Void Nucleation

Void nucleation was firstly quantified by calculating the number of cavities *nc* in every cropped volume. The mean cavities density *N* per cubic mm was calculated by dividing *nc* by the value of the analysed sub–volume. Figure 6 shows the evolution of the void density *N* as a function of the true strain for AISI316L and AISI316. Two samples were tested for the non-charged AISI316L; they are both plotted on the figure and they show a similar behavior. Nucleation being quite exponential with strain in steels (already observed in [15]), we have plotted the results in a logarithmic scale. Note first that the number of nucleated cavities is rather small in these samples. This is because of the homogeneous nature of these materials which present very few inclusions where damage can nucleate. It can be seen that, in the non-charged state, *N* increases very slowly in the AISI316 steel. We have noticed that, surprisingly, for this particular AISI316 sample, nucleation was anomalously small inside the neck and was mainly located at the periphery of the sample, where strain and triaxiality are not at their maximum. This is probably because when nucleation is very scarce, as is the case in these two materials, the random nature of the location of the nucleation site can lead to such surprising observations. We have then decided to reject this sample from the rest of the quantification. From the measurement of the three other materials, where nucleation was more substantial, it appears that hydrogen charging has only a weak effect on the nucleation kinetics, as can be measured by X-ray CT. The dotted curve included in the figure also shows the results that we previously obtained in [17] for a standard non-charged AISI316L sample (of different origin than the one used in this study). For these previous measurements, we were using synchrotron X-ray CT with a pixel size of 1.6 μm so detection capacity was smaller. This explains that the observed number of cavities was smaller in previous study. Despite these differences, we believe that it is comforting to see that the slope of the different curves are similar. The fact that *N* decreases at high strain for the hydrogen-charged AISI316 can be attributed to coalescence.

**Figure 6.** Nucleation quantified as the evolution of the density of cavities with strain. The nucleation in the non-charged AISI316 sample is anomalously small because of a small amount of nucleation in the necked region for this sample. From the behavior of the three other materials, it can be concluded that hydrogen charging has a weak effect on the nucleation kinetics. The measurements by Fabrègue et al. [17] are also shown as a dotted line. These were made using a larger voxel size (1.6 μm pixel size) which explains the lower level of nucleation detected, but the slope of the curve is in line with the measurements of the present paper.

#### *3.5. Void Growth*

In the 3D images, each void is composed of a certain amount of voxels and this allowed us to measure the volume of each cavity *Vi*. From this value, we have then calculated the equivalent diameter of a sphere exhibiting the same volume:

$$D\_{eq,i} = (6V\_i/p)^{1/3}.\tag{4}$$

It has been shown in previous studies that growth could be easily estimated by quantifying the average value of the largest cavities assumed to remain the same from one strain step to the next [23]. Here, we have chosen to work with the 20 largest cavities. Figure 7 shows the evolution of the average equivalent diameter of the 20 largest cavities in the cropped volume as a function of the true strain for the AISI316L non-charged, and for the two charged materials. For the sake of clarity, we have rationalized the values of *Deq* by dividing it by its value at 0 strain *D*0. Previous measurement [17] is also shown as a dotted curve. In terms of growth, we clearly show again here that hydrogen charging has a weak effect of the growth rate of the cavities.

**Figure 7.** Growth of the average equivalent diameter of the 20 largest cavities with strain.

#### *3.6. Aspect Ratio of the Cavities*

The aspect ratio of the cavities has been calculated for the two smooth hydrogen charged samples (AISI316 and AISI316L) just before fracture (same as those shown in Figure 4). For calculating the aspect ratio of the cavities, we used the following simplified formula:

$$Aspect\ ratio = \frac{L\_x + L\_y}{2L\_z} \,\prime \tag{5}$$

where *Lx*, *Ly* and *Lz* are the largest dimensions of the cavity along the different directions of the reconstructed volume (remember that *z* is the tensile axis).

The aspect ratio is smaller than one for cracks and higher when the cavities are elongated along the tensile direction. Figure 8 compares the histogram of the values of the aspect ratio for the 20 largest cavities, for the two charged materials. This comparison is performed for a similar deformation step close to fracture. This histogram confirms the visual impression in Figure 5 i.e., the cavities have a crack–like shape in the case of the AISI316 sample and much less for the AISI316L.

**Figure 8.** Histogram of the distribution of the aspect ratio of the 20 largest cavities in the two hydrogen charged materials in the state just before fracture.
