1° (~0.0174 radian) I d (2a) (R) and (R) (d/2a)(1):
Since DFI = (DP) (R)/2, DFI 0.25 (DP)(D)/a radians 15 (DP)(d)(2). DF II = (DFI) (cosine a), and since (cosine a) → 1 as (a) → zero, (DFII) DFI for (a) 1°.
The total DFII is thus (DFI) (IId), where (πd) is the defect circumference.
The region I strength is (CFS) (t), where CFS is the seal material cohesive failure stress.
Region II strength is (AFS)(AO), where AFS is the adhesive failure stress and AO the area of overlap (0.78) (D2−d2).
Combining these disruptive force–strength relationships for this joint model gives the following: for region I: DP ~> 0.06 (CFS) (t/d); for region II: DP ≤ 0.03 (AFS) (D2/d2 − 1). For example, a lapseal joint with (a) = 1°, (t) = 0.3 cm, (d) = 0.5 cm, (D) = 1.5 cm, and (DP) = 100 mmHg ( 0.132 km/cm2) will have a “required” CFS 3.6 km/cm2 and a “required” AFS 0.550 km/cm2.
For the case in which the substrate contains multiple closely placed defects occupying ~50% of the surface, the “required” AFS will be 1.1 km/cm2, which is approximately the CFS of skeletal muscle.
References
1.
Universal encyclopedia of mathematics. Foreword by James R. Newman. New York: Simon and Schuster; 1964. p. 43–4.
2.
Medical physiology and biophysics. Ruch TC, Fulton JF, editors. 18th ed. Philadelphia: WB Saunders Company; 1960. p. 660–1.
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References 1. Dunn OJ. Basic statistics: A primer for the biomedical sciences. New York: John Wiley and Sons; 1964. p. 103–4, 106–7. 2. Kiemele MJ, Schmidt SR, Berdine RJ, editors. Basic statistics: Tools for continuous improvement. 4th ed. Colorado Springs: Air Academy Press; 1997. |
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