Method for acquiring high-temperature long-time fatigue strength equal-life curve

Abstract

The invention provides a method for acquiring a high-temperature long-time fatigue strength equal-life curve, a relational expression among fatigue strength, temperature and fatigue life is established, and interpolation valuing and extrapolation prediction of high-temperature fatigue performance can be realized through a limited amount of fatigue test data. According to the method, an equal-life curve of long-time fatigue strength and endurance strength at various temperatures is constructed, the method is suitable for high-temperature fatigue strength evaluation and examination of long-time service materials, and the problem that a short-time fatigue test equal-life graph in the prior art is not suitable for evaluating the high-temperature long-time fatigue strength is solved.

Description

Technical Field

[0001] The invention belongs to the technical field of fatigue testing, and in particular relates to a method for obtaining a high-temperature long-time fatigue strength iso-life curve. Background Art

[0002] High cycle fatigue test data is an important indicator for material selection, design and assessment, especially for high temperature structural parts such as steam turbines and boilers in power station equipment, which require structural high temperature fatigue strength design and safety assessment. Fatigue strength assessment is usually based on the Goodman life curve, with the horizontal axis being the tensile strength and the vertical axis being 10 7 The symmetrical tensile and compressive fatigue limits corresponding to the number of cycles are obtained through short-time tensile tests and high-cycle fatigue tests, respectively. However, high-temperature service materials have creep, damage, aging and other phenomena during long-term service, and their corresponding fatigue strength and static strength also degrade accordingly. The Goodman life curve constructed using the fatigue limit and tensile limit obtained by short-time tests can no longer reliably evaluate the safety of materials. Summary of the invention

[0003] In view of the above-mentioned defects, the present invention provides a method for obtaining high-temperature long-time fatigue strength and other life curves, which is suitable for high-temperature fatigue strength evaluation and assessment of long-time service materials.

[0004] The present invention provides a method for obtaining a high-temperature long-term fatigue strength iso-life curve, comprising the following steps:

[0005] Obtain fatigue strength, fatigue life, endurance strength and endurance life of target materials at different test temperatures;

[0006] Set the fatigue-temperature parameter FTP,

[0007] FTP = T K (P F +lgN f ) / 1000 Formula (1)

[0008] Where: T K is the thermodynamic temperature in K, T K =T (unit: °C) + 273.15, P F is the fatigue regression parameter, N f is the fatigue life;

[0009] FTP and fatigue strength σ F Establish a relationship:

[0010]

[0011] Where: m is a positive integer, 0≤x≤m, a x is the first fitting parameter;

[0012] Substituting equation (2) into equation (1) and transforming it, we get:

[0013]

[0014] Substitute the fatigue strength and fatigue life of the target material measured at different test temperatures into formula (3), perform regression calculation on formula (3), and obtain the fatigue regression parameter P F ;

[0015] According to formula (4), σ is fitted F Relationship with FTP:

[0016]

[0017] Where: b x is the second fitting parameter;

[0018] Set the persistence-temperature parameter LMP,

[0019] LMP=T K (C+lgt u ) / 1000 Formula (5)

[0020] Where: C is the persistent regression parameter, t u For longevity;

[0021] The LMP and the endurance strength σ C Establish a relationship:

[0022]

[0023] Where: n is a positive integer, 0≤y≤n, c y is the third fitting parameter;

[0024] Substituting formula (6) into formula (5) for transformation, we get:

[0025]

[0026] Substitute the endurance strength and endurance life of the target material measured at different test temperatures into formula (7), perform regression calculation on formula (7), and obtain the endurance regression parameter C;

[0027] According to formula (8), σ is fitted C The relationship with LMP is:

[0028]

[0029] Where: d y is the fourth fitting parameter;

[0030] According to formula (5) and formula (8), the endurance strength corresponding to the preset temperature and the preset endurance life is calculated;

[0031] Calculate the preset fatigue life of equal life according to the preset endurance life, and calculate the fatigue strength corresponding to the preset temperature and the preset fatigue life according to equations (1) and (4);

[0032] The endurance strength and fatigue strength are used as the horizontal and vertical coordinates respectively, and a curve is drawn to connect the endurance strength and fatigue strength of equal life at the same temperature to obtain an equal life curve.

[0033] Preferably, m=1 or 2, and n=2 or 3.

[0034] Preferably, when calculating the preset fatigue life of equal life according to the preset endurance life, the formula used is: N f =t u ×f×3600, where f is the frequency.

[0035] Preferably, the drawn curve forms include straight lines, elliptical lines and broken lines.

[0036] The invention is beneficial in that it establishes a relationship between fatigue strength, temperature and fatigue life, and can realize interpolation and extrapolation prediction of high-temperature fatigue performance through a limited number of fatigue test data. The invention constructs iso-life curves of long-term fatigue strength and endurance strength at multiple temperatures, which are suitable for high-temperature fatigue strength evaluation and assessment of long-term service materials, and solves the problem in the prior art that short-term fatigue test iso-life diagrams are not suitable for evaluating high-temperature long-term fatigue strength. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 10 of the embodiment of the present invention 5 h Fatigue strength fitting curve and endurance strength fitting curve corresponding to endurance life;

[0038] Figure 2 The high temperature fatigue strength of the embodiment of the present invention is 10 5 h is the lifespan curve. DETAILED DESCRIPTION

[0039] The specific embodiments of the present invention are further described in detail below in conjunction with the accompanying drawings. These embodiments are only used to illustrate the present invention, but not to limit the present invention.

[0040] In the description of the present invention, it should be noted that the terms “first”, “second”, “third” and “fourth” are only used for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0041] The present invention provides a method for obtaining a high-temperature long-term fatigue strength iso-life curve, comprising the following steps:

[0042] S1. Test the target material at different test temperatures T i , different load strength σ Fi High cycle fatigue test is carried out under the conditions of fi .

[0043] S2. Set the fatigue-temperature parameter FTP,

[0044] FTP = T K (P F +lgN f ) / 1000 Formula (1)

[0045] Where: T K is the thermodynamic temperature in K, T K =T (unit: °C) + 273.15, P F is the fatigue regression parameter, N f is the fatigue life, in h.

[0046] S3. FTP and fatigue strength σ F Establish a relationship:

[0047]

[0048] Where: m is a positive integer, 0≤x≤m, a x is the first fitting parameter.

[0049] Substituting equation (2) into equation (1) and transforming it, we get:

[0050]

[0051] S4, the fatigue data T obtained in S1 i , σ Fi and N fi Substitute into formula (3), take m = 1 or 2, perform regression calculation on formula (3), and obtain the fatigue regression parameter P F .

[0052] S5, fitting σ according to formula (4) F Relationship with FTP:

[0053]

[0054] Where: b x is the second fitting parameter.

[0055] S6. Test the target material at different test temperatures T i , different endurance strength σ Cj The endurance test is carried out under the conditions of uj .

[0056] S7. According to the Larson-Miller curve drawing method, set the persistence-temperature parameter LMP.

[0057] LMP=T K (C+lgt u ) / 1000 Formula (5)

[0058] Where: C is the persistent regression parameter, t u is the endurance life, in h.

[0059] S8. LMP and endurance strength σ C Establish a relationship:

[0060]

[0061] Where: n is a positive integer, 0≤y≤n, c y is the third fitting parameter.

[0062] Substituting formula (6) into formula (5) for transformation, we get:

[0063]

[0064] S9, the persistent data T obtained in S6 j , σ Cj and t uj Substitute into formula (7), take n = 2 or 3, perform regression calculation on formula (7), and obtain the persistent regression parameter C,.

[0065] S10, fitting σ according to formula (8) C The relationship with LMP is:

[0066]

[0067] Where: d y is the fourth fitting parameter.

[0068] S11, calculate the preset temperature T0 and the preset endurance life t according to formula (5) and formula (8) u0 The corresponding endurance strength σ C .

[0069] S12, according to formula (9) calculate and preset the endurance life t u0 The preset fatigue life of equal life N f0 ,

[0070] N f =t u ×f×3600 Formula (9)

[0071] Where: f is frequency, unit is Hz.

[0072] S13. Calculate the preset temperature T0 and the preset fatigue life N according to equations (1) and (4). f0 The corresponding fatigue strength σ F .

[0073] S14. Use the endurance strength and fatigue strength as the horizontal and vertical coordinates respectively, and draw a curve connecting the endurance strength σ of the same life at the same temperature C and fatigue strength σ F , and obtain the equal life curve. The curve forms drawn include but are not limited to straight lines, elliptical lines and broken lines.

[0074] The following is a specific embodiment of the present invention:

[0075] S1. In this embodiment, the target material is a 12% Cr alloy, and a high cycle fatigue test is performed on it at a test temperature T i The fatigue strength σ at three temperatures is obtained at 550℃, 600℃, and 630℃ respectively, and the stress ratio R=-1. Fi and the corresponding fatigue life N fi Specifically, the fatigue strength in this embodiment is the symmetrical tensile and compressive fatigue stress amplitude.

[0076] S2. Set the fatigue-temperature parameter FTP,

[0077] FTP = T K (P F +lgN f ) / 1000 Formula (1)

[0078] Where: T K is the thermodynamic temperature in K, T K =T (unit: °C) + 273.15, P F is the fatigue regression parameter, N f is the fatigue life, in h.

[0079] S3. FTP and fatigue strength σ F Establish a relationship,

[0080]

[0081] Taking m=2, formula (2) is:

[0082] FTP=a0+a1lgσ F +a2lg 2 σ F

[0083] Where: a0, a1, a2 are the first fitting parameters.

[0084] Substituting equation (2) into equation (1) and transforming it, we get:

[0085]

[0086] S4. Substitute the 12% Cr alloy high cycle fatigue data obtained in S1 into formula (3) for regression calculation to obtain the fatigue regression parameter P F =7.018.

[0087] S5, according to formula (4) fitting fatigue strength σ F The relationship between fatigue-temperature parameter FTP is as follows: Figure 1 shown.

[0088] lgσ F =b0+b1lgFTP+b2lg 2 FTP (4)

[0089] Wherein: b0, b1, b2 are the second fitting parameters.

[0090] S6. Conduct endurance test on target material 12% Cr alloy, test temperature T i The temperatures are 500℃, 550℃, 600℃, and 630℃ respectively, and the different endurance strengths σ at each temperature are obtained. Cj and the corresponding persistence lifetime t uj .

[0091] S7. According to the drawing method of LM endurance temperature curve, set the endurance-temperature parameter LMP.

[0092] LMP=T K (C+lgt u ) / 1000 Formula (5)

[0093] Where: C is the persistent regression parameter, t u is the endurance life, in h.

[0094] S8. LMP and endurance strength σ C Establish a relationship:

[0095]

[0096] Taking n=3, formula (6) is:

[0097] LMP=c0+c1lgσ C +c2lg 2 σ C +c3lg 3 σ C

[0098] Transforming formula (6), we get:

[0099]

[0100] Where: c0, c1, c2, c3 are the third fitting parameters.

[0101] S9. Substitute the endurance data of the 12% Cr alloy obtained in S6 into equation (7) and perform regression calculation to obtain an endurance regression parameter C=25.

[0102] S10, fitting σ according to formula (8) C The relationship with LMP is as follows: Figure 1 shown.

[0103] lgσ C =d0+d1lgLMP+d2lg 2 LMP+d3lg 3 LMP (8)

[0104] Wherein: d0, d1, d2, d3 are the fourth fitting parameters.

[0105] S11, set the preset temperature T0, the persistent regression parameter C=25, the preset persistent life t u0 =10 5 Substitute h into formula (6) to calculate the endurance-temperature parameter LMP, and then calculate the endurance strength σ corresponding to each preset temperature T0 according to formula (8) C .

[0106] S12, according to formula (9) calculate and preset the endurance life t u0 The preset fatigue life of equal life N f0 .

[0107] N f =t u ×f×3600 (9)

[0108] Where: f is the frequency, the unit is HZ, the frequency f=50HZ selected in this embodiment, which is consistent with the preset endurance life t u0 The preset fatigue life of equal life N f0 =1.8E10cyc.

[0109] S13, set the preset temperature T0, fatigue regression parameter P F =7.018, preset fatigue life N f0 =1.8E10 cyc is substituted into formula (1) to calculate the fatigue-temperature parameter FTP, and then the equivalent life fatigue strength σ corresponding to each preset temperature T0 is calculated according to formula (4) F .

[0110] S14. Use the endurance strength and fatigue strength as the horizontal and vertical coordinates respectively, and draw a curve connecting the endurance strength σ of the same life at the same temperatureC and fatigue strength σ F , and obtain the iso-life curve of 400~650℃, such as Figure 2 shown.

[0111] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and substitutions can be made without departing from the technical principles of the present invention. These improvements and substitutions should also be regarded as the scope of protection of the present invention.

Claims

1. A method for obtaining a high temperature long-term fatigue strength iso-life curve, characterized in that: The following steps are involved: Obtain fatigue strength, fatigue life, endurance strength and endurance life of target materials at different test temperatures; Set the fatigue-temperature parameter FTP, FTP = T K (P F +lgN f ) / 1000 Formula (1) Where: T K is the thermodynamic temperature in K, T K =T (unit: °C) + 273.15, P F is the fatigue regression parameter, N f is the fatigue life; FTP and fatigue strength σ F Establish a relationship: Where: m is a positive integer, 0≤x≤m, a x is the first fitting parameter; Substituting equation (2) into equation (1) and transforming it, we get: Substitute the fatigue strength and fatigue life of the target material measured at different test temperatures into formula (3), perform regression calculation on formula (3), and obtain the fatigue regression parameter P F ; According to formula (4), σ is fitted F Relationship with FTP: Where: b x is the second fitting parameter; Set the persistence-temperature parameter LMP, LMP=T K (C+lgt u ) / 1000 Formula (5) Where: C is the persistent regression parameter, t u For longevity; The LMP and the endurance strength σ C Establish a relationship: Where: n is a positive integer, 0≤y≤n, c y is the third fitting parameter; Substituting formula (6) into formula (5) for transformation, we get: Substitute the endurance strength and endurance life of the target material measured at different test temperatures into formula (7), perform regression calculation on formula (7), and obtain the endurance regression parameter C; According to formula (8), σ is fitted C The relationship with LMP is: Where: d y is the fourth fitting parameter; According to formula (5) and formula (8), the endurance strength corresponding to the preset temperature and the preset endurance life is calculated; Calculate the preset fatigue life of equal life according to the preset endurance life, and calculate the fatigue strength corresponding to the preset temperature and the preset fatigue life according to equations (1) and (4); The endurance strength and fatigue strength are used as the horizontal and vertical coordinates respectively, and a curve is drawn to connect the endurance strength and fatigue strength of equal life at the same temperature to obtain an equal life curve.

2. The acquisition method according to claim 1, characterized in that: m=1 or 2, n=2 or 3.

3. The acquisition method according to claim 1, characterized in that: When calculating the preset fatigue life of equal life based on the preset endurance life, the formula used is: N f =t u ×f×3600, where f is the frequency.

4. The acquisition method according to claim 1, characterized in that: The drawn curves include straight lines, elliptical lines and polylines.

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