Laboratory Report
Microstructure and Mechanical Preperties
The Creep Yufei Chang • Group H
Abstract The progressive deformation of a material at constant stress is called creep.In this experiment we are about find the effect of temperature and stress on steady state creep.The materials of specimen that we used is lead, as it shows poor resistance to creep and can be easily tested at room temperature.
Introduction To determine the engineering creep curve of a metal,a constant load is applied to a tensile specimen maintained at a constant temperature, and the strain of the specimen is determined as a function of time.Although the measurement of creep resistance is quite simple in principle, in practice the elapsed time of such tests may extend from several months to years.
The slope of this curve shows above is the creep rate dt /dÎľ .The curve may show the instantaneous elastic and plastic strain that occurs as the load is applied, followed by the plastic strain which occurs over time. Three stages to the creep curve may be identified: Primary creep: in which the creep resistance increases with strain leading to a decreasing creep strain rate. Secondary (Steady State) creep: in which there is a balance between work hardening and recovery processes, leading to a minimum constant creep rate. And the time elapsed in this stage is considerable long. So the time we measured was in this stage.Tertiary creep: in which there is an accelerating creep rate due to the accumulating damage, which leads to creep rupture, and which may only be seen at high temperatures and stresses and in constant load machines.
The creep will occur at temperatures greater than 0.4 to 0.5 the melting temperature (when the temperature is expressed in degrees Kelvin).The materials will slowly deform under loads which would not cause any plastic deformation at room temperature. The strain, instead of depending only on the stress, also depends on temperature T and time t.
ε = f(σ,t,T) From the graph above,note the point at which the strain rate change occurs is the slowest creep rate. Although accurately called ε min , it is frequently called
εss.Primary creep may be included with the initial elastic strain or treated as a function of time. Tertiary creep is usually not considered since failure by excessive elongation usually occurs prior to tertiary creep. We will concentrate on εss, since this is the most common approach. The stress dependence of εss, at a constant temperature is usually given by a power-law relationship,
ε ss = Bσ n where n is a material constant called the creep exponent and B is a function of temperature. When plotted on log-log coordinates, the data falls along a straight line whose slope is given by n. The temperature dependence of ε ss at a constant stress is usually given by an Arrhenius rate equation,
ε ss = C exp (-Q/RT) where C is a function of stress, Q is the activation energy for creep, R is the universal gas constant and T is in degrees Kelvin. Note that as the temperature increases, the rate increases exponentially. The value of Q is found by plotting the natural logarithm of εss vs. 1/T. The data should fall along a straight line of slope -Q/R. As you might expect, the function of temperature, B, is an Arrhenius rate function and the function of stress, C, is a power function. The general relationship between εss, σ and T is
ε ss = Aσn exp ( -Q/RT ) where A, n and Q are material constant that vary from material to material, and have to be found experimentally. There are four mechanisms of creep: Dislocation glide, Dislocation creep,Diffusion creep and Grain-Boundary Sliding. and these will be discussed in detail in the discusion part.
Experimental Procedure The starting of this experiment is by accurately measuring the gauge length and diameter of the 6 creep rigs.The three buckets that the lead specimens were to be immersed in were then filled with ice, warm water and hot water respectively. The temperature of each bucket was again accurately measured and recorded.With the preparation finished the creep rigs were then assessed, ensuring that the pulley
wire was correctly positioned and under sufficient tension. The lead wire specimens were then fixed into the grips on the pulley wire. To ensure consistent readings were possible the potentiometer spindles were rotated until a reading of approximately zero was obtained. Temperature baths were then placed around the required specimens and the appropriate load was applied simultaneously.As the specimens extended by creep the 250X potentiometer (across which a known voltage was applied) incorporated into each rig rotated.The output from each rig potentiometer was recorded by the chart recorder; the graph produced was in the form of ‘output voltage’ versus ‘time’. After about 30 minutes there was sufficient data to obtain the slope of the line,∆V/∆t .
Results Rig No.
Load Kg
Temp(˚C0
Initial Length (mm)
Initial Diameter (mm)
Engineering Stress(Mpa)
1/Temp(1/ k)
6
2.45
Rt 20.5
200
1.86
8.85
2.18
5
2.6
Rt 20.5
190
1.76
10.48
2.35
4
2.75
Rt 20.5
200
1.84
10.15
2.32
3.1
3
Rt 20.5
200.5
1.74
12.38
2.52
3.2
2.75
52
198.5
1.8
10.6
2.36
2
2.75
10
200
1.75
11.22
2.42
1
2.75
0
200
1.86
9.93
2.3
Slope from recorder mm/s
Strain Rate 1/s
ln dε/dt
Temp K
1/Temp 1/K
4.00E-04
2.00E-06
-13.12
293.65
3.41E-03
1.18E-03
6.18E-06
-11.99
293.65
3.41E-03
1.33E-03
6.65E-06
-11.92
293.65
3.41E-03
2.67E-03
1.33E-05
-11.22
293.65
3.41E-03
1.71E-03
8.61E-05
-11.66
325
3.08E-03
2.38E-04
1.17E-06
-13.66
283
3.53E-03
1.98E-04
9.90E-07
-13.8
273
3.66E-03
Sample Calculation: [1st Row] Engineering Stress, ,σ-eng..=,F-A. where; A= πr²=π(0.93×10¯³)²=2.716×10ˉ⁶m2 F=mg=2.45×9.81≡24.035N ∴ F/A= 24.035/2.63×10ˉ⁶=9.14×10⁶Pa ≡9.14MPa Strain Ratedε/dt=∆l/Lt where ∆l/t = 4×10ˉ⁴mm/sec, which is the slope from the recorder, approximated by taking the gradient of the line of best fit on the graphs of ‘voltage vs. time’ (included in appendix). The extension, ∆l, was then converted from mV into mm on the assumption that 5mV=1mm. The original length, L = 200mm ∴ ∆l/Lt =4×10ˉ⁴/200=2.0×10ˉ⁶secˉ¹ From the above results the graphs of ‘ln Strain Rate vs. 1/Temp’ and ‘ln Strain Rate vs. ln Stress’ can be plotted. The resulting graphs will enable calculation of the activation energy, Q, for steady state creep and the stress exponent of lead, n.
At constant stress the dependence of steady state creep on temperature is given by
dε/dt=Aexp(-Q/RT) Where A = a constant, Q = activation energy, T = temperature in K and R = gas constant = 8.314 Jmol-1K-1 Taking the natural logarithm, ln, of both sides produces an equation that is linear. ln(dε/dt)=lnA-(Q/RT) y=C +ax As the graph plotted is of ln(dε/dt) against 1/T. the gradient of the resulting line of best fit is -Q/R -Q/R= -3921.6 ∴Q= 3921.6×8.314 =32604.2=32.6KJmolˉ¹
The steady state creep rate for varying stresses is defined by; dε/dt=Bσ Where B = a constant, σ = stress in MPa and n = exponent. [3] Again taking the natural logarithm of both sides gives a linear equation ln(dε/dt)=nlnσ+ lnB
y= bx+ C
The gradient of the graph produced is therefore equal to the stress exponent. Thus b=n=5.4506 Sources of Error  Irregularities in the shaped of the lead specimen, i.e. bends, may cause a nonuniformly distributed load and thus change in strain rate.Creep is highly temperature dependent, maintaining the temperature during the experiment proved difficult and thus the temperature of the specimen could have changed by a small amount during testing.Differing specimens will have varying concentrations of dislocations.
Discussion From the experiment we found that creep is a activated process and highly related to temperature and stress act on it.And another fundamental in understanding is the creep resulting form a dislocation moving and the flow of vacancies or interstitials. the chief creep deformation mechanisms can be group as Dislocation glide:involves dislocation moving along slip plane ans overcoming barriers by thermal activation.Dislocation creep:involves the movement of dislocations which overcome barriers by thermally assisted mechanisms involving the diffusion of vacancies or interstitials.Diffusion creep: which involves the flow of vacancies and interstitials through a crystal under the influence of applied stress.Grain boundary sliding: involves the sliding of grain past each other. And as we can related these theory to our experiment, frequently, more than one creep mechanism will operate at the same time.if several mechanisms are operating in parallel.The fastest mechanism will dominate the creep behavior. As we clearly known the mechanism is a stress-temperature combination.A new theory will be introduced. A practical way of illustrating and utilizing the constitutive equations for the carious creep deformation mechanisms is with deformation mechanism maps.
The boundaries of these region in the map obtained by equating the appropriate equations, and solving for stress as a function of temperature. Unlike brittle fracture, creep deformation does not occur suddenly upon the application of stress. Instead, strain accumulates as a result of long-term stress. Creep deformation is "time-dependent" deformation. Another main concern for us as a material engineer is to precent creep in some cases. The normal creep temperature is 0.4-0.5 Tm. Hence, if a material is working at less than 0.3 Tm or other critical temperature.Then no creep will occur.precipitaion hardening is another method in the prevention of creep. In another word, some creep is desirable. Extrusion, hot rolling , hot pressing and forging are carried out at temperature which dislocation creep is the dominate mechanism of deformation.
Conclusion Creep is varying with temperature and stress, ans depend on several deformation mechanisms. The experiment result we got is lower than the anticipated value from the references.
References D. R. Askland, The Science and Engineering of Materials, PWS Engineering, 1984, pp. 138143, 718-719. G. E. Dieter, Mechanical Metallurgy, McGraw-Hill, 1961, pp. 335-347, 354-359. Wulff, Structure and Properties of Materials, Vol. 3, pp. 16-19, 113-118, 133136. L.H. Van Vlack, Elements of Materials Science and Engineering, 5th Ed., pp. 187188, 520-521.