JP2010216883A - Method for leading out and evaluating non-linear fracture mechanics parameter - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method for leading out a high-accuracy non-linear fracture mechanics parameter, even when elastic deformation quantity is large. <P>SOLUTION: In a method for calculating the non-linear fracture mechanics parameter using a simple formula given at every test piece, on the basis of the load-displacement curve calculated from the result of a fatigue crack developing test performed using a predetermined tension governing type test piece, the test piece is a central notched flat plate or both-sided pierced and notched flat plate; and the non-linear fracture mechanics parameter ΔJ is calculated on the basis of the load-displacement curve, by using the simple formula represented by the formula (1) (where ΔKeff is an effective stress intensity range equal to or larger than a crack opening point, E is the Young's modulus, B is plate thickness, W is the width of the test piece and 2a is crack length). <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to a method for deriving and evaluating a nonlinear fracture mechanics parameter.

  In recent years, NG (Liquefied Natural Gas) tank facilities (tank roofs and tank bottom fillet corners), nuclear power generation facilities, boiler facilities, marine structures and other large structures such as defect tolerance standards (maintenance management) As the standard has been relaxed, a soundness evaluation system for evaluating the structural soundness of structures has been introduced.

  When evaluating the structural integrity of the structure, perform periodic inspections and examine defects such as scratches and cracks in the structure using visual or special measurement equipment. Thereafter, it is determined whether or not it is possible to continue driving.

  More specifically, a crack growth analysis is performed on the structure where the defect is found, and to what extent the structural integrity of the structure is guaranteed thereafter, or the operation time until the next inspection In consideration of the above, it is determined whether there is no problem in fracture mechanics even if the operation is performed with defects (remaining life evaluation). If there is a problem, take measures such as repair or stop operation, and if it is judged that the soundness can be maintained even if the structure is operated with defects, it will be used without taking any measures such as repairs. .

  In crack growth analysis, analysis is performed using the relationship between the rate at which cracks (defects) propagate (fatigue crack growth rate) and the fracture mechanics parameters that determine the fatigue crack growth rate. Therefore, in order to accurately evaluate the soundness of the structure, it is important to accurately acquire the relationship between the fatigue crack growth rate and the fracture mechanics parameter.

  As a fracture mechanics parameter used for crack propagation analysis, a linear fracture mechanics parameter (stress intensity factor range ΔK) based on linear fracture mechanics has been conventionally used. However, since this linear fracture mechanics parameter is effective only in a small-scale yield state, the validity of the linear fracture mechanics parameter is lost when the scale of deformation becomes large and a large plastic deformation occurs, for example, in a large earthquake. I cannot use it.

  Therefore, it is necessary to introduce non-linear fracture mechanics parameters in the structural soundness evaluation assuming a case where a large load such as an earthquake is applied.

  As the nonlinear fracture mechanics parameters, simplified formulas have been proposed according to various test pieces. When a central notch flat plate or a both-side through-cut flat plate is used as the test piece, a simple expression of the nonlinear fracture mechanics parameter ΔJ is expressed by the equation (2) shown in [Equation 1] (for example, see Non-Patent Document 1). ).

In Expression (2), S ^* represents energy obtained from a load-displacement curve (load-load line displacement curve, PV curve), and has an area indicated by oblique lines in the PV curve shown in FIG.

Toshihiko Hoshide, Keisuke Tanaka, Masatoshi Nakata, “Experimental Study of Fatigue Crack Propagation under Elastic, Elastic-Plastic and Fully Yield Conditions”, Journal of the Society of Materials Science, “Materials”, Society of Materials Science, June 1982 , Vol. 31, No. 345, pp. 566-572

  However, the simple equation shown in the above equation (2) is such that the nonlinear fracture mechanics parameter ΔJ is approximately given when the amount of elastic deformation is sufficiently smaller than the amount of plastic deformation.

  Therefore, when the amount of elastic deformation is large, this approximation cannot be applied, and there is a problem that the nonlinear fracture mechanics parameter ΔJ that can evaluate the fatigue crack growth rate cannot be derived.

  Therefore, an object of the present invention is to provide a method for deriving and evaluating a nonlinear fracture mechanics parameter capable of accurately deriving a nonlinear fracture mechanics parameter even when the elastic deformation is large, in order to solve the above-described problems. is there.

  The present invention was devised to achieve the above object. A fatigue crack growth test was performed using a predetermined tensile-dominated test piece, and a load-displacement curve was obtained from the results of the fatigue crack growth test. In the method for deriving a nonlinear fracture mechanics parameter using a simplified formula given for each test piece based on the obtained load-displacement curve, the test piece is a central notch flat plate or Both sides are notched flat plates, and based on the load-displacement curve, the formula (1) shown in [Expression 2]

Is a method of deriving a nonlinear fracture mechanics parameter to obtain a nonlinear fracture mechanics parameter ΔJ using a simple formula expressed by

  The fatigue crack growth test may be performed by applying a repeated load so that the load line displacement in the test piece repeats a predetermined value, and the load-displacement curve may be obtained from the result of the fatigue crack growth test. .

  Further, the present invention is based on the nonlinear fracture mechanics parameter ΔJ obtained by the above-described method for deriving the nonlinear fracture mechanics parameter and the fatigue crack growth rate obtained in the fatigue crack growth test, and the nonlinear fracture mechanics parameter ΔJ and This is an evaluation method for obtaining a relational expression with the fatigue crack growth rate and evaluating the soundness of the structure using the relational expression.

  According to the present invention, it is possible to provide a method for deriving and evaluating a nonlinear fracture mechanics parameter that can accurately derive a nonlinear fracture mechanics parameter even when the amount of elastic deformation is large.

It is the schematic of the parameter derivation device used for the derivation method of the nonlinear fracture mechanics parameter of the present invention. It is a flowchart of the derivation method of the nonlinear fracture mechanics parameter of the present invention. FIG. 3A is a perspective view of the central cut-out flat plate, and FIG. 3B is a perspective view of the both-side through cut-out flat plate. 4 (a) and 4 (b) are diagrams for explaining a displacement measuring method in the method for deriving the nonlinear fracture mechanics parameter of the present invention. It is a figure which shows an example of the load-displacement curve (PV curve) calculated | required with the derivation | leading-out method of the nonlinear fracture mechanics parameter of this invention. It is a figure which shows an example of the relationship between the fatigue crack growth rate calculated | required with the evaluation method of this invention, and a nonlinear fracture mechanics parameter. It is a figure explaining the elastic deformation area | region and plastic deformation area | region in a PV curve. It is a figure explaining the energy in the simple type used conventionally. It is a figure explaining that the simple type used conventionally cannot be applied when elastic deformation becomes large. It is a figure explaining the energy in the simple formula used with the derivation | leading-out method of the nonlinear fracture mechanics parameter of this invention. FIG. 11A is a diagram showing a relationship between a nonlinear fracture mechanics parameter obtained by a conventional simple formula and a fatigue crack growth rate, and FIG. 11B is a diagram showing a nonlinear fracture mechanics parameter obtained by the present invention. It is a figure which shows the relationship between a fatigue crack growth rate. FIG. 12A is a perspective view of a CT test piece, and FIG. 12B is a plan view of a three-point bending test piece. It is a figure explaining the energy in the simple type used conventionally.

  Preferred embodiments of the present invention will be described below with reference to the accompanying drawings.

  The method for deriving the nonlinear fracture mechanics parameter of the present invention is a device and a large structure (for example, an LNG tank roof, a tank bottom fillet corner, a nuclear power generation facility, a boiler facility, an ocean, etc.) that can be operated continuously even if defects exist. This is a method for deriving a non-linear fracture mechanics parameter ΔJ when a central notch flat plate or a bilateral through notch flat plate is used as a test piece as a pre-stage for evaluating the structural soundness of a structure or the like).

  First, a parameter derivation device used in the method for deriving nonlinear fracture mechanics parameters according to this embodiment will be described.

  As shown in FIG. 1, the parameter derivation device 1 is used for an experimental data input unit 2 for inputting a result (experimental data) of a fatigue crack growth test using a predetermined tensile-dominated test piece, and the test piece. Material data storage unit 3 for storing material data, analysis condition storage unit 4 for storing analysis conditions, experimental data input to experiment data input unit 2, material data stored in material data storage unit 3, and analysis The analysis unit 5 that performs analysis based on the analysis conditions stored in the condition storage unit 4, the analysis result storage unit 6 that stores the analysis result in the analysis unit 5, and the analysis result stored in the analysis result storage unit 6 An output unit 7 for outputting is mainly provided.

  These experimental data input unit 2, material data storage unit 3, analysis condition storage unit 4, analysis unit 5, analysis result storage unit 6, and output unit 7 are realized by appropriately combining an interface, a memory, a CPU, software, and the like. .

  The analysis unit 5 includes a PV curve creation unit 8 that creates a load-displacement curve (PV curve) based on the experiment data input from the experiment data input unit 2, and a PV curve creation unit 8. Nonlinear fracture mechanics based on the created PV curve, the experimental data input from the experimental data input unit 2, the material data stored in the material data storage unit 3, and the analysis conditions stored in the analysis condition storage unit 4 Based on the ΔJ calculation unit 9 for calculating the parameter ΔJ, the nonlinear fracture mechanics parameter ΔJ calculated by the ΔJ calculation unit 9, the experimental data input by the experimental data input unit 2, and the analysis conditions stored in the analysis condition storage unit 4 And a relational expression deriving unit 10 for obtaining a relational expression between the fatigue crack growth rate da / dN and the nonlinear fracture mechanics parameter ΔJ.

  Next, a method for deriving a nonlinear fracture mechanics parameter according to this embodiment will be described together with the operation of the parameter deriving device 1.

  As shown in FIG. 2, in the method for deriving the nonlinear fracture mechanics parameter according to this embodiment, first, a test piece is prepared (step S1).

As shown in FIG. 3A, in this embodiment, a defect (crack) 33 that penetrates the plate-like member 32 is formed as a test piece at the center of the plate-like member 32 having a width W and a thickness B. The center cutout flat plate 31 is used. The initial height of the defect 33 is V ₀ , and the initial defect length (width) is 2a ₀ . In the present embodiment, the central notch flat plate 31 is used as the test piece. However, as shown in FIG. 3B, the test piece has an initial height V ₀ at the both end portions of the plate-like member 32 and an initial height. Alternatively, both-side through-cut flat plates 35 each having the defect 34 having the defect length a ₀ may be used.

  After producing the central notch flat plate 31 in step S1, a fatigue crack growth test is performed using the produced central notch flat plate 31 (step S2).

The fatigue crack growth test is performed by displacement control and load control. Specifically, for example, a load P is applied to the upper and lower sides of the central notch flat plate 31, and the displacement (load line displacement) V in the load line is 0 (reference value, that is, the initial height V ₀ ) and repeats a predetermined value. As described above, a fatigue crack growth test is performed by applying a repeated load.

  For example, as shown in FIG. 4A, the displacement of the load line is measured by using a knife edge member 41 having an edge at the tip at a position along the load line in the vicinity of the defect 33, and the tip at the defect 33 side. It is good to carry out by attaching so that it may face, and measuring the distance between the edge parts of both the knife edge members 41. FIG. The knife edge member 41 may be fixed to the central notch flat plate 31 by any method such as screwing or using an adhesive.

  When measuring the distance between the edge portions of the knife edge member 41, as shown in FIG. 4B, the probes 43 of the displacement measuring device 42 are brought into contact with the edge portions of both knife edge members 41, respectively. It may be performed by measuring the distance moved from the reference position.

In the fatigue crack growth test, the displacement (height of the defect 33, load line displacement, defect opening displacement) V with respect to the load P is measured, and the change in the defect length 2a of the defect 33 with respect to the number N of repeated loads is measured. Measure and obtain fatigue crack growth rate da / dN. For the displacement V, the initial height V ₀ of the defect 33 (here, the distance between the edge portions of the knife edge member 41) is set to a reference value 0. Further, the effective stress intensity factor range ΔK _eff above the crack opening point is obtained using the load range of the PV curve.

  After performing the fatigue crack growth test in step S2, a PV curve is created based on the experimental data obtained in the fatigue crack growth test (step S3).

  The experimental data of the displacement (height of the defect 33) V with respect to the load P obtained in the fatigue crack growth test is input to the experimental data input unit 2 of the parameter derivation device 1, and based on this experimental data, the analysis unit 5 The PV curve creating unit 8 creates a PV curve. An example of the created PV curve is shown in FIG.

  After the PV curve is created in step 3, the nonlinear fracture mechanics parameter ΔJ is calculated based on this (step S4).

The ΔJ calculation unit 9 of the analysis unit 5 includes a PV curve created by the PV curve creation unit 8 and experimental data input from the experimental data input unit 2 (effective stress intensity factor range ΔK _eff above the crack opening point). , Defect length 2a), material data (Young's modulus E) of the material used for the test piece stored in advance in the material data storage unit 3, and analysis conditions (plate thickness B, test) stored in the analysis condition storage unit 4 Based on the half width W), the nonlinear fracture mechanics parameter ΔJ is obtained using a simple formula expressed by the formula (1) shown in [Equation 3].

  The nonlinear fracture mechanics parameter ΔJ obtained in step 4 is stored in the analysis result storage unit 6 in association with the number of repetitions N.

  After obtaining the nonlinear fracture mechanics parameter ΔJ in step 4, a relational expression between the fatigue crack growth rate da / dN and the nonlinear fracture mechanics parameter ΔJ is obtained based on this (step S5).

  The relational expression derivation unit 10 of the analysis unit 5 plots the relationship between the nonlinear fracture mechanics parameter ΔJ obtained by the ΔJ calculation unit 9 and the fatigue crack growth rate da / dN input by the experimental data input unit 2, and analyzes conditions Based on the analysis conditions stored in the storage unit 4, a relational expression between the fatigue crack growth rate da / dN and the nonlinear fracture mechanics parameter ΔJ is obtained.

  As shown in FIG. 6, the fatigue crack growth rate da / dN and the non-linear fracture mechanics parameter ΔJ have a logarithmic logarithmic relationship, and these relational expressions are expressed by the following expression (3).

da / dN = C _j (ΔJ) ^mj (3)
In Expression (3), C _j and m _j are constants. The relational expression deriving unit 10 calculates the optimum values of the constants C _j and m _j using the plotted data based on the analysis conditions (for example, the least square method) stored in the analysis condition storage unit 4. The relational expression (3) is derived.

  The relational expression between the fatigue crack growth rate da / dN and the nonlinear fracture mechanics parameter ΔJ is stored in the analysis result storage unit 6 and output to an external monitor or the like via the output unit 7.

  Thus, a relational expression between the fatigue crack growth rate da / dN and the nonlinear fracture mechanics parameter ΔJ is obtained. By using the relational expression of the equation (3) expressed by this ordinary differential equation and using a method of calculating while updating the nonlinear fracture mechanics parameter ΔJ and the defect length sequentially by numerical calculation, the remaining life of the structure Can be evaluated.

  Here, the reason why Expression (1) is used as a simple expression of the nonlinear fracture mechanics parameter ΔJ will be described.

  In the present embodiment, Expression (1) shown in [Expression 4] is used as a simple expression of the nonlinear fracture mechanics parameter ΔJ.

  On the other hand, in the conventional method, Expression (2) shown in [Equation 5] is used as a simple expression of the nonlinear fracture mechanics parameter ΔJ.

  In Expressions (1) and (2), the first term on the right side represents the contribution to the nonlinear fracture mechanics parameter ΔJ due to elastic deformation, and is called an elastic term (linear term). The second term on the right side represents the contribution of the plastic deformation to the nonlinear fracture mechanics parameter ΔJ and is called a plastic term (nonlinear term).

Comparing equation (1) and equation (2), the elastic term is exactly the same, and the portion corresponding to the energy S ^* in the plastic term is different. The reason for this will be described below.

  FIG. 7 is a PV curve at a certain number of repetitions N. FIG. As shown in FIG. 7, by extending the lower curve of the PV curve, an opening point O serving as a reference point for the displacement amount is determined. Further, in the PV curve of FIG. 7, a point where the load P and the displacement V are maximum is referred to as a maximum point Z.

The total displacement amount (total displacement amount from the starting point O to the maximum point Z) in the PV curve can be represented by the total value of the elastic displacement amount δ _el and the plastic displacement amount δ _pl .

In consideration of the fact that the load P and the displacement V have a linear relationship in elastic deformation, a tangent along the PV curve is drawn from the maximum point Z, and is drawn horizontally (parallel to the X axis) from this tangent and the starting point O. The amount of displacement on the right side of the intersection X with the straight line, that is, the amount of displacement from the intersection X to the maximum point Z is considered to be the elastic displacement δ _el . Therefore, the amount of displacement from the remaining start point O to the intersection point X becomes the plastic displacement amount δ _pl .

Further, in consideration of the transition from elastic deformation to plastic deformation as the load P increases, the region A (the region on the left in the drawing) A until the displacement amount from the starting point O becomes equal to the elastic displacement amount δ _el is elastic. A deformation region, and a region B (region on the right in the figure) B from there to the maximum point Z becomes a plastic deformation region.

In the simple expression represented by Expression (2) used conventionally, the energy S ^* is the area indicated by hatching in FIG. This area is the area of a triangle represented by _½ · P · (δ _pl + δ _el ) (the left side in the figure) from the area obtained by integrating the load P from the starting point O to the maximum point Z (the diagonally lower diagonal line in the figure). It can be obtained by subtracting the diagonally slanted part.

Thus, in the conventional simple expression, the energy S ^* is obtained in consideration of the entire deformation region including the elastic deformation region and the plastic deformation region. Therefore, an elastic component contributes to the plastic term, although it is a plastic term. Therefore, when the amount of elastic deformation is large, the nonlinear fracture mechanics parameter ΔJ cannot be obtained with high accuracy.

In other words, the conventional simple expression is effective when the elastic displacement amount δ _el is small as shown by the broken line in FIG. 9, that is, when the elastic deformation can be ignored, but the elastic expression as shown by the solid line in FIG. When the displacement amount δ _el is large, an error in the plastic term becomes large, and the nonlinear fracture mechanics parameter ΔJ cannot be obtained with high accuracy.

On the other hand, in the simplified formula used in the present embodiment, the energy considered in the plastic term is the area shown by hatching in FIG. This area is obtained by subtracting the area of the triangle represented by 1/2 · P · δ _pl (the left oblique lower oblique line portion in the figure) from the area obtained by integrating the load P in the plastic deformation region (the oblique lower right oblique line portion in the figure). Is required.

That is, in the simple formula used in this embodiment, only the plastic deformation region is considered except for the elastic deformation region. Therefore, the elastic component does not contribute to the plastic term, and the nonlinear fracture mechanics parameter ΔJ can be accurately obtained even when the elastic displacement amount δ _el is large.

  FIG. 11A shows the relationship between the nonlinear fracture mechanics parameter ΔJ obtained using a conventional simple formula and the fatigue crack growth rate da / dN. FIG. 11B shows the relationship between the nonlinear fracture mechanics parameter ΔJ obtained in the present embodiment and the fatigue crack growth rate da / dN.

  11 (a) and 11 (b), the group population on the left side of the figure shows the experimental results when the deformation amount applied to the test piece is small (load P is small), and the group group on the right side of the figure shows a large deformation amount ( It is an experimental result in the case of increasing the load P). Further, the thickness B of the test piece is different between the round plot and the square plot.

As shown in FIG. 11 (a), the relationship between the nonlinear fracture mechanics parameter ΔJ and the fatigue crack growth rate da / dN obtained by using the conventional simple formula is different from the straight line (shown by the broken line in the figure) depending on the amount of deformation. It can be seen that it cannot be evaluated in a unified manner because it is expressed by a straight line) and becomes a different relational expression for each deformation amount. This is _presumably because the error due to the contribution of the elastic component has an effect because the elastic displacement amount δel changes depending on the amount of deformation.

  Therefore, when using the conventional simple formula, it is necessary to use a relational formula as shown by a solid line in FIG. 11 (a) so as to include all data in order to make a judgment on the safe side. It was a safety decision.

  On the other hand, in the present embodiment using the simplified expression of Expression (1), there is no error due to the contribution of the elastic component. Therefore, as shown in FIG. Regardless of the size, the fatigue crack growth rate da / dN and the non-linear fracture mechanics parameter ΔJ can be expressed by one relational expression, and unified evaluation is possible.

  As described above, in the method for deriving the nonlinear fracture mechanics parameter according to the present embodiment, the equation shown in [Expression 6] is based on the PV curve created using the experimental data obtained in the fatigue crack growth test. (1)

The nonlinear fracture mechanics parameter ΔJ is obtained using a simple expression represented by

As a result, it is possible to eliminate the contribution of the elastic component in the plastic term in consideration of the increment of the elastic displacement amount δ _el that becomes larger as the defect progresses and the change in the plastic displacement amount δ _pl due to the increase. _{Even when el} is large, the nonlinear fracture mechanics parameter ΔJ can be obtained with high accuracy. In other words, the nonlinear fracture mechanics parameter ΔJ can be accurately derived regardless of the plastic displacement amount δ _pl .

  Further, since the nonlinear fracture mechanics parameter ΔJ can be derived with high accuracy, the relational expression between the fatigue crack growth rate da / dN and the nonlinear fracture mechanics parameter ΔJ can be obtained with high precision. It becomes possible to accurately evaluate the health (remaining life) of the body. That is, the relationship between the fatigue crack growth rate da / dN and the nonlinear fracture mechanics parameter ΔJ necessary for the remaining life evaluation can be obtained experimentally.

In the present embodiment, the case where the central notch flat plate 31 or the both side through-cut flat plate 35 is used as the test piece has been described. For example, the CT test piece 120 shown in FIG. 12A or FIG. The present invention can also be applied to test pieces of other shapes such as the three-point bending test piece 121 shown in FIG. That is, in the CT test piece 120 and the three-point bending test piece 121, a simple formula ignoring the elastic displacement amount is proposed for each shape of the test piece, but when the elastic displacement amount δ _el is large, Similar to the present invention, the increment of the elastic displacement amount δ _el may be taken into consideration (contribution due to elastic deformation is excluded in the plastic term).

DESCRIPTION OF SYMBOLS 1 Parameter derivation apparatus 2 Experimental data input part 3 Material data storage part 4 Analysis condition storage part 5 Analysis part 6 Analysis result storage part 7 Output part 8 PV curve creation part 9 ΔJ calculation part 10 Relational expression derivation part

Claims (3)

A fatigue crack growth test is performed using a predetermined tensile-dominated test piece, a load-displacement curve is obtained from the result of the fatigue crack growth test, and each test piece is determined based on the obtained load-displacement curve. In the method of deriving nonlinear fracture mechanics parameters using the simple formula given,
The test piece is a center notched flat plate or a both-side through-cut flat plate, and based on the load-displacement curve, the formula (1) shown in [Expression 1]

A non-linear fracture mechanics parameter derivation method characterized in that a non-linear fracture mechanics parameter ΔJ is obtained using a simple formula expressed by:   The load-displacement curve is obtained from a result of the fatigue crack propagation test by applying a repeated load so that the load line displacement in the test piece repeats a predetermined value. Derivation method of the described nonlinear fracture mechanics parameters.   The nonlinear fracture mechanics parameter ΔJ and the fatigue based on the nonlinear fracture mechanics parameter ΔJ obtained by the method for deriving the nonlinear fracture mechanics parameter according to claim 1 and 2 and the fatigue crack growth rate obtained in the fatigue crack growth test. An evaluation method characterized by obtaining a relational expression with a crack growth rate and evaluating the soundness of the structure using the relational expression.

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