Impact-induced damage analysis tools for laminated composites

Transcription

1 Impact-induced damage analysis tools for laminated composites U. Barberis*, A. Hassim*, C. Ravera* & G. Vanderborck* ^Ansaldo Ricerche s.r.l., Genova, Italy, ^Inria, Rocquencourt, France, ^Thomson Marconi Sonar, Sophia-Antipolis, France. Abstract The aim of the present work is to produce a validated set of design/analysis software tools called ADANIDEC, in the shape of finite element programs, for the selection and impact-induced damage evaluation of laminated composite structures for engineering design. The first part of this paper summarises our previous work[l] on the impactinduced damage analysis of laminated composites which includes: the formulation of material model, based on phenomenological continuum damage mechanics for a number of selected laminated composites, and experimental tests to evaluate the constants in the damage evolution law; development of algorithms and of a computer program to represent the above material models and their incorporation into the dynamic analysis codes using three-dimensional finite element techniques; # the design of a multi-level (component, lamina, laminate) material database to accumulate and to retrieve information on specific composite materials. A Graphical User Interface has been developed and pull-down menus lead the user to multi-level material selection from the database which when combined with the use of finite element based numerical tools enables the rapid identification of the optimum materials for a specific design. In the second part, the structural analysis scheme and the general view on the use of the ADANIDEC program is described. To illustrate the ability of the numerical procedure, the damage accumulation and the global displacement calculations for laminates subjected to local and global impact loads were performed and compared with experimental observations.

2 1 Introduction Advances in Composite Materials and Structures Vll Damage development in composite laminates under impact loading is a complicated process. Such damage which often are undetectable includes matrix cracks, fiber breakages, and fiber-matrix debonding. Although it does not to catastrofic failure, its presence causes stiffness reduction. Hence the studies of the initiation and of the growth of the matrix crack in composites laminates under impact have received considerable attention in recent years [2]. The objectives of the current work are : (1) to develop design tools capable of predicting the gradual development of damage in laminates composites subjected to low-velocity transverse impact, (2) to demonstrate the design tools by comparing numerical results with experimental tests, (3) to consolidate experimental and computational data by constructing a data base of constants associated with each damage model implemented into the design tools, (4) to interface this database with various structural dynamic codes. Because of the wide variety of compositions with which composites can be produced, it is difficult to produce a single material model that will faithfully reproduce the responses of all these composites, not even if they are all subjected to only one type of loading. We have chosen to concentrate on a few composite materials of immediate interest and to produce generic models for these composites. A programme of tests have been carrying out to characterize the composites under low rates of loading. To build up an understanding of the physical processes involved in the growth and accumulation of a variety of damage (e.g. fiber-breakage, matrix cracking, fiber-matrix debonding) in the composite test-specimens, the extend of damage has been assessed by visual and ultrasonic inspection both during and post-test. In order to be fitted to mathematical damage model, each layer of a laminate have been tested separately so that its elastic properties as well as the degradation of these properties are obtained. Thus a large number of tests have been performed on each material specimen involving loading and unloading loops to obtain the required information. These tests have been carried out to a very high standard. Formulations, based on Kachanov's concept [1, 3], have been produced, to simulate the observed experimental phenomena and to correctly model the underlying physical process that cause cumulative damage in the selected composite materials. The approach relates the damage parameters introduced to describe the collective effect of such cracks, to reductions of the elastic constants. The mathematics of these models is based on broad fundamental principles that allows the extension of these models to reasonably similar other composite materials. Global half sine acceleration using a free fall shock test machines as well as local acceleration using a height falling tower system have been imposed on composite laminate specimens and the consequent onset of damage have been investigated during the impact. The non-linear transient dynamic response of the same laminate specimen using the same test configurations have been performed by analytical and numerical methods.

3 Advances in Composite Materials and Structures I'll 2&3 Three-dimensional finite elements have been used to get accurate information for the transient stress and strain distributions through the laminate. Damage based on the above model have been investigated at any instant in the dynamic simulation. Experimental and parametric computational investigations of the nonlinear structural behavior have been compared. A database that contain the relevant elastic and damage-dependent properties of the materials and typical experimental results as well as the results of any analysis have been produced. This database has been interfaced with selected dynamic structural analysis codes. 2 Progressive damage modelling of composites Material models based on phenomenological continuum damage mechanics (CDM) approaches [3] have being developed and introduced in existing finite element code to predict progressive damage growth in laminated composites. These models are applicable at the layer scale : i.e. the laminated composite is divided in a stacked homogeneous plies and each layer is treated as a simple homogeneous (fictitious) material [4]. 2.1 Damage model of a single layer By damage is meant any reduction of the mechanical properties of the fictitious continuous material. Two non-observable damage variable d and d' with (d, d'} [0,1] are introduced in the constitutive equations of the fictitious layer to express the reduction of the elastic constants. Each damage variable varies from 0 (undamaged material) to unity (damage is complete). Evolution laws for the damage variables are obtained from phenomenological observations and the general framework of thermodynamics. The state of the material at a particular instant of time can be completely defined by the value of those internal variables at this instant of time. Described here is the damage model for a layer reinforced by unidirectional fibers and in what follow subscript 1,2, and 3 designate respectively the fiber direction, the transverse direction and the normal direction to the ply. The damage has little or no effect on E\ and 1/12 and : #2 = #2(l-d') ; z/21 = ^i(l-d') (1) ^2, z/2i? O^2 5 Oig are the values for the undamaged material. The other constants Ei,v-2i and G^ maintain their undamaged value. The elastic strain energy in the damaged state is : G23

4 904 Advances in Composite Materials and Structures Vll where the reduced values of the elastic constants have to be used, if necessary. The rate of change of this elastic energy is : " "~ dtrij V ' dd «r W = ij.ff\j + Yd. d + Y^. d' where : V -ew _ i r ^ _L f; J- d o j V ^ M^!_ (^22) + (4) are internal variables associated with damage in the same way as strain is associated with stress. They are expressed in Joules. <. >+ = 0 if (...) is negative, to take into account that the cracks close on compression ( "22 upon compression). Now define one more variable : Y(t) = supr<t ( (r) + b Y,, (r) ) (5) The symbol supr means that the highest value must be taken which r has taken at any time preceding the instant t. b is a material constant. Then the following equations are used to compute the value of the damage variables : d = <-~y >+ if d <1 and Y_ < Y, else d = 1 d' = <-~> >+ if d' < 1 and Y_ < Y',, else d' = I * c (6) YO, YC, YQ, YCJ b and Y/ are material constants of the layer : YO and Yj are threshold values, YC and Y^ represent damage toughness, 6 is a coupling constant of the material, and Y* is the breaking threshold value of the fiber-matrix. The identification of these constants can be carried out from tensile-tensile tests on laminates composed of several plies of the material concerned, with particular orientations of the plies [1]. The computation at the instant t of d and d' requires the knowledge of the stress at this instant. 2.2 Structural analysis formulation This damage evolution at the ply level have been implemented in the design software tool based on a three-dimensional finite elements method. Each layer were considered homogeneous and orthotropic. Because of the nonlinear nature of the damage-dependent constitutive equation, this analysis is performed in a stepwise manner [5]. Equations governing the dynamic response of a composite laminate subjected to transverse low-velocity impact loading can be derived by using the

5 Advances in Composite Materials and Structures 111 no<r principle of virtual work, which states for any compatible displacements the total internal work is equal to the total work done by external loads. Using the finite element formulations together with the principle of virtual work, yields the spatially discretized system of FE equations : [M}{U}n+i + [K(d,d')]{U}n+i = {F}n+i at time tn+i = (n+l)at (7) where [M] is the consistent mass matrix, [K (d, d')] is the nonlinear stiffness matrix, and [F] is the applied force vector. {U} is the vector of nodal displacement and the over-dot indicates differentiation with respect to time (acceleration vector). Using the Newmark's method for time integration [5], the nodal displacement solution / +! at time tn+i is obtained from : where l (8) (9) +! + [M] (^ {{/} + & {U}n + (U}n) 2.3 Structural analysis scheme The numerical solution of the above equations proceeds in the following steps (repeated at each time step) and illustrated in the following structural analysis scheme : First, calculate [K(d, d'}] and {F}n+i at time t + At from eqn (9). Once the value of [K(d, d')] and {F}n+1 is known, the displacement vector solution {[/} at time t 4- At is calculated from eqn (8), and the velocity and acceleration vector at time t -j- At are calculated from the Newmark scheme [5]. From the known displacements, transient dynamic strains and stresses within each layer as a function of time, are calculated. The damage evolution investigated and mechanical properties reduced appropriately, according to eqn (1,4,5,6). 3 The Adanidec software ADANIDEC software is a set of design/analysis tools for the selection and impact-induced damage evaluation of laminated composite materials for engineering design. Adanidec uses a multi-level (component, lamina, laminate) interactive database designed to accumulate and to retrieve information on composite materials. A Graphical User Interface have been developed and a pull-down menus lead the user to multi-level material selection from the database which when combined with the use of finite element based numerical tools enable the rapid identification of the optimum materials for a specific design.

6 286 Advances in Composite Materials and Structures 111 The ADANIDEC SOFTWARE consists of : a material database which contains for a number of composite laminates : (1) at the laminate scale : material description and typical experimental results and the predictions of any numerical analysis, (2) at the layer scale : effective properties, strengths, relevant damage parameters and experimental details, (3) at the component scale (whenever possible) : the moduli of the constituents (fiber, matrix) and the parameters describing the microscopic geometrical layout. a suite of software tools : (1) at the laminate scale : IMPACT to accurately predict the development of damage induced by low velocity impact in laminated composite and the associated strength reduction, (2) at the layer scale : CoMEP to compute the effective properties of a lamina when its construction is based on the component level and VISUA to compute and visualize stresses at component scale from averaged stresses in a finite element of a layer, and (3) to interface the material database with selected dynamic structural analysis code. 3.1 Execution of the adanidec program After Adanidec is invoked, a menu like the one in Figure 1 appears. Figure 1: Adanidec Multi-level Dialog Boxes The help button links with an hypertext version of the User Manual of Adanidec Software. The gen ^ar ray button generates spreadsheet file array.xls containing an array with materials in lines and properties in columns, to be used with Excel or any spreadsheet program. The three basic levels are laminate, lamina and component. Under each level, a new case study or a new simulation can be entered at any time or one can use a previously defined example. These examples can be saved at different levels and ready to be extracted as information for use elsewhere. Click on component button bring up the display like to the one shown for the lamina level (Figure 2). This is the most basic level where the material could be either fiber or matrix. This level in effect provides information to the lamina level where the construction of a lamina is based on the component level. The new menu asks for the designation, manufacture and material properties information. When the cursor is placed on the individual components button that are already existed in the database, a click

7 Advances in Composite Materials and Structures VII 987 provides direct access to the actual components properties. Click on lamina button produces a dialog box, like to the one shown in Figure 2. The new menu asks for the designation of the lamina, manufacture and effective mechanical properties and damage parameters. Figure 2: Lamina level When the construction of the lamina is known at the component level, The effective properties of the laminate may then be computed by using the software tool COMEP (button run simulation) based on a two-scale asymptotic homogenization [?]. Click on laminate button produces the dialog box, like to the one shown for components and laminates (Figure 2). The new command is particularly useful when constructing a new laminate. Along with the building-laminate, select the appropriate layer's name by clicking on it allows users to check material properties. After the laminate was specified, the next step is to make experimental tests or numerical simulation of impact on this laminate by constructing a new case study. The IMPACT software is invoked by a click on the Run simulation button which will transform the problem description to an input data file suitable for impact software. 4 Numerical and experimental examples The effective properties, strengths and damage parameters of the Glass Fabric Reinforced Epoxy (THsi] used in this study are : Mass Density p = 1905 Kgjrr? Young modulus E\ MPa ; E^ MPa Shear modulus Gi MPa ; Poisson's ratio 1/12 =.094 Damage variable % = 1326\/CPa) ; Yo = 56\/(Pa) ; 6 = l.e-3 Damage variable ^ = l.e + Gi/fPa) ; ^ = 0.\/(Pa) Ultimate tensile stress &IR = 515 MPa ; a^r 515 MPa Ultimate tensile strain SIR ; SIR = Local impact bend tests A height falling tower was employed for the low-velocity impact tests. The impactor used are steel cylinders with a tip radius of 10 mm. The impact

8 288 Advances in Composite Materials and Structures Vll measurement system includes an optical system which provides a signal from which the displacement of the impactor can be obtained as a function of time. The specimens (dimensions : 21 * 120 mm) made of 13 plies of THsi and of a total thickness of 3.5 mm, clamped on two opposite sides with a free span of 80 mm have been impacted. The plies orientations was (0 90 ) and the steel impactor mass, radius and initial velocity was respectively 100 g, 10 mm and 10 m/s. Numerous fine matrix cracks normal to the longitudinal direction of the specimen, have been observed near the impacted area, extending over one third of the thickness , Time (ms) Figure 3: Impactor Deflection (mm) -10 f 1 ~ " rime (ms) Figure 4: Impactor Velocity (m/s) 1600 a) impactor mass = 100 g Top layer HWIH-I -H b) impactor mass = 100 Bottom layer Q lime (ms) Figure 5: Contact Force (N) Figure 6: Damage d level

9 Advances in Composite Materials and Structures Figures 3 and 4 illustrate impactor deflection and velocity histories obtained from theoretical analysis (dotted line) and the experimental tests (solid line). Figures 5 illustrates the numerical and experimental contact force histories. Figure 6 show the isovalues of the damage parameter d. The map a) and b) show the level of damage parameter d on the top and the bottom layer (dmax 0.158). 4.2 Global impact bend tests The impact generation system for the global imposed acceleration is a free fall shock test machine which produces in our cases global half sine acceleration of amplitude 200 G to laminates (dimensions : 520 * 520 mm) made of 34 plies of THsi and of a total thickness of 8 mm, clamped on the four sides with a free span of 400*400 mm. Figure 7: Half Sine Acceleration Figure 8: Experimental strain _. 2, 4 6 Time (ms) Figure 9: Computed strain. Figure 10: Damage d level

10 9QQ Advances in Composite Materials and Structures VII Strain histories obtained from theoretical analysis and the experimental results at strain-gage location (center of the plate) have been compared. From the computed strain distributions across the laminate thickness, the damage initiation and progression during the shock have been predicted. Figures 7 and 8 illustrate experimental imposed global half sine acceleration and the strain response at gage location (center of top layer). Figure 9 illustrates the computed strain at gage location, and Figure 10 shows the level of damage parameter d (dmax = 0.131) on the top layer. 5 Conclusions Material model based on damage mechanics approaches have been developed to simulate the behavior of a number of selected composite laminates. A validated set of design/analysis tools called ADANIDEC, in the shape of finite element programs has been produced. ADANIDEC will be very useful to those concerned with the analyze and the prediction of the behavior of composite material. The experience so far accumulated in the Adanidec Material Database will help to reduce and optimize the number of tests to a minimum. It has great potential to expand and could be used as a storehouse of a vast amount of data concerned with composites. Acknowledgements The authors would like to acknowledge the support of the Commission of the European Communities (Brite Project BRE2-CT ). References [1] Hassim, A.; G. Vanderborck, G., Damage tolerance of laminated composites subjected to low-velocity impact, Proc. of the 68th Shock & Vibration Symposium,,, Baltimore, pp [2] Mackerle, J., Structural response to impact, blast and shock loadings. A FE/BE bibliography ( ), Finite Elements in Analysis and design, 24, pp , [3] Ladeveze, P., (D. Baptiste Ed.) Mechanics and Mechanisms of Damage in Composites and Multi-materials, Computational Mechanics Publications, Southampton and Boston, pp , [4] Hassim, A., Characterization of Composite Materials using a two-scale Asymptotic Homogenization Method, Proc. of the Conf. on Smart Structures and Materials, fevrier 1994) Orlando (Floride)- U.S.A. [5] Bathe, K.J, Finite Element Procedures in Engineering Analysis, Printice- Hall 1982.