The Effect of Film Thickness on Coated Glass Response under Spherical Impact

Transcription

1 11 The Effect of Film Thickness on Coated Glass Response under Spherical Impact Dae Sik Jung 1 Kook Chan Ahn 2* and Bong Hwan Kim 3 1 Graduate School Department of Automotive Engineering Gyeongnam National University of Science and Technology Jinju KOREA 2 3 Department of Automotive Engineering Gyeongnam National University of Science and Technology Jinju KOREA kcahn@gntech.ac.kr Abstract Impact on coated system like exterior window film for screen protection and outside weatherable film caused by a foreign object can create internal damage that reduces the strength of the structure significantly. The effect of film thickness on the monolithic glass coated exterior window film is studied by the use of the coded finite element program. To model and predict the impact response of both the monolithic and coated glasses an approach based on the Sun's higher-order beam finite element and Kurapati's generalized power law is proposed. The impact responses such as the time histories of contact force deflection impact energy ball velocity and variation of stress through the thickness regarding change of film thickness of coated glass are compared with each other between the monolithic and coated glass system with the same total glass thickness. Consequently it may be concluded that the existence of the film between the monolithic and coated system has significant effect on impact responses but the variation of the film thickness in coated system does not affect so much. Keywords: Monolithic System (MS) Coated System (CS) Spherical Impact Exterior Film Finite Element 1. Introduction Coated system (CS) like exterior window film for screen protection and outside weatherable film is the perfect application for situations where physical limitation properties prohibit the installation of traditional indoor window film. Coated system has been developed for resisting blast and impact loading and the main purpose of the film is to provide absorption to the impact which puts less stress on the actual glass. When film coated system are subjected to an impact that caused by a sufficient heavy and fast impactor it will break. However unlike the monolithic system (CS) that fails in a brittle manner coated system can reduce the number of dangerous flying fragments as many fragments will be adhered by the film layer. Hence the risk of injuries of people can be significantly reduced. At the same time the film layer can act as a barrier avoiding penetration. Another advantage of coated system over monolithic system is that it is possible to reduce the weight of the glass of the same total thickness. Coated system has been increasingly used in applications such as vehicles aircraft buildings and electronic and protective coatings on engineering structures. The low load and low depth indentation has recently been used to characterize the mechanical properties of films and multilayers. In spite of their advantages however the efficient application of CS is limited because of the difficulties in their strength calculations at the stage of their design. Foreign object like a small stone thrown into the windows shall give an impact to architectural glass. For optimal design of CS that minimizes property damage is required a thorough understanding of the impact behavior of CS subjected to dynamic impact [1]. When material is applied to impact the elastic waves generated in the beam are short wavelength vibration modes. For this prediction Sun and Huang [2] suggested a higher order beam finite element with six degrees of freedom for the dynamic response of elastic isotropic beams subjected to impulsive loadings. This higher order beam theory showed to be more efficient than the conventional element with four degrees of freedom. During the impact the contact force F has been related to the indentation by Hertzian contact law [1] and the modified Hertzian contact law [3]. However when a coated thin film is deposited on a glass the deformation and stress field in the coated system becomes much more complex. The classical Hertz contact law is no longer valid in characterizing the contact force-indentation relation. In recent Kurapati [4] suggested that a generalized power law (load-displacement curve) in coated system vary with the film thickness and modulus. The validity of this generalized power law has been validated with the testing data generated from ABAQUS. The verification of the coded finite element program in conjunction with the modified Hertzian contact law and Kurapati's generalized power law has been already conducted by many published papers and their results showed good agreements with each other [5 6]. In this study a new finite element approach in conjunction with Sun's higher-order finite element and Kurapati s generalized power law as contact law is used to predict the overall impact responses on the MS and CS. The film and glass plies are modeled as linear elastic

2 12 and then the dynamic results such as the histories of contact force deflection impact energy ball velocity and variation of stress through the thickness regarding change of film thickness of coated glass during impact are obtained to study the effect of the film thickness between the MS and CS. From these results the impact behaviors of CS are compared with those of the MS with the same total glass thickness. And also the effect of the film thickness on impact response of CS is studied. 2. Theory and Formulation (2) where C=10^{C 0+C 1(log(E f/e s))+c 2(log(E f/e s)) 2 +C 3(log(E f/e s)) 3 } C 0= (h f/r) (h f/r) (h f/r) 3 C 1= (h f/r) (h f/r) (h f/r) 3 C 2= (h/R) (h f/r) (h f/r) 3 C 3= (h f/r) (h f/r) (h f/r) 3 and p=10^{p 0+p 1(log(E f/e s))+p 2(log(E f/e s)) 2 +p 3(log(E f/e s)) 3 +p 4(log(E f/e s)) 4 } p 0= (h f/r) (h f/r) (h f/r) 3 p 1= (h f/r) (h f/r) (h f/r) 3 p 2= (h f/r) (h f/r) (h f/r) 3 p 3= (h f/r) (h f/r) (h f/r) 3 p 4= (h f/r) (h f/r) (h f/r) 3 Fig. 1 Schematic diagram of spherical impact of Monolithic System (MS) and Coated System (CS). Consider MS and CS consisting of a single layer and multiple layers with glass thickness h s and film thickness subjected to transverse impact by a steel ball of radius with initial impact velocity as shown in Fig. 1. We assume a low velocity impact such that the glass ply does not fracture. The element displacement function is taken as (1) where is the transverse displacement and are constant coefficients. The three degrees of freedom at each node are the transverse displacement the rotation and the curvature k the coefficients in Eq. (1) can be replaced by the six generalized nodal displacements at the two end nodes and as a result the displacement function can be alternatively expressed in terms of the nodal displacements. where F and are the contact force indentation power and contact stiffness respectively. Eq. (2) indicates that for the indentation of any elastic filmglass system the resultant contact force-deflection response follows a general power law relation that is defined by the normalized film modulus and the normalized film thickness. In order to get numerical solution on the impact responses of MS and CS we adopt another equation of a generalized power law Newton's second law for the dynamic equation of the impactor and Newmark's integration scheme for solving the dynamic equations of the target and the impactor for each time step including the governing equation of this structures dynamic behavior by the Hamilton's principle. Similar simulating process is described in detail in Ref. [5 6]. 3. Finite Element Modeling It is applied to a generalized contact law that both loading and unloading process are treated as elastic because the glass is a brittle material. The beams are assumed to be impacted at the center by a steel ball impactor with diameter and initial impact velocity. The models are simply supported on both side edges. The material properties of target and impactor for simulation are shown in Table 1. For contact force and indentation relation a generalized power law [4] by fitting data generated using a wide range of film/glass properties is given as follows

3 13 Target Impactor Table 1: Material properties of target and impactor Materials Film Glass for simulation. Properties 4. Results and Discussion Fig. 2 shows the histories of contact force and deflection for MS with glass and CS with film and glass obtained from the present finite element analysis at velocity 10m/s. From Fig. 2 the maximum contact force for MS and CS occur at 15 and 255 and the contact durations at around 30 and 520 after the initial impact respectively. The maximum deflection does not occur at the maximum contact force. It shows a typical wave-controlled impact that the contact force and beam deflection are never in phase [7-9]. And also it can be seen that the maximum contact force in MS is about ten times larger than that of CS and the deflection in MS much larger than that of CS during impact but contact duration in MS is much smaller than that of CS. And we can see that the film thickness in CS has no significant effect on contact force and deflection for this low velocity impact. Relationship of contact force-indentation and deflectionindentation for MS and CS can be depicted by the curve shown in Fig. 3. The contact force is assumed to approach to elastic behavior in the unloading process after it passes the maximum value of the indentation in the loading process. From Fig. 3 it can be seen that the corresponding power p=1.5 of MS calculated by a generalized power law is consistent with the Hertzian equation but p= and 2.03 in of CS not consistent. We can see that contact law of two systems is dependent on existence of film from Fig. 3. And also contact stiffness of MS is much larger than that of CS This means that CS is much more impact resistant than MS. And we can see that the maximum deflection in of CS is a little larger than that in even though its quantity is very small. Fig. 2 Histories of contact force and deflection of MS and CS. Fig. 3 Relation of contact force-indentation and deflectionindentation of MS and CS.

4 14 Fig. 4 shows contact force-deflection curves on MS and CS at impact velocity. It shows that CS with the film thickness affects so much on the relation of contact force and deflection unlike MS without film. The numerical analysis results for impactor velocity and energy histories in two systems are given in Fig. 5. The energy and velocity at the time zero are the initial velocity and energy of impactor at which the impactor hits the target. Minimum kinetic energy in Fig. 5 occurs when velocity is zero. Velocity curves of Fig. 5 decrease and take negative values and remain constant by time. These negative values represent rebound velocity of the impactor. At these curves the lowest tip of the curve shows minimum kinetic energy and the end of curve that remains constant shows the rebound energy. And also the energy difference between initial energy and rebound energy becomes absorbed energy by target. Fig. 5 The energy and velocity histories of MS and CS. It can be seen that from Fig. 5 the rebounded energy and velocity of CS are larger than those of MS respectively. It can be considered that total thickness of CS is thicker than that of MS and film over glass is very soft and elastic properties. And we can see that the film thickness in CS has no significant effect on the rebounded energy and velocity. Fig. 4 Relationship of contact force and beam deflection of MS and CS. Fig. 6 Variations of stress through the layer of MS and CS at impact point and 30mm apart.

5 15 5. Conclusions A new effective finite element approach based on Sun's higher-order beam theory and Kurapati s generalized power law for the responses of MS and CS under spherical impact is proposed and simulated. The dynamic responses during impact event are additionally obtained and compared with each other between MS and CS with the change of film thickness for studying the effect of the film thickness. Fig. 7 Relationship of maximum in-plane stress and thickness of coated film on each layer of MS and CS. Fig. 6 shows the variations of stress through the thickness of MS and CS at impact point and 30mm apart from impact point. All stress components of MS in Fig. 6 vary linearly through the thickness whereas the variation of stress through the thickness of CS shows its discontinuity due to a significant difference in the material properties between film and glass. Hence film prevents glass of CS ( ) from damage by reducing stress to unlike those stress point and of MS at impact apart respectively whereas MS advances damage from impacted surface to opposite impacted surface rapidly. The maximum stress on impacted glass in MS occurs but in CS occurs on glass under impacted film. We can see that the maximum stress is right underneath the indentor in static analysis for soft film/ hard substrate [4] whereas for this dynamic analysis the value is observed at the interface of thin film and glass. Hence the interface is prone to more failure risk than the other layer of CS. Fig. 7 depicts relation of maximum in-plane stress and thickness of coated film on each layer of MS and CS. The maximum in-plane stress between MS and CS on the impacted surface S1 and the bottom surface S3 is shown a large difference whereas in case of CS the maximum in-plane stresses on S1 and S3 are approximately and independent of film thickness respectively. Hence it can be seen that maximum in-plane stress occurred by low velocity impact depends on the existence of coated film between MS and CS but the increase of film thickness in CS does not affect so much on impact stress. From the present numerical results we can see that a generalized power law applied is very effective on prediction of dynamic responses of MS and CS. Impact responses in MS is more sensitive than those of CS of the same glass thickness and prone to more failure risk. This means that film of CS may eventually be protected from impact damage and CS is more impact resistant than MS. In addition the maximum stress by this impact analysis is observed at the interface of thin film and glass that is the interface between two layers by low velocity impact is subject to more failure risk than the other layer. And also it can be concluded that the film thickness in CS has no significant effect on dynamic behavior under spherical impact of low velocity. References [1] W. Goldsmith Impact Edward Arnold Ltd [2] C. T. Sun and S. N. Huang "Transverse Impact Problems by Higher Order Beam Finite Element" Computers & Structures Vol pp [3] S. H. Yang and C. T. Sun Indentation Law for Composite Laminates ASTM STP 787 DOI: /STP28494S 1982 pp [4] S.N.V.R.K. Kurapati Y. C. Lu and F. Yang "Indentation Load-Displacement Relations for the Spherical Indentation of Elastic Film/Substrate Structures CMC (Computers Materials & Contina) 20(10) 2010 pp [5] B. H. Kim K. C. Ahn and C. W. Lee Low Velocity Impact Behaviors of a Laminated Glass Smart Science 2(4) 2014 pp [6] D. S. Jung and K. C. Ahn "Spherical Impact of Monolithic Glass Coated Exterior Film" J. of Korean Soc. of Mechanical Technology 17(1) 2015 pp [7] R. Olsson Closed Form Prediction of Peak Load and Delamination Onset under Small Mass Impact Composite Structures 59(3) 2003 pp [8] R. Olsson Analytical Model for Delamination Growth during Small Mass Impact on Plates Int. J. of Solids and Structures pp [9] Abrate. S. Modeling of Impacts on Composite Structures Composite Structures pp