JP2019028033A - Fatigue damage analyzer and fatigue damage analysis method - Google Patents

Abstract

To provide a fatigue damage analyzer with which it is possible to improve the accuracy of numerical analysis of a resin crack symptom.SOLUTION: According to one embodiment of the present invention, a fatigue damage analyzer comprises an analysis unit, a computation unit and a determination unit. The analysis unit finds a von Mises strain at each of a plurality of virtual evaluation points arranged at equal intervals on a drawing in which the cross section of a building is modeled. The computation unit sequentially repeats a first computation process for calculating the number of fatigue cycles until breakage at each evaluation point using the von Mises strain, a second computation process for extracting a minimum evaluation point among the plurality of evaluation points where the number of fatigue cycles is smallest and determining the number of fatigue cycles at the minimum evaluation point as the number of crack growth cycles, and a third computation process for calculating a fatigue damage amount at each evaluation point using the number of crack growth cycles. The determination unit determines on the basis of a preset criterion whether or not to stop the operations of the analysis unit and computation unit.SELECTED DRAWING: Figure 1

Description

  Embodiments described herein relate generally to a fatigue damage analysis apparatus and a fatigue damage analysis method.

Since fiber reinforced plastic (hereinafter referred to as FRP) undergoes a plurality of fracture processes before fatigue fracture, it is important to evaluate fatigue strength reflecting the fracture mode. As a technique for evaluating the fatigue strength of FRP, numerical analysis using a computer is known. For example, when analyzing the interfacial debonding phenomenon of FRP, an analysis method for calculating the amount of crack growth by specifying the crack propagation path in advance and calculating the energy release rate by applying the VCCT (Virtual Crack Closed Theory) theory It has been known.
Further, when analyzing a fatigue fracture phenomenon of an isotropic material such as a metal material, for example, an analysis method is known in which an amount of progress is calculated by obtaining an energy release rate by a region integration method.

JP 2013-11504 A JP 2013-185913 A

Tsuda et al., 4 others, “Introduction of fatigue life evaluation tool fe-safe / verity of welded joint”, Materials, 2011, Vol. 60, No. 12, p. 1158-1159

  In FRP fatigue strength evaluation, it is important to numerically analyze the resin cracking phenomenon that occurs in the early stage of fatigue failure. The resin cracking phenomenon is a phenomenon in which a crack is generated from the interface between the fiber and the resin, and the crack propagates and propagates in the resin.

  In the resin cracking phenomenon of FRP, the crack propagation direction is determined under the influence of stress concentration caused by fibers. Therefore, the above analysis method in which the crack propagation path must be specified in advance cannot be applied to the numerical analysis of the resin cracking phenomenon.

  In the region integration method described above, it is difficult to obtain the energy release rate with high accuracy when there are dissimilar materials having different rigidity near the crack tip. The FRP has a resin and fibers having a rigidity different from that of the resin. For this reason, the above-described region integration method cannot numerically analyze the resin cracking phenomenon with high accuracy.

  An object of the present invention is to provide a fatigue damage analysis apparatus and a fatigue damage analysis method capable of improving accuracy related to numerical analysis of a resin cracking phenomenon.

  According to one embodiment, the fatigue damage analysis apparatus includes an analysis unit, a calculation unit, and a determination unit. An analysis part calculates | requires Mises distortion in each of the virtual several evaluation point arrange | positioned at equal intervals on the drawing which modeled the cross section of the structure. The calculation unit uses the Mises distortion to extract a first evaluation process for calculating the number of fatigue cycles until failure at each evaluation point, and a minimum evaluation point with the smallest number of fatigue cycles among the plurality of evaluation points, A second calculation process for determining the number of fatigue cycles at the minimum evaluation point as the number of crack growth cycles and a third calculation process for calculating the fatigue damage amount at each evaluation point using the number of crack growth cycles are sequentially repeated. The determination unit determines whether to stop the operations of the analysis unit and the calculation unit based on a predetermined determination criterion.

  According to this embodiment, it becomes possible to improve the precision regarding the numerical analysis of the resin crack phenomenon.

It is a block diagram which shows the structure of the fatigue damage analyzer which concerns on 1st Embodiment. It is drawing which modeled the cross section of FRP numerically analyzed with the fatigue damage analyzer shown in FIG. It is the enlarged view to which a part of FIG. 2 was expanded. It is a flowchart which shows the operation | movement procedure of the fatigue damage analysis apparatus which concerns on 1st Embodiment. It is drawing for demonstrating the particle method which concerns on 2nd Embodiment.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings. This embodiment does not limit the present invention.

(First embodiment)
FIG. 1 is a block diagram illustrating a configuration of a fatigue damage analysis apparatus 1 according to the first embodiment. FIG. 2 is a drawing in which a cross section of the FRP numerically analyzed by the fatigue damage analysis apparatus 1 is modeled. FIG. 3 is an enlarged view of a part of FIG.

  The FRP shown in FIG. 2 has a resin 101 and fibers 102. For example, when this FRP is used for a welded portion and a load F in the in-plane direction is continuously applied, a crack is generated from the interface between the resin 101 and the fiber 102, and the crack propagates to the inside of the resin 101. A developing phenomenon, that is, a resin cracking phenomenon of FRP may occur.

  The fatigue damage analysis apparatus 1 according to the present embodiment is an apparatus for numerically analyzing this resin cracking phenomenon. The target of the numerical analysis may be a structure including the resin 101 and a different material having a different rigidity from the resin 101, and the different material is not limited to the fiber 102.

  Returning to FIG. 1, the fatigue damage analysis apparatus 1 includes a storage unit 10, an analysis unit 20, a calculation unit 30, and a determination unit 40. The storage unit 10 stores various data necessary for numerical analysis of the FRP fatigue state. For example, node / element data, material data, data indicating boundary conditions, data indicating contact conditions, data indicating analysis conditions, data indicating fatigue damage amount D of each evaluation point, and the like are stored in the storage unit 10 in text data format. Stored. In this embodiment, regarding the data of the fatigue damage amount D, the data value is set to “0” when the FRP has no initial crack, and is set to “1” when the FRP has an initial crack. . In addition, the memory | storage part 10 may be comprised as an external memory | storage device connected to the fatigue damage analysis apparatus 1 instead of the component of the fatigue damage analysis apparatus 1. FIG.

  The analysis unit 20 reads data from the storage unit 10 and numerically analyzes the read data to obtain Mises distortion. In the present embodiment, the analysis unit 20 numerically analyzes data based on a mesh method that is an example of a finite element method. In this mesh method, as shown in FIG. 3, the cross section of the FRP is divided into a square mesh 301, and a plurality of nodes 302 of the mesh 301 correspond to a plurality of evaluation points. The analysis part 20 calculates | requires Mises distortion in all the evaluation points using a static implicit method. The static implicit method is an analysis method in which a static force balance equation is repeatedly calculated to converge an assumed value.

When it is difficult to directly determine the Mises distortion due to the performance of the analysis unit 20, the analysis unit 20 may calculate the Mises distortion ε based on the following equation (1). In Expression (1), σ _m represents Mises stress at each evaluation point, and E represents the Young's modulus of the resin 101. Here, the analysis unit 20 obtains the von Mises stress sigma _m by numerical analysis data storage unit 10, divides the Mises stress sigma _m Young's modulus E.

The calculation unit 30 includes a first calculation unit 31, a second calculation unit 32, and a third calculation unit 33. The first calculation unit 31 executes a first calculation process. Specifically, as shown in the following formula (2), the first calculation unit 31 calculates the fatigue cycle number ΔN _i until failure at all evaluation points based on the modified minor rule. This number of fatigue cycles ΔN _i corresponds to the number of fatigue cycles from the current time to failure. In Formula (2), D _i represents the fatigue damage amount at each evaluation point, and A _i and B _i represent fatigue strength constants. Regarding the fatigue strength constants A _i and B _i , the relationship of the following formula (3) is established. In formula (3), N _f represents the number of break cycles.

The second calculation unit 32 executes a second calculation process. Specifically, the second calculation unit 32 extracts a minimum evaluation point P (see FIG. 3) having the smallest fatigue cycle number ΔN _i from all evaluation points. The minimum evaluation point P indicates a portion having the highest possibility of being cracked next. Therefore, the crack propagation path can be specified by extracting the minimum evaluation point P. The second computing unit 32 determines the fatigue cycle number ΔN _imin at the minimum evaluation point P as the crack _propagation cycle number ΔN.

The third calculation unit 33 performs a third calculation process. Specifically, the third computation section 33, the correction based on Miner's rule, all evaluated fatigue damage quantity D _i where the number of fatigue cycles N is increased by crack growth cycle number ΔN below with respect to point the formula ( 4).

The determination unit 40 instructs the analysis unit 20 and the calculation unit 30 to stop operation when it is determined that the FRP fatigue fracture is sufficiently transmitted and does not hold as a structure. For example, when the analysis step number n exceeds the preset end step number n _max (n> n _max ), the determination unit 40 instructs the analysis unit 20 and the calculation unit 30 to stop the operation. The number n of analysis steps corresponds to the number of repetitions of the operation by the analysis unit 20 and the operation unit 30.

  Hereinafter, an operation procedure of the fatigue damage analysis apparatus 1 according to the present embodiment will be described with reference to FIG. FIG. 4 is a flowchart showing the operation procedure. In the present embodiment, as the initial conditions, the analysis step number n is set to 1 (n = 1), and the fatigue cycle number N is set to 0 (N = 0).

  First, the analysis unit 20 reads data from the storage unit 10 (step S1). Subsequently, the analysis unit 20 numerically analyzes the read data to obtain Mises distortion at all evaluation points (step S2). The analysis unit 20 outputs the obtained Mises distortion to the calculation unit 30.

In the calculation unit 30, the first calculation unit 31 performs the first calculation process described above (step S3). In the first calculation process, the number of fatigue cycles ΔN _i until failure at all evaluation points is calculated based on the Mises distortion obtained in step S2. The first calculation unit 31 outputs all the fatigue cycle numbers ΔN _i to the second calculation unit 32.

  Subsequently, the second calculator 32 executes the above-described second calculation process (step S4). In the second calculation process, the minimum evaluation point P is extracted and the crack propagation cycle number ΔN is determined based on the result of the first calculation process. The second calculation unit 32 outputs the determined crack growth cycle number ΔN to the third calculation unit 33.

  Subsequently, the third calculation unit 33 executes the third calculation process described above (step S5). In the third calculation process, the fatigue damage amount D at all evaluation points is calculated based on the number of crack growth cycles determined in the second calculation process. The third calculation unit 33 stores the calculated fatigue damage amount D in the storage unit 10. Thereby, the data value of the fatigue damage amount D is updated to the calculated value of the third calculation process in the storage unit 10 (step S6).

Next, the determination part 40 performs the determination process mentioned above (step S7). In step S7, when the analysis step number n exceeds the end step number _nmax , the determination unit 40 instructs the analysis unit 20 and the calculation unit 30 to stop the operation. As a result, the analysis process ends. On the contrary, when the analysis step number n does not exceed the end step number _nmax , the analysis step number n and the fatigue cycle number N are updated based on the following equation (5) (step S8). Thereafter, the operations in steps S1 to S6 described above are repeated.

  According to the present embodiment described above, since the analysis of the crack propagation path is performed based on Mises distortion acting on each evaluation point, the numerical value of the resin cracking phenomenon of the FRP in which the resin 101 and the fiber 102 are combined. Analysis is possible. Here, when obtaining the Mises distortion using the mesh method, the Mises distortion depends on the shape of the mesh. Therefore, if the mesh has a non-uniform shape, the intervals between the evaluation points become non-uniform, and the Mises distortion analysis accuracy decreases.

  On the other hand, in this embodiment, as shown in FIG. 3, since the mesh 301 is formed in a square shape, the evaluation points are arranged at equal intervals. As a result, Mises distortion is required with high accuracy, so that the resin cracking phenomenon can be analyzed with high accuracy. In addition, since the number of fatigue cycles until fracture is calculated based on the modified minor rule for the evaluation point near the crack tip, a crack propagation path reflecting an actual physical phenomenon can be derived.

(Second Embodiment)
The configuration of the fatigue damage analysis apparatus according to the present embodiment is the same as that of the fatigue damage analysis apparatus 1 according to the first embodiment described above. Hereinafter, the operation of the fatigue damage analysis apparatus according to the present embodiment will be described focusing on differences from the first embodiment.

  In this embodiment, the analysis part 20 calculates | requires Mises distortion by numerically analyzing data based on the particle method which is another example of a finite element method by step S2. In this particle method, as shown in FIG. 5, the cross section of the FRP is modeled as a particle group having a plurality of virtual particles arranged at equal intervals, and the plurality of particles correspond to a plurality of evaluation points. The analysis part 20 calculates | requires Mises distortion in all the evaluation points using a static implicit method. Thereafter, similarly to the first embodiment, the operations from step S3 (first arithmetic processing) to step S8 are executed.

  Also in this embodiment described above, evaluation points are arranged at equal intervals, and Mises distortion at each evaluation point is obtained. Therefore, similarly to the first embodiment, Mises distortion is obtained with high accuracy, so that the resin cracking phenomenon can be analyzed with high accuracy.

(Third embodiment)
The configuration of the fatigue damage analysis apparatus according to the present embodiment is the same as that of the fatigue damage analysis apparatus 1 according to the first embodiment described above. Hereinafter, the operation of the fatigue damage analysis apparatus according to the present embodiment will be described focusing on differences from the first embodiment.

  In the present embodiment, in step S <b> 2, the analysis unit 20 obtains an energy release rate at each evaluation point instead of the Mises distortion and outputs the energy release rate to the first calculation unit 31. Specifically, the analysis unit 20 obtains the energy release rate by numerically analyzing the data read from the storage unit 10 by the finite element method such as the mesh method or the particle method described above.

In the first calculation process of the next step S3, the Paris law shown in the following formula (6) is applied to the fatigue crack growth model. In equation (6), a is the length of the crack. N is the number of fatigue cycles. G is the energy release rate. C and m are material constants. In the present embodiment in which the Paris rule is applied, the first calculation unit 31 calculates the number of fatigue cycles ΔN _i until failure at each evaluation point using the following equation (7). In Expression (7), L is the distance between evaluation points.

In the second calculation process of the next step S4, the minimum evaluation point with the minimum number of fatigue cycles ΔN _i is extracted. Thereafter, similarly to the first embodiment, the operations from step S5 (third arithmetic processing) to step S8 are executed.

  According to the present embodiment described above, the energy release rate acting on each evaluation point is obtained instead of Mises distortion. Further, when calculating the number of fatigue cycles using the energy release rate, a Paris law suitable for analysis of crack propagation is used. Thereby, it is possible to perform a highly accurate fatigue fracture analysis without arranging the evaluation points at equal intervals.

(Fourth embodiment)
The configuration of the fatigue damage analysis apparatus according to the present embodiment is the same as that of the fatigue damage analysis apparatus 1 according to the first embodiment described above. Hereinafter, the operation of the fatigue damage analysis apparatus according to the present embodiment will be described focusing on differences from the first embodiment.

  In the present embodiment, in step S2, the analysis unit 20 obtains Mises distortion at each evaluation point by numerically analyzing data using a dynamic explicit method instead of the static implicit method. Therefore, as an initial condition, the number n of analysis steps and the number N of fatigue cycles are both set to 1 (n = N = 1). In step S <b> 1, the analysis unit 20 reads data indicating a time width per step, material density, and the like from the storage unit 10.

Thereafter, in the third calculation process in step S5, the third arithmetic unit 33 calculates the fatigue damage quantity D _i of each evaluation point using Equation (8) below. In the equation (8), the lower part means that when the fatigue damage amount D _i is 1 or more, the fatigue damage amount D _i is always 1.

Thereafter, in step S8, the fatigue cycle number N is updated based on the following equation (9).

  As described above, according to the present embodiment described above, since the Mises distortion is obtained at the evaluation points arranged at equal intervals, as in the first embodiment, the resin cracking phenomenon can be analyzed with high accuracy. . Further, in the present embodiment, when obtaining Mises distortion, a simple dynamic explicit method is used as compared with the static implicit method. Therefore, the processing load of the analysis unit 20 can be reduced and the cost can be reduced.

(Fifth embodiment)
The configuration of the fatigue damage analysis apparatus according to the present embodiment is the same as that of the fatigue damage analysis apparatus 1 according to the first embodiment described above. Hereinafter, the operation of the fatigue damage analysis apparatus according to the present embodiment will be described focusing on differences from the first embodiment.

  In the present embodiment, in step S2, the analysis unit 20 obtains Mises distortion or energy release rate and calculates a reaction force RF at an evaluation point corresponding to an FRP restraint location. For example, the analysis unit 20 calculates the reaction force RF by displacement control by numerical analysis of the elastic body by the finite element method. This reaction force RF has a characteristic of decreasing as the fatigue damage region of the structure to be numerically analyzed becomes larger.

Therefore, in the present embodiment, in step S7, the determination unit 40 determines whether to end the analysis process using the above characteristics. Specifically, the determination unit 40 performs a determination process based on the following equation (10). In equation (10), the initial reaction force RF ₁ is a reaction force when the number of analysis steps n is 1 (n = 1). K is a reaction force reduction constant. The reaction force reduction constant k is desirably set to 0.1, for example.

In step S7, the reaction force RF is, it can be determined that when it becomes smaller than the reference value obtained by multiplying the initial resistance RF ₁ to the reaction force decrease constant k, FRP fatigue fracture has propagated sufficiently resin 101 . Therefore, the determination unit 40 instructs the analysis unit 20 and the calculation unit 30 to stop the operation.

  According to this embodiment described above, the analysis unit 20 analyzes the state of FRP fatigue failure, and the determination unit 40 performs analysis processing of the analysis unit 20 and the calculation unit 30 based on the analysis result of the analysis unit 20. Determine the end of the arithmetic processing. As described above, it is possible to prevent useless processing by grasping the time point at which the FRP fatigue fracture has sufficiently progressed.

  Although several embodiments have been described above, these embodiments are presented as examples only and are not intended to limit the scope of the invention. The novel system described herein can be implemented in various other forms. Various omissions, substitutions, and changes can be made to the system configuration described in the present specification without departing from the gist of the invention. The appended claims and their equivalents are intended to include such forms and modifications as fall within the scope and spirit of the invention.

20 analysis units, 30 calculation units, 40 determination units

Claims (10)

A fatigue damage analysis apparatus for numerically analyzing a fatigue state of the structure based on a drawing obtained by modeling a cross section of a structure having a resin and a different material different from the resin,
An analysis unit for obtaining Mises distortion in each of a plurality of virtual evaluation points arranged at equal intervals in the drawing;
Using the Mises strain, a first calculation process for calculating the number of fatigue cycles until failure at each evaluation point, and extracting the minimum evaluation point with the minimum number of fatigue cycles among the plurality of evaluation points, the minimum A second calculation process for determining the fatigue cycle number at the evaluation point as a crack growth cycle number, and a third calculation process for calculating the fatigue damage amount at each evaluation point using the crack extension cycle number, in sequence. A computing unit to repeat;
A determination unit for determining whether to stop the operation of the analysis unit and the calculation unit based on a predetermined determination criterion;
Fatigue damage analyzer with   2. The fatigue damage analysis apparatus according to claim 1, wherein the analysis unit divides the drawing into a square mesh and obtains the Mises distortion by a mesh method using a plurality of nodes of the mesh as the plurality of evaluation points.   The fatigue damage analysis apparatus according to claim 1, wherein the analysis unit obtains the Mises strain by a particle method using a plurality of virtual particles arranged at equal intervals in the drawing as the plurality of evaluation points.   The calculation unit according to any one of claims 1 to 3, wherein the calculation unit calculates the fatigue cycle number in the first calculation process and calculates the fatigue damage amount in the third calculation process based on a corrected minor rule. Fatigue damage analyzer.   The fatigue damage analysis apparatus according to any one of claims 1 to 4, wherein the analysis unit obtains the Mises distortion by a static implicit method or a dynamic explicit method.   The fatigue damage analysis apparatus according to claim 1, wherein the analysis unit calculates the Mises distortion by dividing Mises stress by Young's modulus. A fatigue damage analysis apparatus for numerically analyzing a fatigue state of the structure based on a drawing obtained by modeling a cross section of a structure having a resin and a different material different from the resin,
An analysis unit for obtaining an energy release rate at each of a plurality of virtual evaluation points arranged in the drawing;
A first calculation process for calculating the number of fatigue cycles until failure at each evaluation point based on the Paris law using the energy release rate, and a minimum evaluation point with the minimum number of fatigue cycles among the plurality of evaluation points And calculating a fatigue damage amount at each evaluation point using the second arithmetic processing for determining the fatigue cycle number at the minimum evaluation point as the crack growth cycle number and the crack extension cycle number. An arithmetic unit that sequentially repeats processing,
A determination unit for determining whether to stop the operation of the analysis unit and the calculation unit based on a predetermined determination criterion;
Fatigue damage analyzer with   The determination unit stops the operations of the analysis unit and the calculation unit when a reaction force at the evaluation point corresponding to the constrained portion of the structure is smaller than a reference value among the plurality of evaluation points. The fatigue damage analysis apparatus according to any one of claims 1 to 7. A fatigue damage analysis method for numerically analyzing a fatigue state of the structure based on a drawing obtained by modeling a cross section of a structure having a resin and a different kind of a different material from the resin,
Arranging a plurality of virtual evaluation points at equal intervals in the drawing, obtaining Mises distortion in each of the plurality of evaluation points,
Using the Mises strain, a first calculation process for obtaining the number of fatigue cycles until failure at each evaluation point, and extracting a minimum evaluation point that minimizes the fatigue cycle number among the plurality of evaluation points, the minimum A second calculation process for determining the fatigue cycle number at the evaluation point as a crack growth cycle number, and a third calculation process for calculating the fatigue damage amount at each evaluation point using the crack extension cycle number, in sequence. repetition,
A fatigue damage analysis method for determining the Mises distortion and determining whether or not to end the first to third arithmetic processes based on a predetermined criterion. A fatigue damage analysis method for numerically analyzing a fatigue state of the structure based on a drawing obtained by modeling a cross section of a structure having a resin and a different kind of a different material from the resin,
Arranging a plurality of virtual evaluation points in the drawing, obtaining an energy release rate at each of the plurality of evaluation points,
Using the energy release rate, a first calculation process for obtaining the number of fatigue cycles until failure at each evaluation point, and extracting a minimum evaluation point that minimizes the fatigue cycle number among the plurality of evaluation points, Second calculation processing for determining the number of fatigue cycles at the minimum evaluation point as the number of crack growth cycles, and third calculation processing for calculating the amount of fatigue damage at each evaluation point using the number of crack growth cycles Repeat to
A fatigue damage analysis method for determining the energy release rate and determining whether to end the first to third arithmetic processes based on a predetermined criterion.

Images