Xiulin Zheng

On an unified model for predicting notch strength and fracture toughness of metals

Abstract In the present paper an unified model for predicting the notch strength and the fracture toughness, K IC , is given and checked on the basis of summarizing the recent research. The crack initiation at notch tip may be assumed to occur due to the fracture of the hypothetical material element located at notch root. Hence the crack initiation criterions are developed from the notch strain analysis and the well-known fracture criterions for various kinds of metals. If the fracture of the notched element occurs right after the crack initiation at notch tip without any subcritical crack propagation, the notch strength, i.e. the fracture stress of the notched element will be equal to the stress for crack initiation at notch tip. As a result, the formulae for predicting the notch strength from tensile properties are obtained for various kinds of metals. The formula for predicting the apparent fracture toughness, K 1A , can be also given in the same way. The predicted notch strength of metals agree well with the test results in literature. However, it should be pointed out that the predicted notch strength in plane stress state is the lower limit of the test results. More important may be that a new material constant, the so-called nonsensitivity-to-notch factor, is introduced to evaluate the notch sensitivity, or the notch toughness of metals. It has been pointed out that the crack must be bluntened during loading in order to keep the mechanical equilibrium at crack tip and the radius of the bluntened crack tip must have a critical value. Taking the bluntened crack as a sharp notch and ρ c as the critical radius of the bluntened crack tip, the formula for predicitng the fracture toughness, K IC , from tensile properties is obtained for the ductile metals, based the assumption mentioned above. For the steels with lath Martensite microstructure, ρ c will be equal to the strain hardening exponent in mm, and for steels with mixed Martensite structure ρ c is equal to the uniform elongation in mm, or the Austenite grain size, or 9 times of the dimple size. The difference between the predicted values of K IC and the test results are mostly less than 10. The values of K IC of aluminium alloys can be also predicted by a modified formula and the tensile properties.

A new damage model for ductile materials

Abstract In this paper, based on the irreversible thermodynamics and orthogonal flow rule, a microdamage evolution equation is first formulated, taking advantage of the specific free energy and plastic potential with internal variables. Furthermore, by analogy with the microdamage evolution equation, a macrodamage evolution equation is derived according to the principle of minimum strength. Afterwards, predictions are made for proportional loading and non-proportional loading, and the experimental data available in the relevant literature are used to verify these predictions. It can be concluded that the new damage model can successfully reveal the ductile damage evolution during the plastic deformation process. Thus, it opens the way to predict product quality and material workability for metal forming processes.

A simple formula for fatigue crack propagation and a new method for the determination of ΔKth

Abstract In the present paper test results are given to show that a simple formula for fatigue crack propagation (FCP), the derivation of which is based on the modified static fracture model, can give a good fit to the FCP test results of metals where FCP occurs due to the striation mechanism. Additionally, this simple formula can accurately predict the stress ratio effect on FCP rates. Test results also show that the FCP coefficient can be predicted from Youngs modulus and that the FCP threshold, ΔK th , below or equal to which no FCP occurs, can be directly obtained by extrapolation of the test data. This is a method, believed to be new, which is simple and economical for determining the FCP threshold. Furthermore, the factors which have effect on FCP thresholds are discussed. It is tentatively thought that the FCP threshold depends mainly on the crack closure effect at small stress ratios while other factors will have a greater effect on the FCP threshold as the stress ratio increases.

Fatigue performance of old bridge steel and the procedures for life prediction with given survivability

In the present study, the fatigue life of the steel of an old bridge on the line from Beijing to Shenyang, which was constructed in 1920s and replaced in 1980s, has been experimentally determined by using specimens with the original rivet central holes and the key-hole CT specimens without the damaged surface layer. Procedures are developed to predict the fatigue life of the specimens of the steel of an old bridge under two levels loading. Test results show that the fatigue life determined at the same equivalent stress amplitude follows the usual log-normal distribution, and can be better expressed as a function of the equivalent stress amplitude, which shows the existence of the fatigue threshold. Furthermore, the expressions of the fatigue life for a given survivability are presented. Using these expressions and the procedures proposed in the present study, one can predict the fatigue life of the specimens of old bridge steel under variable amplitude loading. The predicted results show that the fatigue life of old bridge steel specimens follows the log-normal distribution under two-level loading, which is substantiated. Test results and analysis also show that the fatigue performance of the old bridge steel was degenerated due to the surface damage in its long-term operation.

Determination of probability distribution of fatigue strength and expressions of P-S-N curves

Abstract In the present study, new procedures are developed to determine the probability distribution of fatigue strength and the expressions of P-S-N curves. The fatigue test results of 16 Mn steel and the analysis show that the fatigue strength coefficient, the theoretical endurance limit and the fatigue strength at a given life follow the log-normal distribution when the fatigue life follows the log-normal distribution; meantime, the theoretical endurance limit and the fatigue strength follow the normal distribution. The accurate expressions of P-S-N curves can be obtained from the distributions of the fatigue strength coefficient and the theoretical endurance limit in the case that the fatigue life test results follow the log-normal distribution. Also, the dispersion of fatigue life and fatigue strength are discussed. Based on the analysis given in this paper, it may be thought that it is applicable to assume the fatigue strength being a log-normal distribution in engineering applications. However, it may be questionable to assume the standard deviation of fatigue strength being constant. Finally, it should be pointed out that the procedures developed in the present study can be applied in the long life region, where the distribution of fatigue life can not be determined by experiments.

Notch strength of ceramics and statistical analysis

Abstract In the present study, experiments are carried out to measure the notch strength of alumina ceramics. Test results show that the notch strength of ceramics, σ N , follows the normal distribution and the flexible strength of ceramics, σ bb , also follows the normal distribution. Analysis of the test results of the notch strength of ceramics shows that there is a correlation between the mean values of the notch and flexible strength of K t · σ N = σ bb , and the product of the standard deviation of the notch strength, s N and the stress concentration factor, K t , is equal to s f , the standard deviation of the flexible strength, i.e. K t s N = s f . As a result, the probability distribution of the notch strength can be predicted from that of the flexible strength of ceramics tested under identical conditions.

On the expression of fatigue crack initiation life considering the factor of overloading effect

Abstract In the present study attempts are made to give an expression of the fatigue crack initiation life of notched elements with the consideration of overloading effects. This expression may be used to predict the fatigue crack initiation life of notched element under variable amplitude loading. Experimental work on LY12CZ alloy show that the test results of fatigue crack initiation life after tension overloading can be well fitted by the formula developed before for fatigue crack initiation life. Tension overloading increases the fatigue crack initiation threshold but has no effect on the coefficient of the resistance to fatigue crack initiation. The overloading ratio has no markable effect on crack initiation life. The increase of the crack initiation threshold results in the increase of crack initiation life, in particular, in long life range. The same results are also obtained by reanalysing some existing test results of overloading effect on crack initiation life given in literature. Consequently, the expression of the fatigue crack initiation life can be obtained by the method given in this paper. However, the overloading stress should be determined from the theoretical stress concentration factor of notched element and the maximum nominal stress in the load spectrum of elements.

A model for predicting fatigue crack growth behaviour of a low alloy steel at low temperatures

Abstract In the present study, a model to predict the fatigue crack growth (FCG) behaviour at low temperatures is proposed for a low alloy steel (16 Mn). The experimental results indicate that fatigue ductile-brittle transition (FDBT) occurs in 16 Mn steel and the FDBT temperature ( T FDBT ) is about 130 K. When T > T FDBT , the FCG mechanism in the intermediate region is the formation of ductile striation and the FCG rates decrease with decreasing temperature. When T ≈ T FDBT , the FCG mechanism changes into microcleavage and the fatigue fracture toughness K fc of the steel decreases sharply. The FCG rates tend to increase as the temperature is further reduced. The test data of the FCG rates are well fitted by the formula developed by Zheng and Hirt. An approximate method to predict ΔK th of the steel at low temperatures is proposed and then a general expression of the FCG rates is given at temperatures ranging from room temperature to T FDBT . By means of the expressions proposed in this paper, the FCG rates at low temperatures can be predicted from the tensile properties if the endurance limit σ −1 and δk th , at room temperature are known. Finally, a model for FDBT is tentatively proposed. Using this model, one can predict T FDBT from the ductile-brittle transition curve determined from impact or slow bending tests of cracked Charpy specimens.

An energetic approach to predict fatigue crack initiation life of LY12CZ aluminum and 16 Mn steel

Abstract The local strain range is considered to be the main factor controlling the fatigue damage process. An energetic approach is applied to correlate the elastic-plastic stress and strain near a notch with the remotely applied stress. Fatigue crack initiation lives of LYI2CZ aluminum and 16 Mn steel are predicted from a knowledge of the uniaxial data involving parameters such as the elastic modulus, strain hardening strength and strain hardening exponent. These quantities are contained and identified with the fatigue strength coefficient C * which together with the equivalent stress range provide an estimate for the fatigue life of metals. The results agree well with the test data available in the open literature.

Damage characterization of SAE 1020 and 1045 steel under torsion and compression

Abstract A damage model is applied to characterize the ductile deformation of SAE 1020 and 1045 steel. Damage is evaluated for thin-walled cylindrical specimens in torsion and solid bar specimens in compression where stress triaxiality enhances crack initiation. Analyzed are the variations of the damage parameter with the average compressive axial strain at the different locations of the solid bar. Initially, stress triaxiality being largest at the center appeared to dominate damage. With increasing strain, pronounced damage tends to occur in the mid-plane at locations closer to the free surface. Change in the aspect ratio of the cylindrical bar specimens also had an effect on the stress triaxiality and hence the damage parameter. Less damage is prediated for slender bars at the same strain level although the difference is small for height to diameter ratio up to 1.86.