A technique facilitates use of frangible components. The frangible components may comprise components of a gripping tool, e.g. anchor, used in a variety of applications, including well related applications. The tool is provided with a plurality of gripping members which each comprise a frangible structure. The gripping members may be selectively deployed to provide the desired gripping within a tubular structure, e.g. an open wellbore or well casing. The frangible structure in each gripping member is designed to break down into smaller portions after being exposed to a predetermined input, thus facilitating removal of the tool from the tubular structure.