Plasticity theory related to porous

materials

By

Bashar Ridha Younos Al-ogaidi

SUBMİTTED TO

Assistant Prof. ABDULLAH AKPOLAT

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Introduction

Porous materials

Elasticity and plasticity

summary

Contents

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Introduction

Research in plasticity of porous materials has, at least,

a 40 year history. This research appears to have

proceeded in two primary directions:

(A) plasticity at small overall strains, in particular,

determination of the macroscopic yield surface in

stress space, accounting for porosity, in the cases

when such a surface can be clearly identified

and (B) void growth and coalescence at much larger

overall strains

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F. Rouquerol, J. Rouquerol, K. S. W. Sing, Adsorption by Powders and Porous

Solids, Academic Press, 1-25, 1999

WHAT ARE POROUS MATERIALS?

Non-porous solid

Low specific surface area

Low specific pore volume

Porous solid

High specific surface area

High specific pore volume

Porous materials have highly developed internal surface area that can be

used to perform specific function.

Almost all solids are porous except for ceramics fired at extremely high

temperatures5

MEASURE OF POROSITY

Pore size and

its distribution

Specific Surface Area, m2/g =

There are three parameters used as a measure of porosity; specific

surface area, specific pore volume or porosity, and pore size and its

distribution.

Mass of the solid, g

Total surface area, m2

Specific Pore volume, cm3/g

Mass of the solid, g

Total pore volume, cm3

=

Porosity, % =

Volume of solid (including pores)

Volume of poresX 100

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Parameters that effected on porousity :-

1- partical size

2- partical shape

3- partical ditripution

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PARTICLE SIZE

void

smaller, more numerous voids

voids filled by smaller particles, small voids

remain

Mixing particles of different sizes allows decreased porosity and a

higher packing ratio

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PARTICLE SHAPES IN METAL POWDERS

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Figure: Particle shapes in metal powders, and the processes by which

they are produced. Iron powders are produced by many of these

processes.

CONCEPT OF POROSITY: OPEN VS. CLOSED

PORES

Dead end

(open)

Closed

Inter-connected

(open)

Passing

(open)

F. Rouquerol, J. Rouquerol, K. S. W. Sing, Adsorption by Powders and Porous

Solids, Academic Press, 1-25, 1999

Open pores are accessible

whereas closed pores are

inaccessible pores. Open pores

can be inter-connected, passing

or dead end.

Type of porous

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SHAPES OF PORES

Conical

Interstices

SlitsCylindrical

Spherical or

Ink Bottle

Pore

Shapes

F. Rouquerol, J. Rouquerol, K. S. W. Sing, Adsorption by Powders and Porous Solids, Academic

Press, 1-25, 1999

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PROPERTIES OF POROUS METALS

Lightweight structure

Energy absorber

High temperature resistant

Heat exchanger

Biomaterial

Filter

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ADVANTAGES OF FORMING OF POROUS METALS

Forming to desired shape

Control of porosity and morphology

Work hardening of matrix

Improvements in properties

Unusual microstructure

Forming of complicated shapes

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SIZE OF PORES (IUPAC STANDARD)

2 nm 50 nm

Micropores Mesopores Macropores

Zeolite,

Activated

carbon,

Metal organic

framework

Mesoporous silica,

Activated carbon Sintered metals

and ceramics

Porous material are classified according to the size of pores: material with

pores less than 2 nm are called micropores, materials with pores between 2

and 50 nm are called mesopores, and material with pores greater than 50

nm are macrospores

Sing, K. S. W. et al. Reporting Physisorption Data for Gas/Solid Systems. Pure & Appl. Chem. 57,

603-619 (1985).

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Applications of porous materials

BearingsFoam

Filters Electro-

magnetic

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Applications in Biomedical field

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Mesoporous Materials for Bone Tissue Engineering

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ELASTICITY

The property of material by virtue of which deformation caused

by applied loads disappears upon removal of load.

Elasticity of the material is the power of coming back to its

original position after deformation when the stress or load is

removed.

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The physical reasons for elastic behavior can be quite

different for different materials. In metals, the atomic

lattice changes size and shape when forces are applied

(energy is added to the system). When forces are

removed, the lattice goes back to the original lower

energy state.

In engineering, the amount of elasticity of a material

is determined by two types of material parameter.

The first type of material parameter is called

a modulus, which measures the amount of force per

unit area (stress) needed to achieve a given amount of

deformation. The units of modulus are pascals (Pa).

A higher modulus typically indicates that the material

is harder to deform. 26

The second type of parameter measures the elastic

limit. The limit can be a stress beyond which the

material no longer behaves elastic and deformation of

the material will take place.

If the stress is released, the material will elastically

return to a permanent deformed shape instead of the

original shape.

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PLASTICITY:

The plasticity of a material is its ability to undergo

some degree of permanent deformation without rupture

or failure.

Plastic deformation will take only after the elastic limit

is exceeded.

It increases with increase in temperature.

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STRESS-STRAIN CURVE FOR SHOWS

ELASTICITY AND PLASTICITY FOR MATERIALS:

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Porous metal plasticity

– The porous metal plasticity model is intended for

metals with relative densities greater than 90% (i.e.,

a dilute concentration of voids).

– The model is based on Gurson’s porous plasticity

model with void nucleation and failure.

– Inelastic flow is based on a potential function which

characterizes the porosity in terms of a single state

variable—the relative density.

– The model is well-tuned for tensile applications,

such as fracture studies with void coalescence, but

it is also useful for compressive cases where the

material densifies.

– The details of this material model are discussed in

the Metal Inelasticity in ABAQUS lecture notes.30

Porosity --- Strength

Behavior of metal porous under compression31

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The effect of porosity on strength during densification by preform workingcan be analyzed using a simple model. Consider an ideal porous materialof relative strength στ as defined by Haynes (1970):σχ = σ/σ0 = (1 - ρ) (1)where σ is the true stress for flow of the porous preform at a specified level ofstrain, σ0 the true stress for flow of the fully dense material at the same levelof strain, and ρ the percent porosity. In a real (nonideal) situation, the poresgive rise to local stress concentrations in addition to reducing the effectiveload-bearing cross section. If the stress concentration factor due to pores isKp, Eq. (1) is modified intoσχ = σ/σ0 = (1 - p)/Kp (2)

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II. PLASTİC DEFORMATION OF SINTERED POWDER

METAL

1.Physical Model

Investigation of densification of a porous metal is

facilitated by consideration of deformation of a material

element containing a void. It is well known from plasticity

analysis of a thick-walled sphere that it is impossible to

completely colose a hole by hydrostatic pressure of finite

magnitute. The pressure repuired for plastic deformation of

a sphere containing a hole is given by

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where σ0 is the flow stress of the material, r0 the

outside radius (equivalent to mean space between

voids), and ri is the hole radius (equivalent to void

radius). It is clear that voids of large diameter (large

ri ) require less pressure for densification than

small voids, and that, as the void diameter

approaches zero, the pressure required for

densification becomes unbounded. Under

hydrostatic pressure, the void simply changes size,

but not shape, since the pressure is equal in all

directions.

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YOUR ATTENTION

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