T357 Structural Integrity
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• TMA 03
• Question 1 (Block 2 Learning Outcomes 2.6, 2.7, 3.1 and 3.2)
• Question 2 (Block 2 Learning Outcomes 2.2, 2.4)
• Question 3 (Block 2 Learning Outcomes 4.1, 4.2, 4.3, 4.9)
• Question 4 (Block 2 Learning Outcomes 4.1, 4.2, 4.8, 4.13)
This tutor-marked assignment (T357 TMA 03) must be submitted by 12 noon (UK local time) on 16 April 2020.
This module uses the electronic TMA (eTMA) system for submission of TMAs. To submit your TMA, please go to your StudentHome page and follow the link(s) provided.
If you foresee any difficulty with submitting your assignment on time then you should contact your tutor well in advance of the cut-off date.
For further information about policy, procedure and general submission of assignments please refer to the Assessment Handbook, which can also be accessed via your StudentHome page.
TMA 03 covers your learning in Block 2 Parts 1-4.
Question 1 (Block 2 Learning Outcomes 2.6, 2.7, 3.1 and 3.2)
This question carries 33% of the marks for this assignment
i. Figure 1 shows four distinct fracture surface micrographs taken at different magnifications. Discuss the most likely failure mechanism in each case.
ii. Suggest, with justification, which fracture surface among those shown in Figure 1 would most likely be observed in the failure of a ceramic material.
(8 + 2 = 10 marks)
d. Figure 1 Scanning electron micrographs of fracture surfaces for question 1
i. Figure 2 (reproduced from Figure 2.40 in Block 2 Part 2) shows the fatigue-crack growth rate for a metallic material. From the graph, estimate the number of cycles it would take to propagate a crack from 2.0 mm to 2.8 mm in length for a stress intensity range ?K of 20 MPa vm.
Figure 2 Fatigue-crack growth rate for a metallic material for Question 1(b)
ii. When collecting data to construct a graph such as the one shown in Figure 2, explain why it is important to accurately measure the length of the growing crack.
(4 + 4 = 8 marks)
f. A thin walled steel cylindrical pressure vessel with a radius of 800 mm and a wall thickness of 38 mm is designed to carry an internal pressure of 8 MPa. The steel has a fracture toughness of 95 MPa vm and a yield strength of 520 MPa. For this material take the exponent in Paris relation, m = 3 and the coefficient, C = 10-11.
Answer the following questions, stating clearly how you obtained each answer. You will need to use the ‘K calculator’ and ‘Fatigue calculator’ spreadsheets on the module DVD or module website. You may wish to consider including copies of the completed spreadsheet calculations in your answers.
i. What is the maximum crack length through the wall that the vessel can tolerate when operating at the maximum internal pressure to give a reserve factor of 2.5 on the load? (You will need to use the K calculator; as in Block 2 Part 1, modeling the crack using the Plate in tension – through-thickness edge crack geometry.)
ii. On inspecting the vessel, a welding defect in the shape of a through-thickness edge crack is discovered and is measured to be 4 mm long. Determine how many pressurising cycles will it take for the crack to grow to the size determined in part (i) if the vessel is regularly cycled to 90% of its maximum internal pressure? (You will need to use the Fatigue calculator. Use a crack-growth increment of 0.01.)
iii. When the crack has grown to 6.0 mm the vessel is accidently subjected to 100 overload cycles equal to 436 MPa. Again using the fatigue calculator, determine what length the crack will grow to during these overload cycles? What is the percentage reduction in life as found in part (ii) due to these overload cycles?
(5 + 5 + 5 = 15 marks)
Question 2 (Block 2 Learning Outcomes 2.2, 2.4)
This question carries 20% of the marks for this assignment
a. The S-N curve is used to graphically present the fatigue behaviour of a material:
i. With the aid of a sketch, explain what a S-N diagram is. How would a S-N diagram be generated in a laboratory?
ii. Explain the terms: fatigue limit and endurance limit.
iii. What is meant by the term R-ratio?
(6 + 4 + 2 = 12 marks)
b. Commercially pure titanium alloy with an ultimate tensile strength of 550 MPa is tested at an R ratio of 0.1. The endurance limit at 107 cycles is found to be 200 MPa.
i. Calculate the mean stress in a fatigue test with a stress amplitude of 200 MPa and an R ratio of 0.1.
ii. Use the Goodman equation to calculate the endurance limit at a mean stress of 0 MPa for this alloy.
(Hint: if you combine equations 2.1–2.4 in Block 2 Part 2 the following equations can be derived:
You might find them useful)
c. (4 + 4 = 8 marks)
Question 3 (Block 2 Learning Outcomes 4.1, 4.2, 4.3, 4.9)
This question carries 9% of the marks for this assignment
Explain the role played by each of corrosion, corrosion fatigue and stress corrosion cracking in the failure of materials and structures. You can give examples as appropriate. Your answer should not exceed 500 words.
Question 4 (Block 2 Learning Outcomes 4.1, 4.2, 4.8, 4.13)
This question carries 28% of the marks for this assignment
Read the following case study before answering the questions that follow.
Note that this question is designed to test how you utilise the evidence given to you to find a viable solution to an engineering problem. You should only use the information given in the question and should not seek additional information from other sources.
A building worker was seriously injured when he fell from scaffolding whilst installing air-conditioning equipment in a shopping mall. He was working on a temporary tower erected by assembling together frames and tubes (Figure 3). These are made from aluminium alloy, chosen for its light weight and hence ease of use.
Figure 3 Modular scaffolding platform
The frames slot into one another vertically and are braced by diagonal members. The tubes have a spring-loaded claw at each end so that they can be snapped onto a cross-tube and so provide a balustrade (C in Figure 3). Upright parts of the frame allow the horizontal tubes to be attached and remain secure without slipping away. The claw fits over the tube from above. A typical claw is shown in Figure 4. The tubes are extruded, while the fittings, including the claws, are cast from the alloy.
Figure 4 Claw locking mechanism
The mechanism includes a metal crescent (1) that rotates about a pivot (P), and whose position is controlled by a metal finger (2) that rotates about a different pivot point. The finger exerts pressure on the crescent by means of a helical steel spring (S) with two arms that are fitted to the same pivot as that of the finger.
An investigation into the accident was carried out. On retrieving the fallen tube, it was found that the claw at one end was fractured (Figure 5), while that at the other end was intact (Figure 6).
Figure 5 Broken claw
Figure 6 Intact claw
The broken claw showed a brittle fracture surface, with numerous pinholes that indicated porosity in the original material. A sample that included the origin of the fracture was taken for metallurgical analysis, as shown by the rectangular flat part in the upper left-hand corner of the claw arm (Figure 7). The analysis showed that the alloy was within specification. The fracture surface was fresh and unoxidized, and there were no signs of fatigue striations when it was examined under the microscope. The appearance of the fracture suggested that it had been broken by lateral bending. It was also established that the claw had broken during the accident and not from impact with the ground after it had failed, although the matching ends were lost in the shopping mall. The tube had been used without prior problems until the accident.
Figure 7 Fracture surface of claw at top
Examination of the intact claw from the other end of the fallen tube showed that the spring was badly rusted, with both arms having been destroyed. The spring on the broken end was also rusted, although the arms were intact.
The injured worker sued his employers, claiming that the broken claw had been badly made, had excessive porosity, and was thus too weak to support his weight during normal usage.
a. By referring to the two diagrams of Figure 4, describe briefly the action of the claw in holding a tube in a locked position. Start by considering how a tube is pushed into the claw, and the sequence of events that produces a locking force. You may want to sketch the forces acting on the crescent and finger when the tube is locked in place.
Indicate which parts are safety-critical, and explain why.
i. Outline two possible theories to explain the failure of the balustrade tube, using the evidence revealed by the analysis.
ii. Based on the evidence, which is the most likely explanation for the failure?
iii. Would the worker be likely to succeed in his claim as stated? Explain your answer.
(8 + 4 + 4 = 16 marks)
The final 10% of marks for the assignment are awarded for presentation (see ‘Presentation of TMA answers’ on the Assessment tab for guidance). These will be scored as Question 5.