Mechanical Vibration: Technical Review and Case Studies on Fatigue Crack and Welding

This article discusses mechanical vibration, fatigue crack, and welding through technical review and case studies. It covers the different structures that can experience fatigue, the impact of defects in welding on welded structures, and gearbox fault analysis. The article also talks about the future plan of fusion reactors and the ferritic-martensitic steel Eurofer97. The subject is relevant to mechanical engineering and the course code and college/university are not mentioned.

Mechanical Vibration

Contents
Introduction 2
Technical review 4
Case -1 (Fatigue crack) 7
Units 7
Model 7
Mesh 8
Solution (A6) 10
Material data 14
Case 2 (welding) 15
Units 15
Model 16
Mesh 17
Solution (A6) 19
Material data 23
Case -3 25
Units 25
Mesh 26
Solution (A6) 28
Material data 32
References 33
1

Introduction:
At the point, when an individual is exposed to the cyclic loadings repeatedly (because of the
fluctuating stress’s action) there are chances of fatigue. Then, the utilized terminology in EN
1993-1-9 form cracks its development at a specific locations of the structure that, is called the
fatigue phenomenon (Nussbaumer A., 1999). The different sorts of structures like the planes,
bridges, boats, frames, overhead cranes, cranes, parts of the machines, turbines, canal lock
doors, reactors vessels, platforms of offshore, pylons, masts, chimneys and the transmission
towers. The cracks can appear in the structures that are subjected to cyclic loadings which are
repeated and could experience gradual harm that represents it with the propagation of cracks.
Fatigue is nothing but a representation of resistance loss with time and a repeated load’s
physical impact on the material differs from that if the static load (Nussbaumer A., n.d.)
Material is always failure in the form of a brittle crack despite of whether it is a brittle or
ductile material. The stress below the main parameters’ static elastic strength influences the
fatigue life. A member’s fatigue life or the structural details are exposed to the cyclic
loadings in a repeated manner is characterized as the quantity of stress cycles that could
remain prior to any failure takes place. Mostly fatigue failure occur. The member or the
geometry of the structural detail depending upon its fabrication or the utilized material, the
four major constraints could highly effect the fatigue strength (or the resistance, both utilized
in the EN 1993-1-9). Thus, the stress range is the difference in stress, or it is commonly
known as the geometry of the structural detail, the features of the material, and the
environment fatigue. If there is any failure under the fluctuating stress which fluctuates or has
cyclic stresses, then there are chances of failure to occur with lower loads, when compared to
the stress under the static load. Even in the normally ductile materials, the metallic structures
(bridges, aircraft, machine components, etc.) 90% of all failures of Fatigue failure is
somewhat brittle i.e., catastrophic. Then, the initiation of Fatigue Process Crack or the
premature progress of the damage Stage I crack growth or the early crack deepening on the
shear planes Stage II crack growth or the development of the precise crack on the planes that
are normal to greatest tensile stress suddenly happen. The surface quality and stress
concentration of sites (micro cracks, indents, interior corners, scratches, steps for dislocation
of slip and so on.) is the initiation of Fatigue Crack and propagation (II) Crack initiation. The
propagation I is Alternate stresses-> slip bands -> surface rumpling Crack. With the crystal
planes and the highly resolved shear stress contains the slow propagation. The flat fracture
surface II: the fast propagation is generally vertical to the stress that is applied and it involves
2

a few grains. Due to a process that is repeatedly been blunting and have been sharpening at a
crack tip Crack grows. The rough fracture surface Brittle vs. Ductile Fracture (F., 1997).
1. Even before the fracture in the ductile materials, there is high deformation of plastic
along with energy absorption (“toughness”) (Seeram Ramakrishna, 2010).
2. Before fracture, the brittle materials contain some deformation of plastic along with
less absorption of energy. Tran’s granular fracture. (R., 1999)
3. Different orientation of cleavage planes in grains could easily cracks pass across the
grains fracture surface plane texture due to the intergranular fracture: The crack
propagation is next to the boundaries of grains (the grain boundaries are deteriorated
or they are embrittled by the segregation of impurity (Donald R. Askeland, 2016).
Severely embrittle steels at Low temperatures. Example is liberty ships, which were
developed while there was World War II, as the initial all-welded ships. Catastrophic fracture
have substantial amount of failed ships. Due to brittle fracture, it is a brittle fracture where the
fatigue cracks the nucleated down at the square’s corners by being hatched and lets it
continuously propagated. Number of factors which impacts the Application of fatigue life;
force; Atmosphere; stress types, Material, confidence Magnitude of surface’ stress Quality
Solutions, Polish surface. Then, bring forth the compressive stresses (pay for the tensile
stresses that are applied) into the layers of the surface. The shot peening fires a little shot into
the high-tech surface which has particle implantation and the laser peening. The Case
Hardening Steel - makes C-or N-rich external layer with the nuclear dispersion that comes
from the harder external layer surface and presents the compressive stresses, by optimizing
the geometry avoid the inside corners, indents and so on. Environment; Application; Loads:
The material; the types of Stresses; certainty Magnitude of stress Quality of the surface
Solutions Polish surface Introduce compressive stresses (make up for the connected ductile
stresses) into the surface layer that is viable by fatigue. Shot Peening discharge little shot into
the surface of a High-tech - particle implantation, laser peening. C-or N-rich external layer by
the nuclear dispersion from the surface of the harder external layer presents the compressive
stresses which optimizes the geometry and avoids the interior corners, and the indents are
made using the Case Hardening. The strength of the fatigue, then the quantitative connection
that exists among the stress range and the stress cycles’ counts for the failure of fatigue, as
they are utilized for the fatigue evaluation of a specific class of auxiliary detail Derail
classification. The numerical assignment that is granted for a specific detail, to provide
guidance of stress vacillation, by considering the end goal for representing which of the
3

fatigue quality bend is really right for the appraisal of fatigue (A complete classification
number demonstrates the fatigue strength’s reference with, ΔσC in N/mm². Because of the
conditions of stress the constant amplitude fatigue restrains the constraining direct or the
shear stress ranging from lower, where no fatigue harm can happen in tests under a steady
amplitude. No fatigue damage occur when there are conditions of variable amplitude, as each
stress range must be lower than its actual limit. Under a history of steady amplitude stress’
activity, the cut-of-limit restrains under the scopes of stress of the outline range which don't
add to the evaluated combined harm of endurance. The failure is conveyed in terms of cycles.
The position weariness quality the life where the failure is communicated in the form of
cycles, under the history of activities that are related to consistent amplitude stress, where a
some of the histories of load might be basic and recurring, whereas in different cases, it might
be totally irregular. They can also have Constant or variable amplitudes. Fatigue
behaviour/properties for fatigue design for simple cases’ constant amplitude loading is
utilized for material obtaining. A few real life load histories could be modelled occasionally
with the constant amplitude as well. curve has been developed by German August Wohler for
his systematic fatigue tests done in the 1870’s.S-N Curve plots the diagram of amplitude of
the nominal stress as the cycles’ count to the failure for the un-notched (smooth) specimens
Wohler’s Curve, S-N Curve.
Technical review:
1. Recent advances in analytical techniques for estimating fatigue crack initiation lives
of structures and components have made fatigue analysis a valuable tool for design
engineers. A methods for gathering the long duration (in terms of months)
information, utilizing the microcomputer devices, and then data interpretation in a
helpful way for the architect, is described. Then, the role of fatigue and service history
analysis in the overall product design analysis is reviewed and the requirement of a
data collection system defined. (Socie D., 1979).
4

2. From a literature review which was directed for evaluating the impacts of the defects
of weld upon the welded structures’ failures. This exertion was concentrated on the
failure of capacity tank with the emphasis on those that are formed just for the
cryogenic liquid control, so as to evaluate the importance of the past failure of
capacity tank, in respect to nine percent storage tanks of nickel steel, which are
utilised now. The thought of previous failures could be utilized as experience and gain
knowledge from it to protect the vessel’s integrity. Besides the other failures that are
documented, there exists the report of three failures of cryogenic storage tanks.
Among which, the Liquefied Natural Gas (LNG) tank is one, then the rest were
intended for storing the liquid ethylene. In spite of the fact that subtle elements of
configuration contrasted marginally, the general plan referred to the idea of, “Tank
inside a tank”. From the literature review, in every single failure, a break of the
external tank uprightness came about when there was interaction with the cryogenic
liquid and the external tank’s wall. Thus, it recognized the point that the external steel
divider was fragile at the service temperatures. Additionally, in the above discussed
failures, this literature review has uncovered a unique format of failures in the
pressure vessels which are the results of defective welds (typically the filet welds)
related with the attachment of nozzle with the branch networks. Therefore, these are
some of the doubtless zones of distress in the storage tanks that are cryogenic and the
ones that are outlined completely throughout the survey (Barnes C.R. M., 1984).
3. In the beginning, the gearbox’s fault analysis was quite imperative to maintain the
strategic distance from the failures of catastrophic. The Condition indicators (CI) are
then utilized for measuring the vibration level that is produced by the gears that are
defected. An exhaustive correlation of different CIs, i.e., RMS, factor of peak ,
kurtosis, FM0, FM4, M6A, NB4, NA4, vitality ratio, vitality operator and a couple of
newly proposed CIs (PS-I and PS-II), are all executed for no break, introductory split
and propelled split for various profiles that are fluctuating the speed of the input.
Thus, this relative examination demonstrates that there exists indicator responsiveness
towards the detection of crack. The consideration made here refers to, the constrained
speed variances and the quickly fluctuating speed. The outcomes recommend that the
recently proposed CIs are more vigorous, steady and compelling towards the
identification of crack under the profiles of speed that keep fluctuating. Modified time
5

synchronous averaging (MTSA) is likewise proposed for expanding the signal-to-
noise ratio (SNR) (Sharma V., 2016).
4. According to M. Mahler and J. Aktaa, the future plan of the fusion reactors are the
ferritic-martensitic steel Eurofer97, which are the primary contender for the
application of in-vessel auxiliary, for having the capacity of withstanding the cruel
conditions such as, light and the cyclic loading under the temperatures that are
elevated. In the event of high temperatures, the fatigue as well as the creep harm ends
up critically and thus it must be considered. In the previously supported Creep-
Fatigue Assessment (CFA) apparatus, which was created for the Finite Element
software ANSYS APDL, as a post-processor inside the casing of Engineering Data
and Design Integration (EDDI), in the fusion of EURO. This instrument was initially
in view of the elastic Creep-Fatigue principles of ASME Boiler Pressure Vessel Code
(BPVC) Section III Division 1 Subsection NH Appendix T. These days, the
instrument can naturally recognize the basic districts related to the Creep-Fatigue
harm in the ANSYS APDL and in the Workbench with the help of the nearby stress,
greatest range of elastic strain and the temperature from the elastic thermo-mechanical
Finite Element examination. The stress linearization’s utilization in the elastic
investigation permits the count of the adjusted proportional strain run along with the
inelastic impacts for determining the suitable count of the cycles, creep and fatigue
damage division. For the Creep-Fatigue Assessment (CFA), the post-processing
configuration fatigue bends, creep stress versus time to burst the bends, monotonic
and isochronous stress versus strain bends have been utilized as a part of combination
with the Creep-Fatigue harm interaction graph for portraying the Creep-Fatigue
conduct of Eurofer97. As it is notable that the Eurofer97 indicates the cyclic
softening, an adjusted Creep-Fatigue administer has been executed in the CFA device
for enhancing the creep damage’s underestimation. Hence, further it changed the lead
utilization for figuring out the creep harm, where the stress versus strain and
configuration creep bends of the cyclic mollified material, for certain portions of the
lifetime and an enhanced Creep-Fatigue harm interaction chart of Eurofer97. In the
situations where, the elastic investigation of ASME BPVC is excessively
preservationist, inelastic examination can be utilized to ascertain add up to strain
straightforwardly instead of the expectation utilized as a part of the elastic
examination. Hence, such an inelastic method for the Creep-Fatigue Assessment is
6

less entangled when contrasted with the elastic course on the grounds that lone a
couple of ventures according to the ASME BPVC, which are considered as vital. By
the by more endeavors for the Finite Element recreation along with the required
inelastic material conduct. Thus, the summary states that, the CFA apparatus could be
utilized for a quick Creep-Fatigue assessment. It basically permits the quick
distinguishing proof of Creep-Fatigue harm for a basic part that is created by
Eurofer97 (Mahler M., 2018).
5. According to Ojasvi Singh and Vikas Satpal Sharma, the authors have come to a
conclusion that, the tensile testing as well as the fatigue testing is completed with a
thorough analysis in the Ansys workbench at similar load and similar condition. Thus,
such sort of testing are finished on a couple of plates that are welded with the
implementation of filler material among the plate’s three corners, which will be
welded on the substance, of the material’s other face. This research shows that the
plate material are changed every now and then for deciding various outcomes, for the
specific materials. At the point when these plates are broke down under same
condition then least mishaps were checked for different materials such as, Copper
alloy, Aluminum, structural steel and the Stainless steel. All these examination are
finished with the implementation of 1000N power on one of the plates’ face (Singh
O., 2017).
7

Case -1 (Fatigue crack)
Units
We take the unit system Metric (m, kg, N, s, V, A) Degrees rad/s Celsius, angle in degree,
rotational velocity in Rad/s and Celsius for temperature.
Model
The geometry about the model objective name is referred as, Geometry. The state is
completely defined, where the source is C:\users\7\destop\fatigue\part1.Step, Type is step
file, and Length unit is Metres, then the element control is controlled through a Program, the
display style is the Body colour, the Length x is 0.1 m, Length y is 0.1 m, Length z is 0.5 m,
Volume is 3.927e-003 m3, mas is 30.827 kg, Scale factor value is 1, bodies is 1, Actives
bodies is 1, Nodes is 1, Element is 480, then Mesh metric is nothing, the Solid bodies are yes,
the Surface bodies are yes, The Parameter is yes, where the Parameter key is DS, the
Attributes is no, the Named selection is no, the Material properties are no, the Use
Associativity is yes, then the Coordinate System is no, Reader Mode Saves Updated File no,
Use Instances is yes, Compare Part On Update is no, attach file via temp file is yes,
Temporary Directory is C:\Users\AppData\Local\Temp, Analysis Type is 3-D, Mixed Import
Resolution is none, Decomposed Disjoint Geometry is yes, Enclosure and Symmetry
Processing is yes,
8

About the Parts: Object Name is Part 1, state is Meshed, and Visibility is yes, Transparency is
1, Suppressed is no, Stuffiness Behaviour is Flexible, Coordinate System is Default
Coordinate System, Reference Temperature taken By Environment, Assignment is Structural
Steel, Nonlinear Effects is yes, Thermal Strain Effects is Yes, Length X is 0.1 m, Length Y is
0.1 m , Length Z is 0.5 m, Volume is 3.927e-003 m2 , Mass is 30.827 kg, Centroid X is
1.0909e-018 m, Centroid Y is 4.0727e-018 m, Centroid Z is 0.25 m is Moment of Inertia Ip1
is 0.65375 kg m2 , Moment of Inertia Ip2 is 0.65375 kg m2 , Moment of Inertia Ip3 is
3.7662e-002 kg m2 , Nodes is 2467, Elements is 480, Mesh Metric is nothing,
The Coordinate system: Object Name is Global Coordinate System, State is Defined
completely, the type is Cartesian, the Coordinate System ID is 0, the Origin X is 0 m, the
Origin Y is 0.m, the Origin Z is 0.m, then the X Axis Data [1.0.0.], the Y Axis Data is
[0.1.0.], and the Z Axis Data is [0.0.1.],
The Mesh
The Object Name is called as Mesh, the State is resolved, and the Display Style is Body
Colour, the Physics Preference is Defaults, the Relevance is 0, the Use Advance Size
9

Function is off, the Relevance Centre is Coarse, the Element Size Default, Initial size Seed is
Active Assembly, and Smoothing is Medium, the Transition is Fast, Span Angle Centre
Coarse, the minimum Edge Length is 0.157080 m, the Use Automatic Inflation is None,
Inflation Option is Smooth Transition, Transition Ratio is 0.272, Maximum Layers is 5,
Growth Rate is 1.2, Inflation Algorithm is Pre, View Advanced Options is No, Triangle
Surface Masher is Program Controlled, Topology Checking is No, Number Of CPUs for
Parallel Part Meshing is Program Controlled, Shape Checking is Standard Mechanical,
Element Midsize Nodes is Program Controlled, Straight Sides Elements is No, Number of
Retries is Default(4), Extra Retries For Assembly is Yes, Rigid Body Behaviour is
Dimensionally Reduced, Mesh Morphing is Disabled, Pinch Tolerance is Please Define,
Generate Pinch On Refresh is No, Automatic Mesh Based DE featuring is on, DE featuring
Tolerance is Default, Nodes is 2467, Elements is 480, Mesh Metric is Nothing.
Model (A4) > Analysis: Object Name is a Static Structural (A5), State is solved, Physics
Type is Structural, Analysis Type is Static Structural, Solver Target is Mechanical APDL,
Environment Temperature is 22° C, Generate Input Only is No.
Analysis setting of Static Structural (A5) - Model (A4)
In this case the settings of the software are -
Name of the object - Analysis setting
State - Fully defined
Number of steps - 1
Current step number - 1
Step end time - 1 sec.
Auto time stepping program - Controlled
Solve type - Program Controlled
Weak Spring - Program controlled
Solver Pivot checking - program controlled
Large deflection - off
Inertia relief - off
10

Generate restart point - program controlled
Retention of file after solve - No
Newton Rap son - program controlled
Force convergence - program controlled
Moment convergence - program controlled
Rotation convergence - program controlled
Displacement convergence - program controlled
Stabilization - off
Stress - yes
Strain - yes
Line search - program controlled
Nodal Force - No
Stabilization - All time point
Contact Miscellaneous - No
General miscellaneous - No
Nonlinear solutions - No
Solver Unit - Active system
Solver unit system - Mks
Directoryforsolverfileis:- C:\Users\7\AppData\Local\Temp\WB_R7_4676_2\
unsaved_project_files\dp0\SYS\MECH\,
Save MAPDL db - yes
Future analysis - None
Settings of static structural (A5) loads for Model (A4)
In this case software settings are as follows :-
Object name - Fixed Support
11

Scoping Method - Geometry selection
State - Fully defined
Suppress - NO
Geometry - 1 face with fixed support/ movement
Defined - Using Vector
Magnitude - 100 N.m ramped
Behaviour - Deformable
Direction - defined
Pinball region - all
Solution (A6) for Model (A4) using static structural (A5) :-
In thi case settings for software are as given below:-
Object Name - Solution (A6)
Maximum refinement loop - 1
State - solved
Refinement depth - 2
Status - done
Calculation of beam selection result - No
Now calculation is done for object name solution information of Model (A4) for static
structural (A5):-
Object name - Solution information
Solution output - Solver output
State - solved
update interval - 2.5 sec.
Newton rap son residual - 0
Active visibility - Yes
All connection -FE to all nodes
Display point - all
Display type - line
Line thickness - single
12

Line colour - Connection type
Visible on result - no
Now settings for result of the Model (A4) for static structural (A5) in which object name
is equivalent stress :-
Object name - equivalent stress
Scoping method - Geometry selection
Type of geometry - Equivalent stress and total deformation
State - solved
Display time - last
Suppressed - No
Calculate time history - yes
Option for display - Average ( minimum is 87947 pa)
Load step - 1
Substep - 1
Iteration number - 1
13

We find the solution that Maximum stress is - 9.166e+005 and minimum stress is 87947 pa
14

In the result it was found that maximum deformation is - 3.314e-006 and value for minimum
deformation is 0 .
Settings for fatigue tools solution (A6) of model (A4) for static structural (A5):-
object Name - Fatigue tool
State - solved
Fatigue strength factor (kf) - 1
Fatigue strength type - fully revised
Scale factor - 1
Display time - end time
Type of Analysis - Stress life
Component of Stress - equivalent
Mean stress theory - None
15

Unit - Cycle ( 1 cycle = 1 cycle)
For fatigue tools solution(A6) is given Model (A4) for static structural (A5)
16

Results of fatigue tool of solution (A6) for model (A4), static structural (A5):-
Value of design life - 1.e +009 cycle
Minimum life - 1.e+008 cycle
Factor of safety - greater than 15
Data for the material used in the experiment are :-
Material - Structural steel
Density of steel - 7850 kg m-3
Coefficient of thermal expansion - 1.2e-005c-1
Value of specific heat - 434 JKg-1c-1
Thermal conductivity - 60.5 Wm-1c-1
Resistivity - 1.7e-007 ohm m
Compressive ultimate strength - 0
Compressive yield strength - 2.5e+008
Tensile ultimate strength - 4.6e+008
Tensile yield strength - 2.5e+008
Relative permeability - 10000
Reference temperature - 22° c
17

Table for alternating stress and mean stress of structural steel : -
Alternating stress (pa) Number of Cycle Mean stress (pa)
3.99e+009 10 0
2.827+009 20 0
1.896+009 50 0
1.413e+009 100 0
1.069e+009 200 0
4.41e+009 2000 0
2.62e+009 10000 0
2.14e+009 20000 0
1.38e+009 1e+005 0
1.14e+009 2e+005 0
8.62e+009 1e+006 0
Table for Strain life parameter of a structural steel: -
Coefficient
of Strength
(pa)
Exponent of
strength
Coefficient
of Ductility
Exponent of
Ductility
Cyclic
strength
coefficient
pa
Cyclic strain
hardening
exponent
9.2e+008 -0.106 0.213 -0.47 1e+009 0.2
18

Case 2 : Welding
Unit system
Unit system - m, s, V, N, kg, A
Degree - rad/s, celsius
Angle - Degree
Rotational velocity - Rad/s
temperature - celsius
Model for geometry : -
Object name - Geometry
State - fully defined
Source - C:\users\7\desktop\fatigue\part1.Step
Source type - step file
Length unit - metres
Display style - Body color
Element control - program controlled
Length X = 0.2 m , Length Y = 0.1 m and Length Z = 0.7 m
Mass - 33.936 kg
Volume - 4.3231e-003 m3
Bodies - 1
19

Active bodies - 1
Solid bodies - yes
Scale factor - 1
Nodes - 936
Element - 460
Mesh metric - None
Surface bodies - Yes
Parameter - Yes
Parameter key - DS
Attributes - No
Named selection- No
Material properties - No
Use of Associativity - Yes
Coordinate System - No
Reader Mode Saves Updated File no
Use Instances - Yes
Compare Part - On
Update - No
attach file via temp file - Yes
Temporary Directory is C:\Users\AppData\Local\Temp
Type of analysis - 3-D
Mixed Import Resolution - None
Decomposed Disjoint Geometry - Yes
Enclosure and Symmetry Processing - Yes
Description about the parts : -
Name of the object - part 1
State - Meshed
Visibility - Yes
Transparency - 1
Suppressed - No
Stiffness behaviour - Flexible
Coordinate System - Default Coordinate System
Reference Temperature - Taken by Environment
Assignment - Structural Steel
20

Thermal strain effects - Yes
Nonlinear Effects - Yes
Mass - 33.936 kg
Volume - 4.3231ee-003 m3
Length X = 0.1 m, Length Y = 0.1 m , Length Z = 0.7 m
Centroid X = 1.103e-012 m, Centroid Y = -9.727e-014 m, Centroid Z = 0.28216 m
Moment of Inertia Ip1 = 1.0078 kg m2
Moment of Inertia Ip2 = 1.0079 kg m2
Coordinate system:
Object Name - Global Coordinate System
State - Fully Defined,
Type - Cartesian
Coordinate System ID - 0
Origin X = 0 m, Origin Y = 0m, Origin Z = 0m,
X Axis Data = [1.0.0.], Y Axis Data = [0.1.0.], Z Axis Data = [0.0.1.],
Centroid Y = 4.0727e-018 m, Centroid Z =0.25 m
Moment of Inertia Ip1 = 0.65375 kg m2
Moment of Inertia Ip2 = 0.65375 kg m2
Moment of Inertia Ip3 = 3.7662e-002 kg m2
Nodes - 2467
Elements - 480
Mesh Metric - None,
21

Mesh
Object Name - Mesh
State - solved
Style of display - Body Colour
Relevance - 0
Physics Preference - Defaults
Relevance centre - Coarse
Advanced size function - off
Element size - default
Smoothening - medium
Span angle centre - coarse
Transition - fast
Transition ratio - 0.272
Inflation option - Smooth transition
Minimum edge length - 1.5708e-002 m
22

Automatic inflation - none
Growth Rate - 1.2
Inflation algorithm - pre
Maximum layer - 5
View advanced option - No
Topology checking - No
Straight side element - No
Number of CPUs for Parallel Part Meshing - Program Controlled
Shape checking - standard mechanical
Triangle surface mesher - Program Controlled
Element mid size node - program controlled
Number of retries - 4 (default)
Extra retries for assembly - yes
Automatic Mesh Based DE featuring - On
DE featuring tolerance - default
Nodes - 936
Elements - 460
Mesh matrix - None
Pinch Tolerance - please define
Rigid body behaviour - Dimensionally reduced
Mesh morphing - disabled
Generate pint - On
Refresh - No
Analysis for Model (A4): -
Object Name - Static Structural (A5)
State - solved
Type of analysis - Static structural
Type of physics - Structural
Solver Target - Mechanical APDL
Environment Temperature - 22° C
Generate Input Only - No.
Analysis setting of Static Structural (A5) - Model (A4)
In this case the settings of the software are -
23

Name of the object - Analysis setting
State - Fully defined
Number of steps - 1
Current step number - 1
Step end time - 1 sec.
Auto time stepping program - Controlled
Solve type - Program Controlled
Weak Spring - Program controlled
Solver Pivot checking - program controlled
Large deflection - off
Inertia relief - off
Generate restart point - program controlled
Retention of file after solve - No
Newton Rap son - program controlled
Force convergence - program controlled
Moment convergence - program controlled
Rotation convergence - program controlled
Displacement convergence - program controlled
Stabilization - off
Stress - yes
Strain - yes
Line search - program controlled
Nodal Force - No
Stabilization - All time point
24

Contact Miscellaneous - No
General miscellaneous - No
Nonlinear solutions - No
Solver Unit - Active system
Solver unit system - Mks
Directoryforsolverfileis:- C:\Users\7\AppData\Local\Temp\WB_R7_4676_2\
unsaved_project_files\dp0\SYS\MECH\,
Save MAPDL db - yes
Future analysis - None
Settings of static structural (A5) loads for Model (A4)
In this case software settings are as follows :-
Object name - Fixed Support
Scoping Method - Geometry selection
State - Fully defined
Suppress - NO
Geometry - 1 face with fixed support/ movement
Defined - Using Vector
Magnitude - 100 N.m ramped
Behaviour - Deformable
Direction - defined
Pinball region - all
25

Solution (A6) for Model (A4) using static structural (A5) :-
In thi case settings for software are as given below:-
Object Name - Solution (A6)
Maximum refinement loop - 1
State - solved
Refinement depth - 2
Status - done
Calculation of beam selection result - No
Now calculation is done for object name solution information of Model (A4) for static
structural (A5):-
Object name - Solution information
Solution output - Solver output
State - solved
update interval - 2.5 sec.
Newton rap son residual - 0
Active visibility - Yes
All connection -FE to all nodes
Display point - all
Display type - line
Line thickness - single
26

Line colour - Connection type
Visible on result - no
Now settings for result of the Model (A4) for static structural (A5) in which object name
is equivalent stress :-
Object name - equivalent stress
Scoping method - Geometry selection
Type of geometry - Equivalent stress and total deformation
State - solved
Display time - last
Suppressed - No
Calculate time history - yes
Option for display - Average ( minimum is 87947 pa)
Load step - 1
Substep - 1
Iteration number - 1
27

From the above figure values of maximum stress - 8.3882e+006 pa and minimum stress is
3682.7 pa.
28

29

Settings for fatigue tools solution (A6) of model (A4) for static structural (A5):-
object Name - Fatigue tool
State - solved
Fatigue strength factor (kf) - 1
Fatigue strength type - fully revised
Scale factor - 1
Display time - end time
Type of Analysis - Stress life
Component of Stress - equivalent
Mean stress theory - None
Unit - cycle (1 cycle = 1 cycle)
30

Figure 5 : - Solution (A6) for fatigue tools
Results for fatigue tools of solution (A6) for model (A4) static structural (A5) -
Value of design life - 1.e + 009 cycle
Minimum life - 1.e + 006 cycle
factor of safety - Greater than 15
31

Data for the material used in the experiment are :-
Material - Structural steel
Density of steel - 7850 kg m-3
Coefficient of thermal expansion - 1.2e-005c-1
Value of specific heat - 434 JKg-1c-1
Thermal conductivity - 60.5 Wm-1c-1
Resistivity - 1.7e-007 ohm m
Compressive ultimate strength - 0
Compressive yield strength - 2.5e+008
Tensile ultimate strength - 4.6e+008
Tensile yield strength - 2.5e+008
Relative permeability - 10000
32

Reference temperature - 22° c
Table for values of structural steel of alternating stress and mean stress (pa)
Alternating stress (pa) Number of Cycle Mean stress (pa)
3.99e+009 10 0
2.827+009 20 0
1.896+009 50 0
1.413e+009 100 0
1.069e+009 200 0
4.41e+009 2000 0
2.62e+009 10000 0
2.14e+009 20000 0
1.38e+009 1e+005 0
1.14e+009 2e+005 0
8.62e+009 1e+006 0
Table 25
Strain life parameter for structural steel
Coefficient
of strength
(pa)
Exponent of
strength
Coefficient
for Ductility
Exponent of
Ductility
Cyclic
strength
coefficient
(pa)
Cyclic strain
hardening
exponent
9.2e+008 -0.106 0.213 -0.47 1e+009 0.2
33

Case -3
Unit system
Unit system - m, N, s, V, kg, A
Degrees - rad/s , celsius
Angle - Degree
Rotational velocity - rad/sec.
Temperature - celsius
For Model object name is Geometry.
Model for geometry : -
Object name - Geometry
State - fully defined
Source - C:\users\7\desktop\fatigue\part1.Step
Source type - step file
Length unit - metres
Display style - Body color
Element control - program controlled
Length X = 0.2 m , Length Y = 0.1 m and Length Z = 0.7 m
Mass - 33.929 kg
34

Volume - 4.3231e-003 m3
Bodies - 1
Active bodies - 2
Solid bodies - yes
Surface Bodies - yes
Scale factor - 1
Nodes - 1627
Element - 611
Mesh metric - None
Attributes - No
Named selection - No
Parameter - yes
Parameter key - DS
Properties of material - No
Use of Associativity - Yes
Use of coordinate system - No
Temporary Directory - C:\Users\AppData\Local\Temp
Type of analysis - 3-D
Mixed import resolution - None
Update - No
Attache file via temp file - Yes
Compare part - On
Use of instances - Yes
Reader mode can save update file - No
Decomposed Disjoint Geometry - Yes,
Enclosure and Symmetry Processing - Yes
Description about the parts : -
Name of the object - part 1
State - Meshed
Visibility - Yes
Transparency - 1
Suppressed - No
Stuffiness Behaviour - Flexible
Coordinate System = Default Coordinate System
35

Reference Temperature taken By Environment
Assignment - Structural Steel
Nonlinear Effects- Yes
Thermal Strain Effects - Yes
Length X = 0.1 m, Length Y = 0.1 m Length Z = 0.57973 m,
Mass - 1.5357 kg
Volume - 4.0565e-003 m3
Centroid X = -4.6418e-005 m, Centroid Y = 9.0242e-009 m, Centroid Z = 0.25921 m
Moment of Inertia Ip1 = 0.73407 kg , m2 ,
Moment of Inertia Ip2 = 0.7341 kg m2,
Moment of Inertia Ip3 = 3.823e-002 kg m2,
Nodes - 990
Elements - 499
Mesh Metric - None
Coordinate system:
Object Name - Global Coordinate System,
State - Fully Defined,
Type - Cartesian,
Coordinate System ID - 0
Origin of X = 0 m, Origin of Y = 0 m, Origin of Z = 0 m
X Axis Data = [1.0.0.], Y Axis Data = [0.1.0.], Z Axis Data = [0.0.1.]
36

Mesh
Object Name - Mesh
State - solved
Style of display - Body Colour
Relevance - 0
Physics Preference - Defaults
Relevance centre - Coarse
Advanced size function - off
Element size - default
Smoothening - medium
Span angle centre - coarse
Transition - fast
Transition ratio - 0.272
Inflation option - Smooth transition
Minimum edge length - 1.5708e-002 m
37

Automatic inflation - none
Growth Rate - 1.2
Inflation algorithm - pre
Maximum layer - 5
View advanced option - No
Topology checking - No
Straight side element - No
Number of CPUs for Parallel Part Meshing - Program Controlled
Shape checking - standard mechanical
Triangle surface mesher - Program Controlled
Element mid size node - program controlled
Number of retries - 4 (default)
Extra retries for assembly - yes
Automatic Mesh Based DE featuring - On
DE featuring tolerance - default
Nodes - 1627
Elements - 611
Mesh matrix - None
Pinch Tolerance - please define
Rigid body behaviour - Dimensionally reduced
Mesh morphing - disabled
Generate pint - On
Refresh - No
Analysis for Model (A4): -
Object Name - Static Structural (A5)
State - solved
Type of analysis - Static structural
Type of physics - Structural
Solver Target - Mechanical APDL
Environment Temperature - 22° C
Generate Input Only - No.
Analysis setting of Static Structural (A5) - Model (A4)
In this case the settings of the software are -
38

Name of the object - Analysis setting
State - Fully defined
Number of steps - 1
Current step number - 1
Step end time - 1 sec.
Auto time stepping program - Controlled
Solve type - Program Controlled
Weak Spring - Program controlled
Solver Pivot checking - program controlled
Large deflection - off
Inertia relief - off
Generate restart point - program controlled
Retention of file after solve - No
Newton Rap son - program controlled
Force convergence - program controlled
Moment convergence - program controlled
Rotation convergence - program controlled
Displacement convergence - program controlled
Stabilization - off
Stress - yes
Strain - yes
Line search - program controlled
Nodal Force - No
Stabilization - All time point
39

Contact Miscellaneous - No
General miscellaneous - No
Nonlinear solutions - No
Solver Unit - Active system
Solver unit system - Mks
Directoryforsolverfileis:- C:\Users\7\AppData\Local\Temp\WB_R7_4676_2\
unsaved_project_files\dp0\SYS\MECH\,
Save MAPDL db - yes
Future analysis - None
Settings of static structural (A5) loads for Model (A4)
In this case software settings are as follows :-
Object name - Fixed Support
Scoping Method - Geometry selection
State - Fully defined
Suppress - NO
Geometry - 1 face with fixed support/ movement
Defined - Using Vector
Magnitude - 100 N.m ramped
Behaviour - Deformable
Direction - defined
Pinball region - all
40

Settings for solution (A6) of Model (A4) for static structural (A5): -
Object name :- Solution A6
State - solved
Maximum refinement loops - 1
Refinement depth - 2
Status - done
Calculating beam selection result - No
For object name solution information settings are done of model (A4) for static
structural (A5) :-
Object name - Solution information
State - solved
Solution output - solver output
update interval - 2.5 sec.
Newton rap son residual - 0
41

Display point - all FE connection of nodes
Line colour - Connection type
Visible on result - No
Display type - lines
Thickness of lines - single
Active visibility - yes
Result for solution (A6) of model (A4) for static structural (A5) is :-
Name of object - Equivalent stress
Type of State - solved
Scoping method - Geometry selection
Geometry type - Equivalent stress and total deformation
Display time - last
Calculate history for time - yes
Suppressed - No
Option for display - Average
Minimum stress - 87947 pa
Load step - 1
sub step - 1
Number of iteration - 1
Figure given below is for equivalent stress :-
42

Values for maximum equivalent stress - 8.2189e+006 pa and minimum equivalent stress is -
27918 pa.
Solution (A6) for total deformation of static structural is given :-
43

Value for maximum deformation - 1.2366e-005 and value for minimum deformation - 0 .
Settings for object name fatigue tool is described below of model (A4) for static structural
(A5):-
Object name - Fatigue tool
state - solved
Strength factor for fatigue (Kf) - 1
Fatigue type - fully revised
Scale factor - 1
Display time - end time
Mean stress theory - None
Analysis type - stress life
Component for stress - Equivalent
44

Unit name - cycle ( 1 cycle = 1 cycle)
In this graph solution for fatigue tools is given.
Solution (A6) - fatigue tools of Model (A4) for static structural (A5)
After running software we find:-
Design life value - 1.e+009 cycle
Factor of safety maximum - 15
Factor of safety minimum - 1.e +006 cycle
45

Data for the material we used in this experiment are as follows :-
Material - Structural steel
Density - 7850 kg m-3
Thermal expansion coefficient - 1.2e -005c-1
Value of specific heat - 434 Jkg-1c-1
Value for thermal conductivity - 60.5 Wm-1c-1
Resistivity - 1.7e-007 ohm m
Compressive yield strength - 2.5e+008
Compressive ultimate strength - 0
Strength of tensile yield- 2.5e+008
Ultimate strength of tensile- 4.6e+008
reference temperature - 22° c
Relative permeability - 10000,
For the different number of cycles the values of alternating stress and mean stress are
calculated and shown below in table.
46

Alternating stress (pa) Number of Cycle Mean stress (pa)
3.99e+009 10 0
2.827+009 20 0
1.896+009 50 0
1.413e+009 100 0
1.069e+009 200 0
4.41e+009 2000 0
2.62e+009 10000 0
2.14e+009 20000 0
1.38e+009 1e+005 0
1.14e+009 2e+005 0
8.62e+009 1e+006 0
Strain life parameter for structural steel
Coefficient
for strength
(pa)
Exponent of
strength
Coefficient
for ductility
Exponent of
ductility
Coefficient
for cyclic
strength (pa)
Hardening
exponent for
cycling
strain
9.2e+008 -0.1060 0.213 -0.47 1e+009 0.20
47

References
Barnes C.R. M., K. F. W., 1984. Theoretical and Applied Fracture Mechanics.
Structural failures
precipitated by weld discontinuities, pp. 73-93.
Donald R. Askeland, W. J. W., 2016.
Science and Engineering of Materials, SI Edition. Channel Centre
Street : Cengage Learning.
F., E., 1997.
Fatigue Damage, Crack Growth and Life Prediction. Alberta: Fernand Ellyin.
J., S., 2009.
Fatigue of Structures and Materials. Delft: Springer.
Mahler M., A. J., 2018. Nuclear Materials and Energy.
Eurofer97 Creep-Fatigue assessment tool for
ANSYS APDL and workbench, pp. 85-91.
Nussbaumer A., B. L. D. L., 1999.
Fatigue Design of Steel and Composite Structures: Eurocode 3:
Design of. New York: Wiley.
Nussbaumer A., B. L. D. L., n.d.
Fatigue Design of Steel and Composite Structures: Eurocode 3: Design
of .. New York: John Weley & Sons.
R., C., 1999.
Introduction to Manufacturing Processes and Materials. Broken Sound Parkway: CRC
Press.
Seeram Ramakrishna, M. R. T. .. S. K. W. O. S., 2010.
Biomaterials: A Nano Approach. Sound
Parkway : CRS Press.
Sharma V., P. A., 2016. Measurement.
Gear crack detection using modified TSA and proposed fault
indicators for fluctuating speed conditions, pp. 560-575.
Singh O., V. S. S., 2017. Materialstoday.
Analysis and Comparison of Total Deformation of Welded
Plates in Tensile and Fatigue Tests using ANSYS, pp. 8409-8417.
Socie D., S. G. H., 1979. International Journal of Fatigue.
A field recording system with applications to
fatique analysis, pp. 103-111.
48