Deformation (& deformation modes)

# Deformation (& deformation modes)

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## Deformation (& deformation modes)

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1. Deformation (& deformation modes) Parameters in Deformation Stress  Strain Temperature  Strain Rate Mechanics & Mechanical Behaviour Failure MATERIALS SCIENCE & ENGINEERING Part of A Learner’s Guide AN INTRODUCTORY E-BOOK Anandh Subramaniam & Kantesh Balani Materials Science and Engineering (MSE) Indian Institute of Technology, Kanpur- 208016 Email:anandh@iitk.ac.in, URL:home.iitk.ac.in/~anandh http://home.iitk.ac.in/~anandh/E-book.htm INTRODUCTION:DEFORMATION AND MECHANICAL BEHAVIOUR

2. Materials, Structures and Mechanisms • Broadly we can think of materials, structures and mechanisms. • Structures and Mechanisms are made of materials. • A structure (like a building or an anglepoise lamp) may perform multiple roles, but typically all of them bear load. • A mechanism is typically used to transfer power and may involve change in direction, speed or torque. • Compliant mechanisms are structures which play the role of a mechanism. • Structures typically have positive stiffness (i.e. resist the load), but may develop negative stiffness under special circumstances (e.g. buckling)

3. Let us start with some basic definitions and considerations • We can apply forces and moments on a body. • Force(s) can be applied on a body in two ways: (i) Surface forces (by direct contact of one body with another) & (ii) Body forces (force exerted without direct contact, usually throughout the volume of the body). Hammering involves surface forces, while gravitational pull is a body force. • The force can be: (i) Point force (if the area of application is small compared to the overall area of the body) or (ii) Distributed load (loading is over an area). • The force or moment experienced by a member may arise from a ‘support’. A support which prevents translation in a direction gives rise to force in that direction. If on the other hand rotation is prevented, then this results in a moment.

4. Some simple structures • In simple structures like buildings, the load is transmitted to the foundation via beams and columns. • A beam carries loads which act at right angles to the length of the beam, which spans horizontally between supports. They have a small cross-section in comparison to their span. In general the external loads on a beam results in bending moments (M) and shear forces (V). • Some types of beams are: (i) Simple supported (ii) Fixed (iii) Cantilever (iv) Continuous (vi) Overhanging(vii) Restrained.

5. Behaviour of Components in Service and the Testing of Materials • Components and devices in service have to satisfy certain ‘performance parameters’ (load to borne, temperature of operation, environment of operation, etc.). • To satisfactorily perform under a given service conditions, the material should possess certain properties. And, we would like to avoid failure# of these components/devices. • Before we design and test components, we would like to know about the material properties (on which we can base our design). Also, often it is difficult to test entire components (like a gear wheel) or a system of components (like a gear wheel assembly). • Usually, special ‘test rigs’ are designed to test a ‘full’ components or an assembly of components. • Hence, often we rely on test data on ‘model’ samples, with ‘ideal’ geometries. These tests include: hardness test, uniaxial tension test, bending test (3-point, 4-point), torsion test, hardness test, creep test, etc. • The challenge is to use this data obtained from model tests, for the design of components. The component may have a complicated geometry and which experiences a state of stress, which is considerably different from that in the model test. • In the design of structures the (i) strength (), (ii) deformation () and (iii) stability are taken into account. # Failure implies deviation from desired performance.

6. In general failure can be avoided by: (i) a better design of the system (such that the component experiences a lower ‘degree of loading’) and/or (ii) better design of the component. Further, the improvement in the component design could involve a better: (i) geometrical design and/or (ii) material design (i.e. choice of material). • Another way of looking at ways to avoid material failure is: Protect the material (paint to avoid corrosion, cool the material if ‘heating’ is leading to failure) Make a ‘better’ material (design a material to withstand high temperatures, if creep is leading to failure) Have a ‘sacrificial strategy’ (have a sacrificial anode which will corrode in preference to the material of interest, have a shield which will burn up during re-entry of a space vehicle thus protecting the interior) • Most of the engineering failures (~70%) happen due to fatigue and corrosion. • In this chapter we will concern ourselves only with mechanical properties.

7. What kind of mechanical behaviour phenomena does one have to understand? • Phenomenologically mechanical behaviour can be understood as in the flow diagram below (1) Elasticity, (2) Plasticity, (3) Fracture, (4) Fatigue, (5) Creep. • 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. Mechanical Behaviour Release Pushing a spring Regains Original length Original length Elasticity Recoverable deformation Plasticity Permanent deformation Bending of rod of metal A phenomenological classification (not a mechanistic one) Fracture Propagation of cracks in a material* Crack Propagation Crack Propagation Fatigue Oscillatory loading Creep Elongation at constant load (/constant stress) at ‘high’ temperatures # Failure implies deviation from desired performance. * Eventually can lead to breaking of material.

8. There seems to be many ‘phenomenological’ possibilities of deformation (elasticity, plasticity, creep, ...). In a given situation which one will be operative? Funda Check • Each of the phenomenological effects (let us consider creep) may have multiple mechanisms which may give rise to the effect (in creep, grain boundary sliding and diffusion are two of the possible mechanisms). The ‘effect’ in the current context could be an observable like ‘irreversible deformation’ (i.e. plastic deformation). • When there are two (or more) competing mechanisms are available to respond to a stimulus (say applied load which results in a stress state in the material), then the mechanism which operates at a lower magnitude of the stimulus (stress in the current situation) operates (in preference to other competing mechanisms). • Material variables (like grain size, segregation, crystal structure, etc.) and process variable/loading conditions (like temperature, strain rate) will play a key role in determining the mechanism which will be operative.

10. What kind of mechanisms can lead to ‘failure’? 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. Mechanisms / Methods by which a Material can FAIL Elastic deformation** Bond distortion Chemical /Electro-chemicaldegradation Creep Physicaldegradation Fatigue Plastic deformation Fracture Cracks Microstructuralchanges Twinning Wear Slip Dislocations Twinning Erosion Corrosion Etc. Phase transformations Oxidation Grain growth * Beyond a certain limit Particle coarsening ...and more. ** Some may wonder as to how elastic deformation can be construed as failure.

11. Funda Check How can elastic deformation lead to (/constitute) failure? • From a ‘common sense’ perspective, fracture seems to be the ‘real’ failure. • With a little ‘stretch’ we can think of plastic deformation as also ‘failure’. • But, how can elastic deformation constitute ‘failure’? • Let us consider a diving spring board (in a swimming pool). • To get a good dive one needs a good jump. For this the board should provide a good ‘spring-back’. • If the compliance of the board is too much the board will bend and the swimmer will just fall into the pool. The board after some oscillations will return to the approximately horizontal position (i.e. the process is elastic but the board has failed to deliever the desired performance). • However, in most circumstances permanent change in the shape of the component (i.e. involving plastic deformation) or fracture is considered as failure. • Such a failure by plastic deformation and/or fracture can occur due to phenomenological processes like creep and fatigue. • In ductile materials, plastic deformation usually precedes fracture. If acceptable deflection is exceeded Material is elastic but  > c In general If Yield stress is exceeded Failure Plastic deformation is initiated ( > y) If fracture stress is exceeded The material fractures ( > f)

12. Common types of loading and deformation • From a macroscopic perspective we can deform a material in by applying (i) external forces (or (ii) moments) in a few ways. The actual loading on a given component may be complex, involving combinations of these loading types.  Tension/CompressionBendingShear  Torsion. • The kind of loading employed is often dependent on the geometry of the sample (e.g. bending is done on thin long samples, while compression on short cylinders). • The deformation mode experienced by the material and the mechanism(s) involved at the microscopic level has to be separately analyzed. E.g., in a spring, even if tension is applied, a cross-section experiences torsion. Bending Deformed configuration Torsion Note: modes of deformation in other contexts will be defined in the topic on plasticity Shear Tension Compression

13. In a given scenario the general loading will be a combination of the types of loading considered previously. • Basically, we can apply* either:(i) Forces (axial or shear) or(ii) Moments (bending or twisting) Transverse force * As must be obvious to the reader, often one kind of loading employed may result in other kinds of effects at the level of the body/material. E.g. a transverse force can result in shear forces and bending movements.

14. Deformation: a fundamental perspective At a more fundamental (material) 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* • In this chapter (and the course), (most of the time) we will assume that the loading is applied slowly (quasi-statically)  i.e. wave propagation and contact damage effects can be ignored. \$ A general case is a mixture of the two. % In the extreme case the bonds might break. * In torsion the strain varies radially outward.

15. Funda Check What can happen to a ‘material’ body (solid) on the application of external loads/forces/constraints? Contraction/dilation Volume change What can happen to a material body (solid) when we apply forces/constraints to the outside of the body Or a combination of these Shear Shape change Rigid body rotation Orientation change Example showing how parts of a single body may have different responses to loading The region between supports is stressed 3-point bend test Normal reactions The region outside the supports undergoes rigid body rotations and is not stressed

16. What distributed and point loads? What is a rigid body? What are contact and body forces? Q & A • In practice the kind of loads which is applied on materials (structures and mechanisms) is distributed (i.e. spread over an area). Point load is an idealization. Sharp, pointed loads will lead to very high pressures/stresses (infinite in the limit of geometrical point). This will further damage the surface of the material locally. • Similarly a rigid body is an idealization. A rigid body does not undergo any deformation. For a rigid body to be in equilibrium the sum of the external forces has to be zero. If there exists a net force then the body will accelerate (Fresultant = mbodya). • Forces applied on the surface are called contact forces. On the other hand forces like gravity act over all the particles in the entire body and are referred to as body forces. Q & A What is the difference between external force and internal response of a material? • Let us consider the pulling of a body (say a metal with the elastic limit). At equilibrium the internal force (P’) is equal and opposite to the external force (P). This can be better visualized using a cut in the body CC’. The internal force appears due to stretching of the bonds. Materials have positive stiffness and resist deformation. • Structures on the other hand may display negative stiffness under special circumstances (like during buckling).

17. Funda Check What is the difference between simple and pure shear? • Usually we apply ‘simple shear’ forces on a body. Though this is called simple shear it is clear that with just two forces the body will not be in equilibrium (moment balance is not satisfied). This implies that there has to be additional ‘hidden’ forces (as shown in Fig.1b). These forces ensure moment balance. To understand this let us consider a block on a table being sheared by force ‘T’. Friction provides the opposite force on bottom surface (T). • At the material level, pure shear can be considered as simple shear + rotation of /2 (for small shear). Fig.1 b c a Note the bottom For small deformations Usually we apply simple shear forces on a material Simple Shear The way the diagram is drawn the body is not in equilibrium! Pure shear of /2 = Simple shear of  + ACW rotation of /2 Shear OR Pure Shear Simple shear of  = Pure shear of /2 + CW rotation of /2

18. Funda Check What is the difference between three-point and Four-point bend test? • In bending we would like to apply pure bending moments. In practice we employ a 3-point or 4-point bend test. • In the 3-point bend test the bending moment is not constant and additionally shear forces are present. • A constant bending moment, along with zero shear forces are obtained between the loads in the case of the 4-point bend test.

19. Types of Deformation From a common perspective we can have two types of deformation. • Elastic Deformation  wherein body recovers its original shape after removal of ‘force’.Elastic deformation is reversible. 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.Plastic deformation is irreversible (involves dissipation of energy). E.g. bending an Al rod to a new shape  the rod does not come back to its original shape after being bent. Elastic Deformation Plastic • 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

20. How to cause elastic deformation? • 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 many 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). • 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.

21. Forces and Stresses (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 (Often in response to external loads and constraints  but not always! E.g. dislocations in materials lead to stress fields, even in the absence of external loads). * 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). On Heating stresses develop in the body • 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. • The quantities of relevance inside the material are stress and strain and not load and displacement(i.e., what the material ‘experiences’ is stress and strain). More about this later.