Pei Chi Chou

A Stochastic Model for the Growth of Matrix Cracks in Composite Laminates

This paper presents a stochastic simulation model for the growth of multiple matrix cracks in composite laminates subjected to both static and fatigue loads. Working within the premise of ply-elasticity, a new concept of effective flaws is introduced which replaces the conventional constant ply strength criterion. Thus, the model con sists of an application of fracture mechanics and a rational representation of material flaw distributions. Simulation examples are presented on [02/902]s and [0 2/903]s graphite-epoxy laminates which undergo characteristic transverse cracking under uniaxial tension.

Elastic Constants of Layered Media

A three-dimensional laminated medium is studied by an approach which replaces the heterogeneous medium by an equivalent homogeneous material. A set of macroscopic elastic constants is developed in terms of the properties of the constituent layers by considering a representative small element of the laminated medium and imposing the condition of continuity of stress and displacement at the layer interfaces. An example boundary value problem is also considered. Based on the solution of the boundary value problem for the homogeneous material, stress and strain fields corresponding to each layer are then calculated. This individual layer solution contains certain dis continuous stresses and strains as does the exact solution for the layered material.

Residual Strength in Fatigue Based on the Strength-Life Equal Rank Assumption:

Equations for the distribution of the residual strength after fatigue are derived. They are compared with experimental data for a few graphite/ epoxy composites. The theory is based on an assumption first introduced by Hahn and Kim, which states that for a given specimen its rank in static strength is equal to its rank in fatigue life, or the strength-life equal rank assumption. The equations contain a free parameter which is more versatile in matching experimental data. It is found that two processes are present during fatigue, one degradates individual specimens and tends to lower the mean strength, the other is the weeding out of weak specimens by fatigue failure which tends to increase the residual mean strength. The change of residual strength can be of weak degradation, strong degradation, or in crease in strength. Among the test data studied, two have weak degrada tion, two have strong degradation and two have increase in strength.

Analytical Study of Hugoniot in Unidirectional Fiber Reinforced Composites

A theory based on flow across a selected control volume is devel oped to predict the Hugoniot of a shock moving along the longitudinal direction of a unidirectional fiber reinforced composite. From this theory the Hugoniot of a composite may be calculated from the equa tions of state of its constituents. The shear force along the matrix-fiber interface can also be computed. A sample calculation using polyethyl ene as matrix and beryllium as fiber has been made. The calculated shock Hugoniot are not far from linear.

Scale Effect in Fatigue Of Composite Materials

Static strength and fatigue life under compression load are measured for specimens of graphite/epoxy composite materials. The specimens are either a basic element (one drilled hole), or three elements in series (three drilled holes). It is shown that the statistical in-series model (weakest link theory) can be applied to the present strength and fatigue data, and the scale effect in fatigue can be accounted for by statistical scatter of the data.

The Control-Volume Approach to Hugoniot of Macroscopically Homogeneous Composites:

The control-volume approach is applied to a composite that is macroscopically homogeneous and consists of arbitrary number of constituents. This includes true mixtures, certain alloys and any kind of composite whose constituents have dimensions much smaller than the composite. The present work represents a generalization of the control-volume approach which has been proposed recently for uni directional fiber reinforced composites. From the present theory, the Hugoniot of the composite may be computed from the equations of state of its constituents. The calculated results of two sample com posites are presented and compare satisfactorily with test data.

Control Volume Analysis of Elastic Wave Front in Composite Materials

A theory is proposed for the analysis of an elastic wave front in unidirectionally laminated as well as fiber reinforced composite mate rials. According to this theory, which is based on the concept of control volume, elastic wave front due to abrupt loadings propagates at a velocity which is bounded by the wave velocities of the fiber material and of the matrix material. The theory includes a nonlinear effect of area change; the wave front velocity is a function of the impact intensity. But for linearly elastic materials, this non-linear effect is small; if it is neglected, then wave front speed in the com posite becomes independent of the impact intensity. Consideration has also been given to the determination of the shear force along the interface between the reinforcing fiber and the matrix. It is found that for certain combination of fiber and matrix, the shear stress attains an extremum value which may cause debond ing of the composite under moderate impact loading.

The Importance of Signs of Shear Stress and Shear Strain in Composites

The definition and physical significance of the sign conventions for stress and strain components, in particular, shear stress and shear strain, are of vital importance in studying the response of anisotropic composite materials. Designers and analysts who must predict the strength and stiffness characteristics of laminated systems should be thoroughly familiar with the physical interpretations of these signs. In this paper we elaborate on these sign conventions and demonstrate their importance with several illustrative examples.

Effects of Proof Test on the Strength and Fatigue Life of a Unidirectional Composite

The effects of a static proof testing on the statistical distribution of the static strength and fatigue life of a unidirectional graphite-epoxy laminate (AS-3501-05) are investigated experimentally. Loading mode for boththe static and fatigue tests is restricted to uniaxial tension in the fiber direction. Six-ply tension coupons with dimensions of 22.9 cm by 1.9 cm are used; and all tests are conducted using a closed-loop Instron tester, under room temperature (∼21°C) and ambient humidity (∼60% percent relative humidity) conditions. Test data are analyzed by means of a two-parameter Weibull distribution in conjunction with the maximum likelihood method for parameter estimation. Results show that proof testing can guarantee a minimum static strength, and to a lesser degree, the method can also assure a minimum fatigue life.

Plastic Flow Rule of Laminated Composites

A plastic flow rule for laminated media is derived. It is based on a three-dimensional lamination theory which has been used previously to provide an effective elastic stress-strain relation and an anisotropic yield condition. For layers that are isotropic and follow a piece-wise linear flow rule, an explicit anisotropic plastic stress-strain relation for the equivalent composite is obtained. The general form of this flow rule may also be applied to other homogeneous but anisotropic materials. It is concluded that anisotropic flow rules should be governed by tensor quantities, the symmetry of flow may be different from that of yielding, and plastic flow may occur under hydrostatic loading.