Jan L. Teply

Bounds on overall instantaneous properties of elastic-plastic composites

Abstract M inimum principles of plasticity are used to derive upper and lower bounds on ordered eigenvalues and on diagonal terms of instantaneous stiffness and compliance matrices of elastic-plastic composite aggregates subjected to uniform overall stress or strain increments. The method is implemented with the help of a periodic model of binary fibrous composites ; overall properties are derived from incremental solutions of an inclusion problem in a small unit cell. Actual results are found with displacement and equilibrium formulations of the finite element method. In this implementation the instantaneous properties of the inelastic phases of the composite are known only in terms of the approximate values calculated at each step, hence the bounds are valid for an aggregate in which the actual properties have been replaced by the approximate ones. Examples are presented for the fibrous B-A1 system. The technique can be used to evaluate instantaneous element properties in a finite element program for analysis of metal matrix composite structures.

General two-dimensional theory of laminated cylindrical shells

The theory accounts for a desired degree of approximation of the displacements through the thickness, thus accounting for any discontinuities in their derivatives at the interface of laminae. Geometric nonlinearity in the sense of the von Karman strains is also included. Navier-type solutions of the linear theory are presented for simply supported boundary conditions

A Unified Formulation of Micromechanics Models of Fiber-Reinforced Composites

In a micromechanics constitutive model the overall instantaneous properties of fibrous composites are defined by relations between overall stress and strain averages. Such averaging techniques are also known as ‘homogenization’. The models may account for fiber, matrix and fiber-matrix interface properties and their interactions (see [1–5]). Various micromechanics approaches are used to calculate overall stress and strain fields using different representative micro-geometries (i.e. unit cells); see, for example, the self-consistent method of Hill [1], the variational formulation of Hashin [2], the vanishing fiber diameter model of Dvorak and Bahei-El-Din [3], periodic rectangular array of Aboudi [4], and the periodic hexagonal array (PHA) model of Teply and Dvorak [5]. Although various models use different representative geometries of the unit cell and different approximations of the displacements and/or stresses to obtain the overall properties, they all share certain common basis. The present paper has the objectives of finding the common basis so that the models can be related to each other.

Thermomechanical stress fields in high-temperature fibrous composites. I: Unidirectional laminates

Abstract This two-part paper presents a closed-form procedure for evaluation of estimates of local thermomechanical stress fields in two-phase fibrous composites and laminates. The first part is concerned with a unidirectional elastic laminate subjected to uniform mechanical loads and to uniform changes in temperature. Both phases are assumed to be elastic, with temperature-dependent moduli and expansion coefficients; the solution reflects the influence of thermomechanical interactions. Exact solutions are not possible for any real system, because the local geometry is not known in detail. Instead, estimates of the fields are found from a modified Mori-Tanaka approximation. Examples are presented for two SiC/TiAlNb composites. Local stresses of interest are found after cooling from fabrication to room temperature. The presence of local yielding, and the influence of coupling terms on the local stress magnitudes are examined. Extension of the results to laminated plates is presented in Part II (Dvorak, G.J., Chen, T. & Teply, J., Composites Science and Technology, 43 (1992) 359–368, this issue).

Bending, vibration and stability of arall® laminates using a generalized laminate plate theory

Abstract A plate bending element based on the generalized laminate plate theory (GLPT) is used to evaluate new composite laminates known as the ARALL-1 ® Laminates. The plate finite element accounts for the transverse shear deformation and layer-wise description of the displacements. The finite element is used to evaluate the stresses, vibration and buckling characteristics of 2/1 and 3/2 ARALL Laminates.

Thermomechanical stress fields in high-temperature fibrous composites. II: Laminated plates

Abstract The results of Part I of this work are extended to laminated plates. It is assumed that the plates are, at most, macroscopically orthotropic, and that they are subjected to a uniform change in temperature and to in-plane mechanical loads. Average stresses and microstress fields are evaluated in each layer of the plate. Failure envelopes based on critical magnitudes of interface and axial matrix stresses are constructed for one of the SiC/TiAlNb systems of Part I.