A method for predicting fatigue strength of metal materials by hardness

Abstract

The present invention discloses a method for predicting the fatigue strength of metal materials by hardness, belonging to the field of materials science and engineering application technology. The method first establishes a fitting relationship between the hardness value and the fatigue strength coefficient and fatigue strength index based on data such as the material's hardness and fatigue curve, and then establishes a fatigue life prediction formula for the material based on the Basquin formula. The fatigue strength of the material can be obtained by substituting the number of cycles of fatigue test cycle stop (or the number of cycles of the S-N curve platform). This method effectively reduces the amount of experiments required to predict the fatigue strength of the material, greatly saving manpower and financial costs. It has the characteristics of simplicity, speed and accuracy, and can be widely applied to metal materials with different hardness obtained by hot working.

Description

Technical Field

[0001] The present invention relates to the field of material science and engineering application technology, and in particular to a method for predicting the fatigue strength of a metal material through hardness. Background Art

[0002] In mechanical design, fatigue strength is a key indicator of a material's basic fatigue mechanical properties. Currently, fatigue strength is typically determined using the lift-and-fall method of fatigue testing, which requires significant manpower, material, and financial resources. Hardness testing is the simplest mechanical property test, and researchers have proposed a linear empirical formula for hardness and fatigue strength, demonstrating a strong positive correlation between hardness and fatigue strength for metal materials with an HV of ≤400.

[0003] In recent years, with the continuous advancement of materials science and the emergence of high-strength materials, studies have found that after a material's hardness reaches a certain level (HV ≈ 400), the fatigue strength of the material no longer increases linearly with increasing hardness, but instead reaches a peak or even shows a downward trend. In this case, traditional linear empirical formulas are no longer applicable. Therefore, establishing a quantitative relationship between hardness and fatigue strength will effectively achieve simple and rapid prediction of fatigue strength. Summary of the Invention

[0004] In order to reduce the manpower, time and money costs required to obtain the fatigue strength of materials, the present invention provides a method for predicting the fatigue strength of metal materials by hardness. This method obtains the hardness and SN curve data of the material, uses the least squares method to fit the Basquin formula to obtain the fatigue strength coefficient and fatigue strength index, establishes the relationship between the two parameters and the hardness value, and then establishes a fatigue life prediction formula based on hardness. By substituting the number of cycles of fatigue test stop (or the number of cycles when the fatigue platform appears on the SN curve), the fatigue strength of the material can be obtained. This method takes into account the life data of the material under different stress amplitudes, reasonably estimates the number of cycles under fatigue strength, has universality and reliability, is simple and feasible to operate, and greatly reduces the demand for experimental volume.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is:

[0006] A method for predicting fatigue strength of metal materials by hardness, the method specifically comprising the following steps:

[0007] (1) Hardness test:

[0008] Perform microhardness tests on several metal materials of the same series to obtain the microhardness values ​​of several materials (e.g. micro Vickers hardness HV);

[0009] (2) Fatigue test:

[0010] Select 2 to 4 materials from the same series of metal materials to prepare fatigue test samples, perform fatigue tests on them, and draw SN curves. The SN curves are fitted with the least squares method according to the Basquin formula (formula (1)) to obtain the fatigue strength coefficient σ′ f and fatigue strength index b;

[0011] lgσ a =lgσ' f +blg(2N f ) (1)

[0012] In formula (1): σ a is the stress amplitude, N f For the cycle times.

[0013] (3) Parameter fitting:

[0014] The microhardness value HV is respectively f Fitting with b, we obtain formula (2) and formula (3);

[0015] lgσ' f =f(HV) (2)

[0016] b=g(HV) (3)

[0017] (4) Fatigue strength prediction:

[0018] Substituting the above-obtained formulas (2) and (3) into formula (1), the fatigue life prediction formula of the metal material is obtained; the fatigue life prediction formula of the metal material is obtained as follows:

[0019] lgσ a =f(HV)+g(HV)·lg(2N f ) (4)

[0020] The number of cycles when the fatigue test cycle stops (or the number of cycles when the SN curve reaches a platform) N S Substitute into formula (4) N f The fatigue strength value σ of the hardness value HV metal material can be calculated w , as shown in formula (5).

[0021] lgσ w =f(HV)+g(HV)·lg(2N S ) (5).

[0022] In the above step (1), the microhardness value of each group of samples should be the arithmetic average of the microhardness values ​​of more than 5 locations.

[0023] In the above step (2), 3 to 5 stress levels should be selected for each group of samples, and 2 to 4 samples should be selected for each stress level for experiment.

[0024] In the above step (3), formulas (2) and (3) are obtained by data fitting; in formula (2): lgσ′ f It is generally positively correlated with HV; in formula (3): the relationship between b and HV is related to the material, and there is a positive correlation or a relationship as shown in formula (6), which can be adjusted according to the damage mechanism of the material; in formula (6): when HV is less than or greater than a, b is a constant c and αHV+β, respectively, where c, α and β are all constants obtained by data fitting, and a is the hardness value at the intersection of c and αHV+β.

[0025]

[0026] In the above step (4), N S is the number of stopping cycles in the high cycle fatigue test or the number of cycles where the SN curve reaches a platform. Formula (5) is only applicable to the same material with different hardness.

[0027] The advantages and beneficial effects of the present invention are as follows:

[0028] 1. The present invention proposes a method for rapidly predicting the fatigue strength of metal materials, which solves the problem that the current acquisition of fatigue strength of metal materials mainly relies on cumbersome and costly fatigue testing.

[0029] 2. The hardness data of the present invention can be obtained based on the indentation test method, which can greatly ensure the integrity of the in-service structure and can be extended to fields such as industry, nuclear power and aviation.

[0030] 3. The fatigue strength prediction model of the present invention has good universality, especially for metal materials with different hardness obtained by hot working.

[0031] 4. The prediction method of the present invention is computationally simple and highly accurate. By establishing a relationship between static mechanical properties and fatigue strength, fatigue strength can be predicted. Hardness testing requires less time, significantly saving time, manpower, and money. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 The relationship between the fatigue strength coefficient and hardness of AISI 4340 steel.

[0033] Figure 2 It is the relationship between fatigue strength index and hardness of AISI 4340 steel.

[0034] Figure 3 It is the verification of the accuracy of the fatigue strength prediction results of AISI 4340 steel.

[0035] Figure 4 It is the relationship between fatigue strength coefficient and hardness of SCM 435 steel.

[0036] Figure 5 It is the relationship between fatigue strength index and hardness of SCM 435 steel.

[0037] Figure 6 It verifies the accuracy of the fatigue strength prediction results of SCM 435 steel.

[0038] Figure 7 It is the relationship between the fatigue strength coefficient and hardness of pure Cu and Cu-Al alloy.

[0039] Figure 8 It is the relationship between fatigue strength index and hardness of pure Cu and Cu-Al alloy.

[0040] Figure 9 It verifies the accuracy of fatigue strength prediction results of pure Cu and Cu-Al alloy. DETAILED DESCRIPTION

[0041] The present invention is further described below with reference to the embodiments and accompanying drawings.

[0042] Example 1:

[0043] This embodiment predicts fatigue strength of AISI 4340 steel materials with different hardness. Four AISI 4340 steel materials with different hardness are tested (experimental data) and used to predict the remaining untested AISI 4340 steel material (verification data).

[0044] Step 1: Microhardness test of AISI 4340 steel materials with different hardness in the same series. The hardness values ​​HV of the four AISI4340 steel test samples used are 382kg / mm 2 , 404kg / mm 2 、489kg / mm 2 and 544kg / mm 2 .

[0045] In step 2, fatigue tests were conducted on the four selected AISI 4340 steel materials, and the fatigue strengths were 594 MPa, 628 MPa, 693 MPa, and 655 MPa, respectively. The SN curves were fitted according to formula (1) as follows:

[0046] lgσ a =2.8274-0.0064×lg(2N f ) (7)

[0047] lgσa =2.8389-0.0052×lg(2N f ) (8)

[0048] lgσ a =2.9058-0.0078×lg(2N f ) (9)

[0049] lgσ a =3.0504-0.0260×lg(2N f ) (10)

[0050] Among them, lgσ′ f They are 2.8274, 2.8389, 2.9058 and 3.0504 respectively; b are -0.0064, -0.0052, -0.0078 and -0.0260 respectively.

[0051] Step 3: Compare HV obtained in step 1 with lgσ′ obtained in step 2 f and b respectively, such as Figure 1 and Figure 2 As shown. According to formula (2) and (3), they are fitted respectively and the formula is as follows:

[0052] lgσ' f =1.294×10 -3 HVσ2.317 (11)

[0053]

[0054] Step 4: Substitute the above formulas (11) and (12) into formula (1) to obtain the fatigue life prediction formula as follows:

[0055]

[0056] Stop the fatigue test cycle for 10 cycles 9 Substitute into formula (13) N f In the formula, we get:

[0057]

[0058] Formula (14) can be used to predict the fatigue strength of AISI 4340 steel with different hardness values ​​HV.

[0059] Step 5: To verify the accuracy of the predicted data, the fatigue strengths of the four AISI 4340 steel samples calculated using formula (14) are 563 MPa, 602 MPa, 754 MPa, and 601 MPa, respectively. In addition, the hardness of one AISI 4340 steel sample is 444 kg / mm2 , the fatigue strength of the verification sample is predicted to be 634MPa, and the calculated value is 678MPa. Figure 3 As shown (this step is for verification of the method and can be omitted in actual operation).

[0060] Example 2:

[0061] This example predicts the fatigue strength of SCM 435 steel materials with different hardness. Four SCM 435 steel materials with different hardness are tested (experimental data) and used to predict the fatigue strength of the remaining untested SCM 435 steel material (verification data).

[0062] Step 1: Microhardness test of SCM 435 steel materials with different hardness in the same series. The hardness values ​​HV of the four SCM435 steel experimental samples used are 323 kg / mm 2 , 512kg / mm 2 , 531kg / mm 2 and 559kg / mm 2 .

[0063] In step 2, fatigue tests were conducted on the four selected SCM 435 steel materials, and the fatigue strengths were 420 MPa, 691 MPa, 743 MPa, and 737 MPa, respectively. The SN curves were fitted according to formula (1) as shown in formula (15), formula (16), formula (17), and formula (18):

[0064] lgσ a =2.9455-0.036×lg(2N f ) (15)

[0065] lgσ a =3.1501-0.032×lg(2N f ) (16)

[0066] lgσ a =3.1978-0.036×lg(2N f ) (17)

[0067] lgσ a =3.2456-0.041×lg(2N f ) (18)

[0068] Among them, lgσ′ f They are 2.9455, 3.1501, 3.1978 and 3.2456 respectively; b are -0.036, -0.032, -0.036 and -0.041 respectively.

[0069] Step 3: Compare HV obtained in step 1 with lgσ′ obtained in step 2 f and b respectively, such as Figure 4 and Figure 5 As shown. According to formula (2) and (3), they are fitted respectively and the formula is as follows:

[0070] lgσ' f =1.222×10 -3 HV+2.547 (19)

[0071]

[0072] Step 4: Substitute the above formulas (19) and (20) into formula (1) to obtain the fatigue life prediction formula:

[0073]

[0074] Stop the fatigue test cycle for 10 cycles 9 Substitute into formula (21) N f In the formula, we get:

[0075]

[0076] Formula (22) can be used to predict the fatigue strength of SCM 435 steel with different hardness values ​​HV.

[0077] Step 5: To verify the accuracy of the predicted data, the fatigue strengths of the four SCM 435 steel samples calculated using formula (22) are 422 MPa, 719 MPa, 729 MPa, and 708 MPa, respectively. In addition, the hardness of one SCM 435 steel sample is 409 kg / mm 2 , the fatigue strength of the verification sample is predicted to be 621MPa, and the calculated value is 537MPa. Figure 6 As shown (this step is for verification of the method and can be omitted in actual operation).

[0078] Example 3:

[0079] This example predicts the fatigue strength of pure Cu and Cu-Al alloy materials with different hardness. Pure Cu and Cu-15at.%Al alloy materials with two different hardnesses are tested (experimental data) and used to predict the remaining untested Cu-5at.%Al alloy material (verification data).

[0080] Step 1: Microhardness test of pure Cu and Cu-15at.%Al alloys of the same series with different hardness, the hardness values ​​HV are 141kg / mm 2 and 258kg / mm 2.

[0081] Step 2: Fatigue tests were conducted on pure Cu and Cu-15at.%Al alloy, and the fatigue strengths were 100MPa and 200MPa, respectively. The SN curves were fitted according to formula (1) as formula (23) and formula (24):

[0082] lgσ a =3.3499-0.1860×lg(2N f ) (twenty three)

[0083] lgσ a =3.4818-0.1640×lg(2N f ) (twenty four)

[0084] Among them, lgσ′ f are 3.3499 and 3.4817 respectively; b are -0.1860 and -0.1640 respectively.

[0085] Step 3: Compare HV obtained in step 1 with lgσ′ obtained in step 2 f and b respectively, such as Figure 7 and Figure 8 As shown. According to formula (2) and (3), they are fitted respectively and the formula is as follows:

[0086] lgσ' f =1.127×10 -3 HV+3.191 (25)

[0087] b=1.880×10 -4 HV-0.213 (26)

[0088] Step 4: Substitute the above formulas (25) and (26) into formula (1) to obtain the fatigue life prediction formula as follows:

[0089] lgσ a =1.127×10 -3 HV+3.191+(1.880×10 -4 HV-0.213)lg(2N f ) (27)

[0090] Stop the fatigue test cycle for 10 cycles 7 Substitute into formula (27) N f In the formula, we get:

[0091] lgσ w =2.500×10 -3 HV+1.636 (28)

[0092] Formula (28) can be used to predict the fatigue strength of Cu-Al alloys with different hardness values.

[0093] Step 5: To verify the accuracy of the predicted data, the fatigue strengths of three pure Cu and Cu-Al alloy experimental samples were calculated using formula (28) to be 98 MPa and 192 MPa respectively. In addition, the hardness of a Cu-5 at.% Al alloy was 206 kg / mm 2 , the fatigue strength of the verification sample is 170MPa, and the calculated value is 143MPa. Figure 9 As shown (this step is for verification of the method and can be omitted in actual operation).

[0094] The above embodiments are merely illustrative of the principles and performance of the present invention, and are not exhaustive. People can also obtain other embodiments based on this embodiment without creative work, and these embodiments all fall within the scope of protection of the present invention.

Claims

1. A method for predicting fatigue strength of metal materials by hardness, characterized by: The method specifically comprises the following steps: (1) Hardness test: Conduct microhardness tests on several metal materials of the same series to obtain the hardness values ​​of several materials; (2) Fatigue test: Select 2 to 4 materials from the same series of metal materials to prepare fatigue test samples, perform fatigue tests on them, and draw SN curves. The SN curves are fitted with the least squares method according to the Basquin formula (1) to obtain the fatigue strength coefficient σ´ f and fatigue strength index b; (1) In formula (1): σ a is the stress amplitude, N f is the cycle number; (3) Parameter fitting: Establish microhardness value HV and lgσ´ respectively f Connect with b to obtain formula (2) and formula (3); (2) (3) (4) Fatigue strength prediction: Substituting formulas (2) and (3) obtained in step (3) into formula (1), the fatigue life prediction formula for metal materials is obtained as follows: (4) Stop the fatigue test cycle for N cycles S Substitute into formula (4) N f The fatigue strength value σ of the hardness value HV metal material can be calculated w , as shown in formula (5): (5)。 2. The method for predicting fatigue strength of metal materials by hardness according to claim 1, characterized in that: In step (1), the selected metal materials of the same series refer to several materials with different hardness obtained by subjecting the same metal to different heat treatments and / or processing techniques.

3. The method for predicting fatigue strength of metal materials by hardness according to claim 1, characterized in that: In step (1), the hardness values ​​are taken at least 5 times and the arithmetic mean is calculated.

4. The method for predicting fatigue strength of metal materials by hardness according to claim 1, characterized in that: In step (2), 3 to 5 stress levels should be selected for each hardness sample, and 2 to 4 samples should be selected for each stress level for experiment.

5. The method for predicting fatigue strength of metal materials by hardness according to claim 1, characterized in that: In step (3), formulas (2) and (3) are obtained by data fitting; in formula (2): lgσ´ f There is generally a positive correlation between b and HV; in formula (3): the relationship between b and HV is related to the material, and there is a positive correlation or a relationship as shown in formula (6), which can be adjusted according to the damage mechanism of the material; in formula (6): when HV is less than or greater than a, b is a constant c and αHV+β, respectively, where c, α and β are all constants obtained by data fitting, and a is the hardness value at the intersection of c and αHV+β: (6)。 6. The method for predicting fatigue strength of metal materials by hardness according to claim 1, characterized in that: In step (4), N S is the number of stopping cycles in high cycle fatigue test. Formula (5) is only applicable to the same material with different hardness.

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