The Fatigue Crack Propagation Probability Study Under Different Stress Ratio

The fatigue crack propagation is an important part of fatigue fracture. The fatigue crack growth rate da/dN-ΔK curve is the important basis of fatigue damage tolerate design and safety assessment for structures, it is one of the fundamental material property for metal structures. The research of the expression of fatigue crack growth rate da/dN is taken seriously, a lot of mechanics models are put forward by experts. The most widely used method in engineering is Paris formula, which is the basis for the theory of crack growth life. Paris formula has very important practical significance for analysis, forecast remaining life. Among the experimental study, Paris formula has been greatly developed, many scholars have done a lot of correction for the formula’s specific form. But its parameters C and n have not been study and exploration deeply in physical nature.In this thesis, take the Paris formula as a starting point to study the law of the influence of stress ratio on the crack propagation. The study purpose is to reveal the essence of the Paris formula, create a more effective mathematical model, study systematically the probability problems of fatigue fracture under the stress ratio, in order to supplement and improve the probability theory to solve practical problems.Based on relevant literature information and test data,take the Paris formula as the starting point, around the influence of stress ratio on crack propagation, then expand the following work.Firstly the basic law of the effect of stress ratio on fatigue fracture is studied. By the fatigue crack propagation tests of ADB610steel and30CrMnSiNi2A steel under different stress ratio, the fatigue life and crack growth rate have significantly difference with the change of stress ratio in the same conditions. Stress ratio is not seen directly from the Paris formula expression, but studies have shown that the Paris formula parameters C and n correlate with stress ratio. It reveals the parameter C and n have the recessive relationship with stress ratio and proof the law of the Paris formula parameters C and n with the change of stress ratio:C will decrease with the increase of stress ratio, n will increase with the increase of stress ratio.Secondly, the mathematical model of probability of the fatigue fracture under different stress ratio is studied. In consideration of the evident effects of stress ratio on fatigue crack growth rate and the scatter of fatigue crack growth. Based on Paris formula, a probabilistic model is established to describe the random fatigue crack propagation, the probability model can quantitatively show that the relationship between the fatigue crack growth rate and the main parameters (ΔK and stress ratio). It can externalize the effect of the stress ratio on Paris formula parameters C and n. Using linear regression theory,the data processing method of turning non-linear test data into linear data is put forward, and ultimately deduced the mathematical mode based on Paris formula.Provide a theoretical basis for the assessment of the fatigue life of the material under similar conditions, to meet the application requirements in engineering practice.Thirdly, geometry of the fatigue fracture probability under different stress ratio is analyzed. Based on Paris formula, the graphical representation of R-p-da/dN-ΔA: probabilistic model is no longer a simple two-dimensional curve, but it is a three-dimensional surface. From the graphics point of view R-p-da/dN-ΔK probability model is a series of surface family. By R-p-da/dN-ΔK surface family, under different probability requirements,the law of the influence of continuous stress ratio on the crack growth rate can obtain. R-p-da/dN-ΔK surface family under certain conditions can degenerate into p-da/dN-AK curves for engineering probability damage tolerance design and safety assessment.Then the credibility of the fatigue fracture probability is studied under different stress ratio. Considering the laws of influence of the data dispersion and the number of samples probability evaluation, integration of the probability and confidence, the R-p-γ-da/dN-ΔK probability-confidence model is put forward. The parameters of R-p-γ-da/dN-ΔK probability-confidence model are estimated by using the linear principle of no-linear function. The probability-confidence model characterize the credibility of the research work.Finally, the calculation method of fatigue fracture probability is studied. The a-N fitting calculation method is an important prerequisite to obtain high-precision p-da/dN-ΔK fitting curve. In this thesis, considering the random nature of the whole set of data, unified a-N incremental polynomial fitting method is proposed under the same test conditions to provide a scientific basis for the study of the influence of different stress ratio on the fatigue crack propagation. And two p-da/dN data processing methods are given. The statistical analysis of the data processing based on da/dN is more reasonable in theory; derivation calculations based on p-a-N is more convenient for application. The calculation results of the two calculation methods have no significant difference from a statistical point of analysis.The innovation of this thesis is followed:It reveals Paris formula to reflect the effects of stress ratio on fatigue crack propagation. And based on Paris formula, the basic law and mathematical model and geometry, confidence of the effects of stress ratio on fatigue fracture probability have been studied comprehensively and systematically. The research enrich and improve the content of the Paris formula and expand the Paris formula.The specific innovations include:(1) In the role of the basic law of the fatigue fracture under different stress ratio: Revealing the Paris formula can reflect the influence of stress ratio on fatigue crack growth, and find the changing laws of two important parameters of the Paris formula with the change of stress ratio. C will decrease with stress ratio increasing; n will increase with stress ratio increasing.(2) In the role of the mathematical model of the fatigue fracture probability under different stress ratio:Using linearization theory,the data processing method of turning non-linear test data into linear data is put forward, and ultimately deduced a probability mathematical mode based on Paris formula.(3) In the role of the geometry of the fatigue fracture probability under different stress ratio:Pointed out the probability mathematical model is a surface family under different stress ratio. Further discussed the application of R-p-da/dN-ΔK surface family, and analyzed the scope of the surface family.(4) In the role of the confidence of the fatigue fracture probability under different stress ratio:In order to ensure the credibility of that the entire work, propose that should discuss the degree of confidence of the fatigue fracture probability. Considering confidence, the R-p-γ-da/dN-ΔK probability-confidence model is established. The method of parameters is given.(5) In the role of calculation method of the fatigue fracture probability: Unified a-N incremental polynomial fitting is proposed under the same test conditions to provide a scientific basis for the study of the influence of different stress ratio on the fatigue crack propagation. And two p-da/dN data processing methods are given. The statistical analysis of the data processing based on da/dN is more reasonable in theory; derivation calculations based on p-a-N is more convenient for application. The calculation results of the two calculation methods have no significant difference from a statistical point of analysis.