Mechanical Properties

Mechanical Properties

1. Biological systems and mechanical properties

2. Food Rheology and viscoelastic characterization

3. Texture evaluation of foods4. Aero-hydrodynamic properties5. Flow behavior of granular materials

and powder

Mechanical Properties

• Those having to do with the behavior of the material under applied force stress-strain behavior under static and

dynamic loading flow characteristics of the material in

air/water rheology

Biological Systems and Mechanical Properties

• Each unit of food and feed materials is in itself a biological system.

• They are alive, constantly undergoing changes in shape, size respiration,… during development and storage.

• They are sensitive to external factors as humidity, temperature, oxygen, food supply, energy consumption,… So, difficult to control.

Example• Biological solid elasticity age and

physiological conditions

• Biological fluids are mostly non-Newtonian liquids (more complications)

Study of mechanical behavior in biological systems using the application of the fundamental principles of

mechanics and rheology

Rheology• What is Rheology?

– Rheology is the study of the deformation and flow of matter

– flow of salad dressing from a bottle– Rheological properties = mechanical properties

when the action of forces result in deformation and flow in material

• How to determine Rheological Properties?– measuring force and deformation as a function of time

e.g. Time-dependent stress and strain behavior, creep, stress relaxation and viscosity.

What is Rheology?

Study of flow and deformation behavior of materials• Deformation usually applied to materials that are

predominantly solid-like in nature.• Flow usually applied to materials that are

predominantly fluid-like in nature.

Examples:

Liquid Foods:

Flow of water, ketchup, mayonnaise, salad dressings etc.

Solid Foods:

Creep of apples, grains, cheese etc.

Examples of Rheological Properties

• Viscosity

• Power law parameters

• Elasticity

• Stress relaxation function

• Creep compliance function

Why we want to study rheology of Foods?

• Design/select equipment such as pumps, pipelines, extruders, mixers, heat exchangers etc.

• Rheological behavior relates to food texture and sensory data

• To determine ingredient functionality in product development

• Shelf life testing• To obtain some information about atomic and

molecular scale phenomena• To obtain constitutive relations

Fundamentals of Rheology

• Basic assumptions– homogeneous: well-mixed material– isotropic: same response in all directions

• How materials respond to applied forces and deformations?– Stress: force per area (Pascals or Pa)– Strain: deformation per length– Ideally, stress is related directly to strain

Forces and Stress

• Force (F) = mass × length × time-2 = Newton

• Stress = Force/Area = (sigma)= Pascal

= F/A

• Sometimes used “Load”

Applied Forces

• Force applied to a body can cause:

– Tension:

– Compression:

– Shear:

– Extrusion:

– Penetration:

– Flow:

Forces and Stress

• The combination of aforementioned phenomena can result in:– Bending:

• Tension + Compression– Torque:

• Shear– Hydrostatic Compression:

• Tension + Compression + Shear

Stress (ASTM Standard Definition)

• The intensity at a point in a body of the internal forces or components of force that act on a given plane through the point

Stress• Normal stress

– force is directly perpendicular to a surface

– chewing a piece of gum– kneading of dough

• Normal stress may be either:– Tensile stress: Normal stress due

to forces directed away from the plane on which they act

– Compressive stress: Normal stress due to forces directed toward the plane on which they act

tension

compression

Stress• Shear stress

– The stress component tangential to the plane on which the forces act (force is parallel to the sample surface)

– spreading of butter over a slice of toast– brushing of barbecue sauce on chicken– stirring of a hot cup of cocoa

• Torsion stress– The shear stress on a transverse cross

section resulting from a twisting action.

• True stress– The axial stress in a tension or

compression test, calculated on the basis of the instantaneous cross sectional area instead of the original area

torsion

Deformation and strain

All materials change in shape, volume, or both under the influence of an applied stress.

Strain refers to the change in size or shape of a material when it is subjected to a stress.

Strain = (epsilon)

Strain and Strain (Shear) Rate

• Strain– a dimensionless quantity representing the

relative deformation of a material

Normal Strain Shear Strain

Strain• Strain: Physical change in the dimensions of a specimen that

results from applying a load to the test specimen.• Strain calculated by the ratio of the change in length and the

original length. (Deformation)• Strain units (Dimensionless)

– When units are given they usually are in/in or mm/mm. (Change in dimension divided by original length)

• % Elongation = strain x 100%

0l

l l0

lF

Strain Definition

• Dimensional unit : Change in height = l• Simple ratio : engineering strain

– For compression

– For tension00

0

l

l

l

ll

00

0

l

l

l

ll

Strain Definition (cont)

• Logarithmic ratio : Hecky or true or natural strain– Ratio of stressed/unstressed heights

0

lnl

l

Strain• Permanent set is a change in form of a specimen once the

stress ends.• Linear (tensile or compressive strain) is the change per unit

length due to force in an original linear dimension• Axial strain is the linear strain in a plane parallel to the

longitudinal axis of the specimen (occurs in the same direction as the applied stress).

• Lateral/transverse strain is the linear strain that occurs perpendicular to the direction of the applied stress.

• Shear/angular strain is the tangent of the angular change, due to the force, between 2 lines originally perpendicular to

each other through a point in a body.• Poisson’s ratio is ratio of lateral strain to axial strain.

Poisson’s ratio = lateral strain axial strain

– Example• Calculate the Poisson’s ratio of a material with lateral

strain of 0.002 and an axial strain of 0.006• Poisson’s ratio = 0.002/0.006 = 0.333

• Note: For most materials, Poisson’s ratio is between 0.25 and 0.5

• Metals: 0.29 (304 SS) to 0.3 (1040 steel) to 0.35 (Mg)• Ceramics and Glasses: 0.19 (TiC) to 0.26 (BeO) to 0.31

(Cordierite)• Plastics: 0.35 (Acetals) to 0.41 (Nylons)

AxialStrain

LateralStrain

Force-Deformation Curve

Distance

Force

Force –Deformation curve

FORCE

DISTANCE

Firm

Medium

Soft

Stress-Strain Diagrams

• Stress-strain diagrams is a plot of stress with the corresponding strain produced.

• Stress is the y-axis

• Strain is the x-axis

Stress

Strain

Linear(Hookean)

Non-Linear(non-Hookean)

Stress strain diagram

stress

strain

Weak

Strong

hard

soft

Rheology

Deformation Flow

Elastic In-elastic Plastic Viscous

• Hookean (linear)

• Non-Hookean (non-linear)

• Viscoelastic

• Viscoplastic

• Bingham

• Non-Bingham

• Newtonian

• Non-Newtonian

t

t

Time Aspects of Deformation

• Ability to store deformational energy

• Capacity to regain shape after being deformed

Deformation-time relationship for an elastic body under constant stress

Deformation

TimeApplied force

Instantaneous elastic deformation

Instantaneous elastic recovery

Force removed

Not depend on time

Range of Material Behavior

Solid Like Liquid Like

• Stress response combines elastic and viscous behavior

• Mechanical properties are time - and temperature - dependent

Deformation-time relationship for an viscoelastic body under constant force

Deformation

TimeApplied force

Instantaneous elastic deformation

Instantaneous elastic recovery

Force removed

Retarded recovery

Retarded deformation

Permanent deformation

Fluid

• Viscosity of a fluid food is a measure of the resistance to its flow. It indicates the internal friction between individual molecules in a fluid.

• The attractive force acting between molecules of the same substance is called cohesion.

• The attractive force acting between molecules of two different substances is called adhesion.

• Non-wetting fluid vs. Wetting fluid.– Mercury vs. Oil

Fluid Viscosity

• Newtonian fluids– viscosity is constant (Newtonian viscosity, )

• Non-Newtonian fluids– shear-dependent viscosity (apparent

viscosity, )

)(f

Fluid Behavior

• Flow behavior of a food is a physical as well as chemical property determined by rheological methods

• Flow is influenced by:– The shape and arrangements of molecules– Concentration of solid in solution– Temperature– Micelle formation, and– Wetting

Flow Rheograms

• Rheogram: stress versus strain or shear rate• Shear-thinning/pseudoplastic

– thixotropic (time dependent; thin with time)• Shear-thickening/dilatent

– rheopectic (time dependent; thicken with time)

• Yield stress: min. force/stress to initiate flow

Stress-Strain Diagrams

• Stress-strain diagrams is a plot of stress with the corresponding strain produced.

• Stress is the y-axis

• Strain is the x-axis

Stress

Strain

Linear(Hookean)

Non-Linear(non-Hookean)

Deformation of Solids and the Modulus

All materials change in shape, volume, or both under the influence of an applied stress.

When a solid material is exposed to a stress, it experiences an amount of deformation or strain proportional to the magnitude of the stress

Stress () Strain ( or )

Deformation of Solids and the Modulus

The Modulus measures the resistance to deformation of a material when an external force is applied.Modulus = Stress/Strain

We can define three kinds of Moduli for a materialYoung’s Modulus (Modulus of Elasticity): EShear Modulus (Modulus of Rigidity): GBulk Modulus: B

The Three Moduli - Elastic Constants

ShearModulus

BulkModulus

Young’s Modulus

E =

G =

hyd

V/Vo

B =

Where Dashed lines indicate initial stressed state = uniaxial tensile or compressive stress = shear stresshyd = hydrostatic tensile or compressive stress = normal strain = shear strainV/Vo = fractional volume expansion or contraction = volumetric strain

Poisson's Ratio - The Fourth Elastic Constant

Poison's ratio, , is the ratio of transverse (lateral) to axial strain

l0zlz

z

z

lyy 2

ly - l0y

2=

z 2

lz - l0z

2=

= y z

Poisson’s Ratiol0y

Modulus• Modulus of Elasticity (E) or Young’s Modulus

is the ratio of stress to corresponding strain (within specified limits).– A measure of stiffness

• Stainless Steel E= 28.5 million psi (196.5 GPa)• Aluminum E= 10 million psi• Brass E= 16 million psi• Copper E= 16 million psi• Molybdenum E= 50 million psi• Nickel E= 30 million psi• Titanium E= 15.5 million psi• Tungsten E= 59 million psi• Carbon fiber E= 40 million psi• Glass E= 10.4 million psi• Composites E= 1 to 3 million psi• Plastics E= 0.2 to 0.7 million psi

Young’s Modulus of some foods

Food Apparent Young’ Modulus (Pa)

Apple, raw 60-140

Banana, Fresh 8-30

Bread 0.1-0.3

Carrot, raw 200-400

Gelatin 2

Peach, Fresh 20-200

Pear, raw 120-300

Potato, raw 50-140

Modulus Types• Modulus of elasticity: Slope of the

stress-strain curve (the ratio of stress to corresponding strain below the proportional limit).– Initial Modulus: slope of the

curve drawn at the origin.– Tangent Modulus: slope of the

curve drawn at the tangent of the curve at some point.

– Secant Modulus: Ratio of stress to strain at any point on curve in a stress-strain diagram. It is the slope of a line from the origin to

any point on a stress-strain curve.

– Chord modulus: slope of the chord drawn between any two specified points on the stress-

strain curve

Stress

Strain

Initial Modulus

Tangent Modulus

Secant Modulus

Note: for materials where this curve is curvilinear,

one of these modulus may be used.

Basic Parameters and Units

S.I. units = c.g.s. X 10

Stress = Force /Area [Pa] = tensile stress, = shear stress

Strain = Geometric Shape Change [no units] = tensile strain, = shear strain

Strain or Shear Rate = Velocity Gradient or d(strain)/dt [1/s] = tensile strain rate, = shear strain rate

Modulus = Stress / Strain [Pa] E = Youngs or Tensile, G = Shear Modulus

Compliance = Strain / Stress [1/Pa] Typically denoted by J

Viscosity = Stress /Strain Rate [Pa.s or Poise] Denoted by

.

Other ASTM Standard Definitions

• Elastic limit:– the greatest stress which a material is

capable of sustaining without any permanent strain remaining upon complete release of the stress

Proportional Limit

Strain

Str

ess

• Proportional Limit :– the greatest stress which a material is

capable of sustaining without any deviation from proportionality of stress to strain (Hooke’s Law).

• The concept of elastic limit should not be confused with the proportional limit, which is the stress above which the relationship between stress and strain are no longer linearly proportional. Ordinarily, the elastic limit is greater than the proportional limit; however, for many materials (such as steel), the two are close enough to be identical for all practical purposes.

• Breaking Factor Max. Load/Original Width (N/mm)• Shear/Tensile Strength = maximum

shear or tensile stress which a material is capable of sustaining

= Max. Shear or Tensile stress Cross-sectional Area (N/mm2)

Max. Load

Width

Yield Point and Yield Strength• Yield Point = first stress in material, less than maximum attainable stress, at which an increase

in strain occurs without an increase in stress.

• Yield strength = Load or stress at Yield Point/Cross-section Area (N/mm2)

• Strength = the resistance to applied force.

Load

Strain

Load at Yield PointMax. Load or Load at Break

Bioyield and Rupture Point

Load

(N)

Deformation, mm

Firmness

Bioyield point

Max loadRupture point

Bioyield and Rupture Point

• Bioyield point were determined at the first peak of the force-displacement curve (there occurs an increase in deformation

with a decrease or no change of force.• Bioyield point is an indication of initial cell rupture in the cellular

structure of material.• This term is proposed for biological materials to differentiate

this phenomenon from yield point in engineering materials.

• Rupture point is a point at which the axially loaded specimen ruptures under a load. In biological materials, rupture may

cause puncture of shell or skin, cracking, or fracture planes.

A failure in microstructure

A failure in macrostructure

• Bioyield strength = the stress corresponding to bioyield point.

Stiffness or Rigidity or Apparent Modulus

• Stiffness is a measure of the materials ability to resist deformation under load as measured in stress.– Stiffness is measures as the slope of the

initial portion of the stress-strain curve– May be referred to as modulus of elasticity

or Young’s modulus (linear)– In the case of nonlinear stress-strain

behavior, it can be defined in terms of initial tangent, secant or tangent modulus.

E

• Elasticity:– The capacity of a material for taking elastic

or recoverable deformation.

• Plasticity:– The capacity of a material for taking plastic

or permanent deformation.Lo

ad

Strain

LLLinear limit

• Degree of elasticity = the ratio of elastic deformation to the sum of elastic and plastic deformation when a material is loaded to a certain load and then unloaded to zero load.

• Degree of elasticity = De/(Dp+De)– De = elastic or recoverable deformation– Dp = plastic or residual deformation

Load

Deformation

LLLinear limit

Dp DeDp + De

Non recover part

Recover part

• Toughness = Area under of Stress-Strain curve (J or N.m)

• It is the work required to cause rupture in material

Str

ess

Strain

Break or Rupture Point

Area under curve

Resilience• It is the capacity of a material for storage

of strain energy in the elastic range (energy: N.m)

Load

Strain

Energy given back