TMM WS 2013/14

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Prof. Dr.-Ing. P. J. Mauk 12.03.2014 Ch. Overhagen, M.Sc. Institute for Technology of Metals/Metal Forming

Examination: Testing of Metallic Materials / WS 2013/14 Advice: Use a new page for every problem! A minimum of 40 points is necessary for passing the exam! Total: 100 points ; 4.0 = sufficient: 40 min. points ; 1.0 = excellent: 88 min. points

Engineering Strain : ENG True Strain : TRUE

Engineering Stress : ENG True Stress : TRUE

ENG TRUE

0

ENG TRUE

0

F F

A A

dl dld d

l l

1. Problem: (12 Points)

In a part which is made from a steel material with IC 2N

K 17 mmm

, a Griffith-Crack

( 1IY ) is discovered at mode 1 loading. Calculate the critical stress which leads to

unstable crack growth for the following crack lengths: a) a = 2.0 mm b) a = 7.0 mm c) a = 9.0 mm d) The part is loaded at a stress of = 205 N/mm. Calculate the critical crack

length after which unstable crack growth will be encountered. 2. Problem (5 Points): What is the advantage of the J-Integral concept instead of the KIC concept in engineering applications? 3. Problem (12 Points): From an engineering stress-strain curve of a tensile test, it is obviously seen that at the

point where necking starts ENG

ENG

0

is valid. From this equation and the definitions of

true and engineering stress and strain, derive the corresponding equation for TRUE

TRUE

.

TMM WS 2013/14

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4. Problem (18 Points): A tensile test on a sample with diameter d0 = 12 mm and a measuring length of L0 = 70 mm results in a maximum force of Fmax = 120 kN. The force at fracture is Ffrac=50 kN. The elongation at maximum force is a change in length of l = 10.83 mm. The specimen length after fracture is 82.3 mm, the smallest necked diameter of the specimen is 6.5 mm. a) Find the engineering stress and strain and the true stress and strain at

maximum force. b) Find the local true stress and true strain at the smallest necked diameter at

fracture. c) Calculate the fracture strain in % and the reduction of area in %. d) Plot the stress-strain curve of this test with axes scaled (strain in % and stress

in MPa) e) In the elastic region at a force of 20 kN, a change in length of 0.02 mm is

measured with an extensometer, having an initial gauge length of l0,extensometer = 25 mm. Calculate Youngs modulus of this material!

f) For the case according to e), a change in diameter of the sample of -0.003 mm is measured using a biaxial extensometer. Determine Poissons Ratio of this material.

5. Problem (12 Points): Describe the differences between the following items in your own words (short!):

a) Modified Mohr Theory - Internal Friction Theory b) Stress-Strain-Curve Flow Curve c) KIC KIIIC d) Modes I Mode II - Mode III

6. Problem (9 Points): The charpy impact work temperature curve of a material is described according to

0vT T

C T A B tanhC

with the coefficient C = 52.7 C.

The experimental data available are:

Transient Temperature: T0 = +27 C

Cv at +25 C: 128 J

Cv at +250 C: 210 J a) Calculate the parameters A and B from the experimental data given above. b) What impact work can be expected at T = -20 C with A = 135 J and B = 89 J ? c) Draw the Cv(T) curve of this material, using coefficients A and B given under b).

TMM WS 2013/14

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7. Problem (12 Points): A flat tensile specimen with initial dimensions thickness s0 = 1.5 mm, measuring

length L0 = 100 mm and width w0 = 25 mm is being deformed in a testing machine in

the homogeneous strain region with a plastic strain of 12 %. After the deformation,

the width was measured to be w1 = 23.5 mm.

a) Calculate the measuring length of the deformed sample and the degree of

deformation in length direction. b) Calculate the r-value. c) Calculate the final thickness s1. d) The tensile test is repeated with a new sample of the same material, but this

time continued until fracture. At an engineering strain of 1 = 0.1, a force of F1

= 15.0 kN is measured. At an engineering strain of 2 = 0.13, the force is measured to be F2 = 15.8 kN. Calculate the coefficients C and n of the flow

curve function according to nfk C .

8. Problem (8 Points):

A part is loaded swelling at a nominal stress of2

NS 150

mm . The initial crack length

is a0 = 2.5 mm. The following data are given: m = 4 and the geometry factor Y = 2.5 = const.

The Paris equation is valid in the form

REF m

REF

da da K

dn dn K

.

The reference quantities shall be taken as

REF

3da 1 10 mmdn

and

0

REF

a aK K .

Calculate the number of load cycles, until a critical crack length of ac = 25 mm is reached! 9. Problem (16 Points): A tensile test with a fine strain gauge measurement is conducted on a sample of diameter d = 10 mm. The strain gauge has a maximum deviation of 0.001 mm; the force measurement has a maximum deviation of 0.1 kN. For the extensometer, three different measuring lengths are available. Calculate the combined uncertainty resulting from the deviations in the measuring quantities, which can be expected for the measurement of Youngs Modulus from this tensile test. The sample can be treated as perfectly manufactured and aligned in the testing machine. a) L0 = 12.5 mm; measured elongation: 0.005 mm; measured force: 6.597 kN b) L0 = 25.0 mm; measured elongation: 0.012 mm; measured force: 7.917 kN c) L0 = 50.0 mm; measured elongation: 0.03 mm; measured force: 9.896 kN d) Which one of the above configurations is the best?

Hint: Combined Uncertainty: 2 2

E EE F s

F s