Propiedades mecnicas de materiales determinadas mediante el ensayo de traccinEn el ensayo de traccin las columnas giran a velocidad constante haciendo descender la plataforma inferior a velocidad constante v.La probeta est sujeta a la plataforma superior mediante una celda de carga que registra la fuerza aplicada a ella.

Mordazas

Celdas de Carga Extensmetro

Tensin (S) y deformacin (e) de IngenieraEngineering stress:Engineering strain:Original areaS = F/A0

Curva tensin (S) deformacin (e) de IngenieraTensile stress strain curveUTSMPa

Curva tensin deformacin verdaderas

DefinicionesYield strength (Y)Stress at which plastic deformation starts to occurYoungs modulus (E) S = Ee

The slope of the linear elastic part of the curve

Ultimate tensile strength (UTS)Maximum engineering stressStress at which necking or strain localization occurs

2% Offset yield strength Y(0.002)

Tension test sequenceFigure 3.2 Typical progress of a tensile test: (1) beginning of test, no load; (2) uniform elongation and reduction of crosssectional area; (3) continued elongation, maximum load reached; (4) necking begins, load begins to decrease; and (5) fracture. If pieces are put back together as in (6), final length can be measured.

Figure 2.2 (a) Original and final shape of a standard tensile-test specimen. (b) Outline of a tensile-test sequence showing stages in the elongation of the specimen.Note: In this figure, length is denoted bylower case l.

DuctilidadDuctility: Measure of the amount of plastic deformation a material can take before it fractures.% Elongation to Fracture:

% El is affected by specimen gage length. Short specimens show larger % El

% Reduction in Area

No specimen size effect when area in necked region is used

Typical mechanical properties a temperatura ambiente

METALS (WROUGHT)

E (GPa)

Y (MPa)

UTS (MPa)

ELONGATION (%) in 50 mm

POISSONS RATIO (

Aluminum and its alloys

Copper and its alloys

Lead and its alloys

Magnesium and its alloys

Molybdenum and its alloys

Nickel and its alloys

Steels

Stainless steels

Titanium and its alloys

Tungsten and its alloys

69-79

105-150

14

41-45

330-360

180-214

190-200

190-200

80-130

350-400

35-550

76-1100

14

130-305

80-2070

105-1200

205-1725

240-480

344-1380

550-690

90-600

140-1310

20-55

240-380

90-2340

345-1450

415-1750

480-760

415-1450

620-760

45-5

65-3

50-9

21-5

40-30

60-5

65-2

60-20

25-7

0

0.31-0.34

0.33-0.35

0.43

0.29-0.35

0.32

0.31

0.28-0.33

0.28-0.30

0.31-0.34

0.27

NONMETALLIC MATERIALS

Ceramics

Diamond

Glass and porcelain

Rubbers

Thermoplastics

Thermoplastics, reinforced

Thermosets

Boron fiber

Carbon fibers

Glass fibers (S, E)

Kevlar fibers (29, 49, 129)

Spectra fibers (900, 1000)

70-1000

820-1050

70-80

0.01-0.1

1.4-3.4

2-50

3.5-17

380

275-415

73-85

70-113

73-100

-

-

-

-

-

-

-

-

-

-

-

-

140-2600

-

140

-

7-80

20-120

35-170

3500

2000-5300

3500-4600

3000-3400

2400-2800

0

-

0

-

1000-5

10-1

0

0

1-2

5

3-4

3

0.2

-

0.24

0.5

0.32-0.40

-

0.34

-

-

-

-

-

Note: In the upper table the lowest values for E, Y, and UTS and the highest values for elongation are for the pure metals. Multiply GPa by 145,000 to obtain psi, and MPa by 145 to obtain psi. For example, 100 GPa = 14,500 ksi, and 100 MPa = 14,500 psi.

Tensin() y deformacin verdadera () Fig. 3.1 M. P. Groover, Fundamentals of Modern Manufacturing 3/e John Wiley, 2007True stress:True strain:

True Stress () & Strain ()More Accurate MeasurementTrue Stress

True Strain

Comparacin deformacin de ingeniera y verdadera

Engineering Stress (S) /Strain (e) vs. True Stress () /Strain ()True Stress & Engineering Stress (Up to necking)

True Strain & Engineering Strain (Up to necking)

Conservacin de volumen:Al = A0l0

Relacin entre deformacin de Ingeniera y Deformacin Verdadera

Relacin tensin verdadera y tensin de ingenieraSSSSSeng = trueexp (- ) ; true = Sexp ()

Comparacin curvas tensin deformacin de ingeniera y verdaderae a la tensin mxima (UTS) a la tensin mxima (UTS)Trazo negro, la deformacin se mide con el rea del cuello

True Stress-Strain CurveConstitutive Eq. (plastic range)K :strength coefficient(true stress at unit true strain)n :strain hardening exponent ( coeficiente de endurecimientopor deformacin)

Papel grficoLog-Log

Mdulos cuadrados.La escala progresa en mltiplos de 10.El origen puede ser elegido.

10x 10x+1 10x+2 10x+3 10x+4 10y+4

10y+3

10y+2

10y+1

10x

Typical Values for K and n at Room Temperature = Kn

TABLE

K (MPa)

n

Aluminum

1100O

2024T4

6061O

6061T6

7075O

Brass

7030, annealed

8515, cold-rolled

Cobalt-base alloy, heat-treated

Copper, annealed

Steel

Low-C annealed

4135 annealed

4135 cold-rolled

4340 annealed

304 stainless, annealed

410 stainless, annealed

180

690

205

410

400

900

580

2070

315

530

1015

1100

640

1275

960

0.20

0.16

0.20

0.05

0.17

0.49

0.34

0.50

0.54

0.26

0.17

0.14

0.15

0.45

0.10

Coeficiente de endurecimiento por deformacin (n)Se puede demostrar fcilmente que la deformacin verdadera Fmax cuando se llega a la carga mxima es igual a n.F = AdF= ddA+Ad=0 Condicin carga mximad/ = - dA/A = dl/L= d (conservacin de volumen)d/d = Si = KnnKn-1 = Kn Se llega a n=

Por tanto el valor de n sirve para estimar la magnitud de la deformacin a la carga mxima y consecuentemente la deformacin homognea que se puede aplicar a un material.

Typical values of K and n ( = Kn)

MATERIAL

K (MPa)

n

Aluminum, 1100-O

2024-T4

5052-O

6061-O

6061-T6

7075-O

Brass, 70-30, annealed

85-15, cold-rolled

Bronze (phosphor), annealed

Cobalt-base alloy, heat treated

Copper, annealed

Molybdenum, annealed

Steel, low-carbon, annealed

1045 hot-rolled

1112 annealed

1112 cold-rolled

4135 annealed

4135 cold-rolled

4340 annealed

17-4 P-H annealed

52100 annealed

304 stainless, annealed

410 stainless, annealed

180

690

210

205

410

400

895

580

720

2070

315

725

530

965

760

760

1015

1100

640

1200

1450

1275

960

0.20

0.16

0.13

0.20

0.05

0.17

0.49

0.34

0.46

0.50

0.54

0.13

0.26

0.14

0.19

0.08

0.17

0.14

0.15

0.05

0.07

0.45

0.10

Note: 100 MPa = 14,500 psi.

Comportamiento elstico

Transicin elasto-plstica

El comportamiento elstico termina cuando comienza a producirse deformacin plstica, la que ocurre por desplazamiento de dislocaciones (irreversible)La tensin de fluencia o lmite elstico seala el inicio perceptible de la deformacin plstica.En algunos metales (Cu, Al, etc) es difcil determinar la tesnin de fluencia, por tanto convencionalmente se define sta como el nivel de tensin desde el cual, descargando elsticamente, queda una deformacin plstica de 0,2% (0,002)

Comportamiento plsticoValores tpicos de n a temperatura ambiente:acero= 0,01 Cobre = 0,005 Aluminio 0

Tensin de fluencia o lmite elstico al subir la temperaturaLa tensin de fluencia se reduce al subir la temperatura, por esto un material en caliente ofrece menos resistencia a la deformacin plsticaLa tensin de fluencia de un acero de 0,15%C, a 25C es 500 Mpa, a 220C es 400MPa y a 600C es 200MPa

A alta temperatura el nivel de la curva sube si sube d/dt.Por tanto la resistencia a la deformacin plstica a alta temperatura depende de la velocidad de deformacin d/dt.

Coeficiente de sensibilidad a la velocidad de deformacin (m)

At high temperature strain rate is important, but strain hardening is not so important

To calculate the flow stress at high (T/TM>0.5) temperature we will use:At low temperature strain hardening is important, but strain rate is not so important

To calculate the flow stress at low (T/TM