PSI - Issue 13

Fuzuli Ağrı Akçay / Procedia Structural Integrity 13 (2018) 1695 – 1701 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

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bodies. The fracture criterion, which is developed using Karr-Akçay energy balance concept, is based on the continuum modeling of energy release rates. The remainder of the article is organized as follows. The fracture criterion is derived in Section 2, and implemented into an example application in Section 3, including the presentation and discussion of the results. Finally, a summary with conclusion remarks is given in Section 4.

Nomenclature A

area of the fracture plane

I C

specific surface energy density (of Mode I)

c CTOD

(elastic component of) critical crack tip opening displacement components of elastic strain increment tensor (of the unfractured medium) II III de de de elastic strain increments of the unfractured medium in principal directions * * * , , I II III de de de elastic strain increments of the fractured medium in principal directions dw mechanical work increment per unit volume (of the unfractured medium) dW mechanical work increment of the unfractured medium * dW mechanical work increment of the fractured medium I e elastic strain in the first principal direction E Young’s modulus Ic K plane stress fracture toughness (of Mode I) ,0 I l characteristic length (relevant to brittle fracture) , , I II III l l l current dimensions of the volume element in principal directions L critical distance 0 x atomic spacing (at equilibrium) cs  theoretical cohesive strength ij  components of stress tensor (of the unfractured medium) , , I II III    principal stresses of the unfractured medium * * * , , I II III    principal stresses of the fractured medium Ic  critical stress at fracture y  yield stress  Poisson’s ratio s  surface energy per unit area I  critical effective energy release rate (of Mode I fracture) ij de , , I

2. Theory

The brittle fracture criterion of tensile mode for initially crack-free bodies is derived in this section. The derivation is inspired by Karr-Akçay energy balance concept, presented in a recent article (Karr & Akçay, 2016). Karr-Akçay energy balance concept is based on continuum modeling of energy release rates, and it states that the system, seeking a minimum energy state, will fracture if the rate of energy change for the system in the fracture mode becomes less than the un-fractured continuum system. Therefore, the critical state is reached when the rate of energy change of the bulk system is balanced by the rate of energy change of the fractured medium. When a material is exposed to external forces, the external work done is exchanged with the internal energy of the system assuming that the system is in equilibrium and quasi-static conditions apply (i.e., the kinetic energy of the whole system is neglected). In the following, temperature changes are neglected and the material is assumed to remain within the elastic region. Hence, total work increment per unit volume, , can be expressed as ij ij dw de  = (1) where and are the components of stress tensor and elastic strain increment tensor, respectively.