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 diffi...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.展开更多
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 f...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.展开更多
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 r...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.展开更多
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 f...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.展开更多
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 sim...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.展开更多
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 tha...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.展开更多
—The Monte-Carlo method is used to simulate the surface fatigue crack growth rate foroffshore structural steel E36-Z35,and to determine the distributions and relevance of the parameters in theParis equation.By this m...—The Monte-Carlo method is used to simulate the surface fatigue crack growth rate foroffshore structural steel E36-Z35,and to determine the distributions and relevance of the parameters in theParis equation.By this method,the time and cost of fatigue crack propagation testing can be reduced.Theapplication of the method is demonstrated by use of four sets of fatigue crack propagation data foroffshore structural steel E36-Z35.A comparison of the test data with the theoretical prediction for surfacecrack growth rate shows the application of the simulation method to the fatigue crack propagation tests issuccessful.展开更多
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...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.展开更多
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 o...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.展开更多
Based upon an analytical model for predicting the crack growth in fiber reinforced metal laminates (FRMLs), some factors affecting the fatigue crack growth rates of FRMLs were analyzed, including the lay up of FRMLs,...Based upon an analytical model for predicting the crack growth in fiber reinforced metal laminates (FRMLs), some factors affecting the fatigue crack growth rates of FRMLs were analyzed, including the lay up of FRMLs, the modulus of the fibers, the residu展开更多
Based on the investigated microstructure of different zones in the annealed automatic gas tungsten arc weld joint of TA16 and TC4 titanium alloys,the mechanical property of them was assessed under fatigue crack growth...Based on the investigated microstructure of different zones in the annealed automatic gas tungsten arc weld joint of TA16 and TC4 titanium alloys,the mechanical property of them was assessed under fatigue crack growth rate tests.For evaluation of fatigue crack growth rate,three points bending specimens were used.The correlation between the range of stress intensity factor and crack growth rate was determined in different zones of the annealed weld joint.Fatigue crack growth rates were obviously different in different zones of weld joint of dissimilar titanium alloys,due to their different microstructures.Scanning electron microscope examinations were conducted on the fracture surface in order to determine the relevant fracture mechanisms and crack growth mechanisms with respect to the details of microstructure.展开更多
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 capabilit...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.展开更多
The fatigue crack growth rate (CGR) of ultra high strength steel 30CrMnSiNi2A in distilledwater at 18,35 and 55℃ were measured.It was confirmed that the temperature is strongly af-fected on the corrosion fatigue CGR ...The fatigue crack growth rate (CGR) of ultra high strength steel 30CrMnSiNi2A in distilledwater 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 theeffects of Δ K and temperature on the CGR was proposed.The fact that the apparentactivation energy (36.6 kJ/mol) resulted from regressive analysis of CGR data was similarto the activation energy of hydrogen diffusion in γ-Fe,strongly supporting the theory ofhydrogen-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 phenomenonmight be due to the increase of the SCC component of CGR after an overload.展开更多
The creep crack growth（CCG）and the time to carck initiation and rupture of specimen(t<sub>rc</sub>and t<sub>r</sub>)were measured by means of electrical potential method on single edge notche...The creep crack growth（CCG）and the time to carck initiation and rupture of specimen(t<sub>rc</sub>and t<sub>r</sub>)were measured by means of electrical potential method on single edge notchedspecimens at 700℃.The field near the crack tip under steady-state creep was represented byenergy rate integral（C<sup>*</sup>）,and the CCG rate as a function of C<sup>*</sup> has been obtained.Theagreement between the predicted and observed t<sub>rc</sub>values is quite good.It was found that theaddition of small amount of Mg and Zr in the alloys causes t<sub>rc</sub>and t<sub>r</sub> of the specimens to in-crease significantly.展开更多
Alloy 718 is a precipitation strengthened nickel-based superalloy based on the precipitation of γ″-Ni3Nb (DO22 structure) and γ′-Ni3(Al,Ti) (L12 structure) phases. Creep crack growth rate (CCGR) was investigated a...Alloy 718 is a precipitation strengthened nickel-based superalloy based on the precipitation of γ″-Ni3Nb (DO22 structure) and γ′-Ni3(Al,Ti) (L12 structure) phases. Creep crack growth rate (CCGR) was investigated after high temperature exposure at 593, 650 and 677℃ for 2000h in Alloy 718. In addition to the coalescence of γ′/ γ″ and the amount increasing of δ phase, the existence of a bcc chromium enriched α-Cr phase was observed by SEM, and the weight fraction of α-Cr and other phases were determined by chemical phase analysis methods. The CCGR behavior and regulation have been analyzed by means of strength and structure analysis approaches. The experimental results show higher the exposure temperature and longer the exposure time, lower the CCGR. This is probably attributed to the interaction of material softening and brittling due to complex structure changes during high temperature exposure. Therefore, despite α-Cr phase formation and amount enhancement were run in this test range. It seems to us a small amount of α-Cr will be not harmful for creep crack propagation resistance, which is critical for disk application in aircraft and land-based gas turbine.展开更多
基金Supported by Sichuan Provincial Science and Technology Program(Grant No.2022YFH0075)Opening Project of State Key Laboratory of Performance Monitoring and Protecting of Rail Transit Infrastructure(Grant No.HJGZ2021113)Independent Research Project of State Key Laboratory of Traction Power(Grant No.2022TPL_T03).
文摘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.
基金Project supported by the National Natural Science Foundation of China (Nos.50375130and50323003), the Special Foundation of National Excellent Ph.D.Thesis (No.200234) and thePlanned Itemforthe Outstanding Young Teachers ofMinistry ofEducationofChina (No.2101)
文摘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.
基金Project(2005CB623700) supported by the National Basic Research Program of China
文摘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.
基金国家自然科学基金，Special Foundation of National Excellent Ph.D.Thesis，Outstanding Young Teachers of Ministry of Education of China
文摘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.
基金the supports from the Research Foundation for Visiting Scholars of Key Laboratory of Solid Mechanics and FML of Education Ministry,P R Chinathe supports from Japan Society for Promotion of Science
文摘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.
文摘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.
文摘—The Monte-Carlo method is used to simulate the surface fatigue crack growth rate foroffshore structural steel E36-Z35,and to determine the distributions and relevance of the parameters in theParis equation.By this method,the time and cost of fatigue crack propagation testing can be reduced.Theapplication of the method is demonstrated by use of four sets of fatigue crack propagation data foroffshore structural steel E36-Z35.A comparison of the test data with the theoretical prediction for surfacecrack growth rate shows the application of the simulation method to the fatigue crack propagation tests issuccessful.
基金Supported by the National Natural Science Foundation of China(No.51175072 and No.51335003)the Research Fund for the Doctoral Program of Higher Education of China(No.20110042130003)
文摘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.
基金supported by the National Natural Science Foundation of China(11172304 and 11021262)the National Basic Research Program of China (2012CB937500)
文摘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.
文摘Based upon an analytical model for predicting the crack growth in fiber reinforced metal laminates (FRMLs), some factors affecting the fatigue crack growth rates of FRMLs were analyzed, including the lay up of FRMLs, the modulus of the fibers, the residu
基金Funded in Part by the Grant from Technology and Industry for National Defense,China(No.AXXD1818)。
文摘Based on the investigated microstructure of different zones in the annealed automatic gas tungsten arc weld joint of TA16 and TC4 titanium alloys,the mechanical property of them was assessed under fatigue crack growth rate tests.For evaluation of fatigue crack growth rate,three points bending specimens were used.The correlation between the range of stress intensity factor and crack growth rate was determined in different zones of the annealed weld joint.Fatigue crack growth rates were obviously different in different zones of weld joint of dissimilar titanium alloys,due to their different microstructures.Scanning electron microscope examinations were conducted on the fracture surface in order to determine the relevant fracture mechanisms and crack growth mechanisms with respect to the details of microstructure.
文摘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.
文摘The fatigue crack growth rate (CGR) of ultra high strength steel 30CrMnSiNi2A in distilledwater 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 theeffects of Δ K and temperature on the CGR was proposed.The fact that the apparentactivation energy (36.6 kJ/mol) resulted from regressive analysis of CGR data was similarto the activation energy of hydrogen diffusion in γ-Fe,strongly supporting the theory ofhydrogen-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 phenomenonmight be due to the increase of the SCC component of CGR after an overload.
文摘The creep crack growth（CCG）and the time to carck initiation and rupture of specimen(t<sub>rc</sub>and t<sub>r</sub>)were measured by means of electrical potential method on single edge notchedspecimens at 700℃.The field near the crack tip under steady-state creep was represented byenergy rate integral（C<sup>*</sup>）,and the CCG rate as a function of C<sup>*</sup> has been obtained.Theagreement between the predicted and observed t<sub>rc</sub>values is quite good.It was found that theaddition of small amount of Mg and Zr in the alloys causes t<sub>rc</sub>and t<sub>r</sub> of the specimens to in-crease significantly.
基金The authors thank Ladish Co.,Inc.to support the test samples for this analysis.And this work was supported by the National Natural Science Foundation of China(No.50171005)the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE to support it.
文摘Alloy 718 is a precipitation strengthened nickel-based superalloy based on the precipitation of γ″-Ni3Nb (DO22 structure) and γ′-Ni3(Al,Ti) (L12 structure) phases. Creep crack growth rate (CCGR) was investigated after high temperature exposure at 593, 650 and 677℃ for 2000h in Alloy 718. In addition to the coalescence of γ′/ γ″ and the amount increasing of δ phase, the existence of a bcc chromium enriched α-Cr phase was observed by SEM, and the weight fraction of α-Cr and other phases were determined by chemical phase analysis methods. The CCGR behavior and regulation have been analyzed by means of strength and structure analysis approaches. The experimental results show higher the exposure temperature and longer the exposure time, lower the CCGR. This is probably attributed to the interaction of material softening and brittling due to complex structure changes during high temperature exposure. Therefore, despite α-Cr phase formation and amount enhancement were run in this test range. It seems to us a small amount of α-Cr will be not harmful for creep crack propagation resistance, which is critical for disk application in aircraft and land-based gas turbine.
