|Composites redistribute forces from overloaded zones to neighboring ones
by microstructural fractures. This is a reserve effect of a complex microsystem (Machutov,
Koksharov). Stress-strain-damage state (SSDS) of fibre composites is characterized
by damage parameters such as: the fraction of broken fibres ( the ratio of the number of broken structural
elements (SE) to the sum of SEs), and the relative length of delaminations
( the ratio of the average length of delaminations to the total length of fibres).
The strength of the composite does not depend on SSDS at one critical point but in a certain zone V that involves n SEs. Suppose that two cases - damaged composite (Fig.1a) and volume with eliminated parts (Fig.1b) are equivalent. The length of the eliminated fibre C0 is the material constant and has an order of the average length of the delamination. With 'volume' reduction its specific energy uv increases. It is assumed that the failure occurs when uv reaches its critical value uc. Using the terms of nominal stress and equivalent stress acting in the volume gives the direct equation for the equivalent stress. The fibre property is known and can be described by the Weibull distribution with parameters such as the average strength of the fibre SE. The theory provides the nominal stress level at which the breakdown of the multitude of the breakages takes place (Fig.2).
If the number of SEs in the volume V is finite then the binomial distribution provides an estimate of the confidence interval for damage parameter (Fig.3) and critical stress at the prearranged level of the result trustworthiness [P]. The numerical image of the probability distribution function for the nominal critical stress is obtained by analyses at different values of [P]. Compared with the law for fibre SE this function has a lower average value and narrower restricted scatter band. In the low value area, the probability of failure in the volume V (curve 2, Fig.4) has a qualitative distinction from the fibre property (line 1). For a composite structure that involves 1,000,000 V the curve shifts to position (3). By specifying [P] it is possible to estimate a value for the decrease in the carrying ability of the composite fibres (Fig.4). These approaches allow us to not only estimate reliability indices, but also to analyze the effect of the component properties, structure sizes, and initial damages on the composite structure reliability.
Fig.1 Composite and model of eliminated fibres
ALGEBRA OF PROBABILITY DENSITY FUNCTIONS
|Density function transformation for fatigue crack length|
DIFFERENCES BETWEEN THE RELIABILITIES OF HOMOGENEOUS AND COMPOSITE MATERIALS
|Fig.1 Local stress responsible for failure initiation versus nominal stress. All values divided by its critical values.|
|Fig.2 Ratio of the local stresses for homo-geneous and composite materials versus nominal stress.|
|Fig.3 Qualitive picture for probability distribution density function of homogeneous and composite materials.|
|Fig.4 Changes in remaining strength of homogeneous and composite materials.|