Desarrollo del derecho de autor en el tiempo

P. R. Hampson and M. Moatamedi

∗∗∗∗

Stress Analysis Research Group, Institute for Materials Research, University of Salford

Abstract

Numerical validation exercises for low velocity impacts of metal and composite targets has been conducted using examples taken from published literature to determine if the numerical techniques used in the FE software ANSYS/LS-DYNA accurately represents the transient dynamic response of projectile impacts. An instrumented low velocity impact rig has also been constructed to acquire experimental data for comparison with numerical results. Results for both the numerical and experimental work are presented here and are shown to be in good agreement.

Introduction

In this present time composites are still treated with caution because even though we can gain an understanding for their potential, there are still many unknowns with regards to their behaviour; especially after they have been subjected to damage. Take for example the aerospace industry, the knowledge of metallic structures is well documented and experience with these materials has allowed us to predict with great accuracy the behaviour of aircraft structures. Composites are now, however, starting to replace components that were once traditionally constructed from metals; for these new materials and construction methods, the engineer doesn’t have the same extensive historic knowledge base and therefore components are generally over-engineered. Even in this cautionary state the composites offer great advantages, but as time progresses and knowledge increases (in manufacturing, repair, and application), these components can then be optimised to take the greatest advantage of the material properties that composites have to offer.

Since composites have superior strength to weight ratios they are now being widely used in aerospace primary and secondary structures [1] but, as with all engineering materials it is important to fully understand their properties and behaviour before the designer can confidently incorporate them into structures.

An important consideration when designing composite structures is their susceptibility to damage caused by impact loading. Even under low-velocity impact conditions, composites are vulnerable to internal damage caused by transverse loads. Unlike metallic structures, material damage for composites can be hidden within the material and show no form of external damage. In some cases, barely visible impact damage (BVID) may occur which, even if detected by visual inspection, will give no real indication to the severity of the internal material structural degradation.

Since many composites are being used in high-performance applications, it is an important consideration that the formation of damage under impact conditions is understood. Through an understanding of the different damage mechanisms experienced by composite materials, improvements in the damage-resistance characteristics of the composites can be made.

∗

Numerical Modelling

Numerical modelling is carried out using finite element (FE) software for solving a wide variety of mechanical problems. These problems include disciplines such as; static or dynamic structural analysis for both linear (implicit) and non-linear (explicit) problems, thermal and fluid flow, electromagnetics and acoustics.

Composites present greater numerical modelling challenges than those of an isotropic material such as iron or steel, since care needs to be taken when defining the properties and orientations of the various layers that make up the composite because each layer may have different orthotropic material properties. For composites to be used effectively it is important that accurate and reliable predictive techniques can be used to determine information on their failure modes and characterise their fracture behaviour.

In FE software, failure criteria are applied to a model and used to assess the possibility of failure for a particular material. This allows the consideration of orthotropic materials, which might be much weaker in one direction than another. Several criteria originate from those used mainly for the failure of metals, but some have been developed which are specific to composites.

For the numerical work conducted in this study, the finite element software ANSYS/LS- DYNA has been employed. This software provides ANSYS with an interface to the LS- DYNA explicit dynamics program which is suited for the solution of short duration dynamic problems.

The problem is first modelled using the ANSYS PREP7 pre-processor, and then solved explicitly using LS-DYNA. Once a solution has been obtained, the results are then viewed using LS-PrePost.

Numerical Validation Studies

To verify the accuracy of the ANSYS/LS-DYNA software for low velocity contact analysis, a classical impact problem of a metal impactor/metal target, originally solved by Karas [2] was investigated and compared to previously published works presented by Wu and Chang [3] and Chun and Lam [4]. The problem is described as an isotropic steel plate (200 x 200 x 8 mm) which is impacted by a rigid ball of radius 10 mm at its centre at a velocity of 1 m/s. At the very least, the information required to describe an isotropic material in the ANSYS/LS-DYNA software is the Young’s Modulus, Poisson’s ratio and density. The density, ρ, used for the rigid ball impactor is not explicitly stated in any of the published text and only the radius and mass where stated which were given as, 10 mm and 0.0329 kg respectively. Therefore, using the available geometry and mass data provided, the density was calculated as 7854 kg/m3.

The value of 7854 kg/m3 coincided with that of Steel and therefore this assumption was made for the numerical analysis. The plate was modelled with plastic kinematic behaviour and the impactor as a rigid model using the material data shown in table 1.

Plate Impactor

Material Name Steel Steel (Rigid Ball)

Young’s Modulus 200 GPa 200 GPa

Poisson’s Ratio 0.3 0.3

Yield Strength 310x106 Pa [*] -

Tangent Modulus 763x106 Pa [*] -

Density 7854 kg/m3 7854 kg/m3

[*]

ANSYS suggested values

Table 1. Target and Impactor Material Properties

The problem was modelled in ANSYS using solid elements (SOLID 164) for both the plate and the impactor. The plate was assigned fully clamped boundary conditions and the problem solved using the LS-DYNA solver. The transient response of both the plate and impactor was examined.

Once a solution was obtained, the resulting d3plot binary data file was imported into LS- PREPOST and the deflection and velocity data for the points (nodes) shown in figure 1 where extracted.

Figure 1. Points selected for deflection and velocity data

The impactor displacements, ui and plate displacement ut where substituted into the Hertzian

contact law equation [5] to determine the contact force.

In figures 2-4 are comparisons for displacement, velocity and contact force time-histories. It can be seen that the numerical results provided by ANSYS/LS-DYNA are in excellent agreement with previously published literature.

ui, vi

-0.03 -0.025 -0.02 -0.015 -0.01 -0.005 0 0 10 20 30 40 50 60 70 80 90 100 Time (µs) D e fl e c ti o n ( m m ) Karas Wu & Chang Chun & Lam Present Study

Impactor Plate

Figure 2. Comparison of Plate and Impactor Displacement

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 0 10 20 30 40 50 60 70 80 90 100 Time (µs) V e lo c it y ( m /s ) Karas Wu & Chang Chun & Lam Present Study

0 200 400 600 800 1000 1200 1400 1600 1800 0 10 20 30 40 50 60 70 80 90 100 Time (µs) C o n ta c t F o rc e ( N ) Karas Wu & Chang Chun & Lam Present Study

Figure 4. Comparison of Contact Forces

For metal impactor/composite target validation, a paper published by Oguibe and Webb [6] was selected which investigated the response of a fibre-reinforced composite plate subjected to a central impact by a blunt-ended projectile, in which they developed a numerical model which included the effects of transverse shear deformation and a failure algorithm. The numerical work was compared to experimental data and it was found that the results for laminate deformation were shown to compare qualitatively well with experimental tests which utilised a small steel cylinder being fired from a gas gun.

The composite under investigation consisted of three layers of uni-directional fibre-reinforced material, of ply configuration [0,90,0]. Each individual lamina was made from Scotchply 1002 E-glass epoxy which had the following material properties:

E1 = 40.0 GPa E2 = 8.27 GPa

G12 = G13 = 4.13 GPa G23 = 3.03 GPa

ν

12 = 0.26

ρ

= 1901.5 kg/m3

where E is modulus of elasticity, G is the modulus of rigidity and

ρ

is the density of the lamina. 1-Direction is along the fibres, the 2-direction is transverse to the fibres in the surface of the lamina, and the 3-direction is normal to the lamina.

The composite test specimen used was a 140 mm square plate which had a thickness of 4.29 mm. The blunt-ended circular cylinder impactor was made from steel and had a diameter, length and mass of 0.9525 cm, 2.54 cm and 14.175 g, respectively. Initial velocity for the impactor was 22.6 m/s.

For the FE analysis, only one quarter of the impact problem was modelled. The quarter of the cylindrical impactor was modelled using SOLID164 elements and as a rigid body since the stiffness of the steel impactor is much higher than the transverse stiffness of the composite plate. The composite plate was modelled using SHELL163 elements and material behaviour

was assigned a composite damage model. The plate was fully clamped on the edges as reported in the experimental analysis.

Figure 5, shows the composite plate’s central transverse deflection history for Oguibe and Webb’s FE technique with and without failure along with the experimental observations and that determined by the present study.

-3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 0 100 200 300 400 500 600 700 800 900 1000 Time (µs) D e fl e c ti o n ( m m )

Oguibe & Webb - FE (no failure) Oguibe & Webb - FE (failure) Experiment

Present Study

Figure 5. Comparison of experimental and numerical displacement time history for the centre of the composite plate

It can be seen that for the two cases originally solved by Oguibe and Webb, the model which incorporated the failure algorithm agrees more closely with the experimental data. The correlation for present study is also seen to agree closely with that of Oguibe and Webb (with FE failure), and the experimental data.

The impact duration is approximately 700 µs with a maximum experimental central plate deflection of -1.7 mm. The present study does over predict this deflection slightly but this can be explained by the sensitivity for the requirement of having the full material data when modelling composites. For this validation an assumption was made that E3 = 8.27 GPa, and this coupled with Poisson ratio values that would have been calculated by the software can account for the small discrepancy in results. The present study shows a better correlation for the plate deflection as it springs back with the experimental value of +1.4 mm and the present study +1.2 mm; the Oguibe and Webb (with FE failure) although following the experimental data closely for the first 700 µs of the impact, only predicted a deflection of +0.29 mm. A second composite validation study was also conducted. In 1988, Sun and Liou [7] and then later in 1998, Chun and Lam [4] published papers on laminated composite plates when subjected to dynamic impact loading. In order to validate their methodology, each studied the behavioural response for a fully clamped cross ply laminated plate when subjected to central impact.

In this study, the composite under investigation consisted of three layers of uni-directional fibre-reinforced material, of ply configuration [0,90,0]. Each individual lamina was made from graphite-epoxy AS-3501-6 which had the following material properties:

E1 = 142.73 GPa E2 = 13.79 GPa G12 = 4.64 GPa

ν

12 = 0.23

ν

12 = 0.23

ρ

= 1610 kg/m3

T3 = 54 MPa where, T3 is the transverse tensile strength

The composite test specimen used was a 140 mm square plate which had a thickness of 3.81 mm. The blunt-ended circular cylinder impactor was made from steel and had a diameter, length and mass of 0.9525 cm, 2.54 cm and 14.175 g, respectively. Initial velocity for the impactor was 22.6 m/s.

For the FE analysis, only one quarter of the impact problem was modelled. The cylindrical impactor was modelled using SOLID164 elements and as a rigid body. The composite plate was modelled using SHELL163 elements and was fully clamped on the edges as reported in the experimental analysis.

-2 -1.5 -1 -0.5 0 0.5 1 1.5 0 50 100 150 200 250 300 350 400 450 500 Time (µs) D e fl e c ti o n ( m m )

Chun & Lam Sun & Liou Present Study

Figure 6. Comparison of central plate deflection for present study with two other published results

From figure 6, it can be seen that all of the investigations are in close agreement with peak deflection occurring at approximately 190 µs during an impact duration of approximately 370

µs for all results.

Maximum central plate deflection from the two published comparative results are approximately -1.45 mm. A slight over prediction is made in the present study with a value of -1.7 mm, but as before this can be explained by the need for full material data when modelling composites, and for this validation the assumption was made that G = G = 4.14

GPa. Overall, the numerical solution in the present study agreed reasonably well with the published literature.

Low Velocity Experimental Equipment

For the experiment investigation, a low velocity impact rig (figure 7) was built which incorporated an instrumented drop weight which was guided by a tube. The impact rig specifications are shown in table 2.

(a) (b)

Figure 7. (a) Low velocity impact rig, (b) drop weight guided by tube

Maximum drop height 1.8 m Fixed weight impactor 2 kg

Maximum velocity 6 m/s

Maximum energy 35 J

Changeable tip Hemispherical, Flat, Conical (25 mm diameter)

Table 2. Low Velocity Impact Rig Specifications

The impact rig had a choice of three different impactor tups and in order to determine the most suitable for validating the ANSYS/LS-DYNA software, a preliminary investigation was conducted to assess the impact damage caused by the three tups when impacting an aluminium target. As a result of these initial impact tests it was decided that for software validation purposes, it would be suitable to conduct subsequent experimental investigations using only the hemispherical tup.

Before the impactor was instrumented with an accelerometer, some initial calculations were carried out to determine the impact conditions the instrument would need to withstand. Consideration also had to be given to whether a more robust accelerometer would need to be chosen at the expense of reduced sensitivity. Assuming the impactor would fall from the

greatest height allowable by the impact rig it was determined that a general purpose accelerometer with an operating range of ± 500g would be suitable for the low velocity impact rig. An accelerometer (model 3056B1) produced by Dytran Instruments was selected due to its operating range, sensitivity, and frequency response. The ease of connection and compatibility with the existing lab equipment was also an important consideration.

The accelerometer was mounted on the top of the drop-weight impactor using the mounting surface and fittings provided and a data resolution study was conducted to determine the optimum data sampling rate to ensure that peak outputs were captured.

The low velocity experimental rig was set as shown schematically in figure 8.

Figure 8. Schematic Diagram of Instrumented Low Velocity Impact Rig

The computer terminal utilised for the experimental investigation was running on an AMD Athlon processor at 951 MHz with 128 MB RAM and was installed with a DaqBoard 2000 series PCI Data Acquisition card 16-bit, 200 kHz analogue-to-digital converter. This card was used as the main data primary acquisition device for the experiment and provided a data conversion and communications link between the data source and the processor of the host computer. Sensor connection to the data acquisition card was provided via a DBK202 Board which provided screw-terminal signal connections. Data acquisition software was provided through a package called DaqView which provided a graphical user interface for viewing signal channel data.

Metal Impactor/Metal Target Experimental and Numerical Comparison

The metal impactor/metal target experimental investigation was conducted using unalloyed Iotech DaqBoard 2000 PCI Data Acquisition Board Iotech DBK 202 Screw terminal Omega ACC-PS3 Accelerometer Power Supply Impact Rig Test Specimen Dytran Accelerometer 3056B1

impact tup was used from a drop height of 1 m. Three separate drop tests were conducted with data collected at a rate of 40 kHz for a duration of 1.5 seconds which was sufficient to capture the impact event. All three tests resulted in impact responses which were practically identical; these results were then averaged to provide a comparison for the numerical investigation.

For the numerical study only one quarter of the problem was analysed due to symmetry conditions. The target plate was modelled using an elastic-plastic strain hardening material model (Plastic Kinematic) and assigned simply supported boundary conditions. The mild steel drop-weight was modelled as a rigid model and assigned an initial velocity of 4.43 m/s at the point of contact with the aluminium plate. Material properties for the target and drop- weight are shown in table 3.

Target Drop-weight

Material Name Aluminium 1050A Mild Steel

Young’s Modulus 76 GPa 200 GPa

Poisson’s Ratio 0.34 0.3

Yield Strength 0.34475 GPa -

Tangent Modulus 0.6895 GPa -

Hardening Parameter 0.2 -

Density 2720 kg/m3 7854 kg/m3

Failure Strain 0.2 -

Table 3. Metal Impactor/Metal Target Experimental Material Data

From figure 9, it can be seen that there is close agreement between the experimental and numerical impactor acceleration history. Both show a total impact duration of 6.5 ms with a peak acceleration of 1680 m/s2 occurring at 4 ms into the impact.

-500 0 500 1000 1500 2000 0 1 2 3 4 5 6 7 8 Time (ms) A c c e le ra ti o n ( m /s 2) Experimental Numerical

Figure 9: Comparison of Experimental and Numerical Impactor Acceleration (Aluminium Target)

The experimental impact test of the aluminium plates resulted in plastic deformation with an average central plate deflection of 7.9 mm. From figure 10 it can be seen that the numerical result closely predicted this with a value of approximately 8.1 mm.

-14 -12 -10 -8 -6 -4 -2 0 0 1 2 3 4 5 6 7 8 Time (ms) D e fl e c ti o n ( m m ) Numerical Plastic deformation after impact

Figure 10. Central Plate Deflection showing resulting plastic deformation

The comparison between the experimental and numerical investigation shows excellent agreement. Any slight discrepancies can be attributed to the assumption of a negligible frictional loss to the drop-weight as it contacts the guiding tube prior to impact, and hence, a minor reduction in the initial contact velocity. The numerical model also assumes impact at the exact centre of the target plate which experimentally is difficult to achieve with the drop- weight impact rig where usually impact occurs within approximately a 2 cm diameter of the centre.

Metal Impactor/Composite Target Experimental and Numerical Comparison

In document Acceso abierto y derechos de autor : protección y uso (página 95-103)