COMPUTATIONAL MODELING AND SIMULATION OF LOW VELOCITY IMPACT ON FIBROUS COMPOSITE PANELS DROP_WEIGHT UN_PARTITIONED MODEL

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1 VOL. 4, O., PRIL 9 ISS 89-8 RP Journal of Engineering and pplied Sciences 6-9 sian Research Publishing etwor (RP). ll rights reserved. COMPUTTIOL MOELIG SIMULTIO OF LOW VELOCITY IMPCT O FIROUS COMPOSITE PELS ROP_WEIGHT U_PRTITIOE MOEL Umar Farooq and Karl Gregor epartment of Product esign and Engineering, Universit of olton, United Kingdom adalzai3@ahoo.co.u and.r.gregor@bolton.ac.u STRCT computational model was developed to simulate and predict failure response of fibrous composite panels subjected to drop-weight impact on un-partitioned fibrous composite panels using finite element analsis. The mathematical formulation consisting of constitutive, equilibrium, and strain-displacement relations; finite element formulation with contact and eternal forces; failure criteria proposed b Hashin. Finite Element Method (FEM) was chosen to perform simulation in commerciall available software US incorporating dnamic load in timedomain instead of using conventional analsis procedures of quasi-static indentation or drop weight model. To improve convergence, adaptive meshing techniques were emploed to mesh the regions of high stress gradient with fine meshes and coarse meshes for the rest. Results were compared with the results from the available literature and found to be in good agreement. However, some values of acceleration parameters were ver large. That was due to being computed from second order derivates, divided b ver small time step size produced such larger values. Therefore, a four-point moving average filter was applied to remove noise from the results. Some of the results from failure threshold loads were selected and included in the form of tables, contour plots and graphs. Kewords: finite element analsis, composite plates, failure criteria, delamination. ITROUCTIO dvanced fibrous composites are being used in man advanced structural applications. Man of these structures are situated such that the are susceptible to foreign object impacts and in-plane loadings which cause invisible etensive damage. The damage can significantl reduce load bearing capabilit or cause catastrophic failures. Thus there eists the need to investigate the incurred damage to be able to improve tolerance of structures. ue to the complicated interaction of different global, local and torsional bucling; damage mechanisms of fibre-matri de-bonding, matri cracing, fibre cracing, and de-lamination etc., no generall applicable methods for the analsis could have been established. Most of the available literature is eperimental with little discussion on local bucling. Some of the relevant studies are given below. The dnamic response of composite structures subjected to transient dnamic loading has been studied in terms of analtical, numerical (slan, 6) and eperimental wors (Krishnamurth, 3). Pierson and Vaziri (995) presented an analtical model based on the combined effects of shear deformation, rotar inertia and nonlinear Hertzian contact law with an aim of studing the low-velocit impact response of simpl supported laminated composite plates. Sun in (977) applied a modified Hertzian contact law to stud low-velocit impact response analsis of composite laminates. Yang and Sun (98) presented the eperimental indentation law through static indentation tests on composite laminates. Tam and Sun (98) developed their own finite element program to analze impact response of composite laminates and the performed impact tests using a pendulum tpe low-velocit impact test sstem. I Heon Choi and Cheol Ho Lim () proposed a linearized contact law in studing low-velocit impact analsis of composite laminates and compared it to the modified Hertizan contact law (983). sun and Chattopadha, obns (98) and Ramumar and Chen (983) emploed the first-order shear deformation theor developed b Whitne and Pagano (97) in conjunction with the Hertzian contact law to stud the impact of laminated composite plates. Sanar (98) presented a semi-empirical formula in predicting impact characteristics such as the pea force, the contact duration, and the pea strain on the bac surface of laminates. Ganapath and Rao () predict the damage in laminated composite plates and in clindrical/spherical shell panels subjected to low velocit impact. The continuit of the wor conducted b the authors Tibera et al. (5). Gaussian points via our numerical model, and then the failure criterion suggested b Choi and Chang () is used to predict matri cracing and delamination. Impact amage Resistance and amage Tolerance of Fibre Reinforced Laminate Composites were investigated b Ritz in his Ph thesis (James, 6). Tita, V., et al., reported eperimental and numerical approaches in their paper (Tita, 8); however the numerical approach uses fracture mechanics for failure mechanism and prediction. In the past most of the research on the topic has been eperimental. Most of the wor was focusing on 4

2 VOL. 4, O., PRIL 9 ISS 89-8 RP Journal of Engineering and pplied Sciences 6-9 sian Research Publishing etwor (RP). ll rights reserved. developing the phenomenological and the semi-analtical models b maing appropriate assumptions based on the eperimental observations. Therefore, a suitable computational model is essential to eploit the full benefits of the advanced composites. Hence, the problem was transformed into numerical model to obtain adequate, consistent and reliable results. Moreover, an incidental or drop tool ma not alwas impact the panel with a conventional hemisphere impactor, blunt-nozed object are also ver common. Therefore, results from blunt/flat noze shape impactor were selected. Governing equations for laminates From classical laminate plate theor, the etensional stiffness matri [] relates the in-plane forces {} to the mid-plane strains {ε o } and the bending stiffness matri [] relates the moments {M} to the curvatures {κ}. The coupling stiffness matri [] couples the in-plane forces {} with the curvatures {κ} and the moments {M} with the mid-plane strains {ε o }. Where ( ij ) h is the reduced stiffness for laer h, which is a function of the laer angle, θ h, and the laer in-plane orthotropic engineering constants, E s and ν s. Z h and Z h- are the Z co-ordinates of the top and bottom surfaces of the h laer respectivel. Considering a laminate made of "" laers (lamina) of thicness t arranged as shown below. The integral can be replaced b a summation over all laers. z z t / t z z t / t 3 t t 3 z z z z z Figure-: Laminate and plies la-up through-the-thicness stacing. Where is the laer number counting from the bottom up, is the number of laers in the laminate, and z is the coordinate of the top surface of the th laer. oth the mid-surface strains {ε o, εo, ε } and curvatures {K) are independent of z for the laminated plate, i.e., the midsurface strains are at the laminated plate mid-surface (z = ) and the curvature of each lamina is the same. For laminates the stresses can be written as: σ σ σ 6 σ 4 σ 5 = = ε ε γ 6 γ 4 γ 5 The following laminate stiffness equations are obtained: () M M M V V z z = H = H H H γ z γ z Where the, and coefficients are given b ij ε ε γ ( ij ) ( z z ) = ( ij ) t i, j =,, 6 = = = ( ij ) ( z z ) = ( ij ) t z i, j =,, 6 ij = = = ( ij ) ( z z ) = ( ij ) t z i, j =,, 6 ij = = = t ( ij ) ( z z ) = ( ij ) t z + i, j =,, 6 ij = 3 = = () 5

3 VOL. 4, O., PRIL 9 ISS 89-8 RP Journal of Engineering and pplied Sciences 6-9 sian Research Publishing etwor (RP). ll rights reserved. V V H H γ = ( 3 5 H 45 H55 γ ) 4 = t H + i, j = 4, 4 5 ij t t ij z = z t (3) Figure-: In-plane, out-of-plane, and uniforml distributed loads. Figure-3: Moments and uniforml applied eternal load. The summation of moments and forces in the z direction becomes: M M M w w w q (, ) = (4) When the load is not uniforml distributed and shape of the impactor is point load applied at centre (, ) then dirac delta function is, ) ( ) ( ) q( = P δ δ (5) nd for line and patch loads the Heaveside function will be used as follows. + α (, ) = P δ ( ) d δ ( ) α + β q d (6) β These equations represent equilibrium for a laminate subjected to transverse uniforml distributed, point and patch loading. The equations are valid for isotropic as well as anisotropic or composite panels for plies at various rotations. The principal of virtual wor The principal of virtual wor for the model sstem can be written as The dnamic equation is given b: Where [M] and [K] is, respectivel, the mass matri and stiffness matri of the composites, given b (7) (8) (9) Where 6

4 VOL. 4, O., PRIL 9 ISS 89-8 RP Journal of Engineering and pplied Sciences 6-9 sian Research Publishing etwor (RP). ll rights reserved. The interlaminar shear stresses are then determined From the following equilibrium equations: z σ z = + dz h () Where, () Hashin s failure criteria Interlaminar shear is one of the sources of failure in laminated plates. Since the interlaminar strength data are not usuall available, some of the researchers have suggested using z, = = Lt and tz = t. With the use of the present theor, these stresses were calculated as follows: z ( zz z z ) = ( σ zz z z dz σ ) () h Once the pl local stresses are nown, it will be used in the following interaction equation of Hashin: + F su 3 F su 3 3 = 3 Where F su3 and F su3 are the ultimate shear stresses, (3) umerical results and analsis The drop-weight model to predict the composites behaviour was implemented into US. Figure-4: Schematic diagram of specimen and impactor. Composite laminates of diameter.394 m, with stacing sequences [45//-45/9] S, [45//-45/9] S, and [45//-45/9] 3S the effect of impact duration, length and position on the impact loads were studied with.88 m thicness of quasi-isotropic configuration under centrall Located load of K impact at circle of.63 m diameter and length was. of aluminium was studied for various data input and stacing sequences and clamped boundar conditions. The properties of a unidirectional lamina of specimens with geometries and data are given in Table-. Material Properties GPa Table-: Material properties used to develop specimen. E = 5; E = E3 = 5 ( ) ult Ultimate strengths MPa T σ G = 5.7 G 3 = 5.7; G3 =7.6 ( ) ult Poisson's Ratios ν =.33; ν 3 =.3; ν 3 =. T σ ( ) ult C = ( σ ) = 5 ult C = 4 ( σ ) ult = ( ) ult = 53 = Stacing sequences [45//-45/9] S, [45//-45/9] S, [45//-45/9] 3S 7

5 VOL. 4, O., PRIL 9 ISS 89-8 RP Journal of Engineering and pplied Sciences 6-9 sian Research Publishing etwor (RP). ll rights reserved. Table- and Figure-5: Input data and stac of 4 un-smmetric plies. The circular dis and impactor were used in a clamped set-up under a load applied at the centre, shown in the Figure-6 below. Figure-6: Model after appling load and boundar conditions. Meshing using finite elements: (a) shell element S4 and (b) solid element C38 for impactor were created see Figure-7 below. Figure-7: Meshed specimen, impactor, and the model. 8

6 VOL. 4, O., PRIL 9 ISS 89-8 RP Journal of Engineering and pplied Sciences 6-9 sian Research Publishing etwor (RP). ll rights reserved. Given the fied pl thicness for the material results for acceleration, velocit, displacements, stresses and strains were computed. The time duration was considered. µsec for which amplitudes of velocities were used to impact the models. The predicted results were used in Hishon criteria and FPF was achieved with degradation of properties b the weight-drop. Computed values for accelerations were ver large and confusing as values were obtained from secondorder derivative, in such cases even rounding off numbers in the intermediate steps can lead to considerable errors in the final results. Therefore a four-point moving average filter was applied to remove and reduce the noise of computation errors. Table-3: Time versus amplitudes of velocities. Time Sec -3 Velocit -5 m/sec mp mp mp 3 mp 4 mp Runs Table-4: Runs for each amplitude versus computed results. cceleration X 3 m/sec isplacement X -3 m Velocit m/sec Strain X - Stresses GPa

7 VOL. 4, O., PRIL 9 ISS 89-8 RP Journal of Engineering and pplied Sciences 6-9 sian Research Publishing etwor (RP). ll rights reserved. Figure-8: Images of principal stresses in S directions. The images comparison demonstrates that the computation of the inter-laminar shear stresses and peel stress in the lins were realistic. Figure-9: Images of out-of-plane displacements. The images comparison demonstrates that the displacement values are within limits, according to the epectation and were realistic. Figure-: Images of principal strains in X directions. The images comparison demonstrates that the computation of the strain values were within the epected range and were realistic. 3

8 VOL. 4, O., PRIL 9 ISS 89-8 RP Journal of Engineering and pplied Sciences 6-9 sian Research Publishing etwor (RP). ll rights reserved. 3 Graphs Graph-: Graphics of displacements. The graphs comparison demonstrates that the computation of displacement values were realistic. Graph-: Velocities graphs. The graphs comparison demonstrates that the computation of the velocities were realistic. Graph-3: Graph of acceleration values. The graphs comparison demonstrates that the computation of the acceleration were realistic. COCLUSIOS The laminate stress and strength analsis under drop-weight model has been illustrated successfull. The model is capable to simulation impact phenomena of various noze shapes of impactors. However, simulations from flat noze shape impactors were selected. umerical predictions gave consistentl good results, which means that FE code and the panel models are adequate and reliable. Computed values of the principal stresses were compared with the allowable stresses against the given values and Hashin s failure criterion to predict FPF. The results matched and agreed well against the criteria as epected. If the load further increased the damaged areas further increase as well that ma lead to de-lamination growth and failure. In some cases, even rounding off numbers in the intermediate steps can lead to considerable errors in the final results. Therefore, great care was eercised in such calculations for accurate results. In general terms, the present stud has demonstrated the important contribution of blunt shape object/impactor resulting damage and response of composite panels. The predicted results can be used in design development as the have also validated the strategies of eperimental models. 3

9 VOL. 4, O., PRIL 9 ISS 89-8 RP Journal of Engineering and pplied Sciences 6-9 sian Research Publishing etwor (RP). ll rights reserved. REFERECES [] US Users Manual, Version 6.6, 6 US. Inc. [] slan Z., Karauza, R., and Outan. 3. The response of composites under low-velocit impact Compos Struct. 59. pp [3] obns.l. 98. nalsis of simpl supported orthotropic plates subjected to static and dnamic loads I J. 9. pp [5] Vaziri R., uan, X., and Oslon M Impact of composite plates and shells b super finite elements. Int J Impact Engng. 8(7-8): pp [] Whitne J.M. and Pagano.J. 97. Shear deformation in heterogeneous anisotropic plates SME J ppl Mech. 37. pp [7] Yang S.H. and Sun C.T. 98. Indentation law for composites m Soc Test Mater STM STP pp [4] James R.. 6. Impact amage Resistance and amage Tolerance of Fibrous Composites Ph thesis. Universit of olton, UK. [5] Krishnamurth K.S., Mahajan, P., and Mittal R. K. 3. Impact response and damage in composite clindrical shells. Compos Struct. 59. pp [6] Li C.F., Hu,., Yin, Y.J., Seine, H. and Fuunaga H.. Low-velocit impact damage of composites. Part I an FEM model. Comp. pp.55-. [7] Mili F. and ecib.. Impact behavior of crosspl composites under low velocities Compos Struct. 5. pp [8] aidu. V. S. and Sinha P.K. 5. onlinear finite element analsis of shells in hgrothermal environments Compos Struct. 69. pp [9] Pierson M.O. and Vaziri R naltical solution for low-velocit impact response of composites I J. 34. pp [] Ramumar R. L. and Chen P.C Low-velocit impact response of laminated plates I J.. pp [] Sanar.V. 99. Scaling of low-velocit impact for smmetric composites J Reinf Plast Compos.. pp [] Seine H., Hu,., Fuunaga, H., and atsume T., Low-velocit impact response of composite Mech Compos Mater Struct. 5. pp [3] Sun C.T n analtical method for evaluation of impact damage [8] energ of composites m Soc test mater STM STP. 67. pp [4] Tam T. M., Sun C. T. 98. Wave propagation in graphite/epo composites due to impact. SCR