3B4 Lead Creep Eamonn Slattery 12313584 Group 1 Lab Date: 24/03/2015

Abstract

This purpose of this experiment is to examine the material properties of lead with respect to creep.

A standardised test was carried out on a test piece of lead with varying loads and several constants

were extrapolated from the data to accurately represent the mechanical properties of lead

mathematically. During the test it was found that lead will quickly undergo creep after its initial

displacement under a load at room temperature. With increasing load it was found that the creep

rate increased and the steady state creep period (the length under which a material experiences

creep before failure) was shortened.

Introduction

Creep is the slow, continuous deformation of a solid over time where the strain becomes dependent

on stress, temperature and time as opposed to just stress.[1]

For most metals and ceramics, room temperature is considered to be low where their strain can

be represented as:

= ()

However, for some materials such as lead, room temperature is considered hot as it is ~300K

which is half the melting point (600K). This means that at room temperature lead behaves like a

material that has been heated up to a point where it becomes soft. At this softened state a material

is susceptible to creep and its strain depends on the

variables mentioned above:

= (, , )

To be more specific about when a material is susceptible to

creep other than just being considered hot or cold

there is a general rule for defining the temperatures at

which materials will begin to creep. Generally:

> 0.3 0.4

> 0.4 0.5

So for a material such as lead room temperature is over 0.5

times the melting temp which means that it is very much in

the creep range. Other materials which can undergo creep

at room temperature are tin, polyester and acrylic.[1] Figure 1: Bulb filament failed due to creep. The high temperature caused the tungsten filament to undergo creep under its own weight

Creep is an important phenomenon for many areas of engineering such as forensic, design and all

the other core disciplines involving the mechanical use of materials. When designing a system an

engineer must ascertain the operating temperature that the material will work under and deduce

whether that material will be subject to creep deformation. If the material is found to then be

susceptible to creep, the designer must calculate the amount of time that the material can

withstand under the applied load before it will fail due to creep. This time range is known as the

steady state creep and can vary from seconds to years depending on the material and applied load.

As creep failure is dependent on 3 variables,

temperature, time and stress engineers generally

plan work cycles and temperature limits to control

creep.

An example would be a preheating tower and kiln

in a cement processing plant. The inside of the

pipework is lined with ceramic firebricks to

insulate the steel outer from the intense heat,

without this insulation the heat (while not high

enough to melt the steel) would increase the

creep rate so high in the structure that it would

fail under its own weight if it continued operating.

Temperatures are also monitored continuously to

ensure that it stays at a level low enough to

prevent the onset of creep deformation.

Another example is the fire coating that steel

girders are given in skyscrapers. This coating is

applied to the steel even though a fire would not

reach a heat high enough to melt the steel

structure. A fire would however be enough to heat the steel to above its creeping temperature and

the massive self-weight load of a skyscrapers steel lattice would cause the structure to fail after a

short period of steady state creep.

Figure 4: Preheating Tower and Kiln, similar to the one located in Platin, Drogheda. The extreme temperatures require a strict maintenance regime to minimise the risk of creep failure.

Figure 2: Steel with insulation sprayed onto its surface.

Figure 3: After a building fire this steel structure failed under creep. Whereas the burned wooden beams were left supporting the steel.

Theory

Creep happens in a material when an elevated temperature promotes diffusion whilst the material is

subjected to a tensile load that is lower than the materials yield strength. The diffusion allows the

atoms inside the material to rearrange when a stress is applied, this in turn allows the dislocations in

the material to move past obstacles in their path and as a result the material begins to deform even

though the applied load is under its yield strength.

When the load is applied the atoms near the loaded

dislocation treat the dislocation like an area of high

concentration and begin to diffuse towards areas of

lower stress. As these atoms diffuse away the

obstruction blocking the dislocations movement is

dissolved gradually as more and more of its atoms

diffuse and eventually the dislocation is free to move

in the direction of the applied force. This process is

called Climb and since it requires diffusion it can

only happen at temperatures above 0.3-0.4 times its

melting temperature i.e. the creep temperature.[1]

The process of creep happens over three stages, primary creep, secondary (or steady-state) creep and tertiary creep. The initial primary creep is the elastic deformationthat the material undergoes when the load is applied, there is initially a high rate of increasing strain followed by by a gradual drop in strain rate. After this the material begins to exhibit steady state creep and the rate of increasing slope begins to level off towards zero before gradually increasing over a period of time () . Finally at the tertiary creep stage the strain rate accelerates quickly to the point of failure in the material

Both the primary annd tertiary stages are not of much importance to Engineers as the first stage is mainly elastic deformation and at the final stage the material is considered to have all but failed. The important region is the steady state creep, as this gives an Engineer the information he needs to work with and design for. By knowing how long a material will undergo creep for when subjected to a certain load the designer can plan tolerence limits or work cycles to his designs to ensure that a product will not fail when used correctly.

In order to analyse the steady state creep behaviour of a material, we use a standardised test on a specimen with precise dimensions and constant temperatures in order to plot the steady state creep rate over time.

Figure 5: Close up of crystal grain structure (Creative Commons)

Figure 6: The tecquipment machine with a test piece just after failure

By then plotting the Log of the steady state creep against the Log of the stress we can establish that:

=

Where A = the creep, and n = the creep exponent.

This sort of creep is called the power-law creep

The test equipment used a lever with a mechanical advantagein order to impart a tensile load on the test material. Taking into account the beams self weight, the nagers self weight and the mechanical advantage we found the stress equation to be:

=(( 8) + (0.4 4))

The Log of that stress value is then plotted against the the Log of the steady state strain for three different weights and a line is fitted. The equation of the line is thus:

= +

Where LogA is the intercept and n is the slope. We can then use these two values as the material constants for lead in the previous equation =

Materials & Method

Rig

The setup for this experiment was a standardised lead test piece inserted into tecquipment machine.

The tecquipment machine is a basic rig that uses an

8:1 mechanical advantage lever arm to pull a test

piece apart between two pins. A hanger at the end

of the lever allows variable sized weights to be

hung from the rig.

At the other end of the hanger, above the test

piece and lever arm, the LVDT is placed with the

probe touching the top surface of the arm. As the

test piece creeps the lever arm moves upwards and

the transducer registers the movement on an

external computer.

The computer reads in the data from the

transducer and updates a sample every second.

After the piece is loaded in the machine the

computer program is activated and runs a test every second. After the piece has failed the program

is stopped and an output of each displacement per second is output.

Test Piece

The test piece is a cut piece of lead sheet 2mm thick. The thin section

is 5mm wide and 19mm long between both chamfers. The chamfers

remove stress concentrations and ensure that the test works over

the 19mm long straight section.

Procedure

1. The pre-fabricated test pieces are carefully loaded into the tecquipment machine over the

two dowels. Care is taken not to bend the pieces as lead is soft and easily deformed

plastically, which would affect the results.

2. A 1kg weight is carefully loaded onto the hanger at the other end of the rig, care is taken to

ensure the initial loading on the test piece is gradual as even a dynamic load could fail the

piece.

3. The computer program is started and begins to sample the displacement read from the

transducer every second.

4. Eventually the test piece fails under creep, the computer program is stopped, the piece is

removed and the rig is reloaded with a new test piece.

5. The procedure is then repeated with 1.2 and 1.4 kg weights.

6. The results from the experiments are post edited in excel and graphs are used to calculate

the material constants of lead.

Results

The data from the experiment was entered into a excel spreadsheet and the data was created into

three graphs representing 1, 1.2 and 1.4kgs respectively.

The graphs map the displacement of the test piece over time, the initial spike is the loading strain

and elastic deformation of the material. It then levels off somewhat to the steady state phase where

we can then get a value for the steady state strain rate. The graph above was the first test at 1kg and

the steady state strain rate was found to be 0.084s-1

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

1

16

31

46

61

76

91

10

6

12

1

13

6

15

1

16

6

18

1

19

6

21

1

22

6

24

1

25

6

27

1

28

6

30

1

31

6

33

1

34

6

36

1

37

6

Stra

in (

E)

Time (s)

Strain vs Time 1.0kg load

Strain vs Time

The graph above is the second test at 1.2kg weight. The strain curve is very much like the theoretical

image shown in figure 6. The steady state creep ranges from around 17 up to 160 seconds. After 160

seconds the tertiary phase begins and the piece fails completely approximately 10 seconds later.

The 3rd graph is the loading test now with a 1.4kg weight. Again the curve is as expected however

the time to failure from start is much more rapid (~50s) the steady state phase in this test only lasts

approx. 30 seconds before tertiary phase and ultimately failure happens.

After the three tests were ran the steady state

strain rate for each case was found to be as

found on the chart to the right:

Mass Steady State Strain Rate

1.0kg 0.000526

1.2kg 0.001053

1.4kg 0.007368

0

0.1

0.2

0.3

0.4

0.5

0.61 9

17

25

33

41

49

57

65

73

81

89

97

10

5

11

3

12

1

12

9

13

7

14

5

15

3

16

1

16

9

17

7

18

5

19

3

20

1

20

9

Stra

in (

E)

Time (s)

Strain vs Time 1.2Kg Load

Strain vs Time

-0.1

0

0.1

0.2

0.3

0.4

0.5

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57

Stra

in (

E)

Time (s)

Strain vs Time 1.4Kg Load

Strain vs Time

Strain Rate vs Time

Using the previous values for strain against time we then calculate strain rate vs time. Which is the

rate of change of strain (the slope). Using these graphs we can accurately locate the transitions

between either ends of the steady state region, as the steady state region has very little slope.

The first graph indicates the transition from primary to secondary creep quite well. It also reinforces

that there was no tertiary phase during the first test which will be explained further in the

discussion.

The second test had good indications of both primary -> steady state and steady state > tertiary

creep. The slope is shown to be near zero from 15 to 160 seconds.

-0.002

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

1

16

31

46

61

76

91

10

6

12

1

13

6

15

1

16

6

18

1

19

6

21

1

22

6

24

1

25

6

27

1

28

6

30

1

31

6

33

1

34

6

36

1

37

6

Stra

in R

ate

Time (s)

Strain Rate vs Time 1.0Kg

Strain Rate vs Time

0

0.02

0.04

0.06

0.08

0.1

1 9

17

25

33

41

49

57

65

73

81

89

97

10

5

11

3

12

1

12

9

13

7

14

5

15

3

16

1

16

9

17

7

18

5

19

3

20

1

20

9

Stra

in R

ate

Time

Strain Rate vs Time 1.2kg

Strain Rate vs Time

The final test also showed two clear peaks marking the transition between creep phases. The peaks

in this case are less abrupt due to the short overall time of the experiment, there was only 25% of

the amount of samples as the second test. Slope was near zero for approximately 30 seconds.

LogStrain vs LogStress

stress steady state strain log strain steady state

log stress

9417600 0.000526 -3.279014256 6.97394024

10987200 0.001053 -2.977571629 7.04088703

12556800 0.007368 -2.132650383 7.09887898

In order to find the material constants for lead we finally plotted the Log of the strain against the Log

of the stress. The stress was calculated using the formula from the theory section:

=(( 8) + (0.4 4))

The strain at steady state was found from where the strain rate was non-changing and the logs were

taken of both results.

Sample calculations for 1kg case:

=((1 9.81 8) + (0.4 9.81 4))

(0.005 0.002)=

The results were placed on a scatter plot and a linear fit line was fitted. The equation of the line was

then extrapolated and used to find the ultimate values of A and n.

-0.02

0

0.02

0.04

0.06

0.08

0.1

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57

Stra

in R

ate

Time

Strain Rate vs Time 1.4kg

Strain Rate vs Time

The equation of the line for the fitted line was found to be y = 9.056x - 66.531 Which we can then use the equation:

= +

To find the values of A and n:

A = 2.94410-67

N = 9.0056

Questions Estimate the maximum applied stress which the material can withstand without significant creep, defined in two possible ways:

(a) Less than 1% per year. =

= 0.01

=0.01

2.9441067= 3.16 1010

A = 2.94410-67 N = 9.0056

3.16 1010 = 2.944 10679.0056

9.0056 =3.16 1010

2.944 1067

= 3.16 1010

2.944 10 67

9.0056

= .

(b) A total time to failure of more than 10 years.

=

10 ()=

0.471053

3.15569 108= 1.5 109

y = 9.056x - 66.531R = 0.9078

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

6.96 6.98 7 7.02 7.04 7.06 7.08 7.1 7.12LO

G S

TRA

IN

LOG STRESS

LogSteadyStateStrain vs LogStress

LogStrain vs LogStress Linear (LogStrain vs LogStress)

= 1.5 109

2.944 1067

9.0056

= .

Discussion

Strain vs Time

The graphs were produced and appeared exactly as expected with the exception of the 1kg load. For the other two the steady state creep region was reasonably visible with the curve also indicating areas of primary and tertiary stress The first graph may have been recorded in error or there may have been an error in how we set up the apparatus. The data ends at what appears mid-way through the steady state creep. This may have been an error in the recording system or an error in setting up the rig. Another possibility is that the data was set to stop recording automatically when no new data is read after a certain amount of time. Its possible that the intermittent data was updating so slow that the system may have thought the material had failed, although as the last reading was a different value to its previous value this may not have been the case.

Strain Rate vs Time

These graphs give a good indication of the transition of phases and the length of the steady state

creep. The two spikes in the graph represent area of high rate of change in strain and the trough in

between represents the steady state creep where there is an almost zero rate of change.

The first graph further reinforced that an error caused the data recording to end prematurely as

there is no second spike in the graph representing the transition from steady state to tertiary creep.

LogStrain vs LogStress

The scatter plot produced a linear trend line which was used to get a line equation from and then

values of A and n. The value of n was found to be 9.0056 which is within the expected range of 3-10.

After getting the values of our material constants we were then able to answer the two questions

provided. The answers were found to be around 2-3Mpa which is around 20-30% the stress that was

imparted on the material during the experiment. This indicates that at a lower force of 2.1MPa the

lead would not undergo any significant creep and would be able to deform under creep by more

than 10 years before the test would have failed.

Overall the experiment proved to confirm most of the theory regarding creep in materials. The

primary creep was clearly visible on the graph and showed us the material behaving elastically

before the onset of creep. The steady state creep was most visible on the second set of graphs

(strain rate vs time) as a long trough of near zero data between two peaks. And the tertiary creep

was visible as a sharp spike on the strain rate graphs and a sudden rising curve on the strain graphs,

this clearly indicated how the material had begun to fail and was quickly pulled apart in tension after

the dislocations had completely failed in the material.

There was several sources of error that could have affected the results however and some of the

most important are listed as followed:

We did not measure the test pieces before the experiment and have no idea if they had been

machined correctly to the exact tolerances required, it would have been prudent to measure the

dimensions of the piece before starting in order to eliminate this source of error.

If the pieces were machined correctly we have no idea then the conditions they were stored in or

how much they were handled with before the experiment, lead is an extremely soft metal at room

temperature and a person holding the piece could easily have deformed it plastically in their hands.

This would have significantly changed the materials properties under test conditions.

The LVDT was not calibrated before the experiment and as such we have no idea of its accuracy

during the test. Again it would have been wise to check when the device was last calibrated in order

to remove this source of possible error.

Finally the first graph recorded incomplete, this could have been a software error or possibly a

problem with the LVDT but there is no way to know for sure. The process of carrying out the

experiment under 3 different loads minimised this error however and we were still able to get good

data. Had we only carried out the experiment once, the results would have been inconclusive.

Conclusion

The aim of this experiment was to investigate into the phenomenon of creep in materials and specifically the behaviour of lead, a material that is at its creep temperature at room temp, when under a load that is well below its yield strength. At each load the lead was found to undergo creep and eventually fail. For each increasing load the steady state was shortened and the piece failed sooner. After analysing the data the material constants of lead were calculated and used to calculate two design loads for using the test pieces.

This experiment has shown the importance of considering the possibility of creep in future engineering designs and has also shown how experiments can be used to come up with design calculations which can be used to minimise the dangers of creep.

References

1. Jones, A., Engineering Materials 1. 3rd ed. 2005: Elsevier.