PSI - Issue 28

5

Michael Jones et al. / Procedia Structural Integrity 28 (2020) 2078–2085 Author name / Structural Integrity Procedia 00 (2019) 000–000

2082

(a)

Centre

Edge

4 th

3 rd

2 nd

(b)

Centre

Edge

2 nd

3 rd

4 th

(c)

y

3 rd

2 nd

Centre

Edge

4 th

r

Figure 5(a)-(c) – The locations for sampling of the triaxiality and strain data in (a) the small notch, (b) the medium notch and (c) the blunt notch.

4. Comparison of Results In Figure 6 comparisons of the triaxiality (a-c) and axial strain (d-f) values throughout the tests for the three notch geometries. Figure 6(g) shows the legend for all the graphs. The trends shown in Figure 6(a)-(c) are all similar. The experimental values for the triaxiality start at approximately their maximum value. They do not change appreciably for a short period, likely while the deformation is elastic, then continually decrease until the end of the time recorded. Most of the results from the FEA also reach a maximum very early on in the test, but thereafter they do not change much from this value. It can also be seen that for all the geometries the experimental Bridgman values over predict the FEA results. In addition, the position of maximum triaxiality is shown to be at some point between the centre and the edge, and not on the centreline as predicted by Bridgman. As previously mentioned, Bridgman made the assumption that the axial strain across the radius would be uniformly distributed. Figure 6(d)-(f) clearly show that for all notch geometries the strain distribution is not radially uniform. As the notch sharpness increases, the distribution becomes more uniform towards the centre of the sample, but the strain at the edge is also far higher. Although the strain values for the four inner values in the sharp notch specimen are of very similar magnitudes, the strain at the edge is approximately ten times greater. 5. Discussion The results in the previous section clearly show a very poor agreement between the experimental and numerical triaxiality values, and that the assumption of uniform strain across the radius is invalid. It should be noted that Bridgman’s theory was developed for necked geometries, i.e. those that are originally uniform cross-section and subsequently develop a neck at high strains. This likely leads to a significantly different flow pattern and stress distribution from that of an initially notched specimen. The sharp notch used in this testing programme is much more