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 l oading. Although in average the microscopic stresses coincide with the macr oscopic (e.g., externally applied) stress, the local differences (stress fl uctuations) can be high, the magnitude increasing with the volume of the he terogeneous material. In the case of uniform macroscopic loading, Gaussian stress fluctuations lead to a size effect in which the tensile strength red uces 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 acc ounts for a linear stress variation. Comparison of both models with the exp erimental data on macroscopic strength and stress variations in dog-bone sh aped samples (scale range of 1:32), shows that the model based on the assum ption of uniform macroscopic stresses can only explain part of the experime ntal data with unrealistic values of the fitting parameters. The model whic h takes into account the linear part of the macroscopic stress distribution offers reasonably good accuracy. This serves as another indication that ma croscopic stress nonuniformity plays a crucial role in the mechanism of siz e effect.