Mechanics of Materials

MATS23101 Mechanics of Materials 10 Semester 1 Undergraduate Level 5 Timothy Burnett Unit coordinator Department of Materials 1 FHEQ level (Framework for Higher Education Qualifications) ' Middle part of Bachelors ' European Credit Transfer & Accumulation System Rating : 5.0 The unit provides a development of knowledge on the mechanical behaviour of materials acquired during the first year of the course and extends it to deformations in 2- and 3-Dimensions. It also extends the simple introduction to fracture, covered in the first year, to a more formal fracture mechanics approach. The course also provides an introduction to macroscopic plasticity, hardness, friction and wear.  The unit provides a development of knowledge on the mechanical behaviour of materials acquired during the first year of the course and extends it to deformations in 2- and 3-Dimensions. It also extends the simple introduction to fracture, covered in the first year, to a more formal fracture mechanics approach. The course also provides an introduction to macroscopic plasticity, hardness, friction and wear.Lecture topics include<ul> <li>Formal description of Strain and Stress in 2- and3-Dimensions</li> <li>Representation of strain and stress as tensors and the transformation of tensors, Mohr’s Circle.</li> <li>The elastic constants and the stiffness and compliance tensors</li> <li>Experimental measurement of strain</li> <li>Distributions of stress and strain resistance to bending and twisting.</li> <li>Stress and Strain in polar co-ordinate systems,</li> <li>Stress Concentration</li> <li>Fracture mechanics and the fracture toughness</li> <li>Energy dissipation during fracture, plastic zones</li> <li>Measuring fracture toughness</li> <li>Highly brittle materials and the statistics of failure</li> <li>Fatigue mechanisms, Paris Law, Coffin-Manson Law</li> <li>Design against fatigue and fracture</li> <li>Friction and Wear</li> <li>Macroscopic Plasticity, Hardness, Residual Stress</li></ul> The unit aims to:<ul> <li> Introduce the representation of stress and strain as 2nd rank tensors and their relation via the compliance and stiffness tensors.</li> <li> Explain the methods used to measure strain in a body and how these are used in practical engineering situations.</li> <li> Introduce the concepts of a stress distribution and a stress concentration. Explain how stress distributions lead to a resistance to twisting and bending and how the shape of a material influences this resistance.</li> <li> Introduce the concept of fracture mechanics, fracture resistance and critical stress intensity.</li> <li> Introduce simple statistical concepts for the prediction of failure in brittle materials.</li> <li> Introduce the mechanisms for fatigue failure in terms of crack initiation and crack growth.</li> <li> Introduce simple descriptions of macroscopic plastic deformation, hardness, friction and wear.</li></ul>  A greater depth of the learning outcomes are covered in the following sections: <ul> <li> Knowledge and understanding</li> <li> Intellectual skills</li> <li> Practical skills</li> <li> Transferable skills and personal qualities</li> </ul> <ul> <li> Define stress and strain in 3-dimensions and represent them in the form of a tensor in Cartesian and cylindrical co-ordinates. Understand how to manipulate these tensors to represent a state of stress or strain in different spatial orientations of the axes.</li> <li> Determine the principal stresses and strains of a tensor and their invariant values.</li> <li> Identify the relationship of the shape and composition of a beam and rod control their resistance to bending and twisting.</li> <li> Explain the concept of a stress distribution and a stress concentration.</li> <li> Explain the relation between the Griffiths model of fracture and that proposed by Irwin and Orowan.</li> <li> Demonstrate an understanding of the mechanisms that dissipate energy during fracture and now these can lead to size effects in the measurement of fracture toughness.</li> <li> Demonstrate an understanding of the need to use statistical methods for the description of the strength of highly brittle materials.</li> <li> Construct the description of fatigue based on descriptive simple models for fatigue life prediction.</li> <li> Predict macroscopic plasticity and be able to relate materials hardness and flow strength.</li> <li> Demonstrate an understanding of simple models for friction and wear.</li></ul><div>  </div> <ul> <li> Show improved logical reasoning, problem solving and ability in applied mathematics.</li> <li> Show an improved understanding and spatial awareness through solving problems in 2- and 3-dimensions. </li></ul> <ul> <li> Perform simple matrix manipulation and calculations.</li> <li> Quantify the stress intensity factor from measurements made from fracture mechanics specimens.</li> <li> Use photoelastic effect to understand stress concentrations in real materials  </li></ul> <ul> <li> Convert problems described using text into equations to provide numerical answers.</li> <li> Use spreadsheets to analyse data</li> <li> Work effectively in a group to solve problems.</li> <li> Compose simple technical reports on laboratory tests. </li></ul> <div>Lectures, group tutorials (problem sessions), recommended textbooks, web resources, self- teaching worked examples, past exam papers, electronic supporting information (Canvas).   </div>  1 Written exam 70% 2 Written assignment (inc essay) 30% Written and verbal N <ul> <li>Mechanical Metallurgy: G Dieter, 3rd edition or later</li> <li>Deformation and Fracture Mechanics of Engineering Materials: R W Hertzberg, 5th edition or later</li> <li>Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture, and Fatigue: N E Dowling, 3rd edition or later</li> <li>Continuum Mechanics by George E. Mase</li></ul>  Lectures 22 0 78