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INTRODUCCIÓN

Muchos de los elementos de máquinas, tales como cigüeñales, árboles, ejes, bielas yresortes, son sometidos a cargas variables. El comportamiento de los materiales bajo estetipo de carga es diferente a aquel bajo cargas estáticas; mientras que una pieza soporta unagran carga estática, la misma puede fallar con una carga mucho menor si ésta se repite ungran número de veces. Los esfuerzos variables en un elemento tienden a producir grietasque crecen a medida que éstos se repiten, hasta que se produce la falla total; este fenómenose denomina fatiga. Por lo tanto, el diseño de elementos sometidos a cargas variables debehacerse mediante una teoría que tenga en cuenta los factores que influyen en la aparición ydesarrollo de las grietas, las cuales pueden producir la falla después de cierto número derepeticiones (ciclos) de esfuerzo. La teoría que estudia el comportamiento de los materialessometidos a cargas variables se conoce como teoría de fatiga.

El fenómeno de la fatiga de los materiales es uno de los más estudiados en la ingenieríamecánica. La fatiga, es la causa del ochenta por ciento de las fallas en maquinarias. Enmuchos casos hay que analizar elementos de máquina que han fallado bajo la acción deesfuerzos repetidos o fluctuantes y, sin embargo después de un cuidadoso análisis sedescubre que los esfuerzos máximos reales fueron inferiores a la resistencia última delmaterial y, muchas veces aún menos de la resistencia de la fluencia.

Existen varios tipos de ensayos para determinar la vida a fatiga de un espécimen. El másempleado es el de viga rotatoria; este puede ser realizado bien sea con la máquina de Moore[16] o la de tipo viga en voladizo como se muestra en [15]. También existen variantes dedichas máquinas como se observa en [17], [18]. Estas últimas,emplean control por  software.  Las figuras 10 (a) a 10 (d) presentan los modelos demáquinas de ensayo de fatiga por flexión rotativa. Otros modelos como los elaborados porla casa Instron, adjuntan la función de fatiga por tensión axial a las máquinas universales detracción.

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En la figura 10c. Puede observarse que la flexión es producida por un cilindro hidráulico, a

diferencia del modelo de Moore en el cual, la flexión se da mediante unas pesas.

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En los ensayos de fatiga por flexión rotativa, se aplica una carga de flexión al espécimen.Seguidamente, se enciende el motor;  este gira a un determinado número de rpm.Transcurrido un cierto tiempo, la probeta rompe, y es entonces cuando se toma el valor delnúmero de ciclos y el esfuerzo al cual la probeta rompió para construir el diagrama S-Ndescrito anteriormente.

En el caso de un acero, la probeta tarda hasta medio día en alcanzar el millón de ciclos [10],lo cual indica que estos ensayos toman tiempo.

Pruebas hechas en laboratorio [Anexos]

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NORMATIVIDAD PARA LÍMITE IDEAL DE FATIGA

ASTM E466 - 07 Standard Practice for Conducting Force Controlled

Constant Amplitude Axial Fatigue Tests of Metallic Materials Abstract 

Scope 

1.1 This practice covers the procedure for the performance of axial force controlled fatigue tests toobtain the fatigue strength of metallic materials in the fatigue regime where the strains are predominately elastic, both upon initial loading and throughout the test. This practice is limited tothe fatigue testing of axial unnotched and notched specimens subjected to a constant amplitude, periodic forcing function in air at room temperature. This practice is not intended for application inaxial fatigue tests of components or parts.

 Note 1-The following documents, although not directly referenced in the text, are consideredimportant enough to be listed in this practice:

E 739 Practice for Statistical Analysis of Linear or Linearized Stress-Life (S-N) and Strain-Life (- N) Fatigue Data

STP 566 Handbook of Fatigue Testing

STP 588 Manual on Statistical Planning and Analysis for Fatigue Experiments

STP 731 Tables for Estimating Median Fatigue Limits 

ASTM E467 - 08 Standard Practice for Verification of ConstantAmplitude Dynamic Forces in an Axial Fatigue Testing System 

Abstract 

Scope 

1.1 This practice covers procedures for the dynamic verification of cyclic force amplitude control ormeasurement accuracy during constant amplitude testing in an axial fatigue testing system. It is based on the premise that force verification can be done with the use of a strain gaged elasticelement. Use of this practice gives assurance that the accuracies of forces applied by the machine ordynamic force readings from the test machine, at the time of the test, after any user appliedcorrection factors, fall within the limits recommended in Section 9. It does not address staticaccuracy which must first be addressed using Practices E4 or equivalent.

1.2 Verification is specific to a particular test machine configuration and specimen. This standard isrecommended to be used for each configuration of testing machine and specimen. Where dynamic

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correction factors are to be applied to test machine force readings in order to meet the accuracyrecommended in Section 9, the verification is also specific to the correction process used. Finally, ifthe correction process is triggered or performed by a person, or both, then the verification is specificto that individual as well.

1.3 It is recognized that performance of a full verification for each configuration of testing machine

and specimen configuration could be prohibitively time consuming and/or expensive. Annex A1 provides methods for estimating the dynamic accuracy impact of test machine and specimenconfiguration changes that may occur between full verifications. Where test machine dynamicaccuracy is influenced by a person, estimating the dynamic accuracy impact of all individualsinvolved in the correction process is recommended. This practice does not specify how thatassessment will be done due to the strong dependence on owner/operators of the test machine.

1.4 This practice is intended to be used periodically. Consistent results between verifications isexpected. Failure to obtain consistent results between verifications using the same machineconfiguration implies uncertain accuracy for dynamic tests performed during that time period.

1.5 This practice addresses the accuracy of the testing machine"s force control or indicated forces,

or both, as compared to a dynamometer"s indicated dynamic forces. Force control verification isonly applicable for test systems that have some form of indicated force peak/valley monitoring oramplitude control. For the purposes of this verification, the dynamometer"s indicated dynamicforces will be considered the true forces. Phase lag between dynamometer and force transducerindicated forces is not within the scope of this practice.

1.6 The results of either the Annex A1 calculation or the full experimental verification must bereported per Section 10 of this standard.

1.7 This practice provides no assurance that the shape of the actual waveform conforms to theintended waveform within any specified tolerance.

1.8 This standard is principally focused at room temperature operation. It is believed there areadditional issues that must be addressed when testing at high temperatures. At the present time, thisstandard practice must be viewed as only a partial solution for high temperature testing.

1.9 The values stated in inch-pound units are to be regarded as standard. No other units ofmeasurement are included in this standard.

1.10 This standard does not purport to address all of the safety concerns, if any, associated with itsuse. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.

ASTM E467 - 98a(2004) Standard Practice for Verification of ConstantAmplitude Dynamic Forces in an Axial Fatigue Testing System 

Abstract 

Scope 

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1.1 This practice covers procedures for the dynamic verification of cyclic force amplitude control ormeasurement accuracy during constant amplitude testing in an axial fatigue testing system. It is based on the premise that force verification can be done with the use of a strain gaged elasticelement. Use of this practice gives assurance that the accuracies of forces applied by the machine ordynamic force readings from the test machine, at the time of the test, after any user appliedcorrection factors, fall within the limits recommended in Section 9. It does not address static

accuracy which must first be addressed using Practices E4 or equivalent.

1.2 Verification is specific to a particular test machine configuration and specimen. This standard isrecommended to be used for each configuration of testing machine and specimen. Where dynamiccorrection factors are to be applied to test machine force readings in order to meet the accuracyrecommended in Section 9, the verification is also specific to the correction process used. Finally, ifthe correction process is triggered or performed by a person, or both, then the verification is specificto that individual as well.

1.3 It is recognized that performance of a full verification for each configuration of testing machineand specimen configuration could be prohibitively time consuming and/or expensive. Annex A1 provides methods for estimating the dynamic accuracy impact of test machine and specimen

configuration changes that may occur between full verifications. Where test machine dynamicaccuracy is influenced by a person, estimating the dynamic accuracy impact of all individualsinvolved in the correction process is recommended. This practice does not specify how thatassessment will be done due to the strong dependence on owner/operators of the test machine.

1.4 This practice is intended to be used periodically. Consistent results between verifications isexpected. Failure to obtain consistent results between verifications using the same machineconfiguration implies uncertain accuracy for dynamic tests performed during that time period.

1.5 This practice addresses the accuracy of the testing machine"s force control or indicated forces,or both, as compared to a dynamometer"s indicated dynamic forces. Force control verification isonly applicable for test systems that have some form of indicated force peak/valley monitoring oramplitude control. For the purposes of this verification, the dynamometer"s indicated dynamicforces will be considered the true forces. Phase lag between dynamometer and force transducerindicated forces is not within the scope of this practice.

1.6 The results of either the Annex A1 calculation or the full experimental verification must bereported per Section 10 of this standard.

1.7 This practice provides no assurance that the shape of the actual waveform conforms to theintended waveform within any specified tolerance.

1.8 This standard is principally focused at room temperature operation. It is believed there are

additional issues that must be addressed when testing at high temperatures. At the present time, thisstandard practice must be viewed as only a partial solution for high temperature testing.

1.9 The values stated in inch-pound units are to be regarded as standard. No other units ofmeasurement are included in this standard.

1.10 This standard does not purport to address all of the safety concerns, if any, associated with itsuse. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.

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Significance and Use Fatigue test results may be significantly influenced by the properties and history of the parentmaterial, the operations performed during the preparation of the fatigue specimens, and the testingmachine and test procedures used during the generation of the data. The presentation of fatigue testresults should include citation of basic information on the material, specimens, and testing toincrease the utility of the results and to reduce to a minimum the possibility of misinterpretation orimproper application of those results.

ASTM E468 - 90(2004)e1 Standard Practice for Presentation ofConstant Amplitude Fatigue Test Results for Metallic Materials Close Abstract

Abstract 

Scope 

1.1 This practice covers the desirable and minimum information to be communicated between theoriginator and the user of data derived from constant-force amplitude axial, bending, or torsionfatigue tests of metallic materials tested in air and at room temperature.

 Note 1 — Practice E466, although not directly referenced in the text, is considered important enoughto be listed in this standard.

ASTM F2118 - 03(2009) Test Method for Constant Amplitude of ForceControlled Fatigue Testing of Acrylic Bone Cement Materials  

Significance and Use This test method describes a uniaxial, constant amplitude, fully reversed fatigue test to characterizethe fatigue performance of a uniform cylindrical waisted specimen manufactured from acrylic bonecement.

This test method considers two approaches to evaluating the fatigue performance of bone cement:

Testing is conducted at three stress levels to characterize the general fatigue behavior of a cementover a range of stresses. The stress level and resultant cycles to failure of the specimens can plottedon an S-N diagram.Another approach is to determine the fatigue life of a particular cement. The fatigue life fororthopaedic bone cement is to be determined up to 5 million (5 × 106) cycles.

This test method does not define or suggest required levels of performance of bone cement. Thisfatigue test method is not intended to represent the clinical use of orthopaedic bone cement, butrather to characterize the material using standard and well-established methods. The user iscautioned to consider the appropriateness of this test method in view of the material being testedand its potential application.

It is widely reported that multiple clinical factors affect the fatigue performance of orthopaedic bonecement; however, the actual mechanisms involves multiple factors. Clinical factors which mayaffect the performance of bone cement include: temperature and humidity, mixing method, time of

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application, surgical technique, bone preparation, implant design, anatomical site, and patientfactors, among others. This test method does not specifically address all of these clinical factors.The test method can be used to compare different acrylic bone cement formulations and productsand different mixing methods and environments (that is, mixing temperature, vacuum,centrifugation, and so forth).

1. Scope 1.1 This test method describes test procedures for evaluating the constant amplitude, uniaxial,tension-compression uniform fatigue performance of acrylic bone cement materials.

1.2 This test method is relevant to orthopedic bone cements based on acrylic resins, as specified inSpecification F451 and ISO 16402. The procedures in this test method may or may not apply toother surgical cement materials.1.3 It is not the intention of this test method to define levels of performance of these materials. It isnot the intention of this test method to directly simulate the clinical use of these materials, but ratherto allow for comparison between acrylic bone cements to evaluate fatigue behavior under specifiedconditions.

1.4 A rationale is given in Appendix X2.

1.5 The values stated in SI units are to be regarded as standard. No other units of measurement areincluded in this standard.

1.6 This standard does not purport to address all of the safety concerns, if any, associated with its

use. It is the responsibility of the user of this standard to establish appropriate safety and health

 practices and determine the applicability of regulatory limitations prior to use. 

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ANEXOS

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TRABAJO DE DISEÑO MECANICOFATIGA

PRESENTADO POR:

ELJAIK GÓMEZ OMAR DAVID.

GONZÁLEZ VALLEJO EMANUEL.

GUTIÉRREZ VILLARREAL LUIS E.

LEGUIZAMÓN GRANADOS ALFONSO

PRESENTADO A:

ANTONIO SALTARÍN JIMÉNEZ

UNIVERSIDAD DEL ATLÁNTICO

FACULTAD DE INGENIERIA

PROGRAMA DE INGENIERIA MECANICA

2012

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BIBLIOGRAFÍA

  De la página Web: http://www.astm.org/ 

   NORTON, Robert. Diseño Mecánico. Prentice Hall, 2002. Pág. 359 -376