JP4364101B2 - Surface crack growth analysis method and apparatus - Google Patents

Description

  The present invention relates to a surface crack growth analysis method and apparatus for analyzing the growth of a surface crack generated on the surface of a structural member.

In the crack growth analysis on the surface of the conventional structural member, a single relationship is given between the stress intensity factor or its fluctuation range and the crack growth rate, and the crack growth rate in the depth direction of the member, The crack growth rate in the direction of increasing the length on the member surface uses the same relationship between the stress intensity factor and the crack growth rate (see Non-Patent Document 1). Hereinafter, the relationship between the stress intensity factor or its variation range and the crack growth rate is referred to as crack growth characteristics.
Yoshikawa Naoki, Shiratori Masaki, Matsuda Hiroyuki, Matsushita Hisao, Analysis of Stress Intensity Factor of Multiple Surface Cracks by Influence Function Method and Its Application, Proceedings of the 52nd Annual Conference of the Society of Materials Science, May 2003, pp, 321 -322.

  On the other hand, the crack growth rate of a material exposed to a corrosive environment is the same as the environmental state such as dissolved oxygen concentration or impurity ion concentration in both cases of stress corrosion cracking (hereinafter referred to as SCC) and corrosion fatigue. Therefore, it is not uniquely determined only by the stress intensity factor. In surface cracks of structural members that are actually exposed to corrosive environments, capillary condensation and corrosion liquid retention occur in the surface cracks, so that the environmental conditions differ between the deepest surface crack and the member surface. become. Therefore, the crack growth rate in the depth direction of the structural member and the crack growth rate on the surface have different crack growth characteristics.

  Also, in many structural members, the environmental sensitivity of the hardness and crack growth rate changes depending on the material of the member surface layer and the internal material due to processing such as cutting and grinding in the manufacturing stage. Sometimes. As a result, the propagation characteristics in the depth direction of the surface crack may be different from the propagation characteristics on the surface.

  However, the conventional surface crack growth analysis method assumes that both the growth rate in the depth direction of the structural member and the growth rate on the surface can be determined only by the material and the stress intensity factor. The difference between the depth direction and the crack growth characteristics on the surface could not be considered.

  The present invention has been made to solve the above-described problems, and it is possible to consider the difference in crack propagation characteristics between the depth direction and the surface in the analysis of surface crack propagation of a structural member. It is an object of the present invention to provide a method and apparatus for analyzing surface crack propagation.

In order to solve the above-described problems , the surface crack growth analysis method of the present invention calculates the surface crack growth rate in the surface crack growth analysis method for analyzing the surface crack growth of a structural member. In this case, the crack propagation characteristics in the depth direction of the structural member and the crack propagation characteristics on the surface of the structural member are set independently, and the surface crack propagation analysis of the structural member is performed. When one of the crack depth, which is the crack dimension in the depth direction of the structural member, and the crack length, which is the crack dimension on the member surface, reaches a predetermined dimension, the crack is The method is characterized in that any one of the crack dimensions is fixed at a constant value so as not to increase more than the predetermined dimension, and the surface crack growth analysis is continued assuming that only the other crack dimension increases. It is.
Further, in order to solve the above-described problem, the surface crack growth analysis method of the present invention is a surface crack growth analysis method for analyzing the surface crack growth of a structural member. When calculating, the crack propagation characteristics in the depth direction of the structural member and the crack propagation characteristics on the surface of the structural member are set independently, and the surface crack propagation analysis of the structural member When one of the two surface crack tips on the surface of the structural member reaches a predetermined position, the one surface crack tip Is fixed so that it does not propagate more than the predetermined position, and the surface crack propagation analysis is continued on the assumption that only two points of the other surface crack tip and the crack deepest point increase. Is the method.

In order to solve the above-described problems, the surface crack growth analysis apparatus of the present invention is a method for analyzing the surface crack growth of a structural member. An input means for inputting a crack depth in the depth direction of the structural member; a calculation means for calculating a stress intensity factor; a calculation means for calculating a crack growth rate; a crack growth increment calculation means; A crack size update means, and a calculation means for calculating the crack growth rate, when calculating the crack growth rate, the crack growth characteristics in the depth direction of the structural member, and the surface of the structural member The crack growth characteristics above can be set independently, and the crack depth which is the crack dimension in the depth direction of the structural member and the crack length which is the crack dimension on the member surface When one of the above reaches a predetermined dimension, The surface of the structural member is continuously analyzed by assuming that one of the crack dimensions is fixed at a fixed value so as not to increase more than the predetermined dimension, and only the other crack dimension is increased. The present invention is characterized in that a crack propagation analysis is performed.
Furthermore, in order to solve the above-described problems, the surface crack propagation analysis apparatus of the present invention is a surface crack propagation analysis apparatus that analyzes the surface crack propagation of a structural member. Input means for inputting a crack length and a crack depth in the depth direction of the structural member, a calculation means for calculating a stress intensity factor, a calculation means for calculating a crack growth rate, and a calculation means for an increment of crack growth; A crack size update means, and a calculation means for calculating the crack growth rate, when calculating the crack growth rate, the crack growth characteristics in the depth direction of the structural member, and the structural member The crack propagation characteristics on the surface of the structural member can be set independently of each other, and one of the two surface crack tips on the surface of the structural member has one surface crack tip. When the predetermined position is reached, the one table The position of the crack tip is fixed so that it does not progress beyond the predetermined position, and the surface crack growth analysis is continued assuming that only the other surface crack tip and the crack deepest point increase. The present invention is characterized in that the structure crack analysis is performed on the surface crack of the structural member.

  According to the surface crack propagation analysis method and apparatus of the present invention, the crack propagation rate is calculated by setting the crack propagation characteristics in the depth direction and the surface of the structural member independently, and the surface crack propagation analysis is performed. It is possible to perform surface crack growth analysis with high accuracy under conditions that are closer to reality.

  Embodiments of a surface crack propagation analysis method and apparatus according to the present invention will be described below in detail with reference to the drawings.

  The surface crack growth analysis apparatus of the present invention includes an input means for inputting a crack length on the surface of a structural member to be analyzed and a crack depth in the depth direction of the structural member, and a calculation for calculating a stress intensity factor. Means for calculating the crack growth rate, a calculation means for calculating the crack growth rate, a means for calculating the crack growth increment, and a means for updating the crack size. In this case, the apparatus is provided so that the crack propagation characteristic in the depth direction of the structural member and the crack propagation characteristic on the surface of the structural member can be set independently.

  In the surface crack growth analysis method and apparatus of the present invention, the surface crack propagation mechanism may be any of fatigue, stress corrosion cracking, creep, or surface crack growth under their interaction. It may be.

  First, Example 1 of the surface crack propagation analysis method will be described with reference to FIGS. 1 (A), 1 (B), 2 and 3. FIG.

  FIG. 1A shows a surface crack model of a structural member. As shown in FIG. 1A, a surface crack 2 exists on the surface of the structural member 1 and is exposed to a liquid environment such as reactor water of a light water reactor. The length of the surface crack 2 is 2c and the depth is a. The environment to which the crack surface point 4 of the surface crack 2 is exposed is the average water quality of the reactor water, but the environment to which the deepest crack point 3 is exposed is the retention of the reactor water in the surface crack and the capillaries. It differs from the water quality at the crack surface point 4 due to condensation and the like. When this surface crack 2 progresses, it becomes a post-growth surface crack 5 like the post-surface crack growth model of the structural member shown in FIG.

  FIG. 2 shows the relationship between the stress intensity factor and the SCC crack growth rate. The graph of FIG. 2 shows that the SCC crack propagation characteristics of the material differ depending on the combination of the material and the environment.

  That is, as schematically shown in FIG. 2, the SCC crack growth rate 6 in the environment x of the material A, the SCC crack growth rate 7 in the environment y of the material A, and the SCC crack growth rate in the environment x of the material B The speed 8 is represented by a different curve. Note that the crack growth rate on the vertical axis in FIG. 2 is the amount of surface crack growth per unit time.

  Therefore, the crack propagation characteristics are also different due to the difference in water quality at the deepest point 3 and the crack surface point 4 of the surface crack 2 shown in FIGS. 1 (A) and 1 (B). In the case of surface crack growth due to fatigue, the stress intensity factor K in FIG. 2 is set to the stress intensity factor range ΔK, and the SCC crack growth rate da / dt is set to the fatigue crack growth rate da / dN (m / cycle). Each shall be read. Here, the fatigue crack growth rate da / dN represents the amount of surface crack growth due to a single load change.

  FIG. 3 shows a flow of the surface crack propagation analysis method of the present embodiment. Each step in the flow of FIG. 3 shows data processing in each constituent means of the surface crack growth analysis apparatus.

Usually, the growth analysis of the surface crack 2 is performed according to the flow shown in FIG. First, in step 11, the crack depth at a certain time t _i is set to a _i , the crack length is set to 2c _i, and the shape and size of the member and the stress acting on this are taken into consideration. 3 The stress intensity factors Ka and Kc at the crack surface point 4 are obtained.

Next, in step 13, the crack growth rate da / dt at the deepest point 3 is obtained from Ka and the crack growth rate dc / dt at the crack surface point 4 is obtained from Kc using the following relationship.
[Equation 1]
da / dt = f ₁ (Ka)
dc / dt = f ₂ (Kc)
Here, the functions f ₁ and f ₂ are functions related to the crack growth characteristics, and as shown in FIG. 2, indicate the relationship between the crack growth rate and the stress intensity factor that differ for each combination of material and environment. It is a function. In the conventional surface crack growth analysis method, the same function is used as a function f ₁ and a function f ₂ at a deepest point 3 and a crack surface point 4 for a certain surface crack 2.

On the other hand, in the surface crack propagation analysis method of the present invention, considering the fact that the crack growth characteristics are different because the water quality at the crack deepest point is different from the water quality at the crack surface point, for example, for the deepest point 3 Applies the SCC crack growth rate 7 in the environment y of the material A shown in FIG. 2, while the SCC crack growth rate 6 in the environment x of the material A is applied to the crack surface point 4. That is, the function f ₁ for the crack propagation characteristic in the depth direction of the structural member 1 to be analyzed and the function f ₂ for the crack propagation characteristic on the surface of the structural member are set independently.

In this way, with respect to the crack growth characteristics in the depth direction of the structural member 1 and the crack growth characteristics on the surface, the crack growth rates da / dt and dc / dt at the deepest point 3 and the crack surface point 4 are respectively obtained. After the determination, in step 14, the crack depth 3 increment Δa and the crack length 4 increment Δc during a certain minute time increment Δt, respectively, [Equation 2]
Δa = da / dt · Δt
Δc = dc / dt · Δt
In step 15, the crack size after a minute time increment Δt is obtained by adding these increments to the original crack size. That is, if this time is t _{i + 1} ,
[Equation 3]
t _{i + 1} = t _i + Δt
a _{i + 1} = a _i + Δa
2c _{i + 1} = 2 (c _i + Δc)
As described above, the crack size at time t _{i + 1} , that is, the crack depth a _{i + 1} and the length 2c _{i + 1} are determined. As shown in FIG. 1, the shape of the surface crack 5 after growth is assumed to be a semi-ellipse having a crack depth a _{i + 1} and a length 2c _{i + 1} .

  According to the surface crack growth analysis method of the present embodiment, the crack growth rate is set by setting the crack growth characteristics independently in consideration of the environment at the deepest point 3 and the crack surface point 4 of the surface crack 2. Since the surface crack propagation analysis is performed by calculation, it is possible to carry out a surface crack propagation analysis with high accuracy close to a surface crack in a more actual structural member.

In FIG. 3, the function f ₁ and the function f ₂ which are crack propagation characteristics can be stored in advance in a database. With such a configuration, it is possible to call the crack propagation characteristics by inputting the material name of the structural member 1 or selecting a specific material from the material name list.

  Further, the calculation result of the analysis calculated according to the flow of FIG. 3 may be recorded in a storage medium, and the calculation result may be arbitrarily extracted. Furthermore, it is possible to newly perform a surface crack propagation analysis by changing a part of the input data recorded in the storage medium.

  On the other hand, in the calculation of the stress intensity factor in step 12 of the flow of FIG. 3, when a plurality of stress intensity factor calculation formulas are applicable, the plurality of stress intensity factor calculation formulas are prepared as a database. It is also possible to adopt a configuration in which a calculation formula of a suitable stress intensity factor is read by inputting an identification name or selecting from a list.

  Next, a second embodiment of the surface crack propagation analysis method according to the present invention will be described with reference to FIGS.

  Generally, on the surface of the structural member 1 manufactured by machining such as cutting or grinding, there is a processed layer 21 that is a hardened layer by processing as shown in FIG. The processed layer 21 has an increase in dislocation density due to plastic deformation. Therefore, although the chemical component does not change, the material itself changes in terms of strength properties and the like. Therefore, in the graph of FIG. 2, for example, a material that has not undergone processing has a processed layer 21 in the environment x of the material B even though the crack growth rate indicates the SCC growth rate 6 in the environment x of the material A. SCC progress rate may be 8.

  Even in such a case, according to the surface crack growth analysis method of the present invention, it is possible to carry out surface crack growth analysis according to the flow of FIG.

  FIG. 5 shows an example of an SCC surface crack growth analysis result by the surface crack growth analysis method of the present invention. FIG. 5 (A) shows the change over time of the crack depth, and FIG. 5 (B) is a graph showing the change over time of the crack length.

  That is, in the case where the surface crack propagates at a low SCC growth rate at the deepest point 3 and the crack surface point 4, for example, the SCC growth rate 6 in the environment x of the material A shown in FIG. When the surface crack propagates at a high SCC propagation speed, for example, the SCC propagation speed 8 in the environment x of the material B shown in FIG. 2 at the deepest point 3 and the crack surface point 4 (case 2, curve 23), At the deepest point 3, it progresses at a low SCC growth rate, for example, the SCC growth rate 6 in the environment x of the material A shown in FIG. 2, and at the crack surface point 4, it shows a high SCC growth rate, for example, as shown in FIG. It is a graph about the progress analysis of the surface crack about three cases of the case where it progresses with the SCC progress speed 8 in the environment x of the material B ... (case 3, curve 24).

  Here, in the conventional surface crack growth analysis method, since the same crack growth characteristic can be set at the deepest point 3 and the crack surface point 4, the above (Case 1), (Case 2). ) And (Case 3), only two cases (Case 1) and (Case 2) can be analyzed, and the actual surface crack shape change could not be predicted with high accuracy. According to the invention, since the crack growth rate is calculated by independently setting the crack propagation characteristics with the deepest point 3 and the crack surface point 4, the change in the surface crack shape is more improved as in the case of (Case 3). It is possible to analyze realistically.

  According to the surface crack growth analysis method of the present embodiment, the crack propagation characteristics are set independently in consideration of the difference in material between the deepest point 3 and the crack surface point 4 of the surface crack 2, Since the crack growth rate is calculated and the surface crack growth analysis is performed, a highly accurate surface crack growth analysis can be performed under conditions closer to reality.

  Next, Example 3 of the surface crack growth analysis method according to the present invention will be described with reference to FIG.

  In the butt weld joint, since the base material 31 and the base material 32 are joined by the weld metal 33, as shown in FIG. 6, the weld metal 33 is sandwiched between the base material 31 and the base material 32. It has become. In the case of a certain type of material, the weld metal 33 is much more sensitive to SCC than the base material 31 and the base material 32, and the SCC surface crack generated in the weld metal 33 propagates only in the weld metal 33. The base material 31 and the base material 32 may be regarded as not progressing.

  In such a case, according to the surface crack growth analysis method of the present embodiment, while the crack deepest point 3 and the crack surface point 4 are both in the weld metal 33, the crack surface point at the deepest point 3. Surface crack growth analysis is performed by giving the same crack growth characteristics to 4. Next, after the crack length on the surface reaches the width of the weld metal 33, the crack growth rate at the crack surface point is set to 0 regardless of the value of the stress intensity factor, and the surface crack growth analysis is continued. By this method, a surface crack shape such as the surface crack 5 after growth shown in FIG. 6 can be obtained, and a model in which the surface crack propagates only in the depth direction can be analyzed. .

  According to the present embodiment, when the surface crack 2 reaches a material having different crack growth characteristics, the crack growth rate is independently reset at the deepest point 3 and the crack surface point 4 to perform surface crack growth analysis. Therefore, it is possible to perform surface crack growth analysis on a welded joint made of materials having different SCC sensitivities with high accuracy.

  Next, a fourth embodiment of the surface crack growth analysis method according to the present invention will be described with reference to FIG.

  In contrast to the third embodiment, the surface crack propagation analysis method of the present embodiment analyzes the case where the base material 41 is more sensitive to SCC than the weld metal 42. In the present example, one end of the crack surface point 43 reached the weld metal 42 among the crack surface point 43 and the crack surface point 44 that are the tips of the surface crack 2 in the process of the propagation analysis of the surface crack 2. At that time, the crack growth rate at the crack surface point 43 is set to 0 regardless of the value of the stress intensity factor, and the surface crack growth analysis is continued. By this method, a surface crack shape such as a surface crack 5 after growth can be obtained.

  According to the present embodiment, when one of the two crack surface points 43 and the crack surface point 44 of the surface crack 2 approaches a material having different crack propagation characteristics, Since the surface crack growth analysis is performed by independently resetting the crack growth rate at the crack surface point 44 and the deepest crack point 3 on the other side, the surface crack of the welded joint composed of materials having different SCC susceptibility is performed. Progress analysis can be performed with high accuracy.

  Next, a fifth embodiment of the surface crack growth analysis method according to the present invention will be described with reference to FIG. The surface crack growth analysis method of the fifth embodiment is a method characterized by changing the analysis model in accordance with the growth of the surface crack.

  When the surface crack 2 exists on the surface of the structural member 1 as shown in FIG. 1, first, a surface crack propagation analysis is performed as a flat plate model 52 having a surface crack 51 as shown in FIG. .

  Next, when it is determined that the surface crack 51 has reached the end of the flat plate model 52, the surface crack 51 is replaced with an enveloping corner surface crack 53, and as shown in FIG. Surface crack propagation analysis is continued as a flat plate model 54 having a corner surface crack 53.

  Further, when the corner surface crack 53 grows and the crack depth reaches the entire plate thickness of the flat plate model 54, the corner surface crack 53 is replaced with an enveloping plate-thickness two-dimensional surface crack 55. As shown in FIG. 8C, surface crack propagation analysis is performed as a flat plate model 56 having a plate thickness penetrating two-dimensional surface crack 55. The plate thickness penetration two-dimensional surface crack 55 has a surface crack shape as shown in the plan view of the flat plate model 56 shown in FIG.

  According to the surface crack growth analysis method of the present embodiment, the surface crack growth analysis is performed in which the model is sequentially replaced according to the size of the surface crack. It is possible to perform crack growth analysis with higher accuracy.

(A) is a schematic diagram which shows the surface crack of a structural member, (B) is a schematic diagram which shows the surface crack after progress. The figure which shows typically the example of the relationship between a SCC crack growth rate and a stress intensity factor. The figure which shows the flow of the growth analysis of the surface crack which concerns on this invention. The figure which shows the structure of the propagation analysis of the surface crack of Example 2. FIG. (A) is a graph which shows the time-dependent change of the crack depth by the surface crack growth analysis method of Example 2, (B) is a graph which shows the time-dependent change of the crack length. FIG. 10 is a diagram showing a configuration of a surface crack growth analysis method of Example 3. The figure which shows the structure of the growth analysis method of the surface crack of Example 4. FIG. (A) is a side view of a flat plate model having a surface crack, (B) is a side view of a flat plate model in which the surface crack has progressed to a corner surface crack, and (C) is a thickness of the corner surface crack. The side view of the flat plate model which progressed to the penetration two-dimensional surface crack, (D) is a top view of the flat plate model of (C).

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Structural member 2 Surface crack 3 Crack deepest point 4 Crack surface point 5 Surface crack 6 after growth 6 SCC propagation speed 7 in the environment x of the material A 8 SCC propagation speed 8 in the environment y of the material A 8 Environment x of the material B SCC progress rate in step 11 Step 12 Step 13 Step 14 Step 15 Step 21 Processed layer 22 Case 1
23 Case 2
24 Case 3
31 Base material 32 Base material 33 Weld metal 41 Base material 42 Weld metal 43 Crack surface point 44 Crack surface point 51 Surface crack 52 Flat plate model with semi-ellipse surface crack 53 Corner surface crack 54 Corner surface crack Plate model 55 with plate thickness penetration 2D surface crack 56 plate model with plate thickness penetration 2D surface crack

Claims (10)

In the surface crack growth analysis method to analyze the surface crack growth of structural members,
When calculating the growth rate of the surface crack, the crack propagation characteristics in the depth direction of the structural member and the crack propagation characteristics on the surface of the structural member are set independently ,
When performing the surface crack propagation analysis of the structural member, one of the crack depth which is the crack dimension in the depth direction of the structural member and the crack length which is the crack dimension on the member surface is When a predetermined dimension is reached, one of the crack dimensions is fixed at a fixed value so that it does not increase more than the predetermined dimension, and only the other crack dimension is increased. A method for analyzing the growth of a surface crack, characterized by continuing the analysis of the crack propagation. In the surface crack growth analysis method to analyze the surface crack growth of structural members,
When calculating the growth rate of the surface crack, the crack propagation characteristics in the depth direction of the structural member and the crack propagation characteristics on the surface of the structural member are set independently,
When performing the surface crack propagation analysis of the structural member, one of the two surface crack tips on the surface of the structural member has reached a predetermined position. In this case, it is assumed that the position of the surface crack is fixed so that the one surface crack tip does not advance more than the predetermined position, and only the other surface crack tip and the deepest crack point are increased. A method for analyzing the propagation of a surface crack characterized by continuing the propagation analysis. Claim 1 or 2, characterized in that determining the surface-out the shape of the crack assumes a semi-elliptical shape, can裂深prudent crack length of only using the information half-elliptical shape surface-out裂形shaped The method for analyzing the growth of a surface crack as described in 1. 3. The surface crack growth analysis method according to claim 1 or 2, wherein an analysis model for surface growth analysis is changed as the surface crack grows. Surface crack growth analyzer that analyzes the progress of surface cracks in structural members
Input means for inputting a crack length on the surface of the structural member and a crack depth in the depth direction of the structural member;
A calculation means for calculating a stress intensity factor;
A calculation means for calculating the crack growth rate;
Means for calculating the crack growth increment;
A crack dimension updating means,
When calculating the crack growth rate in the calculation means for calculating the crack growth rate, the crack growth characteristic in the depth direction of the structural member and the crack propagation characteristic on the surface of the structural member are calculated. A configuration that can be set independently ,
When one of the crack depth, which is a crack dimension in the depth direction of the structural member, and the crack length, which is a crack dimension on the surface of the member, reaches a predetermined dimension, Either one of them is fixed at a constant value so that it does not increase more than the predetermined dimension, and the surface crack growth analysis is continued by assuming that only the other crack size is increased. A surface crack growth analysis device characterized in that the analysis is performed. Surface crack growth analyzer that analyzes the progress of surface cracks in structural members
Input means for inputting a crack length on the surface of the structural member and a crack depth in the depth direction of the structural member;
A calculation means for calculating a stress intensity factor;
A calculation means for calculating the crack growth rate;
Means for calculating the crack growth increment;
A crack dimension updating means,
When calculating the crack growth rate in the calculation means for calculating the crack growth rate, the crack growth characteristic in the depth direction of the structural member and the crack propagation characteristic on the surface of the structural member are calculated. A configuration that can be set independently,
When one of the two surface crack tips on the surface of the structural member has reached a predetermined position, the one surface crack tip is at the predetermined position. The position is fixed so that it does not progress further, and only the other surface crack tip and the crack deepest point are increased, and the surface crack growth analysis is continued to analyze the surface crack growth of the structural member. A surface crack propagation analysis device characterized by comprising The crack growth characteristic data of the material according to claim 5 or 6, wherein the crack growth characteristic data of the material is provided as a database in advance, and the crack growth characteristic data is read by inputting a material name or selecting from a material name list. Surface crack growth analyzer. 7. The surface crack growth analysis apparatus according to claim 5 or 6 , further comprising a storage medium that records a calculation result of the surface crack propagation analysis and can extract the calculation result. 9. The surface crack propagation analysis according to claim 8, wherein after the past input data recorded in the storage medium is read, a part of the input data is changed to perform surface crack propagation analysis. apparatus. When multiple stress intensity factor formulas are applicable when calculating the stress intensity factor of a surface crack, these multiple stress intensity factor formulas are provided as a database, and an identification name is entered or selected from a list. 7. A surface crack growth analysis apparatus according to claim 5 or 6, wherein a stress intensity factor calculation formula adapted to be read is read.

Images