fracture specimen stree analysis

7/24/2019 Fracture Specimen Stree Analysis

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Final Project MEC455/530

MEC455/530

Applied Stress AnalysisSpring - 2014

( Final Project )

Finite Element Analysis of

Fracture Specimen

Gaurav Pundir

(109597135)

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Index

Sl. No. Descrition Pa!es

1. Introduction 03

2. Description of Specimen 0

2.1 !oadin" and #oundar$ %onditions 05

3. Procedure for &ode'in" in & 05 * 11

. +esu'ts

.1 Stress Intensit$ actor 12*1

.2 #e,avior of t,e openin" stress -$ around

t,e crac

1

5. Discussion 15

". Introd#ction

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/,e purpose of t,is proect is to carr$ out finite e'ement ana'$sis of a standard

compact tension specimen usin" #S. compact tension specimen is a

notc,ed samp'e (S,o4n in i".1 e'o4) and is a standard specimen for carr$ out

fracture ana'$sis as perS/& standards. /,e notc,ed samp'e simu'ates a crac

and under t,e app'ied 'oads provides t,e fracture mec,anism of a crac. /,e crac

4i'' e"in on t,e point of t,e notc, and propa"ate a,ead in t,e samp'e. %ompacttension specimens are used e6tensive'$ in t,e area of fracture mec,anicsin order to

esta'is, fracture tou",nessva'ues for a materia'.

i".1 (%ompact /ension Specimen)

/,e na'$sis carried out in t,is report assumes t,e !inear 'astic racture

&ec,anics (!&) 4,ic, primari'$ means t,at t,e &ateria' is isotropic 'inear e'astic.

/,e ana'$sis process of t,is report inc'udes t,e mode'in" of specimen in #S

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http://en.wikipedia.org/wiki/ASTMhttp://en.wikipedia.org/wiki/Fracture_mechanicshttp://en.wikipedia.org/wiki/Fracture_toughnesshttp://en.wikipedia.org/wiki/Fracture_mechanicshttp://en.wikipedia.org/wiki/Fracture_toughnesshttp://en.wikipedia.org/wiki/ASTM


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and e6amine t,e fracture parameters 'ie stress concentration factor and e,avior of

openin" stress around crac tip.

$. Descrition o% Seci&en

/,e specimen "eometr$ is considered accordin" to S/& standards under t,e p'ane

strain conditions. Durin" mode''in" in & t,e ori"in of coordinate s$stem isconsidered at crac tip. /,e "eometr$ of specimen is as "iven e'o4 in i".28

i".2 (Geometr$ of %ompact /ension Specimen)

,ere is 4idt, of t,e specimen and 4e ,ave considered it to e 50mm or 0.05mt,e t,icness of t,e specimen is considered to e 1m. /,e 'en"t, of t,e crac (a) isca'cu'ated as a : (0.5 ; 5


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$." 'oadin! and o#ndar Conditions

Due to t,e s$mmetr$ of t,e compact tension specimen on'$ upper ,a'f of t,e

specimen is mode''ed in & to improve t,e resu'ts $ ,avin" more numer ofnodes as 4e are restricted to 1000 nodes on'$. /o simu'ate t,e oundar$ conditionsin ,a'f mode' ro''er are provided in t,e ottom re"ion a,ead of crac restrictin" t,emotion in B direction on'$ and 'ast point is fi6ed in ot, 6 and $ directions. /osimu'ate t,e 'oadin" conditions a point 'oad of 100CPa is app'ied on t,e top node oft,e circu'ar ,o'e. /,e aove detai's are as s,o4n in i".3 e'o48

i" 3 (!oadin" and #oundar$ %onditions)

3. Proced#re %or Modellin! in FEM*

or mode''in" t,e #S


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Fig.4 (Partition of Part for generating proper Mesh)

2. Assign the Material Properties

In Propert$ modu'e 4e define t,e materia' properties and app'$ t,em to t,edomain. /,e properties of t,e stee' defined in t,is modu'e are e'astic :200GPa : 0.3. /,e materia' created is app'ied to t,e section 4,ic, is t,epart created is previous step.

3. +sse&,le t-e &odel./,e assem'$ modu'e is used to create an instance of t,e ori"ina' part on4,ic, ana'$sis can e performed.

. Create t-e ste.In #S t,e ana'$sis is carried out is steps for 4,ic, step modu'e is used.or ana'$sis of t,is report t4o steps are reEuired. /,e initia' step is $ defau'tdefined 4,ic, taes care of t,e oundar$ conditions t,at constrained t,especimen. n additiona' step Fstep*1 is created for t,e process of app'$in"t,e 'oad on t,e domain.

5. De%inin! ,o#ndar conditions and loadin!./,e 'oad modu'e is used to app'$ 'oad and oundar$ conditions on t,edomain. /,e ottom ed"e a,ead of t,e crac is provided 4it, ro''er $restrictin" motion in B*directions 4,ic, is defined as 2 in #S. /oprevent t,e trans'ation of domain t,e ri",t most node on t,e ottom ed"e oft,e domain is provided 4it, oundar$ condition of restrictin" motion in ot, 6and $ direction. point 'oad of 100CPa is app'ied on t,e top node of t,ecircu'ar ,o'e.

@. Create t-e &es-.In t,e mes, contro's p'ane strain 4it, non*reduced inte"ration condition is

specified for t,e ana'$sis 4,ic, is ca''ed %P e'ements. /,e mes, for t,e

domain is created usin" t,e structured Euad e'ements in "enera' and s4eep

mes, e'ements near t,e crac tip re"ion. /,e mes, created ,as tota' 917

e'ements and 990 nodes. /,e mes, for t,e domain created is "iven in i".5

and en'ar"ed vie4 of mes, around crac tip is s,o4n in i".@

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i".5 (&es, of t,e %omp'ete Domain)

i".@(n'ar"ed vie4 of mes, near crac tip re"ion)

7. Create t-e analsis jo,./,e o modu'e is used to create t,e o for ana'$sis 4,ic, is sumitted to#S for ana'$sis.

. is#aliation/,e visua'iHation modu'e is used for vie4in" t,e stresses in t,e domain and

t,e resu't of app'ied 'oad 4it, "iven oundar$ condition. i". 7 "iven in ne6tpa"e s,o4s t,e oundar$ conditions and 'oad position on t,e nodes. >e6tt,e stress contours are p'otted on t,e deformed mode's. e ,ave p'otted vonmises stress and -$ on t,e 4,o'e mode' as s,o4n in i". 9 i". 10. 'so dueto 'ar"e concentration and "radient of stress around t,e crac tip t,esestresses are a'so s,o4n in en'ar"ed vie4 of t,e crac tip refer i".11 i".12.

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i". 7 (&es, p'ot of t,e deformed s,ape indicatin" oundar$ conditions and 'oadin" point)

i". A (&es, p'ot of t,e deformed s,ape near t,e crac tip)

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i". 9 (%ontour p'ots of ?on mises stress over t,e domain)

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i". 10 (%ontour p'ots near crac tip)

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i". 11 (%ontour p'ots of von mises stress near crac tip)

i". 12 (%ontour p'ots of -$near crac tip)

4.0 1es#lts*2

4." Stress Intensit Factor.

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+. /,e stress intensit$ factor CIis a proportiona'it$ constant re'atin" stress fie'dto r. ver$ materia' ,as some critica' va'ue for stress intensit$ factor C I and $determinin" CIfor a "iven "eometr$ under "iven oundar$ conditions it can epredicted 4,et,er t,e crac 4i'' propa"ate or not. /,ere are t,ree differentmodes of fracture 'eadin" to different stress intensit$ factor. Jur specimen fa''

under mode*I or openin" mode in 4,ic, t,e od$ is 'oaded $ tensi'e forcessuc, t,at t,e crac surfaces are pu''ed apart in t,e $ direction. or &ode* I,C1 va'ue is ca'cu'ated usin" ,andoo formu'a "iven e'o48

+

+

+=

432

2

3 66.572.1422.1364.4866.0

1

2

w

a

w

a

w

a

w

a

w

a

w

a

w

PKI

Puttin"P : 100Cpa 4 : 0.05m a : 0.025m a


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+

=

2

3sin

2sin1

2os

2

rK

fe

ystress

I

str ess

IK

at ever$ nodes is ca'cu'ated and t,e difference et4een t,is and e6act C I at

eac, node is a'so ca'cu'ated for findin" error in percenta"e point as s,o4n in ta'e

e'o48

/a'e *2 (Stress intensit$ factor)

Coordinates N

(De"rees)

r (m) -B(Pa) stressI

K Difference

from CI

rror

(K)=(m) B(m)

3.5A*0 .73*05 7.53 3.@1*0 A.5A;07

.0;0@

2.9;05 @.A

5.9*0 1.@0*0 15.0 @.15*0 @.@;0

7

3.97;0

@

3.71;05 A.5

A.@*0 3.5A*0 22.53 9.35*0 5.@;0

7

3.9A;0

@

3.5A;05 A.3

1.1@*03 @.@9*0 30.03 1.3*03 .7A;0

7

3.A;0

@

5.00;05 11.5

1.7*03 1.12*03 37.5 1.A5*03 .29;0

7

3.A5;0

@

.A5;05 11.2

1.75*03 1.7@*03 5.02 2.A*03 3.@A;07

3.@7;0@

@.@7;05 15.

/,e

stres s

IK

va'ues indicated in aove ta'e are p'otted a"ainst r as s,o4n e'o4 in

i".138

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0 0 0 0 0 0 0

3!500!000'00

3!#00!000'00

3!$00!000'00

3!%00!000'00

3!&00!000'00

4!000!000'00

4!100!000'00

r (m)

i". 13 (Grap, et4een CIstress and r)

4.$e-aior o% t-e oenin! stress aro#nd t-e crac

/o furt,er esta'is, t,e accurac$ of t,e resu'ts otained t,rou", & t,e an"u'ar

variation of t,e computed stress is compared 4it, t,e an"u'ar variation of actua' C*

fie'd stress. or t,is ana'$sis 1 nodes around t,e crac tip (0 L N L O) are se'ected

and for eac, node coordinates and -$ is recorded. irst t,e stress is norma'iHed for

eac, node usin" actua' C( 4it, fo''o4in" formu'a8

I

fe

yfe

yK

r

2! =

(1)

>o4 t,e an"u'ar variation of stress accordin" to t,e C*fie'd so'ution is ca'cu'ated as

e'o48

+=

2

3sin

2sin1

2os)(!

y

(2)

sin" aove formu'as of eEuation 1 2 norma'iHed stress va'ue is ca'cu'ated for a''

se'ected nodes and ot, t,e norma'iHed stress va'ues are p'ot a"ainst an"'e N as

s,o4n in i".1.

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0 30 #0 &0 120 150 1%0

0

2

4

#

%

10

12

2"

1"

6 (De!ress)

i". 1 (Grap, of norma'ised stress va'ues as a function of an"'e N)

rom t,e aove "rap, it can easi'$ een oserved t,at t,e ot, va'ues are ver$

c'ose to eac, ot,er over various va'ues of an"'e N and can reaffirms t,at t,e resu'ts

otained $ our mes, ,ere are reasona'e to consider for t,e fracture ana'$sis of

"iven specimen.

5. Disc#ssions

/,e process of ana'$Hin" standard fracture specimen usin" & as is t,e case in

t,is proect is Euite usefu' in savin" time and resources "iven t,e accurac$ of resu'ts

otained ,ere. In ever$ va'ue otained from & t,e error from actua' va'ue is 4it,in

a fe4 percenta"e point 4,ic, presents a stron" case for carr$in" out suc, &

ana'$sis in t,e fie'd of fracture mec,anics especia''$ 4,en 4e 4ant to "et t,e resu'ts

4it,in s,ort period of time and are 'acin" in resources for carr$in" out actua' tests.

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fracture specimen stree analysis

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