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In the case of a pulsed laser, solidification occurs in discrete melting events; it follows that a solidification crack must be of length equal to or smaller than a single melt pool radius. Conversely, any crack of length greater than one melt pool radius must have propagated as a solid-state crack, although of course one cannot eliminate the possibility that the solid-state crack propagated from a solidification crack. In order to provide quantitative information, the perimeter to area ratio (units \(\mu \)m\(^{-1}\)) of cracks was assessed. Images were taken at a magnification of 100\(\times \), giving a resolution high enough to identify the jagged features of solidification cracks. A further 70 images were taken of each alloy to compare the contributions of each mechanism on a representative scale; where cracking occurred, many thousands of cracks were analyzed.
(a) Schematic diagram showing the L-PBF build process, whereby a laser melts powder in consecutive layers, (b) the material state and length scale at which solidification and solid-state cracking occur with corresponding SEM image examples of a (c) solidification crack and (d) a solid-state crack in IN939 as well as (e) SEM micrographs of etched CM247LC in the as-printed condition showing the \(\gamma \) matrix and MC carbide and CM247LC in the heat treated condition (reprinted from Ref. [4] under the terms of the Creative Commons CC BY 4.0 license) with \(\gamma ^\prime \) precipitates
Optical micrographs taken of the XZ plane exemplifying cracks observed at the edge and within the bulk of CM247LC, IN939, ExpAM, and IN713, as well as SEM micrographs of solidification and solid-state cracks observed in respective alloys on the XZ plane
In order to strengthen our findings further, detailed quantitative stereological analysis has been employed to quantify the extent to which solidification and solid-state cracks occur in each alloy, and to allow for distinguishing between them. We emphasize first the quantification of cracks at depth in the bulk, since these are the greatest in number and since it may be possible to improve the surface cracking susceptibility by tailoring the processing conditions at the surface. The morphology of cracks in different alloys is summarized by the kernel density estimate of the probability distribution of the perimeter to area ratio \(\mu \)m\(^{-1}\) of cracks in each of the 6 cracked alloys, see Figure 7. Solidification cracks, distinguished by their characteristic jagged morphology and lower perimeter to area ratio, arise to greater extent in the IN738LC, IN939, CM247LC and ABD850AM+CB. This is proven by the deviation of their perimeter to area ratio distributions, which possess a smaller median, interquartile range, and lower/upper adjacent values relative to IN713 and ExpAM. Solid-state cracking is the dominant mechanism in IN713 and ExpAM; in these alloys, cracks are longer and straighter, exemplified by the shift of their perimeter to area distributions towards greater values. Nevertheless, overlap between the distributions for some alloys is apparent for approximately 0.5 < perimeter/area < 0.7, suggesting that the two mechanisms are both operating simultaneously and competing against each other. Cracks in this range are of mixed mode, indicating they began as solidification cracks and then propagated further in the solid-state. The probability distribution of ABD850AM+CB is cut off at 0.19 and 0.67 as the distribution is comprised of only 24 cracks observed.
Violin plots showing the median, interquartile range, lower/upper adjacent values, and probability distribution of the perimeter/area ratio. As well as examples of solidification and solid-state cracks and their corresponding perimeter/area values
The results presented above are insightful and confirm that a strong inter-dependence exists between processability and alloy composition. Nevertheless, further understanding can be gained via more detailed analysis. We consider each of the solid-state and solidification cracking phenomena in turn.
Our calculations indicate a critical minimum ductility in the range 0.5 to 1 pct is likely to be needed for the avoidance of ductility-dip cracking in the critical temperature range of 700 °C to 900 °C. These findings rationalize the poor resistance of the likes of IN713 and ExpAM to solid-state cracking.
So far, the occurrence of solidification cracking has been correlated with the magnitude of the freezing range and presence of continuous films of solute enrichment at crack tips. But a number of composition-dependent solidification cracking criteria should be considered, for example those due to Clyne & Davies (CD),[44] Rappaz, Drezet, & Gremaud (RDG)[45] and Kou.[46] In each case, a parameter \(\Phi \) can be identified, which is predicted to scale with cracking susceptibility. The CD approach for instance considers the dimensionless ratio of the time during solidification during which the alloy is vulnerable to cracking \(\Delta t_{\text{vulnerable}}\) to the time during which it can relieve the accumulated stress \(\Delta t_{\text{stress relief}}\). Assuming a constant cooling rate this ratio is proportional to each respective temperature range, consistent with
A dependence of processability on alloy composition has been proven. Of the twelve alloys studied, quantitative stereology confirmed that half are susceptible to processing-induced crack defect formation under the experimental conditions employed. In particular, IN713 and ExpAM compositions were shown to be prone to solid-state cracking, whilst CM247LC, IN738LC, ABD850AM+CB and IN939 exhibited a tendency towards solidification cracking.
A thermal-elastic-plastic-viscoplastic analysis of a 1D constrained bar has shed light on the factors exacerbating solid-state cracking. It seems likely that this effect is not strongly affected by creep-driven stress-relaxation, under the cooling rates experienced. Instead, processing is compromised by brittleness in the ductility-dip regime. Nevertheless, at any given strength level it appears to be possible to find alloys which are processable, and others which are not.
Our results suggest pathways by which the new alloys may be further improved. Since creep relaxation does not seem to play a role in the solid-state cracking phenomena, it might prove possible to design alloys of creep resistance equivalent to the very best conventionally-cast grades which are amenable to AM processing, provided that they resist solidification cracking.
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