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Procedía Engineering 173 (2017) 409 - 416
Procedía Engineering
www.elsevier.com/locate/procedia
11th International Symposium on Plasticity and Impact Mechanics, Implast 2016
An Impact induced damage in composite laminates with intra-layer
and inter-laminate damage
Sanan H Khana *, Ankush P Sharmaa, Venkitanarayanan Parameswarana
a Department of Mechanical Engineering, Indian Institute of Technology Kanpur, 208016, India
Abstract
Low velocity experimental and numerical study have been performed on four layer [0°/90°]s and [90°/ - 45°/ + 45°/0°]s composite laminates at three different energy levels to observe the damage mechanism and delamination pattern. Experiments were performed using a drop weight testing machine as specied in ASTM D5628 FA while numerical analysis was executed using Abaqus Explicit. Hashin failure criteria is used to capture the intra-layer damage modes while surface based cohesive behaviour with quadratic stress failure criteria was used to predict delamination. It was observed from the results that matrix cracking occurred first followed by the delamination. The tensile fiber failure mode triggered at the peak force after which the damage energy stabilises to a particular value. For [0/90]s laminate, larger peanut shaped delamination profile is noticed on the third interface from the impact face along the 0°fiber direction. However, [90/ 45/+ 45/0] sequence profile was oriented along -45°laminate in the second interface from the impact face. The size of profile increases from impact side interface to non-impact side interface due to the increasing flexural stresses. The area of the profile tends to increase with increasing energy and this increase is dominated by the length rather than width. Results of numerical simulations were found to be in good agreement with the experimental results. © 2017 The Authors.PublishedbyElsevierLtd. Thisis an open access article under the CC BY-NC-ND license (http://creativecommons.Org/licenses/by-nc-nd/4.0/).
Peer-review under responsibility of the organizing committee of Implast 2016 Keywords: Drop weight impact, Damage process, Cohesive surface, Delamination
1. Introduction
Its important to understand the behaviour of composite structures under different types of loading. In various applications composites are subjected to low velocity impact loading like dropping of tool during maintenance or flying debris on the runway striking the aircraft during takeoff or landing [1]. A combination of matrix damage, delamination and fiber breakage are the energy dissipation mechanisms occurring during such impacts. These internal damages may considerably reduce the capacity of the composite laminate to support loads further [2]. Hence it is important to analyse the shape and size of the damage with respect to the boundary condition and test parameter (impact velocity, energy, etc.) to understand the damage mechanism better [3].
In some of the recent studies [4,5] attempts were made to model the behaviour of composite laminates using finite element method (FEM). FEM has proven to be effective and less expensive tool to analyze composite structures
* Corresponding author. Tel.: +91 9045043698 ; fax: +91 512 2597408. E-mail address: shkhan@iitk.ac.in
1877-7058 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Peer-review under responsibility of the organizing committee of Implast 2016
doi: 10.1016/j.proeng.2016.12.039
exhibiting different damage modes and delamiantion pattern. In this work, low velocity drop weight experiments were performed on a four layer cross ply and quasi-isotropic composite laminates at different energy levels. This study was supplemented with numerical simulation which was able to predict the failure modes as observed in the laminates during the experiments.
2. Material damage model
2.1. Intra-laminar model
Damage in composites can be quantified using stress or strain based criteria or using a suitable polynomial criteria like Tsai Wu or Tsai Hill. But the polynomial failure criteria are not applied at the ply level and is only used to predict the failure envelope of the laminate subjected to different multi-axial loading. Hashin proposed [6] and later modified [7] a failure criteria that can be applied at the ply level to predict four major damage modes in laminates. These failure modes are discussed below, wherein f and m denote fiber and matrix and t and c denote tension and compression respectively. Fiber tension (<r11 > 0)
Ff -( +"(£)2
Fiber compression (<xn < 0)
Matrix tension (<x22 > 0)
Matrix compression (<x22 < 0)
Fc -Ff -
^ll Xc
&22 2ST
&22 Y'
^22 Yc
^12 SL
In eqn (1)-(4), &ij(i, j = 1,2) is effective stress tensor,X'(Xc) and Y'(Yc) denote the tensile and compressive strength of uni-directional laminate in longitudinal and transverse direction respectively. Also, S j( j = L, T) represents in plane and out of plane shear strength of composites respectively. Here coefficient a in eqn (1) denote contribution of shear stress in fiber tension mode. In eqn (1)-(4) the condition Fj = 1 (i = f, m and j = c, t) indicates that failure has occurred in the corresponding mode. Once the damage initiation criteria is satisfied, damage evolution law needs to be specified as further loading will cause degradation of the material. The damage evolution law is based on the fracture energy dissipated during the damage process. After initiation of damage, the damaged elasticity matrix Cd is defined as follows:
Cd - D
(1 - df)Ei (1 - df)(1 - dm)V21 El 0 (1 - df )(1 - dm)V12E2 (1 - dm)E2 0
0 0 (1 - ds)GD)
where, D = 1 - (1 - df )(1 - dm)vi2v2i and df, dm, ds represents respectively the current state of fiber damage, matrix damage and shear damage. The variables df, dm, ds are evaluated from the damage variables corresponding to the four damage modes dij(i = f, m and j = t, c) defined as follows
idf',& 11 > 0, df - \dfc,&11 < 0} m -
< 0) ds - 1 - (1 - df')(1 - dfc)(1 - dm')(1 - dmc)
2.2. Inter-laminar damage model
To capture the delamination between two plies of the laminate the classical bi-linear traction separation law was used. In this approach a nodal contact point is used like a material point in an element and traction separation damage
onset and degradation schemes were applied. The nodal contact point consists of two coincident nodes shared by the surfaces of adjacent plies. Based on the stiffness of the plies sharing the node, the node can be considered as master or slave. The traction's Ti induced at the contact point is defined as Ti = KijUj(i, j = n, s, t) where Uj = [usfave - urmaster] is the relative displacement of the contact pair node while Kij is the uncoupled penalty stiffness of the interface. A higher value of Kij may critically reduce the stable time increment of the solution while a smaller value may cause interpenetration of nodes. Turon et al. [8] have proposed a tentative expression for its evaluation as Knn = yE22/t where y is a coefficient set as 50, E22 is the transverse modulus of the laminate and t is the thickness of adjacent ply. Kss and Ktt are obtained by replacing G12 with E22 in the above expression. A failure onset of the contact point was modelled using quadratic stress criteria as follows.
W+(fi+(!)" (7)
where (•) is the Macaulay bracket and prevents penetrations of slave nodes on master surface. Here, ti represent the stress in the normal and two shear directions while ti is the maximum defined stress in each corresponding direction. Degradation of the contact point is evolved through mixed mode Benzeggagh and kenane criteria [9] which is defined as follows:
Gc = Gic + (Giic - Gic)Pn (8)
here Gc is mixed mode fracture toughness, p is local mixed mode ratio defined as p = Gshear/(GI) + Gshear) and n is mixed mode interaction parameter obtained from experiments as reported in [4].
3. Experiments and numerical modeling
3.1. Impact tests
Impact tests were performed on [0°/90°]s and [90°/ - 45°/ + 45°/0°]s laminates at three different energy levels. The laminates were fabricated using E-glass fiber as reinforcement and epoxy LY-556 as resin using the hand layup and vacuum bag method. After vacuum bagging, the assembly was cured under a pressure of 4.7 MPa at room temperature for 24 hours. After curing of laminate, 100x100 mm2 size specimens were cut and tested using an Instron drop weight testing machine according to ASTM D5628 FA. The specimens were clamped between two steel fixtures with an effective opening of 70 mm diameter as shown in Fig-1. The impactor had a hemispherical head of 16 mm diameter with a fixed weight of 3.132 kg. Desired impact energy levels of 5J ,10J and 15J were obtained by adjusting the drop height to 162.7 mm, 325.4 mm and 488.2 mm respectively. Three samples were tested for each case to check the consistency of the results. The initial velocity of the impactor was measured by a velocity sensor while the contact force history between specimen and impactor was measured by a force sensor located inside the impactor.
3.2. Numerical modeling and boundary condition
The composite laminate was modelled as a deformable body with continuum shell elements (SC8R). The continuum shell elements have the capability of simulating systems that are globally three dimensional but locally planer [10]. The laminate was partitioned to make impact zone and local deformation zone as shown in Fig-2. The impact zone had a mesh of 0.5x0.5 mm3 while a coarser size of 1x 1 mm3 was used for the rest of the plate. These sizes were obtained after performing a mesh convergence study. Results of the mesh convergence study are shown in Fig-3a and 3b and it was observed that around 1,40,000 elements for the model is sufficient for convergence resulting in a simulation time of 12 hours. Due to the poor mesh generation at the curvatures, variable mass scaling was used to ensure that stable time increment is not controlled by the 'bad' element. The impactor was modelled with rigid shell elements (R3D4) with the reference point at its center of mass where the initial velocity was prescribed. A rigid support plate was used under the laminate to clamp its base such that only 70 mm effective diameter is unsupported. The top clamping plate was modelled by applying 0.25 MPa pressure over the clamped part of the laminate as shown in Fig-2.
Fig. 1: Experimental Set-up
Fig. 2: Numerical model and boundary condition (sectioned view)
Fig. 3: Mesh convergence study
3.3. Contact algorithm and material properties
The contact between the impactor and top surface of the laminate is modeled using penalty contact algorithm while the contact between the plies was initiated by bringing them under general contact domain. A hard contact with pressure over closure and friction coefficient of 0.3 were used between the impactor and top laminate while a friction coefficient of 0.7 was used between the different plies, based on reported studies [11,12] The material properties used in the FE analysis are summarised in table 1. The elastic properties and tensile strength were obtained from simple uni-axial tensile tests in two directions while the other properties were obtained from Soden et.al. [13]. The interface material properties were considered matrix dominated and hence were assumed as: normal strength, tn = Yt and shear strength, ts = tt = S12.
Table 1: Parameter used in FE Analysis
E-glass/epoxy LY556 Parameters
Elastic,E1 = 30.50GPa, E2 = E3 = 4.02GPa, V12 = V13 = 0.29, v23 = 0.39, G12 = G13 = 2.08GPa, G23 = 1.44GPa
Strength(MPa), X, = 686, Xc = 270, Yt = 35, Yc = 88, S12 = 52, S23 = 27 Fracture energy (N/m), Gu = 62000, G1c = 47000, G2l = 250, G2c = 920 Interface parameters
Stiffness (N/m3), Kn = 4.02 x 1014, Ks = Kt = 4.41 x 1013
Strength (MPa), tn = 35, ts = t, = 52
Fracture energy (N/m), Gi = 280, Gn = Gm = 440
4. Results and discussion
4.1. Force ra time
In Fig. 4a and 4b force-time history for 5J,10J and 15J energy levels are shown and compared with FE results for [0°/90°]s and [90°/ - 45°/ + 45°/0°]s laminates respectively. The initial part of the curve shows oscillations due to the elastic vibrations between impactor and specimen and is well predicted by the FE analysis, but after the peak force FE results predicts more time for the impactor to rebound. This may be due to the contact forces initiating between the delaminated plies because of the contact algorithm. Moreover, increasing energy level increases the loading slope of the force time curve, but the increase from 5J to 10J is more significant than increase from 10J to 15 J. This is observed for both the laminate sequence
4.2. Force ra displacement
The graph of Fig 4c and 4d shows the comparison of experimental and numerical force-displacement curves. During the loading phase and till the peak load, same slope is noticed in experiments but in the unloading phase the composite plate returns back more slowly and less completely than predicted by FE analysis. The area enclosed by the loading and unloading curves is a measure of the energy absorbed in the laminates due to intra-laminar and interlaminar damage.
4.3. Energy ra time
Fig. 4e and 4f compares the experimental and FE energy histories for different impact energy events with good accuracy between the two. The impactor transfers all its energy to the plate, after which, it rebounds due to the elastic recovery of the plate. The energy utilized for the recovery was less than the impact energy because of the different damage dissipation phenomenon occurring during the event. The energy is dissipated in different failure modes (i.e.
Fig. 4: Comparison between the two laminate sequence (a,b). Force history curve. (c,d) Force displacement curve (e,f) Energy history curve.
Fig. 5: Comparison of the experimental and FE analysis of delamination profile for 10J energy level for two laminate cases. Mark-1 indicate the first interface from the impact face and further follows
Intra-laminar and inter-laminar modes) and due to the friction between impactor and plate and between different plies of the laminate. During the rebound completion stage the net absorbed energy stabilizes to a particular value. FE analysis under-predicts the energy absorbed by the laminate(s).
4.4. Delamination analysis
During the loading the delamination initiated at the center and propagated along the direction of lamina orientation. Fig 5a observes the delamination profile obtained for [0°/90°]s laminate for 10J of energy level. Marking 1-3 indicate the order of interface from impact face.Since the tensile stress are maximum at the non-impact side of the specimen,
the delamination profile is larger (mark-3) than the profile obtained at the impact side (mark-1). A typical peanut shaped profile is observed for all three energy levels and it propagates along the 0° oriented ply direction. Similarly, [90°/ - 45°/ + 45°/0°]s laminate features a small peanut profile following a larger profile corresponding to interface 1 (90°/ - 45°) and interface 2 (-45°/ + 45°) of the specimen respectively. The first profile was oriented along the 45° direction followed by the second profile along -45° as shown in Fig 5. For both the laminate cases, the length and width of the profile was well captured by the FE analysis. Numerical simulation was able to predict the delamination pattern observed in the experiments. Output of delamination pattern in FE was obtained through CSDMG damage variable available in the output deck card of Abaqus Explicit.
5. Concluding remarks
In this study cross-ply and quasi-isotropic laminates were analysed using low velocity drop weight set-up at three different energies to observe their inter-laminar and intra-laminar behaviour. Higher oscillations in force-time graph were noticed at the peak force indicating the initiation of fiber failure in tension. After this no further energy is absorbed by the specimen during the rebound stage. The delamination profile at the non-impact side of specimen is like a peanut shape for both the laminate sequences and it propagates along the orientation of the laminate interface with increasing energy level.
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