Measurement and determination of crystallographic texture with respect to position
An example method includes measuring, by at least one of a polarized light device, a spatially resolved acoustic spectroscopy device, or an eddy current device, an alpha phase data set indicative of an alpha phase of a crystalline structure of a material. The method includes receiving, by processing circuitry, the alpha phase data set, wherein the alpha phase data set comprises a plurality of pixels, wherein each pixel of the plurality of pixels includes a position, a first Euler angle, a second Euler angle, and a third Euler angle, wherein the third Euler angle is missing or erroneous. The method also includes adjusting, by the processing circuitry, the third Euler angle of a pixel of the plurality of pixels and storing, by the processing circuitry and based on adjusting the third Euler angle of the pixel reducing a total beta phase misorientation, the alpha phase data set.
1 . A method comprising:
measuring, by at least one of a polarized light device, a spatially resolved acoustic spectroscopy device, or an eddy current device, an alpha phase data set indicative of an alpha phase of a crystalline structure of a material;
receiving, by processing circuitry, the alpha phase data set, wherein the alpha phase data set comprises a plurality of pixels, wherein each pixel of the plurality of pixels includes a position, a first Euler angle (φ 1 ), a second Euler angle Φ, and a third Euler angle (φ 2 ), wherein the third Euler angle (φ 2 ) is missing or erroneous;
adjusting, by the processing circuitry, the third Euler angle (φ 2 ) of a pixel of the plurality of pixels; and
storing, by the processing circuitry and based on adjusting the third Euler angle (φ 2 ) of the pixel reducing a total beta phase misorientation, the alpha phase data set.
2 . The method of claim 1 , wherein the material comprises a titanium alloy.
3 . The method of claim 1 , wherein the pixel is a first pixel, the method further comprising:
determining, by the processing circuitry, an alpha grain of each pixel of the plurality of pixels based on a position of each pixel and the first and second Euler angles (φ 1 , Φ) of each pixel;
determining, by the processing circuitry, which alpha grains of the plurality of pixels may be from the same prior beta grain, and
adjusting, by the processing circuitry, the third Euler angle (φ 2 ) of a second pixel of the plurality of pixels,
wherein adjusting the third Euler angle (φ 2 ) of the first pixel and the second pixel is based on:
the first and second pixels are from different alpha grains,
the first and second pixels being from the same prior beta grain, and
the first and second pixels being adjacent to each other.
4 . The method of claim 3 , wherein determining which alpha grains of the plurality of pixels may be from the same prior beta grain comprises:
randomly selecting a pixel of the plurality of pixels as the first pixel, wherein the first pixel is from a first alpha grain;
selecting the second pixel based on the second pixel being from a second alpha grain different from the first alpha grain and the second pixel being adjacent to the first pixel; and
determining that a c-axis misorientation between the first and second pixels is one of about 0°, about 60°, or about 90°.
5 . The method of claim 4 , further comprising:
assigning, by the processing circuitry, a random angle value to the third Euler angle (φ 2 ) of the first pixel;
assigning, by the processing circuitry, a different angle value to the third Euler angle (φ 2 ) of the second pixel such that the c-axis misorientation between the first and second pixels is one of about 0°, about 60°, or about 90°;
assigning, by the processing circuitry, the random angle value to the third Euler angle (φ 2 ) of each pixel of the plurality of pixels that is from the first alpha grain; and
assigning, by the processing circuitry, the different angle value to the third Euler angle (φ 2 ) of each pixel of the plurality of pixels that is from the second alpha.
6 . The method of claim 5 , further comprising:
determining, by the processing circuitry, a first Burgers inverse transform (IT) solution to transform the first pixel to a first beta phase pixel of a beta phase data set and a second Burgers inverse transform (IT) solution to transform the second pixel to a second beta phase pixel of the beta phase data set,
wherein determining the first and second Burgers IT solutions is based on reducing the total beta phase misorientation of the beta phase data set after transforming the first and second pixels by the first and second Burgers IT solutions.
7 . The method of claim 6 , wherein the first and second Burgers IT solutions are selected from a subset of less than all six of a set of six unique Burgers IT solutions that transform an alpha phase crystal to a beta phase crystal.
8 . The method of claim 7 , further comprising:
determining, by the processing circuitry, a Burgers IT solution from the subset of less than all six unique Burgers IT solutions for each pixel of the plurality of pixels based on reducing the total beta phase misorientation of the beta phase data set after transforming each pixel by the respective Burgers IT solution; and
subsequently determining, by the processing circuitry, a Burgers IT solution from the subset including all six unique Burgers IT solutions for each pixel of the plurality of pixels based on reducing the total beta phase misorientation of the beta phase data set after transforming each pixel by the respective Burgers IT solution.
9 . The method of claim 8 , further comprising:
changing, by the processing circuitry, the value of the third Euler angle (φ 2 ) of the first pixel by at least one of 30°, 10.53°, or 5.16°; and
determining, by the processing circuitry, a Burgers IT solution from the subset including all six unique Burgers IT solutions for each pixel of the plurality of pixels based on reducing the total beta phase misorientation of the beta phase data set after transforming each pixel by the respective Burgers IT solution.
10 . The method of claim 9 , wherein a blade of a gas turbine engine comprises the material, the method further comprising:
determining, by the processing circuitry and subsequent to changing the value of the third Euler angle (φ 2 ) of the first pixel, at least one microtexture region (MTR) based on the alpha phase data set;
outputting, by the processing circuitry, an alert based on determining the at least one MTR;
determining, by the processing circuitry, a status of the blade based on at least one of the alpha phase data set or the at least one MTR; and
outputting, by the processing circuitry, the status of the blade.
11 . A device comprising:
a measurement device configured to measure a crystalline structure of a material and output an alpha phase data set indicative of the measurement of the crystalline structure;
a memory; and
one or more processors implemented in circuitry and in communication with the memory, the one or more processors configured to:
receive the alpha phase data set, wherein the alpha phase data set comprises a plurality of pixels, wherein each pixel of the plurality of pixels includes a position, a first Euler angle (φ 1 ), a second Euler angle Φ, and a third Euler angle (φ 2 ), wherein the third Euler angle (φ 2 ) is missing or erroneous;
adjust the third Euler angle (φ 2 ) of a pixel of the plurality of pixels; and
store, based on adjusting the third Euler angle (φ 2 ) of the pixel reducing a total beta phase misorientation, the alpha phase data set.
12 . The device of claim 11 , wherein the material comprises a titanium alloy.
13 . The device of claim 11 , wherein the pixel is a first pixel, wherein the one or more processors are further configured to:
determine an alpha grain of each pixel of the plurality of pixels based on a position of each pixel and the first and second Euler angles (φ 1 , Φ) of each pixel;
determine which alpha grains of the plurality of pixels may be from the same prior beta grain, and
adjust the third Euler angle (φ 2 ) of a second pixel of the plurality of pixels,
wherein adjusting the third Euler angle (φ 2 ) of the first pixel and the second pixel is based on:
the first and second pixels are from different alpha grains,
the first and second pixels being from the same prior beta grain, and
the first and second pixels being adjacent to each other.
14 . The device of claim 13 , wherein, to determine which alpha grains of the plurality of pixels may be from the same prior beta grain, the one or more processors are configured to:
randomly select a pixel of the plurality of pixels as the first pixel, wherein the first pixel is from a first alpha grain;
select the second pixel based on the second pixel being from a second alpha grain different from the first alpha grain and the second pixel being adjacent to the first pixel; and
determine that a c-axis misorientation between the first and second pixels is one of about 0°, about 60°, or about 90°.
15 . The device of claim 14 , wherein the one or more processors are further configured to:
assign a random angle value to the third Euler angle (φ 2 ) of the first pixel;
assign a different angle value to the third Euler angle (φ 2 ) of the second pixel such that the c-axis misorientation between the first and second pixels is one of about 0°, about 60°, or about 90°;
assign the random angle value to the third Euler angle (φ 2 ) of each pixel of the plurality of pixels that is from the first alpha grain; and
assign the different angle value to the third Euler angle (φ 2 ) of each pixel of the plurality of pixels that is from the second alpha.
16 . The device of claim 15 , wherein the one or more processors are further configured to:
determine a first Burgers inverse transform (IT) solution to transform the first pixel to a first beta phase pixel of a beta phase data set and a second Burgers inverse transform (IT) solution to transform the second pixel to a second beta phase pixel of the beta phase data set,
wherein determining the first and second Burgers IT solutions is based on reducing the total beta phase misorientation of the beta phase data set after transforming the first and second pixels by the first and second Burgers IT solutions.
17 . The device of claim 16 , wherein the first and second Burgers IT solutions are selected from a subset of less than all six of a set of six unique Burgers IT solutions that transform an alpha phase crystal to a beta phase crystal.
18 . The device of claim 17 , wherein the one or more processors are further configured to:
determine a Burgers IT solution from the subset of less than all six unique Burgers IT solutions for each pixel of the plurality of pixels based on reducing the total beta phase misorientation of the beta phase data set after transforming each pixel by the respective Burgers IT solution; and
subsequently determine a Burgers IT solution from the subset including all six unique Burgers IT solutions for each pixel of the plurality of pixels based on reducing the total beta phase misorientation of the beta phase data set after transforming each pixel by the respective Burgers IT solution.
19 . The device of claim 18 , wherein a blade of a gas turbine engine comprises the material, wherein the one or more processors are further configured to:
change the value of the third Euler angle (φ 2 ) of the first pixel by at least one of 30°, 10.53°, or 5.16°;
determine a Burgers IT solution from the subset including all six unique Burgers IT solutions for each pixel of the plurality of pixels based on reducing the total beta phase misorientation of the beta phase data set after transforming each pixel by the respective Burgers IT solution;
determine, subsequent to changing the value of the third Euler angle (φ 2 ) of the first pixel, at least one microtexture region (MTR) based on the alpha phase data set;
output and alert based on determining the at least one MTR;
determine a status of the blade based on at least one of the alpha phase data set or the at least one MTR; and
output the status of the blade.
20 . A non-transitory computer-readable storage medium having stored thereon instructions that, when executed, configure a processor to:
receive an alpha phase data set, wherein the alpha phase data set comprises a plurality of pixels, wherein each pixel of the plurality of pixels includes a position, a first Euler angle (φ 1 ), a second Euler angle Φ, and a third Euler angle (φ 2 ), wherein the third Euler angle (φ 2 ) is missing or erroneous;
adjust the third Euler angle (φ 2 ) of a pixel of the plurality of pixels; and
store, based on adjusting the third Euler angle (φ 2 ) of the pixel reducing a total beta phase misorientation, the alpha phase data set.