bending effect analysis of metallic z pins on mode i



  1. 18 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS BENDING EFFECT ANALYSIS OF METALLIC Z-PINS ON MODE I DELAMINATION TOUGHNESS OF DCB SPECIMEN S.L. Zhong 1& , L. Tong 2 * 1 Chengdu Aircraft Design and Research Institute, Sichuan Province, P.R. China, 2 School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW 2006, Sydney, Australia * Corresponding author ( ) Keywords : delamination, toughness, z-pinning, DCB specimen virtual crack closure technique (VCCT) is used to 1 Introduction  calculate mode I strain energy release rate (SERR) at the crack tip. Some numerical results are presented Composite materials have gained their acceptance among structural engineers during the last decades. and discussed and shown to be in agreement with In recent years, a substantial amount of airframe existing experimental and numerical results. research has focused on developing advanced composites for use as heavily-loaded primary 2 Basic Model and Concepts structures such as wing, fuselage and empennage components for both commercial and military Consider a DCB specimen reinforced with discrete z-pin rows as shown in Fig. 1. The total length, aircraft [1]. width and thickness of the DCB specimen are L , B Delamination is an important failure mode in laminated composite structures due to their low and 2 H , respectively. Each row may have more than one z-pin dependent on the z-pin area density and interlaminar fracture toughness. Through-thickness the pitch distance d p between the z-pin rows along reinforcements, such as z-pinning, stitching, 3D the crack extension direction. The initial crack is weaving and braiding, can remarkably delay and/or created in the laminate mid-plane with length a 0 . resist delamination propagation in laminates [1-13]. The distance of the initial crack tip to the first row of Z-pinning technology has emerged in 1990s as a the z-pins is denoted by a s . With an increase in the practical and cost-effective method in improving crack opening displacement δ and the induced delamination resistance and already has shown a external load P , the crack propagates along the mid- variety of potential applications in engineering plane. When the delamination crack propagates into structures. the z-pinned zone, the z-pins in the crack wake will According to Freitas et al [6], short z-pins can be carbon and glass fiber, titanium, stainless steel or exert the bridging traction loads and bending moments to limit the creation of delaminated crack aluminum etc. For fibrous pin at larger deflection, surfaces. Thus a higher external load, compared to the fiber tow can be split in the form of micro cracks running parallel to the fibers within the pin. The an un-pinned case, is developed in further crack propagation. Therefore z-pins can improve the strands formed by splitting slide relative to each delamination toughness of composite laminates. other to accommodate large shear strain, which limits the magnitude of bending moment carried by The basic assumptions for developing the axial force-displacement relationship are similar to that the tow [7]. In contrast, metallic pins can have presented by Jain and Mai [4] for independent relatively higher bending resistance than fibrous ones. Therefore it is important to study the effect of through-thickness stitches. It is assumed that the z- pin is circular cylindrical and the bond between bending moments reacted by a z-pin within crack matrix and z-pin is completely frictional. The bridging zone on crack growth resistance [11]. deformation in the matrix is assumed to be In this paper, a new discrete analytical model for negligible. The frictional shear stress at the matrix- metallic z-pin is presented to consider the traction pin interface is also assumed to be a constant value. loadings combining the axial force and bending In this paper the effect of fiber abrasion or matrix moment of the z-pin. Geometrical and material crumbling during z-pin stretching, bending action nonlinearity of the z-pin model are taken into and pull-out is neglected. No z-pin breakage occurs account in the bending moment calculation. The which is usually the case in mode I delamination of DCB specimen with small thickness and  This work was conducted during the period as a visiting independent z-pinning reinforcements. scholar at the University of Sydney.

  2. The Timoshenko beam theory is used to consider the usually be found in Ref. [14]. This relation applies effect of the shear deformation of the delaminated primarily to metallic material of work harden type. substrate. That assumes constant rotations of the The maximum extensibility ratio r for nonlinear cross sections for shear load with a shear elastic material of work harden type is given by deformation coefficient considered in the calculation n    d H 2   of the shear deformation of the beam. When   f r (5)     n 1 A considering the shear deformation of the substrate at   f 0 the crack tip, the zero slope of the substrate 3.2 Analytical Beam Model of Z-Pin deflection curve, which is imposed in this study, will result in rotation of the cross section plane of the Due to symmetrical assumption in Section 2, an substrate at the crack tip. analytical beam model between the crack plane at A simple analytical z-pin model with the span from end A and the centroid of delaminated arm B at z-pin the centroid axis of the substrate to the assumed row location is provided to develop the traction symmetrical delamination plane is developed in the force and bending moment of a single z-pin to the derivation of the bending moment reactions of the z- delaminated arm as shown in Fig. 2. The rotation at pins to the substrate. The local elastic deformation in end B is denoted by ψ r which is the rotation of the the matrix due to bending reaction of the z-pin is cross section of the delaminated arm at a z-pin row assumed to be negligible. In order to consider the location. The rotation at end A is zero due to elastic-plastic behavior of the metallic pin which symmetry. The span of the z-pin model L r is may happen in bending action, a nonlinear stress- approximately the sum of deflection w r and half the strain power law of the z-pin material is employed thickness of the delaminated arm. The symmetrical constraining tensile force T and bending moment M A are applied at end A . For 3 Modeling of a Metallic Pin equilibrium of the force system, the sum of the 3.1 Axial Forces-Displacement Relation of Z-Pin constraining forces at end A and B should be zero. The internal force T and bending moment M B at end The axial force-displacement relation for the pull- B are schematically shown in Fig. 2. Neglecting the out of a single z-pin is based on frictional model [4]. uneven pressure at the interface of the matrix-z-pin The axial force in the z-pin can be written as   due to rotation ψ r in obtaining the axial force F of         F d YU ( ) ( H S )( 1 U ( ) U ( ) (1) f 1 1 2 the z-pin in Section 3.1, the resultant force T at end where B can be considered as the sum of the axial force F   H and the uneven normal pressure acting on the z-pin            2 H ln 1 r 1 r   1 f cylinder, i.e. T = F /cos ψ r . From Fig. 2, the bending  r  (2) moment at a location x on the central axial of the     H 2 f beam is and τ is the frictional shear stress at the matrix-z-pin     M ( x ) M T ( y ) (6) interface. d f is the diameter of the z-pin, δ f is the B v For a uniform circular cross-section Bernoulli-Euler crack opening displacement at the z-pin location. beam of non-linear elastic Ludwick type materials, U ( ξ 1 ) and U ( ξ 2 ) are the Heaviside step functions. assuming that the average axial tensile strain is small The extensibility ratio r is defined as compared to the maximum bending strain, the  d H  f nonlinear differential equation for the deflection of r (3) A E the z-pin beam model is given as follows: f f   where A f and E f are the cross-sectional area and the n y M  (7) Young’s modulus of the z-pin, respectively.   ( 1 y 2 ) 3 / 2 K n To consider the nonlinear behavior of bending   n n where K I , and I f can be obtained by moment of metallic z-pin, a simple non-linear n 0 f material model is employed and the stress-strain law  ( 3 n 1 ) / n  d   2 n    f is represented by the Ludwick relation, i.e. I (8)   f  3 n 1 2      0  1 / n (4) and d f is the diameter of the z-pin, coefficient β can where σ is the stress, ε is the permanent or elastic be determined by the following integral: small strain at a point of a cross section of the beam,    n 1   and σ 0 and n are given material constants which can     sin d (9) n 0


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