Fracture of metallic materials

Prof. Barbara Rivolta

Course of Mechanical Metallurgy

October 2014, Lecco

Barbara Rivolta

2 Introduction

Fracture can be classified into two general categories:

ductile fracture: characterized by plastic deformation before and

during the propagation of the crack. An appreciable amount of

deformation can be observed at the fracture surface

brittle fracture: characterized by a rapid rate of crack propagation,

with no appreciable deformation and very little

microdeformation

The process of fracture can be considered to be made up of two

components:

crack initiation

crack propagation

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3 Introduction

Ductile fracture

Brittle fracture

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4 Introduction

Types of fractures observed in metals subjected to uniaxial tension

(a) Brittle fracture of single crystals and polycristals; (b) shearing fracture

in ductile single crystal; (c) completely ductile fracture in polycristals; (d)

ductile fracture in polycristals

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5 Theoretical cohesive strength

The variation of the cohesive force between

two atoms as a function of the separation

between two atoms.

= theoretical cohesive strength

x = a-a0 = displacement in atomic

spacing

l = wave length in a lattice For small displacements, sin x~x, hence:

(1)

(2)

a0 = interatomic space in the unstrained

condition

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6 Theoretical cohesive strength

If we restrict consideration to a brittle elastic solid, from Hookes law:

(3)

Substituting (3) in (2):

(4)

If we make the assumptions that a0~l/2, then

high values of cohesive strength!!!

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7 Theoretical cohesive strength

If the energetics of the fracture process are considered, the fracture work

done per unit area during fracture is given by:

This energy is equal to the energy required to create the two new

fracture surfaces (2gs):

Or:

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8

Substituting in (4):

Theoretical cohesive strength

Example:

Estimate the theoretical fracture stress of iron if the surface energy is 1.2

J/m2

E = 200 GPa; a0 = 0.25 nm

max = ?

Experience with high strength steels shows that a fracture strength in

excess of 2 GPa is exceptional. Engineering materials typically have

fracture stresses that are 10 to 1000 times lower than the theoretical value.

This leads to the conclusion that flaws or cracks are responsible for the

lower than ideas fracture strength of engineering materials.

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9 Theoretical cohesive strength

thin elliptical crack in an infinitely wide plate

the crack has a length 2c

radius of curvature at its tip r

The maximum stress at the tip of the crack is:

Equating it to the equation

We can solve for which is the nominal fracture

stress f of the material containing cracks:

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10 Theoretical cohesive strength

The sharpest possible crack is when rt = a0, so that:

Example:

Calculate the fracture stress for a brittle material with the following

properties:

E = 200 GPa; gs = 1.2 J/m2; c = 2.5 mm

f = ?

Note that the theoretical cohesive strength was 31 GPa!!!!

This means that a very small cracks produces a very great

decrease in the stress for fracture.

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11 Griffith theory of brittle fracture

The first explanation of the discrepancy between the observed fracture

strength of crystals and the theoretical cohesive strength was proposed

by Griffith (1920).

Griffiths theory in its original form is applicable only to a perfectly brittle material:

a population of fine cracks is present inside a brittle material

these cracks produce a stress concentration so that the theoretical cohesive strength is reached in localized region even if the nominal

stress is lower than the theoretical value

a crack will propagate when the decrease in elastic strain energy (released as the crack spreads) is at least equal to the energy

required to create the new crack surface

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12 Microscopic fracture mechanisms

brittle fracture:

cleavage mechanism

intergranular mechanism

ductile fracture:

microvoid coalescence mechanism

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13 Cleavage fracture

Cleavage fracture is the most brittle form of fracture which can occur in crystalline materials

The possibility to have cleavage fracture is increased by lower temperature and higher strain rates

Cleavage fracture of metals occurs by direct separation along crystallographic planes due to a simple breaking of atomic

bonds. For example, iron cleaves along the cube planes (100) of its

unit cell.

(100)

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14

This causes the relative flatness of a cleavage crack within one grain.

The neighboring grains have different orientations, so the cleavage crack

changes direction at a grain boundary to continue propagation on the

preferred cleavage plane.

Cleavage fracture

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15

Microscopically

Cleavage fracture

Transgranular cleavage

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16

Inside the grain, the fracture can propagate on two parallel

crystallographic planes.

Cleavage fracture

The two parallel cracks can join by overlapping if they are on the same

plane, or by a secondary cleavage to form a step.

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17

A number of cleavage steps may join and form a mutiple step.

Macroscopically, the merge of cleavage steps results in the so-called river patterns because of its similarity to a river and its tributaries. River patterns often form at the passage of a grain boundary.

Cleavage fracture

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18 Cleavage fracture

When the crack passes a grain boundary, two situations can occur:

if the twist angle is low, the crack propagates from a grain to the other with continuity

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19 Cleavage fracture

if the twist angle is high (a grain with different orientation), the crack must reinitiate on the now differently oriented cleavage plane.

It may do so at a certain number of places and spread out in the new

crystal. This gives rise to the formation of a number of cleavage steps,

which may join and form a river pattern.

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20 Cleavage fracture

The convergence of river patterns is always downstream; this gives the

possibility to determine the direction of local crack propagation in a

micrograph.

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21

Under normal circumstances face-centered-cubic (fcc) crystal structures do not exhibit cleavage fractures: extensive plastic

deformation will always occur in these materials before the cleavage

stress is reached.

Cleavage occurs in body-centered-cubic (bcc) and many hexagonal-close-packed (hcp) structures. It occurs particularly in iron and low

carbon steel. Tungsten, molybdenum, chromium (all bcc) and zinc,

beryllium and magnesium (all hcp) are materials capable of cleaving.

Cleavage fracture

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22 Intergranular fracture

It is the fracture mechanism wherein the crack prefers to follow the grain

boundaries.

The occurrence of intergranular fracture can result from a number of

processes:

nucleation and coalescence at inclusions or second-phase particles located along grain boundaries;

grain-boundary crack and cavity formations associated with elevated temperature stress rupture conditions;

decohesion between contiguous grains due to the presence of impurity elements at grain boundaries and in association with aggressive

atmosphere such as gaseous hydrogen and liquid metals;

stress corrosion cracking processes associated with chemical dissolution along grain boundaries

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23 Intergranular fracture

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24 Intergranular fracture

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25 Intergranular fracture

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26 Ductile fracture

A crack often origins from second phases, i.e. from particle of different

dimensions.

Three types of particles can be distinguished:

Large particles 1-20 m; visible under the light microscope. They usually consist of complicated compounds of various alloying elements.

These particles do not contribute to strengthen the material.

Intermediate particles 50-500 nm; only visible by means of the electron microscope. They also consist of complex compounds of

different alloying elements. They contribute to strengthen the metallic

matrix significantly.

Small particles - 5-50 nm; in certain cases visible by means of electron microscope. They are developed by means of solution heat treatment and

ageing and they serve to give the alloy its required yield strength.

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27

The large particles are often very brittle and they cannot accomodate the plastic deformation of the matrix. They fail early, with small

amount of plastic deformation. The do not play a role in the process of

ductile fracture itself.

The fracture is often induced by the intermediate size (sub-micron) particles. The mechanism is the following: the dislocations have the

possibility to slip and tend to pile-up near a particle, inducing the

formation of microvoids.

Ductile fracture

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28 Ductile fracture

cavities

microvoids

coalescence

of microvoids

Final rupture

Oval dimples

Fracture

by shear

Equiaxial and

round shape

dimples

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29 Ductile fracture

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30 Ductile fracture

Large voids in AISI 4340 linked by

narrow void sheets consisting of small

microvoids.

Schematic representation

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31 Ductile fracture

As the nucleation and coalescence of dimples are linked to a plastic deformation, more deep and wide the dimples are, higher the plastic

strain energy is.

The shape of the dimples is influenced by the applied stress field:

equiaxed dimples with a tensile stress

parabolic dimples with a shear or tear stress

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32 Ductile fracture

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33 Ductile fracture