Biomedical Engineering Reference
In-Depth Information
Virial stress represents internal resistance offered by a material to an
externally imposed load [84]. Since virial stress is an internal quantity, it is
also an indicator of the increase in the stress concentration caused by the
presence of an inhomogenity in an otherwise homogenous body. This
characteristic is used to analyze the effect of the cracks in the presented
analyses. The focus of the analyses is on developing an understanding of the
correlations between particle size, particle placement with respect to a
bicrystalline interface and the strength against crack propagation.
Figure 5.9 shows the stress field in a monolithic Si 3 N 4 sample of the same
size as that of the CFEM meshes shown in Fig. 5.7 as the crack propagates.
As shown, the crack tip stress field is resolved using the CFEM mesh used in
the research. As shown in the inset, the fine size of the mesh does not allow
extreme distortion of the finite elements. In order to understand the stress
distribution and damage evolution, the damage parameter (D (equation
5.2)) and the maximum principal stress (
σ max ) distributions are analyzed in
all microstructures. As explained earlier, 0
1, with D=0 indicating
fully recoverable interfacial separation and D=1 signifying complete
separation or fracture. The results for damage distribution in all three types
D
￿ ￿ ￿ ￿ ￿ ￿
5.9 Stress distribution as a function of damage progression in the case
of bulk Si 3 N 4 at the loading rate of 2 m/sec at time (a) 0.01312
μ
sec, (b)
0.01688
sec. The close-up inset in each plot shows
how the crack tip stress field is resolved and elements distorted as crack
progresses.
μ
sec, and (c) 0.02437
μ
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