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.

Anisotropic FCGR behaviour in hot-rolled Mg-3Al-0.5Ce alloy

In this work,anisotropic fatigue crack growth rate(FCGR)behaviour in a hot-rolled Mg-3wt%Al-0.5wt%Ce alloy was investigated using compact tension(CT)specimens with notch(an)parallel to the rolling direction(RD)and transverse direction(TD).The FCGR tests were conducted at a constant load ratio(R=0.1)and maximum stress intensity factor(KMax=15.6 MPam)to investigate the crack closure effect.For both constant R and KMax conditions:(i)the load-displacement curves for every loading cycle were linear for anto RD and TD,indicating no crack closure;(ii)the FCGR was found to be lower for anRD than anTD over the entire stress intensity factor range(△K).The hot-rolled sample contained long-aligned Al11Ce3 intermetallic phase within grain boundaries that are elongated along RD.During the FCGR test,{10.12}10.11extension twins(ET)with lamellae∼||⊥and c-axis∼||to these elongated intermetallics along RD developed irrespective of the notch orientation.During the loading cycle,these intermetallics along RD generate back-stresses,reducing the in-plane tensile stress∼||and∼⊥to crack-tip to∼0 for anto RD and TD,respectively.Hence,lenticular ET∼||⊥and∼||,with c-axis∼||and∼⊥to crack path activates,leading to trans and inter lamellar crack for anto RD and TD,respectively,and anisotropic FCGR.Translamellar crack in anRD reduces the FCGR due to plastic energy dissipation as perceived by comparatively more geometrically necessary boundaries(GNBs).On the other hand,faster FCGR was obtained for anTD due to interlamellar cracking.Thus,the crack growth through the matrix-ET interfaces was favoured due to strain incompatibility.The Fractography for anRD shows smaller elongated grooves along crack propagation,which indicates crack arrest.However,larger elongated grooves for an||TD indicated easy crack propagation due to favourable interlamellar crack.

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.

A new measurement method of crack propagation rate for brittle rock under THMC coupling condition

A new electrical method of conductive carbon-film(with waterproof and anticorrosion ability)was proposed to continuously measure crack propagation rate of brittle rock under THMC coupling condition.A self-designed coupling testing system was used to conduct THMC coupling fracture tests of the pre-cracked red sandstone specimens(where the temperature is only changed)by this new electrical method of conductive carbon-film.Calculation results obtained by the energy method coincide well with the test results.And the higher the temperature is,the earlier the crack is initiated and the larger the crack propagation rate and accelerated velocity are,which can prove the validity of the new electrical method.This new electrical method has advantages of continuously measuring crack propagation rate over the conventional electrical,optical and acoustic methods,and can provide important basis for safety assessment and cracking-arrest design of deep rock mass engineering.

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.

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-AK 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 discussed.

Crack initiation rate of brittle rock under thermal-hydro-mechanical coupling condition

A calculation formula of thermal-hydro-mechanical(THM)coupling crack initiation rate for brittle rock was derived based on the energy conservation law.The self-designed THM coupling fracture test with conductive adhesive electrical measurement method was applied to measuring the THM coupling crack propagation rate of brittle rock continuously.Research results show that both calculation and test results of crack initiation rate increased with increase of the temperature and the hydraulic pressure.They are almost in good agreement,which can prove validity of the calculation formula of THM coupling crack initiation rate.

Influence of welding parameters on fracture toughness and fatigue crack growth rate in friction stir welded nugget of 2024-T351 aluminum alloy joints

Friction stir welding （FSW） was performed on 2024-T351 aluminum alloy plates. Metallographic analysis, Vickers microhardness and XRD tests were conducted to determine the properties of the welded zone. FE simulation of the FSW process was implemented for the different welding conditions to extract the residual stress and stress intensity factor （SIF）. Fracture and fatigue behaviors of the welds which have the initial crack in the nugget zone and the crack orientation along the welding direction, were studied based on standard test methods. Fracture behavior of the welds was also evaluated by shearography method. The results showed that the tool rotational and traverse speeds affect the fracture toughness and fatigue crack growth rate. FSW provides 18%-49% reductions in maximum fracture load and fracture toughness. A slight diminution in fracture toughness of the joints was observed for lower traverse speed of the tool, and at higher traverse or rotational speeds, increasing the probability of defects may contribute to low fracture toughness. Fatigue crack propagation rate of all welds was slower than that of the base metal for low values of stress intensity factor range ΔK （ΔK〈13 MPa·m^1/2）, but is much faster for high values of ΔK.

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.

An Improved Unique Fatigue Crack Growth Rate Curve Model and Determination of the Model Shape Exponents

It is essential to precisely predict the crack growth,especially the near-threshold regime crack growth under different stress ratios,for most engineering structures consume their fatigue lives in this regime under random loading.In this paper,an improved unique curve model is proposed based on the unique curve model,and the determination of the shape exponents of this model is provided.The crack growth rate curves of some materials taken from the literature are evaluated using the improved model,and the results indicate that the improved model can accurately predict the crack growth rate in the nearthreshold and Paris regimes.The improved unique curve model can solve the problems about the shape exponents determination and weak ability around the near-threshold regime meet in the unique curve model.In addition,the shape exponents in the improved model at negative stress ratios are discussed,which can directly adopt that in the unique curve model.

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 firing equation and the p-da/dN-△K 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.

Correlation of crack growth rate and stress ratio for fatigue damage containing very high cycle fatigue regime

A model is proposed to correlate the crack growth rate and stress ratio containing very high cycle fatigue regime.The model is verified by the experimental data in literature.Then a formula is derived for the effect of mean stress on fatigue strength,and it is used to estimate the fatigue strength of a bearing steel in very high cycle fatigue regime at different stress ratios.The estimated results are also compared with those by Goodman formula.

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.

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.

FACTORS AFFECTING FATIGUE CRACK GROWTH RATES OF FIBER REINFORCED METAL LAMINATES

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Effect of Strain Rate on Compression Behavior of Vinyl Ester Resin Casting

Quasi-static and high strain rate compressive experiments on vinyl ester casting were carried out by means of MTS (Material Test System) and Hopkinson bar. The behaviors of the compressed unstable and fracture of the resin casting at different strain rates were investigated.The results indicate that the response behavior of the resin casting is controlled by different mechanisms at different strain rate, and some mechanical properties of vinyl ester casting are rate-dependent: the casting are destroyed in toughness model under strain rate 3.3×10 -4～6.6×10 -3/s, while the casting are destroyed in brittleness model under strain rate 950～5800/s. The yield stress, yield strain energy density are all increased with the increasing strain rates at quasi-static as well as at high strain rates. What is interesting is that the yield strain decreased with the strain rates increasing at quasi-static while increased at high strain rates. It is considered that the casting occurred forcing high elastic deformation at high strain rates. The damage of the specimens is mainly controlled by axial stress before unstable deformation, while mainly controlled by shear stress after unstable deformation, and then developed to fracture finally. This progress is rate-dependent: the development of the cracks inside the castings increased with the strain rate increasing.

Effect of corrosive environment on fatigue property and crack propagation behavior of Al 2024 friction stir weld

In this investigation, 2024 aluminium alloy plates were friction stir welded, a sequence of experiments was performedincluding fatigue and crack propagation tests in air, under pre-corrosion and in a 3.5% NaCl solution, in combination withfractography analyses of near-threshold region, Paris region and finial fracture region with the aid of scanning electron microscopy（SEM）. Results showed that the corrosive environment caused a dramatical decrease in fatigue lives of FS welds, the corrosionfatigue lives of FS welds were almost a half of those of the as-welded specimens. The crack growth rates in FS welds were higherthan their counterparts in base materials, under the corrosive environment, the crack growth rate differences between base materialsand FS welds become increasingly apparent with the increase of stress intensity factor range ΔK, but the pre-corrosion process hadlittle effect on the FS welds’ crack propagation behavior except for shortening the crack initiation lives greatly.

A GENERAL CONSTITUTIVE RELATION FOR FATIGUE CRACK GROWTH ANALYSIS OF METAL STRUCTURES

Crack growth rate curves are the fundamental material property for metal structures under fatigue loading. Although there are many crack growth rate curves available in the literature, few of them showed the capability to explain various special phenomena observed in tests. A modified constitutive relation recently proposed by McEvily and his co-workers showed very promising capability. This modified constitutive relation is further generalized by (1) introducing an unstable fracture condition; (2) defining a virtual strength to replace the yield stress; and (3) defining an overload and underload parameter. The performances of this general constitutive relation for fatigue crack growth is extensively studied and it is found that this general constitutive relation is able to explain various phenomena observed with particular strong capability on load sequence effect.

Analysis Approach to Durability Based on Material Initial Fatigue Quality and S-N Curve

Based on probabilistic fracture mechanics approach, a new concept of material initial fatigue quality （MIFQ） is developed. Then, the relation between S-N curve and crack propagation curve is studied. From the study, a new durability analysis method is presented. In this method, S-N curve is used to determine crack growth rate under constant amplitude loading and evaluate the effects of different factors on durability and then the structural durability is analyzed. The tests and analyses indicate that this method has lower dependence on testing, and higher accuracy, reliability and generality and is convenient for application.

Mechanical properties and microstructure of an α+β titanium alloy with high strength and fracture toughness

The Ti-Al-Sn-Zr-Cr-Mo-V-Si （Ti-62A） alloy, an alpha-beta alloy with high strength and fracture toughness, is currently used as an advanced structural material in aerospace and non-aerospace applications. Thermo-mechanical processes can be used to optimize the relationship between its strength and fracture toughness. A Ti-62A alloy bar can be machined through a transus β-forged plus α＋β solution treated and aged specimen with a lamellar alpha microstructure. The effects of heat treatment on the mechanical properties were discussed. Heat treatment provided a practical balance of strength, fracture toughness, and fatigue crack growth resistance. A comparison of the Ti-62A alloy with the Ti-62222S alloy under the same thermo-mechanical processing conditions showed that their properties are at the same level.