Introduction

In this lecture we will first present the issues or difficulties in failure theories for composite as compared to the homogeneous and isotropic materials. Then we will introduce some failure theories for unidirectional composites. We will conclude this lecture with some numerical examples.

Many theories are available for predicting failure of composites. These theories predict the failure of a lamina or laminate. Hence, these theories are called “lamina failure” or “laminate failure” theories. Further, these theories predict the very first failure in a lamina. Hence, these theories are popularly known as “first-ply failure” theories.

The macroscopic theories presented here are the early theories. From a designer point of view, any theory should be applicable at lamina, laminate as well as at component level. The aims of these theories were to give reasonably accurate prediction of failure as compared to experimental results and ease of implementation for analysis and design. Hence, some of theories were based on physical basis. Some of them were just extensions of theories for homogeneous; isotropic materials to composite materials. While most of the theories provided mere mathematical expressions such that it gave a best fit of the available experimental data.
           
All together, these theories are not good enough to predict the failure at all levels (like constituent, lamina and laminate). Further, none of them can be used for a general loading and any composite material as most of them were loadings and materials specific. At present, a significant progress has been made to address most of these issues.

Issues in Failure Theories for Unidirectional Composites:

The failure theories for unidirectional composites have some difficulties when they are extended from homogeneous, isotropic materials. In the following, we list some of the issues related to composite failure theories.

1. The composites are heterogeneous and orthotropic in nature. Hence, the effective properties in three directions need to be found.

2. The unidirectional laminae are orthotropic in nature. Hence, the strength parameters (like ultimate stress or strain) in three directions will be different.

3. In a given direction, the strength parameters will be different in tension and compression.

4. The strengths in normal direction and in shear directions are different.

5. For off axis laminae, the shear strength is different in positive and negative directions. If one is using the global coordinate system to decide the shear failure, then the positive and negative shear should be considered carefully. However, in principal material directions the positive and negative shear has no effect on shear strength.

6. The strength parameters are generally obtained experimentally in principal directions. Hence, the stresses or strains used in the failure theories should also be in principal directions. Thus, the transformation of stresses or strains from global coordinate system to principal material direction in each lamina is imperative.

7. Most of the theories do not give the mode of failure (like fibre breaking, matrix cracking, etc.). It just mentions that the lamina has failed. Further, they do not give propagation of damages until final failure.

8. The link between damage and first-ply failure is difficult to establish for failure theories.

Note: (We refer to point 6 in the above.) One should not transform the strength parameters from principal coordinate system to global coordinate system to use it in a failure theory. This transformation from principal to global direction is not known. The strengths should be obtained by experiments on off-axis laminae.