Biomedical Engineering Reference
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∆L total = ∆L fiber + ∆L grip
(3)
∆L fiber = σ Span/E 0 ∆L grip = α.(A.σ)
(4)
α = (∆L total - ∆L fiber )/(A σ)
(5)
Corrected modulus and strain to failure can be calculated by the following equations:
α i = ∆L total /F - L 0 /E 0 .A i
(6)
∆L total /F = ε L 0 /σ A i = 1/E L 0 /A i
(7)
Equations for strain correction:
∆L grip /L 0 = α l (A i σ)/L 0
(8)
∆L fiber /L 0 (Corrected) = (∆L total /L 0 -∆L grip /L 0 )
(9)
where,
α i = Machine constant for each fiber
L 0 = Original span length
E = Young's modulus (elastic modulus or E-modulus) for each fiber
E 0 = Extrapolated modulus
A i = Cross-sectional area for each fiber
F = Force
ε = Strain
σ = Stress
On the other hand, tensile strength and strain to failure decreased with an increase
of span length. As mentioned by Bledzki and Gassan (1999), the longer the stressed
distance of the natural fiber, the more in homogeneity will be in the stressed fiber seg-
ment, weakening the structure. Thus, the strength decreased with fiber length. Tensile
properties of silk fibers are summarized in Table 1.
Figure 3. Stress-strain curves of silk fibers from tensile testing for 25 mm span length.
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