Crack density

The refractograp of figure 4 shows highly oriented micro cracks of a polystyrene sample. The orientation of the cracks is perpendicular to the mechanical strain direction. The X-ray refracted intensitiy can be interpreted as crack density, i.e. the inner surfaces within a unit volume. Changing the tilt angle (of polystyrene and polystyrene blend samples) with respect to the primary beam leads to significantly different distributions of crack orientation (Fig. 5). 

Microstructural examinations revealed that the tube was annealed brass. All cracks originated on the internal surface at pit sites. Cracks were fine, branched, and ran through the metal grains (transgranular). Crack density over the specimens examined averaged 40 cracks per linear inch (16 cracks/cm) of surface. 

The transverse orientation of the cracks, coupled with their predominance along one side, reveals that bending of the tube induced the responsible stresses. The rapidity of crack propagation and the high crack density indicate that the stress level was high. 

Figure 22. Effect of crack density on coefficient of thermal expansion of a T300/5208 composite laminate [OjAWJj. (Reproduced from reference 4.)...

Let us -assert, however, that the input of mechanical energy into solids in the sense of tribochemistry always results in a change of their kinetic behavior. The change in point defect concentration, dislocation or crack density, and structure influences the transport coefficients and reactive properties (e.g., catalytic activity, nucleation rate, etc.). 

Let us consider the case where the pore space is a network of saturated cracks. In order to implement the classical micromechanical estimates of the strain concentration tensor A introduced in (14), the cracks are modelled as flat oblate spheroids. For simplicity, a uniform crack radius a is considered. N denotes the crack density. For an isotropic distribution of crack orientations, the macroscopic behavior derived from (15) is isotropic as well (Deude et al., 2002) ... 

The morphological parameter C which controls the damaging effect of cracks appears to depend only on the crack density and the crack radius. In the case of cracks, the macroscopic mechanical loading defined by Ii or p is expected to induce a strong heterogeneity of the mechanical affinity, due to the stress/strain concentration in the vicinity of the crack tips. 

No particular quench temperature at which crack density increased markedly is observed using dye penetrant for the spinel composites, in contrast to the MgO materials. It is clearly seen that there is a gradual development of a dense microcrack network in the spinel composites, with increase in the quench temperature. 

Compositions of EVA with 5phr of crude or purified CNTs (MWNTs), 2.5 phr of each CNTs and organomodified layered silicate (dimethyl distearyl ammonium) were tested using the cone calorimeter80-81 at 35 kW/m2. It was found that crude CNTs were as effective in the reduction of PHRR as purified CNTs. A synergistic effect for flame retardancy between CNTs and organoclays was observed. Moreover, the residues revealed a reduction in the crack density for the sample with CNTs and organoclay. 

Fig. 1.24 (a) Simulation of crack evolution for various matrix flaw distributions characterized by Xs when the shape parameter matrix crack density with stress for unidirectional SiC/CAS. 

At stress, erxrs, the crack density remains essentially constant. It has thus been assumed that there is no additional stress transfer between the fibers and the matrix. In this case, the tangent modulus is given by 14... 

The constituent properties from Table 1.3 can, in turn, be used to simulate the stress-strain curves (Fig. 1.31). The agreement with measurements affirms the simulation capability whenever the constituent properties have been obtained from completely independent tests (Table 1.1). This has been done for the SiC/CAS material, but not yet for SiC/SiC. While the limited comparison between simulation and experiment is encouraging, an unresolved problem concerns the predictability of the saturation stress, crs. In most cases, ab initio determination cannot be expected, because the flaw parameters for the matrix (processing sensitive. Reliance must therefore be placed on experimental measurements, which are rationalized, post facto. Further research is needed to establish whether formalisms can be generated from the theoretical results which provide useful bounds on as. A related issue concerns the necessity for matrix crack density information. Again, additional insight is needed to establish meaningful bounds. Meanwhile, experimental methods that provide crack density information in an... 

The function g depends on whether the transverse fibers either remain in contact with the matrix upon loading, or separate. The relative unloading modulus associated with such tunnel cracks, E/E, depends primarily on the crack density, tp L, with L being the mean crack spacing in the 90° plies.94,96 At large crack densities, a limiting value is reached, given by,... 

There are a number of indicators of fatigue damage that have attracted interest in the literature. During the life of a component subjected to fatigue, the material can exhibit changes in modulus, permanent offset strain, shape of the hysteresis loops, and temperature rise of the specimen surface. Direct evidence of matrix crack density can be obtained by surface replication, while a more detailed analysis of microstructural damage requires scanning electron microscopy (SEM). 

In system F, the evolution of the crack density with the longitudinal strain shows that the presence of a thin thermally grown Al Oj interlayer modifies the cracking response of the SiO 4.5 wt.% P film. First, as noted previously,... 

Fig. 10 Typical evolution of the crack density with longitudinal strain. The occurrence of the four damage stages is indicated.

Table 1. Analytical Expressions for Crack Density vs Longitudinal Strain Obtained...

Directly from the in situ observations, the multiple film cracking is analyzed through the evolution of the crack density with the longitudinal strain applied to the system. Before any deformation, a representative zone of the sample is chosen. Its total length is 0.55 mm, extended parallel to the longitudinal axis of the sample. This initial length is denoted For any further deformation, it is denoted X(e) and corresponds to ... 

N(e) is the number of transverse cracks which intercept the length X(e). The error introduced when counting the number of cracks is 2 cracks per millimeter. In order to describe the cracking response of our passivation films, the experimental values of the crack density as a... 

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