the bullet is about 830 m/s in both. Perforation tests have been carried out using adjusted ammunition to determine the ballistic limit of the various steels. In the tests, a target thickness of 6 mm and 6 + 6 = 12 mm was used for protection class BR6 and BR7, respectively. A material test programme was conducted for all steels to calibrate a modified Johnson–Cook constitutive relation and the Cockcroft–Latham fracture criterion, while material data for the bullets mainly were taken from the literature. Finally, results from 2D non-linear FE simulations with detailed models of the bullets are presented and the different findings are compared against each other. As will be shown, good agreement between the FE simulations and experimental data for the AP bullets is in general obtained, while it was difficult to get reliable FE results using the Lagrangian formulation of LS-DYNA for the soft core Ball bullet.     

Quasi-static perforation of thin aluminium plates

This paper presents an experimental and numerical investigation on the quasi-static perforation of aluminium plates. In the tests, square plates were mounted in a circular frame and penetrated by a cylindrical punch. A full factorial design was used to investigate the effects of varying plate thickness, boundary conditions, punch diameter and nose shape. Based on the results obtained, both the main and interaction effects on the maximum force, displacement at fracture and energy absorption until perforation were determined. The perforation process was then computer analysed using the nonlinear finite element code LS-DYNA. Simulations with axisymmetric elements, brick elements and shell elements were conducted. Quasi-static, isothermal versions of the Johnson–Cook constitutive relation and fracture criterion were used to model the material behaviour. Good qualitative agreement was in general found between the experimental results and the numerical simulations. However, some quantitative differences were observed, and the reasons for these are discussed.     

Ballistic penetration of steel plates

This paper presents a research programme in progress where the main objective is to study the behaviour of Weldox 460 E steel plates impacted by blunt-nosed cylindrical projectiles in the lower ordnance velocity regime. A compressed gas gun is used to carry out high-precision tests, and a digital high-speed camera system is used to photograph the penetration process. A coupled constitutive model of viscoplasticity and ductile damage is formulated and implemented into the non-linear finite element code LS-DYNA, and the material constants for the target plate are determined. The proposed model is applied in simulations of the plate penetration problem and the results are compared with test data. Good agreement between the numerical simulations and the experimental results is found for velocities well above the ballistic limit, while the ballistic limit itself is overestimated by approximately 10% in the numerical simulations.     

3D numerical simulations of sharp nosed projectile impact on ductile targets

Three-dimensional FE model is presented for perforation under normal and oblique impact of sharp nosed projectiles on single and layered ductile targets. Numerical simulations have been carried out to study the behavior of Weldox 460 E steel and 1100-H12 aluminum targets impacted by conical and ogive nosed steel projectiles respectively. Weldox 460 E steel targets of 12 mm thickness in single and double layered combination (2 × 6 mm) and 1100-H12 aluminum targets of 1 mm thickness in single and double layered combination (2 × 0.5 mm) impacted at 0°, 15° and 30° obliquity were considered for simulations. The results of monolithic and layered targets were compared for each angle of impact. Monolithic targets were found to have higher ballistic resistance than that of the layered in-contact targets of equivalent thickness. Failure of both the targets occurred through ductile hole enlargement. However, ogive nosed projectile failed 1 mm thick aluminum target through petal formation and conical nosed projectile failed 12 mm thick steel target through a circular or elliptical hole enclosed by a bulge at rear surface. The explicit algorithm of ABAQUS finite element code was used to carry out the numerical simulations. Various parameters which play critical role in numerical simulation such as element size and its aspect ratio have been studied.     

Evaluation of six fracture models in high velocity perforation

A systematic evaluation of six ductile fracture models is performed to identify the most suitable fracture criterion for high velocity perforation problems. Included in the paper are the Wilkins, the Johnson-Cook, the maximum shear stress, the modified Cockcroft-Latham, the constant fracture strain, and the Bao-Wierzbicki fracture models. These six fracture models are implemented into ABAQUS/Explicit by means of a user material subroutine (VUMAT), and applied to model the failure processes of a steel and an aluminum target plate impacted by a projectile. The numerical simulations are examined by comparing with the experimental results published in the open literature. The Wilkins fracture model predicts spallation of the impacted zone of the target plate beneath the projectile. This unrealistic result is due to its power law form of the pressure term. The maximum shear stress fracture criterion fails to capture the shear plugging failure pattern in a wide range of the impact velocity. Material fracture properties cannot be fully characterized with the constant fracture strain and the modified Cockcroft-Latham fracture models. Various tensile tests on round bars do not give a consistent critical damage. The calculated residual velocities of the projectile are sensitive to the magnitude of the fracture parameters. The Johnson-Cook and the Bao-Wierzbicki fracture models formulated in the space of the stress triaxiality and the equivalent plastic strain to fracture are capable of predicting the realistic fracture patterns and at the same time the correct residual velocities. Finally, the limitations of the Johnson-Cook fracture model are discussed.     

Observations on shear plug formation in Weldox 460 E steel plates impacted by blunt-nosed projectiles

Shear plug formation in circular Weldox 460 E steel plates impacted by blunt-nosed cylindrical projectiles with striking velocities between 100 and 500 m/s has been investigated. Target thickness and projectile impact velocity were the primary variables, and for each target thickness the ballistic limit curve of the material was precisely determined. The test at an impact velocity just below the ballistic limit for each target thickness was selected for a microscopic examination of shear localisation and fracture. In these tests, the plug was pushed only partway through the target, and the localised shear zones outlining the fracture were easily recognised both in the optical and scanning electron microscope. Clear evidence of adiabatic shear bands and material damage due to void growth was found in several of the target plates. Analytical models available in the literature were compared with the results from the experimental and microscopic studies. Reasonable agreement was found between calculations and experiments.     

Initiation of adiabatic shear failure in a clamped circular plate struck by a blunt projectile

This paper presents an analytical model for studying the material failure in shear hinges formed during the dynamic plastic response of a circular plate under projectile impact. Analytic solutions for the ballistic perforation performance of a fully clamped circular plate struck by a blunt projectile are obtained. It takes into account both the global response (plate bending) and the localized shear. Based on the estimations of the shear strain and the size of shear hinge, condition for the initiation of an adiabatic shear band is formulated. The effectiveness of the present model is demonstrated by reasonable agreement between the theoretical predictions and the available experimental data for the perforation of Weldox 460E steel plates.     

Numerical modelling of the structural behaviour of thin-walled cast magnesium components using a through-process approach

A through-process methodology for numerical simulations of the structural behaviour of thin-walled cast magnesium components is presented. The methodology consists of casting process simulations using MAGMAsoft, mapping of data from the process simulation onto a FE-mesh (shell elements) and numerical simulations using the explicit FE-code LS-DYNA. In this work, generic High Pressure Die Cast (HPDC) AM60 components have been studied using axial crushing, 3-point bending and 4-point bending tests. The experimental data are applied to obtain a validated methodology for finite element modelling of thin-walled cast components subjected to quasi-static loading. The cast magnesium alloy is modelled using a user-defined material model consisting of an elastic–plastic model based on a modified J2-flow theory and the Cockcroft–Latham fracture criterion. The fracture criterion is coupled with an element erosion algorithm available in LS-DYNA. The constitutive model and fracture criterion are calibrated both with data from material tests and data from the process simulation using MAGMAsoft.     

A thermo-visco-plastic damage model and SPH simulations of plugging failure

ABSTRACT

A thermo-visco-plasticity model, recently developed based on a microinertia driven dynamic flow rule, is exploited to account for damage due to fracture. This is accomplished by adjoining the equations for thermo-visco-plasticity, herein discretized through the smooth particle hydrodynamics (SPH), with a “pseudospring” based discrete damage model. In treating ductile fractures, this coupled material model accounts for the inertia associated with moving microstructural defects and time lags for the dissipative fluxes to attain the steady state. In this approach, while the microinertia-driven flow rule provides a vehicle to evolve plastic strain, pseudosprings are exploited to treat material damage and the resulting reduced force transfer. The current scheme does not necessitate the introduction of a yield or damage surface in evolving the plastic-strain/damage parameters, and thus the numerical implementation avoids a computationally intensive return mapping. We demonstrate the performance of the proposed model through SPH-based numerical simulations and also undertake a validation exercise against experimental observations from gas-gun penetration tests on an 8-mm thick Weldox 460 E steel plate.     

Perforation of AA5083-H116 aluminium plates with conical-nose steel projectiles – Calculations

The use of aluminium alloys in lightweight protective structures is increasing. Even so, the number of experimental and computational investigations that give detailed information on such problems is limited. In an earlier paper by some of the authors, perforation experiments were performed with 15–30 mm thick AA5083-H116 aluminium plates and 20 mm diameter, 98 mm long, HRC 53 conical-nose hardened steel projectiles. In all tests, initial and residual velocities of the projectile were measured and the ballistic limit velocity of each target plate was determined. In the present paper, an analytical perforation model based on the cylindrical cavity-expansion theory has been reformulated and used to calculate the ballistic perforation resistance of the aluminium plates. In addition, non-linear finite element simulations have been carried out. The target material was modeled with the Johnson–Cook constitutive relation using 2D axisymmetric elements with adaptive rezoning. To allow ductile hole growth, a pin-hole was introduced in the target. The analytical and numerical results have been compared to the experimental findings, and good agreement was in general obtained. A parametric study was also carried out to identify the importance of the different terms of the Johnson–Cook constitutive relation on the perforation resistance of the target. The results indicate that thermal softening cannot be neglected, so an alternative procedure for identification of the material constants in the power-law constitutive relation used in the cavity-expansion theory has been proposed.     

Meshfree simulations of thermo-mechanical ductile fracture

In this work, a meshfree method is used to simulate thermo-mechanical ductile fracture under finite deformation. A Galerkin meshfree formulation incorporating the Johnson-Cook damage model is implemented in numerical computations. We are interested in the simulation of thermo-mechanical effects on ductile fracture under large scale yielding. A rate form adiabatic split is proposed in the constitutive update. Meshfree techniques, such as the visibility criterion, are used to modify the particle connectivity based on evolving crack surface morphology. The numerical results have shown that the proposed meshfree algorithm works well, the meshfree crack adaptivity and re-interpolation procedure is versatile in numerical simulations, and it enables us to predict thermo-mechanical effects on ductile fracture.     

Low velocity perforation of AA5083-H116 aluminium plates

This paper presents an experimental and numerical investigation on low velocity perforation (in the velocity range 3.5–15.8 m/s) of AA5083-H116 aluminium plates. In the tests, square plates were mounted in a circular frame and penetrated by a cylindrical blunt-nosed projectile. The perforation process was then computer analysed using the nonlinear finite element code LS-DYNA in order to investigate the effects of anisotropy, dynamic strain aging (causing negative strain rate sensitivity) and thermal softening in low velocity impacts on the present aluminium alloy. Dynamic strain aging has been shown to influence both the predicted force level and fracture, while thermal softening only influences fracture prediction. No significant effect of plastic anisotropy has been observed.     

Normal and oblique impact of small arms bullets on AA6082-T4 aluminium protective plates

Normal and oblique impact on 20 mm thick AA6082-T4 aluminium plates are studied both experimentally and numerically. Two types of small arms bullets were used in the ballistic tests, namely the 7.62 × 63 mm NATO Ball (with a soft lead core) and the 7.62 × 63 mm APM2 (with a hard steel core), fired from a long smooth-bore Mauser rifle. The targets were struck at 0°, 15°, 30°, 45° and 60° obliquity, and the impact velocity was about 830 m/s in all tests. During testing, the initial and residual bullet velocities were measured by various laser-based optical devices, and high-speed video cameras were used to photograph the penetration process. Of special interest is the critical oblique angle at which the penetration process changes from perforation to embedment or ricochet. The results show that the critical oblique angle was less than 60° for both bullet types. A material test programme was also conducted for the AA6082-T4 plate to calibrate a modified Johnson-Cook constitutive relation and the Cockcroft-Latham failure criterion, while material data for the bullets mainly were taken from the literature. 3D non-linear FE simulations with detailed models of the bullets were finally run. Good agreement between the FE simulations and the experimental results for the APM2 bullets was in general obtained, while it was more difficult to get reliable FE results for the soft core Ball bullets.     

基于微观机理的Q460钢材角焊缝搭接接头延性断裂研究

该文基于微观断裂力学的方法,针对Q460钢材角焊缝搭接接头的断裂行为进行了研究。分别通过对接焊缝试件的静力拉伸试验得到了焊缝材料的本构关系,11个开圆弧形平滑槽圆形截面拉伸试件标定了焊缝材料微孔扩张模型VGM和应力修正临界应变模型SMCS的断裂参量η、α,5个正面角焊缝搭接接头拉伸试验获得了焊接接头的荷载-变形曲线并进行了数值模拟。试验结果表明,E55-D2型焊材的角焊缝搭接接头拉伸破坏形式呈延性破坏。断裂参量结果分析表明,焊材的化学成分会导致焊缝金属断裂性能的差异。该文研究成果为焊缝材料建立了准确的数值模型,同时为高强度钢材焊缝的设计和焊接结构的破坏预测提供了一种有效的方法。     

不锈钢母材及其焊缝金属材料单拉本构关系研究

为研究国产双相型S22053和奥氏体S30408不锈钢母材及其焊缝金属材料的单拉本构关系和破坏模式,对4组共12个材性试样进行了单向拉伸试验,并对其破坏截面进行了电镜扫描。基于试验曲线,利用修正的Ramberg-Osgood （R-O）模型对材料本构关系参数进行了拟合,进而对不锈钢母材和焊缝金属的单拉本构关系进行了对比分析。结果表明:不锈钢母材和焊缝金属材料均发生韧性破坏,其本构关系都表现出明显的非线性;焊缝金属材料的屈服强度和极限强度均高于不锈钢母材,而延性低于母材;修正的R-O模型与母材和焊缝金属材料试验曲线吻合良好;在焊缝连接承载力精确分析中,应考虑焊缝金属材料与母材本构关系的差异,分别使用相应的本构关系模型。     

Comparative analysis of perforation models of metallic plates by rigid sharp-nosed projectiles

Based on the mode of ductile hole enlargement, the present paper compares the models of a rigid sharp-nosed projectile perforating the ductile metallic target plate, given by Chen and Li [1] and Forrestal and Warren [2], respectively. It indicates that the formulae of ballistic limit and residual velocity of these two perforation models are consistent in form but with different applicable range, which due to them employing the spherical cavity expansion theory and cylindrical cavity expansion theory, alternately. Further analyses are conducted to discuss the effects of target material and plate thickness on the terminal ballistic performance with referring the experimental results of aluminum alloy and Weldox E steel plates. It is confirmed that the perforation mechanisms may transform with increasing the plate thickness and the strength of target material.     

船板钢焊接接头的断裂失效行为及GTN模型的数值分析

船舶钢结构皆采用焊接方法建造而成,在实际工况及环境载荷作用下,焊接接头的力学性能及其断裂强度,直接影响船舶整体结构的强度和寿命。该文针对常用的船板钢材料(Q345和Q690),首先对母材进行单向拉伸试验,获得其各自的应力-应变曲线,进而评估其断裂性能;基于Gurson-Tvergaard-Needleman (GTN)损伤模型,通过程序代码的调试和一系列的数值模拟分析,提出了母材本构关系的表达函数及最优GTN模型参数,且与实测的应力-应变曲线高度吻合。同时,针对满足焊接规范要求的船板钢对接焊接头,进行了单向拉伸试验获得其应力-应变曲线;考虑焊缝微观缺陷以及焊接残余应力的影响,提出修正GTN损伤模型中的初始空穴体积分数f₀和材料的幂函数塑性强化参数,预测焊接接头的断裂强度,且与试验测量数据吻合一致。