Fatigue Strength Coefficient Research Articles

High cycle fatigue behavior of 316L stainless steel

Axial fatigue experiments have been conducted employing notched samples of a 316L stainless steel under both constant and variable amplitude loading. A number of samples were subjected to high cycle fatigue (HCF) in the range of ∼144,000–271,000 cycles and subsequent tensile tests, in order to evaluate the change in tensile mechanical properties due to prior fatigue damage. The results obtained have shown that HCF in this range of cycles gives rise to a significant increase in the yield stress of the material, while other mechanical properties determined in tension remain almost constant. It has been determined that the increase in yield stress with the cyclic ratio ( D) is more significant as the maximum stress applied to the material increases. Such a behavior has been described by means of a simple parametric relationship, which could be employed for the practical determination of D in parts and components made of this material, by means of simple tensile testing. A plausible explanation of the increase in yield stress with D, based on the development of the dislocation substructure able to modify such a property, has been proposed. The fractographic analysis that has been conducted on the samples tested in tension after fatigue damage indicates that such a phenomenon also gives rise to the development of fatigue cracks, whose size increases with D. It has been shown that the number of cycles to fracture in two-stress step fatigue tests can be satisfactorily predicted by means of the Palmgren–Miner linear damage cumulative rule. A non-linear numerical procedure has been presented in order to re-compute the fatigue strength coefficient and fatigue exponent of the material, from data obtained under variable amplitude loading conditions, whose values give rise to a satisfactory description of the S–N experimental data. The use of more complex non-linear damage cumulative rules has not given rise to any significant improvement in the number of cycles recorded in the second stress step. It is believed that, due to the significant plastic deformation that occurs at the notch root during fatigue testing, cyclic creep (or ratcheting) damage in addition to fatigue damage could also be present.

Tensile and high cycle fatigue test of copper thin film

AbstractThis paper presents the results of tensile and high cycle fatigue tests for copper thin film. Copper films coated by Sn are often used in various electro devices. Especially, when the film is used in tape carrier package (TCP), the film is repeatedly exposed to mechanical or(and) thermal stresses which results often in the failure of the component. Therefore, to guarantee the reliability of the electrical devices using a film, tensile and fatigue characteristics of the film are important. In this study, to obtain the tensile and fatigue characteristics of the film, the specimen was fabricated by an etching process to make a smooth specimen of 2000 μm width, 8000 μm length and 15.26 μm thickness. The tensile and high cycle fatigue tests were performed with the specimen using the test machine developed by the authors. These specimens had measured values of Young's modulus (72 GPa) and a 0.2 % offset yield and an ultimate strength of 358 MPa and 462 MPa, respectively. A closed‐loop feedback control of the magnetic‐electric actuator allowed load‐controlled fatigue tests with 20 Hz frequency, in ambient environment and at two levels of mean stresses. The fatigue strength coefficient and exponent at 0.5 times of the ultimate tensile strength were 431 MPa and ‐0.0843, respectively. The fatigue strength coefficient and exponent at 0.6 times of the ultimate tensile strength were 371 MPa and ‐0.0923, respectively. The Goodman method is recommended when the fatigue life of thin film with mean stress will be estimated. The fatigue strength coefficient and exponent of copper thin film modified using Goodman method were 910 MPa and ‐0.0896, respectively.

Fatigue Properties of Surface-Micromachined Al-3%Ti Thin Films

This paper describes new structure of specimen easy to manipulate, align and grip a thin-film and test machine for a fatigue test. High cycle fatigue test has been performed on tensile type specimen of Al-3%Ti alloy using the newly developed fatigue test machine. The material used in this study was Al-3%Ti thin film, which was used in RF MEMS switch. The structure of the suggested specimen has two holes and several bridges. The holes at centre of grip end are able to make alignment and gripping easy. The bridges are to remove the side support strip easily and extract specimen from wafer without sawing. The test machine was developed using the voice coil of speaker. The new tensile loading system has a load cell with maximum capacity of 0.5N and a non-contact position measuring system based on the principle of capacitance micrometry with 0.1nm resolution for displacement measurement. Fatigue tests was performed on 7 specimens. The thickness and width of the thin film of specimen are 1.0μm and 150μm, respectively. The fatigue strength coefficient and the fatigue strength exponent of Al-3%Ti alloy micro-sized specimen are determined to be 164MPa and -0.01322, respectively

Torsional Fatigue of 63Sn-37Pb and Sn-0.7Cu Solders

A series of torsional fatigue tests were conducted on 63Sn-37Pb and Sn-0.7Cu solders. A continuous load drop was observed during the test. It was found that the load drop percentage had little effect on the elastic strain-life curve but strong effect on the plastic strain-life curve. The fatigue strength coefficient, fatigue strength exponent and fatigue ductility exponent had no great changes with the load drop. However, fatigue ductility coefficient showed a great difference and was linearly varying with load drop. A fatigue criterion of Coffin-Manson type was proposed in relation to load drop. The descending curve of the stress range with cycle was observed to consist of transient, steady state and tertiary regions. The percentage of load drop corresponding to the turning point from the steady state to the tertiary region was about 25% for all strain ranges of 63Sn-37Pb, and 30% for all strain ranges of Sn-0.7Cu. The torsional fatigue lives were correlated with von Mises equivalent strain amplitudes well. The fatigue behavior of Sn-0.7Cu is better than that of 63Sn-37Pb.

Variation in fatigue properties of cast A359-SiC composites under total strain controlled conditions: Effects of porosity and inclusions

Abstract The effects of casting defects, such as inclusions and porosity on fatigue properties of permanent mold cast bars of A359-20 vol% SiC particle composites cast and heat treated under identical conditions, were studied under total strain control conditions. The fatigue fracture surfaces and the near fracture regions were observed using optical stereo-microscope and scanning electron microscope (SEM) to identify the effects of microstructure and casting defects on fatigue properties of pairs of specimens tested under the same total strain that showed large scatter in fatigue life. It was found that the largest porosity size on the fracture surfaces of the fatigue specimens measured was around 700 μm, whereas the average dendrite arm spacing was 60–100 μm and the size of SiC particle clusters in the near fracture region was around 100 μm. Fracture surfaces of the composite bars showed that fatigue cracks frequently initiated from porosity present near the surface of the samples. Test specimens containing larger porosity size were observed to have lower fatigue life. However, some specimens with larger amounts of inclusions had a lower fatigue life than those with larger porosity size within the range observed in this study. The size and amount of inclusions, and the size and shape of the porosity near the surface seems to have the greatest influence in decreasing fatigue life. Fatigue strength, and fatigue ductility constants for permanent mold cast A359-20 vol% SiC composite were determined from the strain controlled fatigue data. They were as follows: fatigue strength exponent (b) is −0.1145, fatigue strength coefficient ( σ f ′ ) is 558 MPa, fatigue ductility exponent (c) is −0.6066 and fatigue ductility coefficient ( e f ′ ) is 0.0108.

Fatigue life prediction under conditions where cyclic creep–fatigue interaction occurs

A stress-based model is proposed for correlating data and predicting fatigue life under conditions where cyclic creep–fatigue interaction occurs. This model is an extension of the Basquin’s stress–life relation and considers that both the fatigue strength coefficient σ f ′ and fatigue strength exponent b are sensitive to mean stress, both decreasing as an exponential function of the ratio of mean stress-to-stress amplitude. By combining the respective mean-stress functions with the Basquin relation, an equivalent stress–equivalent life relation is derived which is very similar to the original Basquin equation. Thus, the Basquin equation is a particular case of the present model for the case where mean stress is zero. The model depends on a single parameter λ, known as the mean stress sensitivity factor to cyclic loading, and depends on material and probably on test conditions as well. The mean stress sensitivity factor may be determined from experimental data at fixed ratio of mean stress-to-stress amplitude, other than zero, or by trial-and-error method to fit experimental mean-stress data onto the S–N curve due to zero mean stress. The model is tested on published creep–fatigue data of copper, steels and β-Ti-alloy and agreement is found to be very good.

Studies and applications of calculation methods on small crack growth behaviors for elastic-plastic materials

Based on the standpoint to take for the crack size a also to be a damage variable like the damage variable D, by means of the bidirectional combined coordinate system, three kinds of calculating methods with respect to the small crack growth rate and its life of elastic-plastic materials:the singleparameter method, the ratio method and the multiplication method are suggested. A lot of new calculating equations are given. Besides a new concept has also been provided on the compositive material constants A1, B1, A' and A*, which are functional relations with each typic material parameters: the fatigue strength coefficient σ f' , the fatigue strength exponent b1' , the fatigue ductility coefficient e f' , the fatigue ductility exponent c1' , average stress, average strain and critical loading time, etc. In addition, as an example a part of car is calculated, and its calculating results make out some comparisons. The calculating methods have practical significance to avoid unnecessary fatigue tests, to stint times, manpower and capitals, and are convenient for engineering applications in a degree.

Fatigue Test of Al-3%Ti Using Axial Loading Testing Machine for RF MEMS Switch

This paper presents high cycle fatigue properties of a Al-3%Ti thin film, used in a RF (radio-frequency) MEMS switch for a mobile phone. The thickness and width of the thin film of specimen are 1.1μm and 480.0μm, respectively. Tensile tests of five specimens are performed, from which the ultimate strength is found to be 144MPa. High cycle fatigue tests of six specimens are also performed, from which the fatigue strength coefficient and the fatigue strength exponent are found to be 336MPa and –0.1514, respectively.

Studies and Applications of Three Kinds of Calculation Methods by Describing Damage Evolving Behaviors for Elastic-Plastic Materials

By means of bidirectional combined coordinate system, three kinds of calculation methods are proposed with respect to the damage evolving rate and the life of elasticplastic material, which include the singleparameter method, the ratio method and the multiplication-method. In this work a lot of new calculation equations are given; a new concept on the all around material constant is provided, which has functional relations with each of the typical material parameters: the fatigue strength coefficient óf, the fatigue strength exponent b'1, the fatigue ductility coefficient ɛ'f, the fatigue ductility exponent ć1, the average stress, the average strain, critical loading time and so on. In addition, an example of a carpart is given, and some comparisons of calculation results are made. The calculation methods will have practical significance in avoiding the unnecessary fatigue tests, saving time, manpower and capital, as well as providing the convenience for engineering applications in a certain degree.

Fatigue life of 63Sn–37Pb solder related to load drop under uniaxial and torsional loading

The low cycle fatigue behavior of 63Sn–37Pb solder was investigated under strain controlled uniaxial and torsional loading. A continuous load drop was observed during the test. It was found that the load drop percentage had little effect on the elastic strain–life curve but a strong effect on the plastic strain–life curve. The fatigue strength coefficient, fatigue strength exponent and fatigue ductility exponent had no great changes with the amount of load drop. However, the fatigue ductility coefficient showed a great difference and was linearly varying with load drop. A fatigue criterion of Coffin–Manson type was proposed in relation to load drop. The descending curve of the peak stress with cycle was observed to consist of transient, steady state and tertiary regions. The percentage of load drop corresponding to the turning point from the steady state to the tertiary region was about 25% for all strain ranges of uniaxial fatigue and 20–30% for all strain ranges of torsional fatigue. The von Mises stress–strain data under uniaxial and torsional cyclic loading can be fitted by the Ramberg–Osgood relationship. The uniaxial and torsional fatigue lives were correlated with von Mises equivalent strain amplitudes well.

Experimental study on thermal and mechanical behavior of polypropylene, talc/polypropylene and polypropylene/clay nanocomposites

In the present paper, thermal and mechanical behavior of neat polypropylene, 40 wt.% talc-filled polypropylene and 5 wt.% silicate-clay filled polypropylene nanocomposite were tested and evaluated. TGA and DSC results show that filling the talc particle or nano clay into polypropylene can increase the decomposition temperature, but has no effect on glass transition temperature and melt temperature. Tensile results show that 40 wt.% talc particle can increase the modulus, but decrease the yield strength, 5 wt.% nano clay can improve both modulus and yield strength by 90 and 5%, respectively. Fatigue results show that the nanophased polypropylene exhibited the highest fatigue performance, and fatigue strength coefficient, σ f, of nanophased polypropylene was 13.3% higher than that of the neat propyropylene and 50% higher than that of talc-filled polypropylene. At last, a three-parameter non-linear constitutive equation was developed to describe strain rate depend strain softening behavior of three materials.

Application of artificial neural network for predicting strain-life fatigue properties of steels on the basis of tensile tests

The applicability of artificial neural networks (ANN) in predicting the strain-life fatigue properties using tensile material data for 73 steels was investigated by conducting four separate neural networks for individual fatigue properties. The fatigue data of these steels extracted from available literatures were used in the formation of training set of ANN. Results of neural network modelling indicated that fatigue strength coefficient and fatigue ductility (strain) coefficient values, which primarily characterize the curves of the strain amplitude versus life reversals, were predicted with high accuracy of approximately 99 and 98%, respectively. It was concluded that predicted fatigue properties by the trained neural network model seem more reasonable compared to approximate methods, which were formerly suggested based on tensile material data. It is possible to claim that, ANN is fairly promising prediction technique if properly used.

A Study on Poly Butylene Terephthalate Gears Filled with Glass Fibers.

We tested poly butylene telephthalate (PBT) as a gear material in our previous study and found that it had larger fatigue strength and lower coefficient of friction than those of polyacetal used as a gear material currently. In the present study, since plastic gears that can transmit high power have been strongly demanded by the industrial world, we reinforced PBT by compounding grass fibers for higher power transmission than normal PBT and conducted operation tests on gears made of reinforced PBT. Wear behavior was particularly investigated under a relatively larger torque since plastic gears filled with grass fibers were expected to be worn significantly due to a fall of grass fibers from the mother material. Availability of PBT filled with grass fibers for a gear material was discussed by comparing basic operational characteristics with those of normal PBT gears.

An exponential stress function for predicting fatigue strength and life due to mean stresses

An exponential stress function that relates the effect of mean stress on the fatigue strength and life is presented. This stress-based approach is based on the premise that mean stress directly affects the fatigue strength coefficient σ ′ f, of the Basquin stress–life relation. The severity of damage depends on the relative measure of mean stress to the ultimate tensile strength of the material. Thus, the fatigue strength parameter σ ′ f, is a function of the ratio of mean stress to the ultimate tensile strength, i.e. σ ′ f= f( σ m/ σ u). It is shown that a number of previously proposed stress-based damage relations are particular cases of the present approach. The predictive capability of the proposed method is found to be superior to the popular strain-based Smith–Watson–Topper (SWT) approach when tested on some of the published experimental data.

A Generalized Random Variable Approach for Strain-Based Fatigue Reliability Analysis

A new reliability technique for strain-based fatigue life design is developed in this paper. An empirical mean stress modified strain-life equation is used as performance function, in which: material property parameters, as fatigue strength coefficient and fatigue ductility coefficient; and mean stress and applied strain are taken as random variables. A major feature of this work is that, in the performance function, the terms involving material property parameters are combined into one generalized random variable as “capacity,” and the terms involving mean stress and applied strain are combined into another generalized random variable as “demand.” The limit state is then analyzed by using the interference technique to evaluate the reliability under a specified life. Another significant feature is that in order to meet the need of fatigue life design application, for a given cyclic strain history, a numerical method is developed to inversely search the life when certain reliability is specified. Two numerical cases are presented to demonstrate the method. [S0094-9930(00)01202-6]

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

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.

Low cycle fatigue of thin copper foils

The fatigue and monotonic tensile properties of two electrodeposited and one wrought thin foil of copper were measured in a way similar to that used for bulk in order to determine if there is a difference. The graphs of the Basquin equation, which all foils obeyed, of the thin and the bulk wrought copper differed only slightly indicating that the thickness had only a minor effect on the fatigue properties. The order of the magnitudes of the fatigue strength coefficients was the same as that of the tensile strength being larger for the electrodeposited foils. The higher strength of the plated foils was attributed to higher dislocation and twin densities and smaller grains. The fatigue strength coefficients were related to the cyclic hardening exponents. Cyclic hardening, which occurred primarily in the initial stages of fatigue, was a result of dislocation tangle and cell-wall formation when the grain size exceeded 2 μm. No dislocation cell structures were observed when the grain size was smaller than 2 μm.

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

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.

An expression for fatigue life and probability distribution of fatigue strength under repeated torsion

An expression for the fatigue life under repeated torsion (torsion fatigue) is developed and checked by using the test results of metals in the available literature. The shear fatigue strength coefficient, A′, and the theoretical shear fatigue limit, τ ac , in the expression mentioned above are the material constants. The statistical analysis of the data of A′ and τ ac obtained from the regression analysis of test results shows that A′ and τ ac follow the log-normal distribution and that τ ac also follows the normal distribution. Using the expression for the torsion fatigue life developed in this study and the distribution of A′ and τ ac , one can easily obtain the expressions for the torsion fatigue life with given survivability, which are in good agreement with test results. The probability distribution of the shear fatigue strength can also be obtained from the above-mentioned expression and the distribution of A′ and τ ac . It is shown that the shear fatigue strength follows a log-normal distribution in the medium and long-life region. Therefore, the log-normal distribution of the shear fatigue strength can be applied in the fatigue reliability assessment of elements subjected to repeated torsion.

Correlation of cavitation erosion behavior with mechanical properties of metals

Good correlations are presented between material removal rates and cyclic deformation parameters, a strong indication that damage in cavitation erosion is a fatigue process. The predominant property in cavitation erosion resistance is shown to be the fatigue strength coefficient σ f ′ which accounts for most of the differences among materials. Correlations are further improved by incorporating the cyclic strain-hardening exponent n′ in a combined parameter σ f ′ n′. This combined parameter also correlates well with the stacking fault energy, a primary determinant of deformation modes in many of the materials used in past experiments.