Probabilistic approach to the mechanics of unidirectional composites with heterogeneous reinforcement

摘要

Fibrous composites have proved their exceptional mechanical properties throughout the 20th century. Especially due to their high stiffness and strength to weight ratio the use of fibrous composites is exponentially growing. Since the material structure is highly anisotropic and the constituents exhibit random features, the design is a challenging task. This fact is reflected in an overwhelming number of modeling approaches that have been formulated to date. This thesis describes a modeling framework that is based on a special class of mechanical models - probabilistic models. The behavior of unidirectional composites with brittle matrix subjected to tensile loading is studied by evaluating their statistical average response. Considering the highly random nature of geometry, bond and failure of the reinforcing micro-fibers, models involving parameters as random variables are the appropriate approach to an accurate simulation of the composite mechanics. A multiscale model is described in this thesis with three distinguished scales:a) Micro-scale: individual fibers and fiber-matrix bondb) Meso-scale: single composite crack bridge with smeared fiber propertiesc) Macro-scale: composite with multiple, serially coupled matrix cracks The composite response is thoroughly examined from the view point of engineering design, i.e. serviceability limit state as well as ultimate limit state are considered. Thus the developed modeling framework is a practice relevant comprehensive tool for the analysis, optimization and probabilistic design of unidirectional composites.Based on the work of the numerical modeling group of the multidisciplinary project SFB 523 Textile reinforced concrete - the development of a new material, the author of this thesis further develops the analytics at the meso scale (crack bridge) and the macro scale (multiple cracking). In particular, the modeling framework is extended to cover also the mechanics of short fibers and hybrid reinforcement, it includes the effect of elastic deformations of the matrix, a thorough statistical analysis of fiber damage and the evaluation of crack widths and their statistical distribution. Considering the multiple cracking level, a model involving the random matrix strength is formulated, which allows for robust predictive capabilities without requirement of a priori information on the saturated state or other heuristic inputs as is the case in most existing models.