CN114693620B - Characterization method of second phase space distribution uniformity in cast aluminum alloy - Google Patents
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Abstract
The invention discloses a characterization method of second phase space distribution uniformity in cast aluminum alloy. The method comprises the following steps: acquiring a cast aluminum alloy X-ray three-dimensional tomographic image of a sample, moderately cutting, and then carrying out noise reduction and binarization to acquire a three-dimensional characteristic and a distribution diagram of a second phase in the aluminum alloy; based on a multi-fractal algorithm, calculating probability measures of second phase space distribution in boxes with different scales through a box counting dimension method; constructing a distribution function by utilizing probability measurement of the second phase, calculating a quality index according to the distribution function, and judging the calculated adaptability range of the multi-fractal method; constructing normalized q-order moment of probability measure, calculating multi-fractal spectrum parameters of second phase space distribution in the aluminum alloy according to the normalized q-order moment, drawing multi-fractal spectrum, and quantitatively representing uniformity of the second phase space distribution in the aluminum alloy. The invention overcomes the defects of the analysis method in the prior art, can accurately identify the spatial distribution characteristics of the second phase with complex morphology, and quantitatively describe the spatial distribution uniformity of the second phase.
Description
Technical Field
The invention belongs to the technical field of material distribution uniformity characterization, and particularly relates to a characterization method of second phase spatial distribution uniformity in cast aluminum alloy.
Background
The aluminum alloy has the characteristics of good forming property, high specific strength, excellent corrosion resistance, diversified structures and the like, and is widely applied to daily life and industrial production, especially in the fields of automobiles and aerospace industry. A great deal of work has been done by researchers to develop aluminum alloy materials that have both high strength and high toughness. In general, the strength is improved by adding new alloying elements and utilizing second phase strengthening, and the method is one of important methods for developing high-performance cast aluminum alloys. The uniformity of the distribution of the second phase in the cast aluminum alloy is closely related to the mechanical properties of the alloy. The solidification condition of the casting is changed under different processes, the nucleation and growth of the second phase particles are changed, and the final size and distribution are different; meanwhile, the actual casting has complex shape (such as an engine cylinder body and a cylinder cover), even under the same process condition, the difference of cooling and solidification of each part also causes the final size and distribution of the local second phase particles to change, and the mechanical properties of the local second phase particles are necessarily different; therefore, the uniformity of the second phase particle distribution is accurately analyzed, and the mechanical property can be evaluated, so that the casting process parameters are optimized, and the method has important significance and effect.
In the aspect of analyzing the uniformity of the second phase distribution in the cast aluminum alloy, the prior art mainly uses manual characterization, namely, two-dimensional observation is carried out on a golden phase diagram or a scanning electron microscope diagram and the like, then judgment is carried out, and the method is only qualitative characterization and can bring errors due to subjective factors of people. In addition, since the mutually independent phases observed in two dimensions are possibly connected in space, the two-dimensional metallographic or scanning electron microscope image is only one section in three dimensions, so that the distribution characteristic of the second phase on the two-dimensional section is different from the actual spatial morphology characteristic, and errors are generated when evaluating the uniformity of the second phase in the aluminum alloy.
In summary, the characterization method for the uniformity of the second phase in the cast aluminum alloy in the prior art has insufficient feature characterization accuracy, cannot quantitatively describe the uniformity of the second phase, and cannot embody the actual shape and distribution characteristics of the second phase space. Therefore, there is a need to develop a method capable of quantitatively characterizing the spatial distribution uniformity of the second phase in the aluminum alloy scientifically, accurately and comprehensively. The method quantitatively analyzes the uniformity of the spatial distribution of the second phase in the cast aluminum alloy, and judges the difference of casting performance, so that optimized casting process parameters are selected, and the actual production is guided.
Disclosure of Invention
The invention aims to solve the technical problems of overcoming the defects of the prior art, and provides a quantitative characterization method for the spatial distribution uniformity of a second phase in a cast aluminum alloy.
In order to solve the technical problems, the invention adopts the following technical scheme:
s1, acquiring three-dimensional characteristic images of aluminum alloy of the same parts of castings with different process parameters or samples of different parts of castings with the same process through an X-ray three-dimensional tomography and reconstruction technology, and then moderately cutting the images;
S2, denoising the cut three-dimensional characteristic image by using image processing algorithms such as non-local mean filtering and the like, and performing binarization processing on the denoised image by using algorithms such as Wellner self-adaptive threshold and the like to obtain a second-phase three-dimensional characteristic and a distribution image;
S3, covering the binary image by utilizing boxes with different scales according to a multi-fractal algorithm, and calculating probability measures of second phases in the boxes with different scales according to a box counting method;
s4, constructing a distribution function by utilizing probability measurement of the second phase, calculating a quality index according to the distribution function, and judging the calculated adaptability range of the multi-fractal method;
S5, constructing a normalized q-order moment of probability measure, calculating multi-fractal spectrum parameters of second phase spatial distribution in the aluminum alloy according to the normalized q-order moment, drawing a multi-fractal spectrum, and quantitatively representing uniformity of the second phase spatial distribution in the aluminum alloy according to the multi-fractal spectrum width of the second phase, wherein the smaller the multi-fractal spectrum width is, the more uniform the second phase spatial distribution is.
The above method, further, the step S3 is:
S31 are respectively scaled as delta x delta (delta=2 n, n=1, 2,3, the box cover binarized image, the number of boxes in each direction is noted m:
Wherein l= (L 1,L2,L3) is the side length of the binarized image; m= (m 1,m2,m3) is the number of boxes with single side length.
Recording the number N ijk (delta) of second phase pixels in the box (i, j, k);
boxes (i, j, k) represent that when a binarized image is covered with a cubic box of a certain delta scale, the whole three-dimensional image is covered with m 1×m2×m3 boxes, and specific coordinates of each box in the three-dimensional space are represented by (i, j, k);
S32, dividing N ijk by the total number N of pixels of the second phase in the binary image to obtain the proportion of the second phase in each box with the scale delta, wherein the proportion is a probability measure P ijk (delta), and the probability measure P ijk (delta) is as follows:
Wherein α ijk is a singularity index, which characterizes the distribution of the second phase in the box (i, j, k).
S33, when the side length of the box is δ, if M (α ijk) boxes with probability measures of P ijk (δ) exist in [ α ijk,αijk+Δαijk ], f (α ijk) is defined as the fractal dimension of the singularity index α ijk as follows:
When the box size goes to 0, then there are:
Alpha ijk is obtained by taking the logarithm of both sides of the equation (2). Δα ijk represents a minimum value under the discrete formula. f (. Alpha. ijk) is directly defined by the formula (3). The definition and meaning of these parameters is based on fractal theory and metric theory.
The above method, further, the step S4 is:
s41, constructing a distribution function. The q-order moments of the box probability measures are summed to obtain a partitioning function X (q, delta) as follows:
wherein the range of the q-order moment is (- ≡, ++ infinity a) of the above-mentioned components, the specific range is determined according to the calculation error.
S42, constructing a quality index. According to the fractal theory, the following relationship exists between the distribution functions X (q, delta) and delta:
Selecting the value range of the box dimension delta, fitting the lnX (q, delta) to lndelta curve, and when lnX (q, delta) to lndelta is approximately a straight line, namely the mass index tau (q) is approximately a constant, indicating that the multi-fractal method in the range can be used for analyzing the distribution uniformity of the second phase three-dimensional characteristics in the cast aluminum alloy.
The above method, further, the step S5 is:
S51, constructing normalized q-order moment of probability measure. The calculation of α and f (α) is achieved by a normalized q-order moment μ ijk (q, δ) of the probability measure. Alpha refers to the singular index of the entire three-dimensional computation space, and f (alpha) refers to the fractal dimension of alpha. The following is shown:
wherein the range of the q-order moment is (- ≡, ++ infinity a) of the above-mentioned components, the specific range is determined according to the calculation error.
S52, binding equation (2), then directly calculating the multi-fractal singular index using μ ijk (q, δ):
Combining equation (4), then directly calculating the multi-fractal spectral function using μ ijk (q, δ):
And obtaining multi-fractal spectrums f (alpha) -alpha according to the formula, and calculating the spectrum width delta alpha, wherein the spectrum width delta alpha=alpha max-αmin,αmax is the maximum singularity index, and the spectrum width alpha min is the minimum singularity index. The smaller Δα, the more uniform the spatial distribution of the second phase, and conversely, the more non-uniform.
The beneficial effects of the invention are as follows:
1. the invention takes the X-ray three-dimensional tomographic image of the second phase in the cast aluminum alloy as a processing object, and the X-ray three-dimensional tomographic image technology can accurately identify the three-dimensional real appearance and distribution of the second phase in the aluminum alloy due to the advantages of high spatial resolution, accurate measurement and the like.
2. The method is based on a multi-fractal method, is not limited by the morphology and the spatial distribution state of the second phase, and can obtain objective and quantitative analysis results on the spatial distribution uniformity of the second phase with simple or complex morphology and spatially dispersed or aggregated morphology.
3. According to the invention, based on the real appearance and characteristics of the second phase in the aluminum alloy obtained by X-ray three-dimensional tomography, based on a multi-fractal method, the multi-fractal spectrum parameter and the multi-fractal spectrogram of the second phase spatial distribution are combined, so that the multi-fractal spectrum width is obtained by calculation, and the accurate quantitative characterization of the uniformity of the second phase spatial distribution in the aluminum alloy is realized.
4. According to the invention, through accurately and quantitatively characterizing the spatial distribution uniformity of the second phase of the aluminum alloy, the difference of the structural performance of the same part of the casting under different process parameters or each part of the casting under the same process can be estimated and evaluated, so that the selection of optimized process parameters is guided, and the actual production is optimized.
Drawings
FIG. 1 is a flow chart of a characterization method provided by the present invention.
FIG. 2 shows a three-dimensional tomographic image of a cast aluminum alloy X-ray after cutting in an embodiment of the present invention, (a) sample 1, (b) sample 2.
Fig. 3 shows a spatial distribution diagram of a second phase in an aluminum alloy obtained by noise reduction and binarization in the embodiment of the present invention, (a) sample 1, and (b) sample 2.
Fig. 4 is a multi-fractal spectrum of the uniformity of the distribution of the second phase in the aluminum alloy in the examples of the present invention, (a) sample 1, (b) sample 2.
Detailed Description
In order to make the technical problems solved, the technical scheme adopted and the technical effects achieved by the invention more clear, the technical scheme of the invention will be described in detail in the following with reference to the embodiment, but the protection scope of the invention is not limited thereby.
A characterization method of second phase space distribution uniformity in cast aluminum alloy can be used for selecting optimized process parameters and guiding actual production, and the characterization flow chart is shown in fig. 1, and comprises the following steps:
al-7Si-3.5Cu alloy is prepared under different technological parameters:
technological parameters I:
Before the smelting experiment, the surfaces of the smelting tool and the cavity of the experimental die are coated with ZnO coating so as to prevent additional iron from being introduced into the experiment, and then the die is placed in a box-type resistance furnace for heating and heat preservation at 300 ℃. In the experimental process, a pure aluminum ingot (99.95%), al-20wt.% Si and Al-50wt.% Cu intermediate alloy are placed in a crucible resistance furnace for smelting, and after the alloy ingot is completely melted, the alloy ingot is uniformly stirred and then is kept warm for 30min, so that the components of the aluminum liquid are fully uniform. After melting, adding modifier Al-10wt.% Sr and refiner Al-5wt.% Ti-B, and stirring uniformly. The melt was incubated at 700℃and degassed with argon for 5min, followed by standing and deslagging. After the alloy is smelted, the die is taken out from the box-type resistance furnace and assembled, the temperature of the die cavity is measured by an infrared thermometer, and casting is carried out when the temperature of the die cavity is 250 ℃.
And the process parameters are as follows:
Before the smelting experiment, the surfaces of the smelting tool and the cavity of the experimental die are coated with ZnO coating so as to prevent additional iron from being introduced into the experiment, and then the die is placed in a box-type resistance furnace for heating and heat preservation at 300 ℃. In the experimental process, a pure aluminum ingot (99.95%), al-20wt.% Si and Al-50wt.% Cu intermediate alloy are placed in a crucible resistance furnace for smelting, and after the alloy ingot is completely melted, the alloy ingot is uniformly stirred and then is kept warm for 30min, so that the components of the aluminum liquid are fully uniform. After melting, adding modifier Al-10wt.% Sr and refiner Al-5wt.% Ti-B, and stirring uniformly. The melt was incubated at 720℃and degassed with argon for 5min, followed by standing and deslagging. After the alloy is smelted, the die is taken out from the box-type resistance furnace and assembled, the temperature of the die cavity is measured by an infrared thermometer, and casting is carried out when the temperature of the die cavity is 250 ℃.
After the experiment was completed, two castings obtained at different process parameters (different casting temperatures) were sampled and recorded as sample 1 and sample 2. The spatial distribution uniformity of the Al 2 Cu phase in the two samples is characterized, and the optimal process parameters are further determined according to the spatial distribution uniformity of the Al 2 Cu phase:
S1, acquiring three-dimensional characteristic images of aluminum alloy under different process parameters through an X-ray three-dimensional tomography and reconstruction technology, and then moderately cutting the images, as shown in FIG. 2;
s2, denoising the cut three-dimensional characteristic image by using a non-local mean value filtering image processing algorithm, and then performing binarization processing on the denoised image by adopting a Wellner self-adaptive threshold algorithm to obtain a second-phase three-dimensional characteristic and a distribution image, as shown in FIG. 3;
S3, covering the binary images by utilizing boxes with different scales according to a multi-fractal algorithm, and calculating probability measures of Al 2 Cu phases in the boxes with different scales according to a box counting method;
S4, constructing a distribution function by utilizing probability measurement of an Al 2 Cu phase, calculating a quality index according to the distribution function, and judging the calculated adaptability range of the multi-fractal method;
S5, constructing a normalized q-order moment of probability measurement, calculating multi-fractal spectrum parameters of Al 2 Cu phase spatial distribution in the aluminum alloy according to the normalized q-order moment, drawing a multi-fractal spectrum, and quantitatively representing the uniformity of Al 2 Cu phase spatial distribution according to the multi-fractal spectrum width of a second phase, wherein the smaller the multi-fractal spectrum width is, the more uniform the Al 2 Cu phase spatial distribution is;
s6, selecting optimized process parameters according to the quantized spatial distribution uniformity of the Al 2 Cu phase.
The above method, further, the step S3 is:
S31 are respectively scaled as delta x delta (delta=2 n, n=1, 2,3, box cover binarized image, box count in each direction is noted m:
Wherein l= (L 1,L2,L3) is the side length of the binarized image, in this embodiment, L 1＝L2＝L3＝1024;m＝(m1,m2,m3 is the number of boxes with side length, in this embodiment, m 1＝m2＝m3.
Recording the number N ijk (delta) of second phase pixels in the box (i, j, k);
S32, dividing N ijk by the total number N of pixels of the second phase in the binary image to obtain the proportion of the second phase in each box with the scale delta, wherein the proportion is a probability measure P ijk (delta), and the probability measure P ijk (delta) is as follows:
Wherein α ijk is a singularity index, which characterizes the distribution of the second phase in the box (i, j, k).
S33, when the side length of the cubic box is δ, if M (α ijk) boxes with probability measures of P ijk (δ) exist in [ α ijk,αijk+Δαijk ], f (α ijk) is defined as the fractal dimension of the singularity index α ijk as follows:
When the box size goes to 0, then there are:
the above method, further, the step S4 is:
s41, constructing a distribution function. The q-order moments of the box probability measures are summed to obtain a partitioning function X (q, delta) as follows:
wherein the q-order moment has a value range (-4, +4) and an interval of 0.5.
S42, constructing a quality index. According to the fractal theory, the following relationship exists between the distribution functions X (q, delta) and delta:
Selecting the value range of the box dimension delta, fitting the lnX (q, delta) to lndelta curve, and when lnX (q, delta) to lndelta is approximately a straight line, namely the mass index tau (q) is approximately a constant, indicating that the multi-fractal method in the range can be used for analyzing the distribution uniformity of the second phase three-dimensional characteristics in the cast aluminum alloy.
The above method, further, the step S5 is:
S51, constructing normalized q-order moment of probability measure. The calculation of α and f (α) is achieved by a normalized q-order moment μ ijk (q, δ) of the probability measure. The following is shown:
Wherein the q-order moment has a value range (-4, +4) and an interval of 0.5.
S52, binding equation (2), then directly calculating the multi-fractal singular index using μ ijk (q, δ):
combining equation (4), then directly calculating the fractal dimension of the multi-fractal spectrum using μ ijk (q, δ):
the multi-fractal spectra f (α) to α are obtained according to the above formula, as shown in fig. 4. As can be seen from fig. 4, the spectral width Δα of sample 1 is 0.114, and the spectral width Δα of sample 2 is 0.345. It can be seen that the spatial distribution of the Al 2 Cu phase in sample 1 is more uniform than that of sample 2. The Al 2 Cu phase obtained by the first technological parameter is more uniformly distributed in the space of the same alloy component, so that the casting performance can be judged to be better.
The above examples are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above examples, and any other changes, modifications, substitutions, combinations, and simplifications that do not depart from the spirit and principle of the present invention should be made in the equivalent manner, and the embodiments are included in the protection scope of the present invention.
Claims (3)
1. A method for characterizing the uniformity of the spatial distribution of a second phase in a cast aluminum alloy, comprising the steps of:
s1, acquiring three-dimensional characteristic images of aluminum alloy of the same parts of castings with different process parameters or samples of different parts of castings with the same process through an X-ray three-dimensional tomography and reconstruction technology, and then moderately cutting the images;
s2, denoising the cut three-dimensional characteristic image by using an image processing algorithm, and then binarizing the denoised image to obtain a second-phase three-dimensional characteristic and a distribution image;
S3, covering the binary image by utilizing boxes with different scales according to a multi-fractal algorithm, and calculating probability measures of second phases in the boxes with different scales according to a box counting method;
s4, constructing a distribution function by utilizing probability measurement of the second phase, calculating a quality index according to the distribution function, and judging the calculated adaptability range of the multi-fractal method;
S5, constructing a normalized q-order moment of probability measure, calculating multi-fractal spectrum parameters of second phase spatial distribution in the aluminum alloy according to the normalized q-order moment, drawing a multi-fractal spectrum, and quantitatively representing uniformity of the second phase spatial distribution in the aluminum alloy according to the multi-fractal spectrum width of the second phase, wherein the smaller the multi-fractal spectrum width is, the more uniform the second phase spatial distribution is;
The step S3 specifically comprises the following steps:
S31, covering the binarized image by boxes with the scale of delta multiplied by delta respectively, δ=2 n, n=1, 2, 3, …, the number of boxes in each direction being noted m:
Wherein l= (L 1,L2,L3) is the side length of the binarized image; m= (m 1,m2,m3) is the number of boxes with single side length;
Recording the number N ijk (delta) of second phase pixels in the box (i, j, k); boxes (i, j, k) represent that when a binarized image is covered with a cubic box of a certain delta scale, the whole three-dimensional image is covered with m 1×m2×m3 boxes, and specific coordinates of each box in the three-dimensional space are represented by (i, j, k);
S32, dividing N ijk by the total number N of pixels of the second phase in the binary image to obtain the proportion of the second phase in each box with the scale delta, wherein the proportion is a probability measure P ijk (delta), and the probability measure P ijk (delta) is as follows:
wherein α ijk is a singularity index, characterizing the distribution of the second phase in the box (i, j, k);
s33, when the side length of the box is δ, if M (α ijk) boxes with probability measures of P ijk (δ) exist in [ α ijk,αijk+Δαijk ], f (α ijk) is defined as the fractal dimension of the singularity index α ijk as follows:
When the box size goes to 0, then there are:
Wherein, alpha ijk is obtained by taking the logarithm of the two sides of the formula (2); Δα ijk represents a minimum value in the discrete formula;
The step S4 is as follows:
s41, constructing a distribution function, and summing the q-order moments of each box probability measure to obtain a distribution function X (q, delta), wherein the distribution function X (q, delta) is as follows:
Wherein the range of the q-order moment is (- ≡, + -infinity), the specific range is determined according to the calculation error;
s42, constructing a quality index, and according to a fractal theory, the following relation exists between a distribution function X (q, delta) and delta:
Selecting a value range of a box scale delta, fitting a lnX (q, delta) to lndelta curve, and when lnX (q, delta) to lndelta is approximately a straight line, namely the mass index tau (q) is approximately a constant, indicating that the multi-fractal method in the range can be used for analyzing the distribution uniformity of the second phase three-dimensional characteristics in the cast aluminum alloy;
The step S5 is as follows:
S51, constructing a normalized q-order moment of the probability measure, and calculating alpha and f (alpha) through the normalized q-order moment mu ijk (q, delta) of the probability measure, wherein alpha refers to a singular index of the whole three-dimensional calculation space, and f (alpha) refers to a fractal dimension of alpha; the following is shown:
Wherein the range of the q-order moment is (- ≡, + -infinity), the specific range is determined according to the calculation error;
S52, binding equation (2), then directly calculating the multi-fractal singular index using μ ijk (q, δ):
Combining equation (4), then directly calculating the multi-fractal spectral function using μ ijk (q, δ):
and obtaining multi-fractal spectrums f (alpha) -alpha according to the formula, and calculating the spectrum width delta alpha, wherein the spectrum width delta alpha=alpha max-αmin,αmax is the maximum singularity index, and the spectrum width alpha min is the minimum singularity index.
2. The method for characterizing the spatial distribution uniformity of a second phase in a cast aluminum alloy as recited in claim 1, wherein in step S2, the cropped three-dimensional feature image is noise reduced by non-local mean filtering.
3. The method for characterizing spatial distribution uniformity of a second phase in a cast aluminum alloy as defined in claim 1, wherein in step S2, a Wellner adaptive thresholding algorithm is used to binarize the denoised image.
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| CN109961465A (en) * | 2017-12-21 | 2019-07-02 | 东莞东阳光科研发有限公司 | A kind of etched foil surface Tunnel-hole uniformity characterizing method based on multi-fractal |
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| 分形理论盒维数与第二相颗粒相体积的关系研究;何振娟;王录全;彭小明;庾正伟;冷茂林;杨天华;;粉末冶金技术;20160227(第01期);全文 * |
| 测定显微组织中第二相颗粒分布均匀性的定量金相法的介绍;徐炜新;谢崇津;杨伟宁;顾艳;常红英;;理化检验(物理分册);20090808(第08期);全文 * |
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