B51EM Advanced Mechanics of Materials I
B51EM Advanced Mechanics of Materials I
Re-Assessment Assignment August 2023
This assignment is in two parts:
Part 1: The role of defects in metallic pressure vessels (60%)
Part 2: Wind turbine blade design (40%)
Sub-section part-marks are give below
Both parts, must be submitted via the Canvas Portal by
11th August at 23:00, UK time
Guidance: This assignment is open-ended in that you will need to bring information to it yourself. You must acknowledge the source of any such information. You will also need to make simplifying assumptions beyond those which are recommended in the brief. You must state clearly any assumptions that you make and discuss their implications on your final answer. You will not be penalised for making assumptions, but may be penalised for not discussing the implications.
The assignment is designed to test your understanding and competence across the whole course and you should aim to draw from as much of the course material as you can.
Credit will be given for competence in using the analytical and numerical techniques covered in the course, for dealing with uncertainty (i.e. making appropriate assumptions in the face of missing information). You will also be given credit for reading outside the supplied course material and for bringing references not supplied as part of this brief. Try to avoid cluttering your answers with unnecessary detail. Keep detailed calculations in an evidence file, but do not submit this. However, you will need to be able to produce the evidence files if asked by the marker.
Ensure that your submission contains the standard University declaration about plagiarism and collusion. Submissions not containing such a declaration will not be marked.
Part 1: The role of defects in metallic pressure vessels
1a (5marks): Carry out a review of published information on failures of gas-containing pressure vessels. You should use an appropriate database (such as EI Compendex) as well as newspaper reports and other public output (such as reports of public enquiries). Write a brief report (around 500 words) on your findings, with proper use of references, commenting on the measures that are required in the design, manufacture and operation of such vessels.
Credit will be given for the scope of your review, but, as a starting point, you may use the extract below, which describes the failure of an ammonia vessel during testing at the fabricators site. The fragment of the wall ejected into the car park is still on display at the Welding Institute in Cambridge.
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1b (5 marks): Using the dimensions of the ammonia vessel described above, write down equations for both the Tresca and von Mises stresses on the outer and inner surfaces at failure using both the thick cylinder solution and the thin cylinder approximation. For each of the four cases determine the worst possible orientation (3D plane) for a weld defect.
Comment on your results in light of the fact that the vessel failed due to a series of defects in the Heat Affected Zone of the circumferential weld holding the end cap to the cylinder.
1c (15 marks): The figure below shows a more detailed design of a vessel similar to the one considered in 1a. For the purposes of this assignment, you may ignore the detail on the head end and consider the ends to be simple torispherical caps. The analysis will focus on the cylindrical portion and its penetrations (nozzles).
First, assuming the vessel to be a simple cylinder, calculate the wall thickness for the vessel so that the von Mises stress nowhere exceeds 80% of yield at the proof test pressure. Also, calculate the wall thickness of the 12 penetrating nozzle tubes considering them all to be of 250mm inner diameter and of the same material as the vessel.
Construct an FE model of the vessel with its penetrations. Use simple torispherical end caps of the same thickness as the main vessel. Sculpt the high stress areas to keep the von Mises stress below 80% of yield at the proof test pressure.
1d (15 marks): Constrain your FE model at the (bottom) torispherical end. The welds holding on the ends and the nozzles will be through-thickness and can be considered to be of the same material as pipe and vessel. Using FEA, determine the worst possible orientation (3D plane) and position of a weld defect on each of the outer and inner surfaces of the welds.
1e (10 marks): Using your answer from 1d, use a two criteria (R6) approach to find the critical defect depth to resist both plastic collapse and linear elastic fracture in the plane of the maximum principal stress.
1f (10 marks): Obtain from literature suitable values for the Paris Law coefficients and determine the number of cycles that it would take for a crack to grow from the smallest size that can bet detected visually to critical size. Hence recommend a suitable inspection interval for checking that cracks are not growing at the weld toe.
Part 2: Wind turbine blade design
The design relates to a domestic heavy-duty wind turbine. You should choose a turbine from published sources for farm/domestic use and state clearly what the shape and dimensions of the blades are. The blades must be made of carbon fibre epoxy laminate of lay-up [0/45/90/-45]2s. You are advised to adopt a simple model of the wind loading as shown in the diagrams below. You need only consider static wind loading of the blades by the fluid pressure Fw=12Cdv2-207645189865Figure 1: General turbine arrangement
Nacelle/turbine
Wind pressure
Anchor plate
Blades (all)
Figure 2: Blade loading model
Blade (single)
Blade anchor
Wind pressure
Mast
Figure 1: General turbine arrangement
Nacelle/turbine
Wind pressure
Anchor plate
Blades (all)
Figure 2: Blade loading model
Blade (single)
Blade anchor
Wind pressure
Mast
2a (10 marks): Use the simple cantilever model of a turbine blade in Figure 2 and assume it to be a rectangular sheet. Using the recommended lay-up, and a choice of fibre from Table 1, write down the compliance matrices of the plies and hence the orthotropic moduli of the sheet. Hence find a suitable value for the maximum wind speed so that the end deflection of a blade does not exceed 1/20 of its length. You will need to adjust the volume fraction of fibres and the thickness of the plies to obtain a reasonable answer2b (10 marks): Using generic values for failure stresses given in Table 2, ensure that the composite sheet will meet the Tsai-Hill criterion in each layer at the maximum loading conditions with a small factor of safety (say 20%).
Material Youngs Modulus (GPa) Poissons ratio UTS (MPa)
Matrix (epoxy) 2.4 0.34 60
Fibre 1 (std. modulus carbon) 230 0.25 3200
Fibre 2 (int. modulus carbon) 285 0.25 5750
Fibre 3 (high modulus carbon) 400 0.25 2900
center10160Table 1: Matrix and fibre properties for turbine blades
0Table 1: Matrix and fibre properties for turbine blades
Fibre volume fraction Longitudinal fracture stress (MPa) Transverse fracture stress (MPa) Shear fracture stress (MPa)
0.3 150 35 100
0.4 200 50 150
0.5 250 55 200
-4186892332Table 2: Generic values for ply strengths. Can be used for any material at a given volume fraction of fibres
0Table 2: Generic values for ply strengths. Can be used for any material at a given volume fraction of fibres
2e (10 marks): Using the orthotropic modulus from Part 1, build an FE model of the simplified structure you used (Figure 3) and validate your end deflection under the maximum loading that you used in 2a.
Next, build what you consider to be a realistic model of the entire blade. You will need to make a number of assumptions about the structure for this, so make it very clear what these assumptions are. Again, apply the maximum loading and determine the resulting end deflection.
2f (10 marks): Using the orthotropic modulus and simplified model from 2a, assess the fatigue life of the blade, assuming an R-ratio of -1, and what you consider to be an appropriate value of stress range. Use the Goodman diagram given in Figure 3.
5321303865245Figure 3: Goodman diagram for [0/45/90/-45]2s carbon fibre epoxy laminate
020000Figure 3: Goodman diagram for [0/45/90/-45]2s carbon fibre epoxy laminate
