STATISTICAL INVESTIGATION OF THE EFFECT OF LABORATORY AIR ON THE FATIGUE BEHAVIOUR OF A CARBON STEEL

In order to clarify the effect of the atmospheric conditions on fatigue damage, rotary bending fatigue tests were carried out on smooth specimens of a normalized 0.37% carbon steel in controlled laboratory air. The air conditions used in the tests were moist air at 20 °C, moist air at 35 °C and dry air at 35 °C. The influence of atmosphere on crack initiation and propagation behaviour was investigated in detail based on successive observations of the surface. Experimental results showed that the fatigue life was superior at 20 °C compared to 35 °C by a factor of 2, while the effect of moisture was small compared to that of temperature. The statistical investigation of crack initiation and propagation behaviour indicated that the temperature strongly affects the crack initiation process; conversely, moisture plays an important role in the propagation process of cracks smaller than 0.3  mm. Moreover, the distribution characteristics of crack initiation life, crack propagation life, fatigue life and crack growth rate were analysed by assuming either a Weibull distribution or a log-normal distribution.     

Modeling the brittle–ductile transition in ferritic steels. Part II: analysis of scatter in fracture toughness

A dislocation simulation model has been proposed to predict the brittle–ductile transition in ferritic steels in Part I. Here we extend the model to address the problem of inherent scatter in fracture toughness measurements. We carried out a series of Monte Carlo simulations using distributions of microcracks situated on the plane of a main macrocrack. Detailed statistical analysis of the simulation results showed the following: (a) fracture is initiated at one of the microcracks whose size is at the tail of the size distribution function, and (b) the inherent scatter arises from the distribution in the size of the critical microcrack that initiates the fracture and not from the variation of the location of the critical microcrack. Utilizing the weakest-link theory, Weibull analysis shows good agreement with the Weibull modulus values obtained from fracture toughness measurements.     

STATISTICAL INVESTIGATION OF THE BEHAVIOUR OF SMALL CRACKS AND FATIGUE LIFE IN CARBON STEELS WITH DIFFERENT FERRITE GRAIN SIZES

Abstract— In order to study the relation between the scatter characteristics of small crack growth behaviour and fatigue life, rotatory bending fatigue tests of smooth specimens were carried out using 0.21% carbon steels of different ferrite grain sizes. Fifteen to eighteen specimens were fatigued at each stress amplitude, and the initiation and propagation behaviour of the cracks which led to the final fractures were examined for all the specimens. The physical basis of scatter in fatigue life was investigated, based on the successive observation of fatigue damage on the surface using the plastic replica technique, followed by an analysis of the data assuming a Weibull distribution. A statistical investigation of the physical basis of scatter in relation to the ferrite grain size was performed, i.e. the distributions for crack initiation life, crack propagation life, fatigue life and growth rate of small cracks. Finally, the fluctuation of crack growth rate was studied in relation to the application of a crack growth law for microstructurally small cracks.     

SCATTER CHARACTERISTICS OF FATIGUE LIFE AND THE BEHAVIOUR OF SMALL CRACKS

Usually, there is large scatter in fatigue data and this should be evaluated quantitatively when fatigue data are applied to the design of machines and structures. Consequently it is important to clarify the physical basis of scatter in fatigue life. In this present study, rotary bending fatigue tests were performed on an annealed 0.21% carbon steel. At least sixteen smooth specimens were fatigued at each of three stress ranges and successive observations of the surface were studied for all the specimens using the plastic replica method. By examining the initiation and propagation behaviour of cracks the physical basis of scatter in fatigue life is analysed and discussed. To estimate the scatter characteristics quantitatively, the distributions of crack initiation life, propagation life, fatigue life and crack length were individually studied by assuming a Weibull distribution for each set of data.     

An approach for determining an appropriate assumed distribution of fatigue life under limited data

The case of limited data implies that some unknown uncertainties may be involved in fatigue reliability analysis. For the sake of statistical convenience, for consistency with the relevant physical arguments and, most importantly, to ensure the safety in design evaluation, an approach is developed to determine an appropriate distribution, from four possible assumed distributions—three-parameter Weibull, two-parameter Weibull, lognormal and extreme maximum-value distributions. The approach makes allowance for consistency with the fatigue physics and checking tail fit effects. An application to nine groups of fatigue life data of 16Mn steel (Chinese steel) welded plate specimens shows that the lognormal distribution and the extreme maximum-value distribution may be the appropriate distributions of the fatigue life under limited data.     

SCATTER IN SMALL CRACK PROPAGATION AND FATIGUE BEHAVIOUR IN CARBON STEELS

In order to investigate the physical basis of scatter in fatigue behaviour, rotatory bending of smooth fatigue specimens was carried out using two steels with different microstructures (ferrite/pearlite and tempered martensite). Fifteen or sixteen specimens were fatigued at each stress, and the initiation and propagation behaviour of a crack which led to the final fracture were examined for all the specimens. The emphasis was to investigate the scatter characteristics of fatigue behaviour based on the scatter of small crack propagation data. The data were analysed by assuming the Weibull distribution, and a statistical investigation of the physical basis of scatter was performed, i.e. the distributions for fatigue life, crack propagation life and growth rate of small cracks were established and the relation between the scatter in those distributions was studied.     

A STATISTICAL INVESTIGATION OF THE FATIGUE LIVES OF Q235 STEEL-WELDED JOINTS

An investigation into the fitting of six assumed distributions (three-parameter Weibull, two-parameter Weibull, extreme minimum value, extreme maximum value, normal and lognormal distributions) of 23 groups of fatigue life data for Q235 steel-welded joints is performed in terms of linear regression analyses. The results reveal that the fatigue life distribution shapes mostly tend to be positively skewed. Therefore, the extreme minimum value and normal distributions are not the most appropriate distributions to assume for a fatigue life evaluation. The three-parameter Weibull distribution may give misleading results in fatigue reliability analyses because the shape parameter is often lesss than 1. This means that the hazard rate decreases with fatigue cycling. This is contrary to the general understanding of the behaviour of welded joints. Reliability analyses may also be affected by slightly non-conservative evaluations in tail regions of the three-parameter Weibull distribution. The two-parameter Weibull distribution does not give as good a fit as either the extreme maximum value distribution or the lognormal distribution. On the other hand, the extreme maximum value and lognormal distributions can be safely assumed in reliability analyses due to the good total fit effects and the conservative evaluations in tail regions. In addition, the extreme maximum value distribution is in good agreement with the general physical understanding of the structural behaviour of welded joints.     

Brittle fracture local criterion and radiation embrittlement of reactor pressure vessel steels

The application of local criteria for predicting brittle fracture of reactor pressure vessel steels is discussed with an emphasis on radiation embrittlement. An association of the radiation-induced damages and the processes of initiation and propagation of cleavage microcracks is analyzed from the standpoint of the local criterion for fracture. Physical-mechanical models are put forward to describe the influence of radiation damages on the cleavage microcrack initiation. The influence of the material hardening caused by neutron irradiation and plastic deformation on the fracture toughness is studied.     

FATIGUE MICROCRACKS IN TYPE 304 STAINLESS STEEL AT ELEVATED TEMPERATURE

Microcracking of type 304 stainless steel at 538°C has been studied, in particular, the initiation, growth and coalescence, of fatigue microcracks on smooth specimens via surface replicas and photomicrographs. Quantitative information, such as, initiation period, growth and coalescence behaviour, statistical distributions of crack length, density of cracks, distribution patterns and crack growth properties, were obtained. Knowledge of these parameters is critical for the application of fracture mechanics to fatigue life assessment and the damage evaluation of structures at elevated temperature.     

DETERMINATION OF THE ENERGETIC PARAMETERS CONTROLLING CLEAVAGE FRACTURE INITIATION IN STEELS

Abstract— The process of brittle fracture in steels can be divided into three distinct steps: (1) initiation of a microcrack in a brittle particle, (2) propagation of the microcrack into the surrounding matrix and, finally, (3) crack progression through the matrix. Depending on microstructure, temperature and loading rate, the critical step which controls cleavage fracture is subject to change. In this work the behaviour of different microalloyed steels is considered and the energies γ_pm and γ_mm, which define the stress necessary for the microcrack to surmount steps 2 and 3 have been experimentally determined. While the γ_pm value remains constant around 7 J/m², it has been observed that γ_mm is dependent on temperature. At −196°C the value is lower than 50 J/m² and at room temperature it is higher than 200 J/m². This increase in the matrix-matrix energy with temperature increases the probability of microcracks, generated in particles, arresting at grain boundaries. This is the reason why refinement of grain size has an important effect in improving the fracture toughness at room temperature.     

FATIGUE MICROCRACKS IN A LOW CARBON STEEL

Abstract— The behaviour of a low carbon steel has been studied, in particular the initiation, growth and coalescence of fatigue microcracks on the surfaces of smooth specimens via surface replicas and photomicrographs. From the study, quantitative information on the initiation period, growth and coalescence of cracks, statistical distributions of crack length and crack depth, density of cracks, distribution pattern and characteristics of the major crack, were obtained. Knowledge of these parameters is critical for non-destructive inspection during service life and the application of fracture mechanics to life assessment.     

Fatigue reliability under multiple-amplitude loads

A method to determine the fatigue of structures subjected to multiple-amplitude loads is presented. Unlike the more common cumulative damage methods, which are usually based on fatigue life data, the proposed method is based on tensile strength data. Assuming the Weibull distribution for the initial tensile strength and the fatigue life, the probability distributions for the residual tensile strength in both the crack initiation and the crack propagation stages of fatigue are determined. The method is illustrated for two-amplitude loads by means of experimental results obtained by testing specimens of a structural steel and is shown to be more accurate than the Palmgren-Miner cumulative damage method.     

Numerical analysis of interaction and coalescence of numerous microcracks

The deformation and failure behaviors of brittle or quasi-brittle solids are closely related to interaction and propagation of stochastically distributed microcracks. The influence of microcrack interaction and evolution on the mechanical properties of materials presents a problem of considerable interest, which has been extensively argued but has not been resolved as yet. In the present paper, a novel numerical method is used to calculate the effective elastic moduli and the tensile strength, and to simulate the failure process of brittle specimens containing numerous microcracks. The influences of some crack distribution parameters reflecting the non-uniform spatial concentration, size and orientation distributions are examined. The effective elastic moduli and the tensile strength of brittle materials exhibit different dependences on microcrack interaction. For example, two microcrack distributions that lead to the identical effective elastic moduli may cause a pronounced difference in the tensile strengths and failure behaviors of materials. By introducing two criteria for microcrack growth and coalescence in terms of Griffith’s energy release rate, the above numerical method is extended to simulate the coalescence process of microcracks that results in a fatal crack and the final rupture of a specimen.     

LZ50钢断裂韧度的合理统计模型

试验研究了LZ50车轴钢的断裂韧度的合理统计模型。结果表明,LZ50钢是一种偏脆性的材料,应当严格控制铁道车辆车轴的制造表面质量。同时证实了现有正态分布模型不能合理描述试验数据。为此,通过比较三参数Weibull、两参数Weibull、正态、对数正态、极小值和极大值6种常用统计分布对试验数据的拟合优度、数理一致性和尾部安全性,说明了极小值分布是良好统计模型。建立了断裂韧度的极小值概率测定方法,测定了典型存活概率和置信度下的材料断裂韧度值。     

两种国产涡轮盘材料疲劳寿命概率分布规律初探

基于两种国产发动机轮盘材料GH4133和1Cr11Ni2W2MoV低循环疲劳实验数据,选择三种常用的分布函数(对数正态分布、双参数Weibull分布和三参数Weibull分布),用概率图法和柯尔莫哥洛夫-斯米尔诺夫检验方法进行拟合优度检验,以考察分布函数的总体拟合效果.通过经验失效率的变化趋势来评估分布函数是否符合疲劳失效机制.结果表明:形状参数大于1的三参数Weibull分布函数是建立国产轮盘材料GH4133和1Cr11Ni2W2MoV疲劳寿命分布的理想数学模型.对数正态分布函数在本工作所研究的轮盘材料低循环疲劳寿命范围内是合理的.双参数Weibull分布函数用作国产轮盘材料疲劳寿命分布模型时必须进行假设检验.     

On fatigue reliability under random loads

We consider the problem of estimating the probability of survival (non-failure) and the probability of safe operation (strength greater than a limiting value) of structures subjected to random loads. These probabilities are formulated in terms of the probability distributions of the loads and the material strength. For the material strength, the Weibull distribution is assumed, the parameters of which are estimated by a statistical analysis of the experimental tensile strength of steel specimens subjected to different periods of random loads. The statistical analysis shows that, with the application of random loads, the initial homogeneous distribution of strength changes to a two-component distribution, reflecting the two-stage fatigue damage. In the crack initiation stage, the strength increases initially and then decreases, while an abrupt decrease of strength is seen in the crack propagation stage. The consequences of this behaviour on the fatigue reliability are discussed.     

FATIGUE LIFE DISTRIBUTION AND GROWTH OF CORROSION PITS IN A MEDIUM CARBON STEEL IN 3%NaCl SOLUTION

Abstract— Statistical fatigue tests have been conducted on a structural medium carbon steel, S45C, in room air and in 3%NaCl solution, using five cantilever-type rotary bending fatigue testing machines which were specially manufactured for the purpose of the present study. Fatigue life distribution was examined at three and five stress levels in air and in 3%NaCl solution, respectively, and twenty specimens were allocated to each stress level. In room air, it was found that fatigue life distributions followed the three-parameter Weibull distribution, which were closely related to fracture morphology. In 3%NaCl solution, they also followed the Weibull distribution, but the scatter in fatigue life was smaller in comparison to that in air. It is suggested that the decrease in the scatter of fatigue life may be attributed to a smaller fraction of crack initiation life in 3%NaCl solution. The growth of corrosion pits was investigated using a laser microscope. The distribution of corrosion pit depths followed the log-normal distribution, and the corrosion pit depths increased with increasing time or the number of cycles. It was found that the growth of corrosion pits was accelerated by stress cycling and the depths increased with increasing stress level. Based on these results, a growth law of corrosion pits, including the effect of stress cycling, is proposed.     

Three-parameter vs. two-parameter Weibull distribution for pultruded composite material properties

The three-parameter and two-parameter Weibull distributions are compared using 26 mechanical property data sets of fiber-reinforced polymeric (FRP) composite materials manufactured by the pultrusion process. Both strength and stiffness properties were examined. The probability distributions were compared on the basis of goodness of fit, nominal design values, and allowable load to achieve uniform reliability. It is recommended that the two-parameter Weibull distribution be used to characterize FRP composite material properties. The primary basis for this recommendation is small differences in nominal design values and small differences in allowable loads between the two-parameter and three-parameter Weibull distributions. Other supporting reasons for the recommendation are similar observed significance levels in distribution fitting, computational efficiency, and the fact that the location parameter of the three-parameter Weibull distribution is near the first order statistic.     

Estimation of Parameters in Compound Weibull Distributions

The two-parameter Weibull distribution has been recognized as a useful model for survival populations associated with reliability studies and life testing experiments. In the analysis of atmospheric data, the distributions encountered are often a result of combining two or more component distributions. These compound distributions are consequently of interest to aerospace scientists. Presented is a method for estimation of the parameters of a compound Weibull distribution with two shape parameters, two scale parameters and a proportionality factor.