Design of a Double Cantilever Beam Test Specimen and Fixture for Kink Band Formation in Unidirectional Fibre Reinforced Composites.

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Design'of'a'Double' Cantilever'Beam'Test'

Specimen'and'Fixture'for' Kink'Band'Formation'in' Unidirectional'Fibre>

Reinforced'Composites'

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Bachelor Degree Project in Mechanical Engineering C-Level 22.5 ECTS

Spring term 2015

Juan Antonio Cámara Vela Juan Manuel Sánchez Molina

Supervisor: Moyra McDill

Examiner: Karl Mauritsson

Abstract

Composite"materials"are"widely"used"in"demanding"applications"in"aerospace"and"other"industries."In"

order" to" understand" the" complex" behaviour" of" the" composite" materials" and" their" components,"

standardised"test"methods"are"used."One"example"is"the"double"cantilever"beam"(DCB)"test"in"which"

the"test"specimen"is"loaded"in"an"opening,"i.e.,"tensile"mode."Failures"in"composite"materials"loaded"

compression"are"different"from"those"in"tension,"for"example,"kink"band"or"bucklingClike"failures"can"

occur."

In"this"project,"several"DCBs"are"designed"and"a"new"fixture"which"allows"for"compression"testing"of"a"

DCB"is"developed"for"an"existing"Instron"testing"machine."The"fixture"overcomes"a"known"problem"of"

tensile" peak" causing" the" failure" of" the" adhesive" at" the" inner" surfaces" of" the" DBC" by" applying"

additional"compressive"loads"along"the"outer"surfaces"of"the"DBC."The"compressive"forces"can"induce"

the"desired"kink"band"formation"so"that"researchers"can"better"study"the"failure"mode."

The"conceptual"development"of"the"new"DCBs"and"the"new"fixture"are"presented."Several"prototypes"

of" the" specimens" and" the" fixture" are" modelled" using" the" threeCdimensional" (3D)" computerCaided"

design"software"Creo"Parametric"2.0.""One"of"the"fixtures"is"selected"to"further"study."The"different"

DCB" specimens" are" studied" in" order" to" obtain" information" about" the" kink" band" using" 3D" finite"

element" analysis" with" the" software" programme" Abaqus" CAE." The" selected" fixture" is" analysed" to"

determine"if"there"are"any"areas"of"concern."Finally,"the"behaviour"of"the"compression"stress"along"

the"DCB"using"two"pairs"of"forces"is"studied.""

Unfortunately," it" is" determined" that" the" tensile" peak" experienced" by" the" adhesive" cannot" be"

eliminated"by"the"application"of"two"pairs"of"compressive"loads,"one"at"the"free"end"and"the"other"in"

the"vicinity"of"the"tensile"peak."Several"suggestions"are"made"for"future"work"which"might"serve"to"

reduce"the"tensile"peak;"e.g.,"the"movable"force"couple"is"applied"as"a"surface"load"instead"of"a"point"

load."For"this,"the"fixture"will"have"to"be"modified"with"a"new"geometry,"although"the"DCB"could"be"

the"same."This"will"allow"further"work"to"focus"on"the"combined"behaviour"of"the"tensile"peak"and"

the"fixture."

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Certification+

This"thesis"has"been"submitted"by"Juan"Antonio"Cámara"Vela"and"Juan"Manuel"Sánchez"Molina"to"the"

University" of" Skövde" as" a" requirement" for" the" degree" of" Bachelor" of" Science"in" Mechanical"

Engineering."The"undersigned"certify"that"all"the"material"in"this"thesis"that"is"not"our"own"has"been"

properly"acknowledged"using"accepted"referencing"practices"and,"further,"that"the"thesis"includes"no"

material"for"which"we"have"previously"received"academic"credit."

"

"Juan"Antonio"Cámara"Vela""" " " """""""""""""""""""""""""Juan"Manuel"Sánchez"Molina""

Skövde"2015C06C1"

Institutionen"för"Ingenjörsvetenskap/"Department"of"Engineering"Science"

! !

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Acknowledgements+

We"would"like"to"express"our"gratitude"to"the"University"of"Skövde"for"giving"us"the"opportunity"to"

study"for"one"year"in"Skövde"and"to"do"this"final"thesis."We"would"also"like"to"thank"the"teachers"that"

this" year" taught" us" all" we" need" to" know" to" deal" with" this" thesis," especially" Tobias" Andersson" that"

apart" from" being" our" teacher" of" the" finite" element" method" was" our" client" for" this" thesis" and" has"

helped"us"with"all"the"challenges"that"we"have"had."To"all"our"friends"that"this"year"have"lived"with"us"

and"they"have"experienced"this"thesis"as"we"have"suffered,"“gracias”."To"our"family"that"from"Málaga,"

they" have" supported" us" and" without" them," we" would" not" be" here." Most" of" all," to" Moyra," our"

supervisor," for" her" understanding," enthusiasm" and" wisdom," we" only" can" say:" “thank" you" for" your"

infinite" patience”." She" pushed" us" since" the" first" meeting" and" she" always" gave" us" the" energy" to"

continue"the"thesis."

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Table+of+Contents+

Abstract"..."ii"

Certification"..."iii"

Acknowledgements"..."iv"

List"of"Figures"..."vii"

List"of"Symbols

"..."x"

1."Introduction"..."1"

1.1." Proposed"use"of"the"double"cantilever"beam"(DCB)"..."3"

1.2."The"double"cantilever"beam"in"compression"..."4"

1.2.1."Initial"concept"..."5"

1.2.2."Equipment,"material"and"software"constraints"..."5"

1.3." Technology"Society"and"Environment"..."6"

1.4." Overview"..."7"

2."Method"..."8"

2.1"General"..."8"

2.2"Design"phase"..."8"

2.3."Simulation"phase"..."10"

2.3.1."Modelling"in"Creo"..."10"

2.3.2."Materials"and"properties"..."10"

2.3.3."Discretisation"..."11"

2.3.4."Boundary"conditions"and"forces"..."13"

2.3.5."DCB"analysis"..."15"

2.3.6."Fixture"analysis"..."15"

3."Results"..."16"

4."Discussion"..."19"

5."Conclusions"and"future"work"..."22"

References"..."23"

APPENDIX"..."25"

A1."Division"of"labour"..."25"

"

A2."Work"breakdown"and"Time"Plan"..."26"

A3."Drawings"and"plans"..."29"

A4."Sketches"for"the"fixture"and"final"assembly"..."32"

A5."Properties"and"dimensions"of"the"DCBs"..."33"

A6."Results"in"the"DCBs"and"in"the"fixture"..."36"

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List+of+Figures+

Figure'1.'1'Different'types'of'carbon'fibre'...'1 "

Figure'1.'2'Kink'band,'result'of'compression'loads'(Budiansky'&'Fleck,'1994)'...'2 "

Figure'1.'3'Schematics'and'definition'of'the'kink'band'geometric'parameters:'fibre'angle'α,'band'angle'β'and' band'width'ω'(Pimenta,'et'al.,'2009)'...'2 "

Figure'1.'4'(i)'elastic'domain;'(ii)'softening'domain;'(iii)'fibre'failure'domain'(Pimenta,'et'al.,'2009)'...'3 "

Figure'1.'5'DCB'configuration'in'opening'mode'(Salomonsson'&'Andersson,'2006)'...'4 "

Figure'1.'6'DCB'in'compression'and'the'expected'stress'distribution'along'(x)'the'adhesive'layer'(stiffness'k)' (Stigh,'1988)'...'5 "

Figure'1.'7'Early'conceptual'design'of'the'fixture'showing'additional'compressive'loading'...'5 "

Figure'1.'8'Grip'dimensions'(Instron,'2012)'...'6 "

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Figure'2.'1'A)'3D'model'of'the'grip'B)'3D'model'of'the'DCB'C)'Fixture'with'hinge'...'10 "

Figure'2.'2'Hexahedrons'and'tetrahedrons'elements'(Simulia,'2011)'...'11 "

Figure'2.'3'Linear'and'quadratic'elements'Abaqus'CAE'6.13'...'12 "

Figure'2.'4'Mesh'in'a'DCB'as'seen'from'the'side'...'12 "

Figure'2.'5'Mesh'in'the'fixture'...'12 "

Figure'2.'6'Transformation'from'square'to'trapezoid'(Simulia,'2011)'...'13 "

Figure'2.'7'Boundary'conditions'and'forces'in'the'DCB'...'13 "

Figure'2.'8'Distance'“a”'and'“b”'and'forces'F

,'F

'and'R'...'14 "

Figure'2.'9'Boundary'conditions'and'loads'in'the'main'body'of'the'fixture'and'in'the'hinge.'A)'First'simulation.'B)' Second'simulation'...'15 "

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Figure'3.'1'Parameters'in'the'DCBs'...'16 "

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Figure'4.'1'Curve'obtained'(down)'vs'theoretical'curve'(up)'...'20 "

Figure'4.'2'Stress'curves'in'the'position'I,'II'and'III'in'the'modified'DCB'...'20 "

Figure'4.'3'Variation'of'the'tensile'peak'due'to'the'position'of'F2'...'21 "

Figure'4.'4'Variation'of'the'tensile'peak'position'due'to'the'position'of'F2'...'21 "

"

Figure'A2.'1'Time'comparison'...'26 "

Figure'A2.'2'Time'plan'I'...'27 "

Figure'A2.'3'Time'plan'II'...'28 "

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Figure'A3.'1'Attachment'kit'...'29 "

Figure'A3.'2'DCB'drawing'...'30 "

Figure'A3.'3'Fixture'drawing.'Main'body'...'30 "

Figure'A3.'4'Fixture'drawing.'Hinge'...'31 "

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Figure'A4.'1'Fixture'sketches'A)'Rail'with'two'movable'forces'B)'Semi'rail'with'one'movable'force'C)'Semi'rail' with'sphere'D)'Fastener'...'32 "

Figure'A4.'2'Different'views'for'the'whole'assembly'...'32 "

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Figure'A5.'1'Positions'of'F

'...'33 "

Figure'A5.'2'Dimensions'of'the'DCB'and'position'of'F

'...'33 "

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Figure'A6.'1'Proposed'I,'U'...'36 "

Figure'A6.'2'Proposed'I,'VM'...'36 "

Figure'A6.'3'Proposed'I,'S

'...'37 "

"

Figure'A6.'4'Proposed'I,'S

'...'37 "

Figure'A6.'5'Proposed'I,'Stress'along'the'composite'...'38 "

Figure'A6.'6'ASTM'I,'U'...'38 "

Figure'A6.'7'ASTM'I,'VM'...'39 "

Figure'A6.'8'ASTM'I,'S

'...'39 "

Figure'A6.'9'ASTM'I,'S

'...'39 "

Figure'A6.'10'ASTM'I,'Stress'along'the'composite'...'40 "

Figure'A6.'11'Short'I'composite'75'mm,'U'...'40 "

Figure'A6.'12'Short'I'composite'75'mm,'VM'...'40 "

Figure'A6.'13'Short'I,'S

'...'41 "

Figure'A6.'14'Short'I'composite'75'mm,'S

'...'41 "

Figure'A6.'15'Short'I'composite'75'mm,'Stress'along'the'composite'...'42 "

Figure'A6.'16'Short'II'composite'75'mm,'U'...'42 "

Figure'A6.'17'Short'II'composite'75'mm,'VM'...'42 "

Figure'A6.'18'Short'II'composite'75'mm,'S

'...'43 "

Figure'A6.'19'Short'II,'S

'...'43 "

Figure'A6.'20'Short'II'composite'75'mm,'Stress'along'the'composite'...'44 "

Figure'A6.'21'Short'III'composite'75'mm,'U'...'44 "

Figure'A6.'22'Short'III'composite'75'mm,'VM'...'44 "

Figure'A6.'23'Short'III'composite'75'mm,'S

'...'45 "

Figure'A6.'24'Short'III'composite'75'mm,'S

'...'45 "

Figure'A6.'25'Short'III'composite'75'mm,'Stress'along'the'composite'...'46 "

Figure'A6.'26'Modified'I,'U'...'46 "

Figure'A6.'27'Modified'I,'VM'...'46 "

Figure'A6.'28'Modified'I,'S

'...'47 "

Figure'A6.'29'Modified'I,'S

'...'47 "

Figure'A6.'30'Modified'I,'Stress'along'the'composite'...'48 "

Figure'A6.'31'Modified'II,'U'...'48 "

Figure'A6.'32'Modified'II,'VM'...'48 "

Figure'A6.'33'Modified'II,'S

'...'49 "

Figure'A6.'34'Modified'II,'S

'...'49 "

Figure'A6.'35'Modified'II,'Stress'along'the'composite'...'50 "

Figure'A6.'36'Modified'III,'U'...'50 "

Figure'A6.'37'Modified'III,'VM'...'50 "

Figure'A6.'38'Modified'III,'S

'...'51 "

Figure'A6.'39'Modified'III,'S

'...'51 "

Figure'A6.'40'Modified'III,'Stress'along'the'composite'...'52 "

Figure'A6.'41'Long'I'composite'125'mm,'U'...'52 "

Figure'A6.'42'Long'I'composite'125'mm,'VM'...'52 "

Figure'A6.'43'Long'I'composite'125'mm,'S

'...'53 "

Figure'A6.'44'Long'I'composite'125'mm,'S

'...'53 "

Figure'A6.'45'Long'I'composite'125'mm,'Stress'along'the'composite'...'54 "

Figure'A6.'46'Long'II'composite'125'mm,'U'...'54 "

Figure'A6.'47'Long'II'composite'125'mm,'VM'...'54 "

Figure'A6.'48'Long'II'composite'125'mm,'S

'...'55 "

Figure'A6.'49'Long'II'composite'125'mm,'S

'...'55 "

Figure'A6.'50'Long'II'composite'125'mm,'Stress'along'the'composite'...'56 "

Figure'A6.'51'Long'III'composite'125'mm,'U'...'56 "

Figure'A6.'52'Long'III'composite'125'mm,'VM'...'56 "

Figure'A6.'53'Long'III'composite'125'mm,'S

'...'57 "

Figure'A6.'54'Long'III'composite'125'mm,'S

'...'57 "

Figure'A6.'55'Long'III'composite'125'mm,'Stress'along'the'composite'...'58 "

Figure'A6.'56'Short'I'composite'100'mm,'U'...'58 "

Figure'A6.'57'Short'I'composite'100'mm,'VM'...'59 "

Figure'A6.'58'Short'I'composite'100'mm,'S

'...'59 "

Figure'A6.'59'Short'I'composite'100'mm,'S

'...'60 "

Figure'A6.'60'Short'I'composite'100'mm,'Stress'along'the'composite'...'60 "

Figure'A6.'61'Short'III'composite'100'mm,'U'...'61 "

Figure'A6.'62'Short'III'composite'100'mm,'VM'...'61 "

Figure'A6.'63'Short'III'composite'100'mm,'S

'...'62 "

Figure'A6.'64'Short'III'composite'100'mm,'S

'...'62 "

Figure'A6.'65'Short'III'composite'100'mm,'Stress'along'the'composite'...'63 "

Figure'A6.'66'Long'I'composite'100'mm,'U'...'63 "

Figure'A6.'67'Long'I'composite'100'mm,'VM'...'63 "

Figure'A6.'68'Long'I'composite'100'mm,'S

'...'64 "

Figure'A6.'69'Long'I'composite'100'mm,'S

'...'64 "

Figure'A6.'70'Long'I'composite'100'mm,'Stress'along'the'composite'...'64 "

Figure'A6.'71'Long'II'composite'100'mm,'U'...'65 "

Figure'A6.'72'Long'II'composite'100'mm,'VM'...'65 "

Figure'A6.'73'Long'II'composite'100'mm,'S

'...'65 "

Figure'A6.'74'Long'II'composite'100'mm,'S

'...'66 "

Figure'A6.'75'Long'II'composite'100'mm,'Stress'along'the'composite'...'66 "

Figure'A6.'76'Long'III'composite'100'mm,'U'...'67 "

Figure'A6.'77'Long'II'composite'100'mm,'VM'...'67 "

Figure'A6.'78'Long'II'composite'100'mm,'S

'...'67 "

Figure'A6.'79'Long'II'composite'100'mm,'S

'...'68 "

Figure'A6.'80'Long'II'composite'100'mm,'Stress'along'the'composite'...'68 "

Figure'A6.'81''Fixture'main'body,'U'...'69 "

Figure'A6.'82'Fixture'main'body,'VM'top'view'...'69 "

Figure'A6.'83'Fixture'main'body,'VM'bottom'view'...'69 "

Figure'A6.'84'Fixture'main'body,'VM'rail'view'...'70 "

Figure'A6.'85'Fixture'hinge,'U'...'70 "

Figure'A6.'86'Fixture'hinge,'VM'...'71 "

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List+of+Symbols ¹ +

"

F

Fixed'pair'of'forces'

F

Movable'pair'of'forces'

S

Maximum'compression'stress'

S

Maximum'value'of'the'tensile'peak'

U" Maximum'vertical'displacement'

VM" Maximum'von'Mises'stress'

X" Position'of'F

Y

Position'of'F

'

Z" Position'of'the'maximum'tensile'peak'

E" Young´s'Modulus'

k" Stiffness'of'the'specimen'

α" Fibre'angle'

β" Bond'angle'

ν" Poisson´s'ratio'

σ

" Compressive'stress'

σ

" Yield'limit'

ω" Width'of'the'band'

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"

1. Units,"as"appropriate"are"introduced"in"text."

1.+Introduction+

This"project"deals"with"composite"materials"which"are"attractive"materials"in"applications"where"high"

stiffnessCtoCweight" ratio" and" high" strengthCtoCweight" ratio" are" important" (Beng," et" al.," 2007),"

(Yokozeki,"et"al.,"2006)"and"(Fleck,"et"al.,"1997)."FibreCreinforced"polymers"are"used"in"demanding"and"

critical" applications" in" aerospace," defence" and" other" industries." For" this" reason," it" is" essential" to"

understand" the" complex" failure" and" deformation" mechanisms" under" compression" (US" Congress"

Office"of"Technology"Assessment,"1988).""

Carbon"fibre"exists"in"several"forms:"chopped,"unidirectional,"bidirectional"and"multidirectional."The"

chopped"case"refers"to"carbon"fibre"scattered"in"the"matrix"as"particles."Unidirectional"carbon"fibre"

(UCF)"has"all"fibres"aligned"in"the"same"direction."The"bidirectional"structure"has"the"fibre"alignment"

in"two"different"directions"and"the"multidirectional"structure"uses"layers"of"different"fibre"directions"

as"shown"in"Figure"1.1."

"

"

"

Figure'1.'1'Different(types(of(carbon(fibre(

"

In"this"thesis"only"the"UCF"is"used"and"its"behaviour"in"compression"is"studied."UCF"is"a"material"that"

is"very"good"when"is"used"in"tension,"but"when"it"is"used"in"compression"its"failure"mode"can"be"a"

type"of"fibre"buckling"in"which"a"plane"consisting"of"kinked"fibres"develops"(Berbinau,"et"al.,"1999)."

This" type" of" failure" is" called" kink" bands" and" is" shown" in" Figure" 1.2" where" the" UCF" is" shown" in" a"

polymer"matrix."An"applied"compressive"stress"σ

"is"accompanied"by"a"kink"band"offset"at"an"angle"α."

"

"

"

Particles"

reinforced"fibre" Unidirectional"

fibre"orientation"

Bidirectional"

fibre"orientation" Multidirectional"

fibre"orientation"

"

Figure'1.'2(Kink(band,(result(of(compression(loads((Budiansky'&'Fleck,'1994)'

According" to" Pimenta" (2009)" kink" band" formation" is" the" most" common" failure" in" compression" of"

composite"material;"the"development"of"Figure"1.3"shows"the"parameters"of"this"formation"with"α,"

again," the" fibre" angle," β" the" bond" angle" and" ω" the" width" of" the" band." Berbinau," Soutis" and" Guz"

(1999)," describe" the" kink" band" as" a" local" instability." This" microCbuckling" is" the" result" of" combined"

compression"and"shear"loading"due"to"the"imperfection"of"fibre"misalignment."The"formation"of"the"

kink"band"occurs"in"stages"as"Figure"1.4"shows.""First"elastic"kinking"in"the"fibres"initiates"a"curvature"

in"the"elastic"zone"of"the"material."The"second"stage"involves"a"softening"domain."In"the"third"stage"

the"shear"affects"the"fibres"causing"a"moment"and"finally"collapse"follows."

"

Figure'1.'3'Schematics(and(definition(of(the(kink(band(geometric(parameters:(fibre(angle(α,(band(angle(β(and(band(width(

ω'(Pimenta,'et'al.,'2009)' '

'

"

Figure'1.'4'(i)(elastic(domain;((ii)(softening(domain;((iii)(fibre(failure(domain'(Pimenta,'et'al.,'2009)' '

1.1. Proposed*use*of*the*double*cantilever*beam*(DCB)*

The"DCB"test"methodology"for"tensile"loading"is"described"for"example"in"ASTM"(1999)."A"variation"on"

the" usual" standards" is" described" in" Salomonsson" (2006)" as" shown" in" Figure" 1.5." " The" top" and" the"

bottom"substrates"of"the"DCB"are"made"of"Riggor"Uddeholm"steel"(Eklind,"et"al.,"2014)."Between"the"

steel"layers"there"is"a"composite"material"held"in"place"with"a"thin"adhesive"layer."The"composite"is"

UCF,"it"is"in"an"epoxy"matrix"and"the"fibres"are"aligned"vertically."This"kind"of"specimen"is"commonly"

used" in" three" different" tests:" Mode" I" (tensile" opening)" as" shown" in" Figure" 1.5," Mode" II" (in" plane"

shear);"and"Mixed"Mode"I/II."These"tests"focus"on"the"calculation"of"the"interClaminar"fracture"energy"

(Berbinau,"et"al.,"1999)."Standards"for"the"use"of"the"DCB"in"Mode"I"have"been"developed"by"both"BSI"

and"ASTM"(BS7991,"British"Standard,"2001),"(ASTM,"1999).""Mode"II"and"Mode"I/II"have"other"kinds"of"

standards" e,g." ASTM" D6671/D6671MC13." It" is" important" to" note" that" there" is" no" standard" test" for"

compression"loading"of"the"DCB."

Andersson" (2015)" appears" to" be" the" first" to" study" kink" band" formation" using" a" DCB" loaded" in"

compression," although" kink" band" failure" has" been" studied" by" different" researchers." For" example,"

Narayanan" and" Schadler" (1999)" who" studied" the" kink" band" formation" by" compression" in" graphiteC fibreCreinforced"epoxy"composites."LorenzoCVillafranca"et"al."(2011)"studied"the"kink"band"in"fibres"of"

polybenzobysoxazole"with"and"without"a"plasma"treatment."Jensen"and"Christoffersen"(1996)"studied"

the"sensitivity"of"the"kink"stress"to"fibre"misalignment"and,"Zidek"and"Völlmeck"(2014)"have"said"that,"

“the" imperfections" stemming" from" the" manufacturing" process" influence" the" compressive" strength"

and"fibre"kinking"of"unidirectional"composites"significantly”."

"

"

Figure'1.'5'DCB(configuration(in(opening(mode'(Salomonsson'&'Andersson,'2006)'

1.2.*The*double*cantilever*beam*in*compression*

Andersson" (2015)" has" identified" a" problem" with" the" use" of" the" DBC" in" compression," i.e.," closing"

mode."The"two"outer"steel"layers"are"connected"by"a"carbon"fibreCreinforced"adhesive"as"shown"in"

Figure" 1.6" are" loaded" in" compression." In" the" curve," the" stress" starts" in" compression," then," this"

compression" decreases" and" becomes" to" tensile" stress" and" reaches" a" peak" of" stress." However,"

Andersson" (2015)" said" that" the" adhesive" layer" is" unable" to" support" a" tensile" peak" greater" than" 10"

MPa." In" this" case" the" steel" layers" will" separate." To" prevent" this" separation," Andersson" (2015),"

requested"the"study"of"the"behaviour"of"the"DCB"when"it"is"loaded"in"compression"and"the"design"of"a"

special"fixture"in"which"a"pair"of"additional"movable"compressive"loads"can"be"applied"to"prevent"the"

separation"of"the"layers."

Therefore,"the"aim"of"this"thesis"is"to"develop"a"DCB"and"a"fixture"that"together""allow"the"specimen"

to" experience" the" load" necessary" to" create" the" kink" band," i.e.," " 1" GPa" in" compression," while"

simultaneously"reducing"the"tensile"peak"in"the"UCF"to"under"10"MPa"(Andersson,"2015).""For"this,"

different" DCB" geometries" will" be" analysed" under" loading" in" three" different" positions" in" order" to"

achieve"the"required"stress"curve."Also,"a"fixture"capable"of"creating"the"two"force"pairs"in"the"DCB"

will"be"developed."

"

Figure'1.'6'DCB(in(compression(and(the(expected(stress(distribution(along((x)(the(adhesive(layer((stiffness(k)'(Stigh,'1988)'

"

1.2.1.+Initial+concept+

In" the" initial" concept," as" explained" by" Andersson" (2015)" compression" is" applied" at" the" ends" of"the"

DCB"and"along"the"upper"and"lower"sides"of"the"specimen"as"shown"Figure"1.7."Two"loads"remain"

fixed"at"the"free"end,"and"the"other"two"can"be"moved"along"the"surface,"depending"on"where"the"

peak"is"reached."The"feature"of"mobility"is"novel"as"it"will"be"possible"to"move"the"forces"along"the"

surfaces"in"order"to"obtain"different"results"during"testing."As"will"be"seen,"the"concept"is"expanded"

to"include"redesign"of"the"DCB."

"

Figure'1.'7'Early(conceptual(design(of(the(fixture(showing(additional(compressive(loading'

1.2.2.+Equipment,+material+and+software+constraints+

The"DCB"and"the" fixture"have"been"designed"using"Creo"Parametric"2.0"and"analysed"with"Abaqus"

CAE"6.13."Both"designs,"the"DCB"and"the"fixture,"must"satisfy"the"geometric"constrains"of"the"Instron"

machine." This" machine" is" called" 8802/8803" Floor" Model" Fatigue" Testing" Systems" of" Instron

." The"

""1"GPa"

F"

F"

"

machine,"which"is"found"in"the"mechanical"laboratory"of"the"University"of"Skövde,"can"perform"both"

tensile"and"compression"tests."It"has"two"grips"where"the"specimen"is"positioned"as"shown"in"Figure"

1.8."A"detailed"description"is"attached"in"the"Appendix"A3.""

Creo" Parametric" 2.0" is" a" design" software" programme" to" model" in" three" dimensions" (3D)." This"

programme"is"used"because"of"the"ease"of"export"of"the"design"to"Abaqus"CAE"6.13."The"grip,"the"

specimen"and"the"fixture"are"modelled"in"this"programme."Abaqus"CAE"6.13"is"a"simulation"software"

programme"that"uses"the"finite"element"method"(FEM)."In"this"thesis,"this"programme"was"used"to"

analyse"the"behaviour"of"both"the"specimen"and"the"fixture"under"loading."

"

Figure'1.'8'Grip(dimensions((Instron,'2012)'

1.3. Technology*Society*and*Environment*

In"term"of"technology"different"software"programmes"of"the"engineering"world"will"be"used."The"new"

fixture"will"contribute"to"the"study"of"kink"band"formation"in"UCF"in"composites."

In"the"area"of"society"and"environment"the"use"of"composites"in"automotive"and"aerospace"sectors"

will"continue"to"contribute"to"lower"weight"vehicles"with"lower"emissions,"contributing"to"a"better"

environment."

The"steel"of"the"DCB"will"be"reusable"in"different"tests"because"in"the"compression"test"only"the"UCF"

breaks."Also,"a"new"use"will"be"given"to"the"laboratory"machine"by"the"new"fixture.""The"stainless"

steel"fixture"is"recyclable"

1.4. Overview*

In"the"upcoming"sections"the"method,"the"results"the"discussion"and"the"conclusions"and"future"work"

will"be"explained."

Method'

In" the" method" information" about" the" kink" band," DCBs" and" different" compression" tests" will" be"

searched." After" that," the" DCB" proposed" by" the" client" will" be" created" in" 3D" and" the" fixture" will" be"

developed"and"modelled"in"3D."Since"the"first"DCB"specimen"will"not"be"perfect,"an"iterative"process"

will"be"adapted."When"the"DCB"fails"for"any"reason,"new"dimensions"will"be"reconsidered."Then,"the"

new"model"has"to"be"done"in"Creo"Paramatric"and"after"that,"the"new"simulation"will"be"analysed"in"

Abaqus"CAE."

Also,"in"this"part,"the"material"for"the"fixture"will"be"selected"and"the"material"properties"for"the"DCB"

will"be"searched."Finally,"the"mesh,"the"boundary"conditions,"the"forces"and"the"analysis"of"the"DCB"

and"the"analysis"of"the"fixture"will"be"studied."

Results'

The"different"results"of"each"case"will"be"presented"without"any"interpretation"in"this"section."

Discussion'

In"the"discussion"the"results"will"be"analysed"and"interpreted."A"new"understanding"of"the"problem"

will"be"presented."

Conclusions'and'future'work'

With" the" data" analysed," the" main" ideas" of" the" work" will" be" summarised" in" the" conclusions." In" the"

future"work"new"steps"to"take"and"new"ideas"that"seem"more"promising"will"be"suggested.""

"

"

"

" "

"

2.+Method+

2.1*General**

This" project" followed" a" workflow" that" was" divided" in" two" phases." The" first" phase" was" the" design"

phase." Here," two" modes" were" adapted," the" divergent" period" and" the" convergent" period" (Hales,"

1993)."The"divergent"period"was"characterized"by"searching"for"information"about"the"kink"band,"DCB"

and"similar"projects."Then,"different"sketches"for"the"fixture"were"drawn"in"order"to"choose"the"one"

that"best"addressed"the"problem."After"that,"the"convergent"period"arrived."It"was"characterized"by"

selection"of"the"best"idea,"specifically"the"best"sketch"was"chosen."

The"second"phase"was"the"simulation"phase."Here"the"models"of"the"DCB"and"the"fixture"was"realised"

in"Creo"Parametric."Then,"these"models"were"analysed"in"Abaqus"CAE"by"finite"element"analysis"and"

the"results"were"obtained."This"phase"was"divided"in"two"parts."Firstly,"the"DBC"was"analysed"with"

three"different"geometries:"that"proposed"by"the"client;"one"matching"the"ASTM"standard"(1999)"and"

a"third"modified"version"developed"to"achieve"the"aim"of"the"project."The"client"further"suggested"

creation" of" one" DCB" shorter" than" the" modified" version" and" one" DCB" longer" than" the" modified"

version." These" latter" two" new" DCBs" were" divided" in" two" groups," one" group" with" 100" mm" of"

composite"and"the"second"group"with"the"composite"length"depending"on"the"length"of"steel"in"the"

DCB."After"modelling"all"of"the"new"DCBs,"they"were"analysed."Finally"the"fixture"was"analysed."

2.2+Design+phase+

In"this"phase"some"concepts"of"the"fixture"were"sketched"based"on"measurements"taken"from"the"

Instron"testing"machine."These"concepts"were"designed"in"order"to"accomplish"the"main"objective,"

that"is,"to"create"a"kink"band"in"the"DCB"ensuring"that"the"three"layers"of"steel,"adhesive"and"UCF"

composite"remain"together."It"was"determined"that"the"inclusion"of"a"tab"allowing"the"grip"(Figure"

1.8)" to" hold" the" fixture" was" important" (Zomborcsevics," 2015)." Four" different" fixtures" were" then"

selected"for"further"study"and"evaluated"in"terms"of"their"pros"and"their"cons"as"shown"in"Table"2.1.""

In"Appendix"A4"the"3D"CAD"models"developed"for"each"sketch"are"shown."

Table"2.1"shows"that"the"semi"rail"with"one"movable"force"model"(Appendix"A4,"Figure"A4.B)"is"the"

preferred" design." Accordingly" it" was" presented" to" the" client" who" then" approved" the" concept" for"

further"study"and"analysis."In"the"chosen"fixture"some"changes"were"necessary"to"make"in"order"to"

minimize" the" resulting" moment" that" the" Instron" machine" cannot" support." For" this," a" hinge" was"

imposed"in"the"plane"part"between"the"device"and"the"grip"to"avoid"the"resulting"moment"that"the"

forces"create."Figure"2.1"C,"below,"shows"the"fixture"with"the"hinge"modification."

"

"

Table+2.1+Evaluation+of+the+fixtures+

Name+of+the+fixture+ Pros+ Cons+ !"#$ − !"#$+

Rail+with+two+

movable+forces+

' See!also!Figure!A4.1!A!!

The'rail'is'easy'to' machine' Both'forces'can'move'

along'the'rail' The'fixture'is'easy'to'

fix'in'the'grip'

Difficult'alignment' between'the'upper'

fixture'and'the' downer'fixture'

3>1=2'

Semi+rail+with+one+

movable+force+

+ See!also!Figure!A4.1!B!

The'rail'is'easy'to' machine' One'force'can'move'

along'the'rail' One'force'is'fixed' The'fixture'is'easy'to'

fix'in'the'grip'

Difficult'alignment' between'the'upper'

fixture'and'the' downer'fixture'

4>1=3' '

Semi+rail+with+

sphere+

+ See!also!Figure!A4.1!C!

The'rail'is'easy'to' machine' One'force'can'move'

along'the'rail' One'force'is'fixed'

Difficult'alignment' between'the'upper'

fixture'and'the' downer'fixture' The'sphere'is'not'easy'

to'machine' There'is'a'possible' movement'from'the' cylinder'while'testing'

3>3=0'

Fastener+

+ See!also!Figure!A4.1!D!

The'holes'are'easy'to' machine' One'force'is'fixed'

Easy'alignment' between'the'upper'

fixture'and'the' downer'fixture'

There'are'only'few' positions'of'the'force'

There'is'a'punctual' load'

3>2=1'

"

2.3.+Simulation+phase+

2.3.1.+Modelling+in+Creo+

In"this"phase"the"3D"models"for"the"DCBs,"the"grip"and"for"the"different"parts"of"the"fixture"as"shown"

in"Figure"2.1"were"created"using"Creo"Parametric"2.0."Also,"an"assembly"of"the"all"parts"was"created"

to"visualize"how"all"parts"would"function"together"(Figure"A4.2)."

"

Figure'2.'1(A)(3D(model(of(the(grip(B)(3D(model(of(the(DCB(C)(Fixture(with(hinge' '

2.3.2.+Materials+and+properties+

The"material"of"the"fixture"was"selected"and"the"properties"of"all"the"materials"were"searched."The"

material" of" the" grip" was" stainless" steel" (Euro" Inox," 2007)," the" material" of" the" DCB" was" Rigor" steel"

(Eklind," et" al.," 2014)" and" UCF" (Andersson," 2015)" and" for" the" fixture" the" material" selected" was"

stainless"steel"for"two"reasons:"first"it"was"available"and"the"same"material"as"in"the"grip"and,"second"

stainless"steel"is"recyclable."Table"2.3.1"shows"a"summary"of"the"material"properties"used."

"

"

A

"

B"

C

"

Table+2.3.1+Material+properties+

+ Material+ Yield+limit+(σ

)+

[MPa]+ Young´s++Modulus+(E)+

[MPa]+ Poisson´s+ratio+(ν)+

Rigor'Steel' 500' 190000' 0,31'

UCF' 1000' 117000' 0,31'

Stainless'steel' 502' 180000' 0,305'

"

2.3.3.+Discretisation+

Two"different"types"of"finite"elements"were"used"to"mesh"the"parts;"hexahedrons"and"tetrahedrons,"

as"is"shown"in"Figure"2.2."The"geometric"order"of"the"elements"is"also"important."There"are"two"types"

of" order:" linear" and" quadratic." The" linear" approximation" uses" the" formula" !" + !" between" nodes"

and"the"quadratic"element"uses"!!

+ !" + ! "between"nodes."In"case"of"large"displacements,"the"

quadratic" form" is" better" than" the" linear" (Belytsthko," 2013)." Figure" 2.3" shows" an" 8Cnode" linear"

hexahedron"and"a"10Cnode"quadratic"tetrahedron"as"defined"in"Abaqus"CAE"6.13."

The" geometry" for" the" DCB" specimens" was" freeCmeshed" using" 8Cnode" linear" hexahedrons" with"

reduced"integration"and"hour"glass"control"as"(C3D8R)"as"shown"in"Figure"2.4."The"convergence"was"

studied" in" each" DCB" and" the" resulting" number" of" elements" was" between" 150000" and" 190000"

elements."Table"A5.1"and"Table"A5.2"of"Appendix"A5,"show"the"number"of"elements"in"each"DCB."

While" tetrahedral" elements" can" be" stiffer" than" hexahedral" elements," of" the" same" order," they" are"

often"used"for"meshing"complex"geometries"(Cifuentes,"1992)."As"the"geometry"of"the"fixture"was"

more"complex"than"the"DCB"geometry,"the"two"parts"of"the"fixture"were"freeCmeshed"using"10Cnode"

quadratic" tetrahedrons" (C3D10)" as" is" shown" in" Figure" 2.5." The" quadratic" tetrahedrons" were" more"

demanding"of"CPU"resources"than"the"linear"hexahedrons."The"number"of"elements"in"the"fixture"was"

less"than"in"the"DCB"with"106533"elements"in"the"main"body"145000"in"the"hinge."

"

'

Figure'2.'2(Hexahedrons(and(tetrahedrons(elements((Simulia,(2011)'

"

"

Figure'2.'3 ' Linear(and(quadratic(elements(Abaqus(CAE(6.13'

"

Figure'2.'4(Mesh(in(a(DCB(as(seen(from(the(side(

' Figure'2.'5(Mesh(in(the(fixture(

Reduced" integration" was" selected" for" the" mesh" in" the" DCB" because" of" the" lower" computational"

resources"required"for"this"method."It"uses"only"one"Gauss"point"in"the"centre"of"the"hexahedron"to"

solve"the"integral."With"reduce"integration"a"problem"called"zero"energy"could"appear"(Belytsthko,"

2013)"and"for"this"reason,"hour"glass"control"was"needed."

Hourglass" control" builds" into" the" element" an" artificial" stiffness" to" prevent" zeroCenergy" mode" false"

results."For"example,"in"the"case"of"bending,"the"8Cnode"linear"elements"deform."If"the"value"of"this"

deformation" is" the" same" in" the" top" and" in" the" bottom" but" with" opposite" sign," the" perfect" square"

becomes"a"trapezoid"as"is"shown"in"Figure"2.6."The"area"of"the"trapezoid"is"the"same"as"the"area"of"

the"square,"and"the"single"point"of"integration"is"also"the"same"as"before."This"deformation"produces"

no"strains"hence"no"forces"to"resist"it"(Belytsthko,"2013)."To"avoid"this"problem,"the"hourglass"control"

of"Abaqus"increments"the"stiffness"of"some"nodes"in"the"element"creating"different"displacements.""

+

Figure'2.'6'Transformation(from(square(to(trapezoid((Simulia,'2011)(

2.3.4.+Boundary+conditions+and+forces+

In"the"DCB"models,"the"free"of"the"beam"was"clamped"in"the"xC,"yC"and"zC"directions"at"one"end"of"the"

specimen" as" shown" in" Figure" 2.7." This" zone" was" selected" because" it" was" far" from" the" area" of" the"

adhesive"and"did"not"affect"the"results."

To"apply"the"four"forces"in"the"DCB,"four"small"areas"were"created"in"order"to"apply"each"force"as"

pressures."The"areas"measured"1"mm"by"the"width"of"the"specimen"and"these"areas"were"collocated"

in"different"positions"depending"on"the"forces."The"pair"of"the"fixed"forces"was"called"F

"and"the"pair"

of"the"movable"forces"was"called"F

"as"shown"in"Figure"2.7."

"

Figure'2.'7'Boundary(conditions(and(forces(in(the(DCB(

A" summation" of" moments" with" respect" to" the" centre" of" the" fixture" was" calculated" as" shown" in"

Equation"(1),"where"“a”"is"the"distance"between"the"centre"and"F

"and"“b”"is"the"distance"between"

the"centre"and"F

"as"shown"in"Figure"2.8.""R"is"calculated"in"Equation"(2).""

F

F

F

F

Bounda ry "Condi tions "

"

↺ !!

= 0 → !

=

!

!!

" " " " " (1)"

! = !

+ !

" " " " " " (2)"

"

Figure'2.'8'Distance(“a”(and(“b”(and(forces(F

,(F

(and(R'

In"the"FECanalyses"F

"was"first"applied"to"the"DCB"without"F

and"it"was"increased"until"the"stress"in"

the"UCF"was"observed"to"be"1"GPa."Then,"the"second"force"F

"was"added."In"each"DCB"three"different"

positions"of"F

"were"simulated,"changing"“b”"and"therefore,"according"to"the"Equation"(1),"changing"

the"value"of"F

."Only"F

and"“a”"had"constant"values."

In"the"fixture,"two"different"simulations"were"done"in"order"to"study"the"main"body"of"the"fixture"and"

the"hinge."Firstly,"the"boundary"conditions"in"the"main"body"and"in"the"hinge"were"clamped"in"the"xC,"

yC"and"zC"direction"in"the"hole."The"forces"in"the"main"body,"F

"and"F

,"were"applied"in"a"small"area"as"

a"pressure"where"the"DCB"had"contact"with"the"fixture."Finally,"the"force"R"in"the"hinge"was"applied"

as"a"pressure"where"the"grip"was"attached"the"hinge."Figure"2.9"A"shows"the"boundary"conditions"

and"the"forces"in"the"main"body"of"the"fixture"and"in"the"hinge."

Then,"in"the"second"simulation,"the"location"of"the"boundary"conditions"and"the"forces"were"reversed"

as"shown"Figure"2.9"B."Here,"the"boundary"conditions"in"the"main"body"were"clamped"in"xC,"yC"and"zC"

direction"where"the"DCB"had"contact"with"the"fixture"and"in"the"hinge;"the"boundary"conditions"were"

also"clamped"where"the"grip"was"attached"the"hinge."The"force"was"R"in"both"parts"and"it"was"located"

in"the"hole."

"

Figure'2.'9'Boundary(conditions(and(loads(in(the(main(body(of(the(fixture(and(in(the(hinge.(A)(First(simulation.(B)(Second(

simulation(

2.3.5.+DCB+analysis+

The"DCB"analysis"was"a"long"process"in"which"different"geometries"of"DCB"were"studied."A"number"of"

parameters"were"considered:"

• The"steel"deformation"under"plastic"deformation."

• The"UCF"should"reach"1"GPa"in"compression"in"the"zone"closest"to"the"free"end"(Figure"1.6)."

• The" tensile" peak" should" be" less" than" 10" MPa" (Figure" 1.6)." The" layers" of" the" steel" could" not"

touch"each"other"during"loading,"i.e.,"the"displacement"of"each"layer"should"be"less"than"2.5"

mm."

The"first"DCB"that"was"analysed"was"that"proposed"by"the"client"as"shown"in"Figure"1.5."Then,"the"

ASTM" DCB" geometry" (ASTM," 1999)" was" analysed" and" finally," different" DCBs" were" created" with"

different"dimensions"of"the"steel"and"the"UCF"in"order"to"obtain"better"results."Table"A"and"Table"B"in"

Appendix"A5"show"all"the"dimensions"and"the"number"of"elements"in"the"mesh"for"each"DCB."In"total"

17"separate"cases"were"considered."

2.3.6.+Fixture+analysis+

Once" all" the" results" were" obtained" from" the" studied" DCBs," the" fixture" was" analysed." The" fixture"

analysis"was"divided"in"two"parts:"the"main"body"and"the"hinge."In"both"studies,"the"von"Mises"stress"

and"the"displacements"were"the"parameters"which"were"examined."

A"

B"

"

3.+Results+

In"the"study"of"the"DCB,"the"input"data"were"the"values"of"F

"and"F

"and"the"positions"of"F

"(X)"and"F

"

(Y)"in"each"DCB."Then,"the"output"results"were"the"maximum"displacements"in"the"vertical"direction"

(U),"the"maximum"von"Mises"stress"value"(VM)"taken"in"the"middle"of"the"upper"surface"of"the"steel,"

the"maximum"compression"stress"(S

),"the"maximum"value"of"the"tensile"peak"(S

)"and"the"position"

of"the"maximum"tensile"peak"(Z)."Figure"3.1"identifies"each"of"the"parameters"in"a"DCB."

Table"3.1"shows"the"input"values"and"the"results"for"the"first"three"DCBs,"the"proposed"by"the"client,"

the"ASTM"DCB"and"the"modified"one."In"this"Table,"the"number"I,"II"or"III"that"follows"the"name"of"the"

DCB"represents"that"in"the"same"DCB"the"position"of"F

"is"different."Also,"the"modified"one"is"called"

DCB." The" red" results" in" Table" 3.1" mean" that" the" DCB" fails," therefore," the" rest" of" DCBs" were" not"

analysed."

Once" these" three" DCBs" were" studied," one" shorter" and" one" longer" were" studied." The" first" had" the"

same" composite" length," which" was" 100" mm" and" in" the" second" case" the" composite" length" was"

changed." The" value" of" these" lengths" was" the" half" of" the" steel" lengths." Table" 3.2" and" Table" 3.3"

summarize"the"FEM"results"of"these"DCBs."

"

"

Figure'3.'1'Parameters(in(the(DCBs' '

"

"

Table+3.1+DCB+results+

Specimen+ F

++

[N]+

F

++

[N]+

X++

[mm]+

Y++

[mm]+

U+

[mm]+

VM+

[MPa]+

S

+ [MPa]+

S

++

[MPa]+

Z+

[mm]+

Proposed"I" 2000" 3800" 195" 50" 2.4" 540" C500" 172" 85"

Proposed"II" C" C" 195" 75" C" C" C" C" C"

Proposed"III" C" C" 195" 90" C" C" C" C" C"

ASTM"I" 1500" 2200" 351" 60" 2.85" 443" C760" 117" 148"

ASTM"II" C" C" 351" 120" C" C" C" C" C"

ASTM"III" C" C" 351" 168" C" C" C" C" C"

DCB"I" 15500" 29450" 195" 50" 1.1" 440" C970" 100" 75"

DCB"II" 15500" 58900" 195" 75" 1.1" 445" C1090" 26" 50"

DCB"III" 15500" 147250" 195" 90" 1.17" 510" C1900" 82" 60"

""

Table+3.2+DCBs+with+100+mm+composite+

Specimen' F

++

[N]' F

+ [N]+

X+

[mm]' Y+

[mm]' U+

[mm]'

VM+

[MPa]+

S

[MPa]' S

+ [MPa]'

Z++

[mm]' DCB"short"I" 30000" 84000" 145" 50" 0.4" 405" C960" 39" 74"

DCB"short"II" C" C" 145" C" C" C" C" C" C"

DCB"short"III" 30000" 140000" 145" 90" 0.5" 480" C1840" 89" 55"

DCB"I" 15500" 29450" 195" 50" 1.1" 440" C970" 100" 75"

DCB"II" 15500" 58900" 195" 75" 1.1" 445" C1090" 26" 50"

DCB"III" 15500" 147250" 195" 90" 1.17" 510" C1900" 82" 60"

DCB"long"I" 10000" 16000" 245" 50" 2.12" 436" C820" 115" 72"

DCB"long"II" 10000" 24000" 245" 75" 2.1" 440" C850" 52" 60"

DCB"long"III" 10000" 34286" 245" 90" 2.14" 446" C958" 110" 67"

"

"

"

"

In" the" fixture," the" parameters" studied" were" the" displacements" and" the" von" Mises" stress." The"

maximum"displacement"was"in"the"opposite"side"of"F

"and"the"value"was"0.08"mm."The"maximum"

stress,"according"with"von"Mises,"was"in"the"rounded"edge"that"connected"the"hinge"with"the"main"

body"of"the"fixture"and"the"value"was"460"MPa."In"this"case,"the"rail"and"the"piece"that"applied"F

"also"

had" high" stresses," but," because" of" the" entire" main" body" was" created" as" one" part," there" was"

concentration"of"stress"instead"of"a"problem"of"contact."For"this"reason,"the"high"stress"at"this"area"

was"not"considered"to"be"of"concern."

Finally,"the"hinge"was"simulated"and"the"maximum"displacement"was"in"the"middle"of"the"piece"and"

the"value"was"0.46"mm."The"maximum"stress"according"with"von"Mises"was"in"the"rounded"zone"and"

the"value"was"460"MPa."

Appendix"A6"contains"a"full"set"of"results"including"all"the"figures"with"all"the"FEA"studied"parameters"

for"each"DCB"and"for"the"two"parts"of"the"fixture."

"

"

"

"

" "

Table+3.3+DCBs+changing+the+composite+length+

Specimen' F

++

[N]+

F

++

[N]+

X+

[mm]+

Y+

[mm]+

U+

[mm]+

VM+

[MPa]+

S

[MPa]+

S

++

[MPa]+

Z++

[mm]+

DCB"short"I" 22000" 41067" 145" 37.5" 0.78" 548.5" C963" 43.65" 47.5"

DCB"short"II" 22000" 61600" 145" 50" 0.79" 463" C1024" 30.77" 25"

DCB"short"III" 22000" 154000" 145" 65" 0.88" 534" C1884" 90.66" 30"

DCB"long"I" 13500" 25920" 245" 62.5" 1.77" 475" C911.6" 133.5" 100"

DCB"long"II" 13500" 51840" 245" 93.75" 1.74" 477" C909" 16.5" 75"

DCB"long"III" 13500" 162000" 245" 115" 1.91" 549" C1870" 94.2" 80"