G. Kardomateas - Academia.edu (original) (raw)

Papers by G. Kardomateas

Fatigue cracks growing from micro-notches are used to obtain relationships between the standard d... more Fatigue cracks growing from micro-notches are used to obtain relationships between the standard deviation of crack growth rates, the crack length and the number of grains intersected by a crack front. The growth of micro-cracks on smooth surfaces is also considered. It is suggested that the crack population may be represented by bi-modal distributions consisting of propagating cracks and non-propagating cracks. An experimental procedure for separating the two distributions is proposed.

International Journal of Fracture, 1994

The stability of growth of intemal delaminations in composite plates subjected to compressive loa... more The stability of growth of intemal delaminations in composite plates subjected to compressive loading is investigated. Due to the compressive loading, these structures can undergo buckling of the delaminated layer and subsequently growth of the delamination. The study does not impose any restrictive assumptions regarding the delamination thickness and plate length (as opposed to the usual thin film assumptions). The growth characteristics of the delamination under monotonic compressive loading are obtained on the basis of a combined delamination buckling/postbuckling and fracture mechanics mode.I. The postbuckling solution is derived through a perturbation procedure, which is based on an asymptotic expansion of the load and deformation quantities in terms of the distortion parameter of the delaminated layer, the latter being considered a compressive elastica. The closed form solutions for the energy release rate at the delamination tip versus applied compressive strain during the initial postbuckling phase are used to define the combinations of delamination length and applied strain that lead to unstable growth. This would practically cause either contained "jump" growth or complete (catastrophic) growth of the delamination. Estimates for the lower and upperbounds of the jump distance (unstable growth) are provided. Moreover, a study of the influence of the mode dependence of interface toughness on the conditions of initiation and extent of delamination growth is performed.

AIAA Journal, 2015

The transient blast response of a sandwich panel that consists of a compressible core with in-pla... more The transient blast response of a sandwich panel that consists of a compressible core with in-plane rigidity using the extended high-order sandwich panel theory is presented and compared with elasticity closed-form solutions. The mathematical formulation of the extended high-order sandwich panel theory for the transient dynamic response of sandwich plates is described along with a numerical investigation. The extended high-order sandwich panel theory formulation takes into account the shear resistance of the core and its compressibility, which is envisaged through nonidentical displacements of the upper and the lower facesheets and its in-plane rigidity. The equations of motion and the appropriate boundary conditions are derived using the Hamilton's principle. A numerical investigation is conducted on a simply supported sandwich panel, and its results are compared with a benchmark elasticity closedform solution. The results include deformed shapes at the first millisecond at various time steps; displacements of the various constituents, as well as various stress resultants in the facesheets; and stress distributions within the core and at its interfaces with the facesheets. The extended high-order sandwich panel theory and the elasticity benchmark results correlate very well. Finally, a summary is presented and conclusions are drawn.

International Journal of Solids and Structures, 1990

Abstract The problem of obtaining the thermal stresses and displacements in an orthotropic ellipt... more Abstract The problem of obtaining the thermal stresses and displacements in an orthotropic elliptic cylinder (as can be produced by filament winding on a mandrel of elliptical cross-section) due to a uniform change in temperature, is formulated. The material properties are assumed to be independent of temperature and the anisotropy is referred to the coordinate system that is inherent to the geometry of the filament wound body. A displacement approach is used. Illustrative results are presented for the distribution of stresses and displacements in these orthotropic cylindrical tubes of elliptic cross-section and a comparison with the limit of circular hollow cylinders is made.

International Journal of Solids and Structures, 1991

The analytical solution for the stress field is derived for the case of a non-homogeneous curved ... more The analytical solution for the stress field is derived for the case of a non-homogeneous curved beam in the form of a segment of a plane circular ring fixed at one end and acted upon by a load at the other end. It is assumed that the beam possesses general anisotropy and that the elastic constants are linear functions (with two non-zero coefficients) of the radial distance. The solution is found in a series form with a complex stress function. Numerical examples for the distribution of stresses in comparison with the homogeneous orthotropic case are presented and the effect of the gradient in the elastic constants is discussed.

International Journal of Solids and Structures, 2004

This paper provides a method for obtaining the mixed-mode stress intensity factors for a bi-mater... more This paper provides a method for obtaining the mixed-mode stress intensity factors for a bi-material interface crack in the infinite strip configuration and in the case where both phases are fully anisotropic. First, the dislocation solution in a bi-material anisotropic infinite strip is investigated (the boundary of the strip is parallel to the bi-material interface). A surface distributed dislocation approach is employed to ensure the traction-free conditions at the strip bounding surfaces. Subsequently, the derived dislocation solution is applied to calculate the mixed-mode stress intensity factors of a crack located at, or parallel to, the interface in the bi-material anisotropic infinite strip. The crack itself is modelled as a distribution of the derived dislocation solutions for the strip. Results are presented and the effects of material mismatch, the length of the crack and the material interface on the stress intensity factors are investigated.

29th Structures, Structural Dynamics and Materials Conference, 1988

33rd Structures, Structural Dynamics and Materials Conference, 1992

The stability of equilibrium of a n orthotropic cylindrical shell subjcctcd t o external pressure... more The stability of equilibrium of a n orthotropic cylindrical shell subjcctcd t o external pressure is investigated. In this co~itext , the structure is considered a three dimensional body. T h c results show that the shell theory predictions can produce non-conservative results on the critical load of composite shells with moderately thick constructio~l. T h e solution provides a means of accurately assessing tlie limitations of shell theories in predicting stability loss. Introductioil A class of i11il)ortant structural applicatio~ls of fiberreinforccd composite materials involves the configuration of lanlinatcd shc~lls. Although thin platc co~istruction has been the tlir~lst of the initial applications, l i i ~ ~ l l attent,ion is now being p i d to configurations classified as moderately tllick sl1c.11 st,nlcturcs. S11c11 tlesigns call be used in co~nponents in the aircraft and autolriobile industries, as well as in the marine industry. Moreover. composite laminatf's have been considered in space vehicles in t h r form of circular cylindrical shells as a p r i~nary load carrying s truct l~re. In these light-1vl-c.ig11t shell structures. loss of stability is of p r i~nary concern. This snbject has been researched to-ilat,o through the application of the cylilidrical shcll t,lic~ory (c..g. Sirriitsrs, Shaw and S h e i n m x ~ , 1985). Honcl.sr, prcvious work (Pagano and \4%itliey. 1970; Pagimo. 1971 ) has sliowri that considerable care must be exc,rcisetl in applying thin shell theory formula t io~ls t o predict tllv response of composite rylinders. Besides tlic anisotropy, composite sliells h a w one other important t l is t i~lg~ishing fcat~lrc . namely extensionalto-shear 1llodl1111s ratio m ~ l r h largcr than that of their n ~ e t a l coulltcrpiirt s. 111 ort1c.r t o marc accurately account for the above rnrntioncd cffvcts. various niodificatio~ls in the classical theory of 1;lnlinated shells have generally been performed ( ~ I ' l ~ i t ~ i e ~ and Sun, 1974; Librescu, 1975; Reddy and Liu. 1965. scc also Noor and Burton, 1990 for a review of shear dcfor~nation theories). These higher order shell t11eoric.s can be applied to buckling problems with the potential of improved predictions for tlie critical load ( Aliastnsiadis, 1990). However, tlicsc, lias not yet been any effort to produce a n solutioli I~ascd on three-dimensional elasticity to the ~ x o b l s m of I)llrkling of composite shell structures, against wllicli results fro111 various shell theories could be compared. Towastls this ol>jcrtive, this work presents an elasticity solution to the problenl of buckling of composit? cylindrical ortliotropic shells subjected to external pressure. Colvright 0 1 9 9 2 113. the American Institute of Aeronautics and Astrouautics, Inc. All rights reserved, Formulatioil The equations of cquilibriu~n are taken ill t,erms of the second Piola-I posi t ic)~~. A perturbed posit,ion is de11otcd by where a is an infinitesimally small quantity. Here. C I U ~ ( T . 0. 2). 0 v I ( 7 . B . z ) . ( ~ ~ o l ( r . , 0 , 2) are the tlisplnccxmerits to which the points of tllv body must be s ~ ~ h j c r t c d to shift thenl from the initial position of eq~~i l ih r i~ l rn t o the new equilibrium position. The functions t ~ ~ ( r . 0 . z ) , c l ( r , 6 . z ) , w ~ ( r , 0 z ) are assilmed finite and cu is an infinitcsimally small ql~antity independent of r , 0. z . Following Kardo1ll;rtcas (1991), u7e obtairi the following 1)uc.kling cyl~atioris: ~, 111 t11v ~)rcviot~s equations, IT: and w" J are t , l ~ values of IT,, and d l at tllc initial cquilibrillrn position. i.e. for 11 = uo. 1 % = I." ant1 11% = q. and a:, and w(, arc: t,he values at tliv pr!rt~~rl)td position. i.e. for u = ul. 1 = 211 and 111 = 71.1 . The 1)01111<lary conditions associated with ( l a ) can ljr expressctl as: where f is the, tract icm vector on the surface wllicll hits outward unit norllii11 il = ( 1 ) m , 71 ) before any defor~natimi. Tlic tractioli v c ~ t o r tlcpcrids on the displaceiric.rlt fic.lc1 ? = ( 1 1 . 1.. 1 1 . ) . A~airl . following Iiardolnatcas (1991). U Y ~ o l ~ t a i ~ ~ and for thc lateral surfaces, i.e. for m = n = 0 and 1 = 1, c7:, + ~ : ~ d ; = O , ( 8 a ) Pre-bucklin,q State. The problem at hands is that of a hollow cylinder rigidly fixed at its ends and dcformed by uniformly distributed exter~ial pressure p (Fig. 1). The axially symmetric distribution of external forces produces stresses identical at all cross sections and dependent only on thc radial coordinate I-. In this manner the forces at the ends are distributed identically over both surfaces and rcduce to equal and opposite resultant forccs and moments. Let Rl be the internal and R2 the external radlus and set c = Rl /RE Lekhnitskii (1963) gave thr strcss ficld as follows: Fig. 1. Hollow cylintlvl 111lde1 ext(wla1 prcxssure We denote by r.,] the stlffne5s constants for the orthotropic constitut~vc behavior and by a,, the colnpli ance conc;tantc. i (. .

34th Structures, Structural Dynamics and Materials Conference, 1993

This paper presents a closed form solution for the initial postbuckling and growth behavior of de... more This paper presents a closed form solution for the initial postbuckling and growth behavior of delaminations in plates. The solution is derived with no restrictive assumptions on the delamination thickness and plate length, i.e. the usual thin film assumptions are relaxed. A perturbation procedure is used, based on an asymptotic expansion of the load and deformation quantities in terms of the distortion parameter of the delaminated layer, the latter being considered a compressive elastica. In addition to determining the load and mid-point delamination deflection as a function of the applied compressive displacement the analysis produces closed form expressions for the energy-release rate and the mixity ratio (i.e. Mode I1 vs Mode I) at the delamination tip. A higher Mode I component is found to be present during the initial postbuckling phase for delaminations of increasing ratio of delamination thickness over plate thickness, h/T (i.e. delaminations further away from the surface). Moreover, the energy release rate corresponding to the same applied strain is larger for a higher h/T ratio. The reduced growth resistance of these configurations is verifed by experimental results on unidirectional composite specimens with internal delaminations. Introduction Delaminations or interlayer cracks are developed as a result of imperfections in production technology or due to service loads which may include impact by foreign objects. As a consequence, structural elements with delaminations under compression suffer a degradation of their stiffness and buckling strength and potential loss of integrity from possible growth of the interlayer crack. Besides strength, delaminations can influence other performance characteristics, such as the energy absorption capacity of composite beam systems’. Delamination buckling in plates under compression has received considerable at tention and numerous contributions have addressed related issues in both onedimensional and two-dimensional However, although the critical point can be fairly well determined and has been extensively studied, limited work has focused on the postbuckling behavior, which ultimately governs the growth characteristics of the delamination. The one configuration most thoroughly studied is the one-dimensional delamination, consisting of a delamination in an infinitely thick plate. In this model2, which has also been called “thin film” model, the unbuckled (base) plate is assumed to be subject t o a uniform compressive strain. Closed form expressions for the energy release rate from the thin film model were derived by Chai et a12 by using the strain energy expressions before and after delamination buckling. The other configuration most extensively studied is the axisymmetric counterpart to the one-dimensional delamination, i.e. a circular delamination in a perfectly rigid supporting plate. The latter relates also to the socalled blister test used to determine adhesive and cohesive material properties. For this configuration, Evans and Hutchinson5 derived a formula for the energy release rate by using an asymptotically valid solution to the system of governing equations for small buckling deflections. Results for the energy release rate of a circular delamination were also given by Chai7 and calculated through a path-independent integral approach by Yin’. In the same context, Stordkers and Anderssong derived general potential energy theorems and associated bounds for composite plates within the kinematical assumptions usually attributed to von Karman, and studied in detail the efficiency of different analytical and numerical means for this circular delamination case. For delaminations in plates that cannot fullfil the “thin film” model assumptions, both the critical load and the post-critical behavior are expected to deviate from the predictions of Chai et al’. To this extent, Simitses et a13 studied the citical load for a delamination of arbitrary thickness and size in a finite plate. Their results showed indeed a range of critical load vs thin film load ratios, depending on delamination and base plate dimensions, as well as base plate end fixity (simplysupported vs clamped). Concerning the post-critical behavior of delaminations of arbitrary size, Kardomateas” provided a formulation for studying the postbuckling behavior by using elastica theory for representing the deflections of the buckled layer; this work resulted in a system of nonlinear equations rather than closed form expressions. In this paper, the initial postbuckling behavior of delaminated composites (with no restrictive assumptions on the delamination dimensions) is studied by using a perturbation procedure based on an asymptotic. Copyright 01993 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. 2679 expansion of the load and deformation quantities in terms of the distortion parameter of the delaminated layer, the latter being considered a compressive elastica.…

Scripta Metallurgica, 1986

t'll') 003~-9-JS!S6 53.00 • .00 COt)\'right (c1 1~lSl1 Pe:'gamol1 Press LtJ. oJD PLASTIC CRACK CR... more t'll') 003~-9-JS!S6 53.00 • .00 COt)\'right (c1 1~lSl1 Pe:'gamol1 Press LtJ. oJD PLASTIC CRACK CROInl1 Vol. lO, No. :J r, the apparent crack ductility mlty be found by usuming that the area 1I"r 1 of each parahola open~ up befort, arrival of th(' crack front, and th(' hiliance of the surface it> formed hy tilidinK off. Then Due to the difficulty in meuuring these quantities, only approximate estimations for D AC can be obtllined.

Solid Mechanics and Its Applications, 2011

Results from experimental studies using the debond test specimens introduced in Chapter 10, i.e. ... more Results from experimental studies using the debond test specimens introduced in Chapter 10, i.e. the double cantilever beam (DCB), tilted sandwich debond (TSD), cracked sandwich beam (CSB), single cantilever beam (SCB), three-point sandwich beam (TPSB), mixed mode bending (MMB), and double cantilever beam-uneven bending moments (DCB-UMB) specimens are discussed. Results of particular interest are the compliance and energy release rate,

19th AIAA Applied Aerodynamics Conference, 2001

The paper deals with the theoretical prediction of buckling loads for sandwich columns with metal... more The paper deals with the theoretical prediction of buckling loads for sandwich columns with metallic and laminated facings and foam or honeycomb core. The loading is a uniform axial compression, applied statically (very slowly) and suddenly with constant magnitude and inÿnite duration (step loading). The e ect of length and boundary conditions is assessed and results are presented for the following cases: for a cantilever column, a simply supported column and a clamped column, for several lengths. Several ÿber materials are used in the laminated facings. Two types of core were examined: alloy-foam or hexagonal glass=phenolic honeycomb. The facings are Boron=Epoxy, Graphite=Epoxy and Kevlar=Epoxy laminates with 0 • orientation with respect to the column axis and a metallic one made out of aluminum. These various materials are employed to provide comparative data that can be used in design. Results, for the static case are generated by computer codes as well as by the use of closed form theoretical solutions. For the dynamic case, results are generated by the DYNA3D code.

Recent Advances in Experimental Mechanics, 2002

The objective of the current paper is to present experimental data of interface cracks (delaminat... more The objective of the current paper is to present experimental data of interface cracks (delaminations) in layered Glass/Epoxy and Graphite/Epoxy composites under cyclic compressive (fatigue) and static (Mixed Mode Bending and Double Cantilever Beam) loads. The growth behavior ranges from self-similar growth along the interface in the unidirectional configuration to branching out of the interface in 90 deg. and cross-ply

Mechanics Research Communications, 1994

Journal of Engineering Materials and Technology, 1986

Asymmetries like welds or shoulders, may eliminate one of the two shear zones of symmetrically fu... more Asymmetries like welds or shoulders, may eliminate one of the two shear zones of symmetrically fully plastic cracked parts and thus give crack propagation along the remaining active slip band through pre-strained material instead of through the relatively unstrained region between two shear bands of the symmetric case. One thus expects a reduced ductility in the single shear band asymmetric case. A macro-mechanical analysis provides a physical basis for explaining the development of deformation in both geometries, as observed from tests on several alloys. The asymmetric case is approximated as Mode II shearing, with the crack extension occurring by sliding off along a single slip plane and fracture. In the symmetric Mode I case, the crack is assumed to extend by alternating shear on two symmetric slip planes and fracture.

Journal of Composite Materials, 2009

This article investigates the thermal response of an axially restrained composite column, which i... more This article investigates the thermal response of an axially restrained composite column, which is exposed to a heat flux due to fire. The heat damage, the charred layer formation and nonuniform transient temperature distribution in the column exposed to fire from one side are calculated by the thermal model developed by Gibson et al. [1]. For the thermal response analysis, the mechanical properties of the fire-damaged (charred) region are considered negligible, while the degradation of the elastic properties with temperature in the undamaged layer (especially near the glass transition temperature of the matrix) is accounted for using experimental data for the elastic moduli. Due to the nonuniform stiffness distribution through the thickness and the effect of the ensuing thermal moment, the structure behaves like an imperfect column, and responds by bending rather than buckling in the classical Euler (bifurcation) sense. Another important effect of the non-uniform temperature is that the neutral axis moves away from the centroid of the cross-section, resulting in an additional moment due to eccentric mechanical loading, which tends to bend the structure. The compressive behavior of a column subjected to simultaneous high intensity surface heating and axial compressive loading was investigated experimentally to verify the anticipated theoretical response. All specimens exhibited bending and subsequent catastrophic failure, even at compressive stresses well below these corresponding to the Euler load.

Journal of Applied Mechanics, 1988

Journal of Applied Mechanics, 1993

The initial post-buckling and growth behavior of delaminations in plates is studied by a perturba... more The initial post-buckling and growth behavior of delaminations in plates is studied by a perturbation procedure. In this work, no restrictive assumptions regarding the delamination thickness and plate length are made, i.e., the usual thin film assumptions are relaxed. The perturbation procedure is based on an asymptotic expansion of the load and deformation quantities in terms of the distortion parameter of the delaminated layer, the latter being considered a compressive elastica. Closed-form solutions for the load and midpoint delamination deflection versus applied compressive displacement during the initial post-buckling phase are derived. Moreover, closed-form expressions for the energy release rate and the mixity ratio (i.e., Mode II versus Mode I) at the delamination tip are produced. A higher Mode I component is found to be present during the initial post-buckling phase for delaminations of increasing ratio of delamination thickness over plate thickness, h/T (i.e., delaminatio...

Journal of Applied Mechanics, 1990

The stresses and displacements in the initial phase of applying a thermal load on the bounding su... more The stresses and displacements in the initial phase of applying a thermal load on the bounding surfaces of an orthotropic hollow circular cylinder are obtained using the Hankel asymptotic expansions for the Bessel functions of the first and second kind. Such a load may be constant temperature, constant heat flux, zero heat flux, or heat convection to a different medium at either surface. The material properties are assumed to be independent of temperature. A constant applied temperature at the one surface and convection into a medium at a different temperature at the other surface is used to illustrate the variation of stresses with time and through the thickness in the initial transient phase.

Journal of Applied Mechanics, 1991

The term q2 was omitted in Eq. (14) of the 1989 paper and Eq. (11) of the 1990 paper, and this er... more The term q2 was omitted in Eq. (14) of the 1989 paper and Eq. (11) of the 1990 paper, and this error carried through in the remaining of the equations, which otherwise are correct. To account for this error, replace d4,, and d5,, in these equations (e.g., Eq. (14) of the 1989 paper and all equations thereafter that involve d4,, or dSn) by d4,1q2 and dsr,q2, respectively, as well as replace ql by q,/q2 and q3 by q3/q2.