•  A drinks can has radius r=32mm, thickness t=0.1mm and is made from a 6061 aluminium alloy of   shear stresses are present.  
• (a) Write down an equation for the stresses in the cylindrical wall of the can and therefore write down an expression for the stress tensor in terms of P, r and t. [3 mark]
• (b) Using the generalized Hooke’s law, derive expressions for the principal strains in the cylindrical wall of the can. [3marks]
• (c) Draw Mohr’s circle for strain and find its center and radius. [3 marks]
• (d) A 0/45/90° strain gauge rosette is applied and the pressure in the can is released. By measuring the strain changes, it is found that the strains in the can before the pressure was released were +950, +510 and +200 in the 0, 45 and 90° gauges, respectively. It is assumed that the rosette was misaligned relative to the axial and hoop directions of the can. U pressure P in the can. [8marks]
• (e) Compare the applied von Mises stress to the alloy yield stress of 240 MPa, and comment on what this suggests might be the governing design parameter for the can thickness.

Question 5 – Answer all parts (a) to (f)

An isotropic material is in use for a thin-walled vessel that requires regular inspection. The material has the yield strength of 400 MPa and the ultimate strength of 700 MPa. The material fails at a true plastic strain of 30 % and has a toughness KIc of 35 MPa.

(a) Can an inspector use optical microscopy to examine the material? Justify your answer. [2 mark]

(b) An inspector used a device that can only be able to detect the smallest defect of 1 mm. No defect was found in the inspection. Calculate the maximum stress below that the material can be safely used (Assuming the geometric factor is 1). [4 marks]

(c) The vessel has a thickness of 5 mm and a mean diameter of 500 mm. Calculate the maximum internal pressure to ensure that the material does not yield. [4 marks]

(d) Calculate the principal stresses corresponding to the maximum internal pressure found in (c). [4 marks]

(e) Find the values of the effective stress and effective strain at yield. [4 marks](f) The material fails due to an overload. Select one option below that best characterises the fracture surface: i) River-like cleavage surface ii) Fracture dimples iii) Shiny and flat surface

Question 6 – Answer all parts (a) to (f)

An isotropic material is in use for a thin-walled vessel that requires regular inspection. The material has a yield strength of 400 MPa and the ultimate strength of 700 MPa. The material fails at a true plastic strain of 30 % and has a toughness KIc of 35 MPa.

(a) Define the following terms used to describe fatigue: i. Stress amplitude ii. Mean stress iii. R ratio [3 marks]

(b) Describe the steps involved in a safe life approach to fatigue. [3 marks]

(c) Sketch a graph to show how the da/dN versus K behavior of polymer such as PVC compares to that of bainitic steel, of yield stress 500 MPa, at room temperature. [4 marks]

(d) Why should you consider the relative stiffness of the PVC and steel in making engineering judgments on their fatigue performance? [1mark]

(e) Consider a steel pressurized tube of a wall thickness of 5 cm and a minimum detectable defect size of 2 cm. The values of the constants in the Paris equation are A = 1 x 10^-33(SI units) and m = 3. The tube is subject to fluctuating stress of between +75 and +10 MPa at 30 Hz. Using the Paris Law for fatigue crack growth rate and given the information above calculate: i. The number of cycles until a through-thickness crack causes a leak ii. Time to a through-thickness crack in years.

(f) What evidence did Elber put forward to support the idea of crack closure at low loads?[1 mark]

Answer rating: 100% (QA)

A KIC 35mpa 5m 400 KIC 352 Q 0002437 m 2437... View the full answer