A Strain-Based Fatigue Reliability Analysis Method

1995 ◽  
Vol 117 (2A) ◽  
pp. 229-234 ◽  
Author(s):  
J. D. Baldwin ◽  
J. G. Thacker
Keyword(s):  
Laboratory Data ◽  
Strain Analysis ◽  
Strain Range ◽  
Distribution Model ◽  
Fatigue Reliability ◽  
Gaussian Random Process ◽  
Rainflow Cycle Counting ◽  
Number Of Cycles ◽  
Cycles To Failure ◽  
Notched Components

A new fatigue reliability technique has been developed using a strain-based analysis. A probabilistic strain-life curve, where the variability in cycles to failure at constant strain range has been modeled with a three-parameter Weibull distribution, has been incorporated into the strain-based fatigue analysis. This formulation, which includes a notch strain analysis, rainflow cycle counting and damage accumulation according to Miner’s rule, is used to estimate fatigue life to crack initiation for notched components using smooth specimen laboratory data. Unlike other probabilistic fatigue models, the technique developed here does not include a distribution model for stress peaks such as the commonly-used stationary narrow band Gaussian random process assumption but rather uses strain histories directly. Using this model, techniques have been developed to estimate the number of cycles to failure at a specified reliability and to predict the reliability and failure rate at a specified time in the analysis.

Isothermal Fatigue of 62Sn–36Pb–2Ag Solder

1991 ◽  
Vol 226 ◽  
Author(s):  
Semyon Vaynhan ◽  
Morris E. Fine
Keyword(s):  
Fatigue Life ◽  
Hold Time ◽  
Strain Range ◽  
Effect Of Temperature ◽  
Total Strain Range ◽  
Isothermal Fatigue ◽  
Tensile Hold ◽  
Number Of Cycles ◽  
Cycles To Failure ◽  
Compressive Hold

AbstractThis paper discusses the effects of the most important variables during isothermal fatigue such as strain range, ramp time, tensile and compressive hold times, and temperature on fatigue life of near–eutectic 62Sn–36Pb–2Ag solder at strain ranges below 3.0%. The Coffin-Manson relation does not hold for 62Sn–36Pb–2Ag solder below 1% strain range. Decreasing frequency below 10-2 in no-hold tests reduces the number of cycles to failure. Tensile hold time or compressive hold time alone in the cycle dramatically reduce the number of cycles to failure. Increase of hold time over a few minutes leads to saturation of Nf. Combined tensile and compressive hold times affect the fatigue life of this solder less than either tensile or compressive hold alone. The effect of hold times on fatigue life is much stronger than the effect of ramp time. Practically no ramp time effect was observed in tests with tensile hold times. Very little effect of temperature over the range 25 to 80°C on fatigue life of 62Sn–36Pb–2Ag solder was observed when tested at total strain range of 1%.

Effect of Composition and Microstructure on the Low Cycle Fatigue Strength of Structural Steels

1965 ◽  
Vol 87 (2) ◽  
pp. 269-274 ◽  
Author(s):  
R. D. Stout ◽  
A. W. Pense
Keyword(s):  
Low Cycle Fatigue ◽  
Strain Range ◽  
Structural Steels ◽  
Cycle Life ◽  
Total Strain ◽  
Cycle Fatigue ◽  
Fatigue Data ◽  
Number Of Cycles ◽  
Relationship Of ◽  
Cycles To Failure

In a number of studies of data obtained from fatigue tests on various materials it has been shown that the number of cycles to failure is related to the strain range by a relationship of the form εNm=c where N is the number of cycles to failure, ε the strain range, and m and c are constants. In the low cycle portion of the strain range versus cycles to failure curve, evidence has been presented by several investigators to show that the relationship should be εpN1/2=c where εp is the plastic strain range and c, the constant, can be related to tensile ductility. Some investigators have found the relation εtNm=c more useful. Here εt is the total strain range. As a result of a series of Pressure Vessel Research Committee investigations at Lehigh University, a large body of low cycle fatigue data has been obtained for a wide range of steels, microstructures, heat-treatments, and testing conditions. A study of these data has been undertaken, with special emphasis on the suitability of a relationship of this type for analysis and representation of fatigue data. As a result of this study the following conclusions have been drawn: (a) In the range of 5000 to 100,000 cycles a relation εtNm = c appears to be satisfactory. (b) Using this latter relation, an analysis of the low cycle fatigue behavior of structural steels reveals that they can be classified into three broad groups on the basis of their composition. Each group has a characteristic value of m and c which can be used to predict their behavior over the range 5000–100,000 cycles. (c) The value of m and the total strain for 5000 cycle life can be related to n, the strain hardening exponent, for the steels. The total strain for 100,000 cycle life is related to the ultimate tensile strength of the steels. Using these relationships, the fatigue curve for a structural steel can be estimated from tension test data. (d) The effect of microstructural variations for a steel within any one of the three groups was of secondary importance when compared to the compositional groupings, although some systematic effects of microstructural variations were noted.

An experimental linear cumulative-damage law

1970 ◽  
Vol 5 (3) ◽  
pp. 177-184 ◽  
Author(s):  
K J Miller
Keyword(s):  
Strain Rate ◽  
Room Temperature ◽  
Constant Strain Rate ◽  
Strain Range ◽  
Cumulative Damage ◽  
Damage Law ◽  
Load Sequence ◽  
Number Of Cycles ◽  
Definition Of ◽  
Cycles To Failure

An hypothesis of cumulative damage is presented that may be expressed mathematically as Σn÷Nf = constant where n is the number of cycles performed at a constant strain range and strain rate and Nf is the number of cycles to failure at the same strain range and strain rate. An initial experimental investigation at room temperature shows that, under constant strain-rate conditions, the load-sequence effect is removed, but the value of the constant is dependent on the definition of failure. If failure is defined as complete rupture the summation term is less than unity whatever the sequence of loading. Should failure be defined as the termination of the steady-state period, that is at the point of crack growth instability, then the summation term is greater than unity. This latter definition therefore leads to a linear law of cumulative damage that gives a doubly cautious prediction of life that is of obvious advantage to engineers.

Life Prediction of Notched Components

1995 ◽  
Vol 117 (1) ◽  
pp. 50-55 ◽  
Author(s):  
M. Giglio ◽  
L. Vergani
Keyword(s):  
Strain Energy ◽  
Fem Analysis ◽  
Fatigue Tests ◽  
Pressure Vessel Steel ◽  
Total Strain Energy ◽  
Vessel Steel ◽  
Number Of Cycles ◽  
Experimental Values ◽  
Cycles To Failure ◽  
Notched Components

In this study, keyhole and smooth specimens, made from a low alloy pressure vessel steel (ASTM A-533 grade B), were subjected to monoaxial fatigue tests. The results show the influence of the stress concentration factor, Kt, on the number of cycles to failure, Nf. Total strain energy per cycle, ΔWt = ΔWp + ΔWe, was proved to be a good parameter for predicting the life of notched components. Elasto-plastic FEM analysis, utilizing the cyclic and monotonic curve of the material, showed close agreement with the experimental values.

A Method for Investigating Multi-Axial Fatigue in a PWR Environment

2021 ◽  
Author(s):  
Peter Gill ◽  
Paul Onwuarolu ◽  
Russell Smith ◽  
Ben Coult ◽  
Mark Kirkham ◽  
...  
Keyword(s):  
Fatigue Testing ◽  
Strain Range ◽  
Test Method ◽  
Image Correlation ◽  
Von Mises Stress ◽  
304L Stainless Steel ◽  
Element Analysis ◽  
Uniaxial Test ◽  
Number Of Cycles ◽  
Cycles To Failure

Abstract A significant amount of fatigue testing has taken place over the years to generate relationships between applied stress or strain range and cycles to failure. This has mainly been conducted on uniaxial test specimens in an air environment. More recently, fatigue testing has been conducted in a PWR environment as it is now well known that this has a deleterious impact on life. The test method presented in this paper considers bi-axial loading on a specimen that is compatible with PWR fatigue testing rigs. In order to achieve this, a specimen was designed to convert a uniaxial load into a biaxial load with no internal mechanism. Finite Element Analysis (FEA) was conducted to develop and refine the design, which accounted for frictional contact and bolt up stresses. Initial testing was conducted on a 304L stainless steel specimen in a room temperature air environment. Digital Image Correlation (DIC) was used to validate the FEA and there was excellent agreement between predicted and observed strains. Once the strains were validated, a fatigue test was conducted to confirm that cracking was in the expected location, and that the number of cycles to failure was reasonable. Direct Current Potential Drop (DCPD) was used to indicate when a fatigue crack initiated, which was confirmed by visual inspection. The results showed that cracking occurred in the location of highest accumulated plastic strain and Von Mises Stress, and the number of cycles to failure was slightly lower than predicted but still within scatter.

Fatigue Life of the Human Teeth: A Continuum Damage Approach

2019 ◽  
Vol 43 ◽  
pp. 1-19
Author(s):  
Theddeus Tochukwu Akano
Keyword(s):  
Fatigue Life ◽  
Damage Mechanics ◽  
Stress Amplitude ◽  
Continuum Damage Mechanics ◽  
Continuum Damage ◽  
Elastoplastic Model ◽  
Human Teeth ◽  
Proposed Model ◽  
Number Of Cycles ◽  
Cycles To Failure

Normal oral food ingestion processes such as mastication would not have been possible without the teeth. The human teeth are subjected to many cyclic loadings per day. This, in turn, exerts forces on the teeth just like an engineering material undergoing the same cyclic loading. Over a period, there will be the creation of microcracks on the teeth that might not be visible ab initio. The constant formation of these microcracks weakens the teeth structure and foundation that result in its fracture. Therefore, the need to predict the fatigue life for human teeth is essential. In this paper, a continuum damage mechanics (CDM) based model is employed to evaluate the fatigue life of the human teeth. The material characteristic of the teeth is captured within the framework of the elastoplastic model. By applying the damage evolution equivalence, a mathematical formula is developed that describes the fatigue life in terms of the stress amplitude. Existing experimental data served as a guide as to the completeness of the proposed model. Results as a function of age and tubule orientation are presented. The outcomes produced by the current study have substantial agreement with the experimental results when plotted on the same axes. There is a notable difference in the number of cycles to failure as the tubule orientation increases. It is also revealed that the developed model could forecast for any tubule orientation and be adopted for both young and old teeth.

Unification proposals for fatigue crack propagation laws

2017 ◽  
Vol 13 (2) ◽  
pp. 262-283 ◽  
Author(s):  
Vladimir Kobelev
Keyword(s):  
Differential Equation ◽  
Crack Propagation ◽  
Crack Length ◽  
Closed Form ◽  
Crack Growth ◽  
Stress Ratio ◽  
Elementary Functions ◽  
Content Type ◽  
Number Of Cycles ◽  
Cycles To Failure

Purpose The purpose of this paper is to propose the new dependences of cycles to failure for a given initial crack length upon the stress amplitude in the linear fracture approach. The anticipated unified propagation function describes the infinitesimal crack-length growths per increasing number of load cycles, supposing that the load ratio remains constant over the load history. Two unification functions with different number of fitting parameters are proposed. On one hand, the closed-form analytical solutions facilitate the universal fitting of the constants of the fatigue law over all stages of fatigue. On the other hand, the closed-form solution eases the application of the fatigue law, because the solution of nonlinear differential equation turns out to be dispensable. The main advantage of the proposed functions is the possibility of having closed-form analytical solutions for the unified crack growth law. Moreover, the mean stress dependence is the immediate consequence of the proposed law. The corresponding formulas for crack length over the number of cycles are derived. Design/methodology/approach In this paper, the method of representation of crack propagation functions through appropriate elementary functions is employed. The choice of the elementary functions is motivated by the phenomenological data and covers a broad region of possible parameters. With the introduced crack propagation functions, differential equations describing the crack propagation are solved rigorously. Findings The resulting closed-form solutions allow the evaluation of crack propagation histories on one hand, and the effects of stress ratio on crack propagation on the other hand. The explicit formulas for crack length over the number of cycles are derived. Research limitations/implications In this paper, linear fracture mechanics approach is assumed. Practical implications Shortening of evaluation time for fatigue crack growth. Simplification of the computer codes due to the elimination of solution of differential equation. Standardization of experiments for crack growth. Originality/value This paper introduces the closed-form analytical expression for crack length over number of cycles. The new function that expresses the damage growth per cycle is also introduced. This function allows closed-form analytical solution for crack length. The solution expresses the number of cycles to failure as the function of the initial size of the crack and eliminates the solution of the nonlinear ordinary differential equation of the first order. The different common expressions, which account for the influence of the stress ratio, are immediately applicable.

Lifetime estimation for a land-fast ice sheet subjected to ocean swell

2001 ◽  
Vol 33 ◽  
pp. 333-338 ◽  
Author(s):  
P. J. Langhorne ◽  
V. A. Squire ◽  
C. Fox ◽  
T. G. Haskell
Keyword(s):  
Sea Ice ◽  
Strain Field ◽  
Field Experiments ◽  
Ice Sheet ◽  
Lifetime Estimation ◽  
Spectral Content ◽  
Fast Ice ◽  
Damage Law ◽  
Number Of Cycles ◽  
Cycles To Failure

AbstractIt is well known that an incoming ocean swell produces a strain field in a land-fast ice sheet. The attenuation and spectral content of this strain field can be calculated and has been measured. The response of the sea ice to this type of cyclic forcing has also been measured, and in particular we are able to estimate the number of cycles to failure for sea ice loaded at constant amplitude. In this paper we consider the response of the land-fast ice sheet or vast floe to a measured ice-coupled wave field of variable amplitude. We use the Palmgren-Miner cumulative damage law and stress-lifetime curves taken from field experiments to predict the lifetime of the sea-ice sheet as a function of significant wave height and sea-ice brine fraction. Calculations are performed to account for the swell entering a land-fast sea-ice sheet at arbitrary angle, and the influence of c-axis alignment and the presence of pre-existing cracks are discussed.

Mechanical Fatigue Limit for Rubber

1966 ◽  
Vol 39 (2) ◽  
pp. 348-364 ◽  
Author(s):  
G. J. Lake ◽  
P. B. Lindley
Keyword(s):  
Fatigue Limit ◽  
Growth Behavior ◽  
Energy Characteristics ◽  
Mechanical Fatigue ◽  
Tearing Energy ◽  
Number Of Cycles ◽  
Cycles To Failure ◽  
Limiting Value ◽  
Mechanical Rupture

Abstract Investigations of the dynamic cut growth behavior of vulcanized rubbers indicate that there is a minimum tearing energy at which mechanical rupture of chains occurs. The limiting value is characteristic of each vulcanizate, but is in the region of 0.05 kg/cm. The mechanical fatigue limit, below which the number of cycles to failure increases rapidly, is accurately predicted from this critical tearing energy. Characteristics of cut growth at low tearing energies, and effects of polymer, vulcanizing system, oxygen, and fillers on the critical tearing energy and fatigue limit are discussed.

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