TOUGHNESS DETERMINATION IN COMPOSITE TOUGHNESS DETERMINATION IN - PDF document

18 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS TOUGHNESS DETERMINATION IN COMPOSITE TOUGHNESS DETERMINATION IN COMPOSITE MULTIMATERIAL CLOSED CORNERS MULTIMATERIAL CLOSED CORNERS D. Vicentini, A. Barroso*, J. Justo, V. Manti č , F. París. D. Vicentini, A. Barroso*, J. Justo, V. Manti č , F. París. Group of Elasticity and Strength of Materials, School of Engineering, Group of Elasticity and Strength of Materials, School of Engineering, University of Seville, E-41092 Seville, Spain. University of Seville, E-41092 Seville, Spain. * Corresponding author ( abc@esi.us.es ) * Corresponding author ( abc@esi.us.es ) Keywords : Toughness, Brazilian test, bimaterial corner, stress singularity. Keywords : Toughness, Brazilian test, bimaterial corner, stress singularity. Dempsey and Sinclair (1981), Ting (1997) and 1 Abstract Barroso et al. (2003). In the present work, a general procedure for the experimental evaluation of the generalized fracture Under some simplifying assumptions (e.g. toughness in multimaterial corners is defined. The neglecting the possible existence of logarithmic proposed method is suitable for closed corners (all terms) the series expansion for displacements and material wedges being bonded) having two singular stresses at a corner tip can be written in the terms in the asymptotic stress representation at the following form: corner tip. For a particular corner configuration, the method finds the load configuration at which one of n n            1  u ( r , ) K r g k ( ) , ( r , ) K r f k ( ) k k the singular terms vanishes, thus the main stress     k k   k 1 k 1 contribution being controlled by the other non-      r , (1) vanishing singular term. The experimental test, until failure, using the previously defined load configuration allows the generalized fracture where K k ( k =1,..., n ) are the Generalized Stress Intensity Factors (GSIFs),  k ( k =1,..., n ) are the toughness associated to each singular term to be evaluated. characteristic exponents (0<  k <1, 1-  k being the (  (  k k g ) f ) order of stress singularity) and and   The whole procedure has been applied to a ( k =1,..., n ) are the angular shape functions for bimaterial CFRP-Adhesive bimaterial corner and the k (  k (  g ) g ) displacements ( , ) and stresses generalized fracture toughness values have been  r obtained. The testing of mixed modes has permitted k (  k (  k (  f ) f ) f ) ( , , ), respectively. The   a failure envelope based on the generalized fracture rr r k (  k (  g ) f ) angular shape functions and have toughness values at the corner tip to be defined.   Previously published results, with different been normalized in the present work according to geometries, but involving the same corner, have Pageau et al . (1996). shown that the failure envelope can predict accurately the failure initiation at these corners. Unlike the well defined test standards for the experimental determination of fracture toughness 2 Introduction values for cracks in homogeneous isotropic materials ( K IC , and K IIC respectively for the The stress and displacement fields in the symmetrical and unsymmetrical cases), the lack of neighbourhood of linear elastic anisotropic symmetries in the stress fields in general multimaterial corners, assuming 2D elastic state and configurations of anisotropic multimaterial corners, considering a polar coordinate system ( r ,  ) centred makes difficult to develop a general procedure for at the corner tip, can be represented by an the generalized-fracture-toughness determination in asymptotic series expansion, with variable corners of this kind. separation, see Wieghardt (1907), Williams (1952),

shows a 90º wedge of a unidirectional carbon fibre k (  In this work, the evaluation of  k , g ) and  layer, with the fibre in the x direction, bonded to a k (  f ) is based on a general analytical procedure 270º wedge of adhesive. The bimaterial corner  configuration, shown in Figure 1b, will be the one proposed in Barroso et al . (2003) which applies for chosen for the application of the numerical linear elastic generalized plane strain states, without procedure and experimental testing. any limitation in the number and nature of linear elastic materials. The evaluation of K k is based on a In particular, the procedure consists in the numerical procedure (Barroso et al 2011), which has application of a compressive loading to a specimen proved to be accurate in most difficult cases with like the one shown in Figure 1b, at any generic multiple singularities. position of the external perimeter, and the evaluation of the corresponding generalized fracture toughness The aim of the present work is to propose a values of the two singular modes (critical values of general procedure for the generalized fracture GSIFs K 1 and K 2 ) for each loading angle  , which is toughness determination in 2D multimaterial anisotropic closed corners having two singular terms. schematically depicted in Figure 1c. With two singular terms, the evaluation of generalized fracture toughness K kC ( k =1,2) is based The experimental testing until failure at loading angles  1 (where K 1 =0) and  2 (where K 2 =0) on the possibility of isolating each singular term with a particular external load distribution. allow the evaluation of the critical values of K 2 and K 1 , respectively, which will be defined in what The procedure presented here is only valid for follows as K 2C (for the test at  1 ) and K 1C (for the closed corners (with all materials wedges perfectly test at  2 ). The evaluation of such values is obtained bonded, without any external boundaries, sometimes by substituting the experimental failure load in the referred to as cross-points) and is based on a novel linear elastic simulation of the Brazilian disk (by modified configuration of the Brazilian test means of a FEM model). geometry (introduced almost simultaneously by Carneiro, 1943, and Akazawa, 1943). The y multimaterial corner tip is placed at the centre of the disk and the disk is loaded in compression in the (a) x diametric direction at any generic point along the external perimeter, the procedure being obviously only valid for closed corners. adhesive adhesive 90º For a practical illustration of the procedure in Al 0º 0º the field of composite materials, it has been applied to a particular CFRP-epoxy bimaterial closed corner. y P The experimental results and failure envelope, based (b) (c) K 1  K 2 0º of critical values of the GSIFs, are also presented. x CFRP   2 Previously published results of different geometries adhesive  1 having, locally, the same corner configuration have P shown to agree with the predictions of the failure Fig. 1. Schematic representation of the procedure for envelope. isolating the singular terms. 3. Description of the test procedure 4. Application to a real bimaterial corner Figure 1a shows an example of an adhesively bonded joint between a composite laminate and an The previously introduced procedures will be aluminium plate containing three different applied for the bi-material corner shown in Figure multimaterial closed corners. In particular, Figure 1b 1b. The calculation of the orders of stress