This document discusses fracture mechanics and provides background information on the topic. It introduces key concepts in fracture mechanics including stress intensity factor, linear elastic fracture mechanics (LEFM), ductile to brittle transition, and fracture toughness. Applications of fracture mechanics are described such as its use in analyzing cracking in pavement systems. The document also covers probabilistic fracture of brittle materials and how their strength is affected by the presence of flaws.
This is a ppt which will give u a better understanding of fracture toughness of a material in short time. It also has great exposure to testing method that we do in our laboratory class in undergraduate courses. So good luck with slide.
This PPT discusses Fatigue and Fracture mechanism, some history and problems. It has included on research paper. You can refer the literature review for further study of the topic.
Engineering Fracture Mechanics. Engineers try to have high-strength, high ductility, high crack resistance, and faultless structures. The most reliable approach is "No cracks - no problems,"
When all is not possible, there are different methods of prevention of catastrophic failure: increase crack resistance by ductile material, by local heating; decrease SIF by placing holes on the crack path, by patching, by stiffing elements or by using composite materials. "Leak-before-break" is an effective strategy to prevent catastrophic failure of pressure vessels. It is better to allow a semi-elliptical crack to grow through the wall and to detect it by leaking than to have the dynamic start and failure of the whole vessel. There are two characteristics of the material: crack resistance for semi-elliptical crack and crack resistance for through crack.
This is a ppt which will give u a better understanding of fracture toughness of a material in short time. It also has great exposure to testing method that we do in our laboratory class in undergraduate courses. So good luck with slide.
This PPT discusses Fatigue and Fracture mechanism, some history and problems. It has included on research paper. You can refer the literature review for further study of the topic.
Engineering Fracture Mechanics. Engineers try to have high-strength, high ductility, high crack resistance, and faultless structures. The most reliable approach is "No cracks - no problems,"
When all is not possible, there are different methods of prevention of catastrophic failure: increase crack resistance by ductile material, by local heating; decrease SIF by placing holes on the crack path, by patching, by stiffing elements or by using composite materials. "Leak-before-break" is an effective strategy to prevent catastrophic failure of pressure vessels. It is better to allow a semi-elliptical crack to grow through the wall and to detect it by leaking than to have the dynamic start and failure of the whole vessel. There are two characteristics of the material: crack resistance for semi-elliptical crack and crack resistance for through crack.
Seminar Report on Brittle Fracture of ShipsVISHAL SHARMA
This study investigates the sinking of the Titanic from the theory of Brittle Fracture and
Engineering Failures. This study offers a subjectivist perspective of mental inertia to
understand the Titanic Disaster. Specifically, this study argue that the fall of the Titanic was
mainly due to Brittle Fracture of Rivets and the Hull Steel. Metallurgical and Mechanical
Analysis were performed on steel and rivet samples recovered from the wreck of the RMS
Titanic. It is found that the steel possessed a ductile-to-brittle transition temperature that was
very high with respect to the service temperature, making the material very brittle at ice-water
temperatures. This had been attributed to both chemical and microstructural factors. It is also
been found that the wrought iron rivets used in the construction of Titanic contained an elevated
amount of incorporated slag, and that the orientation of the slag within the rivets may hold an
explanation for how the ship accumulated damage during its encounter with the iceberg.
Keywords- Brittle fracture, Rivets, Hull Steel, Metallurgical Failure, Titanic Disaster.
Lec3 failure.pptx introductionto fialure types and causesssuserac3f5b
define the term failure. types of failures and mechanisms, failure modes. failure mode and criticality analysis.
Failure mechanisms are physical, chemical, or other processes which lead or have led to failure.
Plasticity, Theory of Plasticity ,Creep in concrete ,Creep, Stiffness ,Elasticity ,Plasticity ,Euler-Bernoulli beam equation, Buckling, Ductility VS Malleability, Ductile Materials, Brittle Materials ,Modulus of Elasticity, Plastic Strain, Tensile Strength, Yield Strength, Ultimate Strength, Solid mechanics or Mechanics of solids, Strength of Materials, Types of forces, Normal forces, Fatigue , Resilience, Unit of Resilience, Modulus of rigidity , Modulus of Resilience, Modulus of Toughness Poisson’s Ratio.
Stress-Strain Curves for Metals, Ceramics and PolymersLuís Rita
Homework II - Biomaterials Science
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Ceramics have historically been limited in structural applications due to poor tensile strength and brittle fracture behaviour, leading to structural unreliability.SO To optimize the Zirconiato obtain high hardness and toughness.
MODE II FRACTURE PARAMETERS FOR VARIOUS SIZES OF BEAMS IN PLAIN CONCRETEIJERA Editor
Blended aggregate in concrete and arriving at the structural properties of blended aggregate concrete is a thrust
area. Pumice is very light and porous igneous rock that is formed during volcanic eruptions.Cinder is a waste
material obtained from steel manufacturing units. Shear strength is a property of major significance for wide
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V.Bhaskar Desai is supposed the best suited geometry. In this present experimental investigation an attempt is
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the pumice and cinder in different proportions, and making use of DCN test specimen geometry . By blending
the pumice and cinder in different percentages of 0, 25, 50, 75 and 100 by volumeof concrete, a blended light
weight aggregate concrete is prepared. By using this the property such as in plane shear strength is studied.
Finally an analysis is carried out regarding Mode-II fracture properties of blended concrete. It is concluded that
the Ultimate load in Mode-II is found to decrease continuously with the percentage increase in Pumice aggregate
content. It is also observed that the ultimate stress in Mode II is found to increase continuously with percentage
increase in cinder aggregate content.
Under repeated impact composite domes subjected 6 J energy, changes locally with
increasing drop height. The action of the dynamic load generates reactions at the
support and bending moments at points on the surface of the composite. The peak loads
were noted to increase and stabilise about some mean value; and the 150mm diameter
shell was more damage tolerant compared to the 200 mm diameter one.
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxR&R Consult
CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
Here's a great example: At a large natural gas-fired power plant, where they use waste heat to generate steam and energy, they were puzzled that their boiler wasn't producing as much steam as expected.
R&R and Tetra Engineering Group Inc. were asked to solve the issue with reduced steam production.
An inspection had shown that a significant amount of hot flue gas was bypassing the boiler tubes, where the heat was supposed to be transferred.
R&R Consult conducted a CFD analysis, which revealed that 6.3% of the flue gas was bypassing the boiler tubes without transferring heat. The analysis also showed that the flue gas was instead being directed along the sides of the boiler and between the modules that were supposed to capture the heat. This was the cause of the reduced performance.
Based on our results, Tetra Engineering installed covering plates to reduce the bypass flow. This improved the boiler's performance and increased electricity production.
It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
More examples of our work https://www.r-r-consult.dk/en/cases-en/
Final project report on grocery store management system..pdfKamal Acharya
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This document will discuss each of the underlying technologies to create and implement an e- commerce website.
TECHNICAL TRAINING MANUAL GENERAL FAMILIARIZATION COURSEDuvanRamosGarzon1
AIRCRAFT GENERAL
The Single Aisle is the most advanced family aircraft in service today, with fly-by-wire flight controls.
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Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Vaccine management system project report documentation..pdfKamal Acharya
The Division of Vaccine and Immunization is facing increasing difficulty monitoring vaccines and other commodities distribution once they have been distributed from the national stores. With the introduction of new vaccines, more challenges have been anticipated with this additions posing serious threat to the already over strained vaccine supply chain system in Kenya.
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Courier management system project report.pdfKamal Acharya
It is now-a-days very important for the people to send or receive articles like imported furniture, electronic items, gifts, business goods and the like. People depend vastly on different transport systems which mostly use the manual way of receiving and delivering the articles. There is no way to track the articles till they are received and there is no way to let the customer know what happened in transit, once he booked some articles. In such a situation, we need a system which completely computerizes the cargo activities including time to time tracking of the articles sent. This need is fulfilled by Courier Management System software which is online software for the cargo management people that enables them to receive the goods from a source and send them to a required destination and track their status from time to time.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Forklift Classes Overview by Intella PartsIntella Parts
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Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
Learn about the cost savings, reduced environmental impact, and minimal disruption associated with trenchless technology. Discover detailed explanations of popular techniques such as pipe bursting, cured-in-place pipe (CIPP) lining, and directional drilling. Understand how these methods can be applied to various types of infrastructure, from residential plumbing to large-scale municipal systems.
Ideal for homeowners, contractors, engineers, and anyone interested in modern plumbing solutions, this guide provides valuable insights into why trenchless pipe repair is becoming the preferred choice for pipe rehabilitation. Stay informed about the latest advancements and best practices in the field.
3. WHY IS FRACTURE IMPORTANT?
Brittle fracture can cause sudden failure
Aloha Airlines Boeing 737-297, operating from Hilo to
Honolulu, at Kahului Airport on April 28, 1988 after its fuselage
was torn away during the flight.
Failure was attributed to fatigue fracture of the panels forming
the fuselage in the section weakened by the rivets.
4. WHY IS FRACTURE IMPORTANT?
•Failure of the Liberty Ships & T2
tankers built during Word War II
attributed to the fracture of the
weld due to cold weather &
fatigue.
•Cause of Moonie to Brisbane
pipeline incident that led to the
spilling of 1.9M litres of crude
oil into a mangrove lined canal
flowing into the Brisbane
River(Australia) in 2003.
Failure of pipelines can cause
spills that can damage
ecosystems and lead to big
financial losses.
6. WHY IS FRACTURE IMPORTANT?
•Cracks suddenly appeared on two of three steel girders of the Hoan
bridge. Triaxial constraint due to bracing system led to brittle crack
propagation.
7. WHY FRACTURE MECHANICS?
Conventional design procedures based only on
some maximum stress criterion are not
adequate under all circumstances.
Fracture mechanics determines failure based on
the interaction b/w applied stress, crack(or flaw)
& material parameters(e.g.,fracture toughness).
Instead of magnitude of stress or strain, fracture
mechanics is concerned with the distribution of
stresses & displacements in the vicinity of a
crack tip.
Fracture mechanics is particularly applicable to
the failure of brittle materials but under certain
circumstances to other materials as well.
8. WHY FRACTURE MECHANICS?
The difference between theoretical material
fracture(or cohesive) strength calculated
from the interatomic bonding energy & the
values actually measured is enormous,
perhaps two or three orders of magnitude.
Griffith, in 1920, concluded that any real
material has flaws, microcracks or other
defects that would have the effect of
concentrating the stress in highly localised
regions. Cracks would grow under an applied
stress until failure occured.
9. Background
Stress Concentration
Can be visualised as the
concentration of stress-flow lines
due to a geometrical discontinuity in
the continuum.
A defect or a crack leads to stress
concentration .
The stress concentration increases
as the radius of the tip decreases.
12. Stress Intensity Factor
Kt may be considered as a
single parameter description
of the stress & displacement
fields near the crack tip.
Its calculation considers a
linear elastic material that is
both isotropic &
homogeneous. Although
these are incorrect for most
of the materials, it is
generally assumed that the
approximations involved in
the application of LEFM to
many cases are reasonable.
Kt has the dimension of
stress*(length)1/2 :MPa-
2
3
cos
2
cos
2
sin
2
3
sin
2
sin1
2
cos
2
3
sin
2
sin1
2
cos
2
2/1
1
r
K
xy
y
x
K1is the stress intensity factor
is the Poisson’s ratio
yxz
0 yzxz
13. Stress Intensity Factor
Mode I or opening crack
Where is the applied (nominal or far-field)
stress, a = crack length, F is a function of
geometry and crack length.
aFKt
Or, in another form
Where P is the applied load, d= depth of
specimen or structure, b= out of plane
thickness, (=a/d) = relative crack
length, is a function that depends
on the span/depth ratio.
)(fd
bd
P
Kt
f
14. Linear Elastic Fracture Mechanics(LEFM)
The fracture criterion involves only one material
parameter, which is related to the near-tips stress field
and the energy of the structure
The stresses near the crack-tip have an r-1/2 singularity
(and become infinite at crack tip)
During fracture, the entire body remains elastic and
energy is dissipated only at the crack-tip; i.e., fracture
occurs at a point.
The crack propagates when:
Where K1C is the critical stress intensity factor or fracture
toughness (It is essentially a material property).
The main features of LEFM
are:
CKK 11
15. Typical Fracture Toughness Values
Fracture toughness, Kc (values at room
temperature unless marked with *)
16. LEFM(Contd.)
Crack extension occurs when the energy
available for crack growth is sufficient to
overcome the resistance of the material. The
material resistance may include the surface
energy, plastic work, or other type of energy
dissipation associated with a propagating crack.
The energy release rate, G is defined as the
rate of change in potential energy with crack
area (for a linear elastic material).
Fracture occurs when(Irwin, 1956):
where Gc is the critical energy release rate or
fracture energy.
Another way of considering fracture involves the energy release rate.
cGG
17. Fracture Energy Values
Fig. Typical Fracture Energy
Units of Gc are
J/m2 (or N-
m/m2=N/m)
Toughness, Gc
(values at room
temperature
unless marked
with*)
18. Relationship
Relationship b/w KI & G
KI characterises the stress and displacement fields near the
crack-tip(i.e., local parameter).
G quantifies the net change in potential energy due to an
increment in the crack extension (i.e., describes global
behaviour).
For Linear Elastic materials KI & G are uniquely related.
(Irwin,1957)
Where, for plane stress
for plane strain
E
K
G
2
1
EE
2
1
E
E
19. •Ductile-Brittle Transition
Fracture energy increases with:
• An increase in Temperature
• A decrease in loading rate
• A decrease in triaxiality
When the fracture energy is lower,
the tendency for the failure to be
brittle is higher.
When the fracture energy is
higher, there is a higher
resistance to brittle failure and the
tendency for yield(ductile failure )
is higher.
20. Variation in the Fracture Toughness
Variation of fracture toughness
(curve b) with temperature for a low
alloy of str. steel
21. Brittle Fracture
Fracture in glass and some ceramics
Cleavage fracture due to rupture of interatomic bonds.
22. Elasto-Plastic Fracture
Fracture in ductile metals (i.e., metals that can undergo
large plastic deformation).
Plastic
zone
formation
, ductile
tearing
and crack
blunting.
23. Elasto-Plastic Fracture
When the stress close to the crack-tip reaches yield
stress( ) at some distance ry , it can be considered
that .
The width of the plastic zone, for a state of
plane stress.
Materials with higher yield strength have a smaller
plastic zone; i.e., less ductile fracture.
Most metals contain inclusions around which plastic
flow occurs resulting in elongated cavities. These
cavities link up to cause ductile tearing. This blunts the
crack, lowering the stress concentration. Therefore,
decreases but it is sufficient o cause work hardening
of the material near the crack-tip.
y
y
yLocal
2
2
2 y
I
y
K
r
Local
24. Elasto-Plastic Fracture
Under plane strain conditions, the restraint elevates the
stress required to produce yielding. Therefore, the plastic
zone for plain strain is much smaller than the plain stress
zone. Consequently, for a thick element, the plastic zone
is larger at the surface than in the middle.
Schematic of Mode I
plastic zone varying
from plane stress at
the lateral surfaces to
plane strain at the
mid-section
25. Elasto-Plastic Fracture
Appearance of plane stress plastic
deformation at the front surface, a normal
section and the back surface of a silicon iron
fracture specimen
26. Fracture in Polymers
As in metals, fracture and yielding are
competing failure mechanisms. During failure,
polymers exhibit either shear yielding or crazing.
Shear yielding resembles plastic flow in metals,
with molecules sliding with respect to each other
in a ductile manner.
Crazing is a localised deformation that leads o
cavitation and strains in the order of 100%. On
the macroscopic level, crazing appears as a
stress-whitened region that forms perpendicular
to the maximum principal stress.
27. Fracture in Polymers
At high strains, molecular
chains form aligned
packets called fibrils that
carry very high stresses.
Microvoids form between
28. Fracture In Composites
Fracture in wood and other materials reinforced with
fibres and inclusions.
The toughness of polymers is enormously increased by
reinforcing them with fibres that act as crack
arresters. They deflect the crack and blunt the crack
tip.
29. Fracture In Composites
The load needed to propagate the crack is
higher; fibres and inclusions increase fracture
energy
Rubber toughened polymers derive their
toughness from bridging action of the small
rubber particles that act as springs, tending to
30. Fracture in Concrete
The size of the fracture process zone that occurs
ahead of a propagating crack determines the
toughness of concrete.
Since the toughening mechanisms are weak in
concrete, rocks and some ceramics, they are called
quasi-brittle materials.
31. Nonlinear Fracture Mechanics: R-curve
R-curve
The effect of the toughening mechanisms ahead
of the crack tip is sometimes represented by a
rising resistance curve or R-curve, where the
critical energy release rate, is not constant, but
changes with the crack extension.
As the applied stress increases, the energy
release rate G changes. Until the G function
becomes tangential to the R-curve, the crack
extension is stable.
Conditions for stable crack growth:
Unstable crack growth (failure) occurs when:
da
dR
da
dG
RG
da
dR
da
dG
32. Nonlinear Fracture Mechanics: Cohesive crack
The plastic zone over a length ahead of the traction-free
crack of length 2a is modelled as a crack of length 2a+2
with closure stresses equal to the yield strength over a
certain length near the crack-tip.
This represents the elastoplastic solutions: a through crack
(or traction-free crack) under the applied remote stress and a
through crack with closure stresses at the tip.
YS
33. Nonlinear Fracture Mechanics: Cohesive crack
Fictitious crack model (Hillerborg, 1976)
The effect of the fracture process zone is represented by a cohesive zone.
Fracture criteria:
For w=0, f=ft
For w=wc, f=0
Where w is the crack
opening or width, wc is the
critical crack opening, ft is
the tensile strength, f(w)
are the cohesive stresses
and GF is the fracture
energy.
cw
FGdwwf
0
)(
This can be used in finite element analysis or any other analytical
technique to represent the tensile cracking response of concrete,
rock, ceramics, etc.
34. Applicaton of Fracture Mechanics
Fracture mechanics is
often used in the
framework of the finite
element method to
simulate the failure of a
structure or body through
crack propagation.
Cracking in
pavement overlay
systems (over
concrete substrates)
analysed using
FEMLAB finite
element software.
Shrinkage cracking
due to drying during
37. Defect-Sensitivity
Materials such as glass, ceramics, rigid
polymers and concrete have low fracture
toughness making them vulnerable to the
presence of crack-like defects. Such defect-
sensitive materials are prone to brittle failure
well before they can yield.
Moreover, many of these materials always
contain cracks and flaws. Consequently, their
tensile strengths are low.
Concrete can have flaws in the order of 5-10
mm; brick and stone can have defects of the
order of 2 mm. Engineered ceramics have
smaller defects, in the order of 60 m.
38. Tensile Strength Vs Compressive Strength
a) Under (uniaxial) tension, failure
generally occurs by the
propagation of the longest most
favourably oriented flaw or crack.
b) Under compression, cracks
propagate stable as they change
orientation. Moreover many
cracks have to propagate and join
to cause failure. Consequently,
failure is not dependent on the
characteristics of any one crack
but the average.
The compressive strength of brittle materials is usually about 10-15
times the tensile strength. Also, the variability of the strength is lower
in compression than in tension.
39. Statistics of Strength
Since failure in a brittle
solid is governed by the
presence of defects and
cracks, and these flaws
can vary in size and
orientation within the
body and from specimen
to another, there is a
statistical variation in the
strength.
Instead of defining a
single “tensile strength”,
it is more appropriate to
consider a probability
that the specimen or
body has a certain
tensile strength.
40. Statistics of Strength
Volume or Size
Dependence of Strength
•The distribution of
flaw or crack length is
related to the volume
of material being
considered.
•A larger sample of
the material is more
likely to contain a
larger flaw than a
smaller sample.•Therefore, the (tensile) strength of a larger or longer
specimen is generally lower than that of smaller or shorter
specimen, when the failure is brittle.
41. Statistics of Strength
Tensile Tests of Wires
by Leonardo da Vinci
(c.1500)
Experimental setup consisting of having a
basket by the wire, and slowly adding sand to
the basket until the wire broke. The sand was
weighed and the failure stress was calculated.
•Leonardo da Vinci found that longer wires are
weaker than the shorter wires.
•This observation conflicted with classical
material mechanics theory where the length is
irrelevant. Consequently, it was attributed to an
error in da Vinci’s notes and ignored!
•Da Vinci’s observation is, however, in
accordance with the weakest link theory, where
the chain is said to have the strength of its
weakest link.• Accordingly, a wire would have the strength of its weakest section. A
longer wire has a higher likelihood (probability) of having a weaker section
(i.e., with a longer flaw) than a shorter one.
43. Statistics of Strength
•In all three loading
cases, the failure
occurs due to tensile
cracking, and the
maximum stress (i.e.,
tensile strength) occurs
just after crack
initiation.
•However, the volume
of the material taking
the peak stress is
different in each case;
i.e., the volume of
material where the
crack initiate differs.
Only the flaw size
within this volume
matters.
•The strength is higher when this volume is smaller, independent of the total
volume of the specimen.
44. Statistics of Strength
Weibull Model
In this model, the survival probability
of a sample of volume V0 subjected
to a tensile stress is given as:
Where and m are the parameters
that depend on the material.
Lower the value of m, greater is the
variability of the strength. It is called
the Weibull modulus.
0
m
eVPs
0
)( 0
For brick and concrete, m is about 5; for engineered ceramics, it is about
10; and for steel, it is about 100.
A material with a Weibull modulus, m, of about 100 can be treated as
having a single well-defined tensile strength.
45. Statistics of Strength
The parameters and m can be
determined from tests.
Log-log plots of the failure
probability as a function of
strength for 0.2% plain carbon
steel, a conventional alumina
ceramic and specially processed
alumina with a controlled particle
size.
Weibull Model: Dependence on Stress and Volume
If V0 is the volume of the tested samples of a material with parameters
and m, the survival probability of a sample of any other volume V is
given by:
This is the final design equation that gives the dependence of the
survival probability on both applied stress and critically stressed
0
0
m
s
V
V
VP
00
ln
46. REFERENCES
1.
• Fundamentals of Fracture Mechanics by J.F. Knott,
Butterworths, 1973
2.
• Engineering Materials 1 by M.F. Ashby, D.R.H. Jones,
Elsevier, 2005
3.
• Fracture Mechanics: Fundamentals and applications by T.L.
Anderson, CRC Press, 1991
4.
• Advanced Fracture Mechanics, M.F. Kanninen and C.H.
Popelear, Oxford University Press, 1985
5.
• NPTEL Online course on Modern Construction Materials by
Prof.Ravindra Gettu