PSI - Issue 42

Rafael Magalhães de Melo Freire et al. / Procedia Structural Integrity 42 (2022) 672–679 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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• From the dislocation theory, a short range of the data described in figure 5 (b) could be eliminated since the area does not influence damage in the material and it is related to the reversal movement of dislocations that is not a significant part to account for the final stage of plastic deformation. • Special terms in the equation can modify the fracture toughness results, considering the last cycle of the plastic strain was executed by compression load or tensile load. Taking these factors into account, equations 3 to 5 were formulated for the evaluation of fracture toughness loss. In equation 3 , δ As is the limit CTOD [mm] without pre-strain, while δ sat is the saturation value of fracture toughness reduction (mm) reflecting the decrease in the value. The parameter f( Δ p) is the amount of stroke in the plastic deformation zone during pre-strain tests (mm), and B is the plate thickness of the pre-strained specimen. θ is the angle of the last pre-strain cycle to account for the differences between compression and tensile load in the last pre-strain cycle. For example, θ = 0 is for tension load, while θ = π is for compression. Constants (a, b, and h) were added in the equation to return more accurate values, and they must be calibrated according to a reference value, which is the MOTE of critical CTOD obtained from the fracture toughness test data. Equation 4 can be understood by observing Figure 5 (b), and f (Δp) is equal to the stroke amount of the plastic deformation region in each half cycle of pre-strain ( Δ p,i ), minus the stroke amount of the section of reverse motion of the dislocation immediately after yielding during load reversal ( Δ inv,i ). Where i is an integer number and represents the order of each pre-strain 1/2 cycle. Equation 5 is the definition of Δ inv and it gives a non-zero constant for pre-strain cycles after the first half cycle, which does not have load reversal. k is a constant and γ is a parameter from the mobile hardening law presented in Chaboche (1989) and Lemaitre and Chaboche (1994).

(3)

(4)

(5)

δ As in equation 3 was obtained from the δ cr,MOTE of P9 without pre-straining. Also, γ in equation 5 was determined as 100 from the data, with the aid of EBSD image observation for the pre-strained specimen. For each pre-strain pattern, the constants ( δ sat , a, b, h and k) were calibrated by the least-squares method considering δ true , which is δ cr,MOTE from the fracture toughness test data. The constant values obtained from the fitting are shown in Figure 6 together with the relationship between δ true and δ pre . It confirms that the fracture toughness values can be accurately estimated using the simplified evaluation equation.

Figure 6 - Comparison of true data set and prediction values for the proposed equation