Size effect in tensile strength caused by stress fluctuations

The randomness of microstructure heterogeneous materials leads to creation of microscopic random stress fields within the bulk of the material under loading. Although in average the microscopic stresses coincide with the macroscopic (e.g., externally applied) stress, the local differences (stress fluctuations) can be high, the magnitude increasing with the volume of the heterogeneous material. In the case of uniform macroscopic loading, Gaussian stress fluctuations lead to a size effect in which the tensile strength reduces as square root of logarithm of the sample size. In practice, however, the macroscopic tensile stress fields are usually nonuniform. In this case, failure is determined by the maximum value of the macroscopic stress with the scale effect controlled by the minimum degree of the macroscopic stress decrease from its maximum. Therefore, a second model is proposed which accounts for a linear stress variation. Comparison of both models with the experimental data on macroscopic strength and stress variations in dog-bone shaped samples (scale range of 1:32), shows that the model based on the assumption of uniform macroscopic stresses can only explain part of the experimental data with unrealistic values of the fitting parameters. The model which takes into account the linear part of the macroscopic stress distribution offers reasonably good accuracy. This serves as another indication that macroscopic stress nonuniformity plays a crucial role in the mechanism of size effect.