PSI - Issue 28

Mikhail Perelmuter et al. / Procedia Structural Integrity 28 (2020) 2320–2327 M.N. Perelmuter / Structural Integrity Procedia 00 (2020) 000–000

2323

4

Fig. 3. The deformation energy release rate vs the relative length of the crack bridged zone, c 0 = H / , t = d / , uniaxial tension

where c ( x , u ) is the bonds compliance depending on the distance from the crack tip and the crack opening u . For linear-elastic bonds the compliance does not depend on the crack opening and can be written as c ( x ) = c 0 E b γ ( x ) , c 0 = H (9) where γ ( x ) is the dimensionless function used to describe nonuniform compliance behavior over the bridged zone, H is the length parameter proportional to the bonding zone thickness, E b is the bond e ff ective elastic modulus, c 0 is the relative bonds compliance, this parameter will be used for the results description. Expression (7) can be rewritten using relations (8) as (see details in Perelmuter (2007))

− d

q x ( u ) dx + G Ic − G b

∂ u y ( x ) ∂

∂ u x ( x ) ∂

G bond ( d , ) =

q y ( u ) +

(10)

If we assume that the rate of the energy released at the trailing edge of the bridged zone is equal to the rate of the energy absorbed by newly deformed bonds during the crack tip advancing then in the case of a homogeneous material or an infinite thin adhesive layer joining di ff erent materials

δ cr 0

G Ic = G b =

σ ( u ) du

(11)

then we can write relation (10) as follow

− d

− d

∂ u y ( x ) ∂

∂ u x ( x ) ∂

bond ( d , ) + G y

bond ( d , ) , G y

G bond ( d , ) = G x

q y ( u ) dx , G x

q x ( u ) dx (12)

bond ( d , ) =

bond ( d , ) =

3. Energy characteristics of bridged cracks analysis

Let us consider the e ff ect of mechanical properties of the materials and bonds in the crack bridged zone on the en ergy characteristics (3) and (12). All energy characteristics given in this section in dimensionless form are normalized