 Open Access
 Total Downloads : 0
 Authors : Rabi Pathak , Nabin Giri , Manmohan Thakur , Sujan Uprety Pramod K C
 Paper ID : IJERTV7IS080075
 Volume & Issue : Volume 07, Issue 08 (August – 2018)
 Published (First Online): 05012019
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Determination of Stress Concentration Factor by Different Methods
Determination of Stress Concentration Factor by Different Methods
Stress Concentration Factor
Rabi Pathak,Nabin Giri
UG student(B.E Mechanical)
Nitte Meenakshi Institute of Technology Bangalore,India
Abstract In this modern day, FOS (Factor of Safety) considered is kept low to avoid unnecessary wastage of material due to which the degree of precision of stress value should be greater. The value of stress gets deviated from its precise value due to stress raisers (grooves notches etc.). So it is very important to analyze and find out the stress concentration factor. In this paper we discuss about the methods to determine the stress concentration factor.
INTRODUCTION
What is stress concentration and stress concentration factor?
A stress concentration often called as (stress raiser) is location where stress is concentrated. When a body of discontinuity is subject to different types of loading then more stress is concentrated at the discontinuities. The structure can fail due to such stress concentration, when concentration stress exceeds Material strength. Stress concentration factor Kt is a dimensionless factor that is used to qualify how concentrated the stress is in material. It is defined as the highest stress element to nominal stress in element.
Kt= Max/ Nom
The experimental, numerical and analytical studies were conducted to investigate the stress concentration around a U notch grooved on a shaft.
The tension test was carried out on the grooved shaft using UTM (universal testing machine) and maximum stress is calculated using experimental approach and stress concentration factor was calculated
Kt= Max/ Nom Where,
Nom =Force/Original area
The stress concentration factor was calculated from the graph of stress concentration factor of grooved shaft in tension.We used the graph from DDHB VOLUME 1 by DR. K
Manmohan Thakur,Pramod K.C,Sujan Uprety
UG student(B.E Mechanical)
Nitte Meenakshi Institute of Technology Bangalore,India
METHODS TO DETERMINE STRESS CONCENTRATION FACTOR
NUMERICAL APPROACH
We can find the value of stress concentration factor by using the stress concentration factor graph for respective element , type of discontinuity and the loading condition (Axial,Bending or Torsional) .Here we have a solid shaft with a Ugroove on the circumference and axial loading is given.Thus from the graph we have ;
Fig: Grooved shaft
Diameter of shaft(D)=25mm Diameter at the fillet part(d)=23mm Fillet radius(r)=1mm
Now,
LINGAIAH. Kt values are also calculated using Matlab coding and using software.
For Analytical approach FEA software ANSYS is used where shaft is loaded axially and maximum stress is calculated for calculation of Kt.
r/d = 1/23 = 0.0434
D/d = 25/23 = 1.086
Stress concentration factor for grooved shaft in tension graph
{From DDHB Vol1 Page no:64 (By Dr. K. LINGAIAH)},
Stress Concentration factor is, Kt= 2.57
We obtained stress concentration factor from this method as 2.57.
EXPERIMENTAL APPROACH
Experimentally, the stress concentration factor can be found by using Universal Testing Machine, Instron test machine, polar scope system, etc. Although the most preferred method is by using the UTM. Though according to requirement of precision and availability of resource the other method also can be used.
OBJECTIVE
The purpose of the experiment is to determine the existence of the stress concentration in the vicinity of the geometric discontinuity (here Ugroove) in a solid shaft.
MACHINES USED

Universal testing machine

Extensometer

Mild steel rod
SPECIFICATION OF SOLID MILD STEEL ROD

Material=Mild Steel

Youngs Modulus=210GPA

Initial diameter (D)=25mm

Diameter of Ugroove=25mm

Maximum Load=1000N
STEEL PROPERTIES

Standard grade for High Speed Steel, owing to its balanced composition has good toughness and cutting performance, hence many applications.

HSS containing Cobalt content is a high performance steel with good cutting capability and ensures high red hardness and tempering retention. It is particularly suitable in thermal stress situations and for intermittent cutting.

HSS containing high Molybdenum and Carbon has a wear resistance, high red hardness and good toughness.

HSS containing low Vanadium has a very good grind ability.
RAW MATERIAL SPECIFICATION
The material we used for determination of the stress concentration factor is mild steel which is also known as low carbon steel. It is the most generally used type of steel. This is also the cheapest of its category and its application is almost everywhere. Mild steel has relatively low tensile strength but it is very cheap and easy to form. The surface hardening can also be increased by carburizing
Element
Content(%)
Carbon, C
0.250.29
Iron, Fe
98
Copper, Cu
0.2
Manganese, Mn
1.03
Phosphorous, P
0.04
Silicon, Si
0.28
Sulfur, S
0.05
CHEMICAL COMPOSITION OF RAW MATERIALS
PROPERTIES
METRIC
IMPERIAL
Density
7.85 g/cm3
0.284 lb/in3
Tensile strength
400500 Mpa
5800079800 psi
Yield strength
250 Mpa
36300
Elongation at break in 200 mm
20%
20%
Elongation at break in 50 mm
23%
23%
Modulus of elasticity
210 Gpa
30450 ksi
Poissons ratio
0.3
0.3
Bulk modulus
140 Gpa
20300 ksi
Shear modulus
79.3 Gpa
11500 ksi
MECHANICAL PROPERTIES
APPLICATONS
High performance gear cutting hobs, shapers, milling cutters, Bevel tools, all kinds of highly stressed twist bits & taps, shaped shear blades, for working high strength materials, broaches, cutting tools for roughing and finishing such as helical bits, milling cutters of all types, taps, dies, spindles, reamers, thread cutting tools, drill bits, circular saw segments. Cold forming tools such as dies & punches for cold extrusion
& fine cutting tools. MACHINE SPECIFICATION
Type
Stepped Cone Pulley Engine Lathe
Power Supply
3 Phase 440440 Volts
Motor
1 HP 1440 RPM
No. of Spindle Speeds (without back gear)
04
No. of Spindle Speeds (with back gear)
08
Size of Machine (L*B*H) in mm
1400*450*1270
Swing Over Bed
165mm
Max Centre Distance
620mm
LAHE MACHINE SPECIFICATON\
CUTTER SPECIFICATION
The material we used for cutter is high speed steel. The reason behind we use high speed steel for cutter was these material made cutters can be re sharpened repeatedly throughout the entire life of cutter, without changing the original cutting form.
CUTTER MATERIAL SPECIFICATION
It is a high performance steel with high hardness and good wear resistance properties. It is often used as a cutting tool as it can cut metal at very high rate than any other carbon too steel due to presence of tungsten and cobalt that gives it much higher strength.
CHARACTERISTIC PROPERTIES

working hardness

excellent toughness

high wear resistance

high retention of hardness


Alloying Elements Present in HSS Properties

Carbon: Forms carbides, increases wear resistance, is responsible for basic matrix hardness.

Tungsten and molybdenum: Improved red hardness, retention of hardness and high temperature strength of matrix, forms special carbides of great hardness.

Vanadium: Forms special carbides of supreme hardness, increase high temperature wear resistance

Chromium: Promotes depth hardening, produces readily soluble carbides.

Cobalt: Improves red hardness and retention of hardness of the matrix.
LATHE MACHINE
Used to cut groove in the mild steel specimen for conduction of required specimen.
Capacity
Up to 100KN
1.
Maximum force at full speed
Compatible with full speed
2.
Width
Preferably in the range of 1000 1200mm
3.
Depth
Preferably in the range of 500 600mm
4.
Height
Preferably in the range of 1600 2000mm
5.
Total Crosshead travel
Preferably in the range of 1200 1400mm
6.
Total Vertical Test space
Preferably in the range of 1200 1400mm
7.
Mechanical test to be carried on UTM
Must able to perform all mentioned test
8.
Accuracy
~0.5Âµm
9.
Repeatability
~0.25 Âµm
10.
Should be suitable for mechanical testing of following material:
UTM must be suitable for testing all mentioned materials

Tensile Test

Compressive Test

Ductility Test

Fatigue/Cyclic Test

Flexure/Bending

Shear/Torsion Test

Stainless steel

Modified stainless steel such as SS 316, SS 316 LN

Polymers such FRP, Polyamides, Epoxy esters

Different Metals such as Copper, Aluminium alloys etc
TESTING PROCEDURE

Install the specimen in the UTM machine in tensile test setting

Load the solid steel rod till 1000N

Plot stress strain graph

Find : max and min GRAPH

TECHNICAL SPECIFICATION OF UNIVERSAL TESTING MACHINE
Universal Testing Machine
Universal testing machine is used to conduct the tensile test experiment on the specimen. The specimen with given dimension is clamped between the jaws of UTM and tensile force was applied and results were calculated.
OUTPUT
From Graph,
Max=5.59MPA
Nom=Force/Original area (area before tensile test)
=2.41MPA
Stress concentration factor (K) =Max/Nom
=5.59/2.41
=2.32
RESULT
The stress concentration factor was obtained by a tensile test on mild Steel Specimen with a UGroove of standard dimension and value was obtained as 2.32.
CONCLUSION
The value obtained from experimental approach is 2.32 and from theoretical approach (from graph and software), it is

So the variation is (2.572.32)=0.25 This variation may be due to

Improper gripping of specimen in UTM

Improper taking of readings

Manual errors of considering value in graph

CALCULATION OF STRESS CONCENTRATION FACTOR USING ANSYS FOR ANALYTICAL APPROACH
Ansys software is used for analytical approach. The shaft with groove is designed using Catia V5 software and imported in geometry section of Ansys static structural work bench then the shaft is meshed using triangular meshing of mesh size 0.5mm and mesh refinement is inserted in grooved area then axial force of 1000N is applied on both ends of shaft causing tension in shaft then solver is run and solution is obtained.
GEOMETRY 
SHAFT WITH UGROOVE 
Material properties 
Mild steel 
Density 
7850kg/m3 
Young modulus 
210GPA 
Poissons ratio 
0.3 
Meshing information 

Element size 
0.5mm 
Number of node 
146261 
Number of element 
87648 
Loading information 
Tensile loading of 1000N in y direction 
Boundary condition 
Free at both ends 
Maximum normal stress in Y direction is calculated;
Max=6.725MPA
Kt was calculated by dividing the max value by Nom
value
These things can be minimized by following ways:

Choosing smaller mesh sizing as possible leads to more accuracy in result operation.

Choosing element with more number of nodes leads to appropriate interpolation.

By applying exact boundary conditions, we can get more accurate results.
USE OF SOFTWARE
Many different types of software are used to determine the stress concentration factor. Following software can be used directly used to directly determine the stress concentration factor:

ALFAK SOFTWARE: A software created by faculty of Mechanical engineering Sarajevo. It is a very simple and easy to use software to determine stress concentration factor.

PETERSONS METHOD: This method is explained in Walter Dr. Pikley publication from Virginia Engineering education.

CATIA V5 AND ANSYS: These FEA software can be used to directly find the value and nature of stress concentration in complex geometries.

STRESS CONCENTRATION FACTOR CALCULATOR: This is a basic and simple method of calculating the stress concentration factor. You just need to select the type of specimen and discontinuity, put the condition like load, diameter, moments, etc.
Nom= 1000 ((4) Ã—232) =2.4068 Mpa
The value of Kt from analytical approach i.e. using Ansys is 2.7944 deviates from actual value 2.575 due to following reason:

Due to improper mesh sizing.

Due to improper elemental shapes and number of nodes.

Due to some in accuracy in boundary condition

Due to consideration of less digits after decimal during calculations.
CALCULATION OF STRESS CONCENTRATION FACTOR USING MATLAB

Image display
A figure of the case is displayed on the screen which will aids in better understanding of the parameters entered by the user and would avoid any confusion.Specimen.jpg is the name given to figure which has to be stored in Matlab folder.
[P,map]=imread('specimen.jpg'); imagesc(P,[min(P(:)) max(P(:))]);colormap(map) axis offaxis equal

Prompt
Tis section contains a set of codes that allow the user to input the various parameters that are necessary to compute the stress concentration factor shown in the figure by means of a dialog box that pops up when the program is run.
prompt={'Enter the diameter of cylinder:D',…. 'Enter the depth of U notch:h',……
ktheta1=k1+k2*y+k3*y^2+k4*y^3;
disp('the value of stress concentration factor is:'); disp(ktheta1);
elseif (x>2&x<=50) k1=0.833+2.069*sqrt(x)0.009*x; k2=2.7324.157*sqrt(x)+0.176*x; k3=8.859+5.327*sqrt(x)0.320*x; k4=6.2943.239*sqrt(x)+0.154*x;
ktheta1=k1+k2*y+k3*y^2+k4*y^3;
disp('the value of stress concentration factor is:'); disp(ktheta1);
else
disp('This code is only valid for 0.1<=h/r<=50') end;
'Enter the radius of curvature of U notch:r'}; dlg_title='Inputs';
num_lines=1; answer=inputdlg(prompt,dlg_title,num_lines);
D=str2double(answer(1,1)); h=str2double(answer(2,1)); r=str2double(answer(3,1));

disp('This code is for elastic stress on a cylindrical section with two U notches')
disp('under elastic stress and axial tension')
disp('The output is the factor of stress concentration')


Output
The output, which is the factor of stress concentration is printed out on the screen.
Reasons for variation in result of MATLAB with Theoretical value

Applied boundary condition may not be exact


d) Logic
This section contains the coding that is required to compute the stress concentration factor. A simple ifelse statement is utilized to check the conditions if there is just one condition. If the input parameters do not satisfy the conditions, then This code is not valid for these parameters message is printed.
x=h/r; y=(2*h)/D;
if (x>=0.1&x<=2) k1=0.850+2.628*sqrt(x)0.413*x; k2=1.1194.826*sqrt(x)+2.575*x; k3=3.5630.514*sqrt(x)2.402*x; k4=2.294+2.713*sqrt(x)+0.240*x;
CREATE YOUR OWN SOFTWARE
You can make your own software as per your requirement in order to avoid expensive software. With a good knowledge of programming language, small software application can be developed. The initial approach can be to put the fundamental and relation in stress concentration topic in order to a program than process accordingly. In above method, we have used Matlab to solve a given specific problem. Similarly, that program can be expanded and can be converted into a simple software which can be used to find stress concentration.
Methods used 
Values of (kt ) obtained 
1. Numerical approach 
2.575 
2. Experimental approach 
2.32 
3. Analytical approach (FEA) analysis using ANSYS (workbencp6) 
2.7944 
4. Using software (stress concentration factor calculator ) 
2.57 
5. Mat lab code 
2.7999 
RESULT COMPARISON
The variation in results calculated from different method and their reasons with remedies are explained above in each consecutive approaches.
BIBLIOGRAPHY
Pilkey, W. (1997), Peterson's Stress Concentration Factors, Wiley, New York.
ANSYS Workbench 16, ANSYS, Inc., www.ansys.com Machine Design Data Hand Book By Dr.K. Lingaiah . William J Palm III ,(2007) "A Concise Introduction to Matlab".
A Muminovic, I.Saric, and E.Mesic, CAD, Sarajevo:Faculty of Mechanical Engineering Sarajevo,2012.