Torrent Stress Concentration Crack UPD
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Without post-manufacture HIPing the fatigue life of electron beam melting (EBM) additively manufactured parts is currently dominated by the presence of porosity, exhibiting large amounts of scatter. Here we have shown that the size and location of these defects is crucial in determining the fatigue life of EBM Ti-6Al-4V samples. X-ray computed tomography has been used to characterise all the pores in fatigue samples prior to testing and to follow the initiation and growth of fatigue cracks. This shows that the initiation stage comprises a large fraction of life (>70%). In these samples the initiating defect was often some way from being the largest (merely within the top 35% of large defects). Using various ranking strategies including a range of parameters, we found that when the proximity to the surface and the pore aspect ratio were included the actual initiating defect was within the top 3% of defects ranked most harmful. This lays the basis for considering how the deposition parameters can be optimised to ensure that the distribution of pores is tailored to the distribution of applied stresses in additively manufactured parts to maximise the fatigue life for a given loading cycle.
Previous evidence20, 23 has suggested that fatigue life is most strongly influenced by the area of a defect normal to the applied stress (A n ) rather than its volume. If it is assumed that cracks initiated at the widest cross-sectional area of the pore, then this value can be manually measured on the fracture surface. To reduce measurement error, each pore was measured five times and the mean value calculated. For all samples the standard deviation between measured pore areas was
Both fractography and CT analysis indicate that all the surface pores that led to critical fatigue cracks lay within a diameter of the surface where the rise in K t is most significant. This suggests that the increased stress concentration near a surface is an important contributor to the propensity of fatigue cracks to initiate at surface pores.
Ranking 3: Defect size, location, aspect ratio and proximity to other pores and the surface. Here we rank the pores from the CT data according to the approximate elastic tensile stress concentration. This ranking includes the stress concentration from proximity to a surface K t (surface), the effect of pore aspect ratio K t (AR) (Fig. 6), proximity to other pores K t (proximity) (Fig. 7) and the non-uniform stress σ x (position) (Fig. 8) across the sample:
An algorithm written in MATLAB was used to analyse all the pores detected by CT to determine each pores normal area, radial location and dimensionless values for aspect ratio, d/D and s/D. It was assumed all pores had a smooth spheroidal morphology. The radial location was used to estimate the stress due to the sample geometry (Fig. 8). The dimensionless values were then combined with the results of the FE modelling shown in Figs 6 and 7 to assign each pore an elastic tensile stress concentration value. By multiplying this with the fourth root of the normal area, a relative stress intensity factor was calculated. The methodology is described in more detail in the supplementary information. The empirical nature of equation (2) allows the algorithm to run in orders of magnitude less time than required to mesh and model all the pores within a microstructurally faithful FE model. Clearly, the expression in equation (2) is not the true stress intensity factor for each pore, however it can be used to rank the relative harmfulness of each pore.
Ranking 4: Plastic stress-strain concentration. Cracks were found by Li et al.23 to initiate in aluminium samples at the location of maximum plastic stress-strain concentration (k g ). To evaluate this requires FE modelling of the fatigue test piece and porosity to locate and calculate the location of greatest k g , given by:
where K σ and K ε are the local principal stress and plastic strain concentrations, respectively. While FE meshes can be generated from CT data, the number of pores meant that it was not feasible to individually mesh and model them all, and the computational cost of modelling the entire fatigue gauge length with a fine enough mesh to retain accuracy was prohibitive. Therefore, only those pores judged to be among the 5% most detrimental by method 3 described above were modelled. Sub-volumes around the selected pores were extracted, with a size 5 times the pore diameter and taking into account any other pores or sample surface as originally defined by the CT data. The loading conditions applied to the models were defined by their location within the sample and the stress distribution shown in Fig. 8.
Thus, four methods with varying levels of complexity were used to rank the pores potential relative detrimental effects. In Table 1, the ranking of the pore at which the crack actually initiated by each of the methods outlined above is given. All three ranking methods that take into account the local environment outperformed that based on size alone (ranking 1) confirming the importance of local environment and in particular the importance of proximity to the surface. Overall the best performing are ranking methods 3 and 4, which given the complexity of 4 suggest that it is sufficient simply to take into account the elastic stress concentration arising from proximity to the surface and the neighbouring pores. It is noteworthy that none of the methods applied were able to correctly predict the actual initiating defect, highlighting the stochastic nature of fatigue.
More complex FE modelling of the pores did not result in a significantly more accurate identification of the likelihood of a pore being the crack initiation site. This is in contrast to the work of Li et al.23 who found fatigue crack initiation in aluminium samples occurred at the region of the highest plastic stress-strain concentration calculated with an FE model generated from CT data. This failure to predict the actual defect initiating a crack could be due to a number of factors, including errors in segmentation of the CT data and the lack of any consideration of the local microstructure. Furthermore, the resolution of the CT may have been insufficient to detect the true geometry of the porosity, whereas the pores analysed by Li et al.23 were significantly larger than the voxel size; hence, they would have been able to extract a more accurate representation of the pore.
Since FE modelling of the imaged pores was unable to identify the initiating pore, it suggests that we must either use higher resolution CT to get a more accurate model of the stress distribution or account for effects other than stress. For example, the propensity of surface pores to initiate cracks may have been amplified by the testing taking place in a non-inert atmosphere. However, without carrying out multiple extra tests in an inert atmosphere it is impossible to define how significant this effect is.
By word of caution it is noteworthy that the crack initiating from the large interior pore in sample x-600a (arrowed in Fig. 9a) appears not to have nucleated at the mid-riff where the tensile stress concentration (Fig. 9c) is greatest, but near the pole. Given that the shear stress (Fig. 9d) is large near here this could indicate that in this case the fatigue crack initiation and early growth is dominated by shear within persistent slip bands32. Alternatively, it could be simply an indicator of the stochastic nature of fatigue crack initiation associated with local microstructural factors. Unfortunately, the resolution of the CT data was not high enough to confirm whether this was the case in the other samples, where the pores at the crack initiation site were much smaller.
Fatigue crack initiation location in sample x-600a - Slices of the CT data in: (a) x-y plane and (b) x-z plane. Here, x is both the raking direction during the EBM build and loading direction during fatigue testing, while z is the build direction. Results of the analysis of the pore geometry detected by CT prior to testing with half the model visible, showing (c) tensile stress and (d) shear stress.
Unfortunately, the surface finish of EBM components is currently fairly poor6, so it is likely that some level of surface machining will be required before putting components into service. This could move the pores responsible for the peaks in pore volume fraction identified in Fig. 10b close enough to the surface of components to result in an increase in their stress concentration factor. The CT data from the standard cuboid (Fig. 10b) was therefore interrogated to calculate how many pores would be brought to a detrimental location with different levels of material removal. Between 0.5 mm and 1 mm of material was removed from the virtual model of the as-built sample (likely to be similar that removed in an industrial application) and the number of pores brought within one diameter of the surface calculated. From the calculated number of pores, shown in Fig. 10c binned by size, it is clear that the level of material removal can significantly affect the number of pores present per unit area of machined surface, with a peak at around 0.8 mm, before dropping with further material removal.
The non-uniform spatial distribution of porosity in EBM means that different surface machining operations will lead to different levels of porosity at the machined surface and thus is likely to result in different fatigue lives. By altering the melt strategy and machining depth, it may be possible to optimise the fatigue life by avoiding defects near the surface. This will enable materials scientists and engineers to develop probabilistic models for component life prediction in AM parts - thinking particularly on those components that are designed to exploit AM, e.g. structurally optimised. While it is not possible to conduct X-ray CT on every manufactured article, it could be used along with FE modelling and our stress c