New crack stop hole shape using structural optimizing technique

Ain Shams Engineering Journal (2015) xxx, xxx–xxx

Ain Shams University

Ain Shams Engineering Journal

www.elsevier.com/locate/asejwww.sciencedirect.com

MECHANICAL ENGINEERING

New crack stop hole shape using structural

optimizing technique

* Corresponding author. Tel.: +20 01023900933.

E-mail addresses: [email protected] (M. Fanni), foudanoha@

yahoo.com (N. Fouda), [email protected] (M.A.N. Shabara),

[email protected] (M. Awad).

Peer review under responsibility of Ain Shams University.

Production and hosting by Elsevier

http://dx.doi.org/10.1016/j.asej.2015.02.0102090-4479 � 2015 Faculty of Engineering, Ain Shams University. Production and hosting by Elsevier B.V.This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Please cite this article in press as: Fanni M et al., New crack stop hole shape using structural optimizing technique, Ain Shams Eng J (2015), http://dx.doi.org/j.asej.2015.02.010

M. Fanni a, N. Fouda b, M.A.N. Shabara b, M. Awad b,*

a Dept. of Mechatronics and Robotic Engineering, School of Innovative Engineering Design, Egypt-Japan University of Science& Technology (E-JUST), Egyptb Production Engineering & Mechanical Design Dept., Faculty of Engineering, Mansoura University, Mansoura, Egypt

Received 9 November 2014; revised 20 February 2015; accepted 25 February 2015

KEYWORDS

Stop hole method;

Optimum hole shape;

Initial fatigue life;

Finite element analysis

Abstract In the present study, the stop-hole method was investigated with creating a noncircular

hole. The aim of the present work was to obtain an optimum stop hole shape that gives maximum

fatigue crack initiation life by using finite element program. It was found that the fatigue life

obtained by using the optimum hole shape ranges from 2 to 9 times the fatigue life obtained by

using the circular holes. It was found that the optimum hole shape increased the initial fatigue life

for all specimens used. Opposite to the traditional stress concentration factor minimization problem

where the nominal area remains constant during optimization, here it is allowed to vary nominal

area using design variables resulting in decreasing of the nominal stress in addition to decreasing

of the stress concentration factor. This leads to higher fatigue life compared to previous studies.� 2015 Faculty of Engineering, Ain Shams University. Production and hosting by Elsevier B.V. This is an

open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction

The effect of a geometrical discontinuity such as notch is tointensify the magnitude of the nominal stress in the vicinityof the discontinuity. The localized stresses may cause the

metal in that neighborhood to undergo plastic deformation.Because the nominal stresses are elastic, an elastic-stress field

surrounds the zone of plastically deformed metal in the vicin-

ity of stress concentration. A fatigue crack initiates morerapidly as the magnitude of the local cyclic-plastic deforma-tion increases. That is, when the material in the vicinity of

the notch tip is subjected to stress ranges approximately equalto or larger than the yield stress of the material, the plasticdeformation causes the material to deform along slip planesthat coincide with maximum shear stress, which results in slip

steps on the surfaces of the notch. These slip steps act as newstress raisers that become the nucleation sites for fatiguecracks which initiate along the maximum shear planes and

propagate normal to the maximum tensile stress component[1]. Crack arresting methods have different techniques, suchas method of tensile triangles which had been introduced by

Mattheck et al. [2] for optimizing the shape of notches byadding material at overloaded regions but also to removeunloaded material from an oversized design proposal. Other

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Table 1 RQC-100 steel mechanical properties [12].

Modulus of elasticity (GPa) 207

Yield strength (MPa) 600

Ultimate tensile strength (MPa) 930

Poisson’s ratio 0.3

Table 2 Total number of nodes, elements, and DOF for fine

mesh and course mesh.

Fine mesh Course mesh

Nodes 49,616 2504

Elements 16,441 737

DOF 297,696 15,024

2 M. Fanni et al.

crack arresting methods, such as branching of crack directionare introduced by Shabara [3] and this method could reducecrack growth rate or even stop it for a period of time.

Other researches aimed to reduce the effect of stress raisersto increase crack initiation life, by using a stop hole methodas Wua et al. [4]. Some researchers investigated arresting

crack initiation at stop-drilled hole by drilling ancillary holesaround the principle stop hole Murdani et al. [5]. Fatiguecrack initiation life prediction had been evaluated by

Khoshravan and Hamidi [6] by employing classical strain lifeconcepts properly modified by short crack theory to modelthe stop-hole effect and investigated the best location of stophole and its diameter. Shah [7] studied the effect of drilling

holes in the vicinity of crack tips on the direction of thecrack, time taken for the specimen to fracture, and the break-ing load of the specimen. Others investigated the stress

concentration factors for the stop drilled holes [8], whileothers investigated how the stop drilling procedure improved

Figure 1 Flowchart of hole shape optimization method.

Figure 2 Model geometry.

Please cite this article in press as: Fanni M et al., New crack stop hole shape using structural optimizing technique, Ain Shams Eng J (2015), http://dx.doi.org/10.1016/j.asej.2015.02.010



Figure 5 The objective function for the optimization program is

to minimize strain energy and to maximize the crack initiation life.

New crack stop hole shape 3

the crack initiation life and the total fatigue life [9]. Somewere interested in investigating the efficiency of crack arrest-ing by drilling a stop-hole on riveted girders theoretically and

by full-scale fatigue test series [10]. Investigation of The glo-bal optimum shape was similar to the plastic zone createdaround crack tip that means by drilling optimum shape, it

removes all damage materials, leaving material in virgin stat,so initial fatigue life increases many times. Inserting pins intoholes drilled in the vicinity of the crack tips or the cold

expanded hole had been studied by Makabe et al. [11], whofound that compressive residual stress, which occurred byinserting pins, was more effective to retard the crack growththan reducing the stress concentration around initial crack

tips by drilling holes.Based on the previous literature review, it was found that

almost all researches deal with arresting the fatigue crack with

drilling a circular hole. The effect of changing the hole shapehas not been studied yet. Therefore the objective of this studywas to introduce a new method for improving the crack initia-

tion life by stopping crack growth with modifying the holeshape using optimization technique. The optimum shape ofstop hole at the crack tip will maximize the crack initiation life

of a precracked component subjected to fatigue loadingwithout decreasing nominal area of specimen.

Figure 3 Fine mesh around hole an

Figure 4 Constrains an

Please cite this article in press as: Fanni M et al., New crack stop hole shape using struj.asej.2015.02.010

2. Work plan

This is realized through the following steps to run automatedstructural optimizations:

d courser mesh far from the hole.

d loading conditions.

ctural optimizing technique, Ain Shams Eng J (2015), http://dx.doi.org/10.1016/



Figure 6 Design variables.

Table 3 Optimized design variables that define the optimum hole shape.

1 2 3 4 5 6 7

R 0.9030 0.9836 1.1162 0.9767 0.9689 0.9802 1.0006

ɵ0 00 300 600 900 1200 1500 1780

Figure 7 Comparison between optimum hole size, and circular

hole size.

0

1000000

2000000

3000000

4000000

5000000

6000000

circular hole op�mum hole shape

Figure 8 Initial life using optimum hole shape and initial life

using circular hole shape.

4 M. Fanni et al.

1. Finite Element Method using ANSYS software package fornonlinear static analysis.

In this step the inputs are cyclic properties of specimen

material, specimen geometry, boundary conditions, and load-ing conditions. The outputs of this step are local stresses andstrains results.


2. Shape optimization of the analyzed hole using ANSYS

The maximum local stress and strain are picked up from theprevious step, to calculate the strain energy which will be usedas an objective function. The inputs to this step are the design

variables, and the objective function. The outputs of this stepare the optimum hole shape and minimum strain energy.




0.00E+00

1.00E+02

2.00E+02

3.00E+02

4.00E+02

5.00E+02

6.00E+02

7.00E+02

Von

Mis

es st

ress

(MPa

)

Hole Boundary ɵ (degree)

Von Mises stress for op�mum hole shape

Von Mises stress for circular hole

Figure 9 VonMises stress using optimum hole shape and using

circular hole shape.

0.00E+00

5.00E-04

1.00E-03

1.50E-03

2.00E-03

2.50E-03

3.00E-03

3.50E-03

4.00E-03

Von

Mis

es st

rain

Hole Boundary ɵ (degree)

Von Mises strain for op�mum hole shape

Von Mises strain for circular hole

Figure 10 Von Mises strain using optimum hole shape and using

circular hole shape.


3. Initial fatigue life prediction

The minimum strain energy resulted from optimization stepis input to MATLAB to solve nonlinear Smith Watson and

Topper (SWT) equation to get maximum initial fatigue life.The flowchart of hole shape optimization method is given

in Fig. 1.

3. Modeling and method of analysis

3.1. Model geometry

The studied model is rectangular block, with 80 mm length,40 mm width, and 10 mm thickness. The circular edge notch

has a radius, r, of 1.5 mm, and propagated sharp crack length,a, of 6 mm. The radius R, of the hole at the crack tip equals1 mm [12], as illustrated in Fig. 2.

3.2. Finite element analysis and loading conditions

A two-dimensional simulation finite element model using

ANSYS software package was used. The material used in thisanalysis was RQC-100 steel with mechanical properties shownin Table 1. In this model it was assumed that the material ishomogeneous and isotropic, i.e., without imperfections or

damages.Eight-node plane element (Plane 82) is adopted, because

these quadrilateral elements can deal with problems when ana-

lyzing about a point, such as the crack tip. A very fine meshwith element size equals 0.1 mm has been utilized around thearea of interest (the crack stop hole edge) and a relatively

courser mesh far from the stop hole edge has been used inorder to save simulation time. The total number of nodes,and elements, and DOF are shown in Table 2. The finite

element mesh is illustrated in Fig. 3.Due to the symmetry of the model, only half of the part

was modeled to increase the efficiency of the optimizationprocedure as in Fig 3. Due to the high stress and strain

gradients around the hole edge, it is critical to choose elas-tic–plastic nonlinear static analysis type with small displace-ment to capture these gradients. Methods for analysis in

that case are usually based on the relation between deforma-tions, stresses, and number of loading cycles. Symmetricalconstraints were placed on the specimen along the axis of

symmetry. As along this boundary, the elements cannot movevertically or rotate, while along the notch and hole, theelements could move freely because it was not attached tothe symmetric plane. All constrains and loading conditions

are shown in Fig. 4.Applied stress is a uniaxial cyclic stress with stress ratio

equals, �1 and peak value, 90 MP at the model top line as

illustrated in Fig. 4. Each load step occurred after one unitof time. The load steps were also broken up into substeps inwhich a fraction of the load was applied over an interval of

time between the maximum and minimum loads. When solu-tion is done, the maximum local stresses and strains areobtained at the hole surface. These values of stresses and

strains are used to calculate crack initiation life using SmithWatson and Topper (SWT) equation [13], which can be solvedusing MATLAB software.


3.3. Optimization analysis

3.3.1. Objective function

An optimization program was carried out using ANSYS

software in order to find the optimum shape of the stop hole.The objective function of this research was to obtain the opti-mum hole shape which is corresponding to the minimum value

of strain energy (rmaxe) in order to maximize the crack initia-tion life (2Nf). To evaluate objective, the strain life method isusually used to determine the number of cycles required for

the fatigue crack initiation, where it is assumed that the crackis initiated at the point of the largest stresses in the material.To determine crack initiation life, Smith Watson and Topper

(SWT) equation (1) can be used as follows:

rmax

De2¼ðr0fÞ

2

Eð2NfÞ2b þ r0fe

0fð2NfÞbþc ð1Þ

where 2Nf is number of reversals up to crack initiation, ea istotal strain amplitude, rmax is the maximum equivalent Von

Mises stress, b is the fatigue strength exponent, r0f is the fatiguestrength coefficient, e0f is the fatigue ductility coefficient and, c

is the fatigue ductility exponent. Material characteristics ofRQC-100 steel [14] under cyclic loading are: b = �0.07;r0f ¼ 1240 MPa; e0f ¼ 066; and c = �0.69.




6 M. Fanni et al.

FE program results showed that the maximum Von Misesstress was maximum at the stop hole edge which agreed withRef. [15] results. Because fatigue cracking normally occurs at

the surface, Von Mises stress is a more appropriate criterion.By using MATLAB software, relationship between strain

energy and initial fatigue life for RQC-100 steel is plotted as

illustrated in Fig. 5.

Figure 11 Stress and strain distribution for (a) op

Figure 12 (a) The most important geometrical parameters and (b


The curve showed that

minðrmaxeaÞ ! maxð2NfÞ

3.3.2. Design variables

The geometric representation of the designed boundary foroptimization technique was chosen so that an effective

timum hole shape and (b) circular hole shape.

) flowchart of geometries which have been tested in this study.




540

560

580

600

620

640

660

680

700

1 1.2 1.4 1.6 1.8 2 3

max

imum

stre

ss (M

Pa)

h/w

circular holeglobal optimum hole shapeoptimuum hole for each h/W value

Figure 13 Comparison of maximum stress at hole edge for

circular hole, optimum hole shape, and hole shape obtained from

optimization results for each h/W geometry.

0.00E+00

2.00E-04

4.00E-04

6.00E-04

8.00E-04

1.00E-03

1.20E-03

1.40E-03

1.60E-03

1.80E-03

2.00E-03

1 1.2 1.4 1.6 1.8 2 3

Max

imum

stra

in

h/w

circular holeglobal optimum hole shapeoptimuum hole for each h/W value

Figure 14 Comparison of maximum strain at hole edge for

circular hole, optimum hole shape, and hole shape obtained from

optimization results for each h/W geometry.

0

1000000

2000000

3000000

4000000

5000000

6000000

7000000

8000000

9000000

10000000

1 1.2 1.4 1.6 1.8 2 3

Initi

al fa

tigue

life

h/w

circular holeglobal optimum hole shapeoptimum hole for each h/w value

Figure 15 Initial fatigue life at hole edge for circular hole,

optimum hole shape, and hole shape obtained from optimization

results for each h/W geometry at a/W= 0.1.

0

500000

1000000

1500000

2000000

2500000

3000000

3500000

4000000

1 1.2 1.4 1.6 1.8 2 3

Initi

al fa

tigue

life

h/w




results for each h/W geometry at a/W = 0.2.

0

500000

1000000

1500000

2000000

2500000

3000000

1 1.2 1.4 1.6 1.8 2 3

Initi

al fa

tigue

life

h/w




results for each h/W geometry at a/W = 0.3.

Figure 18 Schematic illustration of the specimen ligament size

used in the numerical simulation.


Please cite this article in press as: Fanni M et al., New crack stop hole shape using structural optimizing technique, Ain Shams Eng J (2015), http://dx.doi.org/10.1016/j.asej.2015.02.010



8 M. Fanni et al.

geometry could be represented by the least possible amount ofparameters. Therefore, half of the hole was modeled by a splineconnecting 7 key points having polar coordinates (R, ). The

design variables are chosen to be the radial coordinates of thesekey points as R1, R2, R3, R4, R5, R6, and R7. The angles, , ofthe key points are changed from 0� to 178� with a constant

increment value equals 30�. These angles are kept constantduring optimization. The design variables are shown in Fig. 6.

The initial values of design variables were initially started

from the circular hole shape (as illustrated in Fig 6). The initialvalue for R1 to R7 was 1 mm. These variables were arrangedfrom R1 at hole edge, up to R7 toward free edge of the speci-men. Design variables were allowed to change within the range

of 0.5–1.5 mm. In the ANSYS program, several differentoptimization tools and methods are available. In this workthe first order method was chosen because, this method uses

derivative information, of gradients of the dependent variableswith respect to the design variables. It is highly accurate andworks well for problems having dependent variables that vary

329.4

329.6

329.8

330

330.2

330.4

330.6

330.8

Nominal area using circular hole

Nominal area using op�mum hole shape

Figure 19 The nominal area increases using optimum hole shape.

Figure 20 (a) Size comparison between optimum hole and circular ho

circular hole.


widely over a wide range of design space. However, thismethod can be computationally intense.

4. Results

4.1. Optimization results

After optimization process was completed, the values of designvariables were changed to the values listed in Table 3. These

values define the optimum hole shape which accomplish theobjective function as illustrated in Table 3.

Table 3 indicates that the optimum hole shape does not

increase the size of initial circular hole, it just reshapes it asillustrated in Fig. 7. This indication has a significant impor-tance for nominal stress and stress concentration as will be

investigated in detail later.

4.2. Confirm the effectiveness of the optimum hole shape results

4.2.1. Optimum hole shape influence on initial fatigue life

Initial fatigue life was calculated for both of circular andoptimum hole shapes. It is found that initial fatigue life using

circular hole was 868,600 cycles, while using optimum holeshape increases initial fatigue life to 5,525,000 cycles as illus-trated in Fig. 8.

4.2.2. Optimum hole shape influence on stresses and strains

The optimum hole shape reduces Von Mises stress, andVonMises strain at hole edge. The maximum reduction of

stress, and strain occurred at hole edge, which is most proba-bly the location for crack initiation, as illustrated in Figs. 9 and10 respectively. The high stress gradient close to the hole was

reduced, resulting in a better stress distribution as illustratedin Fig. 11.

le and (b) maximum stress comparison between optimum hole and




0

1000000

2000000

3000000

4000000

5000000

6000000

7000000

8000000

9000000

Circular hole FEA results

Ref. [3] results

Op�mum hole shape

Ini�

al fa

�gue

life

Figure 21 Comparison between reference [3] results and finite

element results for circular hole and optimum hole.

Figure 22 Schematic representation of the hole drilling method

(a) base type and (b) ancillary holes method.

0

500000

1000000

1500000

2000000

2500000

Circular hole FEA results

Researcher results

Op�mum hole shape

Ini�

al fa

�gue

life

(Re

vers

als)

Figure 23 Comparison between reference [4] results and finite

element results for circular hole and optimum hole.


4.3. The effect of optimum hole shape on fatigue initiation lifefor different specimen geometries

The model geometry has four configuration parameters: heighth, width W, initial crack length a, and the initial stop hole

radius R as shown in Fig. 12. R will be changed duringoptimization process; however its initial value can be obtainedusing previous researches [16–19]. It is found necessary to get aglobal optimum hole shape [it is called global to point out that

it is suitable for all geometries]. If succeeded, it will help theengineers to use it directly in practice, much like the use ofthe stop hole size found in the literature. In order to validate

this optimum shape, it is important to study the effect of usingthis optimum shape on fatigue life for different specimengeometries. According to load direction for this model the

most important configuration parameter is the width W.Therefore, the other two parameters, a and h will be normal-ized by W. The ratio, a/W has a significant importance on

stress distribution, [20]. a/W is varied from 0.1 to 0.3. Forevery value of a/W ratio, h/W values are examined to get itseffect on optimization results as illustrated in Fig. 12.

Each case has its own optimization program and produces

its own optimum hole shape. Figs. 13 and 14 respectively illus-trate the relation between the maximum stresses and strainsobtained at the crack stop hole for different values of h/W.

These figures illustrate the comparison between the stressesand strains using circular hole, the optimum hole shape, andthe optimum shape obtained for each h/W value. It is found

that the global optimum hole shape results are close to eachh/W optimization result. That signifies the ability of applyingoptimum hole shape for all cases and getting nearly optimumresults for each geometry. That has a significant importance in

practical field.The effect of changing the h/W values on the initial fatigue

life is illustrated in Figs. 15–17 for a/W equals 0.1, 0.2, and 0.3,

respectively. These figures illustrate the initial fatigue life whenusing circular hole, global optimum hole, and the optimumhole shape obtained for each h/W geometry. It is noticed that

the values of initial fatigue life using global optimum holeshape for all cases is nearly similar to those optimum shapeobtained for each h/W.

It was found that the optimum shape gave results betterthan circular hole up to 9 times. It is found from all previousFigures that increasing h/W values increased the fatigue life,while increasing a/W values reduced the fatigue life.

4.4. The effect of optimum hole shape on nominal area

As illustrated in Fig. 18 the ligament size (l= W � (a + R1))

has a significant importance on calculating the nominal areaand nominal stress value. R1 equals 1 mm for circular holewhile R1 equals 0.9030 mm that means the nominal area

increased using optimal hole shape that leads to decrease ofnominal stress as illustrated in Fig. 19.

4.5. The effect of optimum hole shape on stress concentration

To study the effect of optimum hole on the stress concentra-tion, two identical specimen models are tested. At the firstspecimen a circular stop hole was applied with a radius of

2 mm, and at the other specimen an optimum hole was applied


with initial radius 1 mm. That indicates the area of the opti-mum hole was nearly half the area of circular hole. As wellknown from previous studies, stress concentration is decreased

as the radius of stop hole increased. But using optimum holecan reduce stress concentration even if optimum hole sizewas nearly half circular hole size as illustrated in Fig. 20.

5. Discussion

In order to validate the results of global optimum hole shape,the results of other published researches were compared.




Figure 24 Material removal of solid plate area (a) when using optimum hole and (b) when using ancillary holes.

0

50

100

150

200

250

300

5 10 15

Max

imum

stre

ss (M

Pa)

Hole diameter (mm)

FE results of this study for circular hole

FE results of ref. [20] circular hole

Experimental results of ref. [20] circular hole

Global op�mum hole shape

Figure 25 Comparison between maximum stress for circular

hole of reference [20] and maximum stress for global optimum

hole shape.

0

5000000

10000000

15000000

20000000

25000000

5 10 15

initi

al fa

tigue

life

(Re

vers

als)

initial hole diameter (mm)

circular hole

global optimum hole shape

Figure 26 Comparison between life for circular hole of reference

[20] and initial life for the optimum hole shape.

10 M. Fanni et al.

5.1. Validation of optimum hole shape to analytical calculationresults of Ref. [4]

Ref. [4] constructs an analytical prediction initial fatigue at thestop-hole roots by local strain life procedures. A finite element


model had been made to imitate model of Ref. [4] by using thesame material type used in the research, the same loading con-

ditions, the same model configuration, and of course the samestop hole radius. It was found that the initial fatigue lifedifference between Ref. [4] and the model carried out by this

analysis was about 0.6% of Ref. [4] results. Then in the samefinite element model, the optimum hole was used instead ofthe circular hole. Initial fatigue life was calculated again.Results showed that the initial fatigue lives increased by nearly

7.62 times, and these results are illustrated in Fig. 21.

5.2. Validation of optimum hole shape to the ancillary holesmethod of Ref. [5]

According to Ref. [5] the maximum reduction of stress concen-tration was obtained by arranging four ancillary holes around

stop hole. The diameters of the ancillary holes were chosen tobe larger than that of the stop hole, as illustrated in Fig. 22.Ref. [5] results indicate that initial fatigue life increased to 6

times more than base type model (model of using stop holeonly). But ancillary hole method has some disadvantages suchas, it requires a space to drill ancillary holes, so it is only suit-able for plate with infinite dimension, it requires removal of

solid plate area which has a bad effect on specimen strength,and although using ancillary hole decreases the maximumstress at stop hole edge, it creates other high stress concentra-

tions at ancillary holes edges. A finite element model wascreated to imitate reference [5] base type model. Then theinitial fatigue life was calculated, difference between the initial

fatigue life of Ref. [5] base type model and the model carriedout by this analysis was about 0.5%, and it was within theacceptable difference range. Then the optimum hole was used

instead of circular hole. Results showed that the initial fatiguelife increased 5.3 times as illustrated in Fig. 23.

Optimum hole method results increase initial fatigue lifevery close to ancillary hole without need to remove any part




Figure 27 Model with a unrepaired crack (a) whole model and (b) magnification of crack region.

Figure 28 Plastic zone size.

Figure 29 (a) Plastic zone size and (b) optimum hole shape size.


of plate material and can be practically drilled at any geometryas illustrated in Fig. 24.

5.3. Validation of optimum hole to experimental results of

Ref. [21]

Ref. [21] evaluates experimentally, and numerically the maxi-mum stresses at the end of the stop hole. Three different holediameters of 5, 10, and 15 mm have been examined. A finite

element model was built using the same procedure explainedbefore but in this case the comparison issue is the maximumstress results at stop hole edge. The difference between experi-

mental results of Ref. [20] and results of FE model carried outby this study was about 5.9% for the specimen with holediameter D= 5 mm, 3% for D= 10, and 4.6% for D = 15,and it was within the acceptable difference range. By applying


the global optimum hole, maximum stress decreased for allcases as illustrated in Fig. 25, while initial fatigue life increasedas illustrated in Fig. 26.

5.4. Relationship between the size and shape of plastic zoneahead of crack tip, and the size and shape of optimum hole

FE model with crack is constructed as illustrated in Fig. 27.

Then plastic zone size is calculated using fracture mechanicstheories [22].

The plastic zone was determined and plotted using

MATLAB software as illustrated in Fig. 28 which agreed withresults of Ref. [23]. Then on the specimen the global optimumhole was applied at the crack tip. The global optimum hole was

plotted as illustrated in Fig. 29(b). At Fig. 29 both of plasticzone and global optimum hole shape are plotted with respectto the same origin and are determined for the same model.Fig. 29 specifies two important results: first: the similarity of

the optimum hole shape to the plastic zone shape, and second:the optimum hole shape size would be sufficient to remove




12 M. Fanni et al.

almost all of the plastically deformed particles ahead of thecrack tip as illustrated in Fig. 29(b).

5.5. Forming method of optimum hole shape

The optimum shape can be formed easily using ElectricalDischarge Machining (EDM). Electrical Discharge

Machining is an advanced machining technique that allowsfor precise, detailed cuts that were once thought to be out ofreach with traditional machining [24].

6. Conclusion

� This study introduces an optimization program to reshapethe crack stop hole in order to have the maximum increase

of crack reinitiating life, without decreasing specimen nomi-nal area.� The optimum shape has been studied for different specimen

geometrical configuration ratios. It had been found that inall cases the initial fatigue life was much greater for the opti-mum shape than for circular hole.

� The initial fatigue life increase ranges from 2 to 9 timesusing the optimum hole shape compared to the circular holeshape for all tested geometries.� The global optimum hole shape is similar to the plastic zone

contour emanates around crack tip, which denotes thatonce global optimum hole is created, it will remove almostall damage materials, leaving material in virgin state. For

that reason initial fatigue life increases many times.� The global optimum hole shape increases specimen nominalarea and reduces nominal stress.

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[24] Suzhou Baoma Numerical Control Equipment Co., Ltd. <www.

bmedm.com/category/wire-cut-edm>.

Mona Awad is an engineer who has done B.SC

in production and mechanical design engi-

neering, M.SC. Mechanical design, produc-

tion and mechanical design engineering, and

her Phd interest is in fracture mechanics and

crack arresting methodology.


http://refhub.elsevier.com/S2090-4479(15)00036-2/h0010











































http://www.bmedm.com/category/wire-cut-edm

http://www.bmedm.com/category/wire-cut-edm




Associate Professor Dr. Noha Fouda, born

1973. She is an Associate Professor at

Mansoura University, Faculty of Engineering,

Mansoura, Egypt. She received her B.Sc.

(Production Engineering) in 1995, her M.Sc.

in 2000 and her Ph.D. in 2006, all from

Mansoura University, Egypt. Her fields of

interest are biomechanics, optimum design,

stress analysis as well as mechanics of mate-

rials.

Mohamed Fanni received the B.E. and M.Sc.

degrees in mechanical engineering from

Faculty of Engineering of both Cairo

University and Mansoura University, Egypt,

in 1981 and 1986, respectively and the Ph.D.

degree in engineering from Karlsruhe

University, Germany, 1993. He is an

Associate Professor with Innovation,

Graduate School of Engineering Science,

Egypt-Japan University of Science and

Technology E-JUST, Alexandria, on leave

from Production Engineering & Mechanical


Design Department, Faculty of Engineering, Mansoura University,

Egypt. His major research interests include robotics engineering,

automatic control, and Mechanical Design. His current research

focuses on Design & Control of Mechatronic Systems, Surgical

Manipulators, Teleoperation systems and Flying/Walking Robots.

Professor Dr. M.A. Shabara born in 25

August 1945. Professor in Mansoura

University, Faculty of Engineering since 1993.

B.Sc. Mechanical Eng. Mansoura Higher

Institute 1967. M.Sc. Mechanical Engineering

Pennsylvania State University, USA, 1971.

Ph.D. Engineering Science and Mechanics

Pennsylvania State University, USA, 1976.

His fields of interest are elasticity and plas-

ticity, stress analysis and fracture mechanics.




New crack stop hole shape using structural optimizing technique

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