Numerical Analysis of Delamination Behavior in Laminated Composite with Double Delaminations Embedded in Different Depth Positions

Numerical Analysis of Delamination Behavior in Laminated Composite with Double Delaminations Embedded in Different Depth Positions Numerical Analysis of Delamination Behavior in Laminated Composite with Double Delaminations Embedded in Different Depth Positions R.G. Wang a,*, L. Zhang a, W.B. Liu b, J. Zhang a, X.D. Sui c, D. Zheng c, and Y.F. Fang b a Center for Composite Materials and Structures, School of Astronautics, Harbin Institute of Technology, Harbin 150001, China b School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, China c Shenyang Aircraft Design & Research Institute, Shenyang 110035, China Summary In this article, the finite element method (FEM) using cohesive element is applied to predict the delamination behavior in laminated composite with double delaminations embedded in different depth positions under compressive load. In particular, compared with single delamination composites, the interaction between delaminations and the complicated propagation behavior are discussed. Furthermore, the study is focused on the significant effects of double delaminations on delamination buckling and growth behavior, such as the distance between double delaminations and the delaminations depth position. 1. Introduction Following with the increasing use of laminated composites in structural applications, as one of the predominant forms of damage, delamination in laminated composites has been of considerable interest and concern in recent years. Delaminations are mainly induced by foreign object impact and manufacture 1, which will lower the load-carrying capacity of composite structures 2-3. Finite element method has become one of the most powerful instruments to predict failure in laminated composite. Especially recently, the cohesive element methods have been used wildly which can predict both delamination initiation and delamination propagation conveniently and accurately 4-7. In previous years, significant progress has been made in studying on the *Corresponding author: E-mail address: wrg@hit.edu.cn (R.G. Wang) Smithers Rapra Technology, 2011 delamination behaviors of laminated composites, some of which devote to the single delaminated composites 8-11, while some others devote to the multiple delamination behavior caused by impact in which the diameters of the delaminations are increased from the top surface to the bottom surface which is an idealized pattern of foreign object impact damage of composite laminates 12-14. However, the interrelationship between delaminations caused during manufacture has not been related yet, in which the embedded delaminations are not an idealized pattern, but may be with equal diameters and placed at different depth positions under a certain distance. Therefore, our objective of this paper is to investigate the delamination buckling behavior and the interrelationship between delaminations of the laminated composites containing two delaminations embedded in different depth positions with cohesive element method, which is based on a mixedmode failure criterion and adopts softening relationships between tractions and separations. The results are obtained by standard ABAQUS procedures. 2. Geometrical model A square panel is adopted, in which double delaminations have been placed in different depth positions in sequence from shallow layer to deep layer. A schematic representation of geometry is given in Figure 1. Only one quarter of the structure (depicted in Figure 1a, b, c, d) has been considered, because geometry, boundary condition and applied loads are all symmetric with respected to the x and y axes. There are several points should be emphasized: U, M and L points represent the center points of the upper layer composite, the middle layer composite, and the bottom layer composite separately. Otherwise, the stacking sequence of the laminate is [45º/0º/-45º/0º/45º/0º/- 45º/0º/45º/0º] 2S. The delaminations Polymers & Polymer Composites, Vol. 19, Nos. 2 & 3, 2011 213

R.G. Wang, L. Zhang, W.B. Liu, J. Zhang, X.D. Sui, D. Zheng, and Y.F. Fang Figure 1. Square panel geometry, boundary condition and applied load (unit in the Figure: mm) sizes are all fixed at 10 mm 10 mm. The thickness of single ply is 0.12 mm. The ply material properties and the interlaminar properties are shown in Table 1. 3. Finite Element Model The square panel has been modeled using the 8-nodes 3Dlayered solid elements which can calculate interlaminate stresses and transverse shear effects accurately. The interface between sub-laminates has been modeled by the 8-nodes 3D cohesive element to predict delamination behavior which is a zero thickness volumetric element and has its own constitutive equations. Figure 2. Cohesive law for single mode loading with bilinear constitutive model 15 The constitutive equation is used to relate the stress σ to the relative displacement δ at the interface which can be demonstrated by strain softening models. For pure Mode I loading, after the interfacial normal stress attains its interlaminar tensile strength (σ c ), the stiffness is gradually reduced to zero. Figure 2 shows the cohesive law for single mode loading with linear elastic-linear softening (bilinear) model, which is the simplest to implement, and is most commonly used 15,16. The interfacial constitutive response shown in Figure 2 can be implemented in the following steps: Table 1. Material properties 11 Mechanical magnitudes Properties Longitudinal Young s modulus E 11 115 GPa Transverse Young s modulus E 22 =E 33 8.5 GPa Shear modulus G 12 =G 23 4.5 GPa G 13 3.3 GPa Poisson s ratio ν 12 =ν 13 0.29 ν 23 0.3 Penalty stiffness K P 850 MPa Interlaminar tensile strength T 3.3 MPa Interlaminar shear strength S 7 MPa Fracture toughness G IC 0.33 N/mm G IIC =G IIIC 0.8 N/mm Step 1: When δ<δ 0, the constitutive equation is given by: σ = K p δ (1) Step 2: When δ 0 δ< δ F, the constitutive equation is given by: σ = (1 D)K p δ (2) where D represents the damage accumulated at the interface, which is zero initially, and gradually reaches 1 when the material is fully damaged. 214 Polymers & Polymer Composites, Vol. 19, Nos. 2 & 3, 2011

Numerical Analysis of Delamination Behavior in Laminated Composite with Double Delaminations Embedded in Different Depth Positions Step 3: When δ δ F, all the penalty stiffness is set equal to zero. Under pure Mode I, II or III loading, the onset of damage at the interface can be determined simply by comparing the stress components with their respective tolerance. However, under mixed-mode loading, damage onset may occur before any of the stress components involved reaches their respective tolerance. Therefore, it is assumed that delamination initiation can be predicted using the quadratic failure criterion 2 σ z + τ 2 xz + τ yz T S S 2 = 1 (3) where σ z is the transverse normal tensile stress, and t xz and t yz are the transverse shear stresses. Under mixed-mode loading, the damage growth can be predicted using the quadratic interaction between the energy release rates in the same way as the delamination initiation can be predicted using the quadratic failure criterion zone II) in order to enhance the computational efficiency under the condition of predicting delamination propagation in the front edge accurately. Surface-to-surface contact element has been placed in the delamination zone to avoid overlaps between elements. The nonlinear solution of the problems presented here is performed using standard ABAQUS procedures. 4. Delamination Buckling 4.1 Effect of Double Delaminations As we all known, delaminated composite plate experiences three main typical buckling modes under compressive load: unbuckling, local buckling and global bucking which can be represented by the out-ofplane displacements for the two characteristic corner points U, L at different loading stages 17. As for the laminated composites containing double delaminations, there is another corner point M which represents the middle sub-layer in our consideration. Figure 5 shows the buckling mode of a laminated composite plate with double delaminations with the same geometrical model as mentioned and the corresponding delamination parameters are shown in Table 2 (model no.1). It is possible to distinguish several characteristic values for the applied load: F B is the local buckling load of the upper sub-laminate, F C is the local delamination buckling load of the middle sub-laminate, F D is the critical delamination propagation load embedded at 1/5 depth position, F E is the global buckling load. As applied Figure 3. Finite element model composed of upper layer, middle layer, two cohesive layers and bottom layer G 1 G IC 2 + G II + G III G IIC 2 G IIIC 2 = 1 (4) The structure of the sub-laminates and interfaces including embedded delaminations are described in Figure 3. The cohesive layer is inserted into adjacent sublaminates (between top layer and middle layer, and between middle layer and bottom layer). The composite layers have been meshed by means of the 8 node solid elements (C3D8RC3). Figure 4. Adopted finite element discretization including delamination area (zone I) and growth area (zone II and zone III) The cohesive elements have been positioned in the area (Figure 4, zone II and zone III) around the embedded delamination (Figure 4, zone I) to predict the delamination growth. The mesh around the embedded delamination is refined and the mesh size gradually increases (Figure 4, Polymers & Polymer Composites, Vol. 19, Nos. 2 & 3, 2011 215

R.G. Wang, L. Zhang, W.B. Liu, J. Zhang, X.D. Sui, D. Zheng, and Y.F. Fang Figure 5. Load-displacement behavior of laminated composites and the buckling mode of laminated composites with 10 mm 10 mm double embedded square delaminations positioned at 1/10 and 1/5 depth positions in sequence (deformation is five times magnified) load increases from F A (0 N) to F E, the laminate statement experiences five stages: 1. Unbuckling regime: when applied load does not reach F B, the two sub-laminates are still in contact in the unbuckling condition. 2. Local buckling regime of the upper sub-layer: when applied load is equal to F B, the upper sub-laminate starts to buckle and the distance between the two characteristic points U and L increases while the points M and L do not change their positions (see configuration (a) in Figure 5). 3. Local buckling regime of the middle sub-layer: when applied load is equal to F C, the middle sub-laminate starts to buckle and the distance between the Table 2. Model parameters of laminated composites containing double delaminations and the corresponding typical critical loads ( presents the value not discussed in this paper; presents the value not existed) Model no. Delamination size (mm) Delamination position of the first delamination Delamination position of the second delamination Local buckling Typical critical load (N) Delamination growth initiation Global buckling 1 10 10 1/10 1/5 5364 31788 36655 2 10 10 1/10 1/4 34097 3 10 10 1/10 3/10 37491 4 10 10 1/10 7/20 40140 5 10 10 1/10 2/5 43902 6 10 10 1/10 9/20 37674 7 10 10 1/10 1/2 34145 8 10 10 3/20 1/4 8907 37365 40948 9 10 10 1/5 3/10 27879 10 10 10 1/4 7/20 26892 11 10 10 3/10 2/5 38288 12 10 10 7/20 9/20 43502 13 10 10 3/20 3/10 8933 41300 53220 14 10 10 1/5 7/20 24986 15 10 10 1/4 2/5 29805 16 10 10 3/10 9/20 31206 17 10 10 3/20 7/20 27746 18 10 10 1/5 2/5 24946 19 10 10 1/4 9/20 30438 20 10 10 3/10 1/2 34890 21 10 10 1/10 34112 22 10 10 1/5 216 Polymers & Polymer Composites, Vol. 19, Nos. 2 & 3, 2011

Numerical Analysis of Delamination Behavior in Laminated Composite with Double Delaminations Embedded in Different Depth Positions two characteristic points M and L increases while the point L doesn t change its position (see configuration (b) in Figure 5) 4. Delamination propagation: when applied load is equal to F D, the embedded delamination placed at 1/5 depth position begins to propagate caused by the local buckling of the middle sub-layer (see configuration (c) in Figure 5) 5. Global buckling regime: when the load approaches to F E, the upper and middle sub-laminates start to change their buckling directions dragged by the bottom one which is also the thickest sub-laminate, and the three points U, M and L generally move in the same direction (see configuration (d) in Figure 5). Figure 6 and Figure 7 show the load-displacement behavior and the buckling mode of laminated composites with single delamination. The delaminations are embedded at 1/10 depth position and 1/5 depth position separately. As shown, those delaminated composites experience only one major buckling state: global buckling. The only difference between them is that the panel containing shallower delamination also experiences a sub-laminate local buckling with minor amount (see configuration (a) in Figure 6). This minor local buckling behavior shows a closure trend, and close as the global buckling occurs because of the same buckling direction (see configuration (b) in Figure 6), which means it does not affect the major buckling mode and not lead to delamination propagation. Therefore, the minor local buckling behavior doesn t belong to the typical local buckling mode as we usually called. Compared with the typical buckling mode, the laminated composite containing double embedded delaminations experiences one more buckling regime and the delamination propagation state is more complicated Figure 6. Load-displacement behavior of laminated composites and the buckling mode of laminated composites with 10 mm 10 mm embedded square delamination positioned at 1/10 depth position (deformation is five times magnified) Figure 7. Load-displacement behavior of laminated composites and the buckling mode of laminated composites with 10 mm 10 mm embedded square delamination positioned at 1/5 depth position (deformation is five times magnified) because of the one more embedded delamination. The significant effect can be obtained by comparison of laminated composites containing single delamination with composite panel containing double delaminations. Only global buckling occurs when the delamination is placed at 1/10 or 1/5 depth position separately, but both local buckling and global buckling occur when double delaminations are placed at both 1/10 and 1/5 depth positions in the same laminated composite. In addition, the delaminations in double Polymers & Polymer Composites, Vol. 19, Nos. 2 & 3, 2011 217

R.G. Wang, L. Zhang, W.B. Liu, J. Zhang, X.D. Sui, D. Zheng, and Y.F. Fang delaminated composites propagates instead of the composite panels containing single delamination. In sum, double delaminations embedded in different depth positions have a significant effect upon structural stabilization, in which the interrelationship between double delaminations is a key problem to solve. Twenty two numerical models of double delaminated composites with the same delamination size (10 mm 10 mm) and different depth positions are computed in this paper. The relevant model parameters and typical critical loads are shown in Table 2. 4.2 Effect of the Distance Between Delaminations on Delamination Behavior Delamination depth position plays a predominant role in determining the buckling behavior, especially for the shallow delamination. Considering that, the first delamination position is fixed at 1/10 depth position, and the effect of distance between delaminations is obtained by changing the other delamination (the second delamination) depth position (see models no. 1-7 in Table 2). Figure 8 shows the variation of critical delamination propagation load as a function of the distance between delaminations. It is easy to notice that the distance between delaminations plays a significant role in the delamination propagation. As the distance between delaminations increases from 2 plies to 6 plies, critical delamination propagation load shows an evident increase. Compared with single delaminated composites (model no. 21 and 22) whose embedded delamination do not propagate, the increasing trend of critical delamination propagation loads indicate that when the second delamination is leaving away from the first delamination, the embedded delamination is more and more difficult to propagate. The interrelationship between double delamination increases with the reduction of the distance between them. When the depth position of the second delamination is deeper than 2/5, the delamination propagation load shows a contrary trend. This phenomenon is not related to the interrelationship between double delaminations, but is caused by the lower stabilization of the thickest sub-laminate. In addition, the double delaminated composites have a very complicated delamination growth behavior. For instance, there is only one ply discrepant between model no. 1 and model no. 2, but the delamination growth states are quite different: for model no. 1, only the middle embedded delamination propagates (see configuration (c) in Figure 5); for model no. 2, as shown in Figure 9, the upper embedded delamination propagates until the deeper embedded delamination is induced to propagate by the upper one. 4.3 Effect of Depth Position on Buckling Behavior As for single delaminated composite plate, the buckling mode is affected by depth position 18. For double delaminated composite plate, this effect is investigated under the condition of a fixed distance between two embedded delaminations which means the two delaminations are considered as a delamination group. 4.3.1 The Distance Between Delaminations is Fixed at Two Plies Figure 10 presents the comparison among characteristic critical loads as a function of delamination depth position when the distance between delaminations is fixed at 2 plies. The configuration can be separated into two regions according to the different buckling modes. In region I, both two delamination groups are placed at shallow depth position, and the buckling behavior can be described as: local buckling before global buckling occurs, and the Figure 8. Variation of the critical delamination propagation load as a function of the distance between delaminations. (a) Delamination growth state when upper delamination begins to propagate; (b) Delamination growth state when deeper delamination begins to propagate; (c) Delamination growth state when global buckling occurs 218 Polymers & Polymer Composites, Vol. 19, Nos. 2 & 3, 2011

Numerical Analysis of Delamination Behavior in Laminated Composite with Double Delaminations Embedded in Different Depth Positions delamination propagation load falls in range between local and global buckling loads and approaches to the global buckling load. The increase of the delamination depth position leads to the buckling mode changing. In region II, only global buckling occurs, and the critical buckling loads increase with delamination depth positions except for 3/10 depth position. This phenomenon is caused by strain-energy degradation originated from the minor local buckling regime as mentioned (see the configuration in Figure 10), which is actually a conversion process of energy from strain-energy to mechanical energy. Figure 9. Delamination growth evolution of composite plates with model no. 1 and model no. 2 4.3.2 The Distance Between Delaminations is Fixed at Three Plies Figure 11 presents the comparison among characteristic critical loads as a function of delamination depth position when the distance between delaminations is fixed at 3 plies. When the first delamination depth position is 3/20, the delamination buckling behavior can be depicted in sequence as: local buckling, delamination propagation and global buckling. When the depth position is larger than 3/20, only global buckling occurs, and the critical buckling load increase with delamination depth position. 4.3.3 The Distance Between Delaminations is Fixed at Four Plies Figure 12 presents the comparison among characteristic critical loads as a function of delamination depth position when the distance between delaminations is 4 plies. It is easy to notice only global buckling occurs, and critical global buckling loads increase with delamination depth positions except for the condition of 3/20 depth position caused by the minor local buckling as mentioned (see the configuration in Figure 12). Figure 10. Comparison among characteristic critical loads (global buckling load, local buckling load, and delamination propagation load) as a function of delamination depth position when the distance between delaminations is fixed at 2 plies (see model no. 1 and 8-12 in Table 2) It is an easy way to notice the delamination depth position plays a Polymers & Polymer Composites, Vol. 19, Nos. 2 & 3, 2011 219

R.G. Wang, L. Zhang, W.B. Liu, J. Zhang, X.D. Sui, D. Zheng, and Y.F. Fang Figure 11. Comparison among characteristic critical loads (global buckling load, local buckling load, and delamination propagation load) as a function of delamination depth position when the distance between delaminations is fixed at 3 plies (see models no. 13-16 in Table 2) containing two delaminations have more complicated delamination buckling modes, lower stabilization, and extremely low delamination propagation load than single delaminated composite, which are affected by the distance between delaminations and the delamination depth position. The interaction between double delaminations increases along with the reducing distance which leads to a lower stabilization. In addition, considering the double delamination as a group, the buckling mode changes as the delamination depth position increases: from local buckling before global buckling occurs into directly global buckling, which is similar to the single delaminated composites. Acknowledgements Figure 12. Comparison among characteristic critical loads (global buckling load, local buckling load, and delamination propagation load) as a function of delamination depth position when the distance between delaminations is 4 plies (see models no. 17-20 in Table 2) The work described in this paper has been supported by the National Natural Science Foundation of China (Grant No. 90916008). The authors are also grateful for software support of the High Performance Computer Center of Harbin Institute of Technology. predominant role in determining the buckling behavior. In conclusion, as the depth location increases, the buckling mode changes from local buckling into global buckling and the composite plate with shallow delamination has extremely low structure stabilization. 5. Conclusions The delamination buckling and growth behavior in double delaminated composites are investigated successfully using a FEM based on the cohesive element. The laminates References 1. Tay T.E., Liu G., Tan V.B.C., Sun X.S., and Pham D.C., Journal of Composite Materials, 42 (2008) 1921-1966. 2. Hwang S.F. and Liu G.H., Composite Structures, 53 (2001) 235-243. 3. Tafreshi A. and Oswald T., International Journal of Pressure Vessels and Piping, 80 (2003) 9-20. 4. Mi Y., Crisfield M.A., and Davies G.A.O., Journal of Composite Materials, 32 (1998) 1246-1272. 5. Dávila C.G., Camanho P.P., and De Moura M.F., Collection of Technical Papers-AIAA/ASME/ASCE/ AHS/ASC Structures, Structural Dynamics and Materials Conference, 3 (2001) 2277-2288. 6. Balzani C. and Wagner W., Engineering Fracture Mechanics, 75 (2008) 2597-2615. 7. Fan C., Ben Jar P.Y., and Cheng J.J.R., Engineering Fracture Mechanics, 75 (2008) 3866-3880. 220 Polymers & Polymer Composites, Vol. 19, Nos. 2 & 3, 2011

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R.G. Wang, L. Zhang, W.B. Liu, J. Zhang, X.D. Sui, D. Zheng, and Y.F. Fang 222 Polymers & Polymer Composites, Vol. 19, Nos. 2 & 3, 2011