Evaluation of Notched Specimens
9.2.3 Comparison with Finite Element Model
Finite element analysis was performed according to Chapter 6, simulating primary-secondary creep on a model of 316H material with the same notch geometry displayed in Figures 6.3 and 9.1. Tertiary creep was modelled using ductility exhaustion concepts to express the amount of damage present within the material (see Equation (2.19) in Section 2.3) in combination with the Cocks-Ashby void growth model for creep in multiaxial stress states [10]. This model was chosen due to its wide use within the field [1, 11, 132, 133].
A conservative measure of the time to failure predicted by the FE model was chosen as being the time at which the first element becomes fully damaged (i.e. ω = 0.999). Using this criteria, the FE model predicts the failure at 753 h for a net stress of 310 MPa, which
is significantly longer than the experimental results (124 h and 86 h for 316N15-1 and 316N15-2 respectively). This can be attributed to material variability, as these tests are relatively short term and so the difference in behaviour appears magnified. The strain variation across the notch throat has been plotted in Figure 9.10 for both after loading and at t = 86 h, the time preceding failure of 316N15-2. Both 316H notched specimens show good agreement with the FE model on loading, which supports the validity of the tensile data used as well as showing that the experimental results are accurate, as it is not expected for elastic-plastic behaviour to vary significantly.
The strain fields produced through FE simulations has been compared with experimental results obtained using DIC for 316N15-1 and 316N15-2 for loading in Figure 9.11. It can be seen that generally the shape of the contours is similar. The FEA contours closer to the notch are narrower than the corresponding DIC contour results for both specimens. If the strain fields immediately preceding failure are compared (Figure 9.12) then it is seen that the maximal contour is larger in the experimental results than the FEA, although the lowest contour is much larger in the latter. Both sets of experimental results underestimate the strain at the notch root, which is due to the resolution of the DIC itself and the individual facet size used. Similarly, both specimens do show slightly more strain occurring further along the throat. This is likely to be due to the machining process, which produces imperfections that blunt the notch and allow more strain to accumulate elsewhere, especially in a material which incurs a lot of plastic strain.
a)
b)
t = 0 h
t = 86 h
Figure 9.10: Comparison of strain distribution along notch throat between experimental results and FE a) at loading, b) t = 86 h
[ε
y] t/t r = 0
316N15-1
316N15-2
FE
4 mm
0.37 0.33 0.29 0.25 0.21 0.17 0.12 0.08 0.04 0.00
Figure 9.11: Comparison of strain fields in region near notch for 316N15-1, 316N15-2 and FE model after loading
316N15-1
316N15-2
FE
4 mm
[ε
y]
0.53 0.47 0.41 0.35 0.29 0.23 0.18 0.12
0.06 0.00
Figure 9.12: Comparison of strain fields in region near notch for 316N15-1, 316N15-2 and FE model at t =86 h
Although the general shape of the contours for Figure 9.12 are similar between all three fields shown, the difference in size is significant as the fact FE is clearly not predicting enough strain to accumulate further away from the notch throat. It has already been noted that the FEA is not conservative with respect to failure time, and when considering the results at failure it appears to be less conservative with respect to strain accumulation.
This is supported by Figure 9.10b, where it is obvious that although the general trends of the experimental results are reasonable when compared to the FE simulations, there remains significant discrepancies between them.
As previously displayed in Figure 9.8, 316N15-1 and 316N15-2 generally show similar results although the latter has less strain at the notch root. Indeed, one reason for the larger peak contour in Figure 9.12 of 316N15-1 is due to the fact that its strain exceeds the peak FE value up to r/a = 0.1. As one moves slightly further away from the notch, the strain gradient is much steeper for FE than the experiments. This is partly because there is more strain along the notch throat for the experimental results than is predicted by the simulation, and it is observed that across a large portion of the throat the experimental results are more than twice the amount of the corresponding FE value.
The difference between the simulations and the experimental results may be due to the fact that the model only simulates the effect of creep damage on the material, where there is an interaction between plasticity and creep deformation of the material where 316H is concerned. Therefore the combination of creep and plasticity, in addition to the variation in material creep behaviour [122,133], may have caused this difference to occur. Overall it may be suggested that without accounting for plastic strain and damage, FE predictions using this kind of model are unlikely to be accurate.
Using results obtained in Chapter 5, a similar model was constructed to simulate the
behaviour of the Alloy 617 specimens. Although more data is required to produce more comprehensive characterisation of the creep behaviour of the material, it was desired to investigate how well the preliminary properties compared to experimental results. An identical creep and damage model was used to that which is described in Chapter 6, with Alloy 617 properties substituted in. Although the uniaxial failure strain (εf) has a dependency on stress (Figure 2.4), for the purposes of this model an average value of 7.38% was used. The model predicted failure occurring for a stress of 300 MPa at t = 309 h. This is in between the two experimental results (194 h and 577 h respectively), suggesting that there is reasonable fidelity between the model and the actual behaviour of the material.
Figure 9.13 shows a strain field comparison between the two specimens and FE results at t = 97 h. As mentioned earlier with respect to Figures 9.6 and 9.7, although the critical region near the notch has been well resolved by DIC, there has been a loss of resolution towards the edges of the specimen meaning it has not been possible to calculate the strain field for parts of the speckle pattern. Regardless, it can be seen that although the FE shows a higher contour of strain at the notch root and in general the field around the notch is similar in size for all three cases. The lower strain occurring at the notch root in the experimental results is likely due to speckle pattern decorrelation towards the edge of the specimens. Figure 9.14 shows a similar plot for t = 135 h. It is evident that 617N15-2 has an almost identical strain field to the FE, and overall from both Figures 9.13 and 9.14 it appears that this specimen has the best agreement with the FE.
The strain distribution along the notch throat is plotted for 617N15-1 in Figure 9.15, showing good agreement with FE for t = 97 h. The peak strain at the notch root is less in the experiment than the FE, which is due to ARAMIS being unable to correlate the
strain field at the edge of the specimen as previously mentioned.
t = 97 h
617N15-1
617N15-2
FE
0 0.6 1.2 1.8 2.4 3.0 3.6 4.0 4.5 [ε
y] x 10
-24 mm
Figure 9.13: Comparison of strain fields in region near notch for 617N15-1, 617N15-2 and FE model at t = 97 h
t = 135 h
617N15-1
617N15-2
FE
0 0.6 1.2 1.8 2.4 3.0 3.6 4.0 4.5 [ε
y] x 10
-24 mm
Figure 9.14: Comparison of strain fields in region near notch for 617N15-1, 617N15-2 and FE model at t = 135 h
The strain distribution along the notch throat is plotted for 617N15-2 in Figure 9.16 compared to FE results for t = 155 h and t = 309 h (corresponding to the midpoint and end of the simulation). Here it is clear that there is good agreement between the two. Although the FE underestimates the strain slightly the trends are very similar and overall the model can be considered to be accurate within the natural variation of the material. This supports the observation in Figures 9.13 and 9.14 that 617N15-2 shows better agreement with the FE than 617N15-1.
It is important to note that the creep properties used for Alloy 617 have been obtained from only four uniaxial creep tests (in Chapter 5), which is insufficient data for a full representation of the material. Therefore, it is a particularly positive outcome that the experimental results show this level of agreement with the model, and indicative that a better fit may be obtained when more data is available.
a)
b)
Figure 9.15: Comparison of strain distribution along notch throat between experimental results and FE for 617N15-1 a) t = 97 h, b) t = 135 h
a)
b)
Figure 9.16: Comparison of strain distribution along notch throat between experimental results and FE for 617N15-2 a) t = 155 h, b) t = 309 h