Fatigue Life Model under the Action of Equal-Amplitude Multiaxial Non-Proportional Loads Based on the Subcritical Interface Method

Abstract

The present invention discloses a fatigue life model under the action of equal-amplitude multi-axial non-proportional loads based on the sub-critical interface method. The shear strain is calculated, and the plane where the maximum shear strain amplitude is located within one loading cycle is defined as the critical interface; the plane with the largest absolute value of the shear strain at a certain moment is defined as the sub-critical interface, and the angle between the sub-critical interface and the critical interface at time t is defined as the deflection angle. The non-proportional additional hardening material parameter a is introduced into the non-proportional additional hardening parameter Γ for quantitatively describing the non-proportional additional hardening degree t , and the equivalent parameter Γ within one cycle is obtained t , and the form of the non-proportional additional hardening parameter d is written thereby, obtaining a new equivalent strain form, and finally obtaining the fatigue life model of the present invention. The present invention introduces the non-proportional additional hardening material parameter into the non-proportional additional hardening parameter to obtain a new damage parameter for quantitatively describing the non-proportional additional hardening effect. On the premise of ensuring the prediction accuracy of the model, the determination process of the material parameters is simplified, which is convenient for engineering applications

Description

Technical Field

[0001] The present invention relates to the technical field of mechanical structure fatigue life models, and particularly to a fatigue life model under the action of equal-amplitude multiaxial non-proportional loads based on the sub-critical plane method and the like. Background Art

[0002] Most metal structures in engineering practice are subjected to multiaxial loads. Some progress has been made in the research on the prediction method of multiaxial constant-amplitude fatigue life. Among them, the multiaxial fatigue life prediction model based on the critical plane method has good development prospects. However, this model method does not explain the non-proportional hardening effect in the case of non-proportional loads, nor does it reveal the physical meaning of the non-proportional additional hardening effect, resulting in certain limitations in some occasions with high-precision requirements. Based on the critical plane method, most do not consider the multiaxial non-proportional additional hardening effect. Subsequently, some people have modified these traditional models and introduced non-proportional additional hardening parameters, and found that the influence of additional cyclic hardening on fatigue life cannot be well reflected in the normal strain offset.

[0003] To solve the above problems, the fatigue damage parameter is modified using the Huber-Mises criterion, and a concept of sub-(sub)-critical plane is proposed to consider the non-proportional additional hardening effect. The fatigue damage parameter for establishing the model combines the material properties and the non-proportional additional hardening caused by the deflection of the principal stress direction, and can be directly established by the Mαnson-Coffin equation. To ensure the accuracy of life prediction, it is necessary to consider the influence of the multiaxial non-proportional additional hardening effect on fatigue life. Therefore, we designed a fatigue life model under the action of equal-amplitude multiaxial non-proportional loads based on the sub-critical plane method to solve the above problems. Summary of the Invention

[0004] Aiming at the problem that the non-proportional additional hardening effect of complex mechanical components is difficult to calculate simply, the present invention proposes a fatigue life model under the action of equal-amplitude multiaxial non-proportional loads based on the sub-critical plane method, introduces a simpler and more accurate non-proportional additional hardening parameter, provides a model basis for the multiaxial fatigue damage analysis and multiaxial fatigue test of mechanical components under tension-torsion multiaxial loads, is an important step in the life experiment evaluation of key components of engineering complex structures under multiaxial actual service loads, realizes the calculation of the non-proportional additional hardening effect based on material static strength parameters, obtains a new non-proportional additional hardening parameter, simplifies the determination process of material parameters on the premise of ensuring the prediction accuracy of the model, and is convenient for engineering application.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A fatigue life model under the action of equal-amplitude multiaxial non-proportional loads based on the sub-critical plane method, and the creation method of the fatigue life model includes the following steps:

[0007] Step 1: Calculate the shear strain change within one cycle, and define the plane where the maximum shear strain amplitude is located within one loading cycle as the critical plane;

[0008] Step 2: Define the plane with the largest absolute value of the shear strain at a certain moment t as the sub-critical plane, and define the acute angle between the sub-critical plane and the critical plane at moment t as the deflection angle;

[0009] Step 3: Combine the equivalent strain parameter form of the Shαng-Wαng model, and obtain the non-proportional additional hardening parameter Γ used to quantitatively describe the degree of non-proportional additional hardening based on the strain parameters on the sub-critical plane t , introduce the non-proportional additional strengthening material parameter a into the non-proportional additional hardening parameter Γ t , and calculate the equivalent parameter Γ within one cycle T ;

[0010] Step 4: Combine the correction coefficient form of the FS model to obtain a new equivalent strain

[0011] Step 5: Finally, substitute the new equivalent strain into the modified Mαnson-Coffin equation to obtain the fatigue life model under multiaxial non-proportional loading.

[0012] Furthermore, in Step 1, the method for obtaining the critical plane is as follows:

[0013] Define the expression of the load borne by a certain thin-walled cylinder as:

[0014]

[0015] wherein, represents the normal strain amplitude; represents the shear strain amplitude; ω represents the frequency, set as a multi-axial load with the same frequency; represents the phase difference; t represents the loading moment, ε represents the normal stress, and γ represents the shear stress;

[0016] The calculation formula for the shear strain of the plane corresponding to any angle α is as follows:

[0017]

[0018] wherein, λ = △γ / △ε represents the amplitude ratio of the strain; v eff represents the effective Poisson's ratio, and the calculation formula is as follows:

[0019]

[0020] wherein, v e and v pare the elastic and plastic Poisson's ratios; △ε e and △γ e are the axial and shear strain ranges, and η is calculated by the following formula:

[0021]

[0022] Since γ α (t) is a quantity that varies with time and is approximately a sine function. The relationship between the shear strain amplitude and the angle is obtained and denoted as △γ α ,

[0023]

[0024] Taking the partial derivative of △γ α with respect to the angle α, the value of α corresponding to the maximum value of △γ α is denoted as α max , α max is the angle corresponding to the plane where the maximum shear strain is located, and this plane is defined as the critical plane.

[0025] Furthermore, in the step 2, according to the shear strain calculation formula, the angle α varies from 0° to 360° in steps of 1°, and the loading process t varies from 0 to T in steps of 0.01T. The shear strain values at each moment are obtained, and the plane where the maximum absolute value of the shear strain is located is defined as the sub-critical plane. The shear strain at this time is denoted as γ t,max , and at the same time, the included angle between the sub-critical plane and the critical plane is defined as the deflection angle △α t , and the normal strain ε γt,max on the sub-critical plane is calculated by the following formula:

[0026]

[0027] where x is calculated by the following formula:

[0028]

[0029] Furthermore, in the step 3, a non-proportional additional hardening parameter Γ t is constructed to describe the non-proportional additional hardening degree corresponding to the sub-critical plane at time t. At the same time, a non-proportional additional strengthening material parameter a is introduced into the non-proportional additional hardening parameter Γ t , and Γ t is calculated by the following formula:

[0030]

[0031] where, ε -1 is the fatigue limit of the normal strain, and γ -1is the shear strain fatigue limit; A is a constant related to the material, and the non-proportional additional strengthening material parameter a is expressed in the following form:

[0032] a = 0.393β + 0.0306, where β is the static strengthening coefficient of the material, and β = σ b / σ y -1;

[0033] σ b is the tensile strength of the material, and σ y is the yield strength of the material;

[0034] Since the non-proportional additional hardening parameter Γ t is a process parameter that changes with time. During a loading cycle, the equivalent strain obtains the equivalent parameter Γ T Γ T The calculation formula of Γ is as follows:

[0035]

[0036] In the formula, T is the step size of the loading process, and t represents the time of a loading cycle.

[0037] Furthermore, in step 4, a parameter d describing the non-proportional additional strengthening effect is introduced, and its expression formula is as follows:

[0038]

[0039] Combined with the correction coefficient form of the FS model, the equation for the new equivalent strain is as follows:

[0040]

[0041] Among them, △ε eq is the equivalent strain range on the critical plane; ε -1 is the normal strain fatigue limit, γ -1 is the shear strain fatigue limit; E is the elastic modulus, and △γ max is the maximum shear strain amplitude; is the positive strain offset on the critical plane.

[0042] Furthermore, in step 5, the new equivalent strain is substituted into the modified Mαnson-Coffin equation to obtain the fatigue life model expression under multiaxial non-proportional loading:

[0043]

[0044] In the formula, △γ △αt,max is the maximum shear strain range on the subcritical plane, and △γ maxis the maximum shear strain range, σ′ f is the fatigue strength coefficient, ε′ f is the fatigue ductility coefficient, b is the fatigue strength exponent, c is the fatigue ductility exponent, N f is the multiaxial fatigue life, and E is the elastic modulus.

[0045] Compared with the prior art, the model used in the present invention is developed based on the Shαng-Wαng model of the critical plane method, retaining the physical meaning of the critical plane method. At the same time, correction parameters for the sub-critical plane and non-proportional additional hardening effects are introduced, making the physical meaning of the model more sufficient and clear. Based on the sub-critical plane method, the present invention introduces the static strength parameters of the material into the calculation of the non-proportional additional hardening parameter to quantitatively describe the degree of non-proportional additional hardening, and combines with the correction coefficient form of the FS model to obtain a new equivalent strain form, thereby calculating the fatigue life model under multiaxial non-proportional load. Based on the sub-critical plane method, the present invention simplifies the calculation of the non-proportional additional hardening parameter. Compared with the existing multiaxial fatigue life prediction models, the parameters that need to be determined in the present invention are all static strength parameters of the material, and relevant parameters in the material handbook can be used for rough life prediction, saving the cost of parameter determination, facilitating engineering applications, and ensuring the prediction accuracy of the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 is the flowchart of the method in the embodiment of the present invention;

[0047] Figure 2 is the constant amplitude tensile-torsional biaxial strain load history diagram borne by the thin-walled circular tube in the example of the present invention;

[0048] Figure 3 is the three-dimensional view of the shear strain magnitude at different phase angles in the example of the present invention;

[0049] Figure 4 is the top view of the shear strain change from the perspective of time t and angle α in the embodiment of the present invention;

[0050] Figure 5 is the schematic diagram of the deflection angle between the sub-critical plane and the critical plane in the embodiment of the present invention;

[0051] Figure 6 is the relationship between the additional strength coefficient of the material and the static strength strengthening coefficient in the embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0052] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments.

[0053] Embodiment:

[0054] As shown Figure 1 in the figure, an embodiment of the present invention proposes a fatigue life model based on the equal - amplitude multi - axis non - proportional load acting on the sub - critical plane method. The creation method of this fatigue life model includes the following steps:

[0055] Step 1: First, query and obtain the values of the parameters of the loading history machine, determine the component morphology and loading position, calculate the shear strain change within one cycle, and define the plane where the maximum shear strain amplitude is located within one loading cycle as the critical plane;

[0056] The method for obtaining the critical plane is as follows. As Figure 2 shown Figure 2 Figure shows the constant - amplitude tensile - torsional biaxial strain load history diagram that a thin - walled circular tube bears in the loading model. The expression of the load borne by this thin - walled cylinder is:

[0057]

[0058] In the formula, represents the normal strain amplitude; represents the shear strain amplitude; ω represents the frequency, which is set as a multi - axis load with the same frequency; represents the phase difference; t represents the loading time, ε represents the normal stress, and γ represents the shear stress;

[0059] Figure 3 is a three - dimensional view of the shear strain magnitude at different phase angles in the example of the present invention, Figure 4 is a top - view of the shear strain change from the perspective of time t and angle α in the embodiment of the present invention. The shear strain calculation formula for the plane corresponding to any angle α is as follows:

[0060]

[0061] In the formula, λ = △γ / △ε represents the amplitude ratio of the strain; n eff represents the effective Poisson's ratio, and the calculation formula is as follows:

[0062]

[0063] Among them, n e and n p are the elastic and plastic Poisson's ratios respectively; △ε e and △γ e are the axial and shear strain ranges, and η is calculated by the following formula:

[0064]

[0065] Since γ α(t) is a quantity that varies with time and is approximated as a sine function. The relationship between the shear strain amplitude and the angle is obtained and denoted as △γ α ,

[0066]

[0067] Take the partial derivative of △γ α with respect to the angle α to obtain the value of α corresponding to the maximum value of △γ α , and denote the value of α as α max , α max is the angle corresponding to the plane where the maximum shear strain is located, and this plane is defined as the critical plane.

[0068] Step 2: As Figure 5 shown, Figure 5 is a schematic diagram of the deflection angle between the sub-critical plane and the critical plane in the embodiment of the present invention. The plane with the maximum absolute value of the shear strain at a certain moment t is defined as the sub-critical plane, and the acute angle between the sub-critical plane and the critical plane at moment t is defined as the deflection angle; according to the shear strain calculation formula, the angle α varies from 0° to 360° in steps of 1°, and the loading process t varies from 0 to T in steps of 0.01T. Calculate the shear strain values at each moment, and define the plane where the maximum absolute value of the shear strain is located as the sub-critical plane. The shear strain at this time is denoted as γ t,max , and at the same time, define the included angle between the sub-critical plane and the critical plane as the deflection angle △α t , and calculate the normal strain ε on the sub-critical plane by the following formula γt,max :

[0069]

[0070] where x is calculated by the following formula:

[0071]

[0072] Step 3: Combine the equivalent strain parameter form of the Shαng-Wαng model and obtain a non-proportional additional hardening parameter Γ for quantitatively describing the degree of non-proportional additional hardening based on the strain parameters on the sub-critical plane t , introduce the non-proportional additional strengthening material parameter a into the non-proportional additional hardening parameter Γ t and calculate the equivalent parameter Γ within one loading cycle T ;

[0073] Specifically, Figure 6 is the relationship between the additional strength coefficient and the static strength strengthening coefficient of the material in the embodiment of the present invention. Construct a non-proportional additional hardening parameter Γ t to describe the degree of non-proportional additional hardening corresponding to the sub-critical plane at moment t. At the same time, introduce the non-proportional additional strengthening material parameter a( Figure 6The material additional strengthening coefficient a) in is attached to the non-proportional additional hardening parameter Γ t , Γ t is calculated by the following formula:

[0074]

[0075] where ε -1 is the normal strain fatigue limit, γ -1 is the shear strain fatigue limit; A is a material-related constant, A = 2, and the non-proportional additional strengthening material parameter a is expressed in the following form:

[0076] a = 0.393β + 0.0306, where β is the static strengthening coefficient of the material ( Figure 6 the static strength strengthening coefficient β in), β = σ b / σ y - 1;

[0077] σ b is the tensile strength of the material, σ y is the yield strength of the material;

[0078] Since the non-proportional additional hardening parameter Γ t is a process parameter and changes with time. In a loading cycle, the equivalent strain obtains the equivalent parameter Γ T , Γ T The calculation formula is as follows:

[0079]

[0080] In the formula, T is the step size of the loading process, and t represents the time of a loading cycle.

[0081] Step 4: Combine the correction coefficient form of the FS model to obtain the new equivalent strain

[0082] Introduce the parameter d that describes the non-proportional additional strengthening effect, and its expression formula is as follows:

[0083]

[0084] Calculate the principal equivalent strain, and the equation for obtaining the new equivalent strain by combining the correction coefficient form of the FS model is as follows:

[0085]

[0086] The right side of the above equation is the Figure 1 new multiaxial fatigue damage parameter referred to in, where △e eq is the equivalent strain range on the critical plane; e -1 is the normal strain fatigue limit, γ-1 is the shear strain fatigue limit; E is the elastic modulus, and △γ max is the maximum shear strain amplitude; is the positive strain offset on the critical plane, and the calculation formula is as follows:

[0087]

[0088] Step 5: Finally, substitute the new equivalent strain into the modified Manson-Coffin equation to predict the fatigue life, and obtain the fatigue life model under multi-axial non-proportional loads. The expression of the fatigue life model under multi-axial non-proportional loads:

[0089]

[0090] In the formula, △γ △αt,max is the maximum shear strain range on the sub-critical plane, and △γ max is the maximum shear strain range, σ′ f is the fatigue strength coefficient, ε′ f is the fatigue ductility coefficient, b is the fatigue strength index, c is the fatigue ductility index, N f is the multi-axial fatigue life, and E is the elastic modulus.

[0091] The present invention is a fatigue life model under constant amplitude multi-axial non-proportional loads based on the sub-critical plane method. For the constant amplitude tension-torsion load spectrum of a hollow thin-walled cylinder component: calculate the shear strain, define the plane with the maximum shear strain within one loading cycle as the critical plane; define the plane with the maximum absolute value of the shear strain at a certain moment t as the sub-critical plane, and define the acute angle between the sub-critical plane and the critical plane at moment t as the deflection angle; obtain Γ based on the strain parameters on the sub-critical plane t to quantitatively describe the degree of non-proportional additional hardening, introduce the non-proportional additional hardening material parameter a into the non-proportional additional hardening parameter Γ t , and obtain the equivalent parameter Γ within one cycle t ; combine the equivalent strain parameter form of the Shang-Wang model and the correction coefficient form of the FS model to obtain a new equivalent strain equation; finally, substitute the new equivalent strain into the Manson-Coffin equation to obtain the fatigue life model under multi-axial non-proportional loads.

[0092] Based on the traditional multi-axial fatigue life prediction model, the present invention adds a non-proportional additional hardening parameter to describe the non-proportional additional hardening effect, and the parameters to be determined are all some static strength parameters of the material. When saving the cost of parameter determination, relevant parameters in the material handbook can even be used for rough life prediction, which is convenient for engineering applications. Compared with the existing multi-axial fatigue life prediction models, the physical meaning is more explicit. The model used in this paper is developed from the Shang-Wang model based on the critical plane method, retaining the physical meaning of the critical plane method, and at the same time introducing a correction parameter for the non-proportional additional hardening effect of the sub-critical plane, making the physical meaning of the model more sufficient. The prediction effect of the present invention is also relatively accurate, and most of the experimental results are distributed within the 2-fold scatter band, which can meet the engineering requirements.

[0093] In summary, based on the sub-critical plane method, the present invention introduces non-proportional additional hardening material parameters into the non-proportional additional hardening parameter to obtain a new damage parameter, which is used to quantitatively describe the non-proportional additional hardening effect. On the premise of ensuring the prediction accuracy of the model, the determination process of the material parameters is simplified, which is convenient for engineering applications.

[0094] As described above, the above are only the preferred specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention, according to the technical solution and inventive concept of the present invention, makes equivalent substitutions or changes, and all should be covered within the protection scope of the present invention.

Claims

1. A fatigue life model under the action of equal-amplitude multi-axial non-proportional loads based on the sub-critical interface method, characterized in that, The method for creating the fatigue life model includes the following steps: Step 1: Calculate the shear strain change within one cycle, and define the plane where the maximum shear strain amplitude is located within one loading cycle as the critical plane; Step 2: Define the plane with the largest absolute value of shear strain at a certain moment t as the sub-critical plane, and define the acute angle between the sub-critical plane and the critical plane at moment t as the deflection angle; Step 3: Combine the equivalent strain parameter form of the Shang-Wang model and obtain the non-proportional additional hardening parameter Γ used to quantitatively describe the degree of non-proportional additional hardening based on the strain parameters on the sub-critical interface t , introduce the non-proportional additional strengthening material parameter a into the non-proportional additional hardening parameter Γ t , and obtain the equivalent parameter Γ within one cycle T , Γ T is calculated by the following formula: Among them, ε -1 is the normal strain fatigue limit, γ -1 is the shear strain fatigue limit; A is a constant related to the material, and the non-proportional hardening material parameter a is expressed in the following form: a = 0.393β + 0.0306, where β is the static strengthening coefficient of the material, β = σ b / σ y - 1; σ b is the tensile strength of the material, and σ y is the yield strength of the material; Due to the non-proportional additional hardening parameter Γ t is a process parameter that changes over time. During a loading cycle, the equivalent strain obtains the equivalent parameter Γ T , Γ T The calculation formula of is as follows: In the formula, T is the step size of the loading process, and t represents the time of one loading cycle; Step 4: Introduce the parameter d to describe the non-proportional additional strengthening effect, and its expression formula is as follows: Combined with the correction coefficient form of the FS model, a new equivalent strain is obtained as follows: where, Δε eq is the equivalent strain range on the critical plane; ε -1 is the fatigue limit of the normal strain, γ -1 is the fatigue limit of the shear strain; E is the elastic modulus, Δγ max is the maximum shear strain amplitude; is the positive strain offset on the critical plane; Step 5: Finally, substitute the new equivalent strain into the modified Manson-Coffin equation to obtain the fatigue life model under multiaxial non-proportional loading, and the expression is as follows: ​ where Δγ Δαt,max is the maximum shear strain range on the subcritical plane, Δγ max is the maximum shear strain range, σ′ f is the fatigue strength coefficient, ε′ f is the fatigue ductility coefficient, b is the fatigue strength exponent, c is the fatigue ductility exponent, N f is the multiaxial fatigue life, and E is the elastic modulus.

2. The fatigue life model based on the isochoric multiaxial non-proportional loading under the sub-critical interface method according to claim 1, characterized in that, In Step 1, the method for obtaining the critical plane is as follows: Define the expression of the load borne by a certain thin-walled cylinder as: In the formula, represents the normal strain amplitude; represents the shear strain amplitude; ω represents the frequency; represents the phase difference; t represents the loading time, ε represents the normal stress, and γ represents the shear stress; The calculation formula for the shear strain of the plane corresponding to any angle α is as follows: where, λ = Δγ / Δε represents the amplitude ratio of strain; ν eff represents the effective Poisson's ratio, and the calculation formula is as follows: where ν e and ν p are the elastic and plastic Poisson's ratios respectively; Δε e and Δγ e are the axial and shear strain ranges, and η is calculated by the following formula: Since γ α (t) is a quantity that varies with time and is approximately a sine function, the relationship between the shear strain amplitude and the angle is obtained and denoted as Δγ α , Take the partial derivative of Δγ α with respect to the angle α to obtain Δγ α The value of α corresponding to the maximum value is denoted as α max , α max is the angle corresponding to the plane where the maximum shear strain is located, and this plane is defined as the critical plane.

3. The fatigue life model based on the isochoric multiaxial non-proportional loading under the sub-critical interface method according to claim 2, wherein In the step 2, according to the shear strain calculation formula, the angle α varies from 0° to 360° with a step of 1°, and the loading process t varies from 0 to T with a step of 0.01T. The shear strain values at each moment are calculated, and the plane where the maximum absolute value of the shear strain at time t is located is defined as the sub-critical plane, and the shear strain at this time is denoted as γ t,max , and at the same time, the acute angle between the sub-critical plane and the critical plane at this time is defined as the deflection angle Δα t , and the normal strain ε on the sub-critical plane is calculated by the following formula γt,max : where ξ is calculated from the following formula:

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