It is about fRACTURE mECHANICS

1. GRIFFTH ANALYSIS
By 1. Chala Tesfaye
2. Henok

2. contents
1: Introduction
2: Griffith's Theory
3: Applications
4: Limitations
5: Conclusions

3. Introduction
• Griffith's theory of brittle fracture is a theory in materials
science that explains the conditions under which a material will
fail due to brittle fracture. The theory was developed by Andrew
A. Griffith in 1921 and states that the critical stress intensity
factor (Kc) at which a material will fail due to brittle fracture is
proportional to the square root of the surface energy of the
material.
• In simple terms, the theory states that the energy required to
initiate a crack in a material is directly proportional to the
square root of the surface energy of the material. If the energy
required to initiate a crack is greater than the energy available,
the material will not fracture. If the energy required is less than
the energy available, the material will fracture.

4. • This theory is widely used in materials science, engineering
and industry to predict the behavior of brittle materials and to
design structures that can withstand fracture. It is also used to
compare the brittleness of different materials.
• Griffith's theory of brittle fracture, also known as the Griffith
criterion, is a theory in materials science that explains the
conditions under which a material will fail due to brittle fracture.
It was developed by Andrew A. Griffith in 1921, it states that the
critical stress intensity factor (Kc) at which a material will fail
due to brittle fracture is proportional to the square root of the
surface energy of the material. The theory is widely used to
predict the behavior of brittle materials in engineering and
industry and to design structures that can withstand fracture. It
is also used to compare the brittleness of different materials.

5. • Griffith's theory of brittle fracture, also known as the
Griffith criterion, is a theory in materials science that
explains the conditions under which a material will fail due
to brittle fracture. The theory was developed by Andrew A.
Griffith in 1921 and states that the critical stress intensity
factor (Kc) at which a material will fail due to brittle
fracture is proportional to the square root of the surface
energy of the material.
• This theory is widely used in materials science,
engineering and industry to predict the behavior of brittle
materials and to design structures that can withstand
fracture. It is also used to compare the brittleness of
different materials.

6. • The theory has been a significant contribution in the field
of materials science, and it has been used as a basis for
many other theories and models related to fracture
mechanics. It also has practical applications in industries
such as aerospace, civil engineering, and oil and gas,
where understanding the behavior of brittle materials is
important for designing safe and reliable structures.
• Griffith's theory of brittle fracture is still widely used today
and continues to be an important area of research in the
field of materials science.

7. Description of Griffith's theory and the conditions under
which a material will fail due to brittle fracture
• Griffith's theory of brittle fracture is based on the concept
of the stress intensity factor (K), which is a measure of the
stress at the tip of a crack in a material. According to the
theory, a material will fail due to brittle fracture when the
stress intensity factor at the tip of the crack exceeds a
critical value, known as the critical stress intensity factor
(Kc).

8. • Griffith's theory states that the critical stress intensity
factor (Kc) is proportional to the square root of the surface
energy (γ) of the material. This relationship is expressed
mathematically as:
Kc = (π/2) * (Y/√πa)
• Where Y is the Young's modulus and a is the crack length.

9. • In other words, Griffith's theory states that the energy
required to initiate a crack in a material is directly
proportional to the square root of the surface energy of
the material. If the energy required to initiate a crack is
greater than the energy available, the material will not
fracture. If the energy required is less than the energy
available, the material will fracture.
• It is important to note that the theory is only applicable to
brittle materials, and not all materials behave according to
the theory. Additionally, The theory has some limitations,
and it is not always accurate in predicting the behavior of
certain materials under specific conditions

10. Equation for calculating the critical stress intensity factor (Kc)
The equation for calculating the critical stress intensity factor
(Kc) according to Griffith's theory of brittle fracture is:
Kc = (π/2) * (Y/√πa)
Where:
Kc is the critical stress intensity factor
Y is the Young's modulus of the material (a measure of the
material's stiffness)
a is the crack length

11. • This equation is based on the assumption that the
material is homogeneous, isotropic and linear-elastic, and
that the crack is a semi-infinite, straight and sharp.
• It is important to note that this equation is a simplified
version of the original equation presented by Griffith and it
also assumes that the material is in a state of plane-
stress, which is not always the case in real-world
applications. The critical stress intensity factor (Kc) can
also be obtained experimentally, by performing fracture
toughness tests on a material, and it can vary for different
materials and different loading conditions. It also assume
that the material is brittle, which is not true for all materials

12. The original equation presented by Griffith
The original equation presented by Griffith in 1921, to calculate
the critical stress intensity factor (Kc) according to his theory of
brittle fracture, is a bit more complex than the simplified equation
I provided earlier:
Kc = (Y/√π) * √(πa/W)
Where:Kc is the critical stress intensity factor
Y is the Young's modulus of the material (a measure of the
material's stiffness)
a is the crack length
W is the work of fracture, which is a measure of the
energy required to create new surfaces in the material

13. • This equation takes into account the energy required to initiate a
crack, represented by the term W, as well as the energy required to
propagate the crack, represented by the term (πa/Y). It also assumes
that the material is homogeneous, isotropic and linear-elastic, and
that the crack is a semi-infinite, straight and sharp.
• It is important to note that this equation is based on the assumptions
made by Griffith, and it may not always accurately predict the
behavior of certain materials under specific conditions. The critical
stress intensity factor (Kc) can also be obtained experimentally, by
performing fracture toughness tests on a material, and it can vary for
different materials and different loading conditions.
• It is also important to note that the Griffith's theory only provides a
criterion for brittle fracture and it does not account for the influence of
other factors that can affect the fracture behavior of a material, such
as the environment, temperature, loading rate, and material
microstructure.

14. Examples of how Griffith’s Theory of Brittle Fracture is used in
materials science, engineering and industry
• Griffith's theory of brittle fracture is widely used in materials science,
engineering, and industry to predict the behavior of brittle materials
and to design structures that can withstand fracture. Here are a few
examples:
• Aerospace Engineering: The theory is used to predict the behavior of
brittle materials such as ceramics and glass-reinforced plastics used
in the construction of aircraft components.
• Civil Engineering: The theory is used to predict the behavior of brittle
materials such as concrete and masonry used in the construction of
bridges and buildings.
• Oil and Gas industry: The theory is used to predict the behavior of
brittle materials such as steel used in the construction of oil and gas
pipelines.

15. • Nuclear Engineering: The theory is used to predict the behavior of brittle
materials such as ceramics and glasses used in the construction of
nuclear fuel rods.
• Automotive industry: The theory is used to predict the behavior of brittle
materials such as glass used in the construction of car windows.
• Biomedical engineering: The theory is used to predict the behavior of
brittle materials such as ceramics and glasses used in the construction of
dental implants and bones.
• It is important to note that the theory is only applicable to brittle materials
and not all materials behave according to the theory, and in many cases,
other theories and models are needed to better understand the fracture
behavior of a material.
• It is also important to note that the theory only provides a criterion for
brittle fracture and it does not account for the influence of other factors
that can affect the fracture behavior of a material, such as the
environment, temperature, loading rate, and material microstructure.

16. Criticisms of Griffith's theory of brittle fracture
• Griffith's theory of brittle fracture, also known as the Griffith
criterion, is a widely accepted theory in materials science that
explains the conditions under which a material will fail due to
brittle fracture. However, like any scientific theory, it also has its
criticisms and limitations. Here are a few examples:
• Simplistic approach: The theory is based on a simplistic
approach and assumes that the material is homogeneous,
isotropic, and linear-elastic, which is not always the case in
real-world applications.
• Plane-stress assumption: The theory assumes that the material
is in a state of plane-stress, which is not always the case in
real-world applications, and it does not take into account the
effect of three-dimensional stress states.

17. • Only applicable to brittle materials: The theory is only applicable to
brittle materials and not all materials behave according to the theory,
and in many cases, other theories and models are needed to better
understand the fracture behavior of a material.
• does not account for other factors that can affect the fracture behavior
of a material: The theory only provides a criterion for brittle fracture
and it does not account for the influence of other factors that can
affect the fracture behavior of a material, such as the environment,
temperature, loading rate, and material microstructure.
• The theory is based on the assumption that the crack is semi-infinite
and sharp which is not always the case in real-world applications.
• It is important to note that despite these criticisms, Griffith's theory of
brittle fracture remains a widely accepted and important theory in the
field of materials science. Its limitations are well understood and many
researchers continue to use the theory as a basis for further studies,
while taking into account its limitations.

18. Limitations of the Griffith's theory of brittle fracture and its applicability
to certain materials
• Griffith's theory of brittle fracture, also known as the Griffith criterion,
is a widely accepted theory in materials science that explains the
conditions under which a material will fail due to brittle fracture.
However, like any scientific theory, it also has its limitations and it is
not applicable to all materials. Here are a few examples:
• Simplistic approach: The theory is based on a simplistic approach and
assumes that the material is homogeneous, isotropic, and linear-
elastic, which is not always the case in real-world applications.
• Plane-stress assumption: The theory assumes that the material is in a
state of plane-stress, which is not always the case in real-world
applications, and it does not take into account the effect of three-
dimensional stress states.

19. • Only applicable to brittle materials: The theory is only
applicable to brittle materials and not all materials behave
according to the theory. It does not apply to ductile
materials, which usually show significant plastic
deformation before failure.
• Plane-stress assumption: The theory assumes that the
material is in a state of plane-stress, which is not always
the case in real-world applications, and it does not take
into account the effect of three-dimensional stress states.

20. • does not account for other factors that can affect the fracture behavior
of a material: The theory only provides a criterion for brittle fracture
and it does not account for the influence of other factors that can
affect the fracture behavior of a material, such as the environment,
temperature, loading rate, and material microstructure.
• The theory is based on the assumption that the crack is semi-infinite
and sharp which is not always the case in real-world applications.
• It is also important to note that the critical stress intensity factor (Kc)
can also be obtained experimentally, by performing fracture
toughness tests on a material, and it can vary for different materials
and different loading conditions, this means that the value of Kc can
change even for the same material based on the loading conditions.
• Despite these limitations, Griffith's theory of brittle fracture remains a
widely accepted and important theory

21. Conclusion on Griffith's theory of brittle fracture
• Griffith's theory of brittle fracture, also known as the Griffith
criterion, is a widely accepted theory in materials science that
explains the conditions under which a material will fail due to
brittle fracture. It was developed by Andrew A. Griffith in 1921,
and it states that the critical stress intensity factor (Kc) at which
a material will fail due to brittle fracture is proportional to the
square root of the surface energy of the material.
• The theory is widely used in materials science, engineering,
and industry to predict the behavior of brittle materials and to
design structures that can withstand fracture. It is also used to
compare the brittleness of different materials.

22. • However, it has some limitations, it is based on a
simplistic approach and assumes that the material is
homogeneous, isotropic, and linear-elastic, which is not
always the case in real-world applications. Also, it
assumes that the material is in a state of plane-stress,
which is not always the case in real-world applications,
and it does not take into account the effect of three-
dimensional stress states. Additionally, it is only applicable
to brittle materials and not all materials behave according
to the theory, and it does not account for other factors that
can affect the fracture behavior of a material, such as the
environment, temperature, loading rate, and material
microstructure.

23. • However, it has some limitations, it is based on a
simplistic approach and assumes that the material is
homogeneous, isotropic, and linear-elastic, which is not
always the case in real-world applications. Also, it
assumes that the material is in a state of plane-stress,
which is not always the case in real-world applications,
and it does not take into account the effect of three-
dimensional stress states. Additionally, it is only applicable
to brittle materials and not all materials behave according
to the theory, and it does not account for other factors that
can affect the fracture behavior of a material, such as the
environment, temperature, loading rate, and material
microstructure.

24. • Despite these limitations, Griffith's theory of brittle fracture
remains a widely accepted and important theory in the field of
materials science. Its limitations are well understood, and many
researchers continue to use the theory as a basis for further
studies, while taking into account its limitations.
• The critical stress intensity factor (Kc) can also be obtained
experimentally, by performing fracture toughness tests on a
material, and it can vary for different materials and different
loading conditions.
• It is important to note that this theory is only a starting point for
understanding the brittle fracture behavior of a material and
other theories and models are needed to better understand the
fracture behavior of a material under specific conditions.

25. Summary of key points on Griffith's theory of brittle fracture
• Griffith's theory of brittle fracture, also known as the Griffith criterion, is a widely
accepted theory in materials science that explains the conditions under which a
material will fail due to brittle fracture. It was developed by Andrew A. Griffith in
1921, and it states that the critical stress intensity factor (Kc) at which a material
will fail due to brittle fracture is proportional to the square root of the surface
energy of the material.
• The theory is widely used in materials science, engineering, and industry to
predict the behavior of brittle materials and to design structures that can withstand
fracture. It is also used to compare the brittleness of different materials.
• The key points of the theory are:
• It's a theory that explains the brittle fracture of materials
• Developed by Andrew A. Griffith in 1921
• Based on the critical stress intensity factor (Kc) at which a material will fail

26. • The theory states that the critical stress intensity factor (Kc) is
proportional to the square root of the surface energy (γ) of the material
• The theory is based on the assumptions that the material is
homogeneous, isotropic, linear-elastic and that the crack is semi-infinite
and sharp
• It's only applicable to brittle materials and does not account for other
factors that can affect the fracture behavior of a material, such as the
environment, temperature, loading rate, and material microstructure.
• The critical stress intensity factor (Kc) can also be obtained
experimentally, by performing fracture toughness tests on a material, and
it can vary for different materials and different loading conditions.
• Despite its limitations, it's widely accepted and important theory in the
field of materials science.

27. • Irwin and Orowan independently extended the Griffith
approach to metals by including the energy dissipated by
local plastic flow.
• Orowan limited practical use to brittle materials while Irwin
made no such restrictions

28. • Griffith used the crack geometry and loading configuration
shown and assumed that the stress would be constant
during any incremental growth of the crack.
• Without plastic work term consideration

29. • Irwin and Orowan incorporated the effects of crack tip
plasticity into the analysis by taking the plastic dissipation
term as constant.
• So that the resistance was defined as the combination of
surface energy absorbed and plastic work dissipated.
Thus, the Griffith-Irwin-Orowan energy balance equation
became…

30. • And the critical stress was…
• Both Irwin and Orowan noted that the plastic dissipation
rate for metals was at least a factor of 1000 greater than
the surface energy absorption rate so

31. • Irwin noted that the driving force/input energy rate G was
directly related to the square of the magnitude of the
crack tip stress field for the Griffith center crack geometry.