Experimental and numerical study on the flight and penetration properties of explosively-formed projectile

The whole process of formation, flying and penetration of explosively-formed projectile (EFP) is simulated by a 3D coupled hydrocode of Ls_dyna. The caliber of the shaped charge is 60 mm and EFP is a kind of overturned shaped charge. The Arbitrary Lagrangian–Eulerian (ALE) method is adopted to consider the fluid–solid coupling problem. The velocity attenuation equation is fitted to forecast the flight distance of EFP. The penetration property of EFP to the armor plate is studied by similarity theory and numerical simulation. For validating the equation, a test is designed to study the residual velocity after penetrating a 25 mm thick steel plate from a distance of 48 m. Therefore, some important solutions are obtained from the comparison of the simulation and experiment. The solutions are optimized charge structure of EFP, the ideal shape of projectile, the attenuation rule of flight process and the penetration property after 48 m flight. The numerical solution fits the experimental data well and the study results provide important reference to the design of EFP in engineering.     

SPH with the multiple boundary tangent method

In this article, we present an improved solid boundary treatment formulation for the smoothed particle hydrodynamics (SPH) method. Benchmark simulations using previously reported boundary treatments can suffer from particle penetration and may produce results that numerically blow up near solid boundaries. As well, current SPH boundary approaches do not properly treat curved boundaries in complicated flow domains. These drawbacks have been remedied in a new boundary treatment method presented in this article, called the multiple boundary tangent (MBT) approach. In this article we present two important benchmark problems to validate the developed algorithm and show that the multiple boundary tangent treatment produces results that agree with known numerical and experimental solutions. The two benchmark problems chosen are the lid‐driven cavity problem, and flow over a cylinder. The SPH solutions using the MBT approach and the results from literature are in very good agreement. These solutions involved solid boundaries, but the approach presented herein should be extendable to time‐evolving, free‐surface boundaries. Copyright © 2008 John Wiley & Sons, Ltd.     

流固耦合问题的PD-SPH建模与分析

针对涉及结构变形破坏的流固耦合(Fluid-structure interaction, FSI)问题,提出一种基于虚粒子和排斥力的近场动力学(Peridynamics, PD)-光滑粒子动力学(Smoothed particle hydrodynamics, SPH)耦合方法。结合PD方法求解不连续问题以及SPH方法在流体模拟方面的优势,分别采用PD方法与SPH方法求解固体域和流体域,并通过流体粒子-虚粒子接触算法处理流-固界面,既能利用粒子间排斥力有效防止粒子穿透现象发生,又能利用虚粒子修正流体粒子的边界缺陷,提高计算精度。采用PD-SPH耦合方法模拟静水压力作用下的铝板变形问题以及溃坝水流冲击弹性板问题,所得结果与解析解或其它数值结果吻合良好,验证了耦合方法的可行性和有效性。进一步应用耦合方法模拟了流体作用下的结构变形、破坏以及破坏后部分结构运动全过程,验证了PD-SPH耦合方法在流固耦合-结构破坏问题模拟方面的适用性。     

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.     

A 3D Lagrangian gradient smoothing method framework with an adaptable gradient smoothing domain-constructing algorithm for simulating large deformation free surface flows

A novel smoothing particle hydrodynamics (SPH)-like Lagrangian meshfree method, named as Lagrangian gradient smoothing method (L-GSM), has been proposed to avoid the “tensile instability” issue in SPH simulation by replacing the SPH particle-summation gradient approximation technique with a local grid-based GSM gradient smoothing operator. The L-GSM model has been proven effective and efficient when applied to a wide range of large deformation problems for fluids and flowing solids in two-dimensional case. In this study, a three-dimensional (3D) L-GSM numerical framework is proposed for simulating large deformation problems with the existence of free surfaces through developing a widely adaptable 3D gradient smoothing domain (GSD) constructing algorithm. It includes three key novel ingredients: (i) the localized GSD based on an efficient distance-oriented particle-searching algorithm enabling both easy implementation and efficient computation; (ii) a novel algorithm for constructing 3D GSD to guarantee the effectiveness of the 3D GSM gradient operator adaptable to any extreme cases; (iii) a robust normalized 3D GSM gradient operator formulation that can restore the accuracy of gradient approximation even on boundary interface. The effectiveness of the proposed 3D GSD-constructing algorithm is first verified under various distribution conditions of particles. The accuracy of the proposed adaptable 3D GSM gradient algorithm is then examined through conducting a series of numerical experiments with different spacing ratios. Finally, the 3D L-GSM numerical framework is applied to solve a practical problem of free surface flows with large deformation: collapse of a soil column. The results reveal that the present adaptable 3D L-GSM numerical framework can effectively handle the large deformation problems, like flowing solids, with a constantly changing arbitrary free surface profile.     

Relation between shear banding and penetration characteristics of conventional tungsten alloys

The dynamic compression failure and ballistic penetration characteristics of conventional tungsten alloys similar in strength were investigated. Dynamic compression failure properties were generated with a symmetric Taylor test technique and penetration characteristics were obtained with 44 mm kinetic penetrators against an 300 HB hardness steel target at 1400 m/s. From shear crack length data generated with Taylor specimens impacted at different impact speeds a critical speed characterizing shear band initiation was deduced. The critical equivalent plastic strain at shear band initiation sites, obtained from the numerical simulation of the Taylor test at the critical impact speed, was found to decrease with the increase of the penetration performance. These results reinforce the argument that shear band formation is a failure mechanism associated with the erosion process for conventional tungsten alloys.     

A transient finite element simulation of the temperature and bead profiles of T-joint laser welds

Laser welding is a high power density welding technology, which has the capability of focusing the beam power to a very small spot diameter. Its characteristics such as high precision and low and concentrated heat input, helps in minimizing the micro-structural modifications, residual stresses and distortions on the welded specimens. In this study, finite element method (FEM) is adopted for predicting the bead geometry in laser welding of 1.6 mm thick AISI304 stainless steel sheets. A three-dimensional finite element model is used to analyze the temperature distribution in a T-joint weld produced by the laser welding process. Temperature-dependent thermal properties of AISI304 stainless steel, effect of latent heat of fusion, and the convective and radiative boundary conditions are included in the model. The heat input to the model is assumed to be a 3D conical Gaussian heat source. The finite element code SYSWELD, along with a few FORTRAN subroutines, is employed to obtain the numerical results. The T-joint welds are made using a Nd:YAG laser having a maximum power of 2 kW in the continuous wave mode. The effect of laser beam power, welding speed and beam incident angle on the weld bead geometry (i.e. depth of penetration and bead width) are investigated. Finally, the shapes of the molten pool predicted by the numerical analysis are compared with the results obtained through the experimentation. The comparison shows that they are in good agreement.     

Ultra-high g deceleration–time measurement for the penetration into steel target

This paper presented an ultra-high g deceleration measurement device for studies of the penetration into steel target. More than 145,000g deceleration value was measured by this device during a penetration experiment where the steel target was 50 mm thick. Both the design of the device and the experiment of penetration into steel target were described in detail. Numerical simulation utilizing ANSYS/LS_DYNA was carried out with the same penetration condition. The numerical simulation analysis results were consistent with the experimental result. However, compared with theoretical analysis result of a previously published penetration model, the experiment one showed some disparities.     

Penetration of a glass-faced transparent elastomeric resin by a lead–antimony-cored bullet

The penetration of the lead antimony-cored 7.62 mm × 51 mm bullet into a glass-faced polyurethane elastomeric polymer resin has been studied. The resulting craters in the resin contained elongated bullet core material that had a significant amount of porosity. A simple linear viscoelastic model was applied to AUTODYN-2D to describe the behaviour of the resin and numerical results of the penetration mechanism and depth-of-penetration appeared to match experimental observations well. Analysis of the high speed photography and a numerical model of this bullet penetrating a viscoelastic polymer showed that during the initial stages of penetration, the projectile is essentially turned inside out. Furthermore, the shape of the cavity was defined by the elastic relaxation of the polymer that led to compression of the core material. A weight analysis of the penetrated materials showed that using a thicker tile of glass resulted in better ballistic performance.     

Topology optimization of plane structures using smoothed particle hydrodynamics method

This paper presents an alternative topology optimization method based on an efficient meshless smoothed particle hydrodynamics (SPH) algorithm. To currently calculate the objective compliance, the deficiencies in standard SPH method are eliminated by introducing corrective smoothed particle method and total Lagrangian formulation. The compliance is established relative to a designed density variable at each SPH particle which is updated by optimality criteria method. Topology optimization is realized by minimizing the compliance using a modified solid isotropic material with penalization approach. Some numerical examples of plane elastic structure are carried out and the results demonstrate the suitability and effectiveness of the proposed SPH method in the topology optimization problem. Copyright © 2016 John Wiley & Sons, Ltd.     

Semi-Lagrangian reproducing kernel particle method for fragment-impact problems

Fragment-impact problems exhibit excessive material distortion and complex contact conditions that pose considerable challenges in mesh based numerical methods such as the finite element method (FEM). A semi-Lagrangian reproducing kernel particle method (RKPM) is proposed for fragment-impact modeling to alleviate mesh distortion difficulties associated with the Lagrangian FEM and to minimize the convective transport effect in the Eulerian or Arbitrary Lagrangian Eulerian FEM. A stabilized non-conforming nodal integration with boundary correction for the semi-Lagrangian RKPM is also proposed. Under the framework of semi-Lagrangian RKPM, a kernel contact algorithm is introduced to address multi-body contact. Stability analysis shows that temporal stability of the kernel contact algorithm is related to the velocity gradient between two contacting bodies. The performance of the proposed methods is examined by numerical simulation of penetration processes.     

Hybrid particle methods in frictionless impact‐contact problems

The dual particle dynamic (DPD) methods which employ two sets of particles have been demonstrated to have better accuracy and stability than the co‐locational particle methods, such as the smooth particle hydrodynamics (SPH). The hybrid particle method (HPM) is an extension of the DPD method. Besides the advantages of the DPD method, the HPM possesses features which better facilitate the simulation of large deformations. This paper presents the continued development of the HPM for the numerical solution of two‐dimensional frictionless contact problems. The interface contact force algorithm which employs a modified kinematic constraints method is used to determine the contact tractions. In this method, both the impenetrability condition and the traction condition are simultaneously enforced. In the original kinematic constraints method, only the former condition is satisfied. A new formulation to find stress derivatives at stress‐free corners by imposing stress‐free boundary conditions is also developed. The results for 1‐D and 2‐D contact problems indicate good accuracy for the contact formulation as well as the corner treatment when compared to analytical solutions and explicit finite element results using the commercial code LS‐DYNA. Copyright © 2004 John Wiley & Sons, Ltd.     

Neutron diffraction measurements of residual stresses in a 50 mm thick weld

Residual stresses were determined through the thickness of a 50 mm thick ferrite steel weld plate using neutron diffraction. Whereas the limiting penetration depth for iron-based alloys is about 25 mm in the most typical neutron diffractometers, we significantly enhanced the penetration depth up to 50 mm with 2 mm spatial resolution by using the neutron wavelength of 2.39 Å. The selected wavelength minimizes the total neutron cross-section and beam attenuation, thereby, maximizes the neutron fluxes at depth. Two-dimensional mapping of the residual stresses shows that significant amounts of the tensile longitudinal stresses (over 90% of yield strength) were developed along the heat-affected zone of the weld.     

A Lagrangian gradient smoothing method for solid‐flow problems using simplicial mesh

A novel Lagrangian gradient smoothing method (L‐GSM) is developed to solve “solid‐flow” (flow media with material strength) problems governed by Lagrangian form of Navier‐Stokes equations. It is a particle‐like method, similar to the smoothed particle hydrodynamics (SPH) method but without the so‐called tensile instability that exists in the SPH since its birth. The L‐GSM uses gradient smoothing technique to approximate the gradient of the field variables, based on the standard GSM that was found working well with Euler grids for general fluids. The Delaunay triangulation algorithm is adopted to update the connectivity of the particles, so that supporting neighboring particles can be determined for accurate gradient approximations. Special techniques are also devised for treatments of 3 types of boundaries: no‐slip solid boundary, free‐surface boundary, and periodical boundary. An advanced GSM operation for better consistency condition is then developed. Tensile stability condition of L‐GSM is investigated through the von Neumann stability analysis as well as numerical tests. The proposed L‐GSM is validated by using benchmarking examples of incompressible flows, including the Couette flow, Poiseuille flow, and 2D shear‐driven cavity. It is then applied to solve a practical problem of solid flows: the natural failure process of soil and the resultant soil flows. The numerical results are compared with theoretical solutions, experimental data, and other numerical results by SPH and FDM to evaluate further L‐GSM performance. It shows that the L‐GSM scheme can give a very accurate result for all these examples. Both the theoretical analysis and the numerical testing results demonstrate that the proposed L‐GSM approach restores first‐order accuracy unconditionally and does not suffer from the tensile instability. It is also shown that the L‐GSM is much more computational efficient compared with SPH, especially when a large number of particles are employed in simulation.     

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.     

The inside–outside contact search algorithm for finite element analysis

A new contact search algorithm (Inside–Outside Algorithm) for the sheet forming simulation has been developed and implemented in the dynamic explicit FE code: ‘DYNAMIC’. The inside–outside algorithm is derived based on the feature of the inside–outside status of a nodal ‘mesh normal vector’ in respect to a surface segment for the judgment of the contact of FE nodes with the tool surface. This new algorithm includes local search, local track and penetration calculation processes. Almost no additional CPU time is required for the local search process, because the calculations for both global and local search are combined. Moreover, the problems of conventional contact searching algorithms, such as iterations for local search and the deadzone problem, are resolved. Therefore, the quick, robust contact searching and accurate evaluation of penetration have been achieved. The numerical results show that the new contact searching algorithm is more cost effective and robust than conventional ones. © 1997 John Wiley & Sons, Ltd.     

The application of the formability utilization indicator for finite element modeling the ductile fracture during the material blanking process

The purpose of researches presented in the paper was to achieve the numerical model of material blanking process for engineering purposes. The beginning and course of the ductile fracture phase has been modeled using so called “formability utilization indicator”. For this reason, the specialized subroutine for MSC MARC/Mentat software has been developed and implemented to calculate the formability utilization indicator, which functions also as a ductile fracture criterion. The original experimental and numerical methodology to determine the formability limit function has been developed. This methodology enables determining the function course based on the tension test and shearing of the original plane specimen with notch. FEM simulation for blanking has been performed for specimens made of sheet steel S355JR (thickness 3.5 mm) for clearance Lj = 0.5 mm and 0.05 mm. The fracture progress has been modeled by step-by-step deleting the segments, where the formability utilization indicator’s critical value has been exceeded. The results of modeling have been compared with experimental results, in particular attention to the cross-cut section shape.     

Modeling of resistance spot welding of multiple stacks of steel sheets

Weld quality is a major challenge for resistance spot welding of multiple stacks of steel sheets. Because of the differences in mechanical and physical properties of steel sheets and the sheet gage variation, the contact state between sheets and welding current flow throughout the stack joint is complicated. As a result, discrepant weld sizes at the faying interfaces become an issue. In this study, a coupled thermal–mechanical/thermal–electrical incremental model has been developed to reasonably predict the weld nugget formation process of resistance spot welding of a sheet stack made of 0.6 mm thick galvanized SAE1004+1.8 mm thick galvanized SAE1004+1.4 mm thick galvanized dual-phase (DP600) steel using published thermal, electrical, and mechanical properties. It was found that the weld nugget on the faying interface of DP600 forms earlier than that on the other interface, which agrees well with the experimental results. Based on the coupled model, the effects of the sheet gage combination and steel grade combination were examined. The results show that, for a multiple stacks of steel sheets SAE1004 + SAE1004 + DP600, the critical ratio of sheet thickness between the top and bottom sheets is approximately 1:3. The model could provide an important guidance in the selection of the welding variables, sheet gage and steel grade to meet the weld quality of steel component.