Composite Structures 75 (2006) 501–513 www.elsevier.com/locate/compstruct
Finite element modelling of impact on preloaded composite panels K.M. Mikkor a, R.S. Thomson b, I. Herszberg a b
b,*
, T. Weller c, A.P. Mouritz
a
School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, GPO Box 2476, Melbourne, Vic. 3001, Australia Cooperative Research Centre for Advanced Composite Structures (CRC-ACS), 506 Lorimer, St. Fishermans Bend, Vic. 3207, Australia c Faculty of Aerospace Engineering, Technion – Israel Institute of Technology, Technion City, Haifa 32000, Israel Available online 12 June 2006
Abstract Composite aircraft structures are susceptible to impact damage during manufacture, maintenance and in-flight. Low energy impact damage is often internal and invisible, but can significantly reduce the stiffness and strength or cause catastrophic failure when the structure is under load during the impact event. This paper describes the development and application of an explicit finite element (FE) model, incorporating a bi-phase material degradation model, to predict the behaviour of loaded carbon/epoxy panels when impacted over a range of low energy levels. Overall, the trends predicted in the FE simulations were consistent with experimental data, although quantitatively the FE results were generally conservative. However, the model greatly underestimated the catastrophic failure boundary. The model was used to investigate the effect of various parameters including magnitude of preload, impact velocity and specimen geometry on the amount of damage and the residual strength of carbon/epoxy panels. 2006 Elsevier Ltd. All rights reserved. Keywords: Impact; Polymer matrix composites; Tensile preload; Finite element modelling; Damage
1. Introduction Fibre–polymer composite materials are competitive with light-weight alloys for use in aerospace structures because of their superior mechanical properties such as high specific stiffness and strength, and their good through-life properties, such as corrosion and fatigue resistance. They are, however, susceptible to impact damage during manufacture, maintenance and in-flight. The damage is often internal and invisible, but can significantly reduce the stiffness, strength and fatigue life of the structure. Catastrophic failure of a structure can occur when it is under load during the impact event. Common examples of this type of impact are bird strike or runway debris thrown against a highlyloaded aircraft structure during take-off or landing. The impact resistance of polymer laminates has been a topic of intensive investigation of many years, which has
*
Corresponding author. Tel.: +61 3 9925 8063; fax: +61 3 9925 8099. E-mail address:
[email protected] (I. Herszberg).
0263-8223/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruct.2006.04.056
been reviewed by Abrate [1] and Reid and Zhou [2]. Most research studies have only considered the impact of unloaded composite structures, and much less is known about the impact performance of composites under load. Early research revealed that catastrophic failure of carbon/epoxy panels supporting tensile or compressive loads occurred when impacted above a specific kinetic energy level [3–8]. This failure did not occur in panels without load, and the kinetic energy at which catastrophic failure occurred decreased when the load acting on the panel was increased. In the early 1980s, Williams et al. [5] and Soderquist [9] identified impact on loaded composite structures as a potential issue in the certification of aircraft. During a NASA workshop on impact damage to aerospace composite materials, held in 1991, it was determined that the effect of preload on impact damage tolerance was an important, but not well understood, issue ([10] quoted in [11]). It is current design practice to consider impact on loaded structures as a design case, and Hachenberg [12] recently presented a number of cases related to impact on loaded fuselage panels to large civil transport. However, very little empirical data has been published on the impact
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response of loaded composite panels [13–19], and a validated model for predicting the impact resistance is not available. Most of the existing knowledge on the impact damage tolerance of loaded composite materials is based on a limited amount of experimental data determined from small-scale impact tests. Explicit FE codes have been used to predict delamination impact damage on unloaded monolithic composite structures [20–23]. The approaches used have included single layer shell elements, stacked shell elements and 3-D analyses. Generally, reasonable agreement with experiment has been achieved, although accurate prediction of delamination area has proven difficult. A reliable model for analysing the amount of damage and the residual mechanical properties of impacted composites under load is required to design impact resistant loaded composite panels. This paper describes the development of a finite element (FE) model, based on the explicit FE code ‘Pam-Crash’, to predict the impact damage tolerance of loaded composite panels The model is designed to predict the extent of damage and the residual tensile and compressive strengths of laminates under static loads. The composite panel was constructed using the bi-phase fabric material model provided in the Pam-Crash software. The FE model was validated using published experimental results for unloaded [24] and loaded [17] carbon/epoxy panels. Parametric studies were performed using the model to determine the effects of the magnitude of preload, impact velocity and modelling parameters on the predicted impact damage tolerance. 2. Finite element modelling The explicit FE software package, Pam-Crash, incorporating the bi-phase progressive failure model for composite materials, was used for modelling impact. Pam-Crash V 2003 produced by Engineering Systems Internationale (ESI) Group was used for the FE analysis. Explicit FE codes are highly suited to modelling dynamic, non-linear, short duration events, such as the impacts that are the subject of this investigation. The bi-phase model defines two separate phases: a unidirectional fibre phase and an isotropic matrix phase [25,26]. The impact damage to the matrix phase can be analysed in terms of deviatoric (shear) matrix damage and volumetric (no shear) matrix damage; however Pam-Crash cannot model delamination that is an important impact damage state for laminates. The loss in stiffness of the fibre and matrix phases is determined by a generalised damage function, which is based upon allowable strains and damage parameters. Because degradation is calculated separately for each phase, the damage in the matrix and fibres can propagate independently. The composite panels were modelled using four-node shell elements. The bi-phase progressive failure model requires separate matrix and fibre properties for stiffness and failure for each ply of the composite material under consideration. In the absence of such data, these properties were obtained by reverse engineering from the tension and
Table 1 Experimental configurations Case A Impact on unloaded plates
Case B Impact on tensile loaded plates
Process Lay-up Fibre vol. fraction Thickness Plate size
Uniweave injectex fabric 90% carbon T300 warp Ciba–Geigy GU230-E01 Ciba composites GY260 epoxy resin HY917 hardener DY070 accelerator RTM 15 layer, ½ð0=90Þ3 =0=90s 62% 3 mm 91.5 · 117 mm
Uniweave injectex fabric 90% carbon T300 warp Ciba–Geigy GU230-E01 Ciba composites GY260 epoxy resin HY917 hardener DY070 accelerator RTM 10 layer, [(0/90)2/0]s 62% 2 mm 90 · 220 mm
Test configuration Preload Impactor
0 kN Steel tup, spherical
Impactor mass Impact velocities Impact energy
12.7 mm diameter 300 g, 650 g 2.5–6.6 m/s 0.3–4.7 J/mm
49–98 kN Steel, spherical projectile 13 mm diameter 8.9 g 20–90 m/s 1–18 J/mm
Test outcomes Visual damage Proj. damage area Residual strength
Visual Visual C-scan C-scan Compression after impact Tensile
Specimens Fibre
Matrix
compression test results on the laminates used to validate the FE model [27]. The lay-up and material properties of the laminates are given in Table 1. The impactor was modelled as a 13 mm diameter ‘‘rigid wall’’. In order to model realistically such phenomena as penetration or catastrophic failure, the element elimination function of Pam-Crash was used to avoid numeric instability. Instability occurs because the bi-phase model reduces the stiffness of the damaged regions until they are almost zero. This in turn leads to unrealistic distortion of the effected elements, causing numeric instability. Element elimination removes elements from the model once particular failure criteria are met. The software [26] allows element elimination to be triggered when a specified value for equivalent shear strain is exceeded or when any one of a number of ultimate strains specified for the material is exceeded. 3. Experimental results Two sets of experimental results, called the ‘‘Unloaded’’ and ‘‘Loaded’’ cases, were used to validate the FE models. A summary of the specimen details, experimental configuration and impact conditions is given in Table 1. Both cases involved impact on carbon/epoxy panels made using the resin transfer moulding (RTM) process. The unloaded case
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involved low velocity impact on a 3 mm thick [0/903/0/90]s T300 carbon/GU230 epoxy panel [24]. The panel in the unloaded condition was impacted with a spherical nose steel tup at incident energies of 0.9 J (0.3 J/mm) to 14.1 J (4.7 J/mm). After impact, the damage was assessed by visual inspection and the projected damage area was determined by through-transmission (C-scan) ultrasonics. The residual compressive strength was then measured using a compression-after-impact test. Further information on the laminate and impact conditions are given in Ref. [24]. The loaded case involved impact of a 3 mm thick [(0/ 90)2/0]s T300 carbon/GU230 epoxy panel loaded in tension [17]. The panel was preloaded at different tensile stress levels and then impacted with a spherical steel projectile at energies between 3 J (1 J/mm) and 57 J (18 J/mm). The damage was assessed by visual inspection and C-scan ultrasonics. The residual tensile strength was then measured using a servo-hydraulic mechanical testing machine. Like the unloaded panel, the impact damage to the loaded panels was determined by visual inspection and C-scan ultrasonics. More information on the laminate, impact conditions and residual tensile measurements are given in Ref. [17].
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4. Finite element analyses 4.1. Impact on unloaded panels 4.1.1. Damage analysis The impact damage to the unloaded [0/903/0/90]s carbon/epoxy panel was predicted using the FE model for different energy levels, and the results compared with experimental damage data from C-scan ultrasonics. As mentioned, the 2-D shell element analysis incorporating the bi-phase model determines three independent damage parameters: shear matrix damage, volumetric matrix damage and fibre damage; but not delamination damage. However, the C-scan image only shows the extent of delamination damage, and does not clearly reveal the other damage parameters. Consequently, it would appear that no comparison is possible between damage measured by Cscan and that predicted by the bi-phase model. However, delamination cracking in impacted laminates is accompanied by transverse matrix cracking which does not extend beyond the delamination region [1]. Transverse matrix cracking is associated with matrix shear damage, and therefore the extent of delamination can be estimated in the FE model by the extent of matrix shear damage.
Fig. 1. Total damage unloaded plotted on the same scale: (a) FE model 14 J impact and (b) C-scan 11 J impact [24].
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Fig. 2. Fibre damage plot on impact surface for 14 J impact – no preload.
The extent of delamination damage indicated by C-scan is dependent on the sensitivity and threshold values set on the equipment. Extensive experience has led to the equipment to be calibrated so that the extent of delamination as measured by C-scan correlates with that observed through microscopic examination of sectioned specimens. Similarly the model predicts large scale damage some of which is of very low intensity and would not be detected experimentally. A threshold value of damage intensity must be defined which represents realistic damage. In the case of damage predicted by the bi-phase model, for low threshold values, the extent of damage is highly sensitive to the threshold value, however, in the range 0.05–0.1 it is relatively insensitive. Unless otherwise indicated, a threshold value of 0.05 was used for all damage types, to represent realistic damage values. The FE model displayed similar trends in terms of damage shape as that observed experimentally. C-scanning of impacted specimens [24] showed that the damage became
increasingly diamond-shaped as the impact energy was increased (see Fig. 1). Fibre rupture was observed to extend in a line through the damage zone in the width-wise direction on the impacted surface. This behaviour was replicated qualitatively by the model, as shown in Figs. 1 and 2. Fig. 3 compares the predicted and measured increase in the damage zone size with impact energy. Because the damage zone has a diamond shape, the extent of damage is defined by the length and width of the zone rather than the total damage area. The model correlates well with experimentally determined damage sizes when the extent of matrix shear damage is used to define the extent of impact damage, however, the correlation with total damage is poor. The majority of this damage was low level matrix volumetric damage. For matrix shear damage comparisons, the agreement with the experimental data is very good at impact energies to about 8 J, but at higher energies the model increasingly over-estimates the amount of damage. This discrepancy probably arises from the inability of the FE model to consider all the energy absorption mechanisms that operate during the impact event. In reality, some of the impact energy is dissipated by damage processes such as fibre bundle splitting, indentation and fibre debonding, which are not considered in the model. These damage processes become increasingly more important with increasing impact energy, and because the model ignores these processes it assumes that a greater percentage of the total impact energy is available for matrix shear damage. As a result, at higher energies the FE model overestimates the extent of impact damage. 4.1.2. Residual strength No experimental data was available for the residual tensile strength of the unloaded composite panel after impact. However, it is expected that the tensile strength will drop with increasing impact energy according to the trend shown schematically in Fig. 4a. This trend is based on experimental measurements of the residual tensile strength
Damage Length/Width (mm)
60 50 40 30 20 FE Total Damage Width FE Shear Damage Width FE Shear Damage Length Experimental Damage Width Experimental Damage Length
10 0 0
5
10
15
Energy (J)
Fig. 3. FE shear matrix damage size compared to experimental C-scan damage size for impact without preload.
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Residual Strength
Residual Compressive Strength (MPa)
350 300 250 200 150 100
FE Model
50
Experimental 0
(a)
Kinetic Energy
5
0
(a)
10
15
Impact Energy (J) 350
Residual Compressive Strength (MPa)
Residual Tensile Strength (Mpa)
250
200
150
100
50
250 200 150 100 FE Model Experimental Experimental
50 0
0 0
(b)
300
5
10
15
Impact Energy (J)
Fig. 4. (a) Typical residual tensile strength curve [1] and (b) FE residual tensile strength curve.
of unloaded composites following impact. The three regions represent different classes of damage: Region I is the lowest energy regime where all the energy is dissipated by elastic processes and no damage or loss in strength occurs; Region II is characterised by the growth of delamination and matrix damage with increasing energy, resulting in a corresponding loss in strength; and Region III is the highest energy regime that involves a complex damage state including delamination, matrix cracking, fibre fracture, indentation and possibly penetration/perforation of the laminate. The FE model is capable of analysing the laminate for the Regions I and II energy regimes but, as mentioned, does not consider many of the damage processes in Region III. The FE model was used to calculate the residual tensile strength of the unloaded panel based on the predicted extent of impact damage and the original strength of the undamaged material. Fig. 4b shows the calculated reduction in the tensile strength with increasing impact energy, and the trend is similar to that depicted in Fig. 4a. The cal-
0
(b)
200
400
600
800
1000
1200
1400
2
Total Damage Area (mm )
Fig. 5. (a) Residual compressive strength vs. impact energy and (b) Residual compressive strength vs. total damage area for impact without preload.
culated residual strength decreases rapidly with increasing impact energy up to 5 J, above which the strength remains low and relatively constant. Fig. 5 shows a comparison of calculated and measured residual compressive strength against impact energy and impact damage area respectively for the unloaded laminate. It may be seen that the prediction of residual compressive strength as a function of total damage area agrees well with experiment up to a damage area of 500 mm2, above which experimental data is not available. However, the FE model predicts that the rate of decline of the compressive strength will lessen above 600 mm2 presumably due to the damage reaching the specimen edges and consequently tending to a constant width. This part of the study has shown that the FE model can predict the amount of impact damage to unloaded composites with good accuracy when matrix shear failure is the dominant damage process, but when higher energy
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Fig. 6. Volumetric matrix damage on impact surface for impact under tensile preload. The preload was in the horizontal direction.
processes become dominant the model overestimates the damage area. On the other hand, for predicting residual compressive strength, the total damage size is the dominant parameter. 4.2. Impact on tensile loaded panels This section applies the FE model to predict the damage tolerance of the [(0/90)20]s carbon/epoxy panel under combined impact and static tensile loading. Studies were performed on the panel at impact speeds up to 90 m/s and applied loads up to 70% of the tensile failure load of the undamaged panel (142 kN). The type and amount of damage was dependent on both the impact speed and preload level. At relatively low impact speeds and/or tensile loads the panel experienced damage upon impact, but survived the event without failing. For velocities and applied loads above a critical value, either penetration or catastrophic failure occurred on impact. These critical velocity/load boundaries were experimentally determined by Herszberg et al. [24]. Finite element analyses were conducted to replicate these conditions. 4.2.1. Damage type An indentation at the point of impact was observed on the panel surface following the experimental tests. The identation was only found on those panels that did not fail catastrophically at high impact speeds and/or loads. Since the FE analysis was performed using 2D shell elements, any through-thickness deformation of the panel (including indentation) could not be modelled. This makes a compar-
ison between the experimental observation of indentation and the FE results difficult. However, volumetric matrix damage calculated using the FE model is related to tensile and compressive matrix cracking, and therefore regions where there is a high concentration of this damage may indicate indentation. Fig. 6 shows FE predictions of the volumetric matrix damage on the impacted surface of the panel for different impact and preload conditions. The mesh size was refined for the low speed/low load conditions to enhance the fidelity of the analysis of the damage zone. Regardless of the impact conditions, it is seen that the damage zone consists of a concentrated region of extensive volumetric damage surrounded by a much larger region of less intense damage. As expected, the size of the damaged region increases with the impact speed and preload. C-scan and visual observations identified four raised lobes surrounding the indentation, which are normally attributed to near-surface delaminations raising the damaged portion of material above the original surface plane. The FE damage plots do not show any shear matrix damage in these regions which might have indicated delamination damage. Furthermore, the volumetric damage on the impacted surface shown in Fig. 6 has an oval shape that is elongated normal to the preload direction, rather than separate ‘lobes’ or regions of damage. However, the FE model predicts the presence of ‘lobe’ shaped regions of damage on the rear surface of the panel, as shown in Fig. 7. Each lobe shaped region of volumetric damage is clearly evident above and below the impact site. It is possible that the raised lobes, observed on the impacted panels, were in fact caused by matrix crushing rather than delam-
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Fig. 7. Volumetric matrix damage plot of rear surface for 88 kN tensile preload. The preload was in the horizontal direction.
ination, with the C-scan recording through-thickness distortions. Fibre damage was evident in experimental tests on the impact surface in the regions of indentations and lobes, while fibre bundle splitting associated with rear-face delamination breakage was visible on the rear surface at a position immediately opposite the impact point. The FE simulations indicated that fibre damage is present on the impact surface at the point of impact. For example, Fig. 8 shows FE images of the impacted panel surface at several speeds and preloads, and the shaded meshes indicate regions of fibre damage. Fibre damage from the experimentation impact tests was also found on the 9th ply immediately above the rear surface ply. In this region fibre damage generally occurred only on fibres in the 90 (transverse to loading) direction. However, as expected, the FE model was unable to predict fibre bundle splitting at or near the rear surface since this is associated with delamination. 4.2.2. Critical velocity boundary Fig. 9 presents plots of impact velocity against preload for the composite panel showing experimental data and
FE predictions. The experimental data, for preloads above 55 kN, are represented by a linear critical velocity boundary above which catastrophic failure occurred. As expected, this boundary intersected the preload axis at the ultimate tensile load of the undamaged panel (145 kN). At a preload of 49 kN, penetration occurred at velocities of 66 m/s which was below the projected catastrophic failure critical velocity boundary. Therefore, the region corresponding to preloads below 49 kN was not experimentally explored. The FE results presented indicate points where the panel was damaged but did not fail catastrophically, points where catastrophic failure occurred on the forward vibration path of the panel and points where it occurred on rebound. Appropriate boundaries are included which separate these points. The FE model predicted the phenomena of penetration and catastrophic failure that occurred in the experiments at high impact speeds, however the predicted critical velocities for catastrophic failure were underestimated by a factor of over three (Fig. 9). Above certain impact velocity/preload combinations, the experimental panels failed catastrophically upon impact. That is, the damage sustained during
Fig. 8. Fibre damage plots on impact surface prior to penetration and catastrophic failure. The preload was in the horizontal direction.
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K.M. Mikkor et al. / Composite Structures 75 (2006) 501–513 Damage Failure on Panel Rebound Failure on Impact Ultimate Strength Behaviour Change Boundary FE Critical Velocity Boundary Experimental Critical Velocity Boundary
80
Impact Velocity (m/s)
70 60 50 40 30 20 10 0 40
50
60
70
80 90 100 110 120 130 140 150 Preload (kN)
Fig. 9. Critical velocity boundary for impact under tensile preload.
impact propagated unstably to the edges of the panel when failure occurred. The FE model was able to predict the
spread of impact damage to the panel edges under high speed, high load conditions, at which point failure is assumed to occur. For example, Fig. 10 shows the initiation and spread of damage in the panel under a relatively high preload (59 kN) condition. The FE model predicted this type of failure mode when the preload was above 55 kN, while at lower loads it is predicted that the impactor will penetrate the panel without causing complete failure (see Fig. 11); the panel retaining the ability to support the preload. The FE results showed an important damage phenomenon which was not apparent from experimental tests. Some of the panels did not fail catastrophically immediately upon impact, but failed immediately after the rebound of the panel. These failures are represented by the circular markers in Fig. 9. For these cases, the applied preload was maintained while the panel was deflected out-of-plane due to the impact. Only at the time of maximum rebound deflection of the centre of the panel did the preload drop to zero and catastrophic failure occurred. The model predicted penetration at velocities above 110 m/s for preloads below about 55 kN. However, the
Fig. 10. Progression of damage causing catastrophic failure for impact with 59 kN tensile preload. The preload was in the horizontal direction.
Fig. 11. Total damage plot of penetration occurring for impact with 49 kN tensile preload. The preload was in the horizontal direction.
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experimental tests revealed that penetration occurred at impact velocities between 60 m/s and 70 m/s. Parametric studies on the FE model, reported in Section 4.3.2 below, indicated that the value of the penetration velocity is highly dependent on the element elimination criterion. 4.2.3. Damage size A conclusion drawn from the experimental testing was that damage size did not depend on the magnitude of the 2000
Experimental ExperimentalTrendline Total Damage>0.05 Total Damage>0.05 Trendline Total Damage>0.1 Total Damage>0.1Trendline
1800
Damage Area (mm2)
1600 1400 1200 1000 800 600 400 200 0 0
10
20
30
40
50
60
70
Impact Velocity (m/s)
Fig. 12. Damage area vs. impact velocity for impact under tensile preload.
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preload, except where the impact velocity approached the critical velocity. The experimental data together with a trendline is included in Fig. 12. This exception was apparent for the 59 kN and 74 kN preloads, where the delamination area increased rapidly as the critical velocity was approached, while at other preloads a different failure mechanism appeared to predominate. FE simulations also showed that the damage area increased with the impact velocity, especially close to the critical velocity. This was the case for all three damage types: shear matrix damage, volumetric damage and fibre damage. At lower preloads the total damage was localised in an area of intense damage surrounding the impact site, often with some elements being eliminated. As the preload increased, the damage area increased with a corresponding reduction in the severity of the damage. At higher preloads the total damage size increased rapidly while approaching the critical velocity to the point where almost the entire panel was subject to some level of damage, as shown in the left side of Fig. 13. However, more severe areas of damage remained relatively constant in size as may be seen from the right hand side of Fig. 13, for which a damage threshold of 10% was applied. FE results for various preloads are plotted in Fig. 12 in comparison with experimental data. Results for damage threshold values of 5% and 10% are ploted. It may be seen from the trendlines that the results are not significantly different. As is the case for impact on unloaded panels, the model overestimates the damage area especially for higher impact velocities.
Fig. 13. Total damage plots threshold >0 and >0.1 for impact under various tensile preloads. The preload was in the horizontal direction.
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4.2.4. Residual tensile strength Experimental data for residual tensile strength were presented by Herszberg et al. [17] and some of these are included in Fig. 14, which presents residual tensile strength as a function of damage area obtained from experimental data and from the FE analysis. The FE simulations predicted that at high preloads (>70 kN) the residual tensile strength will not decrease prior to catastrophic failure, while at lower preloads (0.05 Trendline FE Damage Size>0.1 Trendline
100 0 0
200
400 600 Damage Size (mm2)
800
1000
Fig. 14. Residual tensile strength vs. damage area for impact under tensile preload.
4.3. Sensitivity analysis Sensitivity analyses were conducted to determine the effect of physical and modelling parameters on the critical velocity boundaries, for penetration and catastrophic failure which disagreed with the corresponding experimental results. 4.3.1. Mesh size sensitivity Mesh size sensitivity was examined to determine its effect on the critical velocity boundaries [27]. The mesh sizes used in the analysis ranged from 10 · 10 mm down to 1.5 · 1.5 mm. Analysis of catastrophic failure in model using a fine mesh size (1.5 · 1.5 mm) showed that the panel failed along a single line of elements extending transversely across the panel from the impact point, while all elements adjacent to these suffered little or no damage. This agreed with experimental results, however, the predicted velocities for which such failure occurred were much lower than those observed in the experiment. The mesh size used in the models was investigated to determine if this had a significant effect on the critical velocity boundary. It was found that increasing the mesh size increased the steepness of the critical velocity boundary. It also caused penetration to occur at lower velocities and catastrophic failure to occur at higher velocities. Despite this increased refinement of the mesh size and the expected improvement in computational accuracy, the FE results were lower than the experimental results obtained for all cases except for the unrealistic 10 · 10 mm mesh size. This indicates that mesh size is not the cause of the discrepancy. 4.3.2. Element elimination In order to model realistically such impact phenomena as penetration or catastrophic failure, the element elimination function of Pam-Crash must be used, otherwise, numeric instability results. As mentioned, the instability arises because the bi-phase damage model reduces the stiffness of the regions subject to failure until they are almost zero, which in turn leads to unrealistic distortion of the effected elements. Initial trials for the unloaded panels indicated that using the equivalent shear strain elimination criterion required very high values of this parameter to simulate the extent of damage found in the experimental study, however, the damage shape was not reproduced. This was improved by using the maximum shear strain criterion. Again, high values of the critical values were required. These values (ee = 0.25; ce = 0.7) were initially used in the models for the loaded panels. The critical velocity boundaries for both penetration and catastrophic failure, are presented in Fig. 15. These were calculated from the model using a 3 mm by 3 mm mesh, compared to the 1.5 mm · 1.5 mm mesh used to produce Fig. 9. The lower curve in Fig. 15 represents the critical velocity boundary obtained with a revised element elimination criteria obtained by reducing the elimination strains by an order of magnitude (ee = 0.028; ce = 0.6). This
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rates. However, impact events cause a dynamic load to be applied at a high strain rate to the material. The matrix dominated properties of composite materials often exhibit strain rate sensitivity with increase strain rate, leading to higher failure strains. Including strain rate effects could improve the comparison between simulation and test.
160 Penetration
Impact Velocity (m/s)
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Catastrophic Failure
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5.2. Damage comparison
60 40 20 0 0
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60
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Preload (kN) Original Criteria - Critical Velocity Boundary Modified Criteria - Critical Velocity Boundary Experimental
Fig. 15. Effect of element elimination on critical velocity boundary.
revised boundary is closer to the experimentally determined penetration boundary. Although the use of the revised element elimination criteria had a significant effect on the critical velocity boundary in the region of penetration, it had very little effect at preloads which cause catastrophic failure and it greatly increased the predicted damage area. The limitations on the element elimination procedure, which eliminates elements when one ply exceeds the set threshold, may have a significant effect on the underestimation of the catastrophic failure boundary. 5. Discussion Modelling of impacts under tensile preload simulations displayed similar behaviours and trends to those observed experimentally. However, damage size was generally overestimated and the catastrophic failure boundary was predicted at lower preload-velocity combinations than found in experimental tests. The FE model was found to be reasonably accurate in simulating in-plane static loadings, such as tensile and compressive ultimate strength and residual strength tests. However, FE predictions for transverse dynamic loadings, such as damage size vs. impact velocity, showed a poor correlation with experimental results. Factors which may account for these discrepancies are discussed below. 5.1. Calibration of material properties The bi-phase material properties were calibrated to inplane tensile and compressive coupon tests. During impact, large bending strains are generated. It has been found that the ultimate strength of composite materials can be significantly greater in bending than in-plane. This could be a contribution to the discrepancy between tests and analysis. The experimental tension and compression tests used to calibrate the model were carried out at quasi-static strain
A limitation of the bi-phase model used to conduct the simulations is that while damage can be separated into fibre and matrix phases, the type of damage depicted is not necessarily easily comparable with experimental results. An overall FE damage plot that considers fibre rupture and matrix cracking is not equivalent to a C-scan image of an experimental test specimen which would predominantly show only delaminations. Delamination damage between the plies of the laminate is not accounted for in the models. Since delamination failure absorbs a large amount of energy during impact, the lack of this type of failure mechanism may have a significant effect on the results. The FE model may absorb this energy through a different failure mechanism which may account for the general over prediction of damage size. However, as described in Section 4.1.1 examination of matrix shear damage provides a possible method for predicting the delamination area. 5.3. Failure mechanisms The results of experimental residual strength testing and analysis of damage size suggest that a different failure mechanism is dominant at higher preloads than at lower preloads prior to catastrophic failure. The model predicts for lower preloads that as the impact velocity increases prior to catastrophic failure, the damage size increases and the residual strength of the panel decreases. The damage at these preloads consists of a combination of shear and volumetric matrix damage, as well as some fibre damage and often element elimination. This suggests that at low preloads the damage mechanism and general behaviour of the composite panel may be somewhat similar to that observed in impacts on composite panels not under preload. That is, the energy is likely dissipated through the formation of extensive regions of delamination and indentation, whose size increases with increasing preload. The FE model suggests that at higher preloads low severity matrix cracking (volumetric matrix damage) forms upon impact, possibly a result of the already high in-plane strains and the increased flexural rigidity of the panel due to the applied preload. This damage appears to slightly weaken the structure so that when a significant amount of damage occurs during impact the damage is not arrested (as it is with lower preloads), but continues to extend and causes catastrophic failure.
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5.4. Element elimination The limitations on the element elimination procedure, which eliminates elements when one ply exceeds the set threshold, may have a significant effect on the underestimation of the catastrophic failure boundary. 6. Conclusion Pam-Crash explicit finite element analyses, incorporating the bi-phase degradation model, were conducted to study the effects of solid body impact, at velocities up to 100 m/s, on unloaded and tensile loaded composite panels. Modelling of impact on unloaded panels correlated well with experimental results in terms of damage type and shape. However, the damage size was over-predicted in most cases. The simulation results suggested that the residual strength was a function of the damage size caused by the impact. The FE models displayed similar behaviour to that observed experimentally for impacts under tensile preload. However, damage size was over-estimated and the catastrophic failure boundary was predicted at much lower preload-velocity combinations than found in experimental tests. These discrepancies were likely to be a result of the techniques used in the calibration of the material as well as limitations of the bi-phase material model and the two-dimensional nature of the shell element model in representing delamination damage. The model showed that catastrophic failure of the panel upon impact may occur above a critical impact velocity. This type of failure generally occurred at higher preloads, while at lower preloads the impactor penetrated the panel once a critical impact velocity was exceeded. It was found that the critical velocity decreased with increasing preload. The FE model showed that at lower preloads catastrophic failure was precipitated by an increase in damage size and reduction in residual strength with increasing impact velocity. At higher preloads, increasing the impact velocity did not appear to affect significantly either damage size or residual strength prior to catastrophic failure, although low severity volumetric matrix damage was observed over most of the panel for these preloads. In general, the damage size and residual strength were found to be independent of the preload, except in regions close to the critical velocity. The results indicate that the model could predict the trends in damage and residual strength of composite panels impacted under load, however, a more sophisticated model is required to obtain reliable quantitative predictions. References [1] Abrate S. Impact on composite structures. Cambridge University Press; 1998. [2] Reid SR, Zhou G, editors. Impact behaviour of fibre-reinforced composite materials and structures. Woodhead: CRC Press; 2000. p. 1–32.
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