Relationship of crack fabric tensors of different orders

A lower-order crack fabric tensor can be determined accurately by a higher-order one, but in general the reverse does not hold. In this paper, the approximate dependence of a higher-order fabric tensor on a lower-order one is established based on the properties of orientation distribution functions (ODF). As a demonstration of its application, the approximate relationship is used to simplify the fabric-tensor dependent compliance increment due to the presence of the cracks.