C.T. Sun

Prediction of composite properties from a representative volume element

Abstract A vigorous mechanics foundation is established for using a representative volume element (RVE) to predict the mechanical properties of unidirectional fiber composites. The effective elastic moduli of the composite are determined by finite element analysis of the RVE. It is paramount in such analyses that the correct boundary conditions be imposed such that they simulate the actual deformation within the composite; this has not always been done previously. In the present analysis, the appropriate boundary conditions on the RVE for various loading conditions are determined by judicious use of symmetry and periodicity conditions. The non-homogeneous stress and strain fields within the RVE are related to the average stresses and strains by using Gauss theorem and strain energy equivalence principles. The elastic constants predicted by the finite element analysis agree well with existing theoretical predictions and available experimental data.

Effect of electric field on fracture of piezoelectric ceramics

Closed form solutions for all three modes of fracture for an infinite piezoelectric medium containing a center crack subjected to a combined mechanical and electrical loading were obtained. The explicit mechanical and electrical fields near the crack tip were derived, from which the strain energy release rate and the total potential energy release rate were obtained by using the crack closure integral. The suitability in using the stress intensity factor, the total energy release rate, or the mechanical strain energy release rate as the fracture criterion was discussed.

A HIGHER ORDER THEORY FOR EXTENSIONAL MOTION OF LAMINATED COMPOSITES

A refined laminated plate theory is developed which is applicable to fiber reinforced composite materials under impact loading. In addition to the usual bending and extensional motion, the theory also includes the first symmetric thickness shear and thickness stretch motions as well as the first antisymmetric thickness shear mode. The governing equations reveal that unsymmetrically laminated plates display a coupling phenomenon between all of the deformation modes present in the theory. The frequency spectra for laminates representative of current fibrous composites are derived from the plate theory for one-dimensional wave propagation and compared to exact solutions obtained from dynamic elasticity theory. The higher order theory yields improved results for extensional motion compared to those of existing laminated plate theories.

A Simple Flow Rule for Characterizing Nonlinear Behavior of Fiber Composites

A one-parameter flow rule for orthotropic plasticity was developed to describe nonlinear behavior of fiber composites. Since most fiber composites exhibit in significant plasticity in the longitudinal direction, a plastic potential containing a single parameter was found adequate. Effective stress and plastic strain increment were intro duced to yield a universal nonlinear stress-strain relationship for the orthotropic com posite. This plasticity model was evaluated using experimental results of a boron/ aluminum and a graphite/epoxy composite.

On strain energy release rates for interfacial cracks in bi-material media

Abstract Mode I and Mode II strain energy release rates GI and GII for a crack lying along the interface of two dissimilar elastic media were investigated analytically and by using the finite element method. The analytical solutions indicate that GII and GII do not converge in the form of crack closure integrals although the sum (the total strain energy release rate) is well defined. If the oscillatory terms are neglected, then GI=GII= 1 2 G . The finite element solutions in conjunction with the crack closure method agree with the analytical solutions if the assumed crack extension is larger than the region of violent stress oscillation. Moreover, the finite element solutions also converge to GI = GII = 1 2 G for small crack extensions, before they start to oscillate.

On the Impact of Initially Stressed Composite Laminates

The impact response behavior of initially stressed composite laminates is investigated using the finite element method. An experimentally established contact law is incor porated into the finite element program. The Newmark time integration algorithm is used for solving the time dependent equations of the plate and the impactor. Numerical results, including the contact force history, deflection, and strain in the plate, are presented. Effects of impact velocity, initial stress, and the mass and size of the impactor are discussed.

Indentation law for composite laminates

Static indentation tests are described for glass/epoxy and graphite/epoxy composite laminates with steel balls as the indentor. Beam specimens clamped at various spans were used for the tests. Loading, unloading, and reloading data were obtained and fitted into power laws. Results show that: (1) contact behavior is not appreciably affected by the span; (2) loading and reloading curves seem to follow the 1.5 power law; and (3) unloading curves are described quite well by a 2.5 power law. In addition, values were determined for the critical indentation, alpha sub cr which can be used to predict permanent indentations in unloading. Since alpha sub cr only depends on composite material properties, only the loading and an unloading curve are needed to establish the complete loading-unloading-reloading behavior. Previously announced in STAR as N82-15123

Size-dependent elastic moduli of platelike nanomaterials

A semicontinuum model is presented for nanostructured materials that possess a platelike geometry, such as ultra-thin films. In contrast to the classical continuum theory, the current model accounts for the discrete nature in the thickness direction. In-plane Young’s modulus, and in-plane and out-plane Poisson’s ratios are investigated with this model. It is found that the values of the Young’s modulus and Poisson’s ratios depend on the number of atom layers in the thickness direction and approach the respective bulk values as the number of atom layers increases.

Three-Dimensional Effective Elastic Constants for Thick Laminates

Equivalent homogeneous anisotropic solids are used to represent thick laminates con sisting of large numbers of a repeating sublaminate. The typical sublaminate is used for studying its load-deformation behavior from which the effective elastic constants are derived from the constituent lamina properties. Explicit expressions for effective elastic constants for general thick laminates are presented. Reduced expressions are also derived for balanced laminates containing a single composite system. Numerical examples are in cluded.

Modeling non-linear rate-dependent behavior in fiber-reinforced composites

Abstract The rate-dependent behavior of AS4/PEEK (APC-2) thermoplastic composite has been characterized over a wide strain rate range (10 × 10 −6 to 1000s −1 ). The low to moderate strain rate experiments were conducted with a servo-hydraulic testing machine, while the high strain rate experiments were conducted with a Split Hopkinson Pressure Bar. Two rate-dependent models are introduced to model the material response. Both models are developed by using a one-parameter plastic potential function to describe the non-linear behavior. Off-axis composite specimens are tested in simple tension at different strain rates, and the results are used to determine parameters of these models. Predictions of these models are shown to agree fairly well with the experimental results over a wide range of strain rates.