Provided is a residual stress estimation method and a residual stress estimation device capable of suppressing the number of cut pieces to be collected for measuring inherent strain without deteriorating residual stress estimation accuracy. In a case where it is assumed that the inherent strain is uniformly distributed in one direction in a structure, a user measures residual stress from a cut piece collected in a region in which the inherent strain is uniformly distributed and inputs the measured value to the residual stress estimation device. The residual stress estimation device estimates a two-dimensional inherent strain distribution on an analysis surface perpendicular to the one direction in the structure using the input residual stress measured value, transfers the estimated two-dimensional inherent strain distribution to the one direction, and estimates a three-dimensional inherent strain distribution in the structure.

The present invention relates to a residual stress estimation method and a residual stress estimation device for estimating residual stress of a structure based on an inherent strain method.

Residual stress generated in a structure causes damage such as fatigue cracks in some cases and it is important to accurately grasp the distribution of the residual stress in the structure. As a method of estimating the residual stress of a structure, there has been known a method using an inherent strain method (for example, refer to Patent Documents 1 and 2).

In the method of estimating residual stress based on the inherent strain method of the related art, two kinds of cut pieces are cut out from a structure, the elastic strain or residual stress of each cut piece measured is measured, and the measured value of the elastic strain or residual stress of each cut piece is applied to inverse analysis processing based on a finite element method. In the inverse analysis processing, inherent strain is approximated with a least squares method using a distribution function and a distribution of inherent strain in the structure is determined, thereby calculating the residual strain of the structure before cutting from the obtained inherent strain distribution.

Patent Document 1 discloses that cut pieces of a T piece and an L piece are cut out from a test piece of a structure, and the respective T piece and L piece are further cut and divided into a plurality of small pieces to measure elastic (released) strain.

Patent Document 1: JP-A-2005-181172

Patent Document 2: JP-A-2003-121273

The work for collecting a cut piece from a structure is very complicated and costs and working time also increase. When the number of cut pieces to be measured increases, shape errors, processing errors, and measurement errors are easily incorporated, which causes deterioration in residual stress estimation accuracy. On the other hand, when the number of cut pieces to be collected is too small, the number of measurement of elastic strain or residual stress is not sufficient and thus the residual stress of the structure cannot be estimated with high accuracy.

The present invention is made in consideration of the above circumstances and a primary object thereof is to provide a residual stress estimation method and a residual stress estimation device that can solve the above problems.

In order to solve the above-described problems, a residual stress estimation method according to an aspect of the present invention includes steps of obtaining a measured value related to residual stress measured from a cut piece collected in a region in which the inherent strain is uniformly distributed in a case where it is assumed that the inherent strain is uniformly distributed in one direction in a structure; estimating a two-dimensional inherent strain distribution in a direction crossing the one direction in the structure based on the obtained measured value; and estimating a three-dimensional inherent strain distribution in the structure such that the estimated two-dimensional inherent strain distribution continues in the one direction.

In the aspect, in the step of obtaining a measured value, elastic strain or residual stress measured on a cut surface of the cut piece that is cut in the direction crossing the one direction may be obtained as the measured value.

In the aspect, in the step of estimating a three-dimensional inherent strain distribution, in a three-dimensional model of the structure in which a plurality of calculation points are three-dimensionally arranged, the estimated inherent strain value at each calculation point on one surface crossing the one direction may be given to each calculation point on the other surface crossing the one direction.

In the aspect, in the step of estimating a three-dimensional inherent strain distribution, when a calculation point to which the estimated inherent strain value is not given is present on the other surface, in a case where the one surface is overlapped with the other surface, the inherent strain at the calculation point may be compensated based on the inherent strain of the one surface around the calculation point to which the estimated inherent strain value is not given.

In the aspect, in the step of estimating a three-dimensional inherent strain distribution, a searching region may be set around the calculation point, and in a case where the calculation point of the one surface overlapped with the other surface is present in the searching region, the inherent strain at the calculation point to which the inherent strain is not given may be compensated based on the estimated inherent strain value at the calculation point of the one surface in the searching region.

In the aspect, in the step of estimating a three-dimensional inherent strain distribution, in a case where the calculation point of the one surface overlapped with the other surface is not present in the searching region, a searching region larger than the searching region may be newly set.

A residual stress estimation device according to the other aspect of the present invention includes: an input unit that receives, in a case where it is assumed that inherent strain is uniformly distributed in one direction in a structure, an input of a measured value related to residual stress measured from a cut piece collected in a region in which the inherent strain is uniformly distributed;

a first estimation unit of estimating a two-dimensional inherent strain distribution in a direction crossing the one direction in the structure based on the measured value received by the input unit;

a second estimation unit of estimating a three-dimensional inherent strain distribution in the structure such that the two-dimensional inherent strain distribution estimated by the first estimation unit continues in the one direction; and

a display unit that displays a residual stress estimation result based on the three-dimensional inherent strain distribution estimated by the second estimation unit.

According to the present invention, it is possible to suppress the number of cut pieces to be collected for measuring elastic strain or residual stress without deteriorating residual stress estimation accuracy.

Hereinafter, preferred embodiments of the present invention will be described with reference to the drawings.

A residual stress estimation device according to the present invention is provided for, in a case where it is assumed that inherent strain is uniformly distributed in one direction, estimating a two-dimensional inherent strain distribution on a surface of a structure perpendicular to one direction, transferring the estimated two-dimensional inherent strain distribution to the other surface perpendicular to one direction, estimating a three-dimensional inherent strain distribution in the structure, and estimating residual stress of the structure based on the three-dimensional inherent strain distribution.

A residual stress estimation device **1** is realized by a computer **10**. As shown in **10** includes a main body **11**, an input unit **12**, and a display unit **13**. The main body **11** includes a CPU **111**, a ROM **112**, a RAM **113**, a hard disk **115**, a read-out device **114**, an input/output interface **116**, and an image output interface **117**, and the CPU **111**, the ROM **112**, the RAM **113**, the hard disk **115**, the read-out device **114**, the input/output interface **116**, and the image output interface **117** are connected by a bus.

The CPU **111** can execute a computer program loaded on the RAM **113**. A residual stress estimation program **110** which is a computer program for residual stress estimation is executed by the CPU **111** and thus the computer **10** can function as the residual stress estimation device **1**. The residual stress estimation program **110** is an inverse analysis process program based on a finite element method and a distribution state of inherent strain in the structure can be estimated.

The ROM **112** is configured by a mask ROM, a PROM, an EPROM, an EEPROM or the like and is recorded with the computer program to be executed by the CPU **111** and the data used for the same.

The RAM **113** is configured by an SRAM, a DRAM, and the like. The RAM **113** is used to read out the residual stress estimation program **110** recorded in the hard disk **115**. When the CPU **111** executes the computer program, the RAM is used as a work region of the CPU **111**.

The hard disk **115** is installed with various computer programs to be executed by the CPU **111** such as the operating system, the application program, and the like, and the data used for the execution of the relevant computer program. The residual stress estimation program **110** is also installed in the hard disk **115**.

The hard disk **115** is installed with an operating system such as Windows (registered trademark) manufactured and sold by US Microsoft Co., for example. In the following description, the residual stress estimation program **110** according to the embodiment is assumed to operate on the operating system.

The read-out device **114** is configured by a flexible disk drive, a CD-ROM drive, a DVD-ROM drive, or the like, and can read out the computer program or the data recorded in a portable recording medium **120**. The residual stress estimation program **110** is stored in the portable recording medium **120** to cause the computer to function as the residual stress estimation device. The computer **10** can read out the residual stress estimation program **110** from the portable recording medium **120** and install the residual stress estimation program **110** in the hard disk **115**.

The input/output interface **116** is configured by, for example, a serial interface such as an USB, an IEEE 1394, or an RS-232C, or the like, a parallel interface such as an SCSI, an IDE, an IEEE 1284, or the like, and an analog interface including a D/A converter, an A/D converter, and the like. The input unit **12** including a keyboard and a mouse is connected to the input/output interface **116**, and a user can input data to the computer **10** by using the input unit **12**.

The image output interface **117** is connected to the display unit **13** configured by an LCD, a CRT, or the like, and a video signal according to the image data sent from the CPU **111** is output to the display unit **13**. The display unit **13** displays an image (screen) according to the input video signal.

(1) Calculation of Residual Stress Using Inherent Strain

When inherent strain is ε_{0}, residual stress σ can be expressed by the following expression.

σ=*D*(ε−ε_{0}) (1)

However, D represents an elastic coefficient matrix and ε represents all strains satisfying the relation of the following expression.

[Equation 1]

∫*B*^{T}*νdV=∫B*^{T}*D*(ε−ε_{0})*dV*=0 (2)

Herein, ∫dV represents a volume fraction in the analysis region and B represents a coefficient matrix for relating a node displacement u and ε.

ε=Bu (3)

In a case where the inherent strain is known, residual stress is obtained as follows.

The following expressions are given from Expressions (2) and (3).

[Equation 2]

Ku=P (4)

Herein,

K=∫B^{T}DBdV (5)

P=∫B^{T}Dε_{0}dV (6)

K represents a rigidity matrix and P represents a load vector generated by the inherent strain.

When u is obtained by solving Expression (4), residual stress can be obtained from Expressions (3) and (1).

(2) Calculation of Inherent Strain Using Measured Residual Stress

N measured residual stress values are expressed as σ_{m}. Correspondingly, N calculated residual stress values obtained from the inherent strain are expressed as σ_{c}, and a residue R between the calculated residual stress and the measured residual stress is defined by the following expression.

[Equation 3]

*R*=(σ_{m}−σ_{c}^{T}(σ_{m}−σ_{c}) (7)

The inherent strain at an arbitrary point is expressed as the following linear function by M distribution function parameters a.

[Equation 4]

ε_{0}=Ma (8)

Herein, M represents a coordinate function and the coordinates may not be linear.

When the inherent strain is determined by Expression (8), the measured residual stress is obtained by the method of (1) above and as a result, a linear relation expression can be obtained as follows.

[Equation 5]

σ_{c}=Ha (9)

Herein, H represents a coefficient matrix and the component thereof can be obtained by obtaining residual stress by giving a unit value to each component of a.

When a is determined such that R is the minimum by substituting Expression (9) into Expression (7), an inherent strain distribution in which an error between the measured residual stress and the calculated residual stress at the measurement point is the minimum is determined.

Hereinafter, the operation of the residual stress estimation device **1** according to the embodiment will be described.

The residual stress estimation device **1** performs residual stress estimation processing as described below to estimate the residual stress of the structure.

The structure is formed by plastic processing. Herein, a crank shaft will be described as an example of the structure. As shown in **200** is configured such that a journal shaft **201** and a pin shaft **203** are connected by a crank arm **202**. In the connection place of the journal shaft **201** and the crank arm **202** and the connection place of the pin shaft **203** and the crank arm **202**, great stress is easily generated in use. When tension residual stress is easily generated in these connection places, damage such as fatigue cracks may be caused. In order to improve fatigue life, plastic processing such as roll processing or shot peening is performed on the connection places and compressive residual stress is introduced.

**300** is pressed against the connection place of the journal shaft **201** (or the pin shaft **203**) and the crank arm **202**, the journal shaft **201** is rotated. Thus, in the connection place, a fillet **204** is formed and compressive residual stress is applied such that the residual stress is uniformly distributed in the circumferential direction of the journal shaft **201**.

The roll processing is performed over the whole circumference of the journal shaft **201** and is performed on a part of the pin shaft **203** in the circumferential direction. As shown in **210** over the whole circumference of the journal shaft **201**. Therefore, the filler **204** is formed over the whole circumference of the journal shaft **201**. On the other hand, as shown in **220** of 180° in the pin shaft **203**. Therefore, the fillet **204** is formed in a range of 180° in the pin shaft **203**.

As described above, the residual stress of the structure in which the compressive residual stress is uniformly applied in one direction is estimated using the residual stress estimation device **1**.

A user collects a cut piece by cutting the structure and measures the residual stress from the cut piece (Step S**1**). Specifically, the structure is thinly cut in one direction to collect a cut piece (T piece) and is cut in a direction perpendicular to the one direction to collect a cut piece (L piece).

Here, the residual stress is a value obtained by multiplying elastic strain by a Young's modulus, and measuring elastic strain is equivalent to measuring residual stress. Accordingly, either elastic strain or residual stress may be measured from the cut piece. In the embodiment, a case of measuring the residual stress will be described.

As shown in

Thus, it is possible to reduce the workload of the cutting processing and the measurement of the residual stress of the cut piece.

On the other hand, the inherent strain distribution in the shaft length direction is complicated. Accordingly, it is necessary to collect the L piece in a plurality of places in the shaft length direction.

In a case of having a bent surface like the fillet portion of the crank shaft, instead of the L piece, a conical cut piece (hereinafter, referred to as “C piece”) cut in a direction normal to the bent surface may be collected. In addition, the L piece and the C piece are not collected and only the T piece may be collected. In **500** is obtained by cutting the structure in a direction normal to the bent surface of the fillet, that is, in the radius direction of the arc-shaped fillet in the cross section. Since the journal shaft has an axisymmetric shape, a cross section **501** of the C piece **500** conically extends around the rotation center axis of the journal shaft. Several C pieces are collected by changing the central angle of the fillet (for example, from 20° to 110° at every 10°).

In a case where compressive residual stress is uniformly applied to a rod-like structure long in one direction in the longitudinal direction, only one T piece can be collected in one place in the longitudinal direction.

The user directly measures the residual stress of the cut piece collected as described above with X-rays or the like. In a case of measuring the elastic strain, the user attaches a strain gauge to the cut piece and further cuts the cut piece into a plurality of small pieces to measure released strain (elastic strain) of each small piece. In the measurement of the residual stress or released strain (elastic strain), a plurality of components that are different from each other are measured.

**400** has a cross section **401** perpendicular to the circumferential direction of the journal shaft (or the pin shaft), and the user measures respective components σ_{r }and ∝_{z }in an r direction and a z direction perpendicular to each other in the cross section **401**. Generally, these two components are measured in the T piece and two direction components perpendicular to each other are also measured in the L piece (or the C piece).

**1**. The CPU **111** of the residual stress estimation device **1** receives the residual stress of the cut pieces input from the input unit **12** (Step S**2**).

Next, the CPU **111** determines an inherent strain distribution function (Step S**3**). As the distribution function, an arbitrary multidimensional polynomial or a trigonometric series can be selected. In this case, the CPU **111** may automatically select the distribution function or the user may designate a desired distribution function by using the input unit **12**. In the residual stress estimation device **1**, the distribution function may be set in advance.

The distribution function determined in Step S**3** is provided for estimating the inherent strain of the structure in which inherent strain is uniformly distributed in one direction. Specifically, the distribution function is a distribution function for expressing the two-dimensional inherent strain distribution of the cross section of the journal shaft (or the pin shaft) perpendicular to the circumferential direction. Accordingly, the distribution function for expressing the inherent strain distribution in the circumferential direction is not used.

Next, the CPU **111** optimizes the parameters of the distribution function (Step S**4**). Hereinafter, the processing of Step S**4** will be described in detail.

The CPU **111** first determines H in Expression (9). The procedure thereof is as follows.

(a) a=[1, 0, 0, . . . , 0]^{T }is set and ε_{0}=Ma is obtained.

(b) Expression (4) is solved and u is obtained.

(c) ε is obtained by Expression (3).

(d) σ is obtained by Expression (1).

(e) N values corresponding to the residual stress measurement point are extracted from the components of a and the extracted values are set to a first column of H.

(f) a=[0, 1, 0, . . . , 0]^{T }is set and a second column of H is also obtained in the same procedure of (b) to (f).

Next, the CPU **111** determines “a” such that R of Expression (7) is the minimum. Accordingly, the distribution function parameters are optimized.

Further, the CPU **111** calculates a two-dimensional inherent strain distribution on an analysis surface perpendicular to a direction in which inherent strain is uniformly distributed in the structure (Step S**5**).

In the processing of Step S**5**, in a case where a portion of the crank shaft in which the pin shaft and the crank arm are connected to each other is set as a target to be analyzed, the surface of the pin shaft perpendicular to the circumferential direction becomes an analysis surface. The CPU **111** obtains inherent strain at an arbitrary point of the analysis surface by Expression (8).

Next, the CPU **111** transfers the two-dimensional inherent strain distribution on the calculated analysis surface to the circumferential direction (the direction in which inherent strain is uniformly distributed) (Step S**6**). At this time, in a case where the journal shaft is a target to be analyzed, the CPU **111** transfers the inherent strain in a range of 360°, and in a case where the pin shaft is a target to be analyzed, the CPU **111** transfers the inherent strain in a range of 180°. Accordingly, the inherent strain can be transferred in accordance with an actual processing range.

As shown in **6** is performed on a three-dimensional model (analytical model) of a structure built in a virtual three-dimensional space. The analytical model is constituted by arranging a plurality of three-dimensional elements (a tetrahedron, a hexahedron, or the like). Herein, the calculation point is placed at the center point of the three-dimensional element. In **501**, inherent strain estimated values are given. A case where the inherent strain is transferred to a transfer surface **502** spaced from the analysis surface **501** by θ around a z axis which is the rotation center is considered. The CPU **111** transfers the respective estimated inherent strain values at the calculation points a to e to calculation points a′ to e′ corresponding to the calculation points a to e on the transfer surface. That is, the inherent strain values at the calculation points a′ to e′ are the same as the respective inherent strain values at the calculation points a to e. The CPU **111** performs such processing over the transfer range (in a case of the journal shaft, in a range of 360°, and in a case of the pin shaft, in a range of 180°).

In a case where the target to be analyzed is a structure in which compressive stress is uniformly applied in a liner direction, the CPU **111** transfers the two-dimensional inherent strain distribution on the analysis surface perpendicular to the liner direction to the linear direction.

Next, in a case where a point to which the inherent strain is not transferred (hereinafter, referred to as “defective point”) is present in the analytical model, the CPU **111** compensates the inherent strain of the defective point (Step S**7**).

The processing of Step S**7** will be described using **502** is the defective point, the CPU **111** sets a circular searching region **503** around the defective point P.

The CPU **111** determines whether or not the calculation point of the analysis surface **501** is present in the searching region **503** when the analysis surface **501** is overlapped with the analysis surface **502** by moving the analysis surface **501** around the z axis by θ. In a case where the calculation point of the analysis surface **501** is present in the searching region **503**, the CPU **111** compensates the inherent strain at the defective point from the estimated inherent strain value at the calculation point thereof. In the compensation of the inherent strain, a known interpolation method, extrapolation method, or other estimation methods can be used. For example, the estimated inherent strain value at the nearest calculation point of the defective point can be set as an estimated inherent strain value at the defective point (nearest neighbor interpolation). In a case of searching two or more calculation points, spline interpolation, polynomial interpolation, linear interpolation, and the like (the same is applied to the extrapolation method) may be used and the estimated inherent strain value at each calculation point may be averaged.

In the processing of Step S**7**, at least one calculation point may be searched and a plurality of calculation points may be searched.

In a case where the calculation point of the analysis surface **501** is not present in the searching region **503**, the CPU **111** sets a new searching region one size larger than the searching region to search the calculation point. Subsequently, the CPU **111** sets a searching region that is gradually increased until the calculation point is searched.

When the inherent strains of all the defect points are compensated in Step S**7**, the CPU **111** calculates a residual stress estimated value (Step S**8**).

In the processing of Step S**8**, the CPU **111** obtains u by solving Expression (4) from the inherent strain at each point and the obtained u is applied to Expression (3) to obtain ε. Then, the obtained ε is applied to Expression (1) to obtain σ.

Next, the CPU **111** displays the obtained residual stress estimated value on the display unit **13** (Step S**9**).

After Step S**9**, the CPU **111** ends the processing.

By adopting the above-described configuration, regarding the structure in which residual stress is uniformly distributed in one direction (the circumferential direction around the shaft, the linear direction, or the like), the number of cut pieces to be collected for measuring inherent strain can be reduced without deteriorating residual stress estimation accuracy.

In the above-described embodiment, the estimation of the residual stress in the structure which is subjected to plastic processing is described but the present invention is not limited thereto. Processing such as welding or heat treatment other than plastic processing is performed and the residual stress in the structure in which inherent strain is uniformly present in one direction can be also estimated in the same manner.

In the above-described embodiment, the configuration in which the residual stress is measured from the cut piece of the structure and the parameter of the distribution function is optimized such that a difference between the measured residual stress and the residual stress calculated by the distribution function is the minimum is described, but the present inversion is not limited thereto. A configuration in which the released strain (elastic strain) is measured from the cut piece of the structure and the parameter of the distribution function is optimized such that a difference between the measured released strain and the elastic strain calculated by the distribution function is the minimum may be adopted.

The residual stress estimation method and the residual stress estimation device of the present invention are a residual stress estimation method and a residual stress estimation device for estimating the residual stress of a structure based on an inherent strain method.

The present application is based on Japanese Patent Application (Patent Application No. 2015-043082) filled on Mar. 5, 2015, the contents of which are incorporated herein by reference.

**1**: Residual stress estimation device

**10**: Computer

**12**: Input unit

**13**: Display unit

**110**: Residual stress estimation program

**111**: CPU

**115**: Hard disk

**116**: Input/output interface

**117**: Image output interface

**200**: Crank shaft (structure)

**400**: T piece (cut piece)

**401**: Cross section

**500**: C piece (cut piece)

**501**: Cross section

**503**: Searching region