Fracture strength composites

Many fibrous composites are made of strong, brittle fibres in a more ductile polymeric matrix. Then the stress-strain curve looks like the heavy line in Fig. 25.2. The figure largely explains itself. The stress-strain curve is linear, with slope E (eqn. 25.1) until the matrix yields. From there on, most of the extra load is carried by the fibres which continue to stretch elastically until they fracture. When they do, the stress drops to the yield strength of the matrix (though not as sharply as the figure shows because the fibres do not all break at once). When the matrix fractures, the composite fails completely. 

A composite material for a car-repair kit consists of a random mixture of short glass fibres in a polyester matrix. Estimate the maximum toughness of the composite. You may assume that the volume fraction of glass is 30% the fibre diameter is 15 pm the fracture strength of the fibres is 1400 MPa and the shear strength of the matrix is 30 MPa. 

The preceding analysis is premised on having continuous fibers of equal strength all of which fracture at the same longitudinal position. However, fibers under tension do not all have the same fracture strength nor do they fracture in the same place. Rather, because surface imperfections vary from fiber to fiber, the individual fibers have different fracture strengths. A statistical analysis is then necessary to rationally define the strength of a composite material. 

Other researchers have substantially advanced the state of the art of fracture mechanics applied to composite materials. Tetelman [6-15] and Corten [6-16] discuss fracture mechanics from the point of view of micromechanics. Sih and Chen [6-17] treat the mixed-mode fracture problem for noncollinear crack propagation. Waddoups, Eisenmann, and Kaminski [6-18] and Konish, Swedlow, and Cruse [6-19] extend the concepts of fracture mechanics to laminates. Impact resistance of unidirectional composites is discussed by Chamis, Hanson, and Serafini [6-20]. They use strain energy and fracture strength concepts along with micromechanics to assess impact resistance in longitudinal, transverse, and shear modes. 

Piggott M.R. (1981). Fiber length-strength relationships and the fracture of composites. In Proc. 5th International Conf. Fracture (ICF-5), pp. 465-472. 

In cross-ply laminates, the stress-strain behavior is slightly nonlinear, as illustrated in Figure 5.123. The stress-strain behavior of a unidirectional lamina along the fiber axis is shown in the top curve, while the stress-strain behavior for transverse loading is illustrated in the bottom curve. The stress-strain curve of the cross-ply composite, in the middle, exhibits a knee, indicated by strength ajc, which corresponds to the rupture of the fibers in the 90° ply. The 0° ply then bears the load, until it too ruptures at a composite fracture strength of ct/. 

Matsumaru K, Ishizaki K (2001) Fabrication of Porous Materials with high Fracture Strength. In Singh M, Jessen T (eds) 25th Annual Conference on Composites, Advanced Ceramics, Materials, and Structures B, (Ceram Eng Sci Proc 22). Am Ceram Soc, Westerville, OH, p 197... 

Dependence of the fracture strength of the YMgSiAION glass-SiC composites (28 vol% SiC) on the SiC particle size and the surface finish (after Baron eta ., 2000). 

The high temperature, short-term properties of alumina and alumina/ zirconia composites have been examined in a number of studies.18,19,24-32 Typical fracture strength and toughness at elevated temperatures are summarized in Figs. 2.2 and 2.3. 

The addition of SiC whiskers to silicon nitride matrices resulted in only moderate increases in the fracture toughness a compared to monolithic materials. Fracture strengths of composite materials showed increases in some cases and slight decreases in others. Summaries of the variations in toughness and strength are given in Tables 2.3 and 2.4. The moderate increases in... 

This distribution appears whenever g a) is given by a power law in (j, coming from the power law variation of the density of linear cracks g l) with their length 1. In the random percolation model considered here, this does not normally occur (except at the percolation threshold p = Pc)- However, for various correlated disorder models, applicable to realistic disorders in rocks, composite materials, etc., one can have such power law distribution for clusters, which may give rise to a Weibull distribution for their fracture strength. We will discuss such cases later, and concentrate on the random percolation model in this section. 

This equation applies to systems in which there is no adhesion between the filler and the matrix. The equation predicts that the fracture strength of the composite is reduced as the filler concentration increases. 

This equation predicts that there will be some small gains in fracture strength as filler concentration increases. For fiber-filled composite the following equation was found to be supported by experimental data ... 

As shown above, the ZrO/Ni composites examined by disk-bend testing are found to deform in a nonlinear manner, so that composition-dependent fracture strengths cannot be obtained directly from the stress-strain diagram in Fig. 3. Under the circumstances, we now make a micromechanical analysis to estimate actual stresses to be developed by plastic deformation of the ductile constituent on the basis of an established "mean-field" model [12]. In the following, the macrostress a) is related to the microstresses and (o) such... 

Consider an ordinary substrate-ceramic coating combination. Such a composite system, prepared at elevated temperatures and subsequently cooled to room temperature, will be thermally stressed due to the usually large difference in thermal expansion and elastic moduli of the substrate and coating. These stresses often exceed the fracture strength of the ceramic component, particularly in regions close to free surface near the interface. This leads to either cracking of the ceramic part or to failure at the substrate-coating interface. 

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