Department of Materials Science &
Engineering
Module Description 2013/14
Module Code: MAT348
Module Title: Fracture Mechanics and
Heat Transfer
Module Convenor: Dr A Leyland
Module Links:
Credits: 10
Semester: 1
Pre-requisites:
Co-requisites:
Brief Description (including aims of the course):
This course is a brief introduction to linear elastic fracture mechanics and its
application to both brittle and more ductile materials. The effects of cyclical loading
and the environment on fracture behaviour are also considered. It also introduces
the basic physics of heat transfer, and simple methods by which conduction,
convection and radiation may be analysed. The emphasis of the course is on relating
the formal methods of solution to (relatively) realistic problems that as far as possible
are materials-related.
Course Objectives:
By the end of this course, you should be able to:
•Demonstrate some knowledge of the physics of heat transfer and the ability to
apply some simple analyses of conduction, convection and radiation;
•Display awareness of the important materials properties for heat transfer analyses;
•Demonstrate understanding of fracture mechanics and the ability to apply fracture
mechanics approaches to various problems involving both static and cyclical loading.
Course Content (lecture by lecture):
Lecturer 1: A Leyland
1: Introduction. Why is Fracture Mechanics important – examples of aircraft and rail
accidents caused by fracture and fatigue. Theoretical strength compared to actual
strengths. Inglis analysis of elliptical holes. Griffith’s thermodynamic approach to
sharp cracks.
2: Use of the Griffith equation. Modes of crack growth. Stress analysis round a sharp
crack tip (Irwin) – stress intensity factors.
3: Critical stress intensity factors and fracture toughness. Relationship between
Griffith and Irwin approaches. Stress intensity factors for other geometries. Examples
involving stress intensity factors.
4: Problems involving calculation of stress intensity factors. Leak before break.
5: First and second Irwin plastic zone corrections. Dugdale-Barenblatt calculation of
plastic zone size. Plastic Zone shapes - effect of plane strain and plane stress.
6: Plane strain fracture toughness measurements – single edge notched bend (SENB)
and compact tension (CT) tests. Validity of test measurements. Examples based on
fracture toughness testing.
7: R-curve behaviour. Plane stress fracture toughness – Feddersen approach. Plastic
collapse. Failure assessment diagrams – R6. Example based on the use of failure
assessment diagrams.
8: Cylical fatigue. S-N curves. Crack growth rate versus stress intensity factor range
curve – Paris equation. Lifetime calculation based on Paris equation (analytical
approximation). Examples involving lifetime calculations.
9: Problems involving fatigue lifetime calculations.
10: Lifetime calculation using numerical integration. Consideration of more realistic
crack shapes. Effects of crack closure on crack growth rates – Elber approach and a
brief introduction to some more recent models.
11: Effect of overloads on crack growth rates. Complex (real) loading patterns –
exceedance diagrams. Striations on fracture surfaces. Small crack problem and
initiation of fatigue cracks.
12: Gigacycle fatigue. Introduction to multi-axial fatigue. Environmental effects – K-v
diagrams. Lifetime calculations based on power law approach (analytic
approximation). Example based on power law lifetime calculations. Cyclic fatigue and
environmental interactions – introduction to multiple site damage. Summary of
course.
Lecturer 2: K Travis
1: Introduction. Why is Heat Transfer important to materials scientists and engineers
Three modes of heat transfer – conduction, convection and radiation.Fourier’s law.
Thermal conductivity and diffusivity. 1D electrical resistance model for planar walls
2: Basic introduction to convection and radiation. Incorporating convection and
radiation in the 1D electrical resistance model.1D electrical resistance model for
cylindrical walls.
3: Freezing of metal in a sand mould – semi-infinite model. Semi-infinite model with
convection.
4: Conduction and convection. Cooling of a section. Lumped solution.Finite thickness
plate – Heisler charts
5: Heisler charts for a cylinder and a sphere. Examples of use. Product solutions.
6: Problems class 1.
7: Dimensionless numbers and calculating convective heat transfer coefficients.
8: Steady state conduction with internal heat generation – temperatures in
radioactive wasteforms.Finite difference calculations for steady state problems –
Gaussian elimination.
9: Finite difference calculations. Guass-Seidel iteration. Time dependent finite
difference calculations – forward and backward difference approaches
10: Radiative exchange between black bodies – shape factors.
11: Radiative exchange between grey bodies.Resistance model – shape and surface
resistances.Measuring temperatures in gas flows. Radiation shields. Summary of
course
12: Problems class 2.
Assessment:
Exam: 100%
Individual Report:
Visit/Placement Diary:
Essay:
Practicals:
Oral Presentation:
Group Project Report:
Problem Sheets:
Poster Presentation:
Lab Report:
Other:
(please state type of assessment)
Booklist (A) Core Test; (B) Secondary Text; (C) Peripheral Reading:
(A) JP Holman Heat transfer McGraw-Hill
(A/B) H.L. Ewalds and R.J.H. Wanhill Fracture Mechanics Arnold/DUM (1991). ISBN 07131-3515-8 (Arnold); 90-6562-024-9 (DUM) - good coverage of the course material,
this edition is out of print; it has been reprinted as M Janssen, J Zuidema abd RJH
Wanhill Fracture Mechanics Delft University Press – price is OK if ordered direct from
publishers and not via Blackwells!
(B) D. Broek Elementary Engineering Fracture Mechanics Kluwer Academic Publishers
(1986). ISBN 0317474480. Good, but very expensive.
D. Broek The Practical Use of Fracture Mechanics Kluwer Academic Publishers (1989).
ISBN 0792302230. Also expensive but good on the use of fracture mechanics.
(C) N.E. Dowling Mechanical behavior of materials 2nd edition Prentice Hall (1999).
ISBN 013905720x. Some parts of this text are relevant to the course. Probably too
expensive to buy just to support this course but might be useful for other courses as
well. (C) D.W. Hertzberg Deformation and fracture mechanics of engineering
materials - 4th ed. Wiley (1996). ISBN 0471012149. Similar comments apply as to the
book by Dowling.
(B) J. F. Knott and P. Withey Fracture mechanics: worked examples 2nd ed. Institute of
Materials (1993). ISBN 0901716286. This book contains a useful set of examples and
is relatively cheap.
(B/C)S. Suresh Fatigue of Materials 2nd Edition Cambridge University Press (1998).
ISBN 0-521-578477 - relevant to section 4 of the course.