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.

scholarly journals Mechanical Fatigue of Bovine Cortical Bone Using Ground Reaction Force Waveforms in Running

2018 ◽  
Vol 140 (3) ◽  
Author(s):  
Lindsay L. Loundagin ◽  
Tannin A. Schmidt ◽  
W. Brent Edwards
Keyword(s):  
Cortical Bone ◽  
Stress Fracture ◽  
Ground Reaction Force ◽  
Fatigue Behavior ◽  
Reaction Force ◽  
High Impact ◽  
Loading Rates ◽  
Mechanical Fatigue ◽  
Number Of Cycles ◽  
Cycles To Failure

Stress fractures are a common overuse injury among runners associated with the mechanical fatigue of bone. Several in vivo biomechanical studies have investigated specific characteristics of the vertical ground reaction force (vGRF) in heel-toe running and have observed an association between increased loading rate during impact and individuals with a history of stress fracture. The purpose of this study was to examine the fatigue behavior of cortical bone using vGRF-like loading profiles, including those that had been decomposed into their respective impact and active phase components. Thirty-eight cylindrical cortical bone samples were extracted from bovine tibiae and femora. Hydrated samples were fatigue tested at room temperature in zero compression under load control using either a raw (n = 10), active (n = 10), low impact (n = 10), or high impact (n = 8) vGRF profile. The number of cycles to failure was quantified and the test was terminated if the sample survived 105 cycles. Fatigue life was significantly greater for both impact groups compared to the active (p < 0.001) and raw (p < 0.001) groups, with all low impact samples and 6 of 8 high impact samples surviving 105 cycles. The mean (± SD) number of cycles to failure for the active and raw groups was 12,133±11,704 and 16,552±29,612, respectively. The results suggest that loading rates associated with the impact phase of a typical vGRF in running have little influence on the mechanical fatigue behavior of bone relative to loading magnitude, warranting further investigation of the mechanism by which increased loading rates are associated with stress fracture.

SnAgCu Micro-Ball Grid Array (BGA) Solder Joint Evaluation Using a Torsion Mechanical Fatigue Test Method

2005 ◽  
Author(s):  
Claire Ryan ◽  
Bryan A. Rodgers ◽  
Jeff M. Punch
Keyword(s):  
Fatigue Test ◽  
Solder Joints ◽  
Fatigue Testing ◽  
Ball Grid Array ◽  
Test Method ◽  
Superior Performance ◽  
Cycle Number ◽  
Mechanical Fatigue ◽  
Number Of Cycles ◽  
Cycles To Failure

Due to the hazard which lead poses to health and the environment the EU is banning its use in electrical and electronic equipment from July 2006. This ban along with the market drive to more environmentally friendly products means that tin-lead solders must be replaced with lead-free alternatives. This paper presents the results of an experimental investigation of the mechanical fatigue properties of tin-silver-copper (SnAgCu) solder joints with a baseline of tin-lead (SnPb). The test vehicle comprised of an 8-layer FR4 printed circuit board (PCB) mounted with four micro-ball grid array (BGA) components — each with a total of 100 solder balls in a 10×10 array. The solder joints were formed using surface mount reflow processes optimised for both solder types. A torsion mechanical fatigue test was employed to evaluate the solder joints — the principle of which was to stress the solder joints repetitively in order to determine the number of cycles to failure. The BGA components were daisy-chained — the resistance across each daisy-chain was monitored continuously during the cyclic defection of the test board. A profile of the increase in resistance with cycle number was established and the number of cycles to failure determined. The failure mechanism induced by the cycling was examined using cross-section and scanning electron microscopy (SEM) techniques. The results for SnAgCu joints show a superior performance during torsion mechanical fatigue testing than SnPb joints; giving a greater number of cycles to failure. The results from the tests presented in this paper show that the torsion test method provides a viable alternative to ATC as a qualification method for solder joints, while also providing substantial time savings — taking weeks rather than months to complete.

Thermo-Mechanical Fatigue Crack Growth Modelling in a Ni-Based Superalloy Subjected to Sustained Load

2015 ◽  
Author(s):  
Erik Storgärds ◽  
Kjell Simonsson ◽  
Sören Sjöström ◽  
Johan Moverare
Keyword(s):  
Crack Growth ◽  
Damage Model ◽  
Maximum Load ◽  
Parameter Determination ◽  
Sustained Load ◽  
Growth Modelling ◽  
Notched Specimen ◽  
Mechanical Fatigue ◽  
Number Of Cycles ◽  
Cycles To Failure

Thermo-mechanical fatigue (TMF) crack growth modelling has been conducted on Inconel 718 with dwell time at maximum load. A history dependent damage model taking dwell damage into account, developed under isothermal conditions, has been extended for TMF conditions. Parameter determination for the model is carried out on isothermal load controlled tests at 550–650°C for surface cracks, which later have been used to extrapolate parameters used for TMF crack growth. Further, validation of the developed model is conducted on a notched specimen subjected to strain control at 50–550°C. Satisfying results are gained within reasonable scatter level compared for test and simulated number of cycles to failure.

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.

Contributions of Time Dependent and Cyclic Crack Growth to the Crack Growth Behavior of Non Strain-Crystallizing Elastomers

2002 ◽  
Vol 75 (4) ◽  
pp. 643-656 ◽  
Author(s):  
J. J. C. Busfield ◽  
K. Tsunoda ◽  
C. K. L. Davies ◽  
A. G. Thomas
Keyword(s):  
Crack Growth ◽  
Growth Behavior ◽  
Time Dependent ◽  
Crack Growth Behavior ◽  
Wide Range ◽  
Dependent Component ◽  
Tearing Energy ◽  
Quasi Crystals ◽  
Crack Growth Rates ◽  
Time Dependent Crack Growth

Abstract Engineering components are observed to fail more rapidly under cyclic loading than under static loading. This reflects features of the underlying crack growth behavior. This behavior is characterized by the relation between the tearing energy, T, and the crack growth per cycle, dc/dn. The increment of crack growth during each cycle is shown here to result from the sum of time dependent and cyclic crack growth components. The time dependent component represents the crack growth behavior that would be present in a conventional constant T crack growth test. Under repeated stressing additional crack growth, termed the cyclic crack growth component, occurs. For a non-crystallizing elastomer, significant effects of frequency have been found on the cyclic crack growth behavior, reflecting the presence of this cyclic element of crack growth. The cyclic crack growth behavior over a wide range of frequencies was investigated for unfilled and swollen SBR materials. The time dependent crack growth component was calculated from constant T crack growth tests and the cyclic contribution derived from comparison with the observed cyclic growth. It is shown that decreasing the frequency or increasing the maximum tearing energy during a cycle results in the cyclic crack growth behavior being dominated by time dependent crack growth. Conversely at high frequency and at low tearing energy, cyclic crack growth is dominated by the cyclic crack growth component. A large effect of frequency on cyclic crack growth behavior was observed for highly swollen SBR. The cyclic crack growth behavior was dominated by the time dependent crack growth component over the entire range of tearing energy and/or crack growth rate. The origin of the cyclic component may be the formation/melting of quasi crystals at the crack tip, which is absent at fast crack growth rates in the unswollen SBR and is absent at all rates in the swollen SBR.

scholarly journals Fatigue Strength Analysis of S34MnV Steel by Accelerated Staircase Test

2020 ◽  
Vol 10 (1) ◽  
pp. 394-400 ◽  
Author(s):  
I. M. W. Ekaputra ◽  
Rando Tungga Dewa ◽  
Gunawan Dwi Haryadi ◽  
Seon Jin Kim
Keyword(s):  
Standard Deviation ◽  
Fatigue Strength ◽  
Fatigue Limit ◽  
Fatigue Testing ◽  
Reliability Estimation ◽  
Test Method ◽  
Strength Analysis ◽  
Staircase Method ◽  
Staircase Test ◽  
Number Of Cycles

AbstractThis paper presents the reliability estimation of fatigue strength of the material used for crank throw components. The material used for crank throw components is forged S34MnV steel and subsequently heat-treated by normalising and tempering. High cycle fatigue testing under fully reversed cycling (R = −1) was performed to determine the fatigue limit of the material. The staircase test method is used to obtain accurate values of the mean fatigue limit stress until a number of cycles up to 1E7 cycles. Subsequently, the fatigue test results depend strongly on the stress step and are evaluated by the Dixon-Mood formula. The values of mean fatigue strength and standard deviation predicted by the staircase method are 282 MPa and 10.6MPa, respectively. Finally, the reliability of the design fatigue strength in some selected probability of failure is calculated. Results indicate that the fatigue strength determined from accelerated staircase test is consistent with conventional fatigue testing. Furthermore, the proposed method can be applied for the determination of fatigue strength and standard deviation for design optimisation of S34MnV steel.

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.

On the Critical Resolved Shear Stress and its Importance in the Fatigue Performance of Steels and other Metals with Different Crystallographic Structures

2022 ◽  
pp. 37-65
Author(s):  
M. Mlikota
Keyword(s):  
Shear Stress ◽  
Fatigue Life ◽  
Fatigue Limit ◽  
High Fatigue ◽  
Steel Aisi ◽  
Crystallographic Structures ◽  
Face Centered ◽  
Set Up ◽  
Number Of Cycles ◽  
Critical Resolved Shear Stress

This study deals with the numerical estimation of the fatigue life represented in the form of strength-life (S-N, or Wöhler) curves of metals with different crystallographic structures, namely body-centered cubic (BCC) and face-centered cubic (FCC). Their life curves are determined by analyzing the initiation of a short crack under the influence of microstructure and subsequent growth of the long crack, respectively. Micro-models containing microstructures of the materials are set up by using the finite element method (FEM) and are applied in combination with the Tanaka-Mura (TM) equation in order to estimate the number of cycles required for the crack initiation. The long crack growth analysis is conducted using the Paris law. The study shows that the crystallographic structure is not the predominant factor that determines the shape and position of the fatigue life curve in the S-N diagram, but it is rather the material parameter known as the critical resolved shear stress (CRSS). Even though it is an FCC material, the investigated austenitic stainless steel AISI 304 shows an untypically high fatigue limit (208 MPa), which is higher than the fatigue limit of the BCC vanadium-based micro-alloyed forging steel AISI 1141 (152 MPa).

The Analysis of Metallic Materials Subjected to Cycles of Thermal and Mechanical Fatigue

2016 ◽  
Vol 700 ◽  
pp. 78-85
Author(s):  
Dragoş Cristian Achiţei ◽  
Petrică Vizureanu ◽  
Mirabela Georgiana Minciună ◽  
Mohd Mustafa Al Bakri Abdullah ◽  
Andrei Victor Sandu
Keyword(s):  
Chemical Composition ◽  
Variable Number ◽  
Al Alloys ◽  
Metallic Materials ◽  
Thermal Mechanical Fatigue ◽  
Testing Installation ◽  
Mechanical Fatigue ◽  
Corrosion Phenomenon ◽  
Micro Cracks ◽  
Number Of Cycles

The paper present theoretical and practical aspects concerning to the phenomena of thermal / mechanical fatigue specific to metallic materials, which are found in the structure of industrial parts, subjected to thermal and mechanical requests, also in combination with the corrosion phenomenon, pressure different etc. The analyzed alloys subjected to thermal and mechanical fatigue requests, on a prototype testing installation, using samples from Cu-Zn-Al alloys, which have been processed at standard dimensions by machining. Function of chemical composition of alloy, after a variable number of cycles it was found the micro-cracks appearance that generates crack and finally the break of samples. The SEM realized at different magnifications, highlight the character of samples break.

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.

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