PSI - Issue 13

F.J. Gómez et al. / Procedia Structural Integrity 13 (2018) 267–272 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

268 2

Nomenclature E

Elastic modulus Fracture strength

f t

K I

Stress intensity factor Fracture toughness

K IC K IC K IC

R

Critical notch stress intensity factor

R*

Non-dimensional critical notch stress intensity factor

R

K I l ch L r

Notch stress intensity factor

Characteristic length

Ratio between the maximum load and plastic collapse load

R

Notch radius

SED Strain energy density SED necking Strain energy density under necking

Strain



Failure strain

 f  u  

Strain under necking Fictitious failure strain

f

Stress



Fictitious fracture strength

 f

Elastic stress at the tip of the notch

 max

Ultimate tensile strength

 u  y

Elastic limit

In a cracked structural component and linear elastic material, Fracture Mechanics states that the maximum load is reached when the stress intensity factor is equal to the fracture toughness of the material. This criterion is still valid in elastoplastic materials when the plastic zone is limited to a region close to the crack tip (Irwin 1957). In U notched solids, in linear elasticity, there is no tensional singularity, however, the approximate expression of the stress field at the tip of the notch given by Creager and Paris (1967) permits to stablish similar assessment based on the notch stress intensity factor (Glinka 1985). In elastoplastic materials, Creager and Paris formulation is no longer valid. One possibility to overcome this limitation is to apply tensional corrections as suggested by Neuber (1958) or Glinka (1987), valid under small scale yielding. A.R. Torabi, one of the authors of the present communication, has proposed the Equivalent Material Concept (EMC), based on the strain energy density, to replace the real material with an elastoplastic behavior by a fictitious equivalent linear elastic material (Torabi 2012 and 2013). The EMC can be combined with various failure criteria such as the cohesive zone model or a phenomenological formulation to develop a procedure for predicting the maximum load of components with U-notches. In a linear elastic material, the maximum load that supports a cracked solid in mode I is obtained when the stress intensity factor, K I , which depends on the geometry and the stress, reaches the value of the fracture toughness, K IC : = ( ) (1) Dealing with U-shaped notches, the tensional field can be approximated by Creager and Paris formulation (Creager and Paris 1967) depending on a single factor, K I R , and again a similar criterion can be established: the maximum load is obtained when the notch stress intensity factor reaches a critical value, K IC R , depending on the material but also the notch radius. 2. Failure criteria in linear elastic materials