Crack Growth Rate Model Derived from Domain Knowledge-Guided Symbolic Regression

Machine learning(ML)has powerful nonlinear processing and multivariate learning capabilities,so it has been widely utilised in the fatigue field.However,most ML methods are inexplicable black-box models that are difficult to apply in engineering practice.Symbolic regression(SR)is an interpretable machine learning method for determining the optimal fitting equation for datasets.In this study,domain knowledge-guided SR was used to determine a new fatigue crack growth(FCG)rate model.Three terms of the variable subtree ofΔK,R-ratio,andΔK_(th)were obtained by analysing eight traditional semi-empirical FCG rate models.Based on the FCG rate test data from other literature,the SR model was constructed using Al-7055-T7511.It was subsequently extended to other alloys(Ti-10V-2Fe-3Al,Ti-6Al-4V,Cr-Mo-V,LC9cs,Al-6013-T651,and Al-2324-T3)using multiple linear regression.Compared with the three semi-empirical FCG rate models,the SR model yielded higher prediction accuracy.This result demonstrates the potential of domain knowledge-guided SR for building the FCG rate model.

PROBABILISTIC MODELS FOR LONG FATIGUE CRACK GROWTH RATES OF LZ50 AXLE STEEL

Experimental study is performed on the probabilistic models for the long fatigue crack growth rates (da/dN) of LZ50 axle steel. An equation for crack growth rate was derived to consider the trend of stress intensity factor range going down to the threshold and the average stress effect. The probabilistic models were presented on the equation. They consist of the probabilistic da/dN-ΔK relations, the confidence-based da/dN-ΔK relations, and the probabilistic- and confidence-based da/dN-ΔK relations. Efforts were made respectively to characterize the effects of probabilistic assessments due to the scattering regularity of test data, the number of sampling, and both of them. These relations can provide wide selections for practice. Analysis on the test data of LZ50 steel indicates that the present models are available and feasible.

Simple Predicting Method for Fatigue Crack Growth Rate Based on Tensile Strength of Carbon Steel

Three types of fatigue tests for an annealed carbon steel containing carbon of 0.42%were carried out on smooth specimens and specimens with a small blind hole in order to investigate the fatigue crack growth law.A simple predicting method for crack growth rates has been proposed involving strengthσband the relation between cyclic stress and strain.The validity of proposed method has been confirmed by experiments on several carbon steels with different loadings.

Effects of precipitates on fatigue crack growth rate of AA 7055 aluminum alloy

The effects of precipitates on the fatigue crack growth rate of AA 7055 Al alloy subjected to different ageing treatments were investigated using transmission electron microscope and fatigue crack growth testing.The results show that the T77 treated samples exhibit the lowest crack growth rate,while the crack growth rate of over-aged samples is the highest.In terms of the model based on the reversibility of dislocation motion within the plastic zone close to the crack tip,the improved crack growth resistance is attributed to many precipitates that are coherent with Al matrix in the under-aged and T77 treated samples.When the precipitate is coherent with the Al matrix,the larger the precipitate is,the slower the fatigue crack grows.The effects of grain boundary precipitates and precipitate free zone on the fatigue crack growth resistance are less significant than those of precipitates within grains of the alloy.

Monte-Carlo Simulation of Surface Crack Growth Rate for Offshore Structural Steel E36-Z35

The Monte- Carlo method is used to simulate the surface fatigue crack growth rate for offshore structural steel E36-Z35, and to determine the distributions and relevance of the parameters in the Paris equation. By this method, the time and cost of fatigue crack propagation testing can be reduced. The application of the method is demonstrated by use of four sets of fatigue crack propagation data for offshore structural steel E36-Z35. A comparison of the test data with the theoretical prediction for surface crack growth rate shows the application of the simulation method to the fatigue crack propagation tests is successful.

PROBABILISTIC MODELS FOR LONG FATIGUE CRACK GROWTH RATES OF LZ50 AXLE STEEL

Experimental study is performed on the probabilistic models for the long fatigue crack growth rates （da/dN） of LZ50 axle steel. An equation for crack growth rate was derived to consider the trend of stress intensity factor range going down to the threshold and the average stress effect. The probabilistic models were presented on the equation. They consist of the probabilistic da/dN-△K relations, the confidence-based da/dN-△K relations, and the probabilistic- and confidence-based da/dN-△K relations. Efforts were made respectively to characterize the effects of probabilistic assessments due to the scattering regularity of test data, the number of sampling, and both of them. These relations can provide wide selections for practice. Analysis on the test data of LZ50 steel indicates that the present models are available and feasible.

Fatigue crack growth rate test using a frequency sweep method

Fatigue crack propagation characteristics of a diesel engine crankshaft are studied by measuring the fatigue crack growth rate using a frequency sweep method on a resonant fatigue test rig. Based on the phenomenon that the system frequency will change when the crack becomes large, this method can be directly applied to a complex component or structure. Finite element analyses (FEAs) are performed to calibrate the relation between the frequency change and the crack size, and to obtain the natural frequency of the test rig and the stress intensity factor (SIF) of growing cracks. The crack growth rate i.e. da/dN-ΔK of each crack size is obtained by combining the testing-time monitored data and FEA results. The results show that the crack growth rate of engine crankshaft, which is a component with complex geometry and special surface treatment, is quite different from that of a pure material. There is an apparent turning point in the Paris's crack partition. The cause of the fatigue crack growth is also dis-cussed.

Statistical Analysis Methods of Fatigue Crack Growth Rate

The standard center-cracked tensile specimens M(T) with different widths made of aluminum alloy were designed for fatigue crack growth rate experiments, and the effect of specimen size on the fatigue crack growth rate was discussed. The fitting equation and the p-da/dN-ΔK curve of fatigue crack growth rate(with different confidence and reliability levels) were obtained by one-side tolerance factor analysis. In order to reasonably reflect the dispersion of material properties on the fatigue crack growth rate and fatigue crack propagation life, two novel statistical analysis methods were proposed, which can be used to describe the probability distribution of fatigue crack growth rate. Compared with the traditional statistical analysis method of probabilistic fatigue crack growth rate, the fitted curves from the novel statistical analysis methods yield more objective description on the probability distribution of crack growth rate.

EFFECTS OF HEAT TREATMENT AND ENVIRONMENT ON CRACK PROPAGATION RATE IN STEEL GC-4 UNDER CORROSION FATIGUE AND STRESS CORROSION

Comparative investigations were carried out of the effect of heat treatment regimes Jor steel GC-4(40CrMnSiMoVA)on its crack propagating rates,from corrosion fatigue, (da/dN)_(CF),or stress corrosion cracking,(da/dt)_(SCC),in media with various constituents and pH values.Both(da/dN)_(CF) and(da/dt)_(SCC) accelerate with the increase of yield stress of the steel,yet the former is far less than the later.In comparison with media,the (da/dt)_(SCC) in distilled water is slightly greater than that in 3.5% NaCl solution,and the (da/dN)_(CF) in distilled water is far less than that in 3.5% NaCl solution.With the pH value increasing in 3.5% NaCl solution,the(da/dN)_(CF) lowers down and the(da/dt)_(SCC) speeds up.An explanation was also proposed with concept of the cyclic hardening and softening at crack tip,as well as the crack closure and occluded cell effect.

FACTORS AFFECTING FATIGUE CRACK GROWTH RATES OF FIBER REINFORCED METAL LAMINATES

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Influence of Microstructures and Residual Stress on Fatigue Crack Propagation Rate of High Carbon Steels

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Fatigue crack growth rates of rotor steel at elevated temperatures

Low fatigue samples were obtained from the outer edges of rotor steel (30CrlMolV) which had operated under different temperatures conditions. Based on this data, the effects of temperature on fatigue crack growth rates were investigated. This paper presents a derivation of the superposition expression of two natural logarithms governing crack growth rates and also discusses the relationship between a material’s constants and temperature. These results can provide experimental and theoretical references for fatigue life design of rotor steel in steam turbines.

Effect of strain rate on solidification crack susceptibility of different metals

In this paper,a slow bending speed varestraint test method with con- tinuously adjustable deformation rate for testing hot cracking sensitivity is de- veloped and its working principle is described.From great amounts of tests,it is known that strain rate affects the sensitivity of solidification crack because of its influnce on material ductility in BTR directly.The smaller the strain rate, the better the ductility and the lower the solidification crack sensitivity.The ex- tent of this effect varies with different materials,for LF-6 aluminum alloy,it is great,but for 16Mn,19Mn5 and 20G steels,it is small.Through systematic investigation,it is concluded that strain rate of a metal during welding can be lowered and the resistance to solidification crack can be enhanced by reducing structrual restraint and by adjustment of welding parameters.

EFFECTS OF TRACE Zr ON FATIGUE CRACK GROWTH RATE OF HIGH DAMPING Zn-Al ALLOY

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FATIGUE CRACK PROPAGATION RATE OF ZG35 STEEL WITH SEMI－ELLIPTICAL SURFACE CRACK

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ANALYSIS OF ENERGY RELEASE RATE FOR CRACKED LAMINATES

An interface crack analysis is presented for further understanding the characteristics of the crack-tip field. The conditions under which the energy release rate components would exist are emphasized and the relations between energy release rate components and the stress intensity factors are given. Combining with the results of chasical plate theory analysis. a closed-form solution for stress intensity factors in terms of external loading as well as some geometric and material parameters for fairly general composite laminates is derived Then. an analytical solution for energy release rate components is deduced. In order to get energy release rate components under general loading condition. a mode mix parameter, Ω, must be determined separately. A methodology for determining Ω is discussed. Finally. several different kinds of laminates are examined and the results obtained could be used in engineering applications.

RESEARCH FOR THE STRAIN ENERGY RELEASE RATE OF COMPLEX CRACKS BY USING POINT-BY-POINT CLOSED EXTRAPOLATION APPROACH

A new extrapolation approach was proposed to calculate the strain energy release rates of complex cracks. The point_by_point closed method was used to calculate the closed energy, thus the disadvantage of self_inconsistency in some published papers can be avoided. The disadvantage is that the closed energy is repeatedly calculated: when closed nodal number along radial direction is more than two, the displacement of nodes behind the crack tip that is multiplied by nodal forces, the closed energy has been calculated and the crack surfaces have been closed, and that closed energy of middle point is calculated repeatedly. A DCB (double cantilever beam) specimen was calculated and compared with other theoretical results, it is shown that a better coincidence is obtained. In addition the same results are also obtained for compact tension specimen, three point bend specimen and single edge cracked specimen. In comparison with theoretical results,the error can be limited within 1 per cent. This method can be extended to analyze the fracture of composite laminates with various delamination cracks.

Effects of water intrusion and loading rate on mechanical properties of and crack propagation in coal–rock combinations

Tackling the problems of underground water storage in collieries in arid regions requires knowledge of the effect of water intrusion and loading rate on the mechanical properties of and crack development in coal–rock combinations. Fifty-four coal–rock combinations were prepared and split equally into groups containing different moisture contents(dry, natural moisture and saturated) to conduct acoustic emission testing under uniaxial compression with loading rates ranging from 0.1 mm/min to 0.6 mm/min. The results show that the peak stress and strength-softening modulus, elastic modulus, strain-softening modulus, and post-peak modulus partly decrease with increasing moisture content and loading rate. In contrast, peak strain increases with increasing moisture content and fluctuates with rising loading rate. More significantly, the relationship between stiffness and stress, combined with accumulated counts of acoustic emission, can be used to precisely predict all phases of crack propagation. This is helpful in studying the impact of moisture content and loading rate on crack propagation and accurately calculating mechanical properties. We also determined that the stress thresholds of crack closure, crack initiation, and crack damage do not vary with changes of moisture content and loading rate, constituting 15.22%, 32.20%, and 80.98% of peak stress, respectively. These outcomes assist in developing approaches to water storage in coal mines, determining the necessary width of waterproof coal–rock pillars, and methods of supporting water-enriched roadways, while also advances understanding the mechanical properties of coal–rock combinations and laws of crack propagation.

原油裂解气资源评价的理论技术创新与评价应用——以四川盆地震旦系—寒武系为例

四川盆地震旦系—寒武系天然气资源丰富。近年来,在四川盆地川中古隆起和北部斜坡区先后获得了两个万亿级大气区的重大发现。为了明确该领域天然气的资源规模以及未来的勘探方向和创建一套切实可行的原油裂解气资源量的评估方法,本次研究基于该区天然气为古油藏原油裂解的基本认识,按照干酪根生油,再到古油藏裂解生气的技术路线对原油裂解气的资源量进行计算。应用成因法,采用PetroMod 3D盆地模拟软件,输入地层等厚图、岩相古地理图、烃源岩综合评价图、剥蚀量展布图以及生油动力学参数图版,建立整个盆地的三维地质模型,并切分为5个区块分别计算生油量,然后探讨了石油运聚系数、石油裂解率、天然气散失率以及寒武系石油运移的分配系数,并创建了天然气散失系数计算公式。在以上基础上,恢复了盆地及5个构造单元的生油史,并明确了古油藏形成的关键时刻,最终得到全盆地震旦系—寒武系常规天然气资源量为13.43×10^(12)m^(3),其中寒武系为5.43×10^(12)m^(3),震旦系为8.0×10^(12)m^(3)。并指出除了川中地区以外,川南和川东具有巨大的勘探潜力,尤其是位于川南地区德阳—安岳裂陷槽两侧的台缘带和台内颗粒滩是下一步勘探的现实领域。本次研究在理论创新和勘探实践中都具有重要意义。