- Metals undergo necking after yielding due to strain hardening, which increases load capacity and leads to instability when strain hardening equals stress. Necking can be identified on stress-strain curves by finding the point where the tangent has a slope of 1.
- Sheet specimens exhibit two types of necking: diffuse necking over a large area or localized necking in a narrow band along the thickness. Localized necking restricts area decrease to the thickness direction.
- The point of maximum load is determined using Considere's construction, drawing a tangent line from a reference point on the stress-strain curve with a slope of σ/(1+ε).
Strength of Materials Lecture - 2
Elastic stress and strain of materials (stress-strain diagram)
Mehran University of Engineering and Technology.
Department of Mechanical Engineering.
This presentation is by Flt Lt Dinesh Gupta, Associate Professor (Mechanical Engineering) NIET, Alwar (Rajasthan). It covers topic on Fluctuating Stresses related to Machine Design subject.
Experimental stress analysis BE notes by mohammed imranMohammed Imran
7th semester, Experimental stress analysis notes as per VTU syllabus by Mohammed Imran, Asst. Prof., Department of Mechanical Engineering, Ghousia College of Engineering-Ramanagaram-562159
Strength of Materials Lecture - 2
Elastic stress and strain of materials (stress-strain diagram)
Mehran University of Engineering and Technology.
Department of Mechanical Engineering.
This presentation is by Flt Lt Dinesh Gupta, Associate Professor (Mechanical Engineering) NIET, Alwar (Rajasthan). It covers topic on Fluctuating Stresses related to Machine Design subject.
Experimental stress analysis BE notes by mohammed imranMohammed Imran
7th semester, Experimental stress analysis notes as per VTU syllabus by Mohammed Imran, Asst. Prof., Department of Mechanical Engineering, Ghousia College of Engineering-Ramanagaram-562159
Recrystallization is the process in which deformed grains of the crystal structure are replaced by a new set of stress-free grains that nucleate and grow until all the original grains have been consumed. The process is accomplished by heating the material to temperatures above that of crystallization.
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Mumbai University.
Mechanical Engineering
SEM III
Material Technology
Module 2.2
Fatigue Failure:
Definition of fatigue and significance of cyclic stress, Mechanism of fatigue and theories of fatigue failure, Fatigue testing, Test data presentation and statistical evolution, S-N Curve and its interpretation, Influence of important factors on fatigue, Notch effect, surface effect, Effect of pre-stressing, corrosion fatigue, Thermal fatigue.
Dynamic Mechanical Analysis (DMA) is a technique that is widely used to characterize a material’s properties as a function of temperature, time, frequency, stress, atmosphere or a combination of these parameters.
Recrystallization is the process in which deformed grains of the crystal structure are replaced by a new set of stress-free grains that nucleate and grow until all the original grains have been consumed. The process is accomplished by heating the material to temperatures above that of crystallization.
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Mumbai University.
Mechanical Engineering
SEM III
Material Technology
Module 2.2
Fatigue Failure:
Definition of fatigue and significance of cyclic stress, Mechanism of fatigue and theories of fatigue failure, Fatigue testing, Test data presentation and statistical evolution, S-N Curve and its interpretation, Influence of important factors on fatigue, Notch effect, surface effect, Effect of pre-stressing, corrosion fatigue, Thermal fatigue.
Dynamic Mechanical Analysis (DMA) is a technique that is widely used to characterize a material’s properties as a function of temperature, time, frequency, stress, atmosphere or a combination of these parameters.
The following presentation consists of introduction to dielectrics, and includes following topics - Basic terms, Polarization of Dielectric, Polarization method, Internal Field, Clausius-Mossotti Equation, Types of dielectric, Properties of good Dielectric, and Application of Dielectric.
Modeling, Simulation and Design of a Circular Diaphragm Pressure Sensorkhalil fathi
This paper aim in design and analysis
of MEMS Pressure Sensor by using ANSYS
software. A diaphragm based MEMS sensor in
the range of 25MPa by measured center deflection of the circular pressure-sensitive and using the strain gauge for measurement.
Young's modulus by single cantilever methodPraveen Vaidya
Young's modulus is a method to find the elasticity of a given solid material. The present article gives the explanation how to perform the experiment to determine the young's modulus by the use of material in the form of cantilever. The single cantilever method is used here.
Modeling the combined effect of surface roughness and shear rate on slip flow...Nikolai Priezjev
Molecular dynamics MD and continuum simulations are carried out to investigate the influence of shear rate and surface roughness on slip flow of a Newtonian fluid. For weak wall-fluid interaction energy, the nonlinear shear-rate dependence of the intrinsic slip length in the flow over an atomically flat surface is
computed by MD simulations. We describe laminar flow away from a curved boundary by means of the effective slip length defined with respect to the mean height of the surface roughness. Both the magnitude of the effective slip length and the slope of its rate dependence are significantly reduced in the presence of periodic surface roughness. We then numerically solve the Navier-Stokes equation for the flow over the rough surface using the rate-dependent intrinsic slip length as a local boundary condition. Continuum simulations reproduce the behavior of the effective slip length obtained from MD simulations at low shear rates. The slight discrepancy between MD and continuum results at high shear rates is explained by examination of the local velocity profiles and the pressure distribution along the wavy surface. We found that in the region where the curved boundary faces the mainstream flow, the local slip is suppressed due to the increase in pressure. The results of the comparative analysis can potentially lead to the development of an efficient algorithm for modeling rate-dependent slip flows over rough surfaces.
Modeling the combined effect of surface roughness and shear rate on slip flow...Nikolai Priezjev
Molecular dynamics MD and continuum simulations are carried out to investigate the influence of shear rate and surface roughness on slip flow of a Newtonian fluid. For weak wall-fluid interaction energy, the nonlinear shear-rate dependence of the intrinsic slip length in the flow over an atomically flat surface is computed by MD simulations. We describe laminar flow away from a curved boundary by means of the effective slip length defined with respect to the mean height of the surface roughness. Both the magnitude of the effective slip length and the slope of its rate dependence are significantly reduced in the presence of periodic surface roughness. We then numerically solve the Navier-Stokes equation for the flow over the rough surface using the rate-dependent intrinsic slip length as a local boundary condition. Continuum simulations reproduce the behavior of the effective slip length obtained from MD simulations at low shear rates. The slight discrepancy between MD and continuum results at high shear rates is explained by examination of the local velocity profiles and the pressure distribution along the wavy surface. We found that in the region where the curved boundary faces the mainstream flow, the local slip is suppressed due to the increase in pressure. The results of the comparative analysis can potentially lead to the development of an efficient algorithm for modeling rate dependent slip flows over rough surfaces.
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/
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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.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
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When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
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and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
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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.
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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.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
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This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
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.
2. Ideal plastic materials Undergo necking after yielding with no strain
hardening.
Most metals Necking begins at maximum load with strain
hardening increasing load-carrying capacity
Instability occurs when
>
An increase in stress due to reduced
cross-sectional area
The increase in load-carrying
ability due to strain hardening
2
3. The condition of instability, which leads to localized deformation is defined by dP=0.
From the constancy of volume relationship,
From instability condition
So that at a point of tensile instability
3
4. Therefore the point of necking can be obtained from the true stress-strain curve by
Finding the point on the curve
having a sub tangent of unity
The point where the rate of strain
hardening equals the stress
4
5. The maximum load can be determined from Considère’s construction when the stress-strain
curve is plotted in terms of true stress σ and conventional strain e.
Let point A represent a negative strain of 1.
A line drawn from point ‘A’ which is tangent to the stress-strain curve will give maximum load with
the slope of σ/(1+e).
This strain is the true uniform strain εu.
Considère’s construction for the
determination of the point maximum load
5
6. Necking in a uniaxial cylindrical tensile specimen is isotropic. However in a sheet specimen
where the width of the specimen is much higher than the thickness, there are two types of flow
instability:
1) Diffuse necking
Provide a large extent of necking on the tensile specimen similar to necking from a cylindrical
specimen.
Diffuse necking might terminate in fracture but normally followed by localised necking.
2) Localised necking
Localised necking is a narrow band with about equal to the sheet thickness and inclined at an
angle to the specimen axis, across the width of the specimen.
Give no change in width through the localised neck plain strain deformation.
6
7. With localized necking the decrease in specimen area with increasing strain is restricted to the
thickness direction.
From constancy of volume, dε2= dε3= -dε1/2, and dε3 =dt/t
The increasing in load carrying ability due to strain hardening is given by
Equating above two equation
For a power law flow curve, εu=2n for localized necking.
d
t
dt
wtd
wdt
Ad
wdt
Ad
dP
11
2
1
Ad
dP
d
d
Ad
Ad
Ad
dP
11
2
d
d
7
wdtdA
8. Necking introduces a complex triaxial state of stress in the necked region. The neck region is in
effect a mild notch.
The average true stress at necking, which is much higher than the stress would be required to
cause a normal plastic flow due to stresses in width and thickness directions.
(a) Geometry of necked region
(b) Stress acting on element at point ‘O’ 8
9. Bridgman made a mathematical analysis which provides a correction to the average axial stress
to compensate for the introduction of transverse stresses.
This analysis was based on the following assumptions:
a) The contour of the neck is approximated by the arc of a circle.
b) The cross section of the necked region remains circular throughout the test.
c) The von Mises’ criterion for yielding applies.
d) The strains are constant over the cross section of the neck.
According to Bridgman’s analysis, the uniaxial flow stress corresponding to that which would
exist in the tension test if necking had not introduced triaxial stresses is
where, (σx)avg is the measured stress in the axial direction,
R is the radius of curvature of the neck
a is the linear distance.
RaaR
x avg
2/1ln/21
9
10. Measured elongation in tension specimen depends on the gauge length or cross-sectional
area.
The total extension consists of two components, the uniform extension up to necking and the
localized extension once necking begins.
The extent of uniform extension will depend on the Metallurgical condition of the material
(through n) and the specimen size and shape on the development of necking.
The shorter the gauge length the greater the effect of
localized deformation at necking on total elongation
Variation of local elongation with position along gauge
length of tensile specimen
10
11. The extension of a specimen at fracture can be expressed by
Where, α is the local necking extension
euL0 is the uniform extension
The tensile elongation then is given by
According to Barba’s law, and the elongation equation is
LeLL uf 00
e
LL
LL
e u
f
f
00
0
A0
e
L
A
e uf
0
0
11
12. Dimensional relationships of tensile specimens for sheet and round
specimens
Elongation depends on the original gauge length L0. The shorter gauge length the greater the
percentage of elongation.
12
13. Difference between % elongation and reduction of area
% Elongation:
% Elongation is chiefly influenced by uniform elongation and thus it is dependent on the strain-
hardening capacity of the material.
Reduction of area:
Reduction of area is more a measure of the deformation required to produce failure and its chief
contribution results from the necking process.
Because of the complicated stress state in the neck, values of reduction of area are dependent
on specimen geometry and deformation behaviour, and they should not be taken as true
material properties.
Reduction of area is the most structure-sensitive ductility parameter and is useful in detecting
quality changes in the materials.
13
14. Strain rate is applied to the specimen can have an important influence on the stress.
Strain rate unit is s-1.
14
dt
d
Flow stress dependence of
strain rate and temperature
15. The crosshead velocity is v=dL/dt. The rate expressed in terms of conventional linear starin is
The true strain rate is given by
The above equation indicates that for a constant crosshead speed the true strain rate will
decreases as the specimen elongates.
The true strain rate is related to the conventional strain rate by the following equation:
15
e
00
00 1/L-L
L
v
dt
dL
Ldt
Ld
dt
de
e
L
v
dt
dL
Ldt
d
dt
d
1L/Lln 0
e
e
dt
de
edt
de
L
L
L
v
11
10
16. To maintain a constant true strain rate using open loop control the deformation velocity must
increases in proportion to the increases in the length of the specimen as
For deformation occurring at constant volume a constant true strain rate is obtained if the
specimen area changes as
A general relationship between flow stress and strain rate, at constant strain and temperature as
Where m is strain rate sensitivity.
16
tLv exp0
tAA exp0
12
12
12
12
,, /log
/log
loglog
loglog
log
log
ln
ln
TT
m
17. The velocity dislocation motion was very strongly dependent on stress according to
Strain rate is related to velocity of mobile dislocation by
Therefore,
If there is no change in the mobile dislocation density with increasing stress, m’=1/m.
17
'm
Av
bv
'
ln
ln
m
v
ln
ln
ln
ln
ln
ln1
v
m
ln
ln1
'
m
m
18. Strain rate sensitivity (m) indicates any changes in deformation behaviour. Measurement of
strain rate sensitivity can be linked to dislocation concept.
High strain rate sensitivity is a characteristic of superplastic metals and alloys.
From the definition of true strain rate
Combining above two equations
The above equation states that so long as m is less than 1 the smaller the cross sectional area,
the more rapidly the area is reduced.
18
m
C
A
P
or
mm
AC
P
/1/1
1
dt
dA
Adt
dL
L
11
m
m
C
P
AA
dt
dA
/1
/11
mm
m
AC
P
dt
dA
/1
/1
1
19. When m=1 the deformation is Newtonian viscous and dA/dt is independent of ‘A’ and any neck is
simply preserved during elongation and does not propagate inward. As ‘m’ approaches unity, the
rate of growth of incipient necks is drastically reduced.
19
Dependence of tensile
elongation on strain-rate
sensitivity
Dependence of rate of decrease
of area on cross sectional area for
different values of ‘m’
20. Notch tensile test is used to evaluate notch sensitivity (the tendency for reduced tensile ductility
in the presence of a triaxial stress field and steep stress gradients).
Notch tension specimens have been used for fracture mechanics measurements.
Notch tensile specimen
60° notch with a root radius of 0.025 mm or less introduced into a round (circumferential notch)
or a flat (double-edge notch) tensile specimen.
The cross-sectional area under the notch root is one-half of the unnotched area.
20
Notch tensile specimen Stress distribution around tensile notches
21. Notch strength
Notch strength is defined as the maximum load divided by the original cross-sectional area at
the notch.
Due to the constraint at the notch, the notch strength is higher than the tensile strength of the
unnotched specimen.
Notch-strength ratio (NSR) detects notch brittleness (high notch sensitivity) from
If the NSR is < 1, the material is notch brittle.
21
specimen)unnotchedforstrength(tensile
load)maximumatspecimennotched(for
Su
Snet
NSR