PSI - Issue 7

Igor Varfolomeev et al. / Procedia Structural Integrity 7 (2017) 359–367 Igor Varfolomeev et Al./ Structural Integrity Procedia 00 (2017) 000–000

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Further four specimens were tested until fracture under strain controlled LCF conditions at constant strain amplitudes, thus providing an estimate of the fatigue life curve within the range of about 1,000 to 10,000 cycles, see Fig. 5b. 3.2. Strain hardening and damage modeling The cyclic plasticity model according to Ellyin and Xia (1989) was employed to describe material strain hardening. The model directly uses the monotonic and cyclic stress-strain data (Fig. 5a), whereas the cyclic softening is taken into account by means of a transient hardening term. The model parameters were first calibrated by fitting to the experimental stress-strain hysteresis loops measured in the incremental step tests at = − 1 . Subsequently, the goodness of the model fit was demonstrated by comparing experimental and calculated stress strain hystereses at = 0 , Fig. 6. 1.5 1.5

1.0

1.0

-1.0 Normal ized st ress, σ / σ 0 [MPa] -0.5 0.0 0.5

-1.0 Normal ized st ress, σ / σ 0 [MPa] -0.5 0.0 0.5

-1.5

-1.5

0 2 4 6 8 10 12 14 16

-8 -6 -4 -2 0 2 4 6 8

Normal ized st rain, ε E/ σ 0 [-]

Normal ized st rain, ε E/ σ 0 [-]

Fig. 6. Stress vs. strain hysteresis loops at = − 1 and = 0 . Comparison between experimental measurements (curves) and numerical model (symbols).

Besides cyclic softening, an additional term was included in the plasticity model describing the damage evolution and respective softening of the matrix material. A damage parameter was considered taking values between = 0 (no damage) and = 1 (fully damaged state) and linearly varying with the accumulated plastic strain, , . The damage accumulation was assumed to start at a threshold strain value, , = ℎ , whereas the condition of = 1 was achieved at a critical strain value, , = . The parameters ℎ and were fitted to describe the endurance curve in Fig. 5b which includes test points at two strain amplitudes. The set of parameters ℎ = 0,1 , = 2 was found to yield a reasonable agreement between the model and experimental data. To account for the effect of damage on the element stiffness, the calculated value of was used to alter the flow stress on the cyclic stress-strain curve: this was linearly scaled down along the stress axis from the virgin, non-damaged level (Fig. 5a) at = 0 to 10% of the virgin level at = 1 . A finite, non-zero value of the flaw stress at = 1 was selected to improve the numerical convergence. 3.3. Modeling specimen with a defect field In this analysis step, the damage evolution was numerically modeled for a defect field characteristic of the specimen FZ1, see Fig. 3b. The respective finite-element model, Fig. 7, represents a rectangular cuboid material volume with dimensions 10 × 10 × 5 mm³ and contains a rectangular area of the size 3.2 × 1.6 mm² corresponding with the defect size in FZ1. The defect affected zone with the depth of 0.2 mm is meshed using 40 × 40 × 40 µm³ hexahedron elements, while the connection to the remaining part of the model with a relatively coarse mesh is