Bridging model

Abstract: This paper presents three analytical models for the investigation of the stiffness and strength of woven fabric composites. The “mosaic model” is effective in predicting the elastic properties of fabric composites. The “fibre undulation model” takes into account fibre continuity and undulation and has been adopted for modelling the “knee behaviour” of plain weave fabric composites. The “bridging model” is developed to simulate the load transfer among the interlaced regions in satin composites. The theoretical predictions coincide extremely well with experimental measurements. The elastic stiffness and knee stress in satin composites are higher than those in plain weave composites due to the presence of the bridging regions in the weaving pattern.

Abstract: A new crack bridging model accounting for slip-hardening interfacial shear stress is derived for randomly oriented discontinuous flexible fibers in cement-based composites, based on a micromechanics analysis of single fiber pull-out. The complete composite bridging stress versus crack opening curve (σB − δ relation) and associated fracture energy are theoretically determined. A micromechanics-based criterion which governs the existence of post-debonding rising branch of the σB − δ curve is obtained. Implications of the present model on various composite properties, including uniaxial tensile strength, flexural strength, ductility and critical fiber volume fraction for strain-hardening, are discussed together with an example of a 2% polyethylene fiber reinforced cement composite. It is found that the present model can very well describe the slip-hardening behavior during fiber pull-out which originates from fiber surface abrasion at fiber/matrix interface. In addition, the new model predicts accurately the enhanced toughness in terms of both ultimate tensile strain and fracture energy of the composite and resolves the deficiency of constant interface shear stress model in predicting the crack opening and ultimate strain, which are critical for material design of pseudo strain hardening engineered cementitious composites (ECCs).

Abstract: The overall thermal–mechanical properties of a fibrous composite out of an elastic deformation range can be simply simulated using a recently developed micromechanics model, the Bridging Model. Only the in situ constituent fiber and matrix properties of the composite and the fiber volume fraction are required in the simulation. This general yet easy-to-implement micromechanics model is reviewed and summarized in the present paper. Application of the model to predict various properties of unidirectional laminae and multidirectional laminates, including thermoelastic behavior, elasto-plastic response, ultimate failure strength, strength at elevated temperature, and fatigue strength and S–N curve, is demonstrated. It is suggested that use of the bridging model, appropriately calibrated with experimental data, can therefore inform composite design by identifying suitable constituent materials, their contents, and their geometrical arrangements. Some technical issues regarding applications of the bridging model are also addressed.