PSI - Issue 14

Taslim D. Shikalgar et al. / Procedia Structural Integrity 14 (2019) 529–536 T.D.Shikalgar et al./ Structural Integrity Procedia 00 (2018) 000–000

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3.4. Analysis of p-SPT specimen using GTN damage model To know the accurate crack initiation load in p-SPT specimens, the material constitutive damage model is used. The model is based on ductile damage processes based on nucleation, growth, and coalescence of microvoids. This constitutive damage model is based on flow function introduced by Gurson (1977) and later modified by Tvergaard and Needleman (1982). �� � , � , � , � � � � � � � � 2 ∗ � ���� � 3 � � 2 � � � �� � � � ∗ � � � � � (2) Where σ e is Von-Mises equivalent stress, σ h is hydrostatic stress, σ y is the flow stress of matrix material and f is microvoid volume fraction. The above yield function reduces to von-Mises yield criteria with isotropic hardening when void volume f * equals to zero. The effective void volume fraction f * was also introduced by Tvergaard and Needleman (1984) to predict the rapid loss in material strength after the occurrence of void coalescence. To have a better matching with the experimental results, Tvergaard and Needleman (1982) introduced three constants q 1 , q 2 and q 3 . The suggested values are q 1 =1.5; q 2 =1.0 and q 3 =q 1 2 . Subsequently, Dutta, et al. (2008) suggested a spatial variation of q 2 near the crack tip, as shown below. � � � � �� ���� �� where (3) � � ���� � � (4) Here r is the distance of the material point from the crack tip and l c is the characteristic length. The suggested values of q 2a and q 2b are 0.3 and 8 respectively. FE analysis of the p-SPT specimen is carried out using the GTN material damage model. Earlier reported GTN parameters (P. Kumar et al. (2016)) are used in the present study, which are shown in Table 3. The load v/s displacement data obtained by this analysis are shown in Fig. 9 along with the experimental and elastic-plastic results. It may be observed that peak loads calculated by elastic-plastic analysis and GTN model are same. In the latter part of the curve, load dropped faster due to consideration of damage in the material near a crack tip in GTN model.

Table 3: GTN Parameters used for the present study (P. Kumar et al (2016))

Material

q 1

q 2

q 3

ε n

S n

f 0

f n

f c

f f

20MnMoNi55

1.5 1.5

1.0 1.0

2.25 2.25

0.3 0.3

0.1 0.1

0.00001 0.008

0.02 0.08

0.25 0.20

T91

0.00001

0.01

The computed J-initiation in GTN model is evaluated at the failure of first gauss point nearest to the crack-tip and the value of J-initiation is calculated as 192.18 kJ/m 2 and 264.49 kJ/m 2 of material 20MnMoNi55 and T91 respectively (Fig. 10). It may be noted that punch displacement at this point is significantly lower than the punch displacement at peak load. This shows the crack initiation occurs much before the peak load. The J-initiation calculated by GTN model is still more as compared to J-initiation reported in literature using CT specimens.

Fig. 9. Comparison of FEA, FEA GTN result with experimental data of (a) 20MnMoNi55, (b) T91.