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.

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.

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.

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.

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.

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.

A two-parameter model to predict fatigue life of high-strength steels in a very high cycle fatigue regime

In this paper, ultrasonic （20 kHz） fatigue tests were performed on specimens of a high-strength steel in very high cycle fatigue （VHCF） regime. Experimental results showed that for most tested specimens failed in a VHCF regime, a fatigue crack originated from the interior of specimen with a fish-eye pattern, which contained a fine granular area （FGA） centered by an inclusion as the crack origin. Then, a two-parameter model is proposed to predict the fatigue life of high-strength steels with fish-eye mode failure in a VHCF regime, which takes into account the inclusion size and the FGA size. The model was verified by the data of present experiments and those in the literature. Furthermore, an analytic formula was obtained for estimating the equivalent crack growth rate within the FGA. The results also indicated that the stress intensity factor range at the front of the FGA varies within a small range, which is irrespective of stress amplitude and fatigue life.

CRACK GROWTH BEHAVIOR IN TITANIUM ALLOY TC11 AT ROOM AND HIGH TEMPERATURES

This paper presents some new results of a research on the fatigue crack propagation (FCP) behavior in the titanium alloy TC11. Crack propagation tests were carried out at room temperature by center cracked tension (CCT) specimens under three stress ratios of R=0, 0.5, -1, and at 400 by compact tension (CT) and single edged specimens under stress ratios of R=0.1 and -1, respectively. The crack growth rates were compared by using stress intensity factor and effective stress intensity factor. The results show that the effects of stress ratio and ambient temperature on crack growth rates decreased if they were correlated by using the effective stress intensity factor.

Effects of trace Zr on the microstructure and properties of 2E12 alloy

Al-4.0Cu-1.4Mg-0.6Mn （2E12） and Al-4.0Cu-1.4Mg-0.6Mn-0.3Zr aluminum billets were manufactured by soft-contact electromagnetic continuous casting （EMC）. Subsequent forging and heat treatment were conducted and the effects of Zr on the microstructure and properties of the Al-4.0Cu-1.4Mg-0.6Mn alloy were studied. The results show that the addition of 0.3% Zr can reduce the dendrite and refine grains. During forging and solution treatment, fine and dispersive Al3Zr particles precipitated from the supersaturated α （Al） solid solution in the heating process of the billet can effectively pin dislocations and subgrain boundaries. Because of the addition of Zr, the mechanical properties are improved with the tensile strength, yield strength, elongation, and contraction of the area increasing by 5.4%, 11.3%, 9.7%, and 12.6%, respectively. Moreover, under the condition of R = 0.1, the fatigue crack growth rate （da/dN） of the Al-4.0Cu-1.4Mg-0.6Mn-0.3Zr alloy is lower than that of the Al-4.0Cu-1.4Mg-0.6Mn alloy.

EFFECT OF CATHODIC PROTECTION ON FRACTURE BEHAVIOUR OF LOWALLOY STEELS IN SEAWATER

Fracture behaviour of low-alloy steels AIST4340,HY100,Welten60,AISIA537 and A131 in artificial seawater under static,cyclic loading and at cathodic protection potential has been investigated by using the techniques of fracture mechanics, electrochemistry and electronfractography.The results reveal that at hydrogen evolution potentials(cathodic pro- tection potential)the critical yield strength required for the occurrance of SCC decreases from 985 at corrosion potential(E_c)to 872 MPa.The effect of cathodic protection on crack propagation of corrosion fatigue(CF)is not simple,it is closely related to the yield strength of steels and their SCC behaviour.For the steels with high yield strength,cathodic protection promotes(da/dN)_Ⅱ evidently,and reduces △K_(th) value.The(da/dN)-△K curves dis- play a plateau at the third stage of CF for steels with medium or low yield strength.It is men- tioned that the cathodic protection potential for oceaneering constructures should be control- led at top level of the protective range.It seems reasonable that the strength of steel for oceaneeing use might be increased by 200 or 300 MPa.

Study on the Overload and Dwell-Fatigue Property of Titanium Alloy in Manned Deep Submersible

With the rapid development of ocean technology, the deep-sea manned submersible is regarded as a high-tech equipment for the exploration and exploitation of ocean resources. The safety of manned cabin has a decisive effect on the whole system. Ti-6 Al-4 V with the superior strength-to-weight ratio and corrosion resistance has been used for the manned cabin. The manned cabin experiences loading spectrum with different maximum stresses and different dwell time during their service life. The load sequence effects on dwell fatigue crack growth behavior of Ti-6 Al-4 V under different dwell time are investigated experimentally in this paper. The experimental results show that the crack tip plastic zone is enlarged by the dwell time and the overload retardation zone increases with dwell time under the same overload rate. A dwell fatigue crack growth model is proposed by modifying the crack tip plastic zone under the loading history with combinations of the single overload and dwell time factors are included in the modified model. Based on the experimental data, the overload retardation zone and the crack growth rates of Ti-6 Al-4 V are predicted by the modified model. A reasonable model for the load sequence effect on the dwell fatigue crack growth rates of Ti-6 Al-4 V is verified.

EFFECIS OF TEMPERATURE AND OVERLOAD RETARDATION ON CORROSION FATIGUE CRACK GROWTH OF HIGH STRENGTH STEEL

The fatigue crack growth rate (CGR) of ultra high strength steel 30CrMnSiNi2A in distilled water at 18,35 and 55℃ were measured.It was confirmed that the temperature is strongly af- fected on the corrosion fatigue CGR of ultra high strength steel.An expression concerning the effects of Δ K and temperature on the CGR was proposed.The fact that the apparent activation energy (36.6 kJ/mol) resulted from regressive analysis of CGR data was similar to the activation energy of hydrogen diffusion in γ-Fe,strongly supporting the theory of hydrogen-assisted crack growth.The overload retardation effect was greatly reduced in cor- rosion fatigue crack growth,especially at lower frequency,e.g.,0.1 Hz.This phenomenon might be due to the increase of the SCC component of CGR after an overload.

一种改进的裂纹扩展率单一曲线模型及模型指数确定

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.

Controlling of weld hot cracks of aluminum alloy sheets by transverse pre-stressing

A new ideological and theoretical model—a technology to control weld hot cracks by transverse compressive pre-stress in the welding of aluminum alloy was put forward,which was further proved by the subsequent self-designed test setup.Experiments are conducted on the fishbone shaped specimen under conventional welding and welding with various pre-stress values.The experimental results turn out that,the initiation rate of the weld hot cracks decreases with increasing values of the compressive pre-stress.When the pre-stress reaches 0.3-0.4 of the yield stress,the cracks even disappear.In mechanical viewpoint,the researches here develop a new way to control weld cracks.

Effects of Pitting Corrosion on the Fatigue Behavior of Q235 Steel

In order to analyze the distribution and characterizations of corrosion pits on the corroded surface,the steel surface data was measured. Based on the method of the interacting pits,the types of pits corresponding to different exposure time were observed and categorized for completely understanding the effects on the fatigue behavior. The results showed that the conditions for estimating whether the pits interfere with each other should not be ignored; exposure time with 2 years was a critical time. The exposure time and the interacting pits can observably reduce the fatigue life of corroded steel. From these conclusions,the method of fatigue crack growth rate with the multi-pits interaction(FCGR-MPI) was developed and used to predict the fatigue behavior of corroded steel affected with the interacting pits. The predicted lives were also well agreed with the experimental results.

Effect of electric boundary conditions on crack propagation in ferroelectric ceramics

In this paper, the effect of electric boundary conditions on Mode I crack propagation in ferroelectric ceramics is studied by using both linear and nonlinear piezoelectric fracture mechanics. In linear analysis, impermeable cracks under open circuit and short circuit are analyzed using the Stroh formalism and a rescaling method. It is shown that the energy release rate in short circuit is larger than that in open circuit. In nonlinear analysis, permeable crack conditions are used and the nonlinear effect of domain switching near a crack tip is considered using an energy-based switching criterion proposed by Hwang et al.（Acta Metal. Mater.,1995）. In open circuit, a large depolarization field induced by domain switching makes switching much more diffcult than that in short circuit. Analysis shows that the energy release rate in short circuit is still larger than that in open circuit, and is also larger than the linear result. Consequently,whether using linear or nonlinear fracture analysis, a crack is found easier to propagate in short circuit than in open circuit, which is consistent with the experimental observations of Kounga Njiwa et al.（Eng. Fract. Mech., 2006）.

EFFECT OF Mg AND Zr ADDITION ON CREEP CRACK GROWTH BEHAVIOUR OF A Ni-BASE SUPERALLOY

The creep crack growth(CCG)and the time to carck initiation and rupture of specimen (t_(rc)and t_r)were measured by means of electrical potential method on single edge notched specimens at 700℃.The field near the crack tip under steady-state creep was represented by energy rate integral(C~*),and the CCG rate as a function of C~* has been obtained.The agreement between the predicted and observed t_(rc)values is quite good.It was found that the addition of small amount of Mg and Zr in the alloys causes t_(rc)and t_r of the specimens to in- crease significantly.