Size effect in fiber or bar pullout with interface softening slip

The paper analyzes the size effect, which is an inevitable consequence of softening in the relation of interface shear stress and slip displacement between a fiber or reinforcing bar and the surrounding matrix. The problem is simplified as one‐dimensional. Closed‐form solutions of pull‐pull and push‐pull failures are obtained for a linear softening stress‐slip law with residual strength, and for an exponential law without residual strength. The postpeak softening is shown to lead to localization of slip and interface shear fracture with a process zone of finite length. This zone propagates along the interface during the loading process, causing the distribution of interface shear stress to become strongly nonuniform. The larger the bar or fiber size, the stronger the nonuniformity. The size effect in geometrically similar pullout tests of different sizes is found to represent a smooth transition between two simple asymptotic cases: (1) The case of no size effect, which occurs for very small sizes and is characteristic of plastic failure; and (2) the case of a size effect of the same type as in linear elastic fracture mechanics, in which the difference of the pullout stress from its residual value is proportional to the inverse square root of the fiber or bar diameter. An analytical expression for the transitional size effect is obtained. This expression is found to approximately agree with the generalized form of the size effect law proposed by Bažant. The shape of the size effect curve is shown to be related to the shape of the softening stress‐slip law for the interface. Finally, it is shown how measurements of the size effect can be used for identifying the interface properties, and a numerical example is given.