Mechanical Properties
Mechanical Properties
1. Biological systems and mechanical
properties
2. Food Rheology and viscoelastic
characterization
3. Texture evaluation of foods
4. Aero-hydrodynamic properties
5. 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 nonNewtonian 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:
– Extrusion:
– Compression:
– Penetration:
– Shear:
– 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
tension
• 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
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%
l

l0
l0
lF
Strain Definition
• Dimensional unit : Change in height = l
• Simple ratio : engineering strain
– For compression
– For tension
l 0  l l


l0
l0
l  l 0 l


l0
l0
Strain Definition (cont)
• Logarithmic ratio : Hecky or true or natural
strain
– Ratio of stressed/unstressed heights
l
  ln
l0
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)
Lateral
Strain
Axial
Strain
Force-Deformation Curve
Force
Distance
Force –Deformation curve
Firm
Medium
FORCE
Soft
DISTANCE
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

Linear
(Hookean)
Non-Linear
(non-Hookean)
Strain

Stress strain diagram
stress
hard
Strong
soft
Weak
strain
Rheology
Deformation
Elastic
In-elastic
Flow
Plastic
Viscous
• Hookean (linear) • Viscoelastic
• Bingham
• Newtonian





• Non-Hookean
(non-linear)

• Viscoplastic
• Non-Bingham
t

• Non-Newtonian





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
Not depend on time
Deformation
Force
removed
Instantaneous elastic
deformation
Applied
force
Instantaneous elastic
recovery
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
Force
removed
Retarded
deformation
Instantaneous elastic
recovery
Retarded
recovery
Instantaneous elastic
deformation
Applied
force
Permanent deformation
Time
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

Linear
(Hookean)
Non-Linear
(non-Hookean)
Strain

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
material
Young’s Modulus (Modulus of Elasticity): E
Shear Modulus (Modulus of Rigidity): G
Bulk Modulus: B
The Three Moduli - Elastic Constants
Young’s
Modulus
E=
Where


Bulk
Modulus
Shear
Modulus
G=


B=
hyd
V/Vo
Dashed lines indicate initial stressed state
 = uniaxial tensile or compressive stress
 = shear stress
hyd = hydrostatic tensile or compressive stress
 = normal strain
 = shear strain
V/Vo = fractional volume expansion or contraction = volumetric strain
Poisson's Ratio - The Fourth Elastic
Constant
 Poison's ratio, n, is the ratio of transverse
(lateral) to axial strain
z
z
lz - l0z
= 2
2
ly - l0y y
= 2
2
l
y
lz
l0z
Poisson’s Ratio
 y
n=
z
l0y
z
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
Banana, Fresh
Bread
Carrot, raw
Gelatin
Peach, Fresh
Pear, raw
Potato, raw
60-140
8-30
0.1-0.3
200-400
2
20-200
120-300
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
– Initial Modulus: slope of the
curve drawn at the origin.
Tangent Modulus
– Tangent Modulus: slope of the Stress
Secant Modulus
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
Strain
slope of a line from the origin to
any point on a stress-strain
curve.
Note: for materials where
– Chord modulus: slope of the
this curve is curvilinear,
chord drawn between any two
one of these modulus may
specified points on the stressbe used.
strain curve


Basic Parameters and Units
Stress

 = tensile stress,  = shear stress
Strain

= Force /Area [Pa]
= Geometric Shape Change [no units]
 = tensile strain,  = shear strain
Shear Rate = Velocity Gradient or d(strain)/dt [1/s]
.  = ortensile
strain rate,  = shear strain rate
Strain

Modulus

= Stress / Strain [Pa]
E = Youngs or Tensile, G = Shear Modulus
Compliance

Typically denoted by J
Viscosity

= Strain / Stress [1/Pa]
= Stress /Strain Rate [Pa.s or Poise]
Denoted by 
S.I. units = c.g.s. X 10
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 :
Stress
– the greatest stress which a material is
capable of sustaining without any deviation
from proportionality of stress to strain
(Hooke’s Law).
Proportional Limit
Strain
• 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
Load
• 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 at Yield Point
Max. Load or Load at Break
Strain
Bioyield and Rupture Point
Rupture point
Load
(N)
Max load
Bioyield point
Firmness
Deformation, mm
Bioyield and Rupture Point
•
•
•
•
A failure in
microstructure
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.
A failure in
macrostructure
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.
• 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
  E
behavior, it can be defined in terms of initial
tangent, secant or tangent modulus.
• Elasticity:
– The capacity of a material for taking elastic
or recoverable deformation.
• Plasticity:
Load
– The capacity of a material for taking plastic
or permanent deformation.
LL
Linear limit
Strain
Load
LL
Linear limit
Non recover part
Recover part
Dp
De
Dp + De
Deformation
• 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
• Toughness = Area under of StressStrain curve (J or N.m)
Stress
• It is the work required to cause
rupture in material
Break or Rupture Point
Area under curve
Strain
Resilience
Load
• It is the capacity of a material for storage
of strain energy in the elastic range
(energy: N.m)
Energy
given
back
Strain