Failure Fatigue and Creep

Summary

This script discusses mechanical failures due to fatigue and creep in engineering materials. Fatigue, responsible for 90% of mechanical part failures, is a sudden failure under fluctuating stress, often initiated from surface defects. Creep is the continuous deformation at elevated temperatures under constant stress, progressing through primary, secondary, and tertiary stages. The lecture includes examples of fatigue testing, the significance of stress amplitude and mean stress, and the use of Larson-Miller parameters for estimating rupture times at different temperatures. It emphasizes the importance of understanding these phenomena for predicting material performance and preventing failures.

Takeaways

• 🔩 Fatigue is a type of failure caused by fluctuating stress on structures, such as a bridge with cars driving over it, and can lead to sudden failure without warning.
• 📉 Fatigue can occur even when the maximum stress experienced by a part is less than its yield stress, and it's responsible for about 90% of mechanical engineering failures.
• 🔍 A study by Sherry Labs showed that improperly installed bolts on a mining truck led to sudden wheel detachment, illustrating the real-world consequences of fatigue.
• 🛠️ Fatigue testing machines simulate the dynamic stress on parts to predict their performance and lifespan under cyclic stress conditions.
• 📊 Fatigue behavior is often plotted on a graph with stress amplitude on the y-axis and the number of cycles to failure on the x-axis, showing different behaviors for steels and non-ferrous alloys.
• 🛑 For many steels, there's a 'safe' stress level below which parts won't fail due to fatigue, while non-ferrous alloys often have no fatigue limit and require a specified fatigue strength.
• 🔬 Fractography of failed parts can reveal brittle fracture surfaces and 'beachmarks', which are indicative of fatigue failure and provide insight into the failure process.
• 🛡️ Surface treatments like shot peening and material modifications can enhance a part's resistance to fatigue by reducing stress concentrators and improving surface strength.
• 📈 Creep is the deformation of materials under constant load and elevated temperature, occurring in three stages: primary, secondary, and tertiary creep, with secondary being the most critical for long-term performance.
• ⏱️ The Larson-Miller parameter is a useful tool for estimating rupture times at different temperatures and stresses, allowing for faster testing and extrapolation to service conditions.

Q & A

What is fatigue in the context of mechanical engineering?

Fatigue is a form of failure that occurs in structures subjected to dynamic and fluctuating stress. It can lead to part failure even if the maximum stress is much less than the yield stress measured in tensile testing.

Why is fatigue failure particularly dangerous?

Fatigue failure is dangerous because it can occur suddenly and without warning, similar to a brittle fracture. The fracture surface, when examined, often appears brittle, which can be deceiving about the nature of the failure.

What role does the installation of parts play in fatigue failure?

The installation of parts plays a significant role in fatigue failure. Incorrect installation, as seen in the case of the mining truck wheel studs, can lead to premature failure even when the parts themselves are suitable for the service they are put to.

How can fatigue be simulated to test a part's performance?

Fatigue can be simulated using specialized testing apparatuses that flex the part back and forth, rotating it through multiple directions and subjecting it to sinusoidal stress cycles. The stress parameters such as mean stress, stress amplitude, and frequency can be adjusted to simulate real-world conditions.

What are the two common types of fatigue behavior seen in materials?

The two common types of fatigue behavior are one seen in many steels, where there is a safe stress level below which the part will not fail, and the other seen in non-ferrous alloys, where there is no fatigue limit and the material will eventually fail given enough cycles.

How is fatigue life defined in materials science?

Fatigue life is defined as the number of cycles it takes to cause failure at a specified stress level. It helps predict how long a part will last before needing replacement under cyclic stress.

What are the three stages of fatigue failure?

The three stages of fatigue failure are: 1) crack initiation, where a crack forms at a surface defect, 2) crack propagation, where the crack advances incrementally with each stress cycle, and 3) final failure, which occurs suddenly when the crack reaches a critical size.

What is creep, and how does it differ from fatigue?

Creep is the deformation of a material under constant stress and temperature over time, often occurring in load-bearing parts at elevated temperatures. It differs from fatigue in that it involves continuous deformation rather than cyclic stress leading to sudden failure.

What are the three stages of creep?

The three stages of creep are: 1) primary creep, with an initial instantaneous deformation followed by decreasing strain rate, 2) secondary creep, where the strain rate reaches a steady state, and 3) tertiary creep, where the strain rate increases leading to rupture.

How can the Larson-Miller parameter be used to estimate rupture times?

The Larson-Miller parameter is used to estimate rupture times by plotting it against stress on a graph. By determining the parameter at a high temperature and then extrapolating to the service temperature, one can estimate the time to rupture at that temperature.

Outlines

00:00

🔧 Introduction to Fatigue and Creep

The script begins by defining fatigue as a type of failure in structures under fluctuating stress, such as a bridge with cars driving over it. Fatigue can lead to sudden failure even if the stress is below the material's yield stress. It's responsible for about 90% of mechanical engineering failures and often results in brittle fractures. An example is provided of a failure study by Sherry Labs on mining truck wheel bolts that failed due to incorrect installation. The importance of fatigue testing is emphasized, with machines simulating sinusoidal stress to predict part performance under cyclic stress. The script also introduces the concept of fatigue life and the two types of fatigue behavior observed in materials: one with a fatigue limit and one without.

05:01

📈 Fatigue Behavior and Testing

This section discusses the fatigue behavior of steels and non-ferrous alloys, highlighting that steels have a fatigue limit below which they won't fail, while non-ferrous alloys do not. The concept of fatigue strength is introduced as the stress level for failure at a specified number of cycles. The script also explains the importance of considering probability curves for fatigue life predictions. Fatigue life is described as the number of cycles to cause failure at a specified stress level. The three stages of fatigue failure are outlined: crack initiation, crack propagation, and final failure. The use of fractography to analyze failed parts is discussed, including the identification of beachmarks and striations as indicators of fatigue.

10:01

🌡️ Creep and Its Impact on Materials

The script shifts focus to creep, which affects parts under constant load and elevated temperatures. Creep occurs in three stages: primary, secondary, and tertiary, with the secondary stage being the most critical as it represents the majority of a part's service life. The secondary creep rate is emphasized as a key parameter, and the temperature dependence of creep is discussed, noting that creep becomes significant at temperatures above 40% of a material's melting point. Methods to strengthen materials against creep, such as shot peening and modifying surface conditions, are suggested.

15:02

⏱️ Analyzing Creep Data and Estimations

This part of the script delves into analyzing creep data, with an example problem involving a steel alloy subjected to a tensile stress at a specific temperature. The concept of steady-state creep rate is introduced, and a method to calculate elongation after a given time is demonstrated. The script also covers how to determine the stress exponent 'n' from log-log plots of creep rate versus stress. An example calculation of the activation energy for creep using stress data at different temperatures is provided, illustrating how to use this information to estimate creep rates under different conditions.

20:03

🔬 Advanced Creep Analysis and Extrapolation

The script discusses advanced creep analysis, including the use of Larson Miller parameters and plots to estimate rupture times at different temperatures and stresses. The process of extrapolating creep data from high-temperature tests to predict performance at service temperatures is explained. The importance of understanding material flaws and their impact on failure is reiterated, with a summary of how temperature, stress, and material properties affect failure modes such as fracture, fatigue, and creep.

25:05

📚 Summary of Engineering Materials and Failure Theories

The final part of the script summarizes the key points about engineering materials and failure theories. It emphasizes that materials often fail at stresses lower than predicted due to inherent flaws, which act as stress concentrators. The script outlines how failure types are influenced by temperature, stress, and loading rates, with a brief overview of the factors affecting fracture, fatigue, and creep failures. The summary concludes with a reminder of the importance of understanding these concepts for designing reliable and safe engineering components.

Keywords

💡Fatigue

Fatigue in the context of the video refers to the failure of materials or structures under cyclic or fluctuating stress, even when the stress is below the material's yield stress. This is a critical concept in mechanical engineering, as it explains why parts can suddenly fail without warning. The video emphasizes that fatigue is responsible for approximately 90% of mechanical engineering failures. An example given is a bridge that experiences varying loads from cars, which can lead to fatigue failure over time.

💡Creep

Creep is defined as the gradual deformation of a material under constant stress and temperature over time. Unlike fatigue, creep involves a constant load rather than cyclic loading. The video explains that creep is particularly significant at elevated temperatures, such as those experienced in jet engines. The three stages of creep—primary, secondary, and tertiary—are detailed, with the secondary stage being the most critical as it represents the majority of a material's service life before failure.

💡Stress

Stress is the force applied to a material, and in the video, it's discussed in the context of both fatigue and creep. It's the driving force behind material deformation and failure. The video clarifies that stress amplitude and mean stress are parameters that can be adjusted in fatigue testing to simulate real-world conditions and study a material's response to cyclic loading.

💡Yield Stress

Yield stress is the point at which a material begins to deform plastically under stress. The video script explains that fatigue can lead to failure even when the maximum stress experienced by a part is much less than its yield stress, highlighting the difference between theoretical material strength and real-world performance.

💡Fatigue Life

Fatigue life is the number of cycles a material can endure before failure under cyclic loading. The video discusses how fatigue life is an important parameter in designing parts that are expected to perform reliably over a certain period. It's determined by testing materials under controlled conditions to predict their service life.

💡Fractography

Fractography is the study of fracture surfaces to understand the mechanisms and causes of material failure. The video mentions that fractography can reveal whether a failure was due to fatigue, as the fracture surface often exhibits a brittle appearance even when the failure was due to repeated stress.

💡Shot Peening

Shot peening is a process mentioned in the video as a way to enhance the fatigue life of materials by introducing a compressive residual surface layer. This process can help in reducing the initiation and propagation of cracks, thereby increasing the material's resistance to fatigue.

💡Stress Concentrators

Stress concentrators are features such as notches, grooves, or sudden changes in cross-section that can cause local stress to exceed the average stress on a part. The video explains that these can lead to premature failure due to fatigue, as they are points where cracks are likely to initiate and propagate.

💡Strain Hardening

Strain hardening, also known as work hardening, is a process where a material becomes stronger and less ductile after enduring plastic deformation. In the context of creep, the video describes how strain hardening occurs during the primary creep stage, where the material's resistance to deformation increases over time.

💡Larson-Miller Parameter

The Larson-Miller parameter is a useful tool for extrapolating creep rupture data from short-term tests at high temperatures to longer-term performance at service temperatures. The video explains how this parameter can be used to predict the life of a material under specific stress and temperature conditions, which is crucial for materials expected to last for extended periods.

Highlights

Fatigue is defined as failure due to dynamic and fluctuating stress.

Fatigue can cause failure even if the stress is below the material's yield stress.

Fatigue is responsible for about 90% of mechanical engineering failures.

Fatigue fractures are sudden and can resemble brittle fractures.

A case study from Sherry Labs is mentioned, detailing a failure in mining truck wheel bolts.

Incorrect installation can lead to fatigue failure, as seen in the mining truck wheel case.

Fatigue testing machines simulate dynamic stress to predict part performance.

Fatigue tests can adjust mean stress, stress amplitude, and frequency.

Fatigue life is the number of cycles to failure at a specified stress level.

Fatigue behavior in steels shows a safe stress level below which failure doesn't occur.

Non-ferrous alloys may not have a fatigue limit, requiring a specified fatigue strength instead.

Fatigue life can be plotted on a logarithmic scale with cycles to failure on the x-axis.

Fatigue failure occurs in three stages: initiation, propagation, and final fracture.

Beachmarks or striations on fracture surfaces are indicative of fatigue failure.

Surface treatments like shot peening can improve resistance to fatigue.

Creep is the deformation that occurs under constant load and elevated temperature.

Creep occurs in three stages: primary, secondary, and tertiary, with secondary being the most critical.

The steady-state creep rate is crucial as parts spend most of their life in secondary creep.

Creep rate is influenced by temperature, stress, and material constants.

Larson Miller parameters can be used to estimate rupture times at different temperatures and stresses.

Engineering materials can fail at stresses lower than theoretical predictions due to inherent flaws.

Stress concentrators, such as sharp corners, can lead to premature failure and should be avoided in design.

Transcripts

hi so we're going to talk about fatigue

and creep and failure due to these

mechanisms today so first to Define

fatigue fatigue is defined as a form of

failure that occurs in structures that

are sub subjected to a dynamic and

fluctuating stress so you might imagine

um a bridge with cars driving repeatedly

over it so the number of cars on the

bridge at any given time might vary it

might be bouncy a little bit if it's a

flexible Bridge so you can imagine

something like that the thing about

fatigue is that Parts can fail even

though the maximum stress that the part

might be subjected to is much less than

the yield stress that you might measure

in a tensil testing machine um it's

actually responsible for about 90% of uh

life failures mechanical engineering

failures of parts and the bad part is

that it can occur suddenly and with and

without warning just like a a brittle

fracture um in fact the fracture is

brittle in nature if you examine it

using fractography you can see that the

surface looks like a brittle fracture

surface for for part of the surface at

least um so here in this picture there

was an interesting failure study done by

Sherry Labs the link is given below if

you'd like to read the full study but

the gist of it is these studs are bolts

were used to hold on the Wheel to a big

mining truck and of course the wheel

just fell straight off

um one day after the parts had been in

service for a long time they wanted to

know what went on it turns out that the

the bolts that they were using were okay

for the service that they were being put

to but they were in installed

incorrectly and that's why they failed

um but they failed after a certain

amount of use um and just all of a

sudden without warning so they were

interested in doing the failure study

you can see here if you look at the

bolts and remember what it looked like

when we did those tensile tests um these

do look a lot like brittle fracture so

you see these abrupt kind of um Parts

where you you have little to no necking

and when we zoom in and look at the

parts later we'll see what the fracture

surface actually looks like um but a lot

of it will look like a brittle brittle

surface now you can simulate fatigue of

course if you know that your part is

going to be subjected to fatigue you

would like to test the part and see how

it's going to perform in service and so

they've designed many machines um uh

fatigue testing apparatuses that um Can

can do this for you so a schematic of it

is shown here basically you have

something that flexes the part back and

forth and rotates the part through so

that it gets flexed in multiple

directions um and then it can do that

for as many cycles as you like um

basically what they do is they subject

it to this sort of beautiful sinusoidal

stress now in reality in service the

stress might not be that beautiful in

sinos soidal it might be much more

erratic um but machines do the best they

can to simulate that stress and what

they do is they set this stress

parameter here you can change the mean

or average stress and you can change the

stress amplitude you can change the

frequency of the um oscillations of the

stress and then you just run it to

failure you wait until the part breaks

and you do that for multiple scenarios

on the same type of material so that you

can get a feel for how that part will

perform under a cyclic applied

stress of course you want to replicate

the actual conditions of service as

closely as possible here's some images

of Some Testing apparatus that I found

online um basically the tester will

subject a specimen to a stress amplitude

that's on the order of 2third of the

tensile strength and then what you do is

plot the number of Cycles to failure

versus the stress so here's a a couple

images of those plots so here um what's

plotted in this case is the stress

amplitude you could change it you could

change it to the mean stress you could

plot whatever parameter you're

interested in regarding the stress on

the y axis and then on the x- axis you

plot n which is the number of Cycles to

failure

okay and so this is a logarithmic plot

with Cycles to failure here um there's

basically two types of fatigue behavior

that are seen commonly one type of

fatigue behavior is seen for many

different Steels that's the one up here

at top with this curve and then on the

bottom curve you see that for a lot of

non feris Alloys um and we'll talk about

those two scenarios so for these two

different scenarios here well for both

of them actually higher stress is

actually going to give a lower number of

Cycles to failure that's why the curve

goes up as it approaches and equals uh

low numbers okay it goes up there it

with your stress amplitude Okay so the

part will fail at a lower number of

Cycles if you subject it to a higher

stress not really surprising there okay

so um next what you see with some Steels

with many Steels is that for for these

Steels as long as you keep the stress

below what's termed a safe level the

part won't fail on you okay um so you

have to keep it at a low stress and then

what you are is you're in this safe

region here if because the Curve will

flatten out um as it approaches high

high numbers of Cycles so as long as you

keep it below that stress amplitude then

the part will perform um well okay

that's a Steel type Behavior but for

some materials um there is no fatigue

limit when you approach that limit that

flat out uh that flattening part of the

curve there that's called the fatigue

limit but for some materials non- feris

Alloys there is no fatigue um limit in

those cases they often specify a fatigue

strength instead and the fatigue stress

uh strength is the stress level for

failure at a specified number of Cycles

so you say well I would like my part to

perform for X number of years before I

recommend replacement so what's my

fatigue strength at that and then you

design your part um so that it will have

the specified fatigue strength that you

want for the number of Cycles to failure

that you want

okay okay now you have to be really

careful because those curves that I

showed were actually average curves and

statistically what that means is that

half of them are going to fail below

that level if you if that's your mean

curve then half of them are going to

fail below that a more appropriate

treatment might be a series of

probability curves um and so if you go

on and you become a materials engineer

material scientist I would hope that you

would do this sort of thing okay and

plot plot uh a a parameter and then stay

in the safe limit even for the low

probabilities of failure

now um another important parameter that

sometimes gets cited is the fatigue life

and the fatigue life is the number of

Cycles to cause failure at a specified

stress level so you specify the stress

level and then you see how long it is

till the person has to change that part

out basically um fatigue when it starts

it happens in three stages it usually

starts off with a crack or a scratch or

something like that so you have a a

defect in your surface it could be the

threading on your bolt it could be dent

in your surface a scratch a rusted spot

whatever and then at that point at that

defect a crack will form okay and this

usually happens at the surface and then

in the second stage that crack that's

formed will advance incrementally with

each stress cycle so every stress cycle

the crack will move a little further and

a little further and a little further

when it's reached a certain point some

critical size then the final failure

will happen like that and that's why we

say that you know fatigue failure

happens without warning because if you

don't know the crack is there all of a

sudden the part will just fail one day

and you've got yourself what looks like

a brittle fracture

failure now there's people that do these

analyses like the um example that we

showed earlier and then you can look at

the fracture surface and see what's

going on there's certain characteristic

things that they see um in these fatigue

parts so first of all this is an image

of one of those bolts that failed on

that we showed on that very first slide

and it's exhibiting something called a

beachmark it's also sometimes called

growth rings or uh clam shells um but

anyway it shows this kind of

characteristic layering look kind of

like a tree ring or a go growth ring um

and what happens there is the crack is

advancing but then um and it's being

subjected to stress but then the part is

taken out of service for some time maybe

everybody goes home for the night or

maybe maybe the part is on a bridge and

um there's not too many cars in the

bridge that late at night or whatever

okay so it's allowed to relax a little

bit and then it's subjected to the

stress again allowed to relax a little

bit subjective relax and this forms a uh

very distinct looking pattern that

people have learned to recognize as

being a sign of fatigue

failure um they're bigger they're

visible to the naked eye or with just a

simple little handheld lens now there's

also if you look at the part under an

electron microscope or a high power M

microscope you can see what are known as

striations inside these Beach marks and

the striations are microscopic and it

shows you the advance of the crack front

during just one stress cycle and looks

like little ripples all right now down

here in the lower right hand corner is a

um a part from a totally different

website that I've cited here and what

that looks like it'll show you the crack

formed it initiated down here at the

bottom and then you have your kind of

beachmark looking pattern down here

until the crack Advanced far enough the

flaw Advanced far enough that boom

you've got your brittle fracture failure

and this is what that surface looks like

okay so um so you can figure out a lot

from that

fractography now since most of these um

defects the cracks start at the surface

anything that you can do to strengthen

the surface is a good thing okay so you

can do what's called shot peening which

introduces um uh defects at the surface

um hardening strain hardening um you can

caror it you can alloy it in other words

alloing will strengthen apart and you

can also remove those stress

concentrators um if you have very small

radi of curvature very sharp corners or

anything like that on your part then

your fatigue will want to set in there

so anything that you can do to make the

radius of curvature larger would be good

um so that's also a good thing to think

about okay so that's fatigue and fatigue

life now let's talk about creep there's

some parts that aren't necessarily

subjected to cyclic loads with a stress

that varies in time but there may be a

loadbearing type thing they're supposed

to hold a long tense ESS for a long time

and it's not cyclic in nature just

really heavy all the time for example

those parts are subjected to creep okay

oftentimes these parts um say for

example if it's in a jet engine or

something like that this also happens at

elevated temperatures the part gets

really hot in service so if you have

kind of a constant load over time at an

elevated temperature your part is

subjected to creep okay so there's

there's three stages of creep first of

all when you first place the part in

service

um the very first day or whatever first

few days this is called primary creep

and in that you have first of all an

instantaneous deformation the part will

deform the instant that you put it in

service by some amount it'll get all

stretched out and then um the slope here

this instantaneous deformation the slope

will decrease with time until it reaches

the steady state which is the secondary

part they believe that this DEC decrease

in the slope with time of the strain on

the part which is called The Creep

strain that decrease in the slope is due

to strain hardening so the part the

metal is actually getting tougher in

service then it reaches a plateau where

the strained hardening is actually

battling with the recovery phase for the

part because remember the part is being

subjected to heat and then you have what

looks pretty much like a flat straight

slope there okay um and then that stage

is called secondary creep the um the

slope of that here we're plotting creep

strain versus time of service okay so

the slope of the secondary curve is

really important because the part spends

most of its life in that secondary um

time frame it spends most of that time

in the secondary stage the primary stage

doesn't take very long and neither does

the tertiary maybe just a few days for

each of them the secondary strain um

rate curve can can last for years so

that slope right there is very important

and we'll talk more about that and then

finally it exits the secondary creep and

enters the tertiary creep phase and then

the slope actually increases with time

until the part finally ruptures um so

you want to stay away from

that creep as you can imagine has a

temperature dependence the hotter your

part the more um the more your creep

strain rate will be um the faster the

creep will occur for Metals it becomes

important mostly at G than 40% of the

melting temperature then it really takes

off okay so that's something to bear in

mind okay so let's talk more about that

secondary creep regime okay your steady

state creep rate is actually constant at

a given temperature and stress you're at

that point where the strain hardening is

balanced by recovery and you've got that

constant looking slope okay so given a

temperature okay your your exponential

dependenc of your temperature is here so

you have the activation energy for the

creep and as long as that temperature is

held constant this exponential term here

is constant it's e to the minus Q over

RT um and that's the activation energy

for the creep there that q and then

there's your temperature okay now um

your strain rate is the strain which

remember is the change in length over

the length so that's the definition of

strain and a strain rate is how much

strain happens per per unit time okay so

that's your strain rate Epsilon dot then

you have a material constant in here of

course it's going to be bit different

depending on what your material is and

then you have your applied stress um

times raised to the power of n your

stress exponent

okay now if you do a log plot of these

things then they look like straight

lines okay um so your strain rate

increases with increasing temperature

and increasing stress don't worry too

much about the units on K they're really

strange okay um but it's basically just

a fit parameter that you would you would

get from the fit for a particular

material that you would

have okay so let me do an example

problem for you so that you can see what

some of these creep problems look like I

actually have about three examples here

to go through so this is um a steel

alloy okay s590 alloy and it 750 mm long

initially and it's exposed to a tensile

stress of 80 megapascals at 815 de

Celsius and so using this these plots

what we're going to do is determine the

elongation after 5,000 hours um assuming

that the instantaneous and primary creep

um elongation is 1.5 millimeters so

these curves here show the secondary

creep um Behavior and the instantaneous

and primary creep El a are given to you

basically as 1.5 mm so you just need to

figure out the secondary part and add it

onto the

primary all right so what we can do is

we know that the part was subjected to

80 megapascals at 815 C so I can look at

um my plot here and read off for 80

megapascals um from the 815 C curve

which is that red curve here and see

what the um the the creep rate is at

that value So reading that off the plot

I get 4 * 10- 6 inverse hours again the

units are a little strange on these

things um just Just Go With It okay so

here's my steady stra um steady state

creep rate that's my Epsilon Dot and

then what I can do is it asks me for

5,000 hours so I can multiply my creep

rate by my time so I have 5,000 times 4

* 10- 6 and I get

0.02 okay so that's my creep rate uh so

that'll give me my creep If I multiply

my creep rate by my time I get my creep

and that's equal to remember the uh

strain which is the change in length

over the length which is the change in

length over the initial length of 750

millimeters okay so that means I can

solve for my elongation and it's 15

millimeters and that's for my secondary

stage if I add that to the primary creep

I get 16.5 millimeters of elongation of

that part hopefully that helps

okay here's another question all right

these are all taken from your book if

the log of the creep rate is plotted

versus the log of the stress um as it

was previously a straight line should

result with a slope of n okay so using

the figure determine n for the s59 Alloy

at 925 Dees C that's shown here in the

orange curve okay so we're assuming that

the temperature is held constant so that

exponential term eus Q RT that's a

constant value okay so for this this

curve it's just shown here and it's some

value and so we're assuming here that

Epsilon dot is equal to K Sigma to the N

okay so um what I'm going to do is I'm

just going to choose two data points off

this line and figure out my slope of

that line and from that I can figure out

what my value of n is so the two data

points that I chose are the ones that

kind of crossed over one of these grid

Lanes two cross grid l lines here um and

so the two data points that I chose were

10 Theus 4 and 60 megap pascals it

looked like it intersected there and one

inverse hour or one hour and 200

megapascals so I chose those two data

points now if you look at what the log

log plot would be if I take the log of

both sides of this equation I get log of

my creep rate equals log of K plus n log

Sigma and then what's plotted here

though is the stress on the y a axis

okay so my slope then would not be n it

would be one over N I rearranged my

equation here to show that so I have 1

over n log of my creep rate equals minus

one over n log of K this just becomes my

intercept so it's unimportant to me for

my slope calculation and then that's

equal to the log of Sigma okay so if I

want to solve for just my slope that'll

give me my value of one over n here so I

plug in for my two data points my change

and my y y would be log of 200 minus log

of 60 and then the change in the X would

be the log of 1 minus the log of 10us 4

well if it's a log base 10 then the log

of one is just one right and then I have

minus minus 4 okay because the log of

10us 4 is minus 4 and then when I do

that I get

0146 and that's equal to one over N I

solve for n i get 9.6 so it's basically

10 right

okay so here um next question estimate

the activation energy for creep for the

s590 alloy using the stress data at 300

megap pascals and temperatures of 650c

and 730c assume n is independent of

temperature okay so in my example here

I've got my equation for my creep rate

Epsilon dot is equal to K Sig VN e minus

Q over RT so that's my assumption

there and yet again what I'm going to do

is I'm going to use my two data points

um and here my two data points are for

the 300 megapascal data okay so I have

two data points 300 megap pascals and if

I look at that um my creep rates um for

those 200 Mega 300 megap pascals if I

look at that that intersection of the

data then I get creep rates of 10us 4

inverse hours and - 2 inverse hours for

650 and 730 C which were the temperature

cited now K andn are those constant

those material constants that don't

change because this is for the same

material all these curves are for the

same material the s590 alloy so those

can be assumed to be the same and sigma

is given as 300 megap pascals for both

so from this I've got basically two

equations and two unknowns right um I

know my um my values my creep rate I

know my values of my temperature I don't

know my K Sigma to the n Bits but since

I have two equations I can just subtract

those two equations and then that

constant drops out so I end up with the

log a natural log of 10- 4us the natural

log of 10- 2 = q r * 1 over 13 - 1 923

okay and I solve this equation and I get

my Q there um plugging in for the known

value of my gas constant are 8. 314 Jew

per mole Kelvin now it's really

important that you realize that this

here in order to get rid of this

exponent I took a natural log okay so

that's not a log base 10 so my natural

log of 10us 4 isn't going to give me

minus four anymore you have to actually

plug it into the calculator okay make

sure that you check me out on that make

sure I did my math

right okay now sometimes you want creep

data but it would take a really super

long time to obtain because the life of

the part you expect it to be years for

example but you know that creep happens

at faster at higher temperatures so if

you want to do a test and you want it to

take a reasonable amount of time maybe

you heat the part up to a temperature

far above its service um temperature

that you know far above the temperature

you would expect it to have in service

and then you can extrapolate back for

the temperatures that it would actually

encounter in service and figure it out

that way okay so you just do the test

higher temperature and then figure out

what it would happen at a normal

temperature okay so we can use what are

called Larsson Miller parameters and

lson Miller plots to figure this out now

your lson Miller parameter just comes

from the same old equation that we've

been using this creep rate is equal to K

the n eus q over RT and you just apply a

bit of algebra to it so here's that bit

of algebra if you remember that your

creep rate is just your creep strain or

strain over a Time T then you can

rewrite your equation to look like this

okay so that your time is equal to your

strain over K Over Sigma to the * e q

over RT so basically I just flip the

equation and multiply um divide it

through by my um

string multipli through by my string now

I'm taking all this stuff out front

because I don't really care too much

about it I'm just going to call it a for

some constant right um and then I take

the natural log of both sides and I get

log of um natural log of T equals

natural log of a plus Q RT move things

over to the other side subtract it off

multiply through by my temperature and

then I get this relationship my

temperature times the log natural log of

my time minus that natural log of my

constant now this is equal to Q overr

okay now we can switch this over to a

log base 10 plot so that it more closely

matches your book and all that would do

is just introduce a proportionality

constant that we don't care too much

about anyway and maybe change what this

constant is here inside

okay that's all that would do and then

that is our lson Miller parameter l so

our lson Miller parameter L is the

temperature times the log of the time to

rupture plus some constant C and your

book says it tells you that this

constant C varies a bit but it's about

20 um I'm sure if you went through and

did the math you could figure out why

it's about

20 the repture lifetime is usually cited

in hours and it varies with the stress

so Larson Miller plots look like this

okay here you have your lson Miller plot

Larson Miller parameter times 10 the 3

so this is 12 * 10 3 16 * 10 3 so on and

so forth okay this is yet again for that

s590 iron that we've been citing a lot

and then that's plotted versus the

stress on the Y AIS so if you're an

American material scientist engineer you

have to get used to English units this

is PSI okay not MEAP pascals but PSI so

there it is um on that part of the plot

you can see the uh the SI units in your

book if you choose to do so okay and so

what this does is it shows you the

average of a set of Curves for these

Larson Miller parameters um and uh what

you can do you can use this to estimate

rupture times so you gather the data at

this high temperature yourself and then

you use your um your Larson Miller

parameter here which should be equal to

a constant right that constant Q over R

it should be equal to that constant and

then you can figure out

what the um the value is at the

temperature that you're interested in so

for example here let's estimate the

rupture time for a component made of

s590 iron at 173 Kelvin and a stress of

20,000 PSI okay so if you go to the

stress you're looking at which is 20,000

PSI and you go over to your curve then

you can read off what's your lar sillar

parameter is there and it's 24 * 10 3

okay so then you plug in 24 * 10 3 for

your Larson Miller parameter you plug in

your temperature there on the left hand

side and then you solve for that log of

the time to rupture um and the time to

rupture once you get rid of that log is

233 hours so you can um check that out

but that would be how you would maybe

extrapolate data when you don't want to

run the data at uh for for super long

time you just run it at a higher

temperature for or a shorter amount of

time okay that finishes off um what I

wanted to say about chapter eight in

summary engineering materials are not as

strong as predicted by the theory that

you might get from a ttile stress okay

they can uh fail at stress is much lower

than their yield stress um or their

tensile stress and the reason for that

is first of all because materials are

flawed they have a lot of flaws in them

um and those flaws the scratch as the

dings the dents um or even just voids

inside the part that might not be

visible to the naked eye they act to

stress concentrators and those stress

concentrators can cause failure as

stress is much lower than theoretical

values if you have a sharp corner in

your plot in your part you definitely

want to get rid of that you don't want

that included in your design because

that's a large stress concentration

right there that can help out with

premature failure which is totally

undesirable your failure type is going

to depend upon your temperature and your

stress okay um if you have a simple

fracture like it's

non-cyclic your stress is non- cyclic

and your temperatures are relatively low

then your failure stress is going to

decrease with increased maximum flaw

size decreased temperature and increased

rate of loading if you have a fatigue

situation with a cyclic stress then the

Cycles to fail is going to decrease as

your amplitude of stress

increases and the creep for creep the

time to rupture is going to decrease as

your stress or your temperature

increases so that's kind of a summary

all right um see you in class