CN110288569B - Crack near-field deformation analysis area determination method based on level set method - Google Patents
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Abstract
The invention discloses a crack near-field deformation analysis area determination method based on a level set method, which comprises the following steps of: 1) Setting a crack near-field initial analysis area; 2) Obtaining the coordinate position of the crack propagation track; 3) Calculating a level set function of the crack propagation track; 4) Updating the analysis area; 5) Repeating the step 2-4, and continuously updating the analysis area according to the crack propagation information, so as to complete the self-adaption of the crack near-field analysis area; for the elements and the structural members, the determination of the crack near-field deformation analysis area is realized rapidly under the condition of crack propagation, the method can avoid manually determining the crack near-field analysis area, effectively avoid errors introduced by test personnel in the implementation process, and improve the accuracy and reliability of the crack near-field deformation analysis area; secondly, the analysis efficiency is high, and the updating of the crack near-field analysis area can be completed rapidly; finally, labor cost can be reduced, automation of crack near-field deformation analysis areas is realized, and damage tolerance test technology is improved.
Description
Technical Field
The invention relates to the technical field of damage tolerance in crack propagation tests, in particular to a crack near-field deformation analysis area determination method based on a level set method.
Background
The deformation analysis of the crack near field is realized based on a digital image correlation method, the crack initiation and the crack propagation cause strong discontinuity of an analysis area, the gap formed by the crack causes the change of pixel information in an acquired image, and the pixel information of the gap part can cause error of the deformation analysis, so that the analysis area (Region of Interest, ROI) needs to be removed at the beginning of the analysis, and the analysis area needs to be updated along with the crack propagation. In the crack growth test, a large number of photographs of the crack are required, and if the analysis area is manually updated, analysis efficiency is affected and significant labor costs are incurred.
Aiming at the detection technology of the element and the structural member in the crack propagation test, the invention provides a method for realizing the self-adaption of the crack near-field analysis area.
Disclosure of Invention
The purpose of the invention is that: the method for determining the crack near-field deformation analysis area based on the level set method is used for realizing rapid updating of the crack near-field analysis area along with crack propagation change in a crack propagation test of elements and structural members, improving automatic updating of the crack near-field deformation analysis area, reducing labor cost and improving crack near-field deformation analysis efficiency.
The technical scheme of the invention is as follows:
a crack near-field deformation analysis area determination method based on a level set method comprises the following steps:
step 1: setting a crack near-field initial analysis area;
step 2: obtaining the coordinate position of the crack propagation track;
step 3: calculating a level set function of the crack propagation track;
step 4: updating the analysis area;
step 5: and (2) repeating the steps (2-4) and continuously updating the analysis area according to the crack propagation information, thereby completing the self-adaption of the crack near-field analysis area.
The setting of the crack near-field initial analysis area in the step 1 specifically includes: and setting an initial analysis area of a crack near field according to the geometric shape and the crack shape of the crack-containing test piece, and ensuring that the initial analysis area comprises an effective analysis area of the test piece and does not contain a crack breaking area.
The step 2 of obtaining the coordinate position of the crack propagation track further includes the following steps:
step 2.1: performing correlation analysis on the deformation condition of the crack near field to obtain crack near field deformation information;
step 2.2: and identifying the crack tip, and obtaining the coordinate position of the crack propagation track.
The function of calculating the level set of the crack propagation track in the step 3 further comprises the following steps:
step 3.1: establishing a crack track level set function and a crack tip level set function, wherein the crack track level set function is used for describing the symbol distance from a crack interface, and the crack tip level set function is used for describing the symbol distance from a crack tip tangential vector;
step 3.2: according to the established crack track level set function, calculating the values of the level set functions of all effective points in the analysis area by taking pixels as units;
step 3.3: the absolute value of the level set function value is defined to represent the distance from the definition interface, and the positive and negative signs represent the forward direction or the reverse direction of the definition interface.
Establishing a crack track level set function and a crack tip level set function in step 3.1, wherein the crack track level set function is used for describing a symbol distance from a crack interface, the crack tip level set function is used for describing a symbol distance from a crack tip tangential vector, and the crack track level set function is as follows:
Ψ(x，t)＝±|x-x i |
wherein: x is x i For the ith tip coordinate, x is the coordinate of the tip level set function to be solved, and t is the amount of time.
Establishing a crack track level set function and a crack tip level set function in the step 3.1, wherein the crack track level set function is used for describing the symbol distance from a crack interface, the crack tip level set function is used for describing the symbol distance from a crack tip tangential vector, and the crack tip level set function is that
Wherein: x is x i For the ith split point coordinate, x is the coordinate of the split point level set function to be solved, T is the unit tangential vector of the split point, and T' is the transpose of T.
The updating analysis area in step 4 specifically includes: and (3) setting a threshold according to the values of the level set functions of all the effective points in the area obtained in the step (3.2), and determining non-analysis points according to the threshold.
The non-analysis point is determined according to the threshold value specifically as follows: comparing the absolute value of the crack track level set function with the threshold value in the range that the crack tip level set function is negative, and setting a point with the absolute value of the crack track level set function smaller than the threshold value as a non-analysis point; when the crack tip level set function is in a positive range, a point, where the absolute value of the crack track level set function and the numerical value of the crack tip level set function are simultaneously smaller than a threshold value, is set as a non-analysis point, and the non-analysis point is added into the analysis area to update and generate a new analysis area.
The invention has the beneficial effects that:
the invention provides a crack near-field deformation analysis area determination method based on a level set method, which can be used for rapidly determining a crack near-field deformation analysis area under the condition of crack propagation of elements and structural members, and can avoid manually determining the crack near-field analysis area, effectively avoid errors introduced by test personnel in the implementation process, and improve the accuracy and reliability of the crack near-field deformation analysis area; secondly, the method has high analysis efficiency and can rapidly finish updating the crack near-field analysis area; finally, the method can reduce labor cost, realize automation of crack near-field deformation analysis areas and improve damage tolerance test technology.
Drawings
FIG. 1 is a flow chart of a crack near field deformation analysis region determination method based on a level set method;
FIG. 2 is a schematic diagram of a crack near field initial analysis region;
FIG. 3 is a schematic representation of crack propagation trajectories;
FIG. 4 is a schematic diagram of a level set function calculation;
FIG. 5 illustrates a graph of a split tip level set function calculation.
Detailed Description
The invention relates to a crack near-field deformation analysis area determining method based on a level set method.
The specific flow steps of the invention are as follows:
step 1: setting a crack near-field initial analysis area; the method comprises the following steps: according to the geometric shape or size of the test piece containing the crack and the shape of the crack, as shown in fig. 2, an initial analysis area of a crack near field is set, so that the initial analysis area comprises an effective analysis area of the test piece and does not contain a crack breaking area. Since the pixel information generated in the crack breaking region affects analysis of the crack near-field deformation, the crack near-field analysis region cannot include the crack breaking region, and as can be seen from fig. 2, the crack breaking region includes a crack interface and a crack tip, the internal region serves as an initial analysis region, the initial analysis region does not include the crack interface and the crack tip, and all the pixel points in the initial analysis region are effective analysis points.
Step 2: obtaining the coordinate position of the crack propagation track;
step 2.1: performing correlation analysis on the deformation condition of the crack near field to obtain crack near field deformation information, wherein the correlation analysis can use existing mature commercial software (Vic-2D, vic-3D and the like) and can also write an analysis program by itself;
step 2.2: the identification and positioning of the crack tip can be completed by referring to a method of a displacement field-based crack tip identification algorithm (doi: 10.13224/jcnki.jasp.2018.09.017) in the scientific paper, and the identification and positioning of the crack tip are not the main content of the invention, so that the detailed implementation process is referred to in the literature.
And 2, finally obtaining coordinate information representing the crack propagation track, wherein a schematic diagram representing the crack propagation track by adopting the coordinate positions is shown in fig. 3.
Step 3: calculating a level set function of the crack propagation track;
step 3.1: establishing a crack track level set function and a crack tip level set function, wherein the crack track level set function is used for describing the symbol distance from a crack interface, and the crack tip level set function is used for describing the symbol distance from a crack tip tangential vector;
the crack trajectory level set function is the distance from the point to the crack trajectory, the distance being defined as: if the perpendicular point of the point and the line segment is outside the line segment, the distance is the length of the connecting line of the point and the line segment, which is closest to the perpendicular point, and if the perpendicular point of the point and the line segment is on the line segment, the distance is the length of the perpendicular line of the point and the line segment; and defining a crack trajectory level set function of all points above the crack as positive and below as negative, said crack trajectory level set function being ψ (x, t):
Ψ(x，t)＝±|x-x i |
wherein: x is x i For the ith split point coordinate, x is the coordinate of the split point level set function to be solved, and t is the amount of time;
the crack tip level set function is the sign distance from the point to the normal line of the crack tip, the function value is positive at the outer side of the normal line, the function value is negative at the inner side of the normal line, the crack tip level set function is
Wherein: x is x i For the ith split point coordinate, x is the coordinate of the split point level set function to be solved, T is the unit tangential vector of the split point, and T' is the transpose of T;
step 3.2: according to the established crack track level set function, calculating the values of the level set functions of all effective points in the analysis area by taking pixels as units;
firstly calculating the values of a crack track level set function, wherein fig. 4 shows a schematic diagram of calculating a crack track level set function value by a point 0, wherein a broken line formed by a point A, a point B, a point C and a point D is a crack propagation track, the points A and D are crack points, the distances from the point 0 to a line segment AB, a line segment BC and a line segment CD are respectively |OB|, |OG| and |OC| (the distances from the point 0 to the point B are represented by |OB|, and the like), and the absolute value minimum value in the three distances is taken as the crack track level set function value because the point 0 is positioned above the crack track, so the crack track level set function value of the point 0 is +|OG|; the values of the crack trajectory level set function for all the effective points in the analysis area are calculated in turn using the same method as point 0.
Then calculating the value of the crack tip level set function, and FIG. 5 shows the process of calculating the crack tip level set function value at point 0; for tip A, the unit tangential vector e of tip A 1 Is that
The function value of the split tip level set is +.>
The size is reflected in fig. 5 as —oe|; for the split tip D, the unit tangential vector e of the split tip D 2 Is->
The function value of the split tip level set is +.>
The size is reflected in fig. 5 as- |of|. For the point 0, two values of the crack tip level set function are provided, and the value of the crack tip level set function with the smallest absolute value is taken as the final crack tip level set function value of the point 0, so that the value of the crack tip level set function of the final point 0 is- |OE|; the values of the crack tip level set function for all the effective points in the analysis area are calculated in turn, again using the same method as point 0.
Step 3.3: the absolute value of the level set function value is defined to represent the distance from the definition interface, and the positive and negative signs represent the forward direction or the reverse direction of the definition interface.
Step 4: updating the analysis area; setting a threshold according to the values of the level set functions of all the effective points in the area obtained in the step 3.2, and determining non-analysis points according to the threshold, wherein the non-analysis points specifically are as follows: comparing the absolute value of the crack track level set function with the threshold value in the range that the crack tip level set function is negative, and setting a point with the absolute value of the crack track level set function smaller than the threshold value as a non-analysis point; when the crack tip level set function is in a positive range, a point, where the absolute value of the crack track level set function and the numerical value of the crack tip level set function are simultaneously smaller than a threshold value, is set as a non-analysis point, and the non-analysis point is added into the analysis area to update and generate a new analysis area.
Claims (6)
1. The crack near field deformation analysis area determining method based on the level set method is used for obtaining the analysis area of the crack near field, can be updated rapidly along with the expansion change of the crack, and provides basis for the deformation analysis of the crack near field; the method is characterized in that: the method comprises the following steps:
step 1: setting a crack near-field initial analysis area;
step 2: obtaining the coordinate position of the crack propagation track;
step 3: calculating a level set function of the crack propagation track;
step 4: updating the analysis area; setting a threshold according to the values of the level set functions of all the effective points in the area obtained in the step 3, and determining non-analysis points according to the threshold; the non-analysis point is determined according to the threshold value specifically as follows: comparing the absolute value of the crack track level set function with the threshold value in the range that the crack tip level set function is negative, and setting a point with the absolute value of the crack track level set function smaller than the threshold value as a non-analysis point; when the crack tip level set function is in a positive range, setting a point of which the absolute value of the crack track level set function and the numerical value of the crack tip level set function are smaller than a threshold value as a non-analysis point, adding the non-analysis point into an analysis area, and updating to generate a new analysis area;
step 5: and (2) repeating the steps (2-4) and continuously updating the analysis area according to the crack propagation information, thereby completing the self-adaption of the crack near-field analysis area.
2. The method for determining the crack near-field deformation analysis area based on the level set method according to claim 1, wherein the method comprises the following steps of: the setting of the crack near-field initial analysis area in the step 1 specifically includes: and setting an initial analysis area of a crack near field according to the geometric shape and the crack shape of the crack-containing test piece, and ensuring that the initial analysis area comprises an effective analysis area of the test piece and does not contain a crack breaking area.
3. The method for determining the crack near-field deformation analysis area based on the level set method according to claim 1, wherein the method comprises the following steps of: the step 2 of obtaining the coordinate position of the crack propagation track further includes the following steps:
step 2.1: performing correlation analysis on the deformation condition of the crack near field to obtain crack near field deformation information;
step 2.2: and identifying the crack tip, and obtaining the coordinate position of the crack propagation track.
4. The method for determining the crack near-field deformation analysis area based on the level set method according to claim 1, wherein the method comprises the following steps of: the function of calculating the level set of the crack propagation track in the step 3 further comprises the following steps:
step 3.1: establishing a crack track level set function and a crack tip level set function, wherein the crack track level set function is used for describing the symbol distance from a crack interface, and the crack tip level set function is used for describing the symbol distance from a crack tip tangential vector;
step 3.2: according to the established crack track level set function, calculating the values of the level set functions of all effective points in the analysis area by taking pixels as units;
step 3.3: the absolute value of the level set function value is defined to represent the distance from the definition interface, and the positive and negative signs represent the forward direction or the reverse direction of the definition interface.
5. The method for determining the crack near-field deformation analysis area based on the level set method according to claim 4, wherein: establishing a crack track level set function and a crack tip level set function in step 3.1, wherein the crack track level set function is used for describing a symbol distance from a crack interface, the crack tip level set function is used for describing a symbol distance from a crack tip tangential vector, and the crack track level set function is as follows:
Ψ(x，t)＝±|x-x i |
wherein: x is x i For the ith tip coordinate, x is the coordinate of the tip level set function to be solved, and t is the amount of time.
6. The method for determining the crack near-field deformation analysis area based on the level set method according to claim 4, wherein: establishing a crack track level set function and a crack tip level set function in the step 3.1, wherein the crack track level set function is used for describing the symbol distance from a crack interface, the crack tip level set function is used for describing the symbol distance from a crack tip tangential vector, and the crack tip level set function is that
Wherein: x is x i For the ith split point coordinate, x is the coordinate of the split point level set function to be solved, T is the unit tangential vector of the split point, and T' is the transpose of T.
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