Copyright ⓒ The Korean Society for Aeronautical & Space Sciences Received: March 2, 2017 Revised: May 1, 2017 Accepted: May 8, 2017
236 http://ijass.org pISSN: 2093-274x eISSN: 2093-2480
Paper
Int’l J. of Aeronautical & Space Sci. 18(2), 236–244 (2017) DOI: doi.org/10.5139/IJASS.2017.18.2.236
Numerical Simulation of High Velocity Impact of Circular Composite Laminates
Kyeongsik Woo*
School of Civil Engineering, Chungbuk National University, Cheongju, Chungbuk 28644, Republic of Korea
In-Gul Kim**
Department of Aerospace Engineering, Chungnam National University, Daejeon 34134, Republic of Korea
Jong Heon Kim***
Airframe Technology Directorate, Agency for Defense Development, Daejeon 34060, Republic of Korea
Douglas S. Cairns****
Department of Mechanical and Industrial Engineering, Montana State University, Bozeman, MT 59717, USA
Abstract
In this study, the high-velocity impact penetration behavior of [45/0/-45/90]ns carbon/epoxy composite laminates was studied. The considered configuration includes a spherical steel ball impacting clamped circular laminates with various thicknesses and diameters. First, the impact experiment was performed to measure residual velocity and extent of damage.
Next, the impact experiment was numerically simulated through finite element analysis using LS-dyna. Three-dimensional solid elements were used to model each ply of the laminates discretely, and progressive material failure was modeled using MAT162. The result indicated that the finite element simulation yielded residual velocities and damage modes well-matched with those obtained from the experiment. It was found that fiber damage was localized near the impactor penetration path, while matrix and delamination damage were much more spread out with the damage mode showing a dependency on the orientation angles and ply locations. The ballistic-limit velocities obtained by fitting the residual velocities increased almost linearly versus the laminate diameter, but the amount of increase was small, showing that the impact energy was absorbed mostly by the localized impact damage and that the influence of the laminate size was not significant at high-velocity impact.
Key words: Composite laminates, High velocity impact, Ballistic limit, Damage mode and extent
1. Introduction
In the past decades, there has been a significant increase in the use of composite materials for advanced light-weight aerospace structures. This is due to the excellent specific stiffness, strength and fatigue properties of composites compared to conventional metallic materials, and its use is not only continuously increasing in aerospace applications but also expanding to automobile, civil, and sporting industries
[1-3]. To understand the mechanical behavior and thereby design better and improved composite structures, researchers have been performing numerous studies for several decades in the diverse field of composite materials and structures.
One of the crucial subjects of composite laminate is its impact behavior. Under impact, composite laminates fail in complex mixtures of delamination, fiber and matrix failure modes, depending on the impact velocity, projectile shape, material properties, laminate layup, etc. Since the strengths
This is an Open Access article distributed under the terms of the Creative Com- mons Attribution Non-Commercial License (http://creativecommons.org/licenses/by- nc/3.0/) which permits unrestricted non-commercial use, distribution, and reproduc- tion in any medium, provided the original work is properly cited.
* Professor, Corresponding author: kw3235@chungbuk.ac.kr ** Professor
*** Senior Researcher **** Professor
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Kyeongsik Woo Numerical Simulation of High Velocity Impact of Circular Composite Laminates
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damage, it is very important to accurately predict the mode and extent of damage of impacted composite laminates. For this purpose, a large number of experimental, analytical, and numerical research works have been and currently are being performed [4-6].
In numerical studies of impact damage behavior, composite laminates have been modeled using shell and solid elements. In early studies, shell modeling was preferred owing to its lower computation resource requirement [7-9].
With the development of high speed computers and efficient software, however, the computational burden became less restrictive, and more researchers began to employ three- dimensional solid elements, modeling each ply discretely [9-12].
The use of discrete 3D solid elements enabled the application of damage initiation and evolution schemes related to the failure modes. The composite impact damage models used thus far are largely grouped into 3 categories:
discrete damage models, cohesive zone modeling (CZM), and continuum damage mechanics (CDM) based models.
In discrete damage models, the stiffness of elements for which the failure criterion is met is dropped immediately and the load is redistributed to the neighboring elements [13]. In CZM, cohesive elements are inserted between the edges of regular elements so that the fracture is accounted for by cohesive elements while the continuum response is accounted for by the regular elements (e.g., [14-16]). In the case of CDM, the stiffness of failed elements is softened gradually according to the damage evolution laws. A number of CDM-based composite failure studies were performed in which various damage initiation and evolution models were proposed and composite fracture was successfully predicted with reasonable accuracy (e.g., [11,13,17-18]).
Even with the large number of existing studies, the high- velocity impact damage behavior of composite laminate materials has not been fully understood and further investigation is still needed. In this paper, the high-velocity impact penetration of laminated composite plates was experimentally and numerically studied using explicit finite element analysis. Tests were performed for symmetrically stacked [45/0/-45/90]ns carbon/epoxy laminated circular plate configurations impacted by a steel ball in the lateral direction. The impact tests were then numerically simulated in LS-DYNA by discrete 3D finite element modeling. First, the simulation results were compared to experimental results for the verification of the finite element model. Next, the effect of different thicknesses and diameters of the laminates on the ballistic-limit velocity, as well as modes and extents of damage was investigated. The change in damage behavior
for varying impact velocity was also examined.
2. Experiment
The specimens used in this study are solid composite plates laminated with 16 and 24 plies of graphite/epoxy perpreg (USN150B, SK Chemical Co.) [19-20] having stacking sequences of [45/0/-45/90]2s and [45/0/-45/90]3s. The thickness of a single ply is 0.142 mm, and the thicknesses of 16- and 24-ply laminates are 2.3 mm and 3.4 mm, respectively. The impact specimen and its supporting fixture are shown in Fig. 1. The specimen is placed between clamped steel plates with open holes to allow impact deformation. The size of the specimen is 87.5 mm × 87.5 mm and the diameter of the exposed circular region is denoted as D. The circular region is considered as an effective area of impact and its size is varied to examine the relation between the effective area and impact damage. A spherical steel ball with the diameter d = 6.35 mm (mass: 1.044 g) is used as the impactor.
Three groups of specimens having the diameter ratio of the effective area to the impactor D/d = 3, 4 and 5 were tested to assess the effect of damage amount on the penetration velocity since the damage absorbs and dissipates the kinetic energy of the impactor.
Figure 2 schematically shows the high-velocity impact test
25
Fig. 1 Impact test specimen and supporting steel fixture Fig. 1. Impact test specimen and supporting steel fixture
Fig. 2 Schematic diagram of high-velocity impact test set-up Fig. 2. Schematic diagram of high-velocity impact test set-up
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set-up. The impact facility consists of a pressurized air tank, gun barrel, four magnetic sensors for measuring the steel ball velocity before and after impact, supporting steel fixture, and signal acquisition system [20]. The specimen is placed on a steel fixture, and the steel ball is fired from an air gun and impacts the specimen. After impact, ultrasonic C-scan images of the specimen are taken to examine the amount of impact damage.
3. Analysis
3.1 Finite element modeling
The test configuration was modeled by discrete 3D finite elements in LS-DYNA (v.971-R4). Fig. 3 shows the FE mesh for the 24-ply [45/0/-45/90]3s circular composite laminated plate when the diameters of the plate (D) and the spherical impactor (d) were 31.75 mm and 6.35 mm, respectively.
Hexahedron elements were used for both the laminate and the impactor. Each ply was modeled with 1 element in the thickness direction. The mesh had the highest density at the central impact region where the aspect ratio was approximately equal to 1, while the element size increased gradually when moving toward the outer region. For the mesh shown in Fig. 1, the number of elements was 134,016 for the laminate (5,460 per ply) and 2,976 for the impactor. Plies having the same orientation angle were grouped and defined as a part as represented by the color code in the figure. The front and back halves of the model were defined as separate parts for ease of the pre- and post-processing procedure. In this study, composite plate configurations with 16 and 24 plies, and with the diameter D = 19.25 mm, 25.4 mm, and 31.75 mm (D/d = 3, 4, and 5, respectively) were considered.
The meshes were generated by adding ply elements in the thickness direction for the corresponding number of plies
and by adding or deleting elements in the radial direction for cases with different plate diameters.
All nodes along the outer edge (r = D/2) of the plate were constrained reflecting the gripping condition of the laminated plate of the tests. No constraint was set for the impact projectile other than the initial velocity (vi) assigned to all nodes of the impactor. The contact between the impactor and the composite plate was defined using
*contant_eroding_single_surface with static and dynamic friction coefficients of 0.3 and 0.1. The hourglassing was controlled by IHG = 5 (Flanagan-Belytschko stiffness form with exact volume integration) with the default value of the hourglass coefficient.
3.2 Material modeling
The impactor considered in this study is made of steel with the following properties: E = 210 GPa, ν = 0.3, and ρ = 7860 kg/m3. The material is assumed to behave elastically and is modeled by *mat_elastic (MAT1).
The composite laminate is modeled using *mat_
composite_msc_dmg (*MAT162). In the modeling, the material behaves elastically until failure, after which the material stiffness is decreased by an exponential damage function. The damage initiation is determined by five quadratic failure modes based on Hashin’s criteria for unidirectional lamina. (See Refs. [11, 21-22] for details of the damage initiation criteria and the damage evolution scheme of MAT162.) After the damage initiation, the material property is degraded by a damage parameter (ω) which is defined by a rigorous and physically proper continuum damage mechanics based approach, i.e.,
the material behaves elastically until failure, after which the material stiffness is decreased by an exponential damage function. The damage initiation is determined by five quadratic failure modes based on Hashin’s criteria for unidirectional lamina. (See Refs. [11, 21-22] for details of the damage initiation criteria and the damage evolution scheme of MAT162.) After the damage initiation, the material property is degraded by a damage parameter () which is defined by a rigorous and physically proper continuum damage mechanics based approach, i.e.,
ܧ ൌ ሺͳ െ ߱ሻܧ, (1)
where E0 is the initial modulus and is the damage parameter defined by the following exponential function:
ɘ ൌ ͳ െ ݁భ൬ଵି൬ചച൰
൰
, (2)
where y is the yield strain. The property degradation is performed using four softening parameters (m1~m4) corresponding to the different damage modes: fiber damage in the fiber direction, fiber damage in the matrix direction, fiber crush and punch shear, and matrix cracking and delamination.
The values of the softening parameters (mi) determine the damage evolution behavior; large values are used for brittle fracture and small values for ductile fracture. The post-failed modulus and stress are then expressed as
ܧ ൌ ܧ݁భ൬ଵି൬ചച൰
൰
, (3)
ɐ ൌ ܧɂ ൌ ܧߝ݁భ൬ଵି൬ചച൰
൰. (4)
The post-failure damage evolution behavior with respect to the softening parameters is well-illustrated (1)
where E0 is the initial modulus and ω is the damage parameter defined by the following exponential function:
7
the material behaves elastically until failure, after which the material stiffness is decreased by an exponential damage function. The damage initiation is determined by five quadratic failure modes based on Hashin’s criteria for unidirectional lamina. (See Refs. [11, 21-22] for details of the damage initiation criteria and the damage evolution scheme of MAT162.) After the damage initiation, the material property is degraded by a damage parameter () which is defined by a rigorous and physically proper continuum damage mechanics based approach, i.e.,
ܧ ൌ ሺͳ െ ߱ሻܧ, (1)
where E0 is the initial modulus and is the damage parameter defined by the following exponential function:
ɘ ൌ ͳ െ ݁భ൬ଵି൬ചച൰
൰, (2)
where y is the yield strain. The property degradation is performed using four softening parameters (m1~m4) corresponding to the different damage modes: fiber damage in the fiber direction, fiber damage in the matrix direction, fiber crush and punch shear, and matrix cracking and delamination.
The values of the softening parameters (mi) determine the damage evolution behavior; large values are used for brittle fracture and small values for ductile fracture. The post-failed modulus and stress are then expressed as
ܧ ൌ ܧ݁భ൬ଵି൬ചച൰
൰, (3)
ɐ ൌ ܧɂ ൌ ܧߝ݁భ൬ଵି൬ചച൰
൰
. (4)
The post-failure damage evolution behavior with respect to the softening parameters is well-illustrated in Ref. [11].
(2)
where εy is the yield strain. The property degradation is performed using four softening parameters (m1~m4) corresponding to the different damage modes: fiber damage in the fiber direction, fiber damage in the matrix direction, fiber crush and punch shear, and matrix cracking and delamination. The values of the softening parameters (mi) determine the damage evolution behavior; large values are used for brittle fracture and small values for ductile fracture.
The post-failed modulus and stress are then expressed as
7
the material behaves elastically until failure, after which the material stiffness is decreased by an exponential damage function. The damage initiation is determined by five quadratic failure modes based on Hashin’s criteria for unidirectional lamina. (See Refs. [11, 21-22] for details of the damage initiation criteria and the damage evolution scheme of MAT162.) After the damage initiation, the material property is degraded by a damage parameter () which is defined by a rigorous and physically proper continuum damage mechanics based approach, i.e.,
ܧ ൌ ሺͳ െ ߱ሻܧ, (1)
where E0 is the initial modulus and is the damage parameter defined by the following exponential function:
ɘ ൌ ͳ െ ݁భ൬ଵି൬ചച൰
൰, (2)
where y is the yield strain. The property degradation is performed using four softening parameters (m1~m4) corresponding to the different damage modes: fiber damage in the fiber direction, fiber damage in the matrix direction, fiber crush and punch shear, and matrix cracking and delamination.
The values of the softening parameters (mi) determine the damage evolution behavior; large values are used for brittle fracture and small values for ductile fracture. The post-failed modulus and stress are then expressed as
ܧ ൌ ܧ݁భ൬ଵି൬ചച൰
൰, (3)
ɐ ൌ ܧɂ ൌ ܧߝ݁భ൬ଵି൬ചച൰
൰
. (4)
The post-failure damage evolution behavior with respect to the softening parameters is well-illustrated in Ref. [11].
(3)
Fig. 3 FE mesh for 24-ply laminate and impactor (D = 31.75 mm, d = 6.35 mm) Fig. 3. FE mesh for 24-ply laminate and impactor (D = 31.75 mm, d =
6.35 mm)
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the material behaves elastically until failure, after which the material stiffness is decreased by an exponential damage function. The damage initiation is determined by five quadratic failure modes based on Hashin’s criteria for unidirectional lamina. (See Refs. [11, 21-22] for details of the damage initiation criteria and the damage evolution scheme of MAT162.) After the damage initiation, the material property is degraded by a damage parameter () which is defined by a rigorous and physically proper continuum damage mechanics based approach, i.e.,
ܧ ൌ ሺͳ െ ߱ሻܧ, (1)
where E0 is the initial modulus and is the damage parameter defined by the following exponential function:
ɘ ൌ ͳ െ ݁భ൬ଵି൬ചച൰
൰, (2)
where y is the yield strain. The property degradation is performed using four softening parameters (m1~m4) corresponding to the different damage modes: fiber damage in the fiber direction, fiber damage in the matrix direction, fiber crush and punch shear, and matrix cracking and delamination.
The values of the softening parameters (mi) determine the damage evolution behavior; large values are used for brittle fracture and small values for ductile fracture. The post-failed modulus and stress are then expressed as
ܧ ൌ ܧ݁భ൬ଵି൬ചച൰
൰, (3)
ɐ ൌ ܧɂ ൌ ܧߝ݁భ൬ଵି൬ചച൰
൰
. (4)
The post-failure damage evolution behavior with respect to the softening parameters is well-illustrated in Ref. [11].
(4) The post-failure damage evolution behavior with respect to the softening parameters is well-illustrated in Ref. [11].
Table 1 summarizes the material properties of USN-150B carbon/epoxy lamina used in this study. Elastic and strength properties are given by the manufacturer. MAT162 fracture parameters can be obtained by tests as described in Ref. [22].
Herein, however, these parameters were determined from a series of preliminary analyses that produced matched results compared to those of a selected baseline impact experiment.
The rate effect is assumed negligible and is not considered in this study.
4. Results and discussion
4.1 Penetration behavior
Figure 4 shows the time history of the impact penetration simulation result for the 24-ply laminate with D/d = 5 when the impact velocity was vi = 231 m/s. In the figure, the upper
half of the model in Fig. 3 is plotted. Also plotted in the figure is the damage index of the perpendicular matrix mode (r5) for which the values ‘0’ and ‘1’ indicate the intact and fully failed status. As can be seen in the figure, at t = 0.005 ms after the impact, local deformation due to impact was observed in the entire thickness in the shape of radiating from the impact point. This deformation developed only in the impacted area and did not occur in the other areas, showing the local deformation characteristics due to high-speed impact. At t = 0.05 ms, the center portion of the laminate was cracked open fully through the thickness direction, and the impact projectile pushed the laminate near the failed area continuously increasing the size of the broken part. At t = 0.1 ms, the projectile passed through most of the laminate and was about to exit. Here, a significant portion of the laminate in the projectile path was clearly observed to be failed and erased while some fragments were detached from the main laminate and appeared as flying debris. Furthermore, rebounding deformation started to occur in the laminate near the projectile path. At t = 0.125 ms, the projectile completely penetrated the laminate and exited, and the rebounding deformation continued with the maximum deformation developed around t = 0.15 ms.
In Fig. 4, a cross-sectional view of the time history of perpendicular matrix failure propagation is also plotted.
The matrix failure occurred initially at the region close to the impacted site, following which it propagated radially depending on the fiber orientation angles. In the figure, a much larger damage size appeared for the 90o plies (ply numbers 4-5, 12-13, and 20-21) compared to other plies with 0o and ±45o orientation angles because the figure was plotted for the cross section perpendicular to the y-axis. (If the figure were plotted for the cross section perpendicular to the x-axis (0o) or to the planes rotated by ±45o, the 0o or ±45o plies would show the larger damage size, respectively.)
Table 1. Material properties of USN-150B lamina
8
Table 1 summarizes the material properties of USN-150B carbon/epoxy lamina used in this study.
Elastic and strength properties are given by the manufacturer. MAT162 fracture parameters can be obtained by tests as described in Ref. [22]. Herein, however, these parameters were determined from a series of preliminary analyses that produced matched results compared to those of a selected baseline impact experiment. The rate effect is assumed negligible and is not considered in this study.
Table 1. Material properties of USN-150B lamina (a) Elastic
(b) Strength
(c) MAT162 fracture parameter
SFC (MPa) 3000 eCrush 0.01
SFS (MPa) 300 eExpn 3
SFFC 0.3 m1 2.2
(o) 10 m2 0.2
eDelam 1.2 m3 0.5
max 0.995 m4 0.2
eLimit 0.2 Crate1-4 0
Density (ton/mm3) ρ 1.544x10-9
Thickness (mm) tply 0.141
Young's modulus
(GPa) E11 131
E22=E33 8
Poisson's ratio 12=13 0.018
23 0.47
Shear modulus (GPa) G12=G13 4.5
G23 3.5
Tensile strength (MPa) Xt 2,000
Yt=Zt 61
Compressive strength (MPa)
Xc 2,000
Yc=Zc 200
Shear strength (MPa) S12=S13 70
S23 40
(a) Elastic
8
Table 1 summarizes the material properties of USN-150B carbon/epoxy lamina used in this study.
Elastic and strength properties are given by the manufacturer. MAT162 fracture parameters can be obtained by tests as described in Ref. [22]. Herein, however, these parameters were determined from a series of preliminary analyses that produced matched results compared to those of a selected baseline impact experiment. The rate effect is assumed negligible and is not considered in this study.
Table 1. Material properties of USN-150B lamina (a) Elastic
(b) Strength
(c) MAT162 fracture parameter
SFC (MPa) 3000 eCrush 0.01
SFS (MPa) 300 eExpn 3
SFFC 0.3 m1 2.2
(o) 10 m2 0.2
eDelam 1.2 m3 0.5
max 0.995 m4 0.2
eLimit 0.2 Crate1-4 0
Density (ton/mm3) ρ 1.544x10-9
Thickness (mm) tply 0.141
Young's modulus
(GPa) E11 131
E22=E33 8
Poisson's ratio 12=13 0.018
23 0.47
Shear modulus (GPa) G12=G13 4.5
G23 3.5
Tensile strength (MPa) Xt 2,000
Yt=Zt 61
Compressive strength
(MPa) Xc 2,000
Yc=Zc 200
Shear strength (MPa) S12=S13 70
S23 40
(b) Strength
8
Table 1 summarizes the material properties of USN-150B carbon/epoxy lamina used in this study.
Elastic and strength properties are given by the manufacturer. MAT162 fracture parameters can be obtained by tests as described in Ref. [22]. Herein, however, these parameters were determined from a series of preliminary analyses that produced matched results compared to those of a selected baseline impact experiment. The rate effect is assumed negligible and is not considered in this study.
Table 1. Material properties of USN-150B lamina (a) Elastic
(b) Strength
(c) MAT162 fracture parameter
SFC (MPa) 3000 eCrush 0.01
SFS (MPa) 300 eExpn 3
SFFC 0.3 m1 2.2
(o) 10 m2 0.2
eDelam 1.2 m3 0.5
max 0.995 m4 0.2
eLimit 0.2 Crate1-4 0
Density (ton/mm3) ρ 1.544x10-9
Thickness (mm) tply 0.141
Young's modulus (GPa)
E11 131
E22=E33 8
Poisson's ratio 12=13 0.018
23 0.47
Shear modulus (GPa) G12=G13 4.5
G23 3.5
Tensile strength (MPa) Xt 2,000
Yt=Zt 61
Compressive strength (MPa)
Xc 2,000
Yc=Zc 200
Shear strength (MPa) S12=S13 70
S23 40
(c) MAT162 fracture parameter
28
Fig. 4 Impact penetration history (D/d = 5, nply = 24, vi = 231 m/s) Fig. 4. Impact penetration history (D/d = 5, nply = 24, vi = 231 m/s)
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The time histories of impactor velocity and contact force between the impactor and the laminated plate are plotted in Fig. 5. As can be seen in Fig. 5(a), the velocity of the impactor began to decrease rapidly after collision with the composite laminate. Thereafter, the speed decreased continuously, but as the impactor exited the laminate at around t = 0.125 ms, a constant residual velocity was reached. In Fig. 5(b), the contact force increased sharply after contact between the impactor and the laminate and peaked at about 0.003 ms, following which it decreased sharply. Subsequently, a significant contact force occurred while the impactor was penetrating the laminate. Finally, the contact force was reduced to zero as the impactor exited the laminate. One can notice that a small but negative contact force occurred in the range of 0.09 - 0.125 ms. This was due to the pushing of the impactor by a part of the laminate in the last stage of the penetration, which resulted in a slight increase of impactor velocity in the corresponding time period.
4.2 Residual velocity comparison
Table 2 compares the residual velocity (vr) of the impactor obtained by experiments and analyses. In general, the residual velocities matched well for all cases considered,
which verifies that the numerical modeling was performed properly. This match was thought to be acceptable since near the ballistic limit velocity (vBL or v50), defined as the velocity required for a projectile to penetrate reliably at least 50% of the time, the residual velocity varies very sensitively to the impact conditions including the initial impact velocity (vi).
4.3 Ballistic limit
It is well known that residual velocity can be expressed in terms of impact velocity and ballistic-limit velocity as [23]
4.3 Ballistic limit
It is well known that residual velocity can be expressed in terms of impact velocity and ballistic- limit velocity as [23]
ݒൌ ܽሺݒെ ݒሻభ, (4)
where a and p are coefficients. Setting p = 2 [24], a and vBL can be obtained through least-squares curve fitting from a set of (vi, vr) data. In this study, the curve fitting was performed using the data set obtained from the simulation since experiments were performed for 3 impact velocities for each case.
Figures 6-7 show the variation of residual velocities versus impact velocities. The triangle and circle markers indicate the results from experiment and analyses, respectively, and the solid lines are the curves fitted using eq. (4). The value at which the curve meets the horizontal axis is the predicted ballistic limit velocity. In these figures, one can see that the residual velocities obtained from the analyses agree well with the experimental ones. Furthermore, the predicted ballistic limit velocities generally fall between or very near to the ranges estimated in the experiments.
The variation of ballistic limit velocities is plotted in Fig. 8, which shows an almost linear increase versus the increase of the plate diameter. Different specimen sizes were considered to study the effect of damage amount on the penetration velocity since the kinetic energy of the impactor was absorbed and dissipated by the damage. As described in the following section, the delamination damage propagation was limited by the grip constraint at the outer edge when D/d = 3, while it was almost fully propagated when D/d = 3. (See Fig. 11.) It was found, however, that the effect of the plate diameter on vBL was not significant. While the case with D/d = 5 had a 67% increase in diameter with respect to the case with D/d = 3 (178% increase in volume), the increase in vBL was only 4.2% and 3.6%
when the number of plies was 16 and 24, respectively. This indicates that, for the 16 ply and 24 ply laminated composite plates considered in this study, the elastic and damage response were localized
(5) where a and p are coefficients. Setting p = 2 [24], a and vBL can be obtained through least-squares curve fitting from a set of (vi, vr) data. In this study, the curve fitting was performed using the data set obtained from the simulation since experiments were performed for 3 impact velocities for each case.
Figures 6-7 show the variation of residual velocities versus impact velocities. The triangle and circle markers indicate the results from experiment and analyses, respectively, and the solid lines are the curves fitted using eq. (4). The value at which the curve meets the horizontal axis is the predicted ballistic limit velocity. In these figures, one can see that the residual velocities obtained from the analyses agree well with the experimental ones. Furthermore, the predicted ballistic limit velocities generally fall between or very near to the ranges estimated in the experiments.
The variation of ballistic limit velocities is plotted in Fig. 8, which shows an almost linear increase versus the
29 (a) Impactor velocity
(b) Contact force
Fig. 5 Time history of impactor velocity and contact force (D/d = 5, nply = 24, vi = 231 m/s) 29
(a) Impactor velocity
(b) Contact force
Fig. 5 Time history of impactor velocity and contact force (D/d = 5, nply = 24, vi = 231 m/s) Fig. 5. Time history of impactor velocity and contact force (D/d = 5,
nply = 24, vi = 231 m/s)
(a) Impactor velocity
(b) Contact force
Table 2. Comparison of residual velocity
12 (b) Contact force
Fig. 5 Time history of impactor velocity and contact force (D/d = 5, nply = 24, vi = 231 m/s)
Table 2. Comparison of residual velocity
nply D/d vi (m/s) vr (m/s)
Experiment Analysis
16
3 147
159 185
24.0 NP 94.0
20.61 NP 89.18
4 155
167 184
26.8 NP 86.3
25.25 NP 80.22
5 163
173 182
26.5 NP 61.5
47.84 NP 61.05
24
3 207
216 242
19.4 NP 104.4
18.03 NP 107.16
4 211
223 240
34.83 NP 48.49
30.72 NP 75.45
5 224
231 245
27.2 NP 75.3
42.48 NP 86.67 (NP: No penetration)
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http://ijass.org increase of the plate diameter. Different specimen sizes were
considered to study the effect of damage amount on the penetration velocity since the kinetic energy of the impactor was absorbed and dissipated by the damage. As described in the following section, the delamination damage propagation was limited by the grip constraint at the outer edge when D/d
= 3, while it was almost fully propagated when D/d = 3. (See Fig. 11.) It was found, however, that the effect of the plate diameter on vBL was not significant. While the case with D/d
= 5 had a 67% increase in diameter with respect to the case with D/d = 3 (178% increase in volume), the increase in vBL was only 4.2% and 3.6% when the number of plies was 16 and 24, respectively. This indicates that, for the 16 ply and 24 ply laminated composite plates considered in this study,
the elastic and damage response were localized only at and near the impact site. The major part of the dissipated impact energy was absorbed by the damage at and near the impact penetration path, and the amount of increase caused by the increased plate diameter was relatively small, which is one of the the typical characteristics of high-velocity impact damage behavior.
4.4 Damage mode and extent
The mode and extent of damage were also examined. Fig.
9 shows a cross-sectional view for various failure modes for the case of D/d = 5, nply = 16, and vi = 173 m/s. Here, the damage state was indicated by the color code in which 0 and 1 represent intact and fully failed states, respectively.
It appeared that the fiber damage occurred in a relatively small area, but this was because the elements that were failed completely were eroded and not observed in the figure. While the fiber damage was limited at the area near the impact site, the matrix damage spread out much more in the radial direction with the damage reaching the boundary region for some plies depending on the orientation angle.
The ply-wise distributions of the matrix damage for this case are plotted in Fig. 10. In the figure, ply orientation angles are noted along with ply numbers counted from the exiting side. One can observe that the upper-mid plies had larger perpendicular matrix damage (in-plane matrix failure) and the effect of orientation angles was clearly exhibited in the damage mode. At the lower plies, the amount of perpendicular matrix damage decreased, and the effect of orientation diminished. In contrast, the parallel matrix/
delamination damage (out-of-plane matrix failure) occurred dominantly in the mid-plies. At the plies near the top and bottom surface, the delamination area was much smaller than that in the mid-plies.
30
(a) D/d = 3 (b) D/d = 4 (c) D/d = 5 Fig. 6 Residual velocity results for nply = 16
(a) D/d = 3 (b) D/d = 4 (c) D/d = 5 Fig. 6. Residual velocity results for nply = 16
31
(a) D/d = 3 (b) D/d = 4 (c) D/d = 5 Fig. 7 Residual velocity results for nply = 24
(a) D/d = 3 (b) D/d = 4 (c) D/d = 5 Fig. 7. Residual velocity results for nply = 24
Fig. 8 Variation of vBL versus laminate diameter Fig. 8. Variation of vBL versus laminate diameter
33
Fig. 9 Cross-sectional view of damage index distribution (D/d = 5, nply = 16, vi = 173 m/s) Fig. 9. Cross-sectional view of damage index distribution (D/d = 5, nply
= 16, vi = 173 m/s)
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Int’l J. of Aeronautical & Space Sci. 18(2), 236–244 (2017)
Figure 11 compares the predicted delamination shapes with experimental C-scan images. The predicted delamination shapes were obtained by first drawing the outlines of parallel matrix/delamination damage for each ply such as the ones shown in Fig. 10(b), and then overlaying those. Although it is very difficult to observe accurately all the delamination shapes of in-between plies from the C-scan images for laminates involving a large number of plies, one can still extract the general shape and extent of delamination.
It can be seen that when nply =16, the delamination propagated to the boundary for the case with D/d = 3 while it did not for cases with with D/d = 4 and 5. Here, the analyses seemed to over-predict the delamination extent, but only slightly.
Comparing the ply-wise delamination shapes in Fig. 10(b) with the experimental C-scan image in Fig. 11(a) for the case of D/d = 5 with vi = 173 m/s, one can observe that the extent of delamination would match if the delamination extent was reduced partially at the mid-plies of 4, 6-8, and 10-11.
When nply =24, the delamination propagated to the boundary for the cases with D/d = 3 and 4 since the impact velocities were increased to penetrate the thicker laminates. The delamination extent for D/d = 5 did not fully propagate to the boundary but increased compared to that when nply =16. For this case, the analysis also over-predicted the delamination extent slightly, showing that almost the entire region except small areas at the boundary was marked as delaminated in the overlaid delamination damage maps.
5. Conclusion
In this study, the high-velocity impact penetration behavior of [45/0/-45/90]ns circular carbon/epoxy composite laminates was studied. The considered configuration includes two laminate thicknesses with 16 and 24 plies, and three laminate diameters with three ratios of laminate
34
(a) perpendicular (b) parallel/delamination
Fig. 10 Ply-wise distribution of matrix damage (D/d = 5, nply = 16, vi = 173 m/s) (a) perpendicular (b) parallel/delamination Fig. 10. Ply-wise distribution of matrix damage (D/d = 5, nply = 16, vi = 173 m/s)
(a) nply = 16 (b) nply = 24 Fig. 11 Comparison of experimental and predicted delamination shapes (a) nply = 16 (b) nply = 24 Fig. 11. Comparison of experimental and predicted delamination shapes
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243
Kyeongsik Woo Numerical Simulation of High Velocity Impact of Circular Composite Laminates
http://ijass.org to impact-sphere diameter of 3, 4, and 5. A spherical steel
ball was used as the impactor. First, impact experiments were performed and residual velocity was measured, and C-scan images were taken to estimate the delamination shape and extent. Next, the impact penetration experiment was numerically simulated through finite element analysis.
Numerical simulations were performed using LS-dyna. Each ply in the composite laminates was discretely modeled by three-dimensional solid elements, and progressive material failure was modeled using MAT162. For the contact behavior between the impact projectile and the laminate, *contact_
eroding_single_surface was employed.
The residual velocities obtained from the simulation matched well with those obtained from the experiments, and the predicted delamination shape appeared similar to that of the experimental C-scan image. By analyzing the detailed damage modes obtained from the simulation, it was found that fiber damage was concentrated at and near the impactor penetration path, while matrix and delamination damages were propagated much more and spread out in the radial direction. The shape of matrix and delamination damage showed a definite dependency on the orientation angles and ply locations in the thickness direction. The residual velocities for various impact velocities were obtained through simulations from which the ballistic limit velocities were obtained by fitting the velocity results to the Lambert- Jonas equation. The ballistic limit velocity increased as the number of plies increased. It also increased almost linearly versus the increase of laminate diameter, but the amount of increase was small. This was thought to be because the damage occurred locally and the main part of impact energy was absorbed by this local damage, indicating that the influence of the laminate diameter was not significant at high velocity impact.
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