 Deformation (& deformation modes)  Parameters in Deformation  Stress  Strain  Mechanical Behaviour  Failure INTRODUCTION: DEFORMATION AND MECHANICAL BEHAVIOUR MATERIALS SCIENCE &ENGINEERING Anandh Subramaniam & Kantesh Balani Materials Science and Engineering (MSE) Indian Institute of Technology, Kanpur URL: home.iitk.ac.in/~anandh AN INTRODUCTORY E-BOOK Part of A Learner’s Guide

What kind of mechanical behaviour phenomena does one have to understand? Elasticity Plasticity Fracture Fatigue Mechanical Behaviour Creep Elongation at constant load (/constant stress) at ‘high’ temperatures  Phenomenologically mechanical behaviour can be understood as in the flow diagram below.  Multiple mechanisms may be associated with these phenomena (e.g. creep can occur by diffusion, grain boundary sliding etc.).  These phenomena may lead to the failure of a material #.  Many of these phenomena may occur concurrently in a material. Recoverable deformation Permanent deformation Propagation of cracks in a material* Oscillatory loading Bending of rod of metal Pushing a spring Release Original length # Failure implies deviation from desired performance. * Eventually can lead to breaking of material. Regains Original length A phenomenological classification (not a mechanistic one) Crack Propagation

 The classification presented is for ‘convenience’ and many details have been ignored.  In the uniaxial tension test (loading of specimen in uniaxial tension), dislocation ‘activity’ starts well below the yield stress (as we shall see later )→ plasticity in the microscale (in the ‘elastic’ region!!).  Creep also leads to ‘plastic deformation’!  Fracture in ductile material also involves plasticity at the crack tip level.  During fatigue loading (loading oscillating in load/stress, usually below the yield stress), dislocation activity can lead to surface intrusions and extrusions (plastic deformation at the microscopic level). Notes on the Classification of Mechanical Behaviour  On the application of load/constraint to a material, in may respond in many ways. The response could be reversible (elastic deformation) and or irreversible (plastic deformation & fracture).  The response to the load could be ‘immediate’* or could occur over a period of time.  In some cases (creep and fatigue) the damage may accumulate over a period of time before the component/sample ‘fails’. * More will be said about that, when we talk about anelasticity and creep.

Plastic deformation Mechanisms / Methods by which a Material can FAIL Fracture Fatigue Creep Chemical / Electro-chemical degradation Physical degradation Wear Erosion Microstructural changes Phase transformations Twinning Grain growth Elastic deformation Particle coarsening If failure is considered as deterioration in desired performance*- which could involve changes in properties and/or shape; then failure can occur by many mechanisms as below. * Beyond a certain limit Corrosion Oxidation Slip Twinning What kind of mechanisms can lead to ‘failure’? Etc.

 Tension/Compression  Bending  Shear  Torsion Common types of deformation TensionCompression Shear Torsion Deformed configuration Bending Note: modes of deformation in other contexts will be defined in the topic on plasticity

At a more fundamental level there are only two types of deformations $ :  Tension/compression  wherein bond length is increased/decreased  Usual tension/compression  During bending  Shear  bond angle is distorted  Usual shear  Torsion* $ A general case is a mixture of the two. * In torsion the strain varies radially outward. Deformation: a fundamental perspective

What can happen to a ‘material’ body (solid) on the application of external loads/forces/constraints? Funda Check Contraction/dilation Rigid body rotation What can happen to a material body (solid) when we apply forces/constraints to the outside of the body Shear Volume change Shape change Orientation change Or a combination of these Shear Pure Shear Simple Shear

From a common perspective we can have two types of deformation  Elastic Deformation  wherein body recovers its original shape after removal of ‘force’  E.g. a compression of a spring  the spring comes back to its original shape after load/force is released  Plastic Deformation  permanent deformation (body does not recover its shape after forces are removed  E.g. bending an Al rod to a new shape  the rod does not come back to its original shape after being bent Types of Deformation Deformation Plastic Elastic  Net deformation in a body can comprise of elastic and plastic parts.  Elastic deformation may be linear or non-linear.  There might also be a time dependent component to deformation (i.e. after application of force, full strain may be realized after some time.  Plastic deformation may be caused by many mechanisms (slip, twinning, phase transformation etc.) More about these later

 What is a spring? A spring can be thought of as a ‘device’ which changes tensile loading to torsional loading at the fundamental (material) level!  What is a conducting solenoid? A current carrying wire produces circular magnetic fields. A solenoid can be thought of as a ‘device’ to covert circular fields to a linear field (in the core of the solenoid)  it some sense the opposite of the spring above.  Deformation* can be in:  Force control mode [loads (e.g. hanging weights on a specimen), forces are controlled]  Displacement control mode [a given displacement imposed on the specimen]  Elastic deformation survives only for small strains in typical materials (e.g. metals and ceramics). At larger strains other mechanisms of deformation may take over (e.g. plasticity, fracture, creep etc.). In elastomers like rubber large elastic strains may be obtained.  Applied load can cause other effects like phase transformation etc. which may also additional change in the size/shape of the material.  Deformation (internally represented as stresses and strains) can be caused by other agents apart from loads (e.g. heat, electric field, magnetic field in appropriate materials). How to cause elastic deformation?

(Here we restrict ourselves to ‘solid bodies’)  One can only apply forces or loads (we cannot apply stresses!).  In some sense we can also impose displacements.  Stresses develop inside the body. * We can also impose constraints which can result in stresses in the body (we can heat a block between two ‘rigid’ walls and stresses will develop in the block). Forces and Stresses  Elastic deformation may be linear or non-linear.  There might also be a time dependent component to deformation (i.e. after application of force, full strain may be realized after some time. On Heating stresses develop in the body

 When a load/force or a displacement is applied to a material stresses and strains develop within the material. (Note that we cannot apply stresses, they develop within a material in response to an applied load etc.) Loads/forces are typically applied on the exterior of the material).  Stress (  ij ) and strain (  ij ) are second order tensor quantities, requiring 9 values to be prescribed in 3D (4 in 2D).  In normal materials stress and strain are symmetric tensors (symmetric about the diagonal) and hence it is enough to specify 6 values in 3D (3 in 2D).  At a fundamental level stress or strain can be tensile/compressive or shear. Tensile/compressive stresses lead to volume changes while shear stresses lead to shape changes. Under a general load the body will undergo both volume and shape changes.  In 1D*, for small values of strain, stress and strain can be defined as follows:  = load/area [units: N/m 2 or Pascal], (symbol  is sometimes used for shear stresses)  = change in length/original length [units: dimensionless]  Strain can be separated into elastic part (which is recoverable) and plastic part (permanent). Stress and Strain * Note that these definitions are applicable only in 1D. The symbol  is also used for the shear components.

 It should be noted that under certain circumstances: (i) Stress can exist without ‘net’ strain (strain free stress)  heating a body between rigid walls (ii) Strain can exist without stress (stress free strain)  heating a free-standing body  Stress free strains are also observed during phase transformation Stress and Strain (cotd.) Strain free stress Stress free strain On Heating **Note**

 We had noted before that we cannot apply stresses  we only apply forces/loads.  The forces are typically applied on the external surface of the body; but we can apply body forces too (body forces are applied throughout (or to a part of) the volume of the body; i.e. to every point in the body). Origins of body forces include: (i) gravity  mass in a gravitational field, (ii) magnetic force  magnetic object in a magnetic field, (ii) electric force  charged body in a electric field.  So what does one mean when he/she says that “I applied stress”?! He/she usually implies that a force was applied on a given area of material (on the surface). If the force was normal to the surface  tensile/compressive force If the force was tangential to the surface  shear force What does one imply when he/she says: “I applied stresses” (say shear stresses)? Funda Check

 Even when externally a tension is applied, regions in the material may experience shear stresses  this is an important aspect as microscopically plastic deformation is caused by shear stresses and one observes that plastic deformation can be caused by externally applied tension on a specimen.  To understand this let us consider a small square region ‘R’ in a specimen.  Under the action of the applied load (in the elastic region) the square region R becomes a rhombus. [Plane stress (2D stress) conditions have been assumed here]. A square can become a rhombus only by the action of shear stresses. This implies that there must be shear stresses acting on the planes ‘p1’ and ‘p2’ (figure below).  Note: even if we apply normal loads, shear stresses can develop within the material. How are stress and strains related to the external loading? Learn more about State of Stress and Strain Normal stresses on faces not shown

 We have already seen two important parameters (variables) in deformation → , .  Materials typically ‘soften’ on heating and hence temperature (T) is an important variable.  The rate of loading, which translates into strain rate is another variable → materials which are ductile under slow rate of loading may behave in a ‘less ductile manner’ which loading rate is faster. Typically the strain rate has to be varied by a few orders of magnitude to observe appreciable effects.  In terms of the effet on the plastic deformation behaviour of a material, an increase in strain rate can be visualized as a decrease in temperature.  We will come across other variables as we go along. Parameters (Variables) in Deformation Variables in deformation