Prediction method for multi-scale fatigue crack growth life under spectral loading

Abstract

This paper discloses a method for predicting the multi-scale fatigue crack growth life under spectral loading. The Newman model is used to calculate the crack closure effect under spectral loading, and the effects of microstructural differences and large-scale yield are introduced. Based on the three-dimensional constraint effect of the crack, a method for calculating the constraint factor is proposed. The method is applicable to crack growth life prediction from small cracks to long cracks, and the constraint factor can be directly calculated without the need for specific experimental calibration.

Description

Technical Field

[0001] The present invention relates to the technical field of fatigue life prediction of metal materials, and in particular to a method for predicting multi-scale fatigue crack growth life under spectral loads. Background Art

[0002] Fatigue crack growth life prediction methods are generally based on the Pairs formula. However, for fatigue crack growth life under spectral loading, numerous studies have demonstrated that load interactions can lead to delayed or accelerated crack growth. To address this issue, several theories have been proposed, primarily categorized as crack closure models and residual stress models. Crack closure models, such as the strip yield model, are commonly used in engineering. However, the strip yield model does not consider the microscopic characteristics of the material. Other residual stress models also exist, but they are less commonly used in engineering.

[0003] On the other hand, when the physical scale of the crack is small, the physical size of its plastic zone is close to the size of the crack itself, resulting in large-scale yield phenomenon at the crack tip. This is inconsistent with the small-scale yield condition in linear elastic fracture mechanics based on the Pairs formula, causing the Pairs formula to lose its physical meaning at this stage. This stage is also called the small crack stage. A large number of experiments have shown that the small crack stage accounts for 70%-90% of the total fatigue growth life. Directly applying the long crack stage calculation model will lead to large deviations in the overall life estimation. Therefore, a multi-scale fatigue crack growth life prediction model that can comprehensively describe the growth of small cracks and long cracks is urgently needed in engineering applications.

[0004] Other studies have shown that differences in the material's microscopic characteristics, such as grain size, can also affect crack propagation life. Furthermore, when the physical scale of the crack has not yet reached a stage much larger than the grain size, the local yield strength of the material is less than the macroscopic yield strength, which is inconsistent with the assumptions of existing predictive models.

[0005] In summary, existing fatigue crack growth life predictions have defects such as being inconsistent with experimental phenomena or requiring the use of empirical constants. In engineering applications, there is an urgent need for a universal crack growth life prediction method that can be applied to any material, working environment and loading conditions and can estimate the multi-scale growth life from small cracks to long cracks. Summary of the Invention

[0006] In order to solve the above problems, the present invention provides a method for predicting multi-scale fatigue crack growth life under spectral loads with higher prediction accuracy.

[0007] In order to achieve the above object, the present invention is implemented through the following technical solutions:

[0008] The present invention is a method for predicting multi-scale fatigue crack growth life under spectral loads, comprising the following steps:

[0009] Step 1: Use the constraint factor to calculate the crack closure stress using the strip yield model with combined constraint factors, giving the influence of the closure effect;

[0010] Step 2, calculate the factors affecting large-scale yield;

[0011] Step 3, calculating the difference factors of material microscopic characteristics;

[0012] Step 4, calculate the small crack stage extension threshold;

[0013] Step 5, establish and solve the fatigue crack growth model;

[0014] Step 6: Replace the original crack length with the sum of the original crack length and the crack extension length da obtained by solution, and repeat steps 1 to 5 until the crack length reaches the fracture toughness K IC The cycle is stopped at the corresponding fracture crack length, and the number of cycles is counted to obtain the predicted life.

[0015] A further improvement of the present invention is that the expression of the combined constraint factor in step 1 is:

[0016]

[0017] Where v is Poisson's ratio, r p0 is the size of the monotonic plastic zone in front of the crack tip, K max is the stress intensity factor corresponding to the maximum loading stress, σ y is the yield strength, B is the thickness of the component, and the equivalent thickness B is used here. eq Instead of thickness B, the equivalent thickness calculation method is:

[0018]

[0019]

[0020] Where B eq0 is the minor axis length of the semi-elliptical crack, is the ellipse azimuth corresponding to a point on the leading edge, and t is the ratio of the major axis to the minor axis of the ellipse.

[0021] The calculation expression of the closing stress influencing factor is:

[0022]

[0023] S op / S max =A0+A1R+A2R 2 +A3R3 ,R≥0

[0024] S op / S max =A0+A1R,R<0

[0025] Where R is the stress ratio, A1, A2, A3 are functions related to the material's flow stress σ0 and the constraint factor α, and the material's flow stress σ0 is the material's yield strength σ y and tensile strength σ b The average value of

[0026] Among them, the expressions of A0, A1, A2, and A3 are:

[0027] A0=(0.825-0.34α+0.05α 2 )[cos(πS max / 2σ0)] 1 / α

[0028] A1=(0.415-0.071α)(S max / σ0)

[0029] A2=1-A0-A1-A3

[0030] A3=2A0+A1-1

[0031] Where α is the constraint factor, representing the transformation process of the crack from plane strain state to plane stress state. When α = 3, it is plane strain state, and when α = 1, it is plane stress state. Since the constraint factor needs to be determined based on experience in use and cannot reflect the stress state transformation process, the combined constraint factor α is directly used. g The constraint factor is used in the calculation, and the calculation process of the other coefficients remains unchanged.

[0032] A further improvement of the present invention is that the calculation expression of the large-scale yield influencing factor in step 2 is:

[0033]

[0034] Among them, σ y is the yield strength of the material, σ max is the maximum loading stress of this loading cycle.

[0035] A further improvement of the present invention is that the expression of the material microscopic characteristic difference factor in step 3 is:

[0036]

[0037] in is the local yield strength of the material, Δσ is the stress range of the material in this loading cycle, a is the half length of the crack, r pc is the size of the cyclic plastic zone.

[0038] A further improvement of the present invention is that the calculation expression of the small crack stage extension threshold in step 4 is:

[0039] K th,a =K th,d +(K th,R -K th,d )[1-e -k(a-d) ]

[0040]

[0041] Where d is the microstructural barrier, the average grain size or the maximum grain size of the material, ΔK th,d is the microstructure expansion threshold, ΔK th,R is the macro threshold, Y is the geometric correction coefficient in the stress intensity factor range calculation formula (selected according to the stress intensity factor range calculation method), S e is the fatigue limit of the material, k is the transition rate from microscopic to macroscopic threshold, which is only related to the material, and e is the natural logarithm.

[0042] A further improvement of the present invention is that the expression of the fatigue crack growth model in step 5 is:

[0043]

[0044] Among them, A and n are fitting parameters in the Pairs formula, is the crack growth rate, and ΔK is the stress intensity factor range.

[0045] The beneficial effects of the present invention are: (1) the present invention uses a combined constraint factor instead of a constraint factor, which does not require empirical constants, simplifies the calculation process, and improves the prediction accuracy.

[0046] (2) The invention takes into account the large-scale yield factors and microscopic characteristic difference factors, and is suitable for life prediction from the small crack stage to the long crack stage. Compared with the simple long crack prediction model, it has higher accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a schematic diagram of equivalent thickness in an embodiment of the present invention.

[0048] Figure 2 Schematic diagram showing the change of local yield strength with crack length in an embodiment of the present invention. DETAILED DESCRIPTION

[0049] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only intended to illustrate the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0050] The present invention is a method for predicting multi-scale fatigue crack growth life under spectral loads, comprising the following steps:

[0051] (1) The crack tip closure stress is calculated using Newman's strip yield model. The specific calculation steps are as follows:

[0052] S op / S max =A0+A1R+A2R 2 +A3R 3 ,R≥0 (1)

[0053] S op / S max =A0+A1R,R<0 (2)

[0054] Where R is the stress ratio, A0, A1, A2, A3 are the flow stress σ0 of the material (the yield strength σ y and tensile strength σ b The function of the average value of ) is related to the constraint factor α:

[0055] The expressions of A0, A1, A2, and A3 are:

[0056] A0=(0.825-0.34α+0.05α 2 )[cos(πS max / 2σ0)] 1 / α (3)

[0057] A1=(0.415-0.071α)(S max / σ0) (4)

[0058] A2=1-A0-A1-A3 (5)

[0059] A3=2A0+A1-1 (6)

[0060] Where α is the constraint factor, representing the crack's transformation from a plane strain state to a plane stress state. When α = 3, it is a plane strain state, and when α = 1, it is a plane stress state. In order to clearly characterize this state transition process, the concept of a combined constraint factor is introduced to replace the original constraint factor. The specific solution method for the combined constraint factor is as follows:

[0061]

[0062] Where v is Poisson's ratio, r p0 is the size of the monotonic plastic zone in front of the crack tip, K max is the stress intensity factor corresponding to the maximum loading stress, σ y is the yield strength, and B is the thickness of the component. Considering that Equation (7) is a solution method for the combined constraint factor under the state of penetrating three-dimensional cracks, in order to extend it to the state of non-penetrating cracks, the equivalent thickness B is used. eq Instead of the component thickness B, for a semi-elliptical surface crack, the equivalent thickness can be expressed as:

[0063]

[0064] Where c is the physical thickness of the component, is the direction angle corresponding to a point on the crack front, and is the direction angle corresponding to a point on the crack front like Figure 1 As shown, it is the ratio of the major axis to the minor axis of the semi-elliptical crack, which is determined based on the actual experimental results. (2) Calculate the factors affecting large-scale yielding. The calculation expression is:

[0065]

[0066] (3) Calculate the difference factors of the material microscopic characteristics. The calculation expression is:

[0067]

[0068] in,

[0069]

[0070] Where r pc is the size of the cyclic plastic zone, Represents the local yield strength of the material. Its initial value is the fatigue limit of the material. When the crack gradually changes from a small crack to a long crack, the local yield strength gradually increases to the macroscopic material yield strength, such as Figure 2 As shown, its growth mode is mainly divided into two types: smooth growth and step growth. In actual use, the smooth growth mode is generally selected, which can be written as:

[0071]

[0072] Where β is the rate of transformation, d is the microstructural barrier, according to Figure 2 The larger β is, the faster the crack transition rate from small crack to long crack stage.

[0073] (4) The long crack extension threshold is extended to the small crack stage. It is considered that the small crack stage extension threshold is composed of the material microstructure threshold and the macro threshold. The calculation expression of the small crack stage extension threshold is:

[0074] K th,a =K th,d +(K th,R -K th,d )[1-e -k(a-d) ](13)

[0075]

[0076] Where d is the microstructural barrier, which can be the average grain size or the maximum grain size of the material, ΔK th,d is the microstructure expansion threshold, S e is the fatigue limit of the material, k is the transition rate from microscopic to macroscopic threshold, which is only related to the material, and e is the natural logarithm;

[0077] (5) Establish and solve the fatigue crack growth model;

[0078] The fatigue crack growth model expression is:

[0079]

[0080] Among them, A and n are fitting parameters in the Pairs formula, is the crack growth rate, ΔK is the stress intensity factor range; the circle-by-circle method is used to solve the crack growth length da obtained in each cycle, and the original crack length a is replaced by a+da, and steps (1) to (5) are repeated until the crack length reaches the fracture toughness K IC The corresponding fracture crack length stops and the number of cycles is counted, which is the predicted life.

[0081] It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by those skilled in the art in the art to which the present invention belongs. It should also be understood that terms such as those defined in common dictionaries should be understood to have meanings consistent with their meanings in the context of the prior art and, unless defined as such, will not be interpreted in an idealized or overly formal sense.

[0082] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for predicting multi-scale fatigue crack growth life under spectral loading, characterized by: The steps include: Step 1: Use the constraint factor to calculate the crack closure stress using the strip yield model with combined constraint factors, giving the influence of the closure effect; Step 2, calculate the factors affecting large-scale yield; Step 3, calculating the difference factors of material microscopic characteristics; Step 4, calculate the small crack stage extension threshold; Step 5, establish and solve the fatigue crack growth model; Step 6: Replace the original crack length with the sum of the original crack length and the crack extension length da obtained by solution, and repeat steps 1 to 5 until the crack length reaches the fracture toughness K IC The corresponding fracture crack length stops cycling, and the number of cycles is counted, which is the predicted life; The expression of the combined constraint factor in step 1 is: Where v is Poisson's ratio, r p0 is the size of the monotonic plastic zone in front of the crack tip, K max is the stress intensity factor corresponding to the maximum loading stress, σ y is the yield strength, B is the thickness of the component, and the equivalent thickness B is used here. eq Instead of thickness B, the equivalent thickness B at a certain point on the crack front is eq The expression is: Where B eq0 is the minor axis length of the semi-elliptical crack, is the ellipse azimuth corresponding to a certain point on the leading edge, and t is the ratio of the major axis to the minor axis of the ellipse; The calculation expression of the closing stress influencing factor is: S op / S max =A0+A1R+A2R 2 +A3R 3 ,R≥0 S op / S max =A0+A1R,R<0 Where R is the stress ratio, A0, A1, A2, A3 are coefficients, and the expressions of A0, A1, A2, A3 are: A0=(0.825-0.34α+0.05α 2 )[cos(πS max / 2σ0)] 1 / α A1=(0.415-0.071α)(S max / σ0) A2=1-A0-A1-A3 A3=2A0+A1-1 σ0 is the material flow stress, which is equal to the yield strength σ y and tensile strength σ b The average value of α is the constraint factor replaced by the combined constraint factor α g ; The calculation expression of the large-scale yield influencing factor in step 2 is: Among them, σ y is the yield strength of the material, σ max is the maximum loading stress of this loading cycle; The expression of the material microscopic characteristic difference factor in step 3 is: in is the local yield strength of the material, Δσ is the stress range of the material in this loading cycle, a is the half length of the crack, r pc is the size of the cyclic plastic zone; The calculation expression for the small crack stage extension threshold in step 4 is: K th,a =K th,d +(K th,R -K th,d )[1-e -k(a-d) ] Where d is the microstructural barrier, the average grain size or the maximum grain size of the material is taken, K th,d is the microstructure expansion threshold, K th,R is the macro threshold, k is the transition rate from micro to macro, which is related to the material, Y is the shape correction factor, S e is the fatigue limit of the material, and e is the natural logarithm; The expression of the fatigue crack growth model in step 5 is: Among them, A and n are the fitting parameters in the Pairs formula, ΔK is the stress intensity factor range, is the crack growth rate.

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