MECH4900 Problem Set – 2
Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit
Problem Set – 2
MECH4900
Problem 1:
Although the strain energy release rate can accurately predict when fracture occurs, the stress based approach to fracture was a major breakthrough for fracture mechanics. Why, i.e., what additional information does this method provide us?
Problem 2:
a) What is the biggest allowable edge crack in a plate of 7075-T6 Al such that fracture will not occur before general yielding under uniaxial tensile loading. Assume the plate is very large relative to the crack size, i.e., use the edge crack in semi-infinite plate solution.
7075-T6 Al
σy = 500 MPa
KIC = 24MPa√ m
b) Next, what will happen if we replace the aluminium with an aluminium oxide ceramic and keep the maximum allowable load the same:
Al2O3
σmax = 500 MPa
KIC = 2.2 MPa√ m
Ans:
a) aC = 585 um
b) aC = 4.91 um
Problem 3:
On a bet, your friend who weighs 90 kg has agreed to try to hang from a rope attached to a glass sheet that is 1 meter wide, 3 meters long and only 0.127 mm thick. Your friend will be suspended 15 m in the air, so he asks you to figure out if this will be safe. Upon inspection of the glass you find a crack 3 mm long near the centre. Assume KIC for glass is 0.83 MPa√ m.
a) Assume that the infinite plate K solution applies here. Is your friend safe?
b) Assume that the middle-cracked tension M(T) solution applies here. Is your friend safe?
c) Comment on the difference between your answer to a) and b).
d) What is the maximum crack size for this to be safe?
Ans:
a) KI < KIC . So, your friend is ‘safe’ .
b) KI < KIC . So, your friend is ‘safe’ .
c) -
d) Total crack length: 9.09 mm
Problem 4:
Suppose you have a crack in an infinite plate with a total crack length of 2a = 10 mm. A uniaxial stress σ = 100 MPa is applied along with a crack face load of 100 kN/m distributed through the sample thickness located 2 mm from the crack centre.
a) What is the value of KI ?
b) Why does the superposition of stress intensity solutions only work when adding solutions for a single loading mode?
c) Even within one loading mode, you also cannot superimpose solutions for different
geometries. Which stress intensity solutions on the handout can be superimposed?
Now suppose that there is a second crack face force located on the other side of the centre line:
d) What is the value of KI in this case?
Ans:
a) KI = 13.75 MPa√m
b) -
c) -
d) KI = 14.27 MPa√m
Problem 5:
A 7049-T73 aluminium forging is the material of choice for an 8 cm internal diameter cylindrical hydraulic actuator housing with a wall thickness of 1 cm. After manufacture, each cylinder is subjected to a safety check, involving a single fluid over-pressurization that generates a hoop stress of 50% of GyS . The component design calls for an operating internal fluid pressure corresponding to a hoop stress of 25% of GyS . Prior to over-pressurization, a 2 mm deep semicircular surface flaw that was oriented normal to the hoop stress direction was discovered in
one cylinder. Given that GyS = 460 MPa and KIC = 23 MPa√m, and neglecting the pressure of the fluid inside the crack:
a) What are the fluid pressures associated with the proof and operating stresses?
b) Would the cylinder have survived the over-pressurization test?
c) Would the cylinder experience a leak before break condition under service load?
Ans:
a) PpToof = 57.5 MPa , PwoTking = 28.8 MPa
b) Cylinder will survive the test
c) Yes
2023-01-12