Predicting Stochastic Failures in Fiber Network
Fiber networks materials can be found in both man-made products such as packaging, composites as well as in nature, for example, in biological tissues, cells, and bones. Fiber based materials exhibit a range of unique properties owing to a high stiffness to mass ratio. They can be made from renewable resources at relatively small cost with paper products being an excellent example of that. As with the majority of materials, stiffness and strength of fiber-based materials are among the most important properties in a number of applications. The mechanisms that control these properties originate from the structure at the microscale, where the following contributing factors play the crucial role: fiber mechanical properties, fiber morphology, and orientation, the number of interfiber contacts, bonding properties and disordered nature of the fiber network. Both the network strength and strength distribution are size-dependent in fiber-based materials. The larger the size is, the lower the average strength. The strength distribution follows the extreme Weibull distribution with a long tail toward zero. It was shown, for example, that the strength distributions of dry pulp fiber networks follow weakest links scaling laws starting from a size of about 2x2 cm. This means that once we establish strength statistics at this size, we can effectively predict the statistics of a larger sample, which is often applicable to the practical cases giving a possibility to predict the strength of the fiber-based products. The main question is what controls the strength distributions at the critical size from which the scaling applies. By making a number of controlled numerical experiments, where the size of the network is changed and statistics is extracted, we will identify this critical size and study how the fiber and bonding properties, as well as the details of the network structure, affect the strength and strength statistic. We will use a direct simulation of the network using non-linear finite element solver, resolving the individual fibers with beam element, modeling bonds with the contact elements and bond fracture with subsequent frictional sliding. Although the direct numerical simulations can capture the mechanisms of failure, they cannot be employed for product development due to overwhelming computational costs. Based on the results of the simulation and established scaling laws, we will develop a stochastic multiscale technique for predicting the risk of failure. It effectively combines the power of the direct simulations and structural reliability methods. Using this combination, the prediction of failure will account for randomness in microstructure as well as macromechanical uncertainties such as thickness and load variations and will be applicable to arbitrary geometry. The importance of strength distribution has been recognized in connection with failures of products made of fiber-based materials. Though studying the factors controlling these distributions on the microscale, implementing the upscaling through stochastic multiscale approach, we will be able to predict the performance of the fiber-based materials in end-use applications, which will save material through selecting appropriate safety factors for the given material.