Mechanical Engineering Assignment: Creep Test Determination Calculus

This assignment solution focuses on determining the creep strain rate using differential calculus. The assignment involves explaining how differential calculus can be used to calculate the creep strain rate from a set of data for creep strain as a function of elapsed time, including relevant standard rules. The solution then proceeds to calculate the creep strain rate at 15 hours elapsed time, using a provided polynomial equation fitted to creep test data. The solution demonstrates the differentiation process step-by-step and calculates the final creep strain rate, providing the answer to one significant figure. The solution also provides references to support the calculations and explanations.

Creep Test Determination Using Differential Calculus 1
CREEP TEST DETERMINATION USING DIFFERENTIAL CALCULUS
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Creep Test Determination Using Differential Calculus 2
Task two I,
Explain in words how you can use differential calculus to calculate the creep strain rate from
a set of data for creep strain as a function of elapsed time. State any standard rules that you
would need to apply in obtaining your result. Your answer should be no more than 200
words. You do not need to include equations, but you can include general equations if it
helps with your description. (5 marks)
Solution
Differential calculus helps to obtain a function which gives the outputs of the rate of variation
of one inconstant factor with respect to another one (Kassner, 2015, p. 200).it may be applied
in very many areas such as in the determination of how a material behaves under some kind
of stress or even providing the behavioral characteristic of a material through a slope.
Creep is defined as the behaviour of a material which is solid in nature to slowly or
permanently deform when it is exposed to some kind of mechanical stress. The deformation
is described by its rate which is influenced by its material properties, the temperature under
which it is exposed and even the time taken during the deformation among others functions.
Significantly to the deformation is the size of the applied stress and time which gives the
strain.
Creep deformation always takes place after a period of stress application thus being time
dependent. Since differential calculus helps us to obtain to obtain a function which gives the
outputs of the rate of variation of one inconstant factor with respect to another one, we will be
able to apply it in the determination of creep strain rate (Farahmand, 2009, p. 644).
This can be done by simply taking a set of data in a creep test conducted on a particular type
of material, for an elapsed time and then differentiating to obtain the derivative function after

Creep Test Determination Using Differential Calculus 3
which we substitute with respect to the specified time periods to allow us to obtain the creep
strain rate (Kassner, 2015, p. 995).
Task two ii,
The equation below is a polynomial of order 4, fitted to the data recorded in a creep test
conducted on a particular type of steel, for an elapsed time between 10 to 20 hours.
ε =4 x 10−5 t4−0.0024 t3 +0.0487 t2−0.3428 t+ 1.4532
The data were recorded for % strain versus elapsed time in hours.
Use this equation to calculate the creep strain rate at 15 hours elapsed time. Give your answer
to 1 significant figure. Tip: differentiate dε
dt
Solution
To calculate the creep strain rate for the steel, we will first differentiate the creep strain with
respect to the time elapsed. I.e. the differentiation will start from the highest power going
down to the least power and then to the constant (Farahmand, 2009, p. 787).
ε =4 x 10−5 t4−0.0024 t3 +0.0487 t2−0.3428 t+1.4532
Converting the coefficient of t4to a decimal gives;
ε =0.00004 t4 −0.0024 t3+0.0487 t2−0.3428t +1.4532
We then proceed to the differentiation (Farahmand, 2009, p. 784). i.e. obtaining dε
dt
dε
dt = (4*0.00004) t4−1 – (3*0.002)t3−1 + (2*0.0487) t2−1-(1*0.3228) t1−1+ 0(when
differentiating a constant, the constant changes to zero automatically)

Creep Test Determination Using Differential Calculus 4
dε
dt = (4*0.00004)t3 – (3*0.002)t2 + (2*0.0487) t1-(1*0.3228)t0
Which becomes,
dε
dt = (4*0.00004)t3 – (3*0.002)t2 + (2*0.0487) t- (1*0.3228)
We then perform the multiplication thereby giving us;
dε
dt = 0.00016t3 – 0.006t2 + 0.0974 t- 0.3228
Finally, we substitute the value of time so as to obtain the creep strain rate, where the time is
15 hours as indicated in the question
I.e. t= 15 hours
dε
dt = 0.00016¿ 153 – 0.006¿ 152 + 0.0974 ¿ 15- 0.3228
dε
dt = 0.00016*3375 – 0.006 ¿ 225+ 0.0974¿ 15- 0.3228
dε
dt = 0.54-1.35+1.461-0.3228
Finally we add and subtract to obtain the creep strain rate
dε
dt = 0.3282
We then place our answer to one significant figure, thereby giving us (Kassner, 2015, p. 825).
dε
dt = 0.3

Creep Test Determination Using Differential Calculus 5
References
Farahmand, B., 2009. Virtual Testing and Predictive Modeling: For Fatigue and Fracture Mechanics
Allowables. 3rd Ed. Carlisle: Springer Science & Business Media,
Kassner, M. E., 2015. Fundamentals of Creep in Metals and Alloys. 2nd ed. Chicago: Butterworth-
Heinemann.