Stages of Creep

12 Key excerpts on "Stages of Creep"

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  Thermal Fatigue of Metals

  • Andrzej Weronski(Author)
  • 1991(Publication Date)
  • CRC Press

    (Publisher)

  Creep 2 2.1 INTRODUCTION The term creep denotes slowly proceeding deformation of solid matter under a maintained load. The first systematic studies providing some quantitative informa-tion on the nature of creep were those of Andrade (1910). During World War I, research on creep became more urgent. Impetus was given by the rapid increase in steam admission temperatures in power plants (to about 670 K in the 1920s), approaching the creep range of low-alloy steels. Early researchers were concerned with finding the limiting stress below which creep would not occur, but using more accurate experimental techniques, this idea was subsequently shown to be false. The temperature at which creep becomes important for the designer is about 0.4 of the melting temperature of the material considered, but numerous exceptions bring this rule into question. For example, creep is observed in titanium at lower temperatures than in iron-based alloys, despite the higher melting point of the former. Stress levels under which creep is observable are always much lower than the strength of the material. A creep curve, which is the graphical presentation of the dependence of the strain on time under constant stress and temperature, is shown in Fig. 2.1. The strain £ 0 is developed immediately upon loading; the period of time between £ 0 and is called primary creep. Between ex and e2 the creep rate remains almost constant; this portion of the curve is termed secondary (or steady-state) creep: • * 2 S i £f = -----h ~ h The creep rate increases beyond £ 2 » an<3 this period is called tertiary creep. It is convenient to obtain experimental data under a constant tensile load. As creep proceeds, the true stress increases continually, giving rise to a pronounced change in the creep rate. The tertiary creep, where necking is appreciable, is certainly also 54 Creep 55 Time Figure 2.1 Schematic representation of a creep-rupture curve.

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  Materials Processing and Manufacturing Science

  • Rajiv Asthana, Ashok Kumar, Narendra B. Dahotre(Authors)
  • 2006(Publication Date)
  • Butterworth-Heinemann

    (Publisher)

  From the material and component design perspectives, the steady-state creep rate (d ε s / dt ) is of considerable importance. The steady-state creep rate depends on the magnitude of applied stress, σ , and temperature, T, according to d ε s dt = K σ n exp − Q RT , (1-12) where Q is the activation energy for creep, K and n are empirical constants, and R is the gas constant. The exponent n depends on the dominant mechanisms of creep under a given set of experimental conditions, which include vacancy diffusion in a stress field, grain boundary migration, dislocation motion, grain boundary sliding, and others. The materials used in modern aircraft engines provide a classic example of how high-temperature creep resistance is enhanced through microstructure design in Ni-base alloys by dispersing nanometer-size oxide particles; this is discussed in Chapter 6. Time, t t r Creep strain, e Instantaneous deformation Primary Tertiary Rupture Secondary ∆t ∆e FIGURE 1-29 Schematic creep curve showing strain versus time at constant stress and temper- ature. The minimum creep rate is the slope of the linear region in the secondary creep regime. (W. D. Callister, Jr., Materials Science & Engineering: An Introduction, 5th ed., Wiley, New York, 2000, p. 226). 34 MATERIALS PROCESSING AND MANUFACTURING SCIENCE Deformation Processing A large number of manufacturing processes employ solid-state deformation of hot or cold metals and alloys to shape parts. Hot-working is the mechanical shaping operation that is per- formed at temperatures high enough to cause the processes of recovery and recrystallization to keep pace with the work hardening due to deformation. In contrast, cold-working is performed below the recrystallization temperature of the metal; however, both hot- and cold-working are done at high strain rates. Cold-working strain hardens a metal, and excessive deformation without intermediate annealing causes fracture.

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  Advanced Mechanics of Materials

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

    (Publisher)

  626 CHAPTER 18 CREEP: TIME-DEPENDENT DEFORMATION In this chapter, we are concerned mainly with mathematical equations used to represent creep strain (Figure 18.1) as a function of stress, temperature, and time and the use of these equations to study the effects of creep. Therefore, we assume that an elevated temperature for a material exists so that the material may creep. A phenomenological approach is taken to describe the physical processes that alter the metallurgical structure of a material, allowing creep to occur. Furthermore, we do not attempt to describe in any detail various creep models (viscoelastic, elastic–plastic, etc.) that have been proposed. Rather, we base our study on the typical creep curve (plot of strain versus time; Figure 18.1) and mathematical modeling of the creep curve. Creep curves are ordinarily obtained by tests of bars subjected to sustained axial tension (Loveday, 1988). Standards for creep tests have been established by several technical organizations (ASTM, 1983; BSI, 1987; ISO, 1987). In Section 18.2, we briefly describe the tension creep test for metals. In Sections 18.3 and 18.4, we present one-dimensional creep formulas for metals subjected to stress and elevated temperature. In Sections 18.5 and 18.6, the creep of metals subjected to multidi- mensional states of stress is considered. Some applications to simple problems in creep of metals are discussed in Section 18.7. In Section 18.8, a few observations relative to creep of nonmetals are given. 18.2 THE TENSION CREEP TEST FOR METALS The creep behavior of various materials is often based on a one-dimensional (tension) test. Various standards for creep testing specify the geometric design of test specimens (ASTM, 1983; BSI, 1987; ISO, 1987). Careful control of machined dimensions is specified (Love- day, 1988). During the test, the tension specimen is subjected to sufficiently high stress  and temperature T to produce time-dependent inelastic strain (creep).

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  Deformation and Evolution of Life in Crystalline Materials

  An Integrated Creep-Fatigue Theory

  • Xijia Wu(Author)
  • 2019(Publication Date)
  • CRC Press

    (Publisher)

  Creep deformation as high-temperature design limitations is widely recognized in industrial design codes, e.g., ASME Boiler and Pressure Vessel Code. The creep failure criteria can be given either in terms of creep strain to be reached, e.g. 1%, or hours of service, e.g. 100,000 hours, against which the allowable stress is determined. With regards to the above criteria for component design, a few questions and factors have to be completely understood.

  1.  What is the creep behaviour, including creep strain as function of time and creep rate as function of stress and temperature? 2.  What are the effects of chemical composition and microstructure (via manufacturing process and heat treatment, etc.) on the material’s creep resistance? 3.  Will the material microstructure change during long-time service, and if changed, what would be its effect on the material’s performance? 4.  Does the operating environment have an effect on the material’s performance?

  Experimental studies have shown that creep deformation can occur under stresses well below the material’s yield strength at elevated temperatures, usually above 0.3 Tm (Tm is the material’s melting temperature in Kelvin degree). Figure 5.2 shows a schematic creep curve from a constant-load creep test. The creep elongation generally evolves with time through three stages: 1) primary, 2) secondary (steady-state) and 3) tertiary stages, as indicated in Figure 5.2 . The primary creep exhibits a decelerating creep rate; the secondary creep stage has a nearly constant creep rate, which is usually the minimum creep rate; and the tertiary creep exhibits an accelerating creep rate to rupture. By its nature, the constant minimum creep rate is often used to characterize the material’s creep property.

  Figure 5.2. A schematic creep curve.

  Many models have been proposed to describe the creep-curve. Andrade (1914) first proposed a creep strain function as time to the power of 1/3. Norton and Bailey proposed a general power-law of stress and time (Norton 1929, Bailey 1935). Graham-Walles (1955) extended those power-laws into a power-law series of creep strain equations. Evans and Wilshire (1985) proposed the θ-projection method. In addition, the continuum damage mechanics (CDM) is also developed to describe the creep strain accumulation with σ/(1 − ω), where ω represents the loss of internal area by void growth (Kachanov 1958, Robotnov 1969, Lemaitre and Chaboche 1999, Dyson and McLean 2000, Hayhurst 2005). These models or theories can depict the creep curve, but do not indicate what mechanisms are responsible for the creep curve shape, nor do they contain failure criteria leading to intergranular or transgranular or mixed mode rupture, except parametrically, ω = 1.

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  High Temperature Structures and Materials

  Proceedings of the Third Symposium on Naval Structural Mechanics Held at Columbia University, New York, N.Y., January 23–25, 1963

  • A. M. Freudenthal, B. A. Boley, H. Liebowitz, A. M. Freudenthal, B. A. Boley, H. Liebowitz(Authors)
  • 2013(Publication Date)
  • Pergamon

    (Publisher)

  CREEP RUPTURE AND THE TERTIARY STAGE OF CREEP ARTHUR W . MULLENDORE and NICHOLAS J. GRANT Massachusetts Institute of Technology, Cambridge, Massachusetts. 1. I N T R O D U C T I O N I N considering the nature of the third stage of creep, it is well to examine first our terms of reference. Tertiary creep is defined with reference to the creep strain versus time curve as the period of accelerating creep rate which precedes fracture. This definition is hardly adequate to indicate the nature of tertiary creep since we use it with reference to both the constant load test and the con-stant stress test. The conditions at the incidence of tertiary creep are quite different in the two tests. The beginning of third stage in the constant stress test represents a departure from steady state conditions of stress and creep rate. In the constant load test, however, the second stage of creep is a period of changing conditions. The stress is continuously increasing, structure is changing, and the first intercrystalline cracks are forming; steady state creep is really a slow transition in creep rate through an inflection point of the creep curve. Thus the transition to third stage is not particularly significant with respect to any change in the character of the deformation. One can attempt to characterize third-stage creep in two different ways. First it can be examined with specific reference to the creep data and the criteria of stability of elongation, and secondly it can be treated in terms of structural changes and changes in the deformation and fracture modes. It is the purpose of this paper to examine both points of view and to see to what extent they can complement each other. The ultimate goal of such considerations is to judge the feasibility of designing, in particular applications, on the basis of third stage creep.

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  Mechanical Behavior of Materials

  • Marc André Meyers, Krishan Kumar Chawla(Authors)
  • 2008(Publication Date)
  • Cambridge University Press

    (Publisher)

  Chapter 13 Creep and Superplasticity 13.1 Introduction The technological developments wrought since the early twenti-eth century have required materials that resist higher and higher temperatures. Applications of these developments lie mainly in the following areas: 1. Gas turbines (stationary and on aircraft), whose blades operate at temperatures of 800--950 K. The burner and afterburner sections operate at even higher temperatures, viz. 1,300--1,400 K. 2. Nuclear reactors, where pressure vessels and piping operate at 650--750 K. Reactor skirts operate at 850--950 K. 3. Chemical and petrochemical industries. All of these temperatures are in the range (0.4--0.65) T m , where T m is the melting point of the material in kelvin. The degradation undergone by materials in these extreme condi-tions can be classified into two groups: 1. Mechanical degradation . In spite of initially resisting the applied loads, the material undergoes anelastic deformation; its dimen-sions change with time. 2. Chemical degradation . This is due to the reaction of the material with the chemical environment and to the diffusion of external elements into the materials. Chlorination (which affects the prop-erties of superalloys used in jet turbines) and internal oxidation are examples of chemical degradation. This chapter deals exclusively with mechanical degradation. The time-dependent deformation of a material is known as creep . A great num-ber of high-temperature failures can be attributed either to creep or to a combination of creep and fatigue. Creep is characterized by a slow flow of the material, which behaves as if it were viscous. If a mechan-ical component of a structure is subjected to a constant tensile load, the decrease in cross-sectional area (due to the increase in length resulting from creep) generates an increase in stress; when the stress 654 CREEP AND SUPERPLASTICITY reaches the value at which failure occurs statically (ultimate tensile stress), failure occurs.

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  Gamma Titanium Aluminide Alloys

  Science and Technology

  • Fritz Appel, Jonathan David Heaton Paul, Michael Oehring(Authors)
  • 2011(Publication Date)
  • Wiley-VCH

    (Publisher)

  9.1 demonstrates this behavior on the creep curves of an extruded Ti-45Al-10Nb alloy. When compared with pure disordered metals, the extent of steady-state creep is limited. After primary creep, the creep rate usually reaches only a minimum and then increases again with strain. In engineering test practice the minimum creep rate is often only represented by an inflection between the end of primary creep and the beginning of tertiary creep. This short duration of the minimum creep rate is inconsistent with the traditional understanding of steady-state creep. Thus, the regime with minimum creep rate is often referred to as “secondary creep”. High stresses and temperatures generally reduce the extent of primary creep and practically eliminate the secondary stage, with the result that the creep rate accelerates almost from the beginning of the test.

  Figure 9.1 Creep behavior observed during tensile testing in air under the conditions indicated. The Ti-45Al-10Nb alloy investigated had been extruded at a temperature corresponding to the (α + γ) phase field. (a) Variation of creep strain ε with time t ; (b) creep rate as a function of creep strain ε determined from the creep curve shown in (a).

  The creep stress is usually defined as the constant load divided by the initial specimen area. Thus, for constant-load tensile creep the true stress increases as the specimen area decreases, and in compression the true stress decreases as the specimen area increases. The most important reason for the different responses in tension and compression is that diffusion-assisted dislocation climb is often the dominant deformation mechanism. Tensile stresses expand the lattice and reduce the resistance to diffusion, whereas compressive stresses reduce the lattice dimensions and increase the resistance for diffusion. This aspect could be important if during creep phase transformations occur that are associated with volume changes. The creep life at constant tensile stress is usually longer than that under constant tensile load.

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  Art Conservation

  Mechanical Properties and Testing of Materials

  • W. (Bill) Wei(Author)
  • 2021(Publication Date)
  • Jenny Stanford Publishing

    (Publisher)

  Fig. 5.3 , this is shown as stage III creep and is also known as tertiary creep. In all stages, if the specimen is unloaded, the strain which has occurred during the creep process remains; it is a permanent strain.

  Figure 5.3 Schematic diagram showing the three Stages of Creep.

  The continuous increase in strain during creep is due to many of the same microstructural changes which occur during stress relaxation. This often leads to confusion between the two. Remember that creep is a continuous increase in strain under constant stress, whereas stress relaxation is a decrease in stress which occurs under constant strain. Creep will eventually lead to failure, while stress relaxation may result in some permanent deformation, but at some point, the stress level becomes too low and deformation stops.

  Creep is generally associated with temperatures which are considered high for a particular material. For polymers and plastics, these are temperatures close to the glass transition temperature. Examples of creep at room temperature can be found in contemporary art where artists drape large amounts of fabric, artificial or natural, to obtain the desired effects, see for example [1 ].

  For metals, creep occurs at temperatures higher than approximately 40% of their melting temperature given in absolute temperature, that is in units of Kelvin. Kelvin is the temperature in degrees Celsius + 273.15. Most metals have fairly high melting temperatures, from hundreds to over 1000°C and most conservators will never be confronted with this issue.

  There is one notable exception and that has to do with problems with new bass church organ pipes made of pure lead which were made to replace historic pipes [2 ]. These pipes can be over 4 m long and weigh up to 100 kg. These pipes were found to deform so much at the base after only 20 years (see Fig. 5.4

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  Kinetic Theory

  • George Z. Kyzas, Athanasios C. Mitropoulos, George Z. Kyzas, Athanasios C. Mitropoulos(Authors)
  • 2018(Publication Date)
  • IntechOpen

    (Publisher)

  structure, the vacancy processes, phase transitions, grain size changes in the deformation process and other reasons. The preferential effect of one mechanism in comparison with the others leads to a change of the stages on the creep curve. When constructing these curves, it is assumed that the loading time of the specimen to a given stress is very short compared to the test time. Therefore, the curves ε ( t ) start at the strain corresponding to the ‘ instantaneous ’ loading. The creep theory seeks to determine a relationship between stress σ , time t , creep strain p and temperature T ; this relationship, which is universal, should be capable of determining the creep curve p ( t ) = ε ( t ) � ε 0 ( σ ) at the arbitrary laws of stress σ ( t ) and temperature T ( t ) variations with time. Different problems of the creep theory have been investigated in a number of monographs ([3 – 7], and others). Without loss of generality, here and further on, it is possible to consider isothermal processes occurring at a constant temperature. The transition to other temperatures in creep and long-term strength simulation should be carried out using known temperature-time analogies specified, for example, in [6, 7]. Here, the case is examined where σ ( t ) = const and the specimen is at the steady-state creep stage _ p σ ; t ð Þ ¼ const most of the time. In this case, to describe the behaviour of the material, it is natural to use the relationship of the non-linear viscous flow called the theory of the steady-state creep: _ p ¼ f σ ð Þ (1) (the dot above the symbol indicates the differentiation with respect to time t ). The steady-state creep rate _ p is of special importance, because in many technical applications it accounts for the main part of the accumulated creep strain. In most studies, the function f ( σ ) is a power function of the mechanical stress σ : _ p ¼ A σ n , (2) Figure 1. Dependence of strain on time at different stresses. Kinetic Theory 54

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  Specificity of Deformation and Strength Behavior of Massive Elements of Concrete Structures in a Medium with Low Humidity

  • Koryun Karapetyan(Author)
  • 2019(Publication Date)
  • Butterworth-Heinemann

    (Publisher)

  26] .

  It’s appropriate to present a brief consideration of the graphical method for determining the scope of applicability of the theories of aging, hardening, and heredity to describe the creep process of elements, without delving into the issue of the theoretical justification of this method.

  According to the theory of aging [6 , 23] creep deformation ɛ c (t ) is determined by the duration t of the applied stress and its current value σ (t ), regardless of the history of the change during the period of time of the latter. The basic equation of the theory of aging is written as:

  ɛ c

  t = F

  σ t

  t

  ,

    (4.1)

  where F is the function approximating the experimental creep data at constant stresses.

  The graphical interpretation of dependence (4.1) is shown below.

  In Fig. 4.1 , dashed lines show approximated creep curves at constant stresses σ 1 ; σ 2 ; σ 3 . We assume that up to a certain moment of time t 1 the stress value was equal to σ 1 , and then it was gradually changed to the stress value σ 2 . According to the theory of aging, the creep deformation ɛ c (t ) at the same time abruptly changes from ɛ c (σ 1 , t 1 ) to ɛ c (σ 2 , t 1 ), that is, by the value of the segment A 1  A 2 , and then changes according to the creep curve ɛ c (σ 2 , t ). As soon as the stress increases from σ 2 to σ 3 at the moment of time t 2 , an abrupt change of the deformation occurs by the value of the segment B 2  B 3 and its further development according to the creep curve ɛ c (σ 3 , t ).

  Fig. 4.1

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  The Study of Metal Structures and Their Mechanical Properties

  Pergamon Unified Engineering Series

  • W. A. Wood, William F. Hughes, Arthur T. Murphy, William H. Davenport(Authors)
  • 2014(Publication Date)
  • Pergamon

    (Publisher)

  Because the primary or transient creep depends sensitively on the initial loading and structural state its rate, in practice varies from metal to metal. However, in general, as pointed out by Cottrell (Ref. 14), the variations fall within limits obtained by giving n particular values in the relation ! ocf-n. Thus n = 1 gives one limit, so-called logarithmic creep which dies away most rapidly; n = § gives the somewhat slower but commonly observed Andrade β-flow; and n = 0 would give the final constant rate of a steady state. Before further discussing the various laws it will be convenient to refer to the other variables. (ii) Stress Laws In practical specifications it is only necessary to know that a given stress σ should not produce more than a specified strain in a specified time, for example, not more than 1 percent in 10,000 hours for jet-engine alloys or in 100,000 hours for steam-turbine alloys. Whether the strain occurs by primary creep or by secondary creep is immaterial. However, for theoretical study it would be useful to know how stress affects each type of creep separately. Unfortunately, how it affects primary creep is difficult to deal with in detail; this creep depends too much on the initial condition of the metal and the effect of initial loading or extension e 0 . But how stress affects secondary creep has been reduced to general rules such as the following: € °c σ (when σ is small), e oc o-m (when σ is medium), € oc exp (Βσ) (when σ is large). 331 The Study of Metal Structures and their Properties The rules are sometimes summarized by e oo sinhZkr, which approximates to the others at appropriate ranges of σ. Typical illus-trations of the linear law will be found in work by Chalmers (Ref. 15) on tin; of the power law in work by Weertmann(Ref. 16), Dorn (Ref. 17), and their co-workers, who show too that m tends to 3 for dilute alloys and to 4 for pure fee and cph metals; and of the hyperbolic sine law in work by Harper and Dorn (Ref. 18).

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  Creep and Long-Term Strength of Metals

  • A. M. Lokoshchenko(Author)
  • 2017(Publication Date)
  • CRC Press

    (Publisher)

  N , which are called the structural parameters. The kinetic creep theory consists of the mechanical equation of state

  (1.39)

  p ˙

  = p

  ( σ , T ,

  q 1

  ,

  q 2

  , … ,

  q N

  )

  and a system of kinetic equations for determining the parameters q i . The structural parameters

  q i

  ( i = 1 , 2 , … , N )

  , used in (1.39 ), change during deformation in accordance with the kinetic equations

  (1.40)

  d

  q i

  =

  a i

  d p +

  b i

  d σ +

  c i

  d t +

  g i

  d T

  and the coefficients a i , b i , c i , g i are the functions of p , σ , t , T , and also of q 1 , q 2 , …, q N . The relationships (1.39 ) and (1.40 ) widen the range of theories available for describing the greatly different experimental results. Extensive studies of the creep of metals using the mechanical equation of state in the form (1.39 ), supplemented by the kinetic equations (1.40 ), were carried out in a large number of investigations by Yu.N. Rabotnov and his colleagues.

  We examine the process of creep at a stepped increase of stress σ (t ). The analytical description of the creep curve after a change of stresses is carried out using a system of equations (1.39 ) and (1.40 ). We examine the four variants of the kinetic theory which differ in the number and form of the kinetic parameters.

  1.9.1. The variant of the theory for describing differences in the creep processes with increasing and decreasing stresses

  It is assumed that the creep process in the entire range of the applied stresses is characterised by only a single, steady stage, and the steady-state creep rates with increasing and decreasing stresses differ.

  As an example, we examine the results of tests carried out at the Institute of Mechanics of the Lomonosov Moscow State University [166 ]. These investigations were carried out to study the creep of

  D 16 T

  duralumin alloy at a temperature of T = 200o C in the conditions of the increase of the axial stress σ from 40 to 90 MPa and a subsequent decrease of σ to 40 MPa (Fig. 1.15 ). These experiments resulted in the following experimental values of the steady-state creep rate

  p ˙

  at different stresses σ (Fig. 1.16

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