By John W. Pepi
This article is meant for structural, mechanical, and optical engineers who desire to receive an realizing of the rules of energy choice for optical parts. those that paintings with ground-, air-, or space-based platforms, in addition to with ceramics, semiconductors, and so forth, will achieve an realizing of fracture mechanics purposes. this article expands uncomplicated fracture mechanics thought to incorporate residual pressure, which is never stated on within the literature and will have dramatic results on lifetime. whereas advanced equations are provided and a easy knowing of engineering rules is important, advanced wisdom of fracture mechanics and effort ideas isn't required
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Additional info for Strength properties of glass and ceramics
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From Eqs. 6a), we can compute as follows: c ¼ ðr þ 1Þ2=r , ð3:9Þ ci and S¼ rK Ic ðrþ1Þ=r ðr þ 1Þ Y ðci Þ1=2 , ð3:10Þ which, for point flaws (r ¼ 3) is S¼ 0:47K Ic Y ðci Þ1=2 : ð3:11Þ For the less common line flaw, where r ¼ 1, S¼ 0:25K Ic Y ðci Þ1=2 : ð3:12Þ From Eq. 6) for the line flaw, this is also equivalent to S¼ 0:50K Ic Y ðcÞ1=2 , ð3:13Þ as the crack will grow under the applied load. org/terms Strength with Residual Stress 29 For the residual-stress-free case, where r ¼ 1, we recover the Griffith solution: S¼ K Ic Y ðci Þ1=2 : ð3:14Þ From Eq.
Indeed, crack velocity has been measured for silica glasses at low stress intensities in the vicinity of less than 1 pm/s. A more typical plot of the stress intensity regions, for which region I is typically made linear, is given in Fig. 4. 4 Typical velocity–stress intensity plot of moisture-assisted fused-silica crack growth. 1 Region I relation Note that in the power law relation, time to failure is proportional to the Nth power, where, again, N is material dependent. At first look at Eq. 2), it would appear that the higher the N, the higher the velocity, and hence the shorter the lifetime.
1 Finite bodies and free-surface correction The Griffith formulation of shape factor applies to through flaws that are embedded in an infinite body, as has been shown in Fig. 1. Many handbooks4 and texts show modifications to the shape factor when the body in which the crack is embedded is not infinite. This is depicted in Fig. 3. Such modifications are dependent on the flaw-depth-to-body-thickness ratio, as shown in Fig. 4. The higher the ratio, the higher the stress intensity amplification. 3 Embedded crack in a finite body.
