02 mecc b

Materiali per l’IngegneriaM.Ferraris

“true” engineering curve

necking Formation of pores

Pores coalescenceCrack propagation

http://web.umr.edu/~be120/lessons/intro/tension/testing_st/fracture.gif

Metallic samples for tensile test

Yield strength

(s, y, 0,2)

(s, P(0,2) )

Yield strength or proportional limit (Rp0,2)

Yield Strength (YS, Sy), “Yield Strength (offset = 0.2

Upper and lower yield strength

Upper Yield Strength (UYS) and Lower Yield

Strength (LYS)

(R, Rm)

Tensile Strength (TS, Su, UTS)

elongation %

Maximum elongation (Elmax) 100

Typical stress-strain curves

failure

tensile strength

upper yield point

lower yield pointy

strain

stress

material creeps (extension without increased stress) or

sample ‘necks’

elasticregion

plasticregion

yield elongation ultimate elongation

ultimate strength

material may follow either path

www.matcoinc.com/images/sem1a.jpg

http://www.ndt-ed.org/EducationResources/CommunityCollege/Materials/Mechanical/Tensile.htm

COMPRESSION TEST

Bending or flexural test

THREE POINT BENDING TEST

3 and 4 point bending

Asymmetric 4 point bending for ceramic joined materials

FeFeFiFi

T = Fle - li

le + li

BENDING TEST on Al2O3 and glass

Flexural strength of ceramics

• Draw versus t (strain vs time) when a material is loaded at = constant, in the elastic field

TEST• Draw versus t (strain

vs time) when a material is loaded at = constant, in the elastic field

TEST• Draw versus t (strain

vs time) when a material is loaded at = constant, in the elastic field

Plastic deformation even if stress is in the elastic field

fracture

Elastic deformation

Creep I

Creep III

Creep II

Constant load in the elastic field gang ive to a plastic deformation, progressive to fracture. •Thermally activated process Metals T>0,3-0,4Tfus (K) Ceramics T> 0,6-0,7 Tfus Amorphous materials T>Tg tests: a constant load is applied at a given T, strain is recorded versus time.

CREEP I: cold working higher than anenaling.

CREEP II: constant strain: balance between cold working and annealing

CREEP III: micro-cavity and other macro-defects at the grain boundaries: fracture of the sample

Creep II : steady state

nCRnss A

C = costant depending on materials

= applied stress

n = coefficient depending on materials 3 < n < 8

ECR = activation Energy

R = perfect gas constant

T = test Temperature

CREEP curves when increasing T or applied stress

Curve trend when increasing applied stress or test Temperature

creep curves for a borosilicate glassat 200 and 420 °C, from 18 to 36 MPa)

Creep dCreep degradation of Steelsegradation of Steels for for PipelinesPipelines

100 000 h100 000 h

Initial stateInitial state

Z. L. Kowalewski - IPPT, Poland

Creep Creep development in 13HMF development in 13HMF SteelSteel for for PipelinesPipelines

0 100 200 300 400 500Time [h]

As-received

Exploited

144 000 h144 000 h

Initial stateInitial state

0 0.1 0.2 0.3S tra in

360 h 550 h 988 h

Microscopic view of specimens (40HNMA Steel) after creep tests up to:

Zbigniew L. KowalewskiE-mail: zkowalew@ippt.gov.plZbigniew L. KowalewskiE-mail: zkowalew@ippt.gov.pl

How to increase creep resistance?

• High melting T and E materials • Large grains or mono-crystals (small grains

increase grain motion at the grain boundaries)

• Solid sotutions

• Precipitates

• Second phases (composites)

• Apply a tensile stress to a material in the elastic field.

• Repeat the test several times.

• Is it possible to have the material failure ?

• Apply a tensile stress to a material in the elastic field.

• Repeat the test several times.

• Is it possible to have the material failure ?

• If yes, draw a graph with the applied stress () versus the number of cycles (n) necessary to obtain the material failure

S-N curves: stress (S) vs number of cycles (N) to obtain failure

S Fe, Ti, steels

Al, Cu

Dispersion range

Fatigue limit

Fatigue• Failure of materials due to cyclic loading.

• Main reason of mechanical failure of materials

• Failure happens at stress lower than R or Y

• Catastrophic failure of materials (also for ductile materials !)

• Fatigue tests: materials are cyclically loaded at different stresses up to failure.

• Fatigue limit: when cyclically loaded below this limit, materials do not fail

Fatigue test

Number of cycles (N)

sample Load N

Load N

S-N curve

a max min

S max , min : applied stresses during tests

Fracture zone

Safe zone

Materials and Fatigue

• Between 35-65% of their tensile strength most of metals fail because of fatigue (e.g. Fe, Ti alloys, intrinsical fatigue limit)

• Other metals fail in any case after a given limit (e.g. Al, no intrinsical fatigue limit)

• Fatigue resistence: stress necessary to fracture the material after a given number of cycles at this stress

• Fatigue life: number of cycles necessary to fracture the materials at a given load.

Fatigue: fracture surface

Starting point (surface defect)

Starting point

Fatigue surface, smoothCatastrophic failure,

rough surface

Fatigue: fracture surface

crack propagates by repeated cycles – fatigue

final failure is brittle

http://www.resnapshot.com/MP1198-2.jpg

crack propagates by repeated cycles – fatigue

final failure is brittle

http://www.resnapshot.com/MP1198-2.jpg

Fatigue surface, smooth

Catastrophic brittle failure, also on ductile materials,rough surface

Frattura a fatica

• Ogni processo di frattura a fatica comprende la formazione e la propagazione di cricche– I materiali duttili (metalli, alcuni polimeri) possono

contrastare entro certi limiti la propagazione di una cricca, poi cedono comunque per frattura fragile

– I materiali fragili non sono in grado e vanno incontro a fratture fragili, catastrofiche (ceramici, vetri)

Ductile and brittle fracture• Ductile fracture: high plastic deformation at the

crack tip, slow crack propagation • Brittle fracture: no (or low) plastic deformation at the

crack tip, quick crack propagation, catastrophic failure)

Al steel

Mystery failures - de Havilland Comet

• G-ALYY was leased from B.O.A.C. to South African Airways. Flight SA201 was on its way from London to Johannesburg. After a fuel stop in Rome the plane took-off, but only 36 minutes later the radio-contact was interrupted in the area of Stromboli. January 1954.

• The next morning remains were found in the sea. Since the sea was at this place as deep as 1000 meters, no parts of the aircraft could be inspected. Only four days after the crash the Comet flights were again suspended, one of the reasons being the similarities to the YP crash. G-ALYY had only performed 2704 flighthours. A very intensive flight test program was performed in order to find out the reason of the YY and YP crashes, with no special conclusion.

• Only after a very long expensive investigations, which included the assembly of the remains of the crashed YP and the underwater stress test of the YU Comet which came from B.O.A.C. Finally the fuselage of YU broke up on a sharp edge of the forward escape-hatch. After that this rupture was repaired the tests were restarted, but only shortly afterwards the fuselage broke up. This time the rupture started at the upper edge of a window and was three meters long.

• The YP and YY crashes were due to metal fatigue, which took place because of the crystalline changes in the fuselage skin. They were amplified by the high speed and altitude the Comets were operated. The metal fatigue resulted in ruptures of the fuselage, this had as a consequence a terrible decompression at 33Kft, tearing up the plane with all known consequences.

http://www.geocities.com/CapeCanaveral/Lab/8803/comet.htmhttp://www.baaa-acro.com/Photos-2/G-ALYP.jpg

Stress intensity factor

]21[21

• Macro-defects (pores, cracks) in all materials act as stress concentration factors

• True stress on the material at the tip of the crack ( m) is higher than the nominal stress ( o)

t = radius of the cracka = length of a crack on the

surface

• Critical Defects (Griffith Theory, Fracture mechanics, see )

• Without defects, tensile strength would be close to the theoretical values (as it is for monocrystalline materials or small brittle materials)

Crack propagation

Role of :t = radius of the cracka = length of a crack on the surface

– If plastic deformation is possible, t can increase and decrease m

– If plastic deformation is not possible, there is catastrophic failure.

– Griffith Theory quantify what above with math........

]21[21

• Stress intensity factor for long cracks with small radius

m 2 0at

Callister

o= nominal stress

m= stress on material

K=m/o = stress intensity factor, K=2(a/)1/2

• During crack propagation surface elastic energy s is released

• Griffith Theory: criterion for crack propagation (energy balance)

c = (2 E s / a)1/2 (brittle materials)

c = (2 E (p + s )/ a)1/2

(ductile, plastic material= surface plastic energy =p)

c = critical stress, crack propagation for >c

Crack propagation and critical parameters

c = (2 E (p + s )/ a)1/2

Gc= 2 (p + s )

Gc = a / E

crack propagates when:

a / E > Gc (Griffith theory)

K stress intensity factor (MPa m1/2 )K = (GcE)1/2=Y ( a)1/2

For materials containing macroscopic defects, crack propagation occurs when > c

Y adimentional parameter (depends on sample and crack geometry)

Fracture toughness Kc = Y c ( a)1/2 (MPa m1/2)

KIc = Y c ( a)1/2

Fracture thoughness(mode I)

Crack propagation and critical parameters

KIC critical parameters (defect length and stress) above which there is failure (all materials)

KIc = Y c ( a)1/2

(ASTME 399)

How to increase materials fatigue resistance?

• Surface strengthening methods

• Coatings• Suitable mechanical design • Fatigue and fracture

mechanics to model and predict components life !

(seeThermal fatigue, corrosion, …)

Ni based super-alloy

Fatigue induced intergranular crack

Light (optical) microscopy

HARDNESS

• Material resistance to surface compression

Applied load

Indenter

Sample

Vickers Hardness, HV

Brinell Hardness HB= P/(Dh) = carico/area impronta Vickers Hardness HV= 1.854P/L2

indenter

Sample surface

Rockwell Hardness measure penetration depth

example: 60 HR30W= superficial Rockwell hardness =60 scale 30W

Example: 80 HRB= Rockwell hardness = 80 scale B

Values lower than 20 or higher than 100 are not acceptable

Correlation hardness/tensile properties

Steel TS: about= 3.45 HB

brassCast iron

Hardness profile

Stress

Resilience modulus (Ur)

Ur = ∫ dbetween 0 and y) (ELASTIC FIELD)

= E yy / E

Ur = ½ y y½ y2 /E

strain

Toughness and fracture toughness• Toughness = energy absorbed up to fracture = area of / curve

up to fracture ) (J / m3 )• Fracture toughness = fracture resistance in presence of notches

Stress

strain

Brittle, fragile, low ∫ d

Ductile, tough, plastic…..large ∫ d

Charpy test: Measure of the energy necessary to fracture a notched sample(impact of a hammer)Starting position

hammer

final position

sample

Absorbed impact energy vs temperature for several steels: ductile to brittle transition

Role of C and Fe3C on dislocation motion and ductile to brittle transition

Fracture surfaces after Charpy test (V-notched) at given TDuctile to brittle transition

Effect of ductile to brittle transition...

• 4 °C

• steel

ABSORBED ENERGY (CHARPY TEST) vs T FOR DIFFERENT MATERIALS : DUCTILE TO BRITTLE TRANSITION

(Cu, Al, Ni, Ag, Au

Ex: Cu, Al, Ag, Au

Ex: Fe, W, CrEx: Mg, Ti, Zn

HEXAGONAL

BCC FCC

CHARPY tests on steel at different T

at room T (2.22 J/mm2 )

at -200 °C (0.04 J/mm2 )

Charpy test on steels with same composition but different thermal treatments:

0,89 J/mm2 C40 steel annealed

0,07 J/mm2

C40 steel quenched

DUCTILITY TEST

STRAIN

ll )(100%

necking

AA f )(100%

T1<T2<T3<T4

Stress/strain curves for iron vs Temperature

Stress

Strain

Stress/strain curves vs Temperature

Fepolymers

02 mecc b

gp gs

intrinsical

ferrarischarpy

yield strength

charpy test

ferrarisfatigue

plastic deformation

critical parametersmateriali

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