WO2021227924A1 - Fatigue life prediction method and apparatus based on weighted average maximum shear stress plane - Google Patents

Abstract

A fatigue life prediction method and apparatus based on a weighted average maximum shear stress plane, which belong to the field of multi-axis fatigue strength theories. The method comprises the following steps: (1) synthesizing a multi-axis variable-amplitude load process into an equivalent stress process by means of a von Mises equivalent stress formula, and carrying out cyclic counting on a von Mises equivalent stress process by means of a Wang-Brown multi-axis cyclic counting method; (2) using a proposed weighted average maximum shear stress plane as a critical plane under a high-cycle multi-axis variable-amplitude load; (3) calculating a fatigue damage parameter on the critical plane in each repetition obtained by means of counting; (4) carrying out fatigue damage calculation by using a Zhang-Shang model; and (5) accumulating, by using a Miner linear accumulation rule, the damage calculated in each repetition, and finally calculating the fatigue life of the entire multi-axis variable-amplitude load process. In a weight function proposed in the method, the main fatigue damage mechanism under multi-axis loading can be taken into consideration. A life prediction result indicates that a fatigue life under multi-axis constant-amplitude and variable-amplitude loading can be better predicted by means of the life prediction method.

Description

Fatigue life prediction method and device based on weighted average maximum shear stress plane Technical field

The invention relates to the field of multiaxial fatigue strength theory, and particularly refers to a method and device for predicting fatigue life based on a weighted average maximum shear stress plane.

Background technique

The lithography machine is the core equipment for manufacturing large-scale integrated circuits. The electromechanical system of the lithography machine contains a large number of components, and many components are subjected to complex multi-axis random loads during operation. Under the action of multi-axis random load, mechanical parts will experience sudden fatigue fracture after a period of operation and work, causing huge economic and property losses. The traditional uniaxial fatigue strength theory can no longer meet the design requirements of the strength and fatigue life of the actual engineering components. Therefore, in recent years, more attention has been paid to the research of multi-axis fatigue that is more in line with the actual engineering.

At present, some progress has been made in the research of multi-axis constant-amplitude fatigue life prediction methods, and the theory of multi-axis constant-amplitude fatigue life prediction with critical surface method as the main research method has been formed. However, for the problem of fatigue life prediction under multi-axis variable-amplitude load, because there is no suitable method to deal with multi-axis variable-amplitude load, the existing research results cannot be applied to actual working conditions. Therefore, it is very necessary to conduct in-depth research on the fatigue life prediction method under multiaxial variable amplitude loading. Among them, the method of determining the critical surface under multi-axis variable amplitude load is a key issue, and for the above problems, there is no better solution for the time being.

Summary of the invention

The purpose of the present invention is to provide a multi-axis fatigue life prediction method based on the weighted average maximum shear stress critical plane in response to the requirement of multi-axis fatigue strength design.

The multi-axial fatigue life prediction method based on the weighted average maximum shear stress plane provided by the present invention includes the following steps:

Obtain the load history of the notched part, use the Wang-Brown multi-axis cycle counting algorithm to determine all load repetitions in the load history, and obtain the total load repetition number m;

For the k-th load iteration, calculate the normal stress value on all the planes of the maximum shear stress range in the k-th load iteration, and select the plane with the maximum shear stress range of the maximum normal stress value as the k-th load iteration Critical surface

The phase angle of the critical surface of each load repeated using the weighted sum average method to obtain the maximum shear stress plane based on the weighted average as the critical surface of the entire load history;

According to the critical surface of the entire load history, the fatigue life of each load repeated is determined, and the cumulative fatigue damage of the critical surface of the entire load history is calculated using the Miner linear fatigue damage accumulation theory.

Preferably, the method for determining the fatigue life of each load repetition according to the critical surface of the entire load history, and then determining the cumulative fatigue damage of the critical surface of the entire load history includes:

_{Determine the fatigue life N fk of} each load repetition according to the critical surface of the entire load history, and estimate the fatigue damage D _{k of} each cycle according to formula 11.

The estimation formula of fatigue damage D _{k is:}

Using the Miner linear fatigue damage accumulation theory, calculate the cumulative fatigue damage on the weighted average maximum shear stress plane:

Where D is the cumulative fatigue damage on the weighted average maximum shear stress plane;

Determine the number of load blocks required for fatigue failure N _block :

Preferably, for the columnar notch, the method of obtaining the weighted average maximum shear stress plane based on the weighted average of the phase angles of the critical surfaces where each load is repeated includes:

Establish a rectangular coordinate system OXYZ, where O is the coordinate origin, the coordinate origin O is located on the surface of the notch root, and the X axis is parallel to the axis of the notch. The formula for determining the weighted average maximum shear stress plane is:

in,

with

The phase angle of the weighted average maximum shear stress plane determined for the entire load history; w(k) is the weight function of the k-th load repetition;

In the calculation of the k-th load iteration, the shear stress range on the plane Δ passing through the point O is calculated. The phase angles of the plane Δ are φ and θ, and φ is the normal vector of the plane Δ

The angle with the Z axis, θ is the normal vector of the plane Δ

The angle between the projection on the XY plane and the X axis, the angles φ and θ vary from 0° to 180° and 0° to 360°, respectively. By comparing the values of the shear stress range on different planes Δ, the maximum shear is determined Shear stress range

And maximum shear stress range

The phase angle of the plane, and the maximum shear stress range is solved

Normal stress on the plane, by comparing the maximum shear stress range

The normal stress on the plane, the plane with the maximum shear stress range of the maximum normal tensile stress is defined as the critical surface of the k-th load repetition, correspondingly, the angle of the critical surface of the k-th load repetition is determined φ Denoted as φ _cr (k), θ as θ _cr (k), _{substituting φ cr} (k) and θ _cr (k) into formulas 3 and 4 to solve for the weighted average maximum shear stress plane of the entire load history Phase angle

with

Preferably, the calculation formula of the weight function is:

Among them, the molecule

Is the maximum shear stress range in the k-th load repetition;

Denominator

Is m maximum shear stress range

The maximum value in

The calculation formula is as follows:

Preferably, the maximum shear stress range is calculated by the following formula 8

The normal stress on the plane σ _x′ (t),

Determine the maximum shear stress range in the k-th load iteration by formula 9

The maximum normal tensile stress on the plane,

Among them, t _p is a moment in the k-th load iteration;

t _{start is the start time} of the k-th load iteration;

t _end is the end time of the k-th load repetition.

Preferably, in the Wang-Brown multi-axis cycle counting algorithm, the following steps are included:

Define the maximum von Mises equivalent strain point of the entire load history as the initial reference point, rearrange the load spectrum, and calculate the equivalent relative strain of each point relative to the initial reference point;

Once the equivalent relative strain begins to decrease, the load between the initial reference point and the point at which the equivalent relative strain drops is counted as load repetition, and at the same time the descending point is defined as a new initial reference point. Repeat this process to finally determine the entire The total number of load repetitions in the load history.

Preferably, in the Wang-Brown multi-axis cycle counting method, the calculation formula of the von Mises equivalent stress is:

Among them, σ _x (t), σ _y (t), and σ _z (t) are respectively the tensile and compressive stresses of the corresponding coordinate axis at time t;

τ _xy (t), τ _yz (t), and τ _xz (t) are respectively the shear stress of the corresponding plane at time t;

at time t relative to _{R & lt} equivalent stress time t

The calculation formula is:

Among them, the relative stress in formula (2) σ ^r _x (t), σ ^r _y (t), σ ^r _z (t),

The calculation expressions are: σ ^r _x (t) = σ _x (t)-σ _x (t _r ), σ ^r _y (t) = σ _y (t)-σ _y (t _r ), σ ^r _z (t)=σ _z (t)-σ _z (t _r ),

σ _ij (t _r ) is the stress tensor at time _{t r,}

σ _x (t _r ), σ _y (t _r ), and σ _z (t _r ) are respectively the tensile and compressive stresses corresponding to the coordinate axis at the time _{t r;}

τ _xy (t _r ), τ _yz (t _r ), and τ _xz (t _r ) are respectively the shear stress of the corresponding plane at the time _{t r.}

_{Preferably, the fatigue life N fk} of each load repetition is determined according to the critical surface of the entire load history by using the high cycle fatigue criterion, and the formula is as follows:

Wherein, C _a is the shear stress amplitude (MPa) Critical plane, N _a positive stress amplitude (MPa) Critical surface, N _m is the average normal stress in the critical surface (MPa), f _-1 symmetrical Bending fatigue limit (MPa), t _-1 is the symmetrical pure torsion fatigue limit (MPa), σ _u is the tensile fatigue strength (MPa), τ _{eq, a} is the equivalent shear stress amplitude, and N _fk is the kth load Fatigue life under repeated, C _τ is the fatigue strength coefficient under pure torsion loading, m _τ is the fatigue strength index under pure torsion loading, Sign(N _m ) is a symbolic function, expressed as:

The present invention also provides a multi-axis fatigue life prediction device based on the weighted average maximum shear stress plane, including:

The load repetition determination module is used to obtain the load history of the notched parts, and use the Wang-Brown multi-axis cycle counting algorithm to determine all load repetitions in the load history, and obtain the total load repetition number m;

Critical surface determination module for each load repetition, for the k-th load repetition, calculate the normal stress value on the plane of the maximum shear stress range in the k-th load repetition, and select the maximum shear stress with the maximum normal stress value The scope plane is used as the critical surface of the k-th load repetition;

The critical surface determination module of the critical surface of the entire load history uses the weighted summation method to obtain the phase angle of the critical surface of each load repeated as the maximum shear stress plane based on the weighted average as the critical surface of the entire load history;

The fatigue damage estimation module is used to determine the fatigue life of each load repetition according to the critical surface of the entire load history, and use the Miner linear fatigue damage accumulation theory to calculate the cumulative fatigue damage on the weighted average maximum shear stress plane.

The present invention has the following beneficial effects

1) The proposed weight function does not include material parameters, and can consider the influence of the shear stress range on the maximum shear stress plane in each counted iteration and the normal tensile stress on the fatigue failure process, so the proposed weight function takes into account The main damage mechanism that affects the fatigue failure process;

2) The proposed life prediction method can better predict the fatigue life under high-cycle multi-axial variable amplitude loads, which is convenient for engineering applications.

3) The proposed weighted average maximum shear stress critical plane can more accurately determine the azimuth angle of the critical plane under multi-axis variable amplitude load.

Description of the drawings

By describing its embodiments in conjunction with the following drawings, the above-mentioned features and technical advantages of the present invention will become clearer and easier to understand.

Fig. 1 is a schematic diagram showing the steps of a multi-axial fatigue life prediction method according to an embodiment of the present invention;

Figure 2a is a perspective schematic view showing a notch according to an embodiment of the present invention;

Fig. 2b is a schematic diagram showing an arbitrary material plane Δ in an embodiment of the present invention.

Detailed ways

Hereinafter, embodiments of the high-cycle multi-axial fatigue life prediction method based on the weighted average maximum shear stress plane according to the present invention will be described with reference to the accompanying drawings. Those of ordinary skill in the art can realize that the described embodiments can be modified in various different ways or combinations thereof without departing from the spirit and scope of the present invention. Therefore, the drawings and description are illustrative in nature, and are not used to limit the scope of protection of the claims. In addition, in this specification, the drawings are not drawn to scale, and the same reference numerals denote the same parts.

The high-cycle multiaxial fatigue life prediction method based on the weighted average maximum shear stress plane includes the following steps:

Step 1): Obtain the load history of the notch, as shown in Figure 2a, F _N is the axial force of the load, and M _T is the load to the torque. The notch can be collected by a strain gauge set on the notch. Load history.

Step 2): Use the improved Wang-Brown multi-axis cycle counting algorithm to determine all load repetitions in the load history, and obtain the total load repetition number m.

In the Wang-Brown multi-axis cycle counting method, the maximum von Mises equivalent strain of the entire load history is first defined as the initial reference point, and the load spectrum is rearranged. Then, the equivalent relative strain of subsequent points relative to the reference point is calculated. Once the equivalent relative strain no longer rises monotonously and drops, the load from the reference point to the point where the equivalent relative strain drops is counted as load repetition. At the same time, the descending point is defined as a new relative reference point, and the previous process is repeated to continue counting the subsequent load repetitions, and finally all load repetitions of the entire load history are determined. The calculation formula of the von Mises equivalent stress in the Wang-Brown multi-axis cycle counting method is:

Among them, σ _x (t), σ _y (t), and σ _z (t) are the tensile and compressive stresses of the corresponding coordinate axis at time t respectively; τ _xy (t), τ _yz (t), and τ _xz (t) are respectively Is the shear stress of the corresponding plane at time t.

at time t relative to _{R & lt} equivalent stress time t

The calculation formula is:

Among them, the relative stress in formula (2) σ ^r _x (t), σ ^r _y (t), σ ^r _z (t),

The calculation expressions are: σ ^r _x (t) = σ _x (t)-σ _x (t _r ), σ ^r _y (t) = σ _y (t)-σ _y (t _r ), σ ^r _z (t)=σ _z (t)-σ _z (t _r ),

σ _ij (t _r ) is the stress tensor at time _{t r, that is,}

σ _x (t _r ), σ _y (t _r ), and σ _z (t _r ) are respectively the tensile and compressive stresses corresponding to the coordinate axis at the time _{t r;}

τ _xy (t _r ), τ _yz (t _r ), and τ _xz (t _r ) are respectively the shear stress of the corresponding plane at the time _{t r.}

Step 3): Establish a rectangular coordinate system OXYZ, where O is the coordinate origin, the coordinate origin O is located on the surface of the root of the notch, and the X axis is parallel to the axis of the notch. Using the proposed weighted average maximum shear stress plane as the critical surface of the entire load history under multiaxial variable amplitude load, the formula for determining the weighted average maximum shear stress plane is:

in,

with

The orientation angle of the weighted average maximum shear stress plane determined for the entire load history, m is the total number of load repetitions; w(k) is the weight function of the k-th load repetition, and φ _cr (k) represents the k-th load Normal vector of repeated critical surface

The included angle with the Z axis, θ _cr (k) is the normal vector representing the critical surface of the k-th load repetition

The angle between the projection on the XY plane and the X axis, the calculation formula of the weight function is:

Among them, the molecule

Is the maximum shear stress range in the k-th load repetition, the shear stress range

The larger the value, the more significant the influence of the weight function w(k) in the weighted average process. Denominator

Is m maximum shear stress range

The maximum value in

The calculation formula is as follows:

As shown in Figure 2b, to determine φ _cr (k) and θ _cr (k) of the critical surface of the k-th load repetition, it is necessary to calculate the shear stress on all planes Δ passing through the origin O during the k-th load repetition Scope. In the calculation process, the angles φ and θ of the plane Δ vary from 0° to 180° and 0° to 360°, respectively. Among them, the angle φ is the normal vector of the plane Δ

The angle with the Z axis, the angle θ is the normal vector of the plane Δ

The angle between the projection on the XY plane and the X axis.

The calculation formula of the stress tensor σ′ _ij (including normal stress and shear stress) on the plane Δ is as follows:

Where σ′ _x , σ′ _y , and σ′ _z are the tensile and compressive stresses on the corresponding coordinate axis X'Y'Z' of the plane Δ; τ′ _xy , τ′ _yz , τ′ _xz are the planes respectively Shear stress on Δ;

Among them, M ^T is the transpose of the transformation matrix M, and the expression of the transformation matrix M is as follows:

By comparing the values of the shear stress range on different planes Δ, the maximum shear stress range can be determined

And maximum shear stress range

The phase angle of the plane. It should be noted that in a load repetition, there may be multiple planes with the same maximum shear stress range. Then, calculate the normal stress (ie normal stress) on the plane of these maximum shear stress ranges. The maximum shear stress range can be calculated by the following two formulas

The maximum normal stress on the plane. Among them, the maximum shear stress range is calculated by the following formula 8

The normal stress on the plane σ _x′ (t),

Determine the maximum shear stress range in the k-th load iteration by formula 9

The maximum normal tensile stress on the plane,

Among them, t _p is a moment in the k-th load iteration;

t _{start is the start time} of the k-th load iteration;

t _end is the end time of the k-th load repetition. By comparing the maximum shear stress range

The normal tensile stress on the plane, the plane with the maximum shear stress range of the maximum normal tensile stress is defined as the critical surface of the k-th load repetition, and accordingly, the determined critical surface of the k-th load repetition is determined The angle is expressed as φ _cr (k) and θ _cr (k). Substituting φ _cr (k) and θ _cr (k) into equations 3 and 4, the critical plane angle of the entire load history can be solved

with

It can be seen that in determining the critical surface angle of the entire load history

with

In the process, the proposed critical surface determination method takes into account the shear stress range and normal stress on the plane of the maximum shear stress in each iteration.

The weight function proposed in step 3) is equal to 1 under proportional or non-proportional constant-amplitude sine wave loading. Therefore, under multi-axial proportional or non-proportional constant-amplitude sine wave loading, the critical surface is the one with the maximum normal tensile stress. Maximum cutting plane.

Step 4): For each load iteration, calculate the fatigue damage parameter on the weighted average maximum shear stress plane, and select the high cycle fatigue criterion to calculate the fatigue damage. The high cycle fatigue criterion based on the critical surface method proposed by Zhang and Shang is as follows:

Wherein, C _a is the shear stress amplitude (MPa) Critical plane, N _a positive stress amplitude (MPa) Critical surface, N _m is the average normal stress in the critical surface (MPa), f _-1 symmetrical Bending fatigue limit (MPa), t _-1 is the symmetrical pure torsion fatigue limit (MPa), σ _u is the tensile fatigue strength (MPa), τ _{eq, a} is the equivalent shear stress amplitude, and N _fk is the kth load The fatigue life under repeated, C _τ is the fatigue strength coefficient under pure torsion loading, m _τ is the fatigue strength index under pure torsion loading, and Sign(N _m ) is a symbolic function, which can be expressed as

To estimate the fatigue damage D _{k for} each repeated load, the formula for estimating the fatigue damage D _{k is:}

Step 5): Using the Miner linear fatigue damage accumulation theory, calculate the cumulative fatigue damage on the weighted average maximum shear stress plane:

Where D is the cumulative fatigue damage on the weighted average maximum shear stress plane, and m is the total number of load repetitions.

Step 6): Determine the number of load blocks N _block required for fatigue failure:

The critical surface determination method proposed in step 3) takes into account the shear stress range and normal stress on the maximum shear stress plane in each iteration, and most fatigue cracks originate in the maximum shear plane and are perpendicular to the maximum shear plane. The normal tensile stress can accelerate the fatigue damage process. Therefore, the critical surface determination method proposed takes into account the main damage mechanisms that affect the fatigue failure process.

The above descriptions are only preferred embodiments of the present invention and are not used to limit the present invention. For those skilled in the art, the present invention can have various modifications and changes. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (9)

1. A multiaxial fatigue life prediction method based on the weighted average maximum shear stress plane, which is characterized in that it includes the following steps:

   Obtain the load history of the notched part, use the Wang-Brown multi-axis cycle counting algorithm to determine all load repetitions in the load history, and obtain the total load repetition number m;

   For the k-th load iteration, calculate the normal stress value on all the planes of the maximum shear stress range in the k-th load iteration, and select the plane with the maximum shear stress range of the maximum normal stress value as the k-th load iteration Critical surface

   The phase angle of the critical surface of each load repeated using the weighted sum average method to obtain the maximum shear stress plane based on the weighted average as the critical surface of the entire load history;

   According to the critical surface of the entire load history, the fatigue life of each load repeated is determined, and the cumulative fatigue damage of the critical surface of the entire load history is calculated using the Miner linear fatigue damage accumulation theory.
2. The multi-axial fatigue life prediction method based on the weighted average maximum shear stress plane of claim 1, wherein the fatigue life of each load repetition is determined according to the critical surface of the entire load history, and then the critical surface of the entire load history is determined The methods of cumulative fatigue damage of the interface include:

   _{Determine the fatigue life N fk of} each load repetition according to the critical surface of the entire load history, and estimate the fatigue damage D _{k of} each cycle according to formula 11.

   The estimation formula of fatigue damage D _{k is:}

   

   Using the Miner linear fatigue damage accumulation theory, calculate the cumulative fatigue damage on the weighted average maximum shear stress plane:

   

   Where D is the cumulative fatigue damage on the weighted average maximum shear stress plane;

   Determine the number of load blocks required for fatigue failure N _block :

   
3. The multiaxial fatigue life prediction method based on the weighted average maximum shear stress plane according to claim 1, characterized in that, for cylindrical notched parts, the phase angles of the critical surfaces where each load is repeated are obtained by a weighted sum average method Methods based on the weighted average maximum shear stress plane include:

   Establish a rectangular coordinate system OXYZ, where O is the coordinate origin, the coordinate origin O is located on the surface of the notch root, and the X axis is parallel to the axis of the notch. The formula for determining the weighted average maximum shear stress plane is:

   

   

   in,

   

   with

   

   The phase angle of the weighted average maximum shear stress plane determined for the entire load history;

   w(k) is the weight function of the k-th load iteration;

   In the calculation of the k-th load iteration, the shear stress range on the plane Δ passing through the point O is calculated. The phase angles of the plane Δ are φ and θ, and φ is the normal vector of the plane Δ

   

   The angle with the Z axis, θ is the normal vector of the plane Δ

   

   The angle between the projection on the XY plane and the X axis, the angles φ and θ vary from 0° to 180° and 0° to 360°, respectively. By comparing the values of the shear stress range on different planes Δ, the maximum shear is determined Shear stress range

   

   And maximum shear stress range

   

   The phase angle of the plane, and the maximum shear stress range is solved

   

   Normal stress on the plane, by comparing the maximum shear stress range

   

   The normal stress on the plane, the plane with the maximum shear stress range of the maximum normal tensile stress is defined as the critical surface of the k-th load repetition, correspondingly, the angle of the critical surface of the k-th load repetition is determined φ Denoted as φ _cr (k), θ as θ _cr (k), _{substituting φ cr} (k) and θ _cr (k) into formulas 3 and 4 to solve for the weighted average maximum shear stress plane of the entire load history Phase angle

   

   with

   
4. The multiaxial fatigue life prediction method based on the weighted average maximum shear stress plane according to claim 3, wherein the calculation formula of the weight function is:

   

   Among them, the molecule

   

   Is the maximum shear stress range in the k-th load repetition;

   Denominator

   

   Is m maximum shear stress range

   

   The maximum value in

   

   The calculation formula is as follows:

   
5. The multi-axial fatigue life prediction method based on the weighted average maximum shear stress plane according to claim 3, characterized in that:

   Calculate the maximum shear stress range by the following formula 8

   

   The normal stress on the plane σ _x′ (t),

   

   Determine the maximum shear stress range in the k-th load iteration by formula 9

   

   The maximum normal tensile stress on the plane,

   

   Among them, t _p is a moment in the k-th load iteration;

   t _{start is the start time} of the k-th load iteration;

   t _end is the end time of the k-th load repetition.
6. The multi-axial fatigue life prediction method based on the weighted average maximum shear stress plane according to claim 1, characterized in that:

   In Wang-Brown's multi-axis cycle counting algorithm, the following steps are included:

   Define the maximum von Mises equivalent strain point of the entire load history as the initial reference point, rearrange the load spectrum, and calculate the equivalent relative strain of each point relative to the initial reference point;

   Once the equivalent relative strain begins to decrease, the load between the initial reference point and the point at which the equivalent relative strain appears to decrease is counted as load repetition, and the descent point is defined as the new initial reference point. Repeat this process to finally determine the entire The total number of load repetitions in the load history.
7. The multi-axial fatigue life prediction method based on the weighted average maximum shear stress plane according to claim 6, characterized in that:

   In the Wang-Brown multi-axis cycle counting method, the von Mises equivalent stress calculation formula is:

   

   Among them, σ _x (t), σ _y (t), and σ _z (t) are respectively the tensile and compressive stresses of the corresponding coordinate axis at time t;

   τ _xy (t), τ _yz (t), and τ _xz (t) are respectively the shear stress of the corresponding plane at time t;

   at time t relative to _{R & lt} equivalent stress time t

   

   The calculation formula is:

   

   Among them, the relative stress in formula 2 σ ^r _x (t), σ ^r _y (t), σ ^r _z (t),

   

   The calculation expressions are: σ ^r _x (t) = σ _x (t)-σ _x (t _r ), σ ^r _y (t) = σ _y (t)-σ _y (t _r ), σ ^r _z (t)=σ _z (t)-σ _z (t _r ),

   

   σ _ij (t _r ) is the stress tensor at time _{t r,}

   σ _x (t _r ), σ _y (t _r ), and σ _z (t _r ) are respectively the tensile and compressive stresses corresponding to the coordinate axis at the time _{t r;}

   τ _xy (t _r ), τ _yz (t _r ), and τ _xz (t _r ) are respectively the shear stress of the corresponding plane at the time _{t r.}
8. The multi-axial fatigue life prediction method based on the weighted average maximum shear stress plane according to claim 2, characterized in that the fatigue life N _fk of each load repetition is determined according to the critical surface of the entire load history by adopting the high cycle fatigue criterion To calculate, the formula is as follows:

   

   Wherein, C _a critical shear stress amplitude plane, N _a is the critical stress amplitude positive surface, N _m is the average normal stress in the critical surface, f _-1 symmetrical bending fatigue limit, t _-1 symmetrical The pure torsion fatigue limit, σ _u is the tensile fatigue strength, τ _{eq, a} is the equivalent shear stress amplitude, N _fk is the fatigue life under the k-th load repetition, C _τ is the fatigue strength coefficient under the pure torsion load, m _τ is the fatigue strength index under pure torsion loading, and Sign(N _m ) is a symbolic function, expressed as:

   
9. A multi-axis fatigue life prediction device based on the weighted average maximum shear stress plane, which is characterized in that it comprises:

   The load repetition determination module is used to obtain the load history of the notched parts, and use the Wang-Brown multi-axis cycle counting algorithm to determine all load repetitions in the load history, and obtain the total load repetition number m;

   Critical surface determination module for each load repetition, for the k-th load repetition, calculate the normal stress value on the plane of the maximum shear stress range in the k-th load repetition, and select the maximum shear stress with the maximum normal stress value The scope plane is used as the critical surface of the k-th load repetition;

   The critical surface determination module of the critical surface of the entire load history uses the weighted summation method to obtain the phase angle of the critical surface of each load repeated as the maximum shear stress plane based on the weighted average as the critical surface of the entire load history;

   The fatigue damage estimation module is used to determine the fatigue life of each load repeated according to the critical surface of the entire load history, and use the Miner linear fatigue damage accumulation theory to calculate the cumulative fatigue damage on the weighted average maximum shear stress plane.

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