PSI - Issue 23

Atri Nath et al. / Procedia Structural Integrity 23 (2019) 263–268 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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= { 1⁄ ∑ [( ∗ − ∗ )/ ∗ ] 2 =1 } 0.5 − (6) where n is the number of data points, and ∗ are the stress and modified ratcheting strain recorded from experiments and and ∗ are the predicted stress and modified ratcheting strain using CIKH model. The ratcheting strain data are modified by applying a 5% offset similar to the study by Nath et al. (2019). The adopted optimization technique considerably reduces the value of F error . The comparison of the simulation obtained by using the suggested methodology with the reported response for the investigated materials is examined in the following. 3. Results The suggested methodology is applied to predict the cyclic deformation behavior of two ferrous (CS1026 steel and SA333 C-Mn steel) and two non-ferrous (TA16 titanium alloy and AA 7075-T6 aluminum alloy) materials. The final sets of CIKH model parameters, obtained by suggested methodology for the investigated materials, are summarized in Table 2. The CIKH model parameters are next used to predict the monotonic (wherever available) and cyclic-plastic response of the materials. This study considers ratcheting strain (  r ) for a material as the one used by the concerned investigators (Agius et al., 2017; Hassan and Kyriakides, 1992; Kan et al., 2011; Paul et al., 2010) for subsequent comparison of the current results with earlier predictions; the mean strain is considered as  r for SA333 steel and TA16 titanium alloy, while the peak strain is used as measure of the ratcheting strain for CS1026 steel and AA7075 alloy. The yield stress values and the Young’s modul i used in the constitutive models are estimated here either from the monotonic tensile response of the materials (for TA16 titanium alloy) or from the stress-strain behaviour in the tensile portion of the first cycle under strain-controlled cycling (for CS1026 steel and for AA7075-T6 aluminum, where monotonic tensile response is not available). It may be noted here that SA333 steel exhibited 1.2% Luder’s strain in monotonic deformation (Sivaprasad et al., 2010), and thus the elastic properties are estimated from the tensile portion of strain-controlled cyclic loops.

Table 2: The optimized parameters obtained for the investigated materials using the suggested methodology

Cyclic plastic parameters

Materials

Elastic Parameters

Isotropic hardening

Kinematic hardening

C i=1,2,3,4 (MPa) = 375754.9, 15178.7, 3068.6, 78792.9 γ i=1,2,3,4 = 21902.29, 279.06, 14.29, 4666.64 a 4 = 21.43MPa C i=1,2,3,4 (MPa) = 129261.5, 23275, 2724.8, 4217.2 γ i=1,2,3,4 = 2397.8, 284.3, 10.8, 3090.9 a 4 =16.6 MPa C i =1,2,3,4 (in MPa) =350531.7, 80862.8, 1748.5, 28362.9 γ i =1,2,3,4 = 14731.6,935.4,0.83,665.1 a 4 = 234.8 MPa C i =1,2,3,4 (in MPa) = 192694.5, 22986.6, 73.2, 7437.6 γ i =1,2,3,4 = 16250.3, 1296.8, 0.2, 2139.5 a 4 = 32.8 MPa

E = 181GPa  y 0 = 129.6 MPa E = 200GPa  y 0 = 225 MPa

b = 109.32, Q = 29.43MPa

CS1026 steel

b = 92.62 Q = 14.45MPa

SA333 steel

E = 101 GPa  y 0 = 420 MPa

b = 550.1 Q = -182.5 MPa

TA16

E = 69 GPa  y 0 = 500 MPa

b = 862.6, Q = -27.8 MPa

AA7075

The suggested methodology is capable of simulating both the strain-controlled hysteresis loops and the strain controlled ratcheting response for CS1026 steel as observed in Fig. 1a-b; the predictions obtained by the suggested approach is closer to the experimental cyclic-plastic response than that predicted by Bari and Hassan (2000). The improved accuracy of the suggested methodology with respect to other reported numerical approaches (where the contribution of isotropic hardening was neglected) can be inferred from Fig. 1c; the maximum F error is 4.5% for the