Cyclic Loading

10 Key excerpts on "Cyclic Loading"

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  Reliability-Based Mechanical Design, Volume 2

  Component under Cyclic Load and Dimension Design with Required Reliability

  • Xiaobin Le(Author)
  • 2022(Publication Date)
  • Springer

    (Publisher)

  This chapter will present and discuss different methods to determine the reliability of a component under any cyclic load with plenty of examples. 2.2 FATIGUE DAMAGE MECHANISM Fatigue phenomena were first discovered and studied during the 19th century with the arrival of machines and freight vehicles during the industrial revolution [1]. Fatigue is defined as “failure under a repeated or varying loading, which never reaches a level sufficient to cause failure in a single application.” Fatigue failure of a metal component under Cyclic Loading is a complicated phenomenon, and only partially understood [2]. However, we have a fundamental understanding of fatigue 10 2. RELIABILITY OF A COMPONENT UNDER CYCLIC LOAD failure or fatigue damage. Fatigue damage is the weakening of a metal material due to a gradually crack propagation of inherent existing microscopic cracks or defect inside or on the surface of the metal component under repeated Cyclic Loading. Without a crack inside or on the surface of a metal component, there is no fatigue. If the magnitude of Cyclic Loading is not big enough to generate a crack propagation, there will be no fatigue. The fatigue damage mechanism can be typically described by the following four stages. Let use a microscopic crack on the surface to explain and demonstrate these. Figure 2.1 shows a magnified microscopic crack on the surface of a component under a fully reversed cyclic bending moment. In this example, let us assume that the nominal normal stress due to the bending stress is 20 ksi, and the material yield strength is 60 ksi. 1. Crack initiation. There are always lots of randomly distributed defects inside a component such as voids and dislocations and on the surface of a component such as manufacturing scratches [3]. A fatigue crack will typically initiate at a microscopic crack or defect inside or on the surface of a component.

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  Strength and Failure of Visco-Elastic Materials

  • G. M. Bartenev, Yu. S. Zuyev(Authors)
  • 2013(Publication Date)
  • Pergamon

    (Publisher)

  Secondly, the failure of polymers at Cyclic Loading is mechanicahy accelerated by activating chemical processes^^'. ^' The above mentioned principles are valid for unfiUed rubbers. FiUed rubbers^®^ are characterized by more complicated principles of dynamic fatigue (Fig. 125). The dependence of dynamic fa-tigue of rubber on the magnitude of the static tensile deformation has been investigated. The elastomer was prestressed up to ε^^ t Strictly speaking ν is not zero for the static method but has some small value. This is connected with the fact that one can present the static method as the first half-period of a Cyclic Loading with rectangular cycles. Then τ, the time of effect of the constant load (or durability), is the half-period of the cycle, to which corresponds the frequency ν = ^τ. 218 Strength and Failure of Visco-elastic Materials 0 15 30 A5 Static deformation ε^^iΊo) F I G . 125. Dependence of the number of cycles before failure of unfilled rubber on the static component of deformation under stretching^^^ (constant amplitude of deformation 30%, frequency 50 min-i). 1. S K B + 4 0 g channel black, 115°C. 2. N K + 40 g channel black, 100°C. The number of cycles before failure depends also on the temper-ature; with increasing temperature it decreases at first rapidly and then slowly. 8.2. Calculation of Durability of Plastics and Elastomers under Cyclic Loading The general method of calculating the strength and durability of materials under different methods of deformation, and the calculation of the strength of elastomers at constant strain rates has been examined in Chapter 7. In this section we bring similar calculations for the method of Cyclic Loading. The basic calcula-tion is, as before, the condition of failure by Bailey (see p. 182). Zhurkov and Tomashevsky (see § 2.5) apphed this method to a deformation and then underwent prolonged Cyclic Loading.

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  Cumulative Damage of Welded Joints

  • T R Gurney(Author)
  • 2006(Publication Date)
  • Woodhead Publishing

    (Publisher)

  1 1.1 Background Fatigue can be defined as a mechanism of failure which involves the formation and growth of a crack or cracks under the action of repeated stresses. Ultimately, of course, the crack may propagate to such an extent that total fracture of the member may occur. In other words, fatigue failure can only occur in a structure in which the stresses vary with time in a repeated manner. Note, however, that this does not imply that the various stresses all have to be of the same magnitude; it is much more usual for them to have a wide range of magnitudes, but both types of loading can lead to fatigue failure. Fatigue has, in fact, been recognised as a problem, for more than a century, dating at the very least from the classic fatigue tests on railway axles carried out by Wohler, details of which were published in 1871 (Wohler, 1871). So far as welded joints are concerned, however, the problem really dates only from the Second World War, or even slightly after it, since it was not until then that welding became a major production process, and after that it took a little time for structures to amass sufficient load cycles for fatigue to rear its head. More recently, of course, welding has become the fabrication method of choice for almost all types of structure, so that scope for running into fatigue problems in welded structures is immense. Potentially there are many different sources of Cyclic Loading (often referred to as fatigue loading, for obvious reasons), any or all of which may be relevant in particular situations, and the following list includes some typical types of structure in which they may occur. The list is not by any means exhaustive but is merely intended to show examples. It includes, for example: 1. Fluctuating live loads Bridges, crane gantry girders, diesel engine frames, locomotive underframes and bogies, lorry chassis frames and axles, ships, cranes, earth moving equipment, farm machinery, rock crushers and presses.

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  Alloy And Microstructural Design

  • John Tien(Author)
  • 2012(Publication Date)
  • Academic Press

    (Publisher)

  The meaning of this term is vague in relation to stress and has given rise to many problems in cumulative fatigue. Although metallurgists have understood the nature of damage in terms of microcracking phenomena, they have been unable to make quantita-tive predictions that mechanical engineers feel comfortable in using. In the decades following World War II, increasing service require-ments in transportation, aerospace, and energy conversion led to the recognition of the high strain fatigue problem. Coffin and Manson es-tablished their well-known law of failure for this regime, AepN f n = const, where Δβ ρ is the plastic strain range of the cycle and N f is the number of cycles to failure. This work also emphasized the hardness changes which develop in materials during cycling, because the need to strain cycle naturally caused experimenters to apply many more types of transducers to specimens in a strain regime where property changes were much larger than previously observed at lower stresses. Both cy-clic hardening and softening were observed, depending on the history of the material. The recognition that the unidirectional properties used for static design could be seriously altered by Cyclic Loading also directed more attention to cyclic deformation. Out of this work has emerged a new design approach. In this ap-proach, fully described by Manson (1966), an attempt is made to take plasticity into account. Initially only one cycle of loading was consid-ered in a plastic analysis and the virgin unidirectional stress-strain curve of the material was used as the relevant material plastic property. The strain range during this single cycle was then assumed to be the strain range after a large number of cycles as well. If the strain ranges at the critical points in a component can be calculated by such techniques, then the life may be predicted by the Coffin-Manson law.

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  Physics of Strength and Fracture Control

  Adaptation of Engineering Materials and Structures

  • Anatoly A. Komarovsky, Viktor P. Astakhov(Authors)
  • 2002(Publication Date)
  • CRC Press

    (Publisher)

  467 7 Fatigue: Physical Nature, Prediction, Elimination, and Relief 7.1 Introduction Cyclic Loading is one of the varieties of the force field. Differential form of the thermodynamic equation of state (Section 2.4) makes it possible to derive an equation for thermodynamic fatigue (Section 7.2),. that relates the number of loading cycles (known also as cyclic fatigue life) to working parameters of the alternating force and thermal fields. It also characterizes mechanical fatigue at constant temperature and thermal fatigue in constant force fields. Comparison of theory and experiment yields good coincidence. Section 7.3 shows that the physical nature of fatigue is in the active occurrence of compresson–dilaton phase transitions (following the diagram in Figures 1.15) under thermal insufficiency at alternating deformation. This stimulates for-mation of the flow of failures of interatomic bonds at the Debye temperature. Sometimes fatigue fracture develops at the presence of x-ray radiation. Section 7.4 gives expressions for thermal-radiation, mechanical-radiation, and thermal–mechanical–radiation fatigue as well as their comparison with experiment. The relationships derived allow calculation of fatigue life and also indicate methods for fatigue relief and elimination (Section 7.5). In many respects, they are similar to those described in Section 5.8 and work effi-ciently at the reversible stage of occurrence of deformation processes. 7.2 Equation of Thermomechanical Fatigue Fatigue implies a process of gradual accumulation of damages in the initial structure of a material under the effect of dynamic variations in the parameters of one or several external fields (force, thermal, radiation, chemical, etc.). This leads to initiation of a fatigue crack and its propagation, and ends with 468 Physics of Strength and Fracture Control sudden fracture.

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  High Performance Fiber Reinforced Cement Composites 2

  Proceedings of the International Workshop

  • A.E. Naaman, H.W. Reinhardt(Authors)
  • 2004(Publication Date)
  • CRC Press

    (Publisher)

  This expression is valid only in the range from 10 ^ to 2 * 10 ^ cycles, which is the type of loading to be expected in concrete pavements and bridge decks. 6 Cyclic Behavior and Modeling 6.1 Cyclic Behavior It is appropriate to summarize the important aspects of FRC behavior under Cyclic Loading before reviewing the various theories that have been proposed so far to model this behavior. When concrete with a sufficiently large fiber content cracks in response to monotonically applied load, the cracks are bridged by fibers whose presence retards crack growth and increases the fracture energy. A strength increase is observed only for relatively large fiber volumes because otherwise the strength of the fibers is small compared with the concrete strength. In contrast, ductility and toughness increases can be noted for very low fiber volumes. The same is true in the case of cyclic load response. The fibers contribute an overproportional share to the energy absorption capacity of the composite, because they possess considerable ductility, whereas the concrete matrix does not. Frictional effects on 132 Fatigue behavior of FRC the fiber-matrix interface account for another major contribution. Both of these phenomena greatly retard the damage accumulation in the composite and lengthen its fatigue life. It is not yet clear whether the failure mechanisms for monotonic and cyclic load are fundamentally different. Otter and Naaman's work [44,45] seems to suggest that they are not, because of the strong correlation found between the ultimate failure strains in the two cases. This correlation can be explained with the hypothesis that at the time of failure in both cases the bond between the fibers and the surrounding matrix has been reduced to zero and therefore the failure strain is reduced to that of the monotonically loaded material.

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  Advanced Mechanics of Materials

  • Arthur P. Boresi, Richard J. Schmidt(Authors)
  • 2019(Publication Date)
  • Wiley

    (Publisher)

  CHAPTER 16 FATIGUE: PROGRESSIVE FRACTURE Fatigue has been defined as “the progressive localized permanent structural change that occurs in a material subjected to repeated or fluctuating strains at stresses having a maximum value less than the tensile strength of the material” (ASM, 1975). As noted in Chapter 15, failures occur in many mechan- ical systems. It has been estimated that between 50% and 90% of these failures are due to fatigue (Fuchs and Stephens, 1980). Failures caused by fatigue cul- minate in cracks or fracture after a sufficient number of fluctuations of load. Fracture of a structural member as the result of repeated cycles of load or fluctuating loads is commonly referred to as a fatigue failure or fatigue fracture. The correspond- ing number of load cycles or the time during which the member is subjected to these loads before fracture occurs is referred to as the fatigue life of the member. The fatigue life of a member is affected by many factors (ASM, 1975). For example, it is affected by 1. the type of load (uniaxial, bending, torsion), 2. the nature of the load–displacement curve (linear, nonlinear), 3. the frequency of load repetitions or cycling, 4. the load his- tory [cyclic load with constant or variable amplitude, random load, etc. (Gauthier and Petrequin, 1989; Buxbaum et. al, 1991)], 5. the size of the member, 6. the material flaws, 7. the manufacturing method (surface roughness, notches), 8. the operating temperatures (high temperature that results in creep, low temperature that results in brittleness), and 9. the environmental operating conditions (corrosion, see Clarke and Gordon, 1973). In practice, accurate estimates of fatigue life are difficult to obtain, because for many materials, small changes in these conditions may strongly affect fatigue life. The designer may wish to rely on testing of full-scale members under in-service conditions. However, testing of full-scale members is time consuming and costly.

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  Constitutive Models for Rubber VI

  • Gert Heinrich, Michael Kaliske, Alexander Lion, Stefanie Reese(Authors)
  • 2009(Publication Date)
  • CRC Press

    (Publisher)

  ABSTRACT: The duty cycle of a rubber component in field service often involves time-varying loads applied simultaneously from several directions—ie multiaxial loading. This contribution demonstrates an analysis whereby events occurring in a multiaxial duty cycle can be ranked according to their contribution to the overall damage rate. In order to account for the transformation of multiaxial loading into the experience of localized flaws, the duty cycle on each material plane is considered, along with its corresponding damage rate. Once the damaging events have been identified and ranked, the original duty cycle can then be simplified by constructing a new duty cycle composed from a number of the most damaging events in the original cycle. Calculations are made for a series of duty cycles reconstituted via this procedure, illustrating the degree to which minor cycles influence the overall damage rate, and the selection of the failure plane.

  1 INTRODUCTION

  Under dynamic loads, elastomeric components can fail due to the nucleation and growth of cracks, even when the loads remain always below the static strength of the material. Although much has been learned about the physics and phenomenology of such fatigue failures, there remains a great demand to integrate that knowledge into tools capable to address the materials and duty cycles that occur in everyday use. Consider, for example, that of all product design criteria, fitness for a given service life is often the most costly criterion to evaluate: 1) it is inherently destructive of expensive prototypes, 2) it calls for extended running times, and 3) it requires elaborate systems to apply loading history and collect measurements.

  This contribution describes the application of a new tool—the EnduricaTM fatigue life prediction code (www.endurica.com )—to a common task: the transformation of a long multi-axial, aperiodic duty cycle (perhaps a direct recording of service conditions) into an abbreviated duty cycle (perhaps suitable for use as an accelerated product development test). It is often not initially obvious which events contribute most to the fatigue failure process, and which events may be dropped from consideration. It is desired that the shorter duty cycle retain those features of the original cycle that produce the original mode of failure.

  2 HISTORICAL CONTEXT

  Systematic study of fatigue failure in rubber was made as early as 1940 (Cadwell et al.). Since then, a great deal of knowledge about fatigue in rubber has developed. Available reviews cover: the physics of strength and fatigue (Lake 2003, Persson et al. 2005), available approaches for fatigue analysis (Mars and Fatemi 2002, Mars 2007), the historical development of Fracture Mechanics (Thomas 1994), and factors that affect fatigue (Mars and Fatemi 2004).

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  Mechanical Behavior of Concrete

  • Jean-Michel Torrenti, Gilles Pijaudier-Cabot, Jean-Marie Reynouard, Jean-Michel Torrenti, Gilles Pijaudier-Cabot, Jean-Marie Reynouard(Authors)
  • 2013(Publication Date)
  • Wiley-ISTE

    (Publisher)

  The existence of confining stresses favorably influences the fatigue damage process. This effect is shown by a lower decrease in the longitudinal modulus of elasticity, and increases as the rate of confinement is raised. Similarly, the number of cycles to failure increases with the intensity of the stress of confinement.

  When the two loading components are in phase, the confinement effect is optimal during the duration of the loading cycle. As a result, there is an increase in the number of cycles to failure. Conversely, the effect of confinement is far less efficient when the two components are in opposite phase. The confining stress is then minimal when the longitudinal compressive stress is at a maximum and vice versa. The favorable effect of confinement persists, but the increase in the number of cycles to failure is much more limited.

  As for uniaxial loading, the rate per cycle of the longitudinal strain is strongly correlated with the number of cycles to failure. At a given strain rate, the number of cycles to failure is increased in the presence of a confining stress as in the case of uniaxial Cyclic Loading. This effect is more significant when the two longitudinal and transverse components of the Cyclic Loading evolve in phase. As in the uniaxial case, this property can help in forecasting the residual number of cycles to failure.

  5.6. Fatigue under high-level Cyclic Loading

  The description of the fatigue loading includes two time-related parameters, namely the frequency and the shape of the cycle. The influence of these two parameters is moderate when the maximum level of the cyclic stress is less than 80% of the static strength of the concrete. This threshold corresponds slightly to the long-term static strength of concrete under sustained stress. As seen previously, under this limit the effect of frequency can be taken into account by multiplying the fatigue strength by a corrective coefficient Cf (Aas-Jakobsen’s adjusted formula). Above this limit, this adjustment turns out to be insufficient and leads generally to overestimate the number of cycles to failure. The gap is all the more obvious when the minimum level of the cyclic stress reaches, or even exceeds, this limit.

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  Lightweight Composite Structures in Transport

  Design, Manufacturing, Analysis and Performance

  • James Njuguna(Author)
  • 2016(Publication Date)
  • Woodhead Publishing

    (Publisher)

  10.1. Introduction

  A common form of failure of materials in practical use is fatigue, in which the failure occurs from the cyclic application of stresses. These stresses are applied in various forms, such as sinusoidal (sin and cos), square, and pulsed waves. These kinds of stresses are different according to the magnitude and direction of stress, and also depending on the stress mode (system). Therefore, the failure may occur under applied stresses that are below the level required to cause yield or fracture in the case of a tension test (continuously rising stress).

  The effect of such stresses is to initiate microcracks at the center of the stress concentration within the material or on the surface, and then propagation of cracks, which lead to separation of the material parts and finally to the state of sudden fracture (fatigue fracture).

  10.2. Basic fatigue failure

  First, some important parameters that will be useful in the subsequent discussion of fatigue, as shown in Fig. 10.1 , are as follows:

  Cyclic stress range: Δσ   =  σ max   −   σ min

  Cyclic stress amplitude: σ a   =  (σ max   −   σ min )/2

  Mean stress: σ m   =  (σ max   +  σ min )/2

  Stress ratio: R   =  σ min /σ max

  Number of fatigue cycles: N

  Number of cycles to failure: N f

  In these parameters, σ max and σ min are the maximum and minimum stress levels, respectively [1 –5] .

  These terms are very important for studying fatigue failure mathematically. There are empirical models that deal with various cases or conditions of fatigue and depend on the method of applied load (stress) and the conditions of the components that are subjected to these loads. There are two types of components, uncracked or cracked components, which also affects the σ min and σ max values with respect to yield stress of the material; therefore, we will consider fatigue under zero mean stress (σ m   =  0) and when neither σ max nor |σ min |is above the yield stress, as shown in Fig. 10.2  [2] .

  Figure 10.1  Fatigue parameters. M.F. Ashby, D.R. Jones, Engineering Materials an Introduction to Microstructures, Processing and Design, third ed. (Butter Worth-Heinemann is an imprint of Elsevier).

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