Issue 54

B. Bartolucci et alii, Frattura ed Integrità Strutturale, 54 (2020) 249-274; DOI: 10.3221/IGF-ESIS.54.18

been by far the most important wood for aircraft construction and other specialty uses are ladder rails and sounding boards for pianos.

A PPENDIX – SECTION 2

2 IC KG = E

(1)

f

 

 

I II     K   K

  

  

B B C C 4 u -u -(u -u ) 4 v -v -(v -v )   B B C C  

π

-1

(2)

=

B

8L

F

max

π a 

K = ζ

(3)

IC I

w t 

a W      

(4)

IC C K = σ π a F

C 1 2 P K = Y

(5)

IC

I

bw

IC 3 2 PS a K = f W BW      

(6)

 

(7)

ICg g K =400 S

-1.5

a 1- 

  

 

W

(8)

K =3.657 F

IC

max

0.5

BW

In these equations: a [mm]: initial crack length B : matrix that depends on the stiffness matrices of the wood species

B (or b, or t) [mm]: thickness of the specimen E [MPa]: modulus of elasticity (Young’s modulus) f(a/W) = 2.6625 F max [N]: critical load at which the crack begins to propagate G f [J/m 2 ]: toughness, the energy release rate at which energy is transformed as a material undergoes fracture . Under Mode I loading, the critical energy release rate is related to the Mode-I fracture toughness K IC K I , K II : stress intensity factor in mode I loading (crack opening mode) and in mode II loading (crack sliding mode) K IC [kPa · m ⁰⸱⁵ ]: critical fracture toughness (critical stress intensity factor) L [mm]: element length P c (or P) [N]: critical load value S: centre of the span S g : specific gravity (relative density). Ratio between the density of an object and a standard (generally water H 2 O).

u B , u B ΄ , u C , u C ΄ : node displacements in the “x” direction v B , v B ΄ , v C , v C ΄ : node displacements in the “y” direction W [mm]: distance from the loading line to the end of the specimen

273