Mechanical Materials

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CORK INSTITUTE OF TECHNOLOGY

INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ

Semester 1 Examinations 2011/12

Module Title: Mechanical Materials (3D)

Module Code: MECH8012

School: School of Mechanical & Process Engineering

Programme Title: Bachelor of Engineering (Honours) in Mechanical Engineering

Programme Code: EMECH_8_Y3

External Examiner(s): Prof. Sean Leen, Mr John J. Hayes

Internal Examiner(s): Mr S.F. O Leary

Instructions: Answer THREE questions. All questions carry equal marks.

Duration: 2 Hours

Sitting: Winter-Spring 2011/12

Requirements for this examination:

Note to Candidates: Please check the Programme Title and the Module Title to ensure that you have received the

correct examination.

If in doubt please contact an Invigilator.

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Q1. Three dimensional finite element and photoelastic analyses have been conducted to determine

the positions and magnitudes of stress concentrations in a cyclically loaded machine

assembly. These analyses result in the following maximum and minimum stress component

matrices determined at the critical point of stress concentration in the assembly:-

[

] [

]

These matrices are with respect to a local set of XYZ co-ordinates at the point and represent

stress levels in MN/m2.

Calculate the fatigue life of the assembly using the Octahedral Shearing Stress Theory of

failure together with:-

(a) The Gerber Fatigue Criterion

And

(b) The Modified Goodman Fatigue Criterion.

The assembly is composed of a high strength steel with the following properties:-

Static Tensile Ultimate Stress = 1,900 MPa.

Fatigue Strength Reduction Factor = K = 0.85

Compare the fatigue lives produced by the two criteria. (34 marks)

Given:- (

)

, b =

(

)

(

)

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And Table 1 Q.1.

Fatigue

Criterion

Ductile Steels

(

Brittle (hard) steels

(

Nf Nf Ne

Modified

Goodman

0.9

103

1/2K σu

106

0.9 σu

103

1/3 K σu

108

Soderberg 0.9 103

1/2K σu 106 0.9 σu 10

3 1/3 K σu 10

8

Gerber 0.9 103 1/2K σu 10

6 0.9 σu 10

3 1/3 K σu 10

8

SAE 6 1 1/2K σu 106 σu 1 1/3 K σu 10

8

Table 1 Q1. End Points for S-N Diagram

Q2. (a) Derive, from Simple Torsion Theory, expressions for maximum elastic torque particularly

plastic torque and fully plastic torque developed in a solid circular shaft. Delineate clearly

all assumptions inherent in this proof and illustrate these assumptions where appropriate.

Discuss the implications of the plastic/elastic torque ratio for solid and hollow shaft design.

(20 marks)

(b) A 60mm diameter steel shaft is case-hardened to a depth of 3mm. Assuming that the inner

core remains elastic up to a yield stress in shear of 190 MN/m2 and that the case can also be

assumed to remain elastic up to failure at the shear stress of 340 MN/m2, Calculate:-

(1) The torque required to initiate yielding at the outside surface of the case;

(2) The angle of twist per metre length at this stage.

The Shear Modulus for both the case and core may be taken as 89GN/m2 whilst they remain

elastic. (14 marks)

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Q3. (a) Discuss, with the aid of sketches, how compound cylinders may be used to increase overall

cylinder strength. (10 marks)

(b) A steel thick cylinder of external diameter 150mm has two strain gauges fixed externally,

one along the longitudinal axis and the other at right angles to read the hoop strain. The

cylinder is subjected to an internal pressure of 75 MN/m2 which results in the following

strains:

(i) Hoop Gauge: 455 x 10-6

tensile

(ii) Longitudinal gauge: 124 x 10-6

tensile

Find the internal diameter of the cylinder, assuming closed ends. (17 marks)

Given:-

Young’s Modulus for Steel = 208 GN/m2

Poisson’s Ratio for Steel = 0.283

(iii) Given a yield strength of 160 MN/m2 for steel, investigate whether the cylinder has

failed under the maximum principal stress theory. (7 marks)

Q4. A polymer rotor disc, which is part of a turbine assembly, has a uniform thickness of 60mm.

The disc has an outer diameter of 500mm and a central hole of 120mm diameter. If there

are 100 blades each of mass 0.12 kg pitched evenly around the periphery of the disc at an

effective radius of 265mm, determine the maximum allowable rotational speed, when the

fracture stress for the polymer is 110mm2 and a factor of safety of 2 is required.

Given Polymer Material Properties:-

Poisson’s Ratio = 0.38

Density = 900 kg/m3 (34 marks)

Mechanical Materials

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