Matrix cracking simulations

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. 

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... 

Using this simplified approach, simulations of stress-strain curves have been conducted.89,97 These curves have been compared with experimental measurements for several 2-D CMCs. One result is summarized in Fig. 1.35. It is apparent that the simulations lead to somewhat larger flow strengths than the experiments, especially at small inelastic strains. To address this discrepancy, further modeling is in progress, which attempts to couple the behavior of the tunnel cracks with the matrix cracks in the 0° plies. 

The ZSM-5 additive used in the study was commercially available and contains 25% ZSM-5 zeolite in an inert matrix. The ZSM-5 additive was steamed at conditions (8) chosen to simulate the activity of a commercially equilibrated REX cracking catalyst (Table I). Eight weight percent of the additive was then blended with each faujasite catalyst (two weight percent ZSM-5 zeolite). 

To increase the wear resistance of surfaces, silicon and metals are often coated with a hard nitride, carbide, boride, or oxide film. Nanoindentation and fracture simulations have been used extensively to elucidate failure mechanisms of these typically more brittle surfaces, which include crack propagation and film delamination. Considerable attention has also focused on nanocomposite materials, which possess nanocrystalline inclusions in an otherwise amorphous matrix. The nanocrystalline component is sufficiently small to preclude the formation of stable dislocations, and thus provide a higher hardness. 

Four different three-dimensional numerical infiltration experiments were carried out in a simulated porous medium with a central parallel crack as shown in Fig. 4-2. The lattice size is 10 by 100 by 150 sites in the x, y and z directions, respectively. Solid sites are represented in red. A probabilistic algorithm generated at random the solid distribution of the microporous matrix. The mean microporosity and macroporosity are 0.52, and 0.192, respectively, of the total volume of the medium. A gravity force was simulated as described in Di Pietro et al. (1994), oriented parallel to the crack in the z-downward direction. Void sites (white color in Fig. 4-2) are initially f ss are expressed in arbitrary lat-... 

The whole story from the crack initiation to fracture can he seen in molecular dynamics (MD) computer simulations (51-53). We have already talked about MD simulations of stress relaxation in a previous section. The question to be answered by MD was where in two-phase materials formed by polymer liquid crystals (PLCs) the cracks start They could start in the flexible polymer matrix because it is relatively weak, or inside the LC-rich islands which are more brittle, or at the interface from the matrix side, or else at the interface from the island side. 

An example of the answer is shown in Figure 13 (51). A large crack which is going to cause fracture is formed at the interfaces on the matrix side. The beauty of computer simulations is that we can watch the cracks form and propagate imtil fracture. Animations of this process are made for added perspicuity. 

Computer simulations enabled the different relations between the strength of the matrix and the aggregate grains, influence of increasing load, quality of the matrix/aggregate bond, etc. to be investigated in a systematic way. Examples of crack patterns are shown in Figures 9.15 and 9.16. 

Zaitsev, Y. V., Ashrabov, A. A., Kazatski, M. B. (1986) Simulation of crack propagation in various concrete structures, in Brittle Matrix Composites 1, A. M. Brandt and I. H. Marshall, eds, London Elsevier Applied Science Publishing pp.549-57. 

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