2020 年 61 巻 7 号 p. 1220-1229
To create a new surface with desired microstructural features, the proportion of constituent phases and grain size should be quantitatively characterized. However, it is difficult for titanium alloy due to its adhesion microstructure. In the present study, a novel image processing method was proposed to characterize the microstructure feature of titanium alloy Ti–6Al–4V. Graham scan algorithm is innovatively applied to identify and separate the isolated and adhesive phases. Using the proposed method, the changes of volume fraction and grain size of beta phases induced by peripheral milling are evaluated. The main conclusions are as follows: the isolated and adhesive phases in SEM images of Ti–6Al–4V are well separated, and the correct recognition rate can reach more than 90%. The total volume fraction of the beta phase on the machined surface is larger than that of the original material, and its value increased with the increase of cutting speed. With the cutting speed increases, the content of isolated beta phase decreases but that of adhesive beta phase increases. Length-diameter ratio of the isolated beta phase induced by machining does not change significantly relative to that of the original material, which values are lies in the range of 1.9 to 2.0.
Titanium alloys are widely used in aerospace, power energy, marine, medical, biomaterials and other fields due to its high strength, high toughness, excellent corrosion resistance and biocompatibility, etc.1–3) All these properties of titanium alloy depend on the distribution of the volume fraction and grain size of alpha and beta phases. Sen et al.4) found that the fracture toughness of Ti–6Al–4V alloy increased with the decrease of the size of beta phases. Castany et al.5) pointed out that the barrier effect of beta phase on moving dislocation in Ti–6Al–4V resulted in the compatible deformation between phases, which was beneficial to improve the plasticity of the alloy. Shekhar et al.6) found that solution treatment and aging treatment could inhibit the growth of beta grain and help to improve the strength of the alloy. Meanwhile, the alloy has good plasticity because of the small size of beta grain.
Cutting is one of the major processing technologies in manufacturing titanium alloy parts. Identification and quantitative analysis of the isolated and adhesive beta phases are conducive to optimizing cutting parameters to create a new surface with desired microstructural features. Wang et al.7) studied the relationship between cutting parameters and phase transformations during high speed machining of Ti–6Al–4V, they found that β phase volume fraction increases from 8% to 90% in the serrated chips and the machined surface at the cutting speed range of 50–600 m/min. Yang et al.8) investigated the sensitivity of microstructural changes to milling parameters in machining Ti–6Al–4V. They found that the maximum measured value of change rate of β phase at the machined surface is 141.1%, and the depth of cut is the foremost factor among the three studied parameters. Digital micrographs taken by scanning electron microscope (SEM) and optical metallurgical microscope are commonly used to identify the difference of volume fraction and grain size of the material. Chrapoński et al.9) found that the contrast between microstructures can be obtained under polarized light conditions, and the identification and segmentation of grains and alpha clusters in the Ti–6Al–2Mo–2Cr–Fe alloy are realized by image processing technology. Germain et al.10) found that in IMI834 titanium alloy low-power backscatter electron photographs, the equiaxed alpha phase and transformed beta matrix can be segmented by a single threshold according to the content of alloy elements. Salem et al.11) realized the automatic segmentation of equiaxed alpha phase and transformed beta matrix according to the difference of vanadium content between equiaxed alpha phase and transformed beta matrix in Ti–6Al–4V titanium alloy. However, these excellent studies predate much of the work on identifying and separating the isolated and adhesive phases of titanium alloys. Despite all the work on digital micrographs, there is still a lack of an efficient method to identify and separate the isolated and adhesive phases of titanium alloy, which will have a huge influence on the quantitative results of the volume fraction and grain size of titanium alloys.
Graham scan algorithm12) is a backtracking technique in computational geometry, which is originally designed to calculate convex hulls of any point set in a two-dimensional plane.13,14) Graham scan algorithm draws the minimum convex hull for each phase in the digital image. By searching for these convex hulls, the phases with complex adhesion are expected to be identified. In the present study, Graham scan algorithm is innovatively applied to identify and separate the isolated and adhesive phases. Using the proposed method, the changes of volume fraction and grain size of beta phases induced by peripheral milling are evaluated.
The workpiece material studied is the equiaxed Ti–6Al–4V alloy, which obtained by free forging. The original microstructure of Ti–6Al–4V alloy photographed by scanning electron microscope (SEM) is shown in Fig. 1. As shown in Fig. 1, the original microstructure is composed of alpha phases in dark gray and beta phases in bright gray. Chemical compositions of Ti–6Al–4V alloy which are identified by energy dispersive spectroscopy (EDS) are shown in Table 1.
Original microstructure of the Ti–6Al–4V alloy.
To obtain samples with different surface microstructures, peripheral milling process was applied. The machine tool used is a vertical-type machining center (DAEWOOACE-V500). The size of the workpiece used in the experiment was 50 mm * 30 mm * 5 mm. Four-groove milling cutter with variable helical angles was used in the experiment, and its material was cemented carbide. The radius of the milling cutter was 3 mm and downward milling was adopted. Milling process parameters are selected as shown in Table 2.
The machined surface of workpiece was polished, and then etched at room temperature for 10 seconds under the etching conditions of 5 mL HNO3 (65% concentration) + 3 mL HF (40% concentration) + 100 mL H2O. The removal rate was controlled at 25 nm/s.
2.3 Samples imagingThe microstructures of the etched samples were imaged by SH-3000 Mini-SEM (HIROX, Tokyo, Japan), and SEM images of the machined surface obtained under different cutting conditions are shown in Fig. 2.
SEM images of machined surface obtained under conditions of (a) test 1, (b) test 2, (c) test 3 and (d) test 4.
It can be seen from Fig. 2 that the grain size of alpha and beta phases on the machined surface is different with that of the original material. Moreover, the grain size obtained by different cutting conditions is different. Hence, quantitative characterization of alpha and beta phases is significantly important for the optimized mechanical properties of machined surfaces of titanium alloy.
Digital image processing method was proposed and the program was developed in Opencv software. Steps of the SEM image pre-processing, separation of isolated and adhesive phases and quantitative microstructural characterization are included in image processing method.
3.1 Pre-processing of the SEM imageIn the process of acquisition and preparation of metallographic photographs, there will be uneven brightness and noise in the image due to the limitations of illumination, temperature and equipment performance. In order to eliminate these effects and effectively describe the geometric structure and distribution of microstructures, the pre-processing methods include image gray processing, image filtering and image binarization, should be carried out on the original SEM images.
3.1.1 Gray of SEM imagesThe microstructure image f(x, y) obtained by SEM is RGB format and stored in a two-dimensional matrix with S rows and M columns. The expression is shown as eq. (1). Each element in the matrix is called a pixel, and the values of the pixels represent the brightness attribute of the image.
| \begin{equation} f(x,y) = \begin{bmatrix} f(0,0) & f(0,1) & \cdots & f(0,M-1)\\ f(1,0) & f(1,1) & \cdots & f(1,M-1)\\ \cdots & \cdots & \cdots & \cdots\\ f(S-1,0) & f(S-1,1) & \cdots & f(S-1,M-1) \end{bmatrix} \end{equation} | (1) |
In order to describe the brightness relationship of each phase in the image, the original image was converted into a grayscale image. The cvCvtColor function in Opencv software was used to convert the original image to the quantized gray image with 256 levels (0∼255), where “255” represents pure white and “0” represents pure black. The image obtained by graying (a), (b), (c), (d) in Fig. 2 is shown in Fig. 3.
The microstructure images after gray processing obtained under conditions of (a) test 1, (b) test 2, (c) test 3 and (d) test 4.
Due to the influence of electronic device interference and sensor oscillation, collected metallographic images would contain some salt and pepper noise. Median filtering15) set the gray value of each pixel in the image to the median value of all the pixels in a neighborhood window of the point. This method can effectively suppress noise while maintaining the edge information of the microstructure to the maximum extent. Moreover, median filtering is a non-linear filtering method, which is much less ambiguous than linear filtering methods such as Gaussian filtering and square filtering. It is effective for weakening salt and pepper noise. Therefore, median filtering was chosen to smooth the microstructure image.
For median filtering, the shape and size of the neighborhood window were critical to filter out noise. A square or circular neighborhood window was mainly used for filtering images with long outlines of microstructures. The size of the neighborhood window should not exceed the size of the smallest effective microstructure in the image. In the present study, the 3 * 3 neighborhood window was used to perform median filtering on the microstructure images. The image obtained by median filtering of (a), (b), (c), (d) in Fig. 3 is shown in Fig. 4.
The median filtered images of the microstructure obtained under conditions of (a) test 1, (b) test 2, (c) test 3 and (d) test 4.
It can be seen from Fig. 4 that although there is ambiguity in the process of noise removal, median filter still better preserves the details of microstructure in the image, which is not available in other linear filtering methods.
3.1.3 Binarization of microstructure imagesImage binarization is a method used to convert 256 gray-level microscopic images into two gray-level images. By binarization, the beta phase and the alpha phase are separated from each other, thus facilitating the quantitative characterization of the beta phase. Commonly used binarization methods include Otsu method, iterative threshold method and global threshold method.16) Otsu method is the most widely used binarization method. It divides the image into two parts, background and target, according to the gray level characteristics of the image. The larger the variance between the background and the target, the greater the difference between the two parts of the image. When part of the target is misclassified into background or part of the background is misclassified into objects, the difference between the two parts will become smaller. Therefore, the segmentation that maximizes the between-class variance means that the probability of misclassification is the smallest. The steps of the Otsu method are as follows.
Let the pixels in a given image be divided into L gray levels [1, 2, …, L]. pi is the probability of gray i appearing on the image, and its expression is shown in eq. (2).
| \begin{equation} p_{i} = \frac{n_{i}}{N},\ p_{i} \geq 0,\ \sum_{i = 1}^{L}p_{i} = 1 \end{equation} | (2) |
A gray level k is denoted as the threshold value to divide the pixels of microstructure images into two categories (C0 and C1), C0 represents the background and C1 represents the target. Where, the gray level range of the pixels in C0 is [1, 2, …, k], and the gray level range of the pixels in C1 is [k + 1, k + 2, …, L]. The probability of occurrence (ω0, ω1) and the average gray level (μ0, μ1) of C0 and C1 are shown in eq. (3).
| \begin{equation} \left\{ \begin{array}{l} \omega_{0} = p(C_{0}) = \displaystyle\sum_{i = 0}^{k}p_{i}\\ \omega_{1} = p(C_{1}) = \displaystyle\sum_{i = k + 1}^{L - 1}p_{i}\\ \mu_{0} = \displaystyle\sum_{i = 0}^{k}i \times p(i|C_{0}) = \frac{\displaystyle\sum_{i = 0}^{k}ip_{i}}{\omega_{0}}\\ \mu_{1} = \displaystyle\sum_{i = k + 1}^{L - 1}i \times p(i|C_{1}) = \frac{\displaystyle\sum_{i = k + 1}^{L - 1}ip_{i}}{\omega_{1}} \end{array} \right. \end{equation} | (3) |
The between-class variance $\delta _{B}^{2}$, the within-class variance $\delta _{W}^{2}$, and the total variance $\delta _{T}^{2}$ of levels are shown as eq. (4).
| \begin{equation} \left\{ \begin{array}{l} \delta_{B}^{2}(k) = \omega_{0}(\mu_{0} - \mu_{T})^{2} - \omega_{1}(\mu_{1} - \mu_{T})^{2}\\ \delta_{W}^{2}(k) = \omega_{0}\displaystyle\sum_{i = 0}^{k}(i - \mu_{0})^{2}\,p(i|C_{0})\\ \quad {}+ \omega_{1}\displaystyle\sum_{i = k + 1}^{L - 1}(i - \mu_{1})^{2}\,p(i|C_{1})\\ \delta_{T}^{2} = \delta_{B}^{2}(k) + \delta_{W}^{2}(k) \end{array} \right. \end{equation} | (4) |
Where, μT is the average grayscale of image, which can be expressed as eq. (5).
| \begin{equation} \mu_{T} = \sum_{i=0}^{L-1}ip_{i} \end{equation} | (5) |
Since the total variance is constant, the threshold k* that maximizes the between-class variance is the optimal value. The optimal threshold k* is shown as eq. (6),
| \begin{equation} k^{*} = \textit{Arg} \max\limits_{0 \leq k \leq L - 1} \{\omega_{0}(\mu_{0} - \mu_{T})^{2} - \omega_{1}(\mu_{1} - \mu_{T})^{2}\} \end{equation} | (6) |
Because of the unremoved noise in the feature edge and interior of the image, the binarized noise will cause burrs in the feature edge, which should be removed before the separation of the isolated and adhesive phases. Open operation is a method that first corrodes the image and then expands the result. The open operation can smooth the image contour, remove the edge burr, and keep the size and area of the object unchanged. Therefore, morphological open operation was performed to eliminate image burrs.
Binary images of the Ti–6Al–4V alloy after deburring process are shown in Fig. 5.
SEM images after binary processing obtained under conditions of (a) test 1, (b) test 2, (c) test 3 and (d) test 4.
It can be seen from Fig. 5 that the pepper and a salt noise with small area has been basically removed in the process of median filtering. There are only two phases in a binary image: alpha phase and beta phase. The alpha phase is shown as a black part in the binary image, and the beta phase is shown as the white part in the binary image. The geometric structures of beta phases can be classified into two categories: isolated phases and adhesive phases. The isolated beta phases adhere to each other to form adhesive phases, and the isolated beta phase consists of isolated lamellar beta phases and equiaxed beta phases. Figure 6 shows the independent lamellar beta phase and equiaxed beta phases respectively.
Image of independent beta phases: (a), (b) Independent equiaxed beta phases; (c), (d) Independent lamellar beta phases.
In this section, a threshold method based on Graham scan algorithm is proposed to identify and separate the isolated and adhesive beta phases.
3.2.1 Manual separation methodIn order to identify and separate microstructures in binary images of titanium alloy, some authors use the method of manual separation. Wang17) et al. separated the adjacent alpha phases which tend to be connected by manual method; Collins18) et al. used the manual method to separate the lamellar alpha phases from the equiaxed alpha phases. In this paper, isolated beta phases and adhesive beta phases in Fig. 5 are identified and separated manually. Select the local microstructure image in Fig. 5(a), and use the manual method to identify and separate the isolated beta phases and adhesive beta phases in the image. The results are shown in Fig. 7.
Result chart of manual separation method: (a) Selected local microstructure image in Fig. 5(a); (b) Adhesive beta phases separated by manual method; (c) Isolated beta phases separated by manual method.
It can be seen from Fig. 7(b) and Fig. 7(c) that two kinds of beta phase can be separated by manual method. However, it takes a long time for manual methods to identify and separate isolated beta phase and adhesive beta phase. As the area of microstructure identification becomes larger, the number of phases will gradually increase, and the amount of manual identification and separation will become larger, so it takes more time to identify and separate different kinds of microstructure accurately, which is obviously not an efficient method.
In view of the above problems, this paper proposes an automatic separation method based on Graham scan algorithm. According to the morphological characteristics of isolated beta phases and adhesive beta phases, the reciprocal of the ratio of beta phase area to its corresponding minimum convex hull area is used as the threshold to separate the two kinds of beta phase.
3.2.2 Graham scan algorithmGraham scan algorithm is a method for drawing convex hulls of discrete point sets on a two-dimensional plane. This method constructs the minimum convex hull of the discrete point set Q{P1, P2, …, Pn} by distinguishing whether the loop consisting of any three points on the plane is left-turn angle or right-turn angle. The main steps of Graham scan algorithm are as follows.
Step 1: The point set Q{P1, P2, …, P8} is placed in a two-dimensional plane. The coordinate system is established by taking the point with minimum ordinate as the origin P0. If the ordinates are the same, the point with minimum abscissa is chosen as the origin.
Step 2: Connect P0 to the remaining points. All line segments form an angle with the positive direction of abscissa. The remaining points are recorded as {P1, P2, …, P8} according to the order of composition from small to large.
Step 3: Finding the minimum convex hull that surrounds the discrete point set is implemented. This step judges whether the remaining points are on the convex hull according to the angle turn of the adjacent three points. P0 is the initial point of drawing the minimum convex hull, so P0 must be on the convex hull. Next, it is judged whether P1 is a point on the convex hull. Connect the lines in the order of P0 → P1 → P2 and form an angle. The angle is left turn, P1 is the point on the convex hull. According to the order of P1 → P2 → P3, the angle of connection is the right-turn angle, the point of P2 is not the point on the convex hull. According to this principle, the remaining points in the point set are determined, and the minimum convex hull of the discrete point set Q{P1, P2, …, P8} is shown in Fig. 8.
The minimum convex hull of discrete point set Q{P1, P2, …, P8}.
There are convex and concave areas on the outline of beta phases in the binary image. Thus, Graham scanning algorithm can be used to draw the minimum convex hulls of the beta phases in (a) (b) (c) (d) of Fig. 5, the result is shown in Fig. 9.
The minimum convex hull for beta phases obtained under conditions of (a) test 1, (b) test 2, (c) test 3 and (d) test 4.
As can be seen from Fig. 9, each isolated and adhesive phase correspond to a minimum convex hull. Moreover, because the adhesive phases is connected by two or more isolated phases, the ratio of the pixel number of the adhesive phases to the minimum convex hull is small, while the ratio of the pixel number of the isolated phases to the minimum convex hull is large.
3.2.3 Separation of isolated and adhesive microstructuresTo identify and separate the isolated and adhesive beta phases, a threshold A, which is defined by the ratio of the pixel number of the beta phase to the minimum convex hull, was proposed. And its expression is shown as eq. (7).
| \begin{equation} A = \frac{A_{m}}{A_{c}} \end{equation} | (7) |
Where, Am is the number of pixels of the beta phase, and Ac is the number of pixels of the minimum convex hull which surrounding the beta phase.
The corresponding values A of the isolated and adhesive beta phases are calculated, and partial results are shown in Table 3.
As can be seen from Table 3 that the number of pixels of the adhesive phases is large, while the corresponding value A is small. This is because the beta phases adhere together to form adhesive phases. The number of pixels of isolated phases is small, and the corresponding value A is large.
To study the effect of the threshold value A on the identify accuracy of the beta phases, correct recognition rate S, as expressed in eq. (8), was adopted.
| \begin{equation} S = \frac{S_{i}}{S_{a}} \end{equation} | (8) |
Where, Si is the number of isolated or adhesive phases successfully identified, and Sa is the number of all isolated or adhesive phases.
The number corresponding to Sa is obtained by detecting the contour of each phase in the image, and the result is shown in Fig. 10.
Contour image corresponding to binary image obtained under conditions of (a) test 1, (b) test 2, (c) test 3 and (d) test 4.
It can be seen from Fig. 10 that each beta phase in the image will correspond to a contour, and Sa can be obtained by counting the number of contours.
The relationship curves of threshold A and correct recognition rate S of test 1 to 4 were given in Fig. 11. The abscissa represents the range of value A corresponding to the beta phases in Fig. 9(a), (b), (c) and Fig. 9(d), and the ordinate represents the correct recognition rate changing with value A. Figure 11 shows that the correct recognition rate of the isolated phase can reach more than 90% by selecting the appropriate threshold. As shown in Fig. 5, the isolated beta phase consists of independent lamellar beta phase and equiaxed beta phase. Due to the irregularity of the structure profile of Ti–6Al–4V titanium alloy, the value A of lamellar beta phase is less than that of equiaxed beta phase. With the increase of value A, the number of correctly identified lamellar beta phases increases, and the correct recognition rate increases gradually. When the value A increases to a certain extent, with the increase of the value A, the number of identifiable lamellar beta phases begins to decrease, and the number of identifiable equiaxed beta phases gradually increases. Because the number of equiaxed beta phase is less than that of lamellar beta phase, the correct recognition rate curve decreases slowly, but remains at a high level.
Relationship between the threshold value A and success rate S of tests 1 to 4.
As can be seen from Fig. 11, when the values of A are 0.65, 0.67, 0.66 and 0.66, the correct recognition rate of isolated phase is the highest. Therefore, 0.65, 0.67, 0.66 and 0.66 were chosen as the decision threshold A* to identify and separate phases for the corresponding samples. The phases with a value A less than A* were classified as the adhesive phases, and the phases with a value A greater than A* were classified as the isolated phases. Figure 12 shows the separated images of the isolated and adhesive phases.
Isolated and adhesive phases separated by decision threshold A* obtained under conditions of (a1)–(a2) test 1, (b1)–(b2) test 2, (c1)–(c2) test 3 and (d1)–(d2) test 4.
Figures 12(a1), 12(b1), 12(c1) and 12(d1) are images of isolated phases which were separated, and the correct recognition rates are 94%, 96%, 95%, and 96%, respectively. Phases in Fig. 12(a2), (b2), (c2) and 12(d2) are all adhesive phases, the numbers of which are 69, 62, 77, and 51, respectively. The results show that this method can effectively identify and separate the isolated and adhesive phases of Ti–6Al–4V titanium alloy as long as the appropriate threshold A is selected. Because this method is based on Opencv function library and Visual Studio software, it saves a lot of time compared with the manual method. The method provides a new idea for identifying and separating phases with complex adhesion of the titanium alloy.
Using the proposed method, the volume fraction of the beta phases and the size of the beta grains induced by peripheral milling were quantitatively characterized.
4.1 Volume fraction of beta phasesThe volume fraction V of the beta phases was calculated by eq. (9).19)
| \begin{equation} V = \frac{V_{1}}{V_{2}} \end{equation} | (9) |
Where, V1 is the number of pixels of the target, and V2 is the number of pixels of the image.
By calculation, the volume fractions of the isolated beta phases for Fig. 12(a1) to Fig. 12(d1) are 6.6%, 6.0%, 5.5%, and 5.3%, respectively. And the volume fractions of the adhesive beta phases are 12.0%, 15.0%, 19.8% and 20.6%, respectively. Variation of the volume fraction of beta phase with machining parameter (cutting speed) is given in Fig. 13.
Variation of the volume fraction of beta phase with cutting speed.
As can be seen from Fig. 13 that the total volume fraction of the beta phase is larger than that of the original material, and the total volume fraction of the beta phase increased with the increase of cutting speed. Alpha to beta phase transformation occurs due to high temperature induced by cutting. It also can be found that as the cutting speed increases, the content of isolated beta phase decreases but that of adhesive beta phase increases.
4.2 Size of the isolated beta grainsThe size of the beta grains is described by the length of the long axis LL, the length of the short axis LS and Length-diameter ratio of the isolated beta. The ratio L is shown in eq. (10).20)
| \begin{equation} L = \frac{L_{L}}{L_{S}} \end{equation} | (10) |
Tables 4 to 7 are the partial data of the ratio L of the long axis to the short axis of the isolated beta grains in Fig. 12(a1) to Fig. 12(d1), respectively. And Table 8 is the partial data of the ratio L of the long axis to the short axis of the isolated beta grains in the original material.
It is found from Table 4 to Table 8 that the geometric structure of isolated beta phase induced by machining does not change significantly relative to that of the original material. Where the ratio L of the long axis to the short axis of the isolated beta grains for Fig. 12(a1) to Fig. 12(d1) are 1.92, 1.99, 2.00 and 1.96, respectively. And the value of L for that of the original material is 1.94.
To identify and quantitatively analyze the isolated and adhesive beta phases in titanium alloy Ti–6Al–4V, a novel SEM image processing method was proposed based on the Graham san algorithm. By the proposed method, evolution of volume fraction and grain size of the beta phases induced by peripheral milling were evaluated. Conclusions are drawn as follow.
The proposed method provides a new idea for the identification and separation of microstructures with complex adhesion, which can be used to provide a concise means for optimizing experimental design, and be of great practical value.
The authors would like to acknowledge the financial support from the Natural Science Foundation of China (Grant No. 51975003), Key Natural Science Project of Anhui Provincial Education Department (Grant No. KJ2018A0021), Natural Science Foundation of Anhui Provincial (Grant No. 1908085QE230) and High-level talent fund of Anhui University.
