Experimental Tectonics and Material Characterization in Physics

EXPERIMENTAL TECTONICS

MATERIAL CHARACTERIZATION

»"Recipe" to build up a laboratory model

RECIPES

1. identification of the problem to study
2. application of the similarity criteria
3. determining materials that satisfy the similarity criteria
4. running of models
5. ensure repeatability
6. interpretation of obtained results
7. definition of a theory

MATERIALS?

Structure of simple (molecular) condensed matter

A

GAS

Loose Disordered High mobility Momentum transfer by collisions Newtonian

SOLID

Dense Ordered Fixed structure Jammed network Strong repulsions or attractions Mainly elastic

LIQUID

Dense Disordered Significant agitation Transiently jammed Network Basically Newtonian

1. SOLIDS

Metal Stone I Wood Polymer

Macroscopic behavior

F

Plastic regime

P

Ductile material

Y

F

I I

Brittle material

Elastic regime

Fracture

Δε

O O' 3

Force F 1

Deformation

Elasticity

F=k&

Yielding

F>F

2. LIQUIDS

Water S Mercury Honey Soap Oil

Macroscopic behavior

Simple shear

S

Force F Velocity V H

Shear stress : Τ = F/S Shear rate : } = V / H

Newtonian behavior

τ = μγ

μ

Viscosity (in Pa.s)

T

Int 1

Y.

InComplex fluids

Biological Systems Natural flows Cosmetics Civil engineering Food

Structure of complex fluids

Chocolate Paint Debris flow

Chocolate: fat + milk (powder) + cocoa + sugar Concrete: water + cement + sand + gravels + surfactants + colloids Paint: water + latex + pigments + polymers Mud: water + clays + sand + pebbles Blood Soft cheese Concrete

HOW TO SELECT ANALOGUE MATERIALS?

Not expensive Not toxic

Physical properties

Ingredients to select an analogue material

WHICH PHYSICAL PROPERTIES DO MATTER?

transparency density rheology dimensions (eg., elastic and/or viscous moduli, cohesion, friction, ... ) surface tenson thermal moduli

transparency density rheology dimensions (eg., elastic and/or viscous moduli, cohesion, friction, ... ) surface tenson thermal moduli

12 1 11 10 9 8

Metropolitan Life AND AFFILIATED COMPANIES MADE IN USA 2

ruler

50 60 70 30 10 10 20 80 9|0 100 110 120 130 140 4 8 1 128in 0 1 2 3 4 5 6 7 8 9 0 130 140 150 160 170 1810

compass

caliper

9 becchi 6 1 4 0 10 20 30 40 00 60 70 80 90 100 110 120 130 140 150 3 8 asta 2 cursoio 7 ganasce

VERNIER CALIPER

The nonius gives the precision of the measurement: 1/10, 1/20, 1/50 mm

4 4,7 5 6 L 4,74 AT B 4

Look here for some additional examples: http://macosa.dima.unige.it/diz/c1/calibro.htm

exercise

C L A S S W O R K # 3

1. 9 2. 0 1 3. 7 0 5 10 0 5 10 0 5 10 4. 1 2 0 5 10 0 5 10 0 5 10 7. 5 8. 7 8 0 5 10 9. 0 1 0 5 10 5. 6 6. 4 0 5 10

transparency density rheology dimensions (eg., elastic and/or viscous moduli, cohesion, friction, ... ) surface tenson thermal moduli

READ ME - READ ME READ ME

transparency density rheology dimensions (eg., elastic and/or viscous moduli, cohesion, friction, ... ) thermal moduli surface tenson

Surface tension (or energy)

Surface tension (or energy) is the elastic tendency of liquids (or solid + liquids) which makes them acquire the least surface area possible. At liquid-air interfaces, surface tension results from the greater attraction of water molecules to each other than to the molecules in the air. The net effect is an inward force at its surface that causes water to behave as if its surface were covered with a stretched elastic membrane. Surface tension has the dimension of force per unit length, or of energy per unit area. Several methods to quantify it.

O 9 A B F H H U-shaped wire W +-d- Fa T = F/2W m 0

The suggestion is to try to minimize its contribution in the models.

transparency density rheology dimensions (eg., elastic and/or viscous moduli, cohesion, friction, ... ) surface tenson thermal moduli

Thermal expansion

Thermal expansion (tendency of matter to change in shape area, and/or volume in response to a change in T, through heat transfer) Δρ 1 O= Δp 1 P AT

Thermal conductivity

Thermal conductivity (capability to transmit heat for conduction) K =- Q - 0x ∂T 1-5 W/m K

Thermal diffusivity

Thermal diffusivity (capability to transmit heat/ Info on heat diffusion time) k=K/pc

Heat capacity

Heat capacity (ratio between heat and temperature increase) CIAO At

Specific heat

Specific heat (heat necessary for 1℃ T increase) subscripts p, v c=C/m 1000 J/kg ℃ (mantle)

T is usually neglected in experimental models and only used as strenght controlling factor 10-5 K-1 10-6 m2/s

transparency density rheology dimensions (eg., elastic and/or viscous moduli, cohesion, friction, ... ) surface tenson thermal moduli

Density of a material

The density of a material is its mass per unit volume. The symbol most often used for density is p. Mathematically, density is defined as:

P = M - V kg g [ or m3 cm3 ]

20℃

OLAB !". 50 ml 96 96 AB 50am- 2080 ERICHSEN Mod.290/1 100 cm3/20°C ERICHSEN Mod.290/1 50 cm3/20°C AF02 ERICHSEN Mod.290/ V

METHOD #1: PYCNOMETER

METHOD #1: PYCNOMETER

96 96 NOLAB In DE20℃ . 50 ml Ms = P5 Vs MH20 = PH2OVH2O PH20 = 1 g/cm3 MH2O = VH2O VH2O = Vs Ms Ms Ps = = VH20 MH20

METHOD #1: PYCNOMETER

AF02 ERICHSEN Mod.290/l 100 cm3/20°C ERICHSEN Mod.290/ V AB 50 cm 2080 ERICHSEN Mod.290/1 50 cm3/20°C Ps = Ms Vpicn Ms = Mtot - Mp picn M picn = 52 g V picn = 11.5 ml

https://www.youtube.com/watch?v=5w3IKnovlng https://www.youtube.com/watch?v=StGbFkSevy0

METHOD #2: DENSIMETER

METHOD #2: DENSIMETER (equipped version for density of solids)

Archimede's principle A body immersed in a fluid undergoes an apparent loss in weight equal to the weight of the volume of fluid it displaces

1b 0 1 6 2- 5 3 4 1b 0 7 1 6 2- 5 3 4- 3 3 1b of water 1b

https://www.youtube.com/watch?v=UfMrFUIlxEs

METHOD #2: DENSIMETER (method for solids)

Start the measurement when water tem- perature becomes stable. (Ex: Display of HA) 0.0000 Press the [RE-ZERO key to reset the displayed value to zero. 3 Place the specimen on the upper pan and record its weight A in air. Press the RE-ZERO key to reset the displayed value to zero. Place the specimen on the lower pan and record its weight in water. Adjust the amount of water so that the specimen is about 10 mm below the surface of the water. Obtain the density of the water according to the temperature of water. (See Table 1-1).

METHOD #2: DENSIMETER (method for solids)

7 The density will be found by:

Significant figures is three fiqures. Significant figures is more than four fiqures.

p : Density of specimen [g/cm3] d : Density of air[g/cm3] A : Weight in air [g] B : Mesurment data [g] Po : Density of water [g/cm3]

A p = A IBI Po

p = IBI x ( Po-d) + d

Table 1 Density of water

At sea level (1 atmosphere), the density of water reaches a maximum at 3.98°C. (Unit: g/cm3).

Tempera- ture O 1 2 3 4 5 6 7 8 9 O 0 0. O. 0. 0 0 o 0 0 0 99984 99990 99994 99996 99997 99996 99994 99990 99985 99978 10 99970 99961 99949 99938 99924 99910 99894 99877 99860 99841 20 99820 99799 99777 99754 99730 99704 99403 99678 99368 99651 99623 99594 30 99565 99534 99503 99470 99437 99333 99297 99259

METHOD #2: DENSIMETER (method for liquids)

10.00

The volume of the float is stamped here. About 50 mm

Press the [RE-ZERO] key with the float hanging. 0.0000 g Pour the liquid whose density is to be measured. Adjust the amount of the liquid so that the float is about 10 mm below the surface of the liquid. 3 When the display becomes stable, note down the displayed value without its mi- nus sign. (Suppose that this value is A.) 4 The density of the liquid can be found by substituting the measured value in the following equation:

p=A +d

p : Density of liquid [g/cm3] A : Buoyancy of float (g) V : Volume of float (cm3) d : Density of air [g/cm3]

Example: If the measured value (A) is 9.9704 g, the volume of the float (V) (stamped on the float hook) is 10.01 cm3, the density of air (d) is 0.001 g/cm3), the temperature indicated by the ther- mometer is 25°℃, then we have:

9.9704 + 0.001 = 0.997 g/cm3 (25°C) 10.01

METHOD #3: STOKES FORMULA (also for viscosities!)

0 p Ap R B

A solid body will rise or fall through a fluid if its density is different from the density of the fluid. A buoyant fluid rising through a viscous fluid (Re<1) adopts the shape of the sphere (> Stokes flow)

FORCES

Buoyancy = total force arising from the action of gravity on the density difference between the sphere and its surroundings. B = - 4πr3gΔp/3

Viscous (resisting) stress = proportional to the fluid viscosity and the strain rate τ= εμυ/r R = - 4πr2 . cuv/r = - 4πcrpv

METHOD #3: STOKES FORMULA

FORCE BALANCING

B+R=0 4πεlμυ + 4πro g Δρ/3=0 v= - gΔpr2 /3μ

SEVERAL APPLICATIONS OF THIS RELATIONSHIP!

METHOD #3: STOKES FORMULA

2(Ps-Pf)gr2 V= 9u

METHOD #3: STOKES FORMULA

https://www.youtube.com/watch?v=mQwlmXtRu5k

transparency density rheology dimensions (eg., elastic and/or viscous moduli, cohesion, friction, ... ) surface tenson thermal moduli

ARE YOU ALREADY AWARE OF THE MATERIAL RHEOLOGY?

1

What is rheology?

The name was proposed by E.C. Bingham and M. Reiner. It derives from the Ancient Greek: 'ρεω' to flow; 'λογος' the study, and from Heraclitus's quote 'παντα ρει' everything flows fire & "Rheology" is the study of the deformation and flow of all forms of matter This discipline was coined in April 29, 1929

4

FLUIDS/MODELS

CLASS KEY TIME REPRESENTATIVE WORKS

a) Perfect, rigid bodies

Anti- quity

Archimedes (~250 BCE), Newton (1687)

b) Ideal elastic solids

1600s

Boyle (1660), Hooke (1678), Young (1807), Cauchy (1827)

Ideal mater- ials

c) Inviscid fluids

1700s

Pascal (1663), Bernoulli (1738), Euler (1755)

d) Newton- ian liquids

Early 1800s

Newton (1687), Navier (1823), Stokes (1845), Hagen (1839), Poiseuille(1841), Weidemann (1856)

2

Linear viscoelasticity

Linear viscoelasticity

Mid 1800s

Weber (1835), Kohlrausch (1863), Wiechert (1893), Maxwell (1867), Boltzmann (1878), Poynting & Thomson (1902)

Ideal materials From 250BC to Early 1800

3

Generalized Newtonian (viscous) liquids

Generalized Newtonian (viscous) liquids

Late 1800s- Early 1900s

Schwedoff (1890), Trouton & Andrews (1904), Hatchek (1913), Bingham(1922), Ostwald (1925) = de Waele (1923), Herschel & Bulkley (1926)

Linear Viscoelasticity Mid 1800s

4

Non-linear viscoelasticity

Non-linear viscoelasticity

Early 1900s

Poynting (1913), Zaremba (1903), Jaumann (1905), Hencky (1929)

a) Suspen- sions

Einstein (1906), Jeffrey (1922)

5

Key material descrip- tions

b) Poly- mers

Early 1900s

Schonbein (1847) Baekeland (1909), Staudinger (1920), Carothers (1929)

c) Exten- sional viscosity

Barus (1893), Trouton (1906), Fano (1908), Tamman & Jenckel (1930)

6

The genesis of rheology

The genesis of rheology

1929

Bingham, Reiner and others

Significant rheological works prior to the formal creation of the discipline of rheology in 1929

Non-Linear Viscoelasticity Early 1900s

5

Deepak Doraiswamy, DuPont