Open-hole compressive strength prediction of CFRP composite laminates

Transcription

1 Open-hole compressive strength prediction of CFRP composite laminates O. İnal 1, A. Ataş 2,* 1 Department of Mechanical Engineering, Balikesir University, Balikesir, 10145, Turkey, inal@balikesir.edu.tr 2 National Composites Certification and Evaluation Facility (NCCEF), School of Materials, University of Manchester, Manchester, M13 9PL, UK, akin.atas@manchester.ac.uk Abstract The open-hole compressive (OHC) strength of various T800/924C CFRP laminates was estimated by a linear three-dimensional progressive damage model (PDM). Finite element (FE) models were developed using ANSYS FE software. The load-displacement curves were generated for the FE models and the strengths were calculated using the maximum load sustained. For the layups considered, the hole size effect was captured with the selected damage initiation criteria and elastic material property degradation factors. Keywords: Carbon-fiber reinforced plastic (CFRP) composites, open-hole compressive (OHC) strength, finite element analysis (FEA), progressive damage modelling (PDM). 1 Introduction Open holes/notches are unavoidable in structural parts which are created intentionally for mechanical connections, for access to power and control cables, hydraulic pipes as well as unintentionally created holes due to damage events (Eriksson, 1991). These stress raisers significantly reduce the strength of the composite laminates both in tension and more severely in compression due to the microbuckling of the load bearing fibres. The open-hole compressive (OHC) strength of carbon fibre reinforced plastic (CFRP) composite laminates is found to be approximately half of that unnotched ones (Soutis et al., 1993; Waddoups et al.,1971). Furthermore, considering the lower unnotched compressive strength of the CFRP laminates, which is 60-70% of their respective tensile strength (Soutis, 1991), OHC strength becomes a limiting design parameter for laminated composite structures (Soutis et al., 2000). A linear progressive damage model (PDM) embedded into the ANSYS finite element (FE) software ("ANSYS Academic Research, Release 14.5 ) was used in the present study in order to estimate the OHC strength of various lay-ups as a function of the hole diameter. Development of an appropriate FE model, prediction of damage onset and simulation of the damage propagation are the three main steps of the modelling approach. FE model and solution parameters were determined for a selected reference specimen configuration ([(±45 /0 2) 3 ] s * Permanent Address: Department of Mechanical Engineering, Balikesir University, Balikesir, Turkey. 1

2 ACM2015 lay-up with a 5mm central hole) using experimental data. The load-displacement (P-δ) response was then generated for other FE models using these parameters and the OHC strength was calculated from the maximum value in the P-δ curve. 2 Experimental Data Experimental data for the present study are taken from Soutis and co-workers (Soutis et al., 1993;Soutis & Fleck, 1990; Soutis et al., 1991; Soutis et al., 2000). Composite laminates were manufactured from T800/924C material system using the hand lay-up technique under recommended autoclave curing procedure. All laminates consisted of 24 plies (approximately 3 mm total thickness) and were symmetric about the mid-plane. The lay-ups and corresponding unnotched strength properties are given in Table 1 (Soutis et al., 1993). For comparison purposes, these values will be used to normalise the predicted OHC strengths in the following sections. Table 1. Unnotched strengths of various T800/924C lay-ups (Soutis et al., 1993). Lay-up Ply orientation Unnotched strength (MPa) L1 [(±45 /0 4) 2 ] s 1010 L2 [(±45 /0 2) 3 ] s 810 L3 [(0 /90 2/0 ) 3 ] s 670 L4 [(±45 /0 2/90 2/0 2/90 2/0 2)] s 820 L5 [(±45 /0 /90 ) 3 ] s 568 L6 [(±45 ) 2 /0 /(±45 ) 2 /0 /±45 ] s mm by 50 mm test coupons were cut from the laminates and aluminium alloy end tabs were bonded for testing which resulted in a gauge section of L = 115 mm x W = 50 mm as shown in Fig. 1. Circular holes of various diameters (the range used in the present study is d = 4 15 mm) were drilled at the centre of the specimens using a tungsten carbide drill bit to prevent drilling induced damage. Tests were performed by shear action at a cross-head displacement rate of 1 mm/min. Experimental details are available in Ref. (Soutis et al., 1993). Figure 1. Geometric parameters of an open-hole compression specimen (σ, L, W and d stand for the remote axial stress, specimen length, width and hole diameter, respectively). 3 Modelling and Analysis 3.1 Finite Element Modelling Three-dimensional finite element (FE) models were developed and the open-hole strengths were predicted using ANSYS FE software ("ANSYS Academic Research, Release 14.5 ). Figure 2 shows the volume discretisation of an FE model as an example. One element per laminate layer in through-the-thickness direction was used to model each of the mm thick layers using linear 8-noded brick elements (SOLID 185) with reduced integration formulation. The consecutive laminate layers were connected to each other by shared nodes at their interface. Shared nodes at the interfaces mean that the delamination damage was ignored despite partly taking the stacking sequence into account by incorporating 3-D stress components at the Gauss integration points. Equivalent linear elastic orthotropic material properties (Soutis & Fleck, 1990) (see Table 2) were assigned to each unidirectional composite layer according to pre-defined local coordinate systems which represent the 2

3 O. İnal, A. Ataş individual orientation angles. The fibre direction of the 0 layer coincides with the loading direction (x-axis). Strength values of T800/924C material system are given in Table 3 (Falzon et al., 2000). Figure 2. Volume discretisation of a 3-D FE model (L = 115 mm, W = 50 mm, d = 8 mm), showing the kinematic and loading boundary conditions. Table 2. Elastic properties of T800/924C (Soutis & Fleck, 1990). E 11 (GPa) E 22 =E 33 (GPa) G 12 =G 13 (GPa) G 23 (GPa) ν 12= ν 13 ν 23 * *ν 23 is taken from the manufacturer s data sheet and used for the calculation of G 23 value (G 23 = E 22 /2(1+ ν 23 )). Table 3. Strengths of T800/924C (Falzon et al., 2000). X T (MPa) X C (MPa) Y T = Z T (MPa) Y C = Z C (MPa) S XY = S XZ = S YZ (MPa) All degrees of freedom were constrained at the fixed left end of the laminate in order to simulate the fully clamped laminate end. Appropriate constraint conditions were imposed on the nodes at the right end of the laminate so that all these nodes acted simultaneously with a selected master node. Consequently, an incremental displacement was applied to the laminate through that master node along the (negative) x-direction in order to load the model. The load values corresponding to each prescribed displacement increment was calculated using the reaction forces at the master node. The load-displacement curve was then plotted and the strength was predicted using the maximum load sustained. 3.2 Progressive Damage Modelling (PDM) PDM is used to estimate the ultimate strength by modelling the response of the laminate beyond the damage onset. The laminate layers are modelled as homogenous orthotropic materials and it is assumed that the complex failure events can be represented by failure of the individual elements within the laminate layers. In general, fibre tensile, fibre compressive, matrix tensile and matrix compressive modes are used to describe the meso-scale damage onset for which the experimental procedures of respective strength values are well established. Micromechanical damage modes such as axial splitting, fibre/matrix debonding, fibre pull-out, fibre microbuckling as well as interlaminar delamination damage are generally omitted in PDM for the sake of reasonable modelling effort and acceptable solution time. Instead, they are taken into account by the damage variables as will be explained in the following paragraphs. There are mainly three steps involved in a PDM. The first step is the development of an FE model (details are given earlier). Prediction of the damage onset is the second step which is a fairly simple routine where the stress analysis is followed by the failure check using a selected failure criterion/criteria. In the present study, Hashin failure criteria ("ANSYS Academic Research, Release 14.5 ; Hashin, 1980) were selected which are given in Table 4 through equations

4 ACM2015 Table 4. Hashin failure criteria for different failure modes ("ANSYS Academic Research, Release 14.5 ; Hashin, 1980). Failure Mode Failure Criterion Matrix tensile ( > 0) Matrix compressive ( 0) (1) (2) Fibre tensile (3) ( > 0) Fibre compressive ( 0) (4) Following the onset detection, the last step of the PDM is updating the elasticity matrix of the corresponding element in order to simulate the damage progression. In this study, instant material property degradation method (stiffness degradation) was selected over continuum damage mechanics method due to its simplicity. The constitutive relationship for a damaged material is given as ("ANSYS Academic Research, Release 14.5 ): where, σ: Cauchy stress; ε: total elastic stain, [D] d : damaged elasticity matrix. The damaged elasticity matrix for a general orthotropic material is defined as: (5) (6) where, [C ij ]: compliance matrix of the undamaged material; d f, d m, d s : fibre, matrix and shear damage variables (0: no damage, 1: complete stiffness loss in the affected mode). The damage variables for calculating the damaged elasticity matrix are determined as follows ("ANSYS Academic Research, Release 14.5 ): (7) where,,, and are fibre tension, fibre compression, matrix tension and matrix compression failure indexes, respectively (see, Table 4). 4

5 O. İnal, A. Ataş Once the appropriate criterion was met in an element, the respective elastic material property of that element was reduced by setting the damage variables d f and/or d m to Shear damage variable d s was calculated according to Eq. (7). 4 Results and Discussions Figure 3 shows the PDM prediction curves and experimental data points which are bounded by notch sensitive (σ n /σ un = 1/k t where k t is the stress concentration factor) and notch insensitive (σ n /σ un = 1 - d/w) criteria. The notched (open hole) strength of the laminates was predicted as σ n = P max /wt, where P max is the maximum load obtained from the load-displacement curves of the FE models. All data points were normalised by the unnotched laminate strengths given in Table 1. The PDM curves show good correlation with the experimental data except for the L3 and L6 lay-ups. Figure 3. Normalised Hashin criteria predictions and experimental data (Soutis & Fleck, 1990) for L1-L6 layups as a function of the hole diameter to width ratio (d/w), W = 50 mm. 5

6 ACM2015 The test data for the L6 lay-up are located closer to the notch insensitive curve in which the strength reduction is directly proportional to the cross-section reduction. This is due to the dominance of the ±45 layers which reduce the stress concentration factor (k t = 2.51). In contrast, stress concentration is higher for the L3 lay-up (k t = 5.02) and the data points are closer to the notch sensitive curve. The FE curve for the L3 lay-up shows a sharp kink between the 8 and 10 mm holes due to its highly orthotropic nature. The net section stress for that particular lay-up reaches a critical point at a certain hole diameter (which corresponds to 10 mm) where more elements satisfy fibre tensile failure criterion simultaneously as a result of the high shear stresses (see Table 4). The more elements fail at a certain displacement increment, the lesser the stress concentration around the hole boundary. Therefore, higher strengths were predicted for the models with 10 and 15 mm holes (d/w = 0.2 and 0.3). 5 Conclusions The open-hole compressive strengths of various multidirectional laminates were predicted by the PDM approach once the FE model parameters were determined for the selected reference lay-up and hole diameter. Hashin criteria were implemented for the damage onset prediction while the propagation of the damage was simulated using damage mode dependant stiffness degradation factors. As expected, better predictions were obtained for the laminates with a closer orthotropy level to the reference laminate. The accuracy of the cross-ply (L3) and ±45 dominated (L6) lay-up predictions can be improved by adjusting the modelling parameters for each lay-up itself. Additionally, nonlinear shear stress/strain behaviour has an important influence especially for highly orthotropic laminates which was not taken into account in this study. References ANSYS Academic Research, Release Eriksson, Ingvar. (1991). Strength of notched and unnotched graphite/epoxy laminates loaded in compression. Journal of Reinforced Plastics and Composites, 10(3), Falzon, BG, Stevens, KA, & Davies, GO. (2000). Postbuckling behaviour of a blade-stiffened composite panel loaded in uniaxial compression. Composites Part A: Applied Science and Manufacturing, 31(5), Hashin, Z. (1980). Failure Criteria for Unidirectional Fiber Composites. Journal of Applied Mechanics, 47(2), doi: / Soutis, C. (1991). Measurement of the static compressive strength of carbon-fibre/epoxy laminates. Composites science and technology, 42(4), Soutis, C, Curtis, PT, & Fleck, NA. (1993). Compressive failure of notched carbon fibre composites. Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 440(1909), Soutis, C, & Fleck, NA. (1990). Static compression failure of carbon fibre T800/924C composite plate with a single hole. Journal of Composite Materials, 24(5), Soutis, C, Fleck, NA, & Smith, PA. (1991). Failure prediction technique for compression loaded carbon fibreepoxy laminate with open holes. Journal of Composite Materials, 25(11), Soutis, C, Smith, FC, & Matthews, FL. (2000). Predicting the compressive engineering performance of carbon fibre-reinforced plastics. Composites part A: applied science and manufacturing, 31(6), Waddoups, Mo E, Eisenmann, Jo R, & Kaminski, B Eo. (1971). Macroscopic fracture mechanics of advanced composite materials. Journal of Composite Materials, 5(4),