PSI - Issue 13

Gyo Geun Youn et al. / Procedia Structural Integrity 13 (2018) 1297–1304 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

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3. Determination of the damage model for numerical simulation 3.1. Multi-axial fracture strain energy damage model

In this research, a damage model based on multi-axial fracture strain energy concept is adopted to simulate 0.5T C(T) test. The multi-axial fracture strain energy is known to strongly depend on stress triaxiality as described in Eq. 2 [McClintock, Rice et al, Hancock et al and Johnson et al]. A , B and ψ are material constants and the definition of stress triaxiality is the ratio of mean normal stress σ m and equivalent stress σ e

  

m B     + 

(2)

p W A =

exp

−

f



e

To determine these three material constants, at least three different tests with different stress triaxiality states are required. When the test data are insufficient, Eq. 2 can be simplified into [Nam et al] ( ) exp 1.5 1 p m f e W A n B     = − + +     (3) where n denotes strain hardening exponent. For unaged CF8A, n is determined as 0.586. When load is applied to material, the incremental damage, ∆ ω occurs due to plastic deformation and it is calculated (at each integration point in finite element) as follows:. p when the sum of incremental damage becomes critical value, ω c as shown in Eq. 4, then the stress at the integration point is rapidly reduced to almost zero (30MPa) by ABAQUS user subroutine. This enables to simulate local failure. c    =  = (5) 3.2. Determination of damage model To decide the parameters of damage model, monotonic tensile test simulation should be done [Jeon et al, Oh et al and Kim et al]. Fig. 4a is the FE model to simulate the monotonic tensile test. The simulation is conducted by ABAQUS v6.14. CAX8R element is used with NLGEOM option. p f W W   =  (4)

Fig. 4. (a)FE modelling of tensile specimen (b) FE simulation result for monotonic tensile test of unaged CF8A (c)determined multi-axial fracture strain energy curve versus stress triaxiality

After modelling tensile specimen, simulation was performed for unaged CF8A under monotonic loading. The result is shown in Fig. 4b. From the tensile test simulation, variations of stress triaxiality in terms of plastic strain energy can be extracted from the locus point until failure initiation. (Note that locus point is described in Fig. 4a) From the variations, averaged stress triaxiality at the fracture strain energy can be obtained and the corresponding point is describe d in Fig. 4c as “Smooth bar”.