Reliability analysis of continuous fiber composite laminates

A composite lamina may be viewed as a homogeneous solid whose directional strengths are random variables. Calculation of the lamina reliability under a multi-axial stress state can be approached by either assuming that the strengths act separately (modal or independent action), or that they interact through a quadratic interaction criterion. The independent action reliability may be calculated in closed form, while interactive criteria require simulations; there is currently insufficient data to make a final determination of preference between them. Using independent action for illustration purposes, the lamina reliability may be plotted in either stress space or in a non-dimensional representation. For the typical laminated plate structure, the individual lamina reliabilities may be combined in order to produce formal upper and lower bounds of reliability for the laminate, similar in nature to the bounds on properties produced from variational elastic methods. These bounds are illustrated for a (0/plus or minus 15)sub s Graphite/Epoxy (GR/EP) laminate. And addition, simple physically plausible phenomenological rules are proposed for redistribution of load after a lamina has failed. These rules are illustrated by application to (0/plus or minus 15)sub s and (90/plus or minus 45/0)sub s GR/EP laminates and results are compared with respect to the proposed bounds

Probability techniques for reliability analysis of composite materials

Traditional design approaches for composite materials have employed deterministic criteria for failure analysis. New approaches are required to predict the reliability of composite structures since strengths and stresses may be random variables. This report will examine and compare methods used to evaluate the reliability of composite laminae. The two types of methods that will be evaluated are fast probability integration (FPI) methods and Monte Carlo methods. In these methods, reliability is formulated as the probability that an explicit function of random variables is less than a given constant. Using failure criteria developed for composite materials, a function of design variables can be generated which defines a 'failure surface' in probability space. A number of methods are available to evaluate the integration over the probability space bounded by this surface; this integration delivers the required reliability. The methods which will be evaluated are: the first order, second moment FPI methods; second order, second moment FPI methods; the simple Monte Carlo; and an advanced Monte Carlo technique which utilizes importance sampling. The methods are compared for accuracy, efficiency, and for the conservativism of the reliability estimation. The methodology involved in determining the sensitivity of the reliability estimate to the design variables (strength distributions) and importance factors is also presented

Modeling the Effective Elastic Behavior of a Transversely Cracked Laminated Composite

ABSTRACT The solution for the stress state present in the vicinity of transverse matrix cracks within a composite laminate is typically obtained by assuming a regular crack spacing geometry for the problem and applying a shear-lag analysis. In order to explore the validity of this underlying assumption, the probability density function for the location of the next transverse matrix crack within a crack bounded region is examined. The regular crack spacing assumption is shown to be reasonable from an engineering point of view. Continuing with this assumption, a generalized shear-lag model for multi-layer, off-axis laminates subjected to full in-plane loads is developed. This model is used to quantitatively evaluate the effective elastic properties of the damaged material. The results are applicable to materials such as ceramic matrix or polymer matrix unidirectional fiber systems where damage in the form of transverse matrix cracks arises

Optimal Size and Location of Piezoelectric Actuator/Sensors:

The problem of obtaining the optimal size and location of piezoelectric actuator/sensors is addressed. An optimization problem is formulated for a general beam that has arbitrary boundary conditions and may have as many piezoelectric actuators as desired. The proposed optimization criterion is based on a beam modal cost and controllability index. If the size of the actuator is unbounded, it frequently is optimal if it covers most, if not all, of the length of the beam. This is not realistic because there are cost, weight, and space factors to be considered. By adding a penalty term to the criterion, the size of the actuator/sensor can be reduced to a practical and reasonable size. Thus, there is no need to preselect the size of the actuator/sensor. The optimal size and location for beams wit