Finite-Element Calculations on the Stress of an Aramid Cord in a Clamped and Elongated Goodrich Block Fatigue Specimen

In the Goodrich Block Fatigue Test, a rubber block containing a tire cord is cyclically compressed and extended. The retained strength of the cord, obtained after a certain running time, is a measure of the fatigue resistance of the cord. In this test, the compression and extension is applied to the clamps of the block. This induces an indirect loading of the cord through shear forces in the rubber. This cord load varies along its length and depends on variables such as cord modulus and diameter and rubber modulus and cannot be obtained experimentally. A three-dimensional finite-element model together with a calculation procedure is presented. With these, not only the overall force-displacement behavior of the GBF specimen can be predicted, but also the detailed cord stress distribution, both for clamping and elongating the specimen. Only three different linear finite-element computations have to be performed. Results at any arbitrary elongation of the specimen are obtained by superposition of these calculation results. The accuracy can be enhanced by combining them with the measured value for the elongation at which the cord is just fully tensioned. Experimental verification was carried out for an aramid cord with a diameter of 0.6 mm. The presented model produces results that agree well with the measured values for the force on the specimen (both for clamping and elongating) and for the breaking force of the cord. Clamping of the specimen causes compression of the cord in the center area of the block. For the aramid cord used in this study, this compression area has a length of about 10 mm. At an elongation of approximately 0.4 mm (the corresponding extension setting of the machine is 3%), the cord is just fully tensioned. When elongating the block a certain amount above this setting, the stress in the center of the aramid cord is only 6.3% of the stress of a cord which would be strained the same amount as the block. In this study, no account has been taken of temperature and viscoelastic effects, which may play an important role in the actual fatigue test!