Size Effects at Corners of Anisotropic Material Discontinuities

Reinforcement patches of composite laminates often possess corners due to design and manufacturing necessities. Hence, the patches reconstitute the demanded effective strength or stiffness in the region considered but at their boundaries also constitute a source for stress localizations. The complex potential method is a means for the investigation of such stress localizations. With the help of appropriate complex potentials the mechanical in-plane fields around the reinforcement corner can be expressed as series representations. A first analysis step is to obtain the exponents and corresponding modes which cause singular behavior of the membrane forces. Then, the determination of appropriately defined generalized membrane force intensity factors is used to show whether and how the singularity exponents are in effect. On this basis it is possible to deduce what impact a specific loading condition or the reinforcement corner's material combination and geometry have on the character of the singularity. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Interlaminar Stresses at Corners of Laminate Reinforcements

For inplane loaded plates the use of two laminate patches which are attached symmetrically to a base laminate with respect to the out-of-plane direction is a possibility to reinforce a highly stressed region. But corners at the patches' boundaries constitute a source for stress localizations. The expedient knowledge of the local mechanical inplane fields at such corners can be obtained with the boundary finite element method (BFEM). In order to investigate the intrinsically three-dimensional nature of the laminate corner setup the gradients of the inplane fields are readily evaluated since they are provided by the BFEM in a semi-analytical way. The interlaminar stresses inside the plate are retrieved by equilibrium considerations on a ply-by-ply basis. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Interfacial fracture of layered magnetoelectroelastic materials

A problem for an interface crack located in a layered magnetoelectroelastic material strip of semi-infinite length is solved. A closed-form solution is obtained for anti-plane mechanical and in-plane electric and magnetic fields. Explicit expressions for stresses and electric and magnetic fields, together with their intensity factors and the energy release rate, are obtained. The extreme cases of impermeable and permeable cracks are discussed. Using the basic solution for a single crack, solutions for two collinear interface cracks in an infinitely long layered magnetoelectroelastic medium, an interface crack in an infinitely long layered magnetoelectroelastic medium, and an edge crack at the interface of a semi-infinitely long layered magnetoelectroelastic medium are also obtained. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 2, pp. 145–164, March–April, 2008.     

An exact analysis for mode III cracks between two dissimilar magnetoelectroelastic layers

This paper develops a closed-form solution for an interface crack in a layered magnetoelectroelastic strip of finite width. The strip is subjected to anti-plane mechanical and in-plane electric and magnetic fields. Explicit expressions for the stress, electric, and magnetic fields, together with their intensity factors, are obtained for two extreme cases of an impermeable and a permeable cracks. The stress intensity factor does not depend on the electromagnetic boundary conditions assumed for the crack. However, the electrically and magnetically permeable boundary conditions on the crack profile have a significant influence on the crack-tip electromagnetic field intensity factors. Solutions for some special cases, such as a central crack, an edge crack, two symmetric collinear cracks, and a row of collinear interface cracks, are also obtained in closed forms. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 6, pp. 763–784, November–December, 2008.     

Estudio numérico-experimental de la interfaz hormigón-epoxi-FRP para una estructura reforzada sometida a doble corte

The strengthening of concrete structures with laminates of carbon fibers CFRP (Carbon Fibers Reinforced Polymer) began in the 1980's. Nowdays, this technology is one of the most promising one because of the good mechanical properties of laminates and their easy hand-work. Laminates are bonded to the concrete structure by means of epoxy resins. The load-carrying capacity of the strengthening depends directly on the proper behavior of the interface laminate-concrete. While the concrete is capable of transferring stresses to the laminate, this one becomes in charge and collaborates to the strength mechanism of the structure. The safety factor of the reinforcement can be guaranteed if we can predict the behavior at the interface between both materials. In this work we present a pure shear test and a simulation three-dimensional to characterize the behavior of the interface between the laminate and the concrete.     

Inplane Stress Singularities at the Corner of an Anisotropic Material Discontinuity

In the mechanics of composite laminates the local mechanical inplane fields at corners of anisotropic material discontinuities are of particular interest since they can have singular behavior. In the present study, the stress and strain fields in the local near field of such corners are investigated by an asymptotic analysis. The order of the singularity of these mechanical inplane fields are determined in closed‐form manner by use of the complex potential method based on Lekhnitskii's approach. Various different geometrical setups and material combinations of corners with material discontinuities are investigated with regard to their effect on the singular behavior of the mechanical fields present. These examples show that the order of singularity considered is clearly weaker than the typical crack tip singularity in fracture mechanics. Nevertheless, it may render the corner a critical location for the onset of failure. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonholonomic Mechanical Systems and Kaluza–Klein Theory

In the first part of the paper we present a new point of view on the geometry of nonholonomic mechanical systems with linear and affine constraints. The main geometric object of the paper is the nonholonomic connection on the distribution of constraints. By using this connection and adapted frame fields, we obtain the Newton forms of Lagrange–d’Alembert equations for nonholonomic mechanical systems with linear and affine constraints. In the second part of the paper, we show that the Kaluza–Klein theory is best presented and explained by using the framework of nonholonomic mechanical systems. We show that the geodesics of the Kaluza–Klein space, which are tangent to the electromagnetic distribution, coincide with the solutions of Lagrange–d’Alembert equations for a nonholonomic mechanical system with linear constraints, and their projections on the spacetime are the geodesics from general relativity. Any other geodesic of the Kaluza–Klein space that is not tangent to the electromagnetic distribution is also a solution of Lagrange–d’Alembert equations, but for affine constraints. In particular, some of these geodesics project exactly on the solutions of the Lorentz force equations of the spacetime.     

Numerical elastic-plastic simulation of interlaminar stresses in a notched angle-ply thermoplastic composite laminate

A thermoplastic angle-ply AS4/PEEK laminate with a hole is considered. The interlaminar stresses along the hole edge at different interfaces under uniaxial extension are investigated. According to the symmetries of the structure and loading, a suitable finite-element model is developed. Utilizing a three-dimensional elastic-plastic finite-element procedure elaborated previously, a finite-element modeling of the interlaminar stresses in a thick angle-ply composite laminate is carried out. Based on the interlaminar stresses obtained, the dangerous locations of delamination initiation are predicted. The results obtained indicate that there is some relationship between the dangerous locations and fiber orientations in the adjacent layers, and it maybe inferred that the critical locations are near the regions where the hole edge is tangent to the fiber orientation in the layers adjacent to the interface. The interlaminar stresses at the same interfaces are not sensible to distances from the midplane of the laminate. Very high interlaminar tensile stresses are found to exist on the hole edge at the +25°/+25° or –25°/–25° interfaces, and delaminations can initiate there first. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 3, pp. 427-440, May-June, 2009.     

Two-dimensional Green's function of orthotropic three-phase material under a normal line force with application in the design of composite

Green's function of orthotropic three-phase material is an important and basic problem in the study of mechanics of materials. It is also the foundation of further theoretical researches and engineering applications. Most of adhesive structures in engineering can be well simulated by the mechanical model of orthotropic three-phase material, such as composite laminate, integrated circuit (IC) packaging, micro-electro-mechanical systems (MEMS) and biomedical materials, etc. In order to understand the mechanical properties of the adhesive structure, a two-dimensional Green's function of orthotropic three-phase material loaded with a normal line force is presented. Based on the Green's function proposed in this paper, the stress field of adhesive structure under arbitrary normal loadings can be obtained with superposition method. Besides, this Green's function is convenient to be used in further studies, because it is expressed explicitly in form of elementary functions. Numerical examples are proposed to study the mechanical properties of the adhesive structure in five difference aspects: (1) the distribution rule of stress fields of the adhesive structure; (2) the influence from fiber orientation of composite to the stress fields of the adhesive structure; (3) the influence from elastic modulus of adhesive layer to the stress transfer of the adhesive structure; (4) the influence from the thickness of adhesive layer to the stress transfer of the adhesive structure; (5) the reasonability of spring interface model.     

Semiclassical Analysis for Magnetic Scattering by Two Solenoidal Fields: Total Cross Sections

The fact that vector potentials have a direct significance to quantum particles moving in magnetic fields is known as the Aharonov–Bohm effect (A–B effect). We study this quantum effect through the semiclassical analysis on total cross sections in the magnetic scattering by two solenoidal (point-like) fields with total flux vanishing in two dimensions. We derive the asymptotic formula with first three terms. The system with two parallel fields seems to be important in practical aspects as well as in theoretical aspects, because it may be thought of a toroidal solenoid with zero cross section in three dimensions under the idealization that the two fields connect at infinity in their direction. The corresponding classical mechanical system has the trajectory oscillating between two centers of fields. The special emphasis is placed on analyzing how the trapping effect from classical mechanics is related to the A–B quantum effect in the semiclassical asymptotic formula. Submitted: September 3, 2006. Accepted: January 10, 2007.     

Square and rectangular concrete columns confined by CFRP: Experimental and numerical investigation

The results of an experimental and theoretical investigation into the deformation behavior of CFRP-confined square and rectangular concrete columns under axial loads are presented. Three types of columns are considered: unwrapped; fully wrapped; and fully wrapped, with L-slaped steel angles placed at the corners. A mechanical deformation model for them is proposed, which is based on a nonuniform distribution of the stresses caused by the confining device. The results given by the model are in a good agreement with the experimental results obtained. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 3, pp. 417–442, May–June, 2008.     

The influence of water sorption-desorption cycles on the mechanical properties of composites based on recycled polyolefine and linen yarn production waste

The effect of water on the mechanical properties (tensile modulus, ultimate tensile strength, tensile strain, and specific work at break) of both chemically treated and untreated composites based on a recycled low-density polyethylene and linen yarn production waste is analyzed. It is found that three water sorption-desorption cycles change the tensile properties of both the materials irreversibly. This effect is considered as the result of partial fracture of the fiber-matrix interface. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 6, pp. 839–848, November–December, 2007.     

Thermally stressed state of an ellipsoidal inhomogeneity (inclusion) in the case of polynomial external force and temperature fields

The stress structure inside an ellipsoidal inhomogeneity (inclusion) is studied for polynomial force and temperature interactions of arbitrary order in an elastic isotropic medium. It is shown that with perfect mechanical and thermal contact between the phases, the stressed state within the inhomogeneity is also a polynomial in the cartesian coordinates whose order equals the maximum order of the polynomials for the external force and temperature fields. Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 30, pp. 67–76, 1999.     

Modeling the nonlinear deformation of composite laminates based on plasticity theory

The plasticity theory has been successfully used for describing the nonlinear deformation of laminated composite materials under a monotonically increasing loading. Generally, several tests are needed to determine the parameters of the plastic potential for a laminate. We explore an alternative approach and obtain the plastic potential by using theoretical considerations based on a laminate analysis. The model is shown to provide an accurate prediction for the response of a cross-ply glass/epoxy laminate under uniaxial tensile loading at different angles to the material orthotropy axes. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 3, pp. 309–318, May–June, 2007.     

Thermoelastoplastic deformation of complexly reinforced shells

The problem on the elastoplastic deformation of reinforced shells of variable thickness under thermal and force loadings is formulated. A qualitative analysis of the problem is carried out and its linearization is indicated. Calculations of isotropic and metal composite cylindrical shells have shown that the load-carrying capacity of shell structures under elastoplastic deformations is several times (sometimes by an order of magnitude) higher than under purely elastic ones; the heating of shells with certain patterns of reinforcement sharply reduces their resistance to elastic deformations, but only slightly affects their resistance to elastoplastic ones; not always does the reinforcement in the directions of principal stresses and strains provide the greatest load-carrying capacity of a shell; there are reinforcement schemes that ensure practically the same resistance of shells at different types of their fastening. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 6, pp. 707–728, November–December, 2006.     

CLT for linear random fields with martingale increments

In [V. Paulauskas, On Beveridge–Nelson decomposition and limit theorems for linear random fields, J. Multivariate Anal., 101:621–639, 2010], limit theorems for linear random fields generated by independent identically distributed innovations were proved. In this paper, which can be regarded as a continuation of the above-mentioned paper, CLT for sums of linear random field are proved in the case where innovations form martingale differences on the plane (that can be defined in several ways). In both papers, the so-called Beveridge–Nelson decomposition is used.     

Estimation of laminate stiffness reduction due to cracking of a transverse ply by employing crack initiation-and propagation-based master curves

The applicability range of toughness-and strength-based criteria for progressive cracking of a transverse layer in a cross-ply composite laminate subjected to tensile loading is considered. Using a deterministic cracking model, approximate relations for the crack density as a function of stress are derived for initiation-and propagation-controlled types of cracking. The master-curve approach is applied to progressive cracking in glass/epoxy laminates. The accuracy of estimation of laminate stiffness reduction by using crack density master curves is evaluated. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 5, pp. 633–646, September–October, 2008.     

Hydrodynamic limit for ∇φ interface model on a wall

 We consider random evolution of an interface on a hard wall under periodic boundary conditions. The dynamics are governed by a system of stochastic differential equations of Skorohod type, which is Langevin equation associated with massless Hamiltonian added a strong repelling force for the interface to stay over the wall. We study its macroscopic behavior under a suitable large scale space-time limit and derive a nonlinear partial differential equation, which describes the mean curvature motion except for some anisotropy effects, with reflection at the wall. Such equation is characterized by an evolutionary variational inequality. Received: 10 January 2002 / Revised version: 18 August 2002 / Published online: 15 April 2003 Mathematics Subject Classification (2000): 60K35, 82C24, 35K55, 35K85 Key words or phrases: Hydrodynamic limit – Effective interfaces – Hard wall – Skorohod's stochastic differential equation – Evolutionary variational inequality     

Modeling of cutting force prediction in machining high-volume SiCp/Al composites

Variations in cutting forces significantly influence the tool wear and part quality in machining high-volume SiC-particle-reinforced aluminum matrix (SiCp/Al) composites. Properties of the reinforcement SiC particles, such as size and volume fraction, contribute to the change in the cutting forces. This paper presents a cutting force model based on the geometrical and mechanical nature of the tool and workpiece, considering the effect of the SiC reinforcement particles. The cutting force is predicted as three components (F_z, F_x, and F_y) and the resultant cutting force F_τs. The cutting force was considered to generate three deformed zones: (a) shear deformed zone, (b) friction deformed zone on the chip–tool interface, (c) plow deformed zone. The effect of SiC reinforcement particles on friction deformed zone is analyzed emphatically. The friction force from friction deformed zone was obtained by calculating the sliding friction force and rolling friction force. To verify the feasibility and validity of the predicted model of cutting force, cutting experiments were performed with different combinations of cutting speed, feed rate, depth of cut, and tool nose radius. The predicted cutting force values demonstrate good agreement with the measured experimental cutting force values in most cutting conditions. The average percentages of the prediction error were 1.93%, 6.20%, and 10.48% for the F_z, F_x, and F_y components, respectively, thus proving the validity and accuracy of the predicted model of cutting forces.     

Statics, dynamics, and stability of composite panels with gently curved orthotropic layers. 2. Stability

Two approaches to the study of the stability of gently curved laminate structures are developed. The first approach is based on the analytical separation of variables. In the second approach, a polynomial approximation over the transverse coordinate is assumed. The loss of stability of such structures with various contact conditions for layers is examined. For Report 1, see Mech. Compos. Mater.,35, No. 4, 285–292 (1999). Ukrainian Transport University, Kiev, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 5, pp. 643–652, September–October, 1999.