JP5721227B2 - Multiaxial fatigue life evaluation method - Google Patents

Description

  The present invention relates to a multiaxial fatigue life evaluation method used for evaluating the fatigue life of a general structure including a rotary machine such as an aircraft engine and a supercharger, a pressure vessel, and the like.

  The load received by the actual machine member is a random load that changes with time. Conventionally, in order to evaluate the life of a fluctuating multiaxial load field, the uniaxial evaluation method has been expanded, and equivalent strain and equivalent stress (for example, equivalent strain and equivalent stress of Mises) are used. Evaluation has been made based on uniaxial material data using wave number counting method and cumulative damage law such as minor law (cumulative fatigue damage law).

  However, it is also assumed that the direction of principal stress and principal strain (referred to as the principal axis) changes due to a complexly changing multiaxial load state and structural discontinuity. According to the results of the multiaxial fatigue test in which the main axis direction was changed, the fatigue life became uniaxial life (using equivalent strain or equivalent stress as the phase of shear strain and axial strain or the phase of shear stress and axial stress shifted. It has been reported that the fatigue life is lower than the calculated fatigue life.

  In order to solve these problems, several multi-axis fatigue life evaluation methods that can cope with changes in the spindle have been proposed in consideration of load paths (load paths including changes in the spindle direction).

  Among them, in Non-Patent Documents 1 to 3, a method of quantifying the amount of change in the main axis by paying attention to the principal stress / principal strain surface having the largest principal stress / principal strain during the period to be evaluated, In addition, a multiaxial fatigue life evaluation method (IS (Itoh-Sakane) method) based on load paths (load paths including changes in the main shaft direction) has been proposed.

Takaki Ito, “Non-proportional multiaxial low cycle fatigue life evaluation model”, Materials, Japan Society for Materials Science, December 15, 2001, vol. 50, no. 12, pp. 1317-1322 Takamoto Itoh, Tomohiko Ozaki, Toru Amaya, and Masao Sakane, "DETERMINATION OF STRESS AND STRAIN RANGES UNDER NON-PROPORTIONAL CYCLIC LOADING", 8th International Conference on Multiaxial Fatigue & Fracture, 2007 Takamoto Itoh, Masao Sakane, Takahiro Hata, Naomi Hamada, “A design procedure for assessing low cycle fatigue life under proportional and non-proportional loading”, International Journal of Fatigue 28, 2006, pp. 459-466 Satoshi Kure, Takaki Ito, Yuta Shimizu, Hiroshi Nakamura, Masasuke Takanashi, “Effect of Average Strain on Low Cycle Fatigue Life of Ti-6Al-4V under Non-proportional Multiaxial Load”, M & M 2010 Materials Mechanics Conference CD-ROM, The Japan Society of Mechanical Engineers, October 2010, pp. 1165-1167

  However, in the conventional IS method, the magnitude of the load waveform and the degree of change in the principal axis direction cannot be evaluated with respect to the waveform in which the magnitude of the load changes in a complicated manner.

  Specifically, in the conventional IS method, the amount of change in the main shaft is evaluated over the entire period to be evaluated, and based on the results, the amount of change in the main shaft is taken into account (considering a non-proportional load). The fatigue life is evaluated by obtaining the range or strain range. Since the stress range and strain range used when evaluating fatigue life correspond to the entire period to be evaluated, evaluation was not performed considering fatigue damage in each load waveform. .

  Therefore, for example, when the load size changes complicatedly (or irregularly), such as when a large load is applied only once and a small load is applied many times, how is the period to be evaluated set? Depending on whether or not the fatigue life may be evaluated, it is difficult to predict fatigue damage with high accuracy by the conventional IS method.

  Accordingly, an object of the present invention is to solve the above problems and provide a multiaxial fatigue life evaluation method capable of predicting fatigue damage due to a multiaxial load with high accuracy even when the magnitude of the load changes in a complicated manner. There is to do.

The present invention was devised to achieve the above object, and based on the stress or strain state of the structure to be evaluated, an evaluation surface determination step for determining the principal stress / strain surface of the evaluation object, The magnitude of the principal stress and principal strain at the time is SI (t), and the angle between the principal stress and principal strain axis of the principal stress and principal strain surface to be evaluated is the principal stress and principal strain axis at each time. When ξ (t), the relationship between the principal stress / principal strain acting on the principal stress / principal strain surface to be evaluated with respect to the load pathway length (SI (t) cosξ (t)) and the load pathway An analysis step for obtaining a relationship of a change amount (SI (t) | sinξ (t) |) of a value including a direction change of main stress / strain with respect to the length, and a main of the evaluation target with respect to the load path length Based on the relationship between the principal stress and principal strain acting on the stress and principal strain surface Analyzing the waveform of the principal stress and principal strain acting on the principal stress and principal strain surface of the evaluation object, and analyzing the waveform that contributes to fatigue damage on the principal stress and principal strain surface of the evaluation object (Or a combination of waves) divided and extracted, and for each of the extracted waves (or a combination of waves), a waveform counting step for obtaining a stress range or strain range ΔSI _i acting on the principal stress / strain plane, A non-proportional load coefficient f _{NP — i} corresponding to each wave (or combination of waves) extracted in the waveform counting step based on the relationship between the change amount of the value including the direction change of the main stress / strain with respect to the load path length. Equation (1) shown in [Equation 1]

Based on the obtained non-proportional load coefficient f _{NP_i} and the stress range or strain range ΔSI _i obtained in the waveform counting step, the stress range or strain range ΔSI i_NP considering the non-proportional load is _determined for each wave. The cumulative damage is calculated based on the calculation process to be calculated, the stress range or strain range ΔSI _{i_NP} obtained in the calculation process, and the SN diagram at the time of uniaxial load obtained in advance. And a life prediction step for predicting the fatigue life of the structure.

  The analysis of the waveform in the waveform counting step may be performed based on a rainflow method.

  In the evaluation surface determination step, based on the stress or strain state at each time of the structure to be evaluated, a principal stress / strain surface that is orthogonal to the principal stress or principal strain at each time is determined. For each principal stress and principal strain surface at each obtained time, calculate the value of the principal stress or principal strain vertical component at each time acting on the principal stress and principal strain surface. Based on the calculated value and the SN diagram at the time of uniaxial load obtained in advance, cumulative damage evaluation at each principal stress / strain plane is performed, and it is evaluated that the damage is the largest in the cumulative damage evaluation. The determined principal stress / strain surface may be determined as the principal stress / strain surface to be evaluated.

Wherein in the calculation step, based on the stress range or strain range DerutaSI _i obtained in a non-proportional load factor f _{NP_i} the waveform counting step, the following equation (2)
ΔSI _{i_NP} = (1 + αf _{NP_i} ) ΔSI _i + kS _{i_mean} (2)
Where α is the degree of further curing or non-proportional load
Coefficient to represent
S _{i_mean} : Average stress or average strain at each wave
k: A stress range or a strain range ΔSI _{i_NP} considering a non-proportional load may be calculated from the material constant.

Wherein in the calculation step, based on the stress range or strain range DerutaSI _i obtained in a non-proportional load factor f _{NP_i} the waveform counting step, the following equation (3)
ΔSI _i — _NP = (1 + αf _NP — _i ) ΔSI _i {(1−R _i ) / 2} ^w−1
... (3)
Where α is the degree of further curing or non-proportional load
Coefficient to represent
R _i : Maximum stress or maximum strain in each wave
Ratio to minimum stress or strain
w: A stress range or a strain range ΔSI _{i_NP} considering a non-proportional load may be calculated from the material constant.

  ADVANTAGE OF THE INVENTION According to this invention, even if it is a case where the magnitude | size of load changes complicatedly, the multiaxial fatigue life evaluation method which can predict the fatigue damage by a multiaxial load with high precision can be provided.

It is a flowchart which shows the procedure of the multiaxial fatigue life evaluation method which concerns on one embodiment of this invention. In this invention, it is a flowchart which shows the procedure at the time of determining the main stress and principal strain surface of evaluation object. (A), (b) is a figure explaining the perpendicular | vertical component of main stress and principal strain S (t _i ) of another time t _i which acts on the principal stress and principal strain surface at a certain time t _n in the present invention. It is. In this invention, it is a figure explaining the variation | change_quantity of the value including the magnitude | size of the principal stress and principal strain which acts on the principal stress and principal strain surface of evaluation object, and the principal stress or principal strain. (A) is a figure which shows an example of the stress or distortion state in each time of the structure of evaluation object, (b) is with respect to the load path | route length obtained at the time of the stress or distortion state of (a). It is a figure which shows the relationship between SI (t) cosξ (t) and SI (t) | sinξ (t) |. FIG. 6 is a diagram for explaining wave number counting by a rainflow method when the relationship of FIG. 5B is obtained. It is a figure explaining the area of the load path | route length corresponding to the wave of B of FIG.

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

  First, the IS method used in the multiaxial fatigue life evaluation method according to the present embodiment will be described. Since the IS method is described in detail in Non-Patent Documents 1 and 2, only the outline will be described here.

The IS method is a criterion based on principal stress (strain) and is defined by the following equation (4).
ΔSI _NP = (1 + αf _NP ) ΔSI (4)

In Expression (4), ΔSI is a stress (strain) range calculated as a normal component acting on the principal stress / strain surface to be evaluated, that is, the principal stress / principal on the principal stress / strain surface to be evaluated. When the strain axis is the reference axis, the stress (strain) range is calculated by projecting to the reference axis. Α is a coefficient representing the degree of further curing or life reduction under non-proportional load (load in which the principal axis direction of stress or strain changes), and can also be obtained from the rate of decrease in time intensity due to non-proportional load. it can. Since α is a material constant, it is preferable to obtain it in advance as material data. f _NP is a parameter representing a non-proportional degree of the load path, and is referred to as a non-proportional load coefficient.

The non-proportional load coefficient f _NP is obtained from the equation (5) shown in [Equation 2].

“| E ₁ × e _R SI (t) |” in the integral symbol in equation (5) represents the amount of change of the value including the direction change of the principal stress (principal strain), and ds is the stress (strain). ) Path, that is, a load path. The non-proportional load coefficient f _NP can be obtained by integrating the amount of change of the main stress (strain) along the entire path of the load path. The reason why the integral value is multiplied by π / (2SI _max · L _path ) in Equation (5) is to standardize f _NP . In a circular load in which axial strain ε or axial stress σ and shear strain γ or shear stress τ are loaded with a phase difference of 90 degrees, f _NP is 1.

Further, e ₁ is a unit vector indicating the direction of the maximum principal stress (maximum principal strain), and e _R is the principal stress (principal strain) at a certain time t (time with e ₁ as a reference (time 0)). Is a unit vector indicating the direction of. Thus, the outer product of e ₁ and e _R uses e ₁ and e the angle of _R xi] a (t), it can be represented by sinξ (t). Therefore, “| e ₁ × e _R SI (t) |” in the integral symbol of Expression (5) can also be expressed as “SI (t) | sinξ (t) |”.

  Hereinafter, the multiaxial fatigue life evaluation method according to the present embodiment will be described.

  As shown in FIG. 1, the multiaxial fatigue life evaluation method according to the present embodiment includes an evaluation surface determination step (step S1), an analysis step (step S2), a waveform counting step (step S3), and a calculation step. (Step S4) and a life prediction step (Step S5) are mainly provided.

  In the evaluation surface determination step of step S1, first, in step S11, the main stress or main strain at each time is calculated based on the stress or strain state at each time of the structure to be evaluated. Thereby, the principal stress / strain plane at each time, which is a plane orthogonal to the principal stress or principal strain at each time, is also obtained.

  In addition, as the stress or strain state at each time used for calculation in step S11, for example, when the part where the fatigue life is evaluated is a measurement point where the sensor is arranged, measurement data by the sensor can be used. . Moreover, when evaluating the fatigue life of the site | part which is not a measuring point, the analysis result which analyzed the stress or the strain state by arbitrary methods can be used. Moreover, what is necessary is just to set it as the period which performs evaluation from the starting (operation start) to the stop (operation end) of the structure of evaluation object, for example. Specifically, for example, when the structure to be evaluated is an aircraft, one cycle from take-off to landing, and when the structure to be evaluated is a plant, from the previous periodic inspection to the current periodic inspection. May be set as the period to be evaluated.

  Thereafter, in step S12, the main stress / strain surface to be evaluated is determined. At this time, as has been done conventionally, the surface having the largest principal stress / strain may be the principal stress / strain surface to be evaluated, but in this embodiment, the principal stress with the greatest fatigue damage is obtained. -Obtain the principal strain surface and determine the principal stress / strain surface with the greatest fatigue damage as the principal stress / strain surface to be evaluated.

  This is because, for example, the surface where the principal stress / principal strain is maximized is most subject to fatigue damage depending on the state of stress / strain, such as when many small loads are applied while a large load is applied once. It is because it does not necessarily become large. In such a case, if the fatigue life is evaluated with the surface having the largest principal stress / strain as the evaluation target as before, the surface that is not the surface with the greatest fatigue damage is evaluated, and the evaluation on the dangerous side turn into.

  FIG. 2 shows a specific procedure for determining the principal stress / strain surface to be evaluated in step S12.

As shown in FIG. 2, when determining the principal stress / principal strain surface to be evaluated, first, in step S121, pay attention to the principal stress / principal strain surface at a certain time t _n and act on that surface. The value of the vertical component of the principal stress or principal strain at each other time is calculated.

As shown in FIG. 3A, it is assumed that the principal stress / principal strain at a certain time t _n is S (t _n ), and the principal stress / principal strain surface at the time t _n is a plane indicated by reference numeral 21. . At this time, as shown in FIG. 3B, if the main stress / principal strain at another time t _i is S (t _i ), another stress acting on the principal stress / principal strain surface 21 at time t _n is obtained. The vertical component of the principal stress / principal strain S (t _i ) at time t _i is as shown by S (t _i ) ′ in the figure. Similarly, the vertical components of the principal stress and principal strain at all times acting on the principal stress and principal strain surface 21 at a certain time t _n are calculated.

Thereafter, in step S122, cumulative damage evaluation is performed on the principal stress / principal strain surface at time t _n based on the SN diagram at the time of uniaxial load obtained in advance.

In cumulative damage evaluation, it is recommended to use minor rules or modified minor rules. Specifically, the arbitrary time t _i the number of cycles N _i corresponding to the main stress and principal strain of the vertical component S (t _i) 'together with obtained from SN diagram during uniaxial load calculated in step S121, The number of times n _i at which S (t _i ) ′ is loaded is obtained, and the following equation (6)
D _n = Σ (n _i / N _i ) (6)
Thus, the fatigue damage degree D _n on the principal stress / principal strain surface at time t _n is obtained.

  Thereafter, in step S123, it is determined whether all n have been calculated. If NO is determined, the process returns to step S121. That is, steps S121 and S122 are executed for all times, and the fatigue damage levels on the principal stress / principal strain surfaces at all times are obtained. As for the time interval to be evaluated, the analysis setting (step) may be employed as it is when the analysis result is used, and may be set at an appropriate interval when the measurement result is used. .

Thereafter, at step S124, the main stress and principal strain surface fatigue damage degree D _n obtained is maximum in step S122, i.e., select the primary stress and principal strain plane of maximum fatigue damage were selected principal stress -The principal stress / principal strain axis (that is, the axis perpendicular to the principal stress / principal strain plane) is used as the reference axis, and the selected principal stress / principal strain plane is determined as the evaluation plane.

  Returning to FIG. 1, after determining the main stress / strain surface to be evaluated in step S <b> 12 (steps S <b> 122 to S <b> 124), the analysis process of step S <b> 2 is performed.

  In the analysis process of step S2, the IS method is used to determine the relationship between the principal stress and principal strain acting on the principal stress and principal strain surface to be evaluated with respect to the load path length, and the principal stress and principal strain with respect to the load path length. The relationship between the change amount of the value including the direction change of the main strain is obtained.

As shown in FIG. 4, the magnitude of the principal stress / strain at each time is SI (t), the principal stress / strain axis of the principal stress / strain surface to be evaluated, and the principal stress / strain at each time. When the angle formed by the strain axis (that is, the angle formed by e ₁ and e _R ) is ξ (t), the magnitude of the principal stress / strain acting on the principal stress / strain plane to be evaluated is SI ( t) can be expressed as cosξ (t). Further, the amount of change of the value including the direction change of the main stress or the main strain can be expressed as SI (t) | sinξ (t) |.

  As an example, when a torsional load is applied twice while an axial load is applied once as shown in FIG. 5A, SI (t) cosξ (t), SI ( t) | sinξ (t) | is represented by a solid line and a broken line in FIG. After obtaining the relationship as shown in FIG. 5B, the process proceeds to step S3.

  In the waveform counting step of step S3, the analysis of the waveform of SI (t) cosξ (t) (waveform counting analysis, frequency analysis) is performed based on the relationship of SI (t) cosξ (t) to the load path length. A wave (or combination of waves) that contributes to fatigue damage on the principal stress / strain surface to be evaluated is divided and extracted from the waveform. In this embodiment, a case where a waveform analysis is performed based on a rainflow method will be described. However, the present invention is not limited to the rainflow method, and for example, a range pair method, a hysteresis loop method, or the like can be used.

  The rainflow method is well-known and will not be described. For example, considering the case where the relationship shown in FIG. 5B is obtained in the analysis step of step S2, applying the rainflow method to FIG. As shown, five waves (or combinations of waves) A to E are extracted.

For each of the extracted waves (or combinations of waves), the maximum value S _{i_max} and the minimum value S _{i_min} of the stress or strain are obtained. By taking the difference between these values, the stress / strain surface is _affected. The stress range or strain range ΔSI _i (= S _i — _max −S _i — _min ) can be obtained for each wave (or combination of waves).

In the calculation process of step S4, first, in step S41, based on the relationship of SI (t) | sinξ (t) | with respect to the load path length obtained in the analysis process of step S2, the waveform counting process of step S3. A non-proportional load coefficient f _{NP — i} corresponding to each extracted wave (or combination of waves) is _obtained .

The non-proportional load coefficient f _{NP_i} is _expressed by the equation (1) shown in [Equation 3].

It can be obtained more.

In Expression (1), SI (t) | sinξ (t) | of the section of the load path length corresponding to each extracted wave (or combination of waves) is extracted, and the extracted SI (t) | sinξ The non-proportional load coefficient f _{NP — i} is obtained by standardizing the value obtained by integrating the path integral along (t) |

For example, considering the B wave (combination of waves) in FIG. 6, SI (t) | sinξ (t) | in the section of B1 and B2 is integrated along the load path as shown in FIG. By normalizing the integral value, the non-proportional load coefficient f _{NP_i} can be obtained.

Thereafter, at step S42, a non-proportional load factor f _{NP_i} corresponding to each of the wave (or a combination of waves) the extracted obtained in the step S41, stress range determined by the waveform counting step of step S3 or strain range DerutaSI _i Based on the above, the stress range or the strain range ΔSI _{i_NP} considering the non-proportional load is calculated for each wave.

When obtaining the stress range or strain range ΔSI _{i_NP} considering the non-proportional load, the above formula (4) is applied and the following formula (7)
ΔSI _{i_NP} = (1 + αf _{NP_i} ) ΔSI _i (7)
You may ask for.

  However, for example, with respect to the waves A and E in FIG. 6, since the average value of stress / strain does not become 0, it is more desirable to perform evaluation in consideration of average stress and average strain.

Specifically, based on the stress range or strain range DerutaSI _i obtained in non-proportional load factor f _{NP_i} waveform counting step of step S3, the following equation (2) or the following formula (3)
ΔSI _{i_NP} = (1 + αf _{NP_i} ) ΔSI _i + kS _{i_mean} (2)
Where α is the degree of further curing or non-proportional load
Coefficient to represent
S _{i_mean} : Average stress or average strain at each wave
k: material constant ΔSI _{i —NP} = (1 + αf _NP — _i ) ΔSI _i {(1−R _i ) / 2} ^w−1
... (3)
Where α is the degree of further curing or non-proportional load
Coefficient to represent
R _i : Maximum stress or maximum strain in each wave
Ratio to minimum stress or strain
w: It is desirable to calculate the stress range or strain range ΔSI _{i_NP} in consideration of the non-proportional load from the material constant. In equations (2) and (3), k and w are material constants representing the degree of influence of average stress or average strain obtained from uniaxial load test results, and may be acquired in advance as material data.

In addition, _{Si_mean} in Formula (2) is the following Formula (8)
S _{i_mean} = (S _{i_max} + S _{i_min} ) / 2 (8)
R _i in the equation (3) can be _calculated by the following equation (9).
R _i = S _{i_min} / S _{i_max} (9)
It can ask for. S _{i — max} and S _{i — min} in equations (8) and (9) are the maximum and minimum values of stress or strain in each extracted wave (or combination of waves). Since the grounds of the equations (2) and (3) are described in detail in Non-Patent Document 4, description thereof is omitted here.

In the life prediction process in step S5, first, in step S51, based on the stress range or strain range ΔSI _{i_NP} obtained in the calculation process in step S4 and the SN diagram at the time of uniaxial load obtained in advance, Fatigue damage (fatigue damage) due to each extracted wave (or combination of waves) is calculated.

Specifically, for each of the extracted wave, the stress range or strain range _ΔSI i_NP cycle number N _i corresponding to that obtained by computation step obtained from SN diagram during uniaxial load, the following equation (10)
D _i = n _i / N _i (10)
To obtain the fatigue damage degree D _i for each wave (or combination of waves). In equation (10), n _i is the number of times ΔSI _{i_NP} is loaded. Here, since fatigue damage is calculated for each wave (or combination of waves), n _i = 1.

In step S52, cumulative damage (cumulative fatigue damage) is calculated. Specifically, the following formula (11)
D = ΣD _i (11)
Thus, the cumulative damage D is calculated by adding the fatigue damage degrees D _i of the respective waves (or combinations of waves) obtained in step S51.

  Thereafter, in step S53, the fatigue life of the structure to be evaluated is predicted based on the cumulative damage D obtained in step S52. If D is 1 or more, damage occurs and the service life is reached. For example, fatigue damage accumulated in an arbitrary operation period (for example, one cycle from the operation start to the operation end) is obtained, and until D becomes 1. The fatigue life can be predicted by predicting the time (number of cycles).

  As described above, in the multiaxial fatigue life evaluation method according to the present embodiment, the waves extracted by the rainflow method (or the The fatigue damage is obtained individually for each of the combinations of waves, and these are accumulated to obtain the accumulated damage over the entire evaluation target period. Therefore, even if the magnitude of the load changes in a complicated manner, the direction of the spindle is complicated by using the single axis fatigue life data (that is, the SN diagram) used as conventional design basic data. Fatigue damage due to changing multiaxial loads can be predicted with high accuracy.

  Further, in the multiaxial fatigue life evaluation method according to the present embodiment, the principal stress / principal strain surface with the largest fatigue damage is not evaluated as in the conventional method, but the surface having the largest principal stress / strain is evaluated. Since it is the object of evaluation, it becomes possible to predict fatigue damage due to multiaxial loads in which the size and direction of the main shaft change in a complicated manner with higher accuracy.

  Furthermore, in the multiaxial fatigue life evaluation method according to the present embodiment, attention is paid to the fact that the average value of the waves extracted by the rainflow method is not necessarily 0, and the average is calculated using the above-described equations (2) and (3). Since the evaluation is performed in consideration of the stress and the average strain, the fatigue life can be predicted with higher accuracy.

  The present invention is not limited to the above-described embodiment, and it is needless to say that various modifications can be made without departing from the spirit of the present invention.

Claims (5)

Based on the stress or strain state of the structure to be evaluated, an evaluation surface determination step for determining the main stress / strain surface of the evaluation target;
The magnitude of the principal stress and principal strain at each time is SI (t), and the angle between the principal stress and principal strain axis of the principal stress and principal strain surface to be evaluated and the principal stress and principal strain axis at each time Ξ (t) and the relationship between the load path length and the principal stress / principal strain acting on the principal stress / principal strain surface to be evaluated (SI (t) cosξ (t)) and the load An analysis step for obtaining a relationship of a change amount (SI (t) | sinξ (t) |) of a value including a change in direction of main stress / strain with respect to a path length;
Based on the relationship between the principal stress and principal strain acting on the principal stress and principal strain surface of the evaluation object with respect to the load path length, the principal stress and principal stress acting on the principal stress and principal strain surface of the evaluation object Analyze the waveform of the magnitude of the strain, extract and extract the wave (or combination of waves) that contributes to fatigue damage on the main stress / strain surface of the evaluation object from the waveform and extract the extracted wave ( Or a wave counting step for obtaining a stress range or strain range ΔSI _i acting on the principal stress / strain surface for each of the combinations of waves),
A non-proportional load coefficient f _{NP — i} corresponding to each wave (or combination of waves) extracted in the waveform counting step based on the relationship between the change amount of the value including the direction change of the main stress / strain with respect to the load path length. Equation (1) shown in [Equation 1]
Based on the obtained non-proportional load coefficient f _{NP_i} and the stress range or strain range ΔSI _i obtained in the waveform counting step, the stress range or strain range ΔSI i_NP considering the non-proportional load is _determined for each wave. A calculation process to calculate,
Cumulative damage is calculated based on the stress range or strain range ΔSI _{i_NP} determined in the calculation step and the SN diagram at the time of uniaxial load determined in advance, and based on the calculated cumulative damage, Life prediction process for predicting fatigue life;
A multiaxial fatigue life evaluation method comprising: The multiaxial fatigue life evaluation method according to claim 1, wherein the analysis of the waveform in the waveform counting step is performed based on a rainflow method. In the evaluation surface determination step,
Based on the stress or strain state at each time of the structure to be evaluated, the principal stress / strain surface that is orthogonal to the principal stress or principal strain at each time is obtained,
For each principal stress / strain surface at each obtained time, calculate the value of the principal stress or principal strain component at each time acting on the principal stress / strain surface, and
Based on the calculated value and the SN diagram at the time of uniaxial load obtained in advance, cumulative damage evaluation at each principal stress and principal strain surface is performed,
The multiaxial fatigue life evaluation method according to claim 1 or 2, wherein the principal stress / principal strain surface evaluated as having the greatest damage in the cumulative damage evaluation is determined as the principal stress / principal strain surface to be evaluated. In the calculation step,
Based on the non-proportional load coefficient f _{NP — i} and the stress range or strain range ΔSI _i obtained in the waveform counting step, the following equation (2)
ΔSI _{i_NP} = (1 + αf _{NP_i} ) ΔSI _i + kS _{i_mean} (2)
Where α is the degree of further curing or non-proportional load
Coefficient to represent
S _{i_mean} : Average stress or average strain at each wave
The multiaxial fatigue life evaluation method according to claim 1, wherein k: a stress range or a strain range ΔSI _{i_NP} considering a non-proportional load is calculated from a material constant. In the calculation step,
Based on the non-proportional load factor f _{NP — i} and the stress range or strain range ΔSI _i obtained in the waveform counting step, the following equation (3)
ΔSI _i — _NP = (1 + αf _NP — _i ) ΔSI _i {(1−R _i ) / 2} ^w−1
... (3)
Where α is the degree of further curing or non-proportional load
Coefficient to represent
R _i : Maximum stress or maximum strain in each wave
Ratio to minimum stress or strain
The multiaxial fatigue life evaluation method according to claim 1, wherein w: a stress range or strain range ΔSI _{i_NP} considering a non-proportional load is calculated from a material constant.