Cracking in cement matrices and crack propagation

One of the main phenomena studied in the mechanics of brittle matrix composites is cracking. The cracks may be classified according to various criteria  

A flaw or a crack is defined in the mechanics of solids as a plane 2D discontinuity in a solid body with its two dimensions much larger than the third one. Certain authors reserve the first term - flaw - for those discontinuities that are formed parallel to the smallest dimension without application of any tensile stress. In that convention the term crack covers all other discontinuities just caused by tensile stress. In several manuals, this distinction is not used and both kinds of discontinuities in solids are called cracks for example, Broek (1982). This practice is also followed here. 

Cracks may be characterized by their width, length and pattern. The opening of a crack is always related to the creation of new free surface in the material, where free means that the surface is not loaded by any stress. An amount of energy is required to create a unit area of a new free surface of a crack. It is considered to be an important material characteristic and is called specific fracture energy, which is difficult to directly measure, but may be calculated in an approximate way when the amount of released energy and crack dimensions are estimated and considered to be known. 

The crack shape is usually irregular. The roughness or waviness of the crack surface is characteristic both for the material and for the origin of the crack. Because of this irregularity, the crack length and area of its surface may be considered as fractal objects. It means that they depend on the scale of observation or on the unit of measurement (cf. Sections 9.3 and 10.5.) 

It is generally assumed that in brittle cement matrices the plastic phenomena, similar to those in metals, do not appear. In fact, when in specimens subjected to loading, certain apparently plastic deformations are observed that is, an increase of deformation at a constant load, then this effect is caused by microcracks and therefore the term quasi-plasticity is used. 

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Cracking in cement matrices and crack propagation Table 9.1 Maximum permissible crack width in concrete structures... 

Computer analysis of crack propagation through finite element grids was developed by several authors. Cracks are represented by discontinuities of the finite element mesh, and smeared crack models were also applied. Cement-based matrices were considered as linear elastic bodies up to the point where cracks open and later their behaviour becomes highly non-linear. Various methods are applied to represent non-linear and heterogeneous materials and to simulate their behaviour under load (cf. Petersson 1981). In discrete models, cracks are represented as discontinuities in the finite element mesh. This is also where smeared crack models are introduced. 

The strain necessary for initiation of multiple cracking and crack propagation is lower for a cyclic load than for a static and constant load. The process of fatigue in fibre-reinforced cement composites is similar to the static increase of load in the sense that debonding and pull-out also occur gradually. The fibres used as reinforcement for cement matrices usually do not show fatigue at all because the stress in fibres is maintained at quite a low level as related to their strength, in steel or carbon fibres, for example. 

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