STUDY OF DYNAMIC AND PERMANENT INDENTATION OF LAMINATES SUBJECTED TO - PDF document

18 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS STUDY OF DYNAMIC AND PERMANENT INDENTATION OF LAMINATES SUBJECTED TO LOW-VELOCITY IMPACT U Debo Liu UP * P , U Zhidong Guan U ,Wei He, Jun Wang School of Aeronautics Science and Engineering, Beihang University, Beijing 100191, China *liudebo@ase.buaa.edu.cn Summary A modified Hertzian Contact Law is validated with a new experimental technique using a Non-contact Vibration Measurement (NCVM). Moreover, the relationship of permanent and dynamic indentation is presented in this study, and a new computational method to predict the permanent indentation is developed, which proved to be effective. Keywords : Low-velocity impact; dynamic indentation; Permanent indentation; Contact law through static indentation tests on composite 1 Introduction laminated specimens and they presented the experimental static indentation law[4]. In order to Composite materials are now being used in primary aircraft structures, particularly in helicopters, light follow the approach, researchers needed to develop aircrafts, commercial planes and sailplanes, because their own finite element method (FEM) program. of their numerous advantages including low weight, Many new damage theories and analytical methods high modulus and strengths and the possibility of were established to simulate the damage evolution manufacturing large integral shell structures. process during the impact. However, a well-known problem with composite At present, the dynamic process of the indentation laminates is their poor resistance to accidental growth has been studied a lot by the simulation but impact by foreign objects. The resulting damage due rarely by experiment, because it was impossible to to impacts, often in the form of delamination, matrix observe the details between the impactor and the cracking and fiber failures, may severely reduce the laminates during impact test. Most contact laws are structural strength and stability[1]. Therefore, based on Hertzian/modified Hertzian contact law, considerable amount of research has been done in which was generalized from the static indentation the area of impact of composite structures. test. It is necessary to measure the dynamic changes The relationship between the indentation and impact of the indentation during the impact test to energy has been studied by many investigators[2]. It understand the damage evolution process better. is proved to be an effective method to evaluate the In the present study, firstly, a simplified method was internal damage by observing the indentation. introduced to measure the thickness changes of the Laminated composite panels with BVID (Barely laminates at the impact point during the experiment. Visible Impact Damage) are required to endure the Secondly, a modified Hertzian contact law was full DUL (Design Ultimate Load) in the strength raised based on the dynamic indentation. Thirdly, a criteria usually adopted in composite wing structure calculative method was developed to predict the design in civil aviation. BVID primarily considers permanent indentation. the depth of the permanent indentation. More exactly the depth of indentation after impact is 2 Experiment measured, more accurate evaluation of composite can be made, which provides a reference to the The dynamic indentation is defined as the changes design of composite structure. of the thickness where the specimen is impacted. In With the development of computer, many order to acquire the dynamic indentation, the calculative methods were raised to study the displacements of the impact side and backside of the formation of the indentation, which made it possible specimen should be measured. In the experiment, the to gain an insight into the damage theory of Polytec PSV-400 Vibrometer was used. The PSV- composites. In the simulation of the impact, Hertzian 400 can record the velocity history of the detected contact law has been widely used to calculate the point, then the displacements can be calculated from contact force between the impactor and the the integration of the velocities. The measuring laminates. In 1977, C.T. Sun proposed a modified system is shown in Fig. 1. The test equipment has a Hertzian contact law [3]. In 1981, Yang and Sun high degree of accuracy to ensure the repeatability experimentally investigated indentation phenomena among different specimens.

4 Laser Beam Backside of specimen 3 Guide Rail Impactor Flag 2 Velocity(m/s) 1 0 Impactor -1 -2 Specimen -3 0.000 0.001 0.002 0.003 0.004 0.005 0.006 Time(s) Fig.3 Velocities of impactor and specimen’s backside Laser Beam under 26J impact The histories of dynamic indentation with different impact energies were obtained by the displacements of both sides, which were calculated by integration of the velocities recorded by the PSV-400. The Fig. 1 Schematic illustration of velocity measurement relationship of the dynamic indentation and contact system force are shown in Fig.4 and Fig.5. As we can see, The specimens were T700/5428A laminates with the the dynamic indentation histories are similar to the stacking sequence [45/0/-45/90] R 4S R . Several of them contact force before large damage occurred. were used to detect the velocity of the impact side 0.4 8000 and the others were used to detect that of the Dynamic Indentation backside. The velocity of impactor before contact Contact Force Depth of Indentation(mm) was detected by the flag (shown in Fig.1) using a 0.3 6000 Contact Force(N) high speed data acquisition system. A comparison of the impactor’s velocity between the experimental 0.2 4000 result and the integration of the contact force was made which showed the correctness of the method. 0.1 2000 The velocities of the impactor and backside of the specimen are shown in Fig.2 and Fig.3. From the Figures, the velocities of both sides have a high 0.0 0 0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 accordance except that the backside has some Time(s) vibrations in the earlier stage of impact. Fig. 4 Contact force and dynamic indentation with the 4 impact energy of 17J Backside of specimen 0.5 10000 3 Impactor Dynamic Indentation Contact Force 0.4 8000 2 Depth of Indentation(mm) Velocity(m/s) Contact Force(N) 1 0.3 6000 0 0.2 4000 -1 0.1 2000 -2 0.0 0 0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 -3 Time(s) 0.000 0.001 0.002 0.003 0.004 0.005 0.006 Time(s) Fig. 5 Contact force and dynamic indentation with the impact energy of 26J Fig.2 Velocities of impactor and specimen’s backside under 17J impact

STUDY OF DYNAMIC AND PERMANENT INDENTATION OF LAMINATES SUBJECTED TO LOW-VELOCITY IMPACT  is the maximum indentation, and  3 Computation Where is m cr the critical indentation and it can be estimated by the In the computation, a modified Hertzian contact law has been used to analyze the relationship of the following equation [7]. contact force and dynamic indentation: Z h Loading [5]   c (5) cr E t  k  n (1) f In order to acquire the relationship between the Where f is contact force,  is indentation shown contact force and dynamic indentation, a new contact law was introduced from eq. (1), in which n in Fig.6, k is the contact coefficient, obtained from equals 1.4, k is 0.9×10 P 9 P N/m P 1.5 P calculated by eq. (2). experiments, but can also be approximately The test and fitting curves are shown in Fig.7 and calculated as Fig.8. 4 1 8000  k R (2) i      Imapct test 3 (1 2 ) / 1/ E E   Fitting i i t 6000  and Where R is the radius of the impactor, E i i i Force(N) are respectively the Poisson's ratio and the Young's 4000 modulus of the impactor, and E is the transverse t out-of-plane Young's modulus of the laminated 2000 composite. 0 0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 Time(s) Fig.7 Fitting curve with the impact energy of 17J 10000 Impact test Fitting 8000 6000 Force(N) Fig. 6 Quasi-static indentation with the bottom clamped 4000 Modified unloading [6] 2000   n     0 ( 3 )   f f    m   0 0 m 0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 Time(s) Where n equals 2.5 during the unloading period and Fig.8 Fitting curve with the impact energy of 26J  are equals 1.5 during the loading period, f and The fitting curves are similar with the test results in m m respectively the max contact force and the max the vibration mode and maximum force. Therefore it  indentation during one loading-unloading cycle, could be used in the dynamic analysis of laminates 0 subjected to low-velocity impact. is the depth of the permanent indentation caused by A simple computational method was summarized to  is given by the max contact force f . 0 m estimate the permanent indentation through the maximum contact force which could be obtained     0 m cr from a finite element analysis, in which the modified     2 5     Hertzian contact law was incorporated in the FEM   ( 4 ) 0        1  cr   program CIMPACT written in FORTRAN. The  m m cr         permanent indentation can be obtained from eq. (4), m in which the maximum indentation and critical 3