Abstract
Stress fields were calculated in tire cord adhesion test specimens as a route to the development of improved wire adhesion tests. The calculated stresses were analyzed in order to predict the location of initiation of debonding and to assess the dependence of the cord pullout force on the modulus of the rubber compound. The computational results were validated by experiments on a variety of cord/rubber samples. Conclusions drawn from this study are as follows: The analyzed pull-through test for adhesion of steel wires has a serious drawback. Its major deficiency lies in the presence of a slot under the rubber block specimen. Maximum stresses are consistently higher at the slot edges than at the cord/rubber interface. This is responsible for: (a) initiation of failure at the slot edges rather than at the cord/rubber interface, (b) considerable rubber coverage, and (c) dependence of the cord pullout force on the strength properties of rubber. The test is more likely to test the strength of the rubber compound than it is to test the strength of adhesion. The TCAT test represents a significant improvement over the pull-through test with regard to the location of failure. Stresses at the cord/rubber interface are higher than elsewhere within the sample. Stresses along the cord show a high peak at the cord's embedded end. This highly localized peak initiates debonding at the embedded end and yields good reproducibility (failure is very unlikely to initiate elsewhere). Experiments on the TCAT specimen show a reproducibility of within 4.2%. Maximum stresses in the TCAT specimen vary with approximately the square root of the rubber modulus. Thus, while the TCAT may be an excellent choice for wire studies involving a single control compound, it may be limited when used in compounding studies and other tire applications which involve changes in the rubber properties. In such studies, the dependence on rubber modulus is viewed as a limitation of TCAT because: (a) unintentional changes in the rubber modulus will affect the cord pullout force and can lead to erroneous assessment of the adhesive strength, and (b) intentional changes in the rubber modulus cannot be simply factored out by a square root rule. Our experiments show that the exponent of the rubber modulus depends on how the modulus change is achieved. There are also many definitions of the modulus and several techniques for determining its value. Experiments on the SWAT test show a pullout force proportional to a lower exponent of the rubber modulus than the exponent in the TCAT test. Reproducibility is at 5.6%, i.e., somewhat poorer than the TCAT. The width of the sample, and the presence of cord reinforcements within that width (in addition to the cords being tested), are expected to change the stress distribution along the cords from the distribution in the TCAT test. The 9.5 mm × 9.5 mm steel-backed specimen represents a good alternative for adhesion tests in compounding studies and tire applications. Although its reproducibility is not as good as those of the TCAT and SWAT tests, its independence from the rubber properties and its ease of sample preparation make it a good alternative. Finite element stress analysis of adhesion tests can provide useful information for assessing alternative tests and developing improved tests. Although total cord pullout normally takes place after large deformations in the rubber, simplified, small strain material models can provide a good indication of the behavior of adhesion test specimens.
Analysis of steady flow in a circular cylindrical pipe with hydraulically smooth walls
