Short Notes: Mechanical Properties of Materials | Strength of Materials (SOM) - Mechanical Engineering PDF Download

 Page 1


Mec hanical Prop erties of Mat erials
In tro duction
This do cumen t pro vides an o v erview of the mec hanical prop erties of materials, fo cusing
on stress, strain, and their relationships. It explores ho w materials deform under v arious
forces and the prop erties that define their b eha vior.
1 Stress
Stress (s ) is the in ternal resistance of a material to an external force p er unit area. It
quan tifies ho w a force is distributed o v er a cross-sectional area.
1.1 F orm ula
The form ula for stress is:
s =
F
A
where:
• s : Stress (Units: P ascal (P a), Megapascal (MP a), Gigapascal (GP a))
• F : Applied force (Newton, N)
• A : Cross-sectional area (m
2
)
1.2 T yp es of Stress
• Normal Stress : A cts p erp endicular to the surface (e.g., tension or compression).
• Shear Stress : A cts parallel to the surface, causing la y ers to slide past eac h other.
• Bulk Stress : Uniform pressure applied in all directions, often in fluids or solids
under h ydrostatic pressure.
2 Strain
Strain (? ) measures the deforma tion of a mat erial due to stress. It is a dimensionless
quan tit y , represen ting the relativ e c hange in shap e or size.
1
Page 2


Mec hanical Prop erties of Mat erials
In tro duction
This do cumen t pro vides an o v erview of the mec hanical prop erties of materials, fo cusing
on stress, strain, and their relationships. It explores ho w materials deform under v arious
forces and the prop erties that define their b eha vior.
1 Stress
Stress (s ) is the in ternal resistance of a material to an external force p er unit area. It
quan tifies ho w a force is distributed o v er a cross-sectional area.
1.1 F orm ula
The form ula for stress is:
s =
F
A
where:
• s : Stress (Units: P ascal (P a), Megapascal (MP a), Gigapascal (GP a))
• F : Applied force (Newton, N)
• A : Cross-sectional area (m
2
)
1.2 T yp es of Stress
• Normal Stress : A cts p erp endicular to the surface (e.g., tension or compression).
• Shear Stress : A cts parallel to the surface, causing la y ers to slide past eac h other.
• Bulk Stress : Uniform pressure applied in all directions, often in fluids or solids
under h ydrostatic pressure.
2 Strain
Strain (? ) measures the deforma tion of a mat erial due to stress. It is a dimensionless
quan tit y , represen ting the relativ e c hange in shap e or size.
1
2.1 F orm ula
The form ula for strain is:
?=
?l
l
where:
• ? : Strain (dimensionless)
• ?l : Change in length (m)
• l : Original length (m)
2.2 T yp es of Strain
• Normal Strai n : Deformation along the direction of the applied force.
• Lateral Strain : Deformation p erp endicular to the applied fo rce, often seen as a
con traction when a material is stretc hed.
• Shear Str ain : Angular deformation due to shear stress.
• Bulk Str ain : V olumetric c hange under bulk stress.
3 T rue Stress and T rue Strain
T rue stress and true strain accoun t for c hanges in dimensions during deformation, pro-
viding a more accurate measure for large deformations.
3.1 T rue Stress
T rue stress (s
true
) is the load divided b y the instan taneous cross-sectional area:
s
true
=
F
A
inst
where A
inst
is the curren t area during de formation.
3.2 T rue Strain
T rue strain (?
true
) is the logarithmic strain, calculated as:
?
true
=ln
(
l
l
0
)
where l is the curren t length and l
0
is the original length.
4 S tress-Strain Curv e
The stress-strain curv e illustrates a material’s resp onse to applied stress, sho wing distinct
regions of b eha vior.
2
Page 3


Mec hanical Prop erties of Mat erials
In tro duction
This do cumen t pro vides an o v erview of the mec hanical prop erties of materials, fo cusing
on stress, strain, and their relationships. It explores ho w materials deform under v arious
forces and the prop erties that define their b eha vior.
1 Stress
Stress (s ) is the in ternal resistance of a material to an external force p er unit area. It
quan tifies ho w a force is distributed o v er a cross-sectional area.
1.1 F orm ula
The form ula for stress is:
s =
F
A
where:
• s : Stress (Units: P ascal (P a), Megapascal (MP a), Gigapascal (GP a))
• F : Applied force (Newton, N)
• A : Cross-sectional area (m
2
)
1.2 T yp es of Stress
• Normal Stress : A cts p erp endicular to the surface (e.g., tension or compression).
• Shear Stress : A cts parallel to the surface, causing la y ers to slide past eac h other.
• Bulk Stress : Uniform pressure applied in all directions, often in fluids or solids
under h ydrostatic pressure.
2 Strain
Strain (? ) measures the deforma tion of a mat erial due to stress. It is a dimensionless
quan tit y , represen ting the relativ e c hange in shap e or size.
1
2.1 F orm ula
The form ula for strain is:
?=
?l
l
where:
• ? : Strain (dimensionless)
• ?l : Change in length (m)
• l : Original length (m)
2.2 T yp es of Strain
• Normal Strai n : Deformation along the direction of the applied force.
• Lateral Strain : Deformation p erp endicular to the applied fo rce, often seen as a
con traction when a material is stretc hed.
• Shear Str ain : Angular deformation due to shear stress.
• Bulk Str ain : V olumetric c hange under bulk stress.
3 T rue Stress and T rue Strain
T rue stress and true strain accoun t for c hanges in dimensions during deformation, pro-
viding a more accurate measure for large deformations.
3.1 T rue Stress
T rue stress (s
true
) is the load divided b y the instan taneous cross-sectional area:
s
true
=
F
A
inst
where A
inst
is the curren t area during de formation.
3.2 T rue Strain
T rue strain (?
true
) is the logarithmic strain, calculated as:
?
true
=ln
(
l
l
0
)
where l is the curren t length and l
0
is the original length.
4 S tress-Strain Curv e
The stress-strain curv e illustrates a material’s resp onse to applied stress, sho wing distinct
regions of b eha vior.
2
4.1 Elastic Beha vior
In the elastic region, the material returns to its original shap e after the stress is remo v ed.
The relationship is linear and follo ws Ho ok e’s La w.
4.2 Plastic Beha vior
Bey ond the elastic limit, the material undergo es p ermanen t deformation, en tering the
plastic region. This deformation remains ev en after the stress is remo v ed.
4.3 Ho ok e’s La w
Ho ok e’s La w describ es the linear elastic region:
s =E?
where:
• E : Y oung’s Mo dulus (mo dulus of elasticit y , P a)
• s : Stress (P a)
• ? : Strain (dimensionless)
5 Material Prop erties
Material prop erties define ho w a material resp onds to stress and strain, influencing its
suitabilit y for engineering applications.
5.1 Elasticit y
Elasticit y is the abilit y of a mate rial to return to its original shap e after deformation. It
is dominan t in the elastic region of the stress-strain curv e.
5.2 Plasticit y
Plasticit y refers to a material’s abilit y to retain deformation after the applied stress
exceeds the elastic limit. It is critical for pro cesses lik e forming and shaping.
5.3 Ductilit y
Ductilit y is the abilit y of a material to b e stretc hed in to a wire without breaking. Ductile
materials exhibit significan t plastic deformation b efore failure.
5.4 Brittleness
Brittleness is the tendency of a material to break easily without significan t plastic defor-
mation. Brittle materials fail suddenly under stress.
3
Page 4


Mec hanical Prop erties of Mat erials
In tro duction
This do cumen t pro vides an o v erview of the mec hanical prop erties of materials, fo cusing
on stress, strain, and their relationships. It explores ho w materials deform under v arious
forces and the prop erties that define their b eha vior.
1 Stress
Stress (s ) is the in ternal resistance of a material to an external force p er unit area. It
quan tifies ho w a force is distributed o v er a cross-sectional area.
1.1 F orm ula
The form ula for stress is:
s =
F
A
where:
• s : Stress (Units: P ascal (P a), Megapascal (MP a), Gigapascal (GP a))
• F : Applied force (Newton, N)
• A : Cross-sectional area (m
2
)
1.2 T yp es of Stress
• Normal Stress : A cts p erp endicular to the surface (e.g., tension or compression).
• Shear Stress : A cts parallel to the surface, causing la y ers to slide past eac h other.
• Bulk Stress : Uniform pressure applied in all directions, often in fluids or solids
under h ydrostatic pressure.
2 Strain
Strain (? ) measures the deforma tion of a mat erial due to stress. It is a dimensionless
quan tit y , represen ting the relativ e c hange in shap e or size.
1
2.1 F orm ula
The form ula for strain is:
?=
?l
l
where:
• ? : Strain (dimensionless)
• ?l : Change in length (m)
• l : Original length (m)
2.2 T yp es of Strain
• Normal Strai n : Deformation along the direction of the applied force.
• Lateral Strain : Deformation p erp endicular to the applied fo rce, often seen as a
con traction when a material is stretc hed.
• Shear Str ain : Angular deformation due to shear stress.
• Bulk Str ain : V olumetric c hange under bulk stress.
3 T rue Stress and T rue Strain
T rue stress and true strain accoun t for c hanges in dimensions during deformation, pro-
viding a more accurate measure for large deformations.
3.1 T rue Stress
T rue stress (s
true
) is the load divided b y the instan taneous cross-sectional area:
s
true
=
F
A
inst
where A
inst
is the curren t area during de formation.
3.2 T rue Strain
T rue strain (?
true
) is the logarithmic strain, calculated as:
?
true
=ln
(
l
l
0
)
where l is the curren t length and l
0
is the original length.
4 S tress-Strain Curv e
The stress-strain curv e illustrates a material’s resp onse to applied stress, sho wing distinct
regions of b eha vior.
2
4.1 Elastic Beha vior
In the elastic region, the material returns to its original shap e after the stress is remo v ed.
The relationship is linear and follo ws Ho ok e’s La w.
4.2 Plastic Beha vior
Bey ond the elastic limit, the material undergo es p ermanen t deformation, en tering the
plastic region. This deformation remains ev en after the stress is remo v ed.
4.3 Ho ok e’s La w
Ho ok e’s La w describ es the linear elastic region:
s =E?
where:
• E : Y oung’s Mo dulus (mo dulus of elasticit y , P a)
• s : Stress (P a)
• ? : Strain (dimensionless)
5 Material Prop erties
Material prop erties define ho w a material resp onds to stress and strain, influencing its
suitabilit y for engineering applications.
5.1 Elasticit y
Elasticit y is the abilit y of a mate rial to return to its original shap e after deformation. It
is dominan t in the elastic region of the stress-strain curv e.
5.2 Plasticit y
Plasticit y refers to a material’s abilit y to retain deformation after the applied stress
exceeds the elastic limit. It is critical for pro cesses lik e forming and shaping.
5.3 Ductilit y
Ductilit y is the abilit y of a material to b e stretc hed in to a wire without breaking. Ductile
materials exhibit significan t plastic deformation b efore failure.
5.4 Brittleness
Brittleness is the tendency of a material to break easily without significan t plastic defor-
mation. Brittle materials fail suddenly under stress.
3
5.5 Malleabilit y
Malleabilit y is the abilit y of a material to b e hammered or rolled in to thin sheets. It is
related to plasticit y but fo cuses on compressiv e deformation.
5.6 T oughness
T oughness is the capacit y of a material to absorb energy b efore fracturing. It is the area
under the stress-strain curv e up to the p oin t of failure.
5.7 Hardness
Hardness is the resistance of a material to inden tation or scratc hing. It is often measured
using tests lik e the Vic k ers or Ro c kw ell hardness tests.
5.8 Strength
Strength is the abilit y of a material to withstand an applied force without failure. It
includes tensile strength, compressiv e strength, and shear strength.
6 Elongation
Elongation measures the extension of a material under load, often used to assess ductilit y .
6.1 Uniform Bar
F o r a uniform bar under axial load:
d =
PL
AE
where:
• d : Elongation (m)
• P : Applied load (N)
• L : Original length (m)
• A : Cross-sectional area (m
2
)
• E : Y oung’s Mo dulus (P a)
6.2 Self-W eigh t
F or a bar under its o wn w eigh t:
d =
WL
2AE
where:
• W : W eigh t of the bar (N)
• Other terms are as defined ab o v e.
4