Method for automatic quantification of dendrite arm spacing in dendritic microstructures
View Patent ↗A method to automatically quantify dendrite arm spacing in dendritic microstructures. Once a location of interest in a cast material specimen has been identified, the information contained in it is automatically analyzed to quantify dendrite cell size information that is subsequently converted into a quantified dendrite arm spacing through an empirical relationship or a theoretical relationship. In one form, the relationship between DCS and DAS is such that the DAS in dendritic structure of cast aluminum alloys may be automatically determined from the measurement of one or more of dendrite cell size and the actual volume fraction of the eutectic phases in the local casting microstructure. Non-equilibrium conditions may be accounted for in situations where a theoretical volume fraction of a eutectic phase of the alloy in equilibrium condition is appropriately modified. Thus, in situations where equilibrium conditions—such as those where the casting is cooled very slowly during solidification—does not apply (such as during rapid cooling and consequent solidification), the eutectic measured in the non-equilibrium condition, which can be smaller than the theoretical value in equilibrium, can be accounted for.
1. A method of automatically quantifying dendrite arm spacing in a hypoeutectic aluminum casting, said method comprising: using a computer-based system to acquire an image corresponding to a location of interest in said casting;
using said computer-based system to estimate a dendrite cell size within said location of interest by overlaying said image with a gridded pattern to quantify the number of intersections between at least one cell boundary from said image and at least one portion of said gridded pattern;
using said computer-based system to estimate a volume fraction of eutectic phases in said location of interest;
using said computer-based system to estimate an aspect ratio of at least one dendrite cell within said location of interest; and
using said computer-based system to convert said estimated dendrite cell size, volume fraction and aspect ratio into a quantified dendrite arm spacing and wherein said estimated dendrite cell size (DCS), volume fraction and average aspect ratio into a quantified dendrite arm spacing (DAS) is expressed by:
DAS=(1− Veu )*DCS/sqrt(α)
where Veu defines said volume fraction and α is said aspect ratio.
2. The method of claim 1 , wherein said computer-based system comprises an image analyzer to perform said acquiring and at least a portion of said determining.
3. The method of claim 1 , wherein said gridded pattern comprises a series of linearly-spaced lines.
4. The method of claim 3 , wherein said series of linearly-spaced lines comprises a series of concentric circles.
5. The method of claim 4 , wherein said dendrite cell size is estimated by the formula
DCS= L/n
where L equals a total perimeter length of said series of concentric circles and n equals the total number of intercepts between the circular lines and said at least one cell boundary.
6. The method of claim 1 , wherein said aspect ratio is defined by the ratio of the maximum linear dimension of said dendrite cell to the minimum linear dimension of said dendrite cell.
7. The method of claim 1 , further comprising outputting said quantified dendrite arm spacing into a user-ready format.
8. The method of claim 1 , wherein said using said computer-based system to estimate a volume fraction of eutectic phases in said location of interest comprises converting said acquired image into a eutectic image equivalent.
9. A method of automatically quantifying dendrite arm spacing in a hypoeutectic aluminum casting, said method comprising:
selecting a cast material to be analyzed;
using a computer-based image analyzer to automatically determine dendrite cell size information corresponding to a location of interest in said selected cast material; and
converting said dendrite cell size information to dendrite arm spacing information with said computer-based image analyzer and wherein said dendrite cell size (DCS) information to dendrite arm spacing (DAS) information is expressed by:
DAS=(1 −Veu )*DCS/sqrt(α)
where Veu defines said eutectic phase volume fraction and α defines said aspect ratio.
10. The method of claim 9 , wherein said using a computer-based image analyzer to automatically determine dendrite cell size information comprises:
acquiring an image corresponding to said location of interest; and
estimating dendrite cell size within said location of interest by overlaying said image with a gridded pattern to quantify the number of intersections between at least one cell boundary from said image and at least one portion of said gridded pattern.
11. The method of claim 10 , wherein said converting said dendrite cell size information to dendrite arm spacing information comprises:
using said computer-based image analyzer to estimate a eutectic phase volume fraction in said location of interest;
using said computer-based image analyzer to estimate an aspect ratio of at least one dendrite cell within said location of interest; and
using said computer-based image analyzer to convert said estimated dendrite cell size, volume fraction and aspect ratio into a quantified dendrite arm spacing.
12. The method of claim 9 , wherein said computer-based image analyzer forms part of a computer-based dendrite arm spacing quantifying system.
13. An article of manufacture comprising a non-transitory computer usable medium having computer readable program code embodied therein for automatically quantifying dendrite arm spacing (DAS) for a hypoeutectic aluminum cast material, said computer readable program code in said article of manufacture comprising:
computer readable program code portion for causing said computer to accept data pertaining to digital information of a location of interest within a sample of said cast material;
computer readable program code portion for causing said computer to process said digital information into dendrite cell size information (DCS);
computer readable program code portion for causing said computer to convert said dendrite cell size information into a corresponding dendrite arm spacing through an algorithm based on a volume fraction of eutectic phases in said location of interest and an aspect ratio of at least one dendrite cell within said location of interest; and
computer readable program code portion for causing said computer to produce an output that corresponds to said dendrite arm spacing; and
wherein said computer readable program code portion for causing said computer to convert said dendrite cell size information into a corresponding dendrite arm spacing is expressed by:
DAS=(1 −V eu )*DCS/sqrt(α)
where V eu defines said volume fraction of eutectic phases in said location of interest and α defines said aspect ratio of at least one dendrite cell within said location of interest.