Deformation (& deformation modes)

Parameters in Deformation Stress Strain

Mechanical Behaviour

Failure

INTRODUCTION:

DEFORMATION AND MECHANICAL BEHAVIOUR

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

* Eventually can lead to breaking of material.

Regains

Original length

A p

hen

om

enolo

gic

al c

lass

ific

atio

n

(not

a m

echanis

tic

one)

Crack PropagationCrack Propagation

The classification presented is for convenience and many details have been ignored.

In 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 is 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

Plastic

deformation

Mechanisms / Methods by which a Material can FAIL

FractureFatigue

CreepChemical /

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

Tension Compression

Shear TorsionDeformed configuration

Bending

Note: modes of deformation in other contexts will be defined in the topic on plasticity

Tension / Compression

Torsion

Modes

of

Deformation Shear

Bending

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

ShearPure 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/m2 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.

11 12 13

21 22 23

31 32 33

ij

11 12 13

21 22 23

31 32 33

ij

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)

We will come across other variables as we go along.

Parameters (Variables) in Deformation

Variables in deformation T , , ,