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Fatigue crack propagation modeling method based on uncertain differential equation

A technique of fatigue crack growth and differential equations, applied in the field of fatigue crack growth modeling based on uncertain differential equations

Active Publication Date: 2021-09-10
BEIHANG UNIV
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  • Claims
  • Application Information

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Problems solved by technology

[0007] In view of this, the present invention provides a fatigue crack growth modeling method based on uncertain differential equations, in order to solve the cognitive uncertainty caused by the limited amount of experimental data in fatigue modeling when the fatigue crack growth experiment needs to be reasonable quantitative problem

Method used

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  • Fatigue crack propagation modeling method based on uncertain differential equation
  • Fatigue crack propagation modeling method based on uncertain differential equation
  • Fatigue crack propagation modeling method based on uncertain differential equation

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Embodiment 1

[0121] Step 1: Based on the uncertainty theory, quantify the cognitive uncertainty in four aspects: physical properties, external factors, time dimension and threshold value. According to the quantitative results of cognitive uncertainty and the deterministic law of fatigue crack growth, construct Differential equations for fatigue crack growth models.

[0122] The fatigue crack growth process is regarded as a cumulative and gradual process of small increments, assuming that the crack growth process is described by an uncertain differential equation:

[0123] da n =f(n,a n )dn+g(n,a n )dC n (8)

[0124]Among them, the function f(n, a n ) represents the fatigue crack growth rate, which can be expressed by formula (5), namely:

[0125]

[0126] function g(n,a n ) represents the diffusion coefficient, represented by a constant ε, that is:

[0127] g(n,a n ) = ε (10)

[0128] Among them, σ max Expressed by formula (7), σ op It is solved by formula (6); n represents...

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Abstract

The invention discloses a fatigue crack propagation modeling method based on an uncertain differential equation, which aims at a crack propagation process considering crack closure and a high-load hysteresis effect, and comprises the following steps of: firstly, quantifying cognitive uncertainty in four aspects of physical attributes, external factors, time dimensions and threshold values based on an uncertain theory; constructing a fatigue crack propagation model based on an uncertain differential equation; then, determining model parameters through statistical analysis; then, deriving a definite reliability function to evaluate the definite reliability; and finally, predicting the crack propagation process and the fatigue life. According to the fatigue crack propagation modeling method based on the uncertain differential equation, a choice for reasonably quantifying cognitive uncertainty in a fatigue crack propagation experiment is given, so that the recognition of a fatigue rule is more accurate, and the crack propagation process is described based on the uncertain differential equation, so that the fatigue crack propagation accuracy is improved. The accuracy of crack propagation and fatigue life prediction can be improved.

Description

technical field [0001] The invention relates to the technical fields of fatigue modeling and reliability modeling, in particular to a fatigue crack growth modeling method based on uncertain differential equations. Background technique [0002] In engineering practice, the fracture damage caused by fatigue of metal materials accounts for 50%-90% of all mechanical damage, and is the most common form of mechanical and structural failure. At present, many progresses have been made in the study of fatigue, including the fatigue model describing the law of fatigue degradation. Usually, the fatigue model describes the deterministic causal relationship between fatigue life or crack growth rate and factors such as material, geometry, load, etc. Uncertainties caused by material properties, load changes, etc. are also worthy of attention in fatigue modeling. Therefore, in order to understand fatigue laws more accurately, these uncertainties need to be carefully classified and scientif...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F30/17G06F30/20G06F17/13G06F111/08G06F119/02G06F119/14
CPCG06F30/17G06F30/20G06F17/13G06F2111/08G06F2119/02G06F2119/14
Inventor 李晓阳陶昭
Owner BEIHANG UNIV
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