Stephen W. Tsai

A General Theory of Strength for Anisotropic Materials

An operationally simple strength criterion for anisotropic materials is developed from a scalar function of two strength tensors. Differing from existing quadratic approximations of failure surfaces, the present theory satisfies the invariant requirements of coordinate transforma tion, treats interaction terms as independent components, takes into account the difference in strengths due to positive and negative stresses, and can be specialized to account for different material symmetries, multi-dimensional space, and multi-axial stresses. The measured off-axis uniaxial and pure shear data are shown to be in good agreement with the predicted values based on the present theory.

Nonlinear Elastic Behavior of Unidirectional Composite Laminae

Complementary elastic energy density is used to derive a stress-strain relation, which is linear in uniaxial loadings in the longitudinal and trans verse directions, but nonlinear in shear. In the case of composite laminae under plane stress, one additional fourth-order constant is introduced. Comparison is shown between the present theory and experimental data on off-axis tests.

ANISOTROPIC STRENGTH OF COMPOSITES

The present investigation is concerned with the development of a theory of strength of anisotropic composite materials and the establishment of sound experimental procedures for the confirmation of the predicted results. A general theory is stated whereby the strength of laminated as well as unidirectional composite materials subjected to any state of combined stress can be predicted once the basic strength characteristics of a unidirectional layer have been determined.The transversely isotropic layer is treated in detail and, based on the understanding of the mechanical behavior of laminated composites, the procedure outlined for determining the strength of laminated systems. An experimental program was conducted, using glass-filament-reinforced resin test spceimens, and data obtained confirmed the results predicted for the strength of unidirectional composites.Based on the results of the analysis presented, composites may then be designed to incorporate an optimum utilization of the inherent strength characteristics of the constitutent materials.

On the Behavior of Composite Laminates After Initial Failures

Bilinear stress-strain relation of symmetric, [0/90] composite laminates is shown to be associated with gradual, not complete, degradation of 90° layers. Difference between the complete failure model and gradual failure model is discussed, complemented by pertinent experimental evidences. Experimental data on glass/epoxy and graphite/epoxy cross-ply laminates are compared with the theoretical predictions. The effect of strain biaxiality on failure of 90° layers is shown to be negligible when the laminate is subjected only to a uniaxial tension.

The Influence of Random Filament Packing on the Transverse Stiffness of Unidirectional Composites

Existing micromechanics analyses for the prediction of composite material properties, which are based upon the assumption of various idealized regular filament packings, indicate the significant influence of the assumed geometry on numerical results obtained. To represent the random filament packing of actual composite materials more accurately, a method of analyzing random arrays is presented in this paper. Although certain geometric constraints have necessarily been retained for mathematical reasons, it has been dem onstrated that as the degree of randomness is increased, the agree ment between analytical predictions and available experimental data is improved. Because of the necessary approximations and additional complexities involved in random array analyses, the methods presented here are not intended to replace regular array analyses, but rather to supplement them, indicating the influence of this difficult-to-predict characteristic of real materials.

A Survey of Macroscopic Failure Criteria for Composite Materials.

Popular failure criteria of fiber-reinforced composite materials are described and compared. These criteria are empirical and should only be judged from the standpoint of the fitness to data and the ease of application. The criteria for orthotropic plies of unidirectional composites are extensions of those for isotropic materials. The quadratic criteria are considered to be the most suitable for both isotropic and composite materials. Macroscopic criteria are essential for design and for providing guidelines for materials improvements. Strictly speaking, failure criteria for multidirectional laminants are valid up to the first-ply failure envelope; i.e., before transverse cracking and delamination occur. Finally, conditions for fully optimized ply properties are easily derived from the quadratic failure criterion.

Measurements of Complex Dynamic Moduli for Laminated Fiber-Reinforced Composites

Measurements of storage and loss moduli are reported for laminated glass fiber reinforced epoxy composite beams at frequencies up to 9400 Hz. The storage moduli were relatively insensitive and the loss moduli sensitive to the frequency at which they are measured. The storage moduli of the laminates can be predicted from a knowledge of constituent layer properties, but only qualitative predictions of the loss moduli can be so obtained. The loss moduli are equal to or larger than those predicted from ply properties.

Simplified design of composite materials

Abstract An internally consistent theory of micro- and macromechanics has been formulated to link materials, geometric and environmental parameters that affect the stiffness and strength ofstructural elements made of multidirectional composite laminates. Design simplifications are presented and other unique features ofthis integrated framework are discussed. The framework has been implemented on a personal computer in a spreadsheetformat and validated using organic fibre-matrix composite materials data.

Off-axis plies made by folding

A technique of paper folding can be applied to form off-axis plies in a multidirec tional laminate. Advantages of this approach include reduced labor, scrappage and cutting. Additional features are the self-checking of ply orientations, and ready adop tion to automation.

Editorial: A Matured Technology

INCE THE BEGINNING of this Journal is 1966, the technology of composite materials. has made significant advances. Graphite and Kevlar fibers are produced in millions of pounds per year and plans are underway to triple the current capacity. Applications of composite materials in aerospace vehicles are expanding. Nearly every new military aircraft in the world has components made of composite materials. There is an all-composite aircraft, the Learfan 2100, scheduled for test flight before the end of 1980. Ford made an all-composite automobile. The Prince graphite tennis racket is one of the best selling rackets in the United States.