8. TIME DEPENDENT BEHAVIOUR: CREEP

1 8. TIME DEPENDENT BEHAVIOUR: CREEPIn general, the mechanical properties and performance of materials change withincreasing temperatures. Some properties and performance, such as elastic modulusand strength decrease with increasing temperature. Others, such as ductility, increasewith increasing is important to note that atomic mobility is related to diffusion which can bedescribed using Ficks Law:D=DOexp QRT ( )where D is the diffusion rate, Do is a constant, Q is the activation energy for atomic motion,R is the universal gas constant ( K) and T is the absolute temperature. Thus,diffusion-controlled mechanisms will have significant effect on high temperaturemechanical properties and performances.

2 For example, dislocation climb, concentrationof vacancies, new slip systems, and grain boundary sliding all are diffusion-controlled andwill affect the behaviour of materials at high temperatures. In addition, corrosion oroxidation mechanisms, which are diffusion-rate DEPENDENT , will have an effect on the lifetime of materials at high is a performance-based behaviour since it is not an intrinsic materialsresponse. Furthermore, creepis highly DEPENDENT on environment including temperatureand ambient conditions. CREEP can be defined as time- DEPENDENT deformation atabsolute temperatures greater than one half the absolute melting. This relativetemperature (T(abs)Tmp(abs)) is know as the homologous temperate.

3 CREEP is a relativephenomenon which may occur at temperatures not normally considered "high." Severalexamples illustrate this ) Ice melts at 0 C=273 K and is known to CREEP at -50 C=223 K. The homologoustemperature is 223273= which is greater than so this is consistent with thedefinition of ) Lead/tin solder melts at ~200 C=473 K and solder joints are known to CREEP at room temperature of 20 C=293 K. The homologous temperature is 293473= is greater than so this is consistent with the definition of Stress RuptureT/Tmp > Load- Low Loads - High Loads- Precision Strain - Gross Strain Measurement ( f< ) Measurement ( f up to 50%)- Long term (2000-10,000 h) - Short term (<1000 h)- Expensive equipment - Less expensive equipmentEmphasis on minimum Emphasis on time to failure atstrain rate at stress and at stress and temperaturetemperature DisplacementFigure Comparison of CREEP and stress rupture testsc) Steel melts at ~1500 C=1773 K and is known to CREEP in steam plantapplications of 600 C=873 K.

4 The homologous temperature is 8731773= whichis equal to so this is consistent with the definition of ) Silicon nitride melts/dissociates at ~1850 C=2123 K and is known to CREEP in advanced heat engine applications of 1300 C=1573 K. The homologoustemperature is 15732123= which is greater than so this is consistent with the definition of a CREEP test is rather simple: Apply a force to a test specimen andmeasure its dimensional change over time with exposure to a relatively high a CREEP test is carried to its conclusion (that is, fracture of the test specimen), oftenwithout precise measurement of its dimensional change, then this is called a stressrupture test (see Fig ). Although conceptually quite simple, CREEP tests in practice aremore complicated.

5 Temperature control is critical (fluctuation must be kept to < C). Resolution and stability of the extensometer is an important concern (for materials, displacement resolution must be on the order of m).Environmental effects can complicate CREEP tests by causing premature failures unrelatedto elongation and thus must either mimic the actual use conditions or be controlled toisolate the failures to CREEP mechanisms. Uniformity of the applied stress is critical if thecreep tests are to interpreted. Figure shows a typical CREEP testing basic results of a CREEP test are the strain versus time curve shownschematically in Fig. The initial strain, i= iE, is simply the elastic response to theapplied load (stress).

6 The strain itself is usually calculated as the engineering strain, = LLo. The primary region (I) is characterized by transient CREEP with decreasing creepstrain rate (d dt= ) due to the CREEP resistance of the material increasing by virtue ofmaterial deformation. The secondary region (II) is characterized by steady state CREEP ( CREEP strain rate, min= ss, is constant) in which competing mechanisms of strainhardening and recovery may be present. The tertiary region (III) is characterized byincreasing CREEP strain rate in which necking under constant load or consolidation offailure mechanism occur prior to failure of the test piece. Sometimes quaternary regionsare included in the anlaysis of the strain-time curve as well, although these regions arevery specific and of very short Typical CREEP test Time, tPrimary ISecondary IITertiary IIIC onstant LoadConstant StresstfFigure Strain time curve for a CREEP testIn principle, the CREEP deformation should be linked to an applied stress.

7 Thus, asthe specimen elongates the cross sectional area decreases and the load needs to bedecreased to maintain a constant stress. In practice, it simpler to maintain a constantload. When reporting CREEP test results the initial applied stress is used. The effect ofconstant load and constant stress is shown in Fig. Note that in general this effect(dashed line for constant stress) only really manifests itself in the tertiary region, which isbeyond the region of interest in the secondary region. The effects of increasingtemperature or increasing stress are to raise the levels and shapes of the strain timecurves as shown in Figure Note that for isothermal tests, the shapes of the curves forincreasing stress may change from dominant steady state to sigmoidal with little steadystate to dominant primary .

8 Similar trends are seen for iso stress tests and increasingtemperature (see Fig. ). CREEP mechanisms can be visualized by using superposition of various strain-timecurves as shown in Fig. An empirical relation which describes the strain-time relationis: = i1+ t1/3()exp(kt)( )where is a constant for transient CREEP and k is related to the constant strain rate. A"better" fit is obtained by: = i+ t1 exp(rt)()+t ss( )where r is a constant, t is the strain at the transition from primary to secondary CREEP and ss is the steady-state strain rate. Although no generally-accepted forms of nonlinearstrain-time relations have been developed, one such relations is: = i+B mt+D 1 exp( t)()( )where B, m, D, a and b are empirical , t > > > 111223 Iso thermal TestsTime, t > > > 111223 Iso stress TestsFigure Effect of stress and temperature on strain time CREEP curvesIn this relation, if t >ttransient then = i+B mt+D ( )and the strain rate is the steady-state or minimum strain rate:d dt=B m= ss( )The steady state or minimum strain rate is often used as a design tool.

9 Forexample, what is the stress needed to produce a minimum strain rate of 10-6 m/m / h ( or10-2 m/m in 10,000 h) or what is the stress needed to produce a minimum strain rate of 10-7 m/m / h ( or 10-2 m/m in 100,000 h). An Arrhenius-type rate model is used to include theeffect of temperature in the model of Eq. such that: ss= min=A nexp QRT ( )where n is the stress exponent, Q is the activation energy for CREEP , R is the universal gasconstant and T is the absolute determine the various constants in Eq. a series of isothermal and iso stresstests are required. For isothermal tests, the exponential function of Eq. becomes aconstant resulting in ss= min=B n( )Equation can be linearized by taking logarithms of both sides such thatlog ss=log min=log B+n log ( ) , tTime, tTime, tTime, t=++ i iTotal CREEP Curve Sudden Strain Transient CREEP Viscous CREEP Figure Superposition of various phenomenological aspects of creepLog-log plots of min= ss versus (see Fig.)

10 Often results in a bilinearrelation in which the slope, n, at low stresses is equal to one indicating pure diffusioncreep and n at higher stresses is greater than one indicating power law CREEP withmechanisms other than pure diffusion ( , grain boundary sliding).For iso stress tests, the power dependence of stress becomes a constant resultingin ss= min=C exp QRT ( )Equation can be linearized by taking natural logarithms of both sides such thatln ss=ln min=ln C QR1T( )Log-linear plots of min= ss versus 1T (see Fig. ) results in a linear relation in whichthe slope, QR, is related to the activation energy, Q, for n=1 (diffusion CREEP )n>1 (power law CREEP ) .Figure Log-log plot of minimum CREEP strain rate versus applied stress showingdiffusion CREEP and power law Log-linear plot of minimum CREEP strain rate versus reciprocal of temperatureshowing determination of activation goal in engineering design for CREEP is to predict the behaviour over the longterm.