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Promotor: Prof. dr. ir. L.J. Sluys Copromotor: Dr. ir. J. Weerheijm Composition of the doctoral committee:
Rector Magnificus Delft University of Technology, Chairman Prof. dr. ir. L.J. Sluys Delft University of Technology, Promotor
Dr. ir. J. Weerheijm Delft University of Technology and TNO, Copromotor
Independent members:
Prof. P. Forquin Université Grenoble Alpes, France
Prof. dr. S.J. Picken Delft University of Technology, Netherlands
Prof. dr. ir. H.E.J.G. Schlangen Delft University of Technology, Netherlands
Dr. ir. E.P. Carton TNO, Netherlands
Reserve member:
Prof. dr. ir. J.G. Rots Delft University of Technology, Netherlands
The research presented in this Ph.D thesis has been financed by the Dutch Technology Foundation (STW) under grant 10615 and by TNO.
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Rec syst Org mat elas Kno for imp of th Aga com part poly In t are com tens (iii) Hop com exp resi dev com syst Firs com be r The poly syst Afte vari reco used Dyna cently, rese tems (layere ganisation fo terials for th stomeric po owledge abo propellants pact-induced he propellan ainst this ba mputational ticle(s)-poly ymer is the the computa developed mplexity is sion of (i) a ) a multiple pkinson bar mpression ( erimental r stant devic elopment o mputational tem for prot stly, the exp mpression (S reliable for e details on ymer materi tem were gi erwards, th ious strain r ord the dyn
d to carry ou amic respon earch on th ed and part for Applied he applicati lymer, Clea out the imp s, consisting d damage w nt. ackground, modelling ymer system matrix mat ational part d. In the e conducted a monolithic e-particles-p r (SHB) dev (SHPB) an results are ce of a so f a particle( models fo tective appl perimental SHPB) tests dynamic te n the techno
ial, the sing iven, as wel he dynamic rate levels. namic loadin ut the post-nse of a pol Expe he impact r icle-matrix Scientific R ion in prote ar Flex 75 ( act resistan g of a poly will change a combined g was defi ms under terial, which t, multi-scal experimenta for studyi c polymer m polymer sys vice develop nd tension important oft polyme (s)-polymer or designing ications. setups wer s. These tw ests on a sof ology for c gle-glass-po ll as the basi tension an During the ng process test analysi Summary lymer and p erimental St resistance systems) h Research (T ection conce (CF 75 in s nce of partic ymer binde the combus d research p fined on th dynamic lo h is embedd le modellin al part, a ing the dyn matrix, (ii) stem. The ped at TU D
(SHTB) for (i) the er material r system for g a rigid-p re built for wo setups w ft polymer m casting the olymer syste ic physical nd compres ese tests, a and a scann s. y polymer co tudies of transpar has been con
TNO), show epts. A soft hort) was s cle(s)-polym er and soli stion proper programme he mechan oading. In ded with sin ng techniqu step-wise namic resp a single-pa used appar Delft, which tests at v evaluation backed b propellants particle-mod high-strain ere carefull material at specimens em and the properties o ssion experi high-speed ning electro omposite sy rent hybrid nducted at t wing the po t, transparen elected as m mer systems d energetic rties and th e of experim nical respo this progr ngle and mu es for dyna approach w onse in co article-polym atus is a sm h can condu various stra of a trans by rigid gl s and (iii) th dified comp n-rate tensio ly evaluated different st of the mo multiple-pa of CF 75 po iments wer d camera wa on microsco Summ ystems d glass-poly the Netherl otential of t nt polyureth matrix mate is also rele c particles. he performa mental tests onse of hy ramme, CF ultiple parti amic condit with increa ompression mer system mall scale uct the dyna ain rates. sparent imp lasses, (ii) he calibratio mposite mat on (SHTB) d and prove train rate lev onolithic CF articles-poly olymer mate re conducte as employe opy (SEM) mary ymer ands these hane erial. evant The ances and ybrid F 75 cles. tions asing and m and split amic The pact-the on of terial and ed to vels. F 75 ymer erial. ed at ed to was
From the dynamic tension tests, the damage, fracture and toughness mechanisms of the monolithic CF 75 polymer material were revealed. The rate dependency of the mechanical properties and dynamic deformation behaviour were characterized. Then, the bonding of the glass-polymer interface was also characterized by dynamic tension loading on a single-glass-polymer system of the CF 75 polymer matrix with an embedded single 3mm-diameter glass particle. Debonding, cavitation and necking were illustrated, as well as the effects on the stress-strain response at various strain rates.
Dynamic compression tests were carried out to characterize the impact-resistant performance of the monolithic CF 75 polymer material. They revealed the deformation behaviour, damage mechanisms, fracture characteristics, rate dependency of mechanical properties and temperature rise. Then, the single-glass-polymer system was tested by dynamic compression tests. The results clarify the particle effect on the dynamic compressive response. The debonding-induced decrease of yield stress and the contribution of glass particle failure to fracture energy are quantitatively characterized at various strain rates.
Finally, the impact-resistant performance of the multiple-particles-polymer systems of CF 75 polymer matrix with embedded 25wt.% and 50wt.% 0.5mm-diameter PMMA particles was characterized by dynamic compression tests. For the multiple-particles-polymer systems, an improved static stiffness is explained. Multiple cracking from the particle-polymer interface is observed, which induces the decrease of yield stress. A high particle density results in the decrease of maximum stress and strain energy. However, crushing of the particles causes a faster increase of maximum stress and strain energy with increasing strain rate (indicated by a higher strain rate sensitivity index).
In this thesis, a systematical investigation about the dynamic mechanical response of soft polymers was carried out. It includes the monolithic polymer material (as matrix material in the particle(s)-polymer system), the single-glass-polymer system (for studying the interfacial bonding and single particle effect), and the multiple-particles-polymer system (as a representative of the real particle(s)-multiple-particles-polymer system for impact-resistant applications).
Samenvatting
Samenvatting
Dynamische respons van een polymeer en polymeer composiet systemen
Experimentele Studies
Recent onderzoek naar de schokbestendigheid van transparante hybride glass-polymeren uitgevoerd door TNO heeft de potentie van deze materialen voor de toepassing in pantsertoepassingen aan het licht gebracht. Een zachte, transparante polyurethaan elastomere polymeer Clear Flex 75 (CF 75) is geselecteerd als matrix materiaal. De kennis over de schokbestendigheid van deeltjes-versterkte polymeersystemen is ook van belang voor drijfgassen gemaakt van een polymeren binder met energetische deeltjes. De schade onder schokbelasting verandert de verbrandingseigenschappen van het drijfgas.
Tegen deze achtergrond is een programma gedefinieerd voor gecombineerd experimenteel en numeriek onderzoek naar de mechanische respons van hybride deeltjes-versterkte polymeersystemen onder dynamische belasting. In dit onderzoek is CF 75 het matrixmateriaal, enkelvoudig of meervoudig versterkt met deeltjes. In het numerieke gedeelte worden multischaal modelleertechnieken voor dynamische belastingen ontwikkeld. In het experimentele gedeelte wordt een stapsgewijze aanpak met toenemende complexiteit gehanteerd voor het bestuderen van de dynamische respons onder druk en trek van (i) monolithisch polymeermatrix, (ii) polymeermatrix met een enkel deeltje en (iii) polymeermatrix met meerdere deeltjes. Een kleinschalig split Hopkinson bar (SHB) apparaat, ontwikkeld aan de TU Delft, wordt gebruikt voor dynamische compressie (SHPB) en trek (SHTB) testen met verschillende reksnelheden. De experimentele resultaten zijn van belang voor het doorrekenen van een transparante constructie ter bescherming tegen schokbelasting gemaakt van zacht polymeer versterkt met glas, evenals voor het ontwikkelen van een deeltjes-versterkte polymeer als drijfgas en voor het kalibreren van numerieke modellen voor systemen van deeltjes-versterkte composieten voor pantsertoepassingen.
Ten eerste zijner experimentele opstellingen gemaakt voor hoge snelheidstesten onder trek (SHTB) en druk (SHPB). De twee opstellingen zijn zorgvuldig getest en hun betrouwbaarheid voor het dynamisch testen van zachte polymeren onder verschillende reksnelheden is aangetoond. Vervolgens zijn de geometrie en afmetingen van de proefstukken bepaald. De technologische details voor het gieten van de verschillende proefstukken (monolithisch, enkelvoudig versterkt en meervoudig versterkt CF 75) zijn gedocumenteerd, evenals de fysische eigenschappen van CF 75 polymeermateriaal.
Vervolgens zijn dynamische experimenten uitgevoerd onder trek en druk voor verschillende reksnelheden. Tijdens de experimenten is een hogesnelheidscamera
gebruikt om het dynamische belastingsproces op te nemen. Een elektronenmicroscoop (SEM) is gebruikt voor de analyse achteraf.
De dynamische trektesten hebben de schade, breuk en taaiheid van het CF 75 materiaal aan het licht gebracht. De snelheidsafhankelijkheid van de mechanische eigenschappen en de dynamische vervormingen zijn gekarakteriseerd. Verder zijn de eigenschappen van de interface tussen glas en polymeer gekarakteriseerd door middel van de dynamische trektesten op het enkelvoudig versterkte systeem met een glasdeeltje met diameter van 3 mm. Onthechting, cavitatie en insnoering zijn geobserveerd evenals de effecten van de reksnelheid op de constitutieve relatie. Deze resultaten bieden fundamentele kennis voor het onderzoek van deeltjes-versterkte polymeren onder schokbelasting.
Dynamische druktesten zijn uitgevoerd om de schokbestendigheid van monolithisch CF 75. Deze testen hebben kennis opgeleverd over het vervormingsgedrag, de schademechanismen, de breukeigenschappen, de reksnelheids-afhankelijkheid van de mechanische eigenschappen en de temperatuurtoename. De dynamische druktesten met enkelvoudig versterkte polymeren verhelderen de invloed van deeltjes op de dynamische respons onder druk. De afname van de vloeispanning als gevolg van onthechting en de bijdrage van het glasdeeltje aan de bruekenergie zijn gekarakteriseerd voor verschillende reksnelheden.
Tot slot is de schokbestendigheid van meervoudig versterkte CF 75 polymeer met 0,5 mm PMMA deeltjes (met gewichtsfracties van 25% en 50%) gekarakteriseerd met dynamische druktesten. Een toename in statische stijfheid is aangetoond. Meervoudige scheuren van de interface tussen deeltje en polymeer zijn geobserveerd, met een afname in vloeispanning tot gevolg. Een hoge dichtheid van deeltjes resulteert in de afname van de maximale spanning en rek-energie. Echter, onder toenemende reksnelheid veroorzaakt het verbrijzelen van deeltjes een snellere toename in maximale spanning en rek-energie, wat is gereflecteerd in een hogere reksnelheids-afhankelijkheidsindex.
In dit proefschrift is systematische kennis over de dynamische eigenschappen van versterkte en onversterkte polymeren ontwikkeld. Beschouwd zijn monolithisch polymeermateriaal (als matrix materiaal in deeltjes-versterkte polymeersystemen), enkelvoudig glasversterkte polymeersystemen (voor het bestuderen van binding en het effect van enkelvoudige deeltjes) en meervoudige deeltjes-versterkte polymeersystemen (als vertegenwoordiger van realistische deeltjes-versterkte polymeersystemen voor pantsertoepassingen).
Nomenclature
Nomenclature
Greek stress, MPa strain strain rate, /s density, kg/m3 Poisson ratiospecimen’s stress, MPa specimen’s strain specimen’s strain rate, /s
transmitted strain history, με reflected strain history, με yield stress, MPa
maximum stress, MPa
maximum stress at the crack tip, MPa
theoretical cohesive strength of the material, MPa elastic stress in front of the crack tip, MPa
critical stress of craze initiation, MPa true stress, MPa
true strain
engineering stress, MPa engineering strain
∆ difference of the two stresses applied on the specimen end surfaces, MPa average of these two stresses applied on the specimen, MPa
fraction of the deformation strain energy goes to heating of the specimen ƒ gage factor strain gages
specimen rate, specimens/s
Alphabets
a given height, m
acceleration ratio of gravity, m/s2 calibration factor of a drop weight
integral of the output voltage signal of strain gage bridge ∆ change of the velocity of impactor, m/s
0 length of cylindrical specimen, m velocity, m/s
length of the deformed specimen, m
length of the undeformed part in the deformed specimen, m total length of the specimen after test, m
specimen diameter, m specimen length, m Young’s modulus, N/m2
cross sectional area, m2
specimen’s initial cross sectional area of the gauge section, m2 wave velocity in the incident bar, m/s
material parameter in power-law function strain-rate sensitivity (SRS) index stress concentration factor 2 crack length, m
initial flaw size, m correction factor
stress intensity factor of the material, MPam1/2 fracture toughness of material, MPam1/2 distance from the crack tip, m
parameter to evaluate the stress equilibrium in the specimen
∆ difference of the two forces applied on the specimen end surfaces, N average of these two forces applied on the specimen, N
Nomenclature
force applied on the specimen end surface by the transmitter bar, N strain energy, MJ/m3
fracture energy in plane strain, MJ/m3 specific heat capacity, J/kg/K ∆ temperature rise, K
temperature, K
constant depending on the material density and the thermal conductivity fracture energy, MJ/m3
width of the gage section, m width of the grip section, m
length that includes the gage length and the shoulders, m current diameter after compression deformation, m current thickness after compression deformation, m
maximum original specimen diameter, m
diameter of the bars, m cross-sectional area of the bars, m2
length of the incident bar and transmitter bar, m distance between the begin of incident bar and first set of strain gages, m distance between first set of strain gages and second set of strain gages, m distance between second set of strain gages and end of the incident bar, m length of the striker bar, m
distance between the laser points to measure the speed of striker bar, m ∆ time difference between two specimens, s
theoretical wave speed in the bars, m/s speed of the striker bar, m/s
size of the plastic zone, m
Subscripts and superscripts
monolithic CF 75 polymer material glass-polymer system
multiple-particles-polymer system
Abbreviations
TNO Netherlands Organisation for Applied Scientific Research TU Delft Delft University of Technology
SHB Split Hopkinson Bar
SHPB Split Hopkinson Pressure Bar SHTB Split Hopkinson Tension Bar SB striker bar
IB incident bar TB transmitter bar DIF dynamic increase factor ISR intermediate strain rate HSR high strain rate VHSR very high strain rate 1D one-dimensional CF 75 Clear Flex 75
SEM scanning electron microscopy IR camera infrared radiation camera CTOD crack tip opening displacement XRD X-ray diffraction
TGA thermo gravimetric analysis DSC differential scanning calorimeter CMRR common mode rejection ratio PSRR power supply rejection ratio L/D length-to-diameter
Sum Sam Nom 1. 1 1 1 1 1 2. 2 2 2 d 2 3. mat 3 3 3 3 3 3 mmary ... menvatting menclature Introduct .1. Back .2. Rese .3. Rese .4. Thes .5. Refer Literatur .1. Intro .2. Revie 2.2.1. C 2.2.2. M 2.2.3. P .3. Revie dynamic mat 2.3.1. D 2.3.2. T 2.3.3. S .4. Refer High-stra terial* ... .1. Abstr .2. Intro .3. Expe .4. Expe 3.4.1. M 3.4.2. M 3.4.3. C .5. Summ .6. Refer ... ... e ... tion ... kground ... arch motiva arch approa is outline ... rences ... re review ... duction ... ew on mate Concrete ma Metal materi Polymer mat ew on the e terial respon Drop weight Taylor impa Split Hopkin rences ... ain-rate ten ... ract ... duction ... erimental pr erimental re Mechanical p Macroscopic Craze evolut mary ... rences ...
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... ... ... ... ... ... ... ... ... ... ... mpact-resist stant applica nt applicatio tant applica gy developm ... ... ... ... ... onse of a po ... ... ... ... ... train rates ... l fracture be and toughen ... ... T ... ... ... ... ... ... ... ... ... ... ... tant applica ation ... on ... ation ... ment for cha ... ... ... ... ... olyurethane ... ... ... ... ... ... ehaviour ... ing mechan ... ... Table of cont ... ... ... ... ... ... ... ... ... ... ... ation ... ... ... ... aracterizing ... ... ... ... ... e elastomer ... ... ... ... ... ... ... nism ... ... ... tents ... I .. III .... V ... 1 ... 1 ... 2 ... 4 ... 5 ... 6 ... 9 ... 9 ... 9 ... 10 ... 13 ... 14 ... 18 ... 19 ... 21 ... 23 ... 31 ric ... 39 ... 39 ... 40 ... 40 ... 42 ... 42 ... 45 ... 49 ... 54 ... 554. poly 4 4 4 4 4 4 5. 5 5 5 5 5 5 5 6. 6 6 6 6 Glass inte yurethane 4.1. Abstr 4.2. Intro 4.3. Expe 4.3.1. Q 4.3.2. D 4.4. Expe 4.4.1. D 4.4.2. M 4.4.3. F 4.5. Conc 4.6. Refer Dynamic .1. Abstr .2. Intro .3. Expe 5.3.1. T 5.3.2. T .4. Expe 5.4.1. D 5.4.2. L 5.4.3. L .5. Discu .6. Conc .7. Refer Compress .1. Abstr .2. Intro .3. Expe 6.3.1. S 6.3.2. Q 6.3.3. D .4. Expe 6.4.1. D erface effec elastomeric ract ... duction ... erimental pr Quasi-static Dynamic me erimental re Dynamic def Mechanical p Fracture orig clusions ... rences ... compressiv ract ... duction ... erimental pr The quasi-st The dynamic erimental re Deformation Loading spe Loading spe ussion ... clusions ... rences ... sive respon ract ... duction ... erimental pr Specimen pr Quasi-static Dynamic me erimental re Dynamic def ct on high-s c polymer m ... ... rocedure ... mechanical echanical pr sults and di formation b properties a gin and char ... ... ve mechani ... ... rocedures ... atic mechan c mechanica sults... n and fractur ed effect on ed effect on ... ... ... nse of a glas ... ... rocedure ... reparation ... mechanical echanical pr sults and di formation b strain-rate material* .. ... ... ... l properties roperties tes iscussions ... behaviour ... at various st racteristics . ... ... ical respon ... ... ... nical proper al propertie ... ure behaviou n the dynam n the temper ... ... ... ss-polymer ... ... ... ... l properties roperties tes iscussion .... behaviour ... tensile resp ... ... ... ... test ... st ... ... ... train rates ... ... ... ... nse of a soft ... ... ... rties test ... es test ... ... ur under hig mic mechani rature rise .. ... ... ... r system at ... ... ... ... tests ... sts... ... ... ponse of a s ... ... ... ... ... ... ... ... ... ... ... ... t polymer m ... ... ... ... ... ... gh-speed loa ical properti ... ... ... ... various str ... ... ... ... ... ... ... ... soft ... ... ... ... ... ... ... ... ... ... ... ... material* ... ... ... ... ... ... ... ading ... ies ... ... ... ... ... rain rates* ... ... ... ... ... ... ... ... ... 59 ... 59 ... 60 ... 61 ... 61 ... 64 ... 64 ... 64 ... 68 ... 70 ... 73 ... 74 ... 79 ... 79 ... 80 ... 81 ... 81 ... 82 ... 86 ... 86 ... 92 ... 95 ... 96 ... 99 . 100 . 105 . 105 . 106 . 107 . 107 . 107 . 109 . 111 . 111
6 6 7. stra 7 7 7 7 7 7 8. 8 8 8 App A.1 A A A A A.2 A A A 6.4.2. L 6.4.3. D .5. Conc .6. Refer Compress ain rates* ... .1. Abstr .2. Intro .3. Expe 7.3.1. S 7.3.2. Q 7.3.3. D .4. Expe 7.4.1. D 7.4.2. L 7.4.3. P 7.4.4. D .5. Conc .6. Refer Conclusio .1. Conc .2. Reco .3. Refer pendices .... . Material A.1.1. Mate A.1.2. Spec A.1.3. Spec A.1.4. Mate . Split Hop A.2.1. Intro A.2.2. Build A A.2.2.1. D A.2.2.2. A.2.3. Build Loading spe Dynamic fra clusions ... rences ... sive respon ... ract ... duction ... erimental pr Specimen pr Quasi-static Dynamic me erimental re Dynamic def Loading spe Particle dens Dynamic fra clusions ... rences ...
ons and fut
clusions ... ommendatio rences ... ... preparatio erial prepara imen prepa imen prepa erial basic p pkinson bar duction ... d-up of split Apparatus st Data acquisi d-up of split ed effect on acture origin ... ... nse of multi ... ... ... rocedure ... reparation ... mechanical echanical pr sults and di formation b ed effect on sity effect o acture origin ... ... ture work .. ... ons for futur ... ... on and basi ation proced ration for d ration for d roperties .... r technolog ... t Hopkinson tructure and ition and ins t Hopkinson n the mecha n and charac ... ... iple-particl ... ... ... ... ... l properties roperties tes iscussion .... behaviour ... n the mecha on dynamic n and charac ... ... ... ... re work ... ... ... ic propertie dures ... dynamic ten dynamic com ... gy ... ... n pressure b d key parts .. strumentatio n tension ba anical prope cteristics .... ... ... les-polymer ... ... ... ... ... test ... st ... ... ... anical prope compressiv cteristics .... ... ... ... ... ... ... ... es... ... sion test ... mpression te ... ... ... bar ... ... on ... ar ... T erties ... ... ... ... r systems a ... ... ... ... ... ... ... ... ... erties ... ve response . ... ... ... ... ... ... ... ... ... ... ... est ... ... ... ... ... ... ... ... Table of cont ... ... ... ... at various ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... tents . 114 . 118 . 121 . 122 . 127 . 127 . 128 . 129 . 129 . 129 . 132 . 134 . 134 . 136 . 140 . 143 . 146 . 147 . 153 . 153 . 157 . 159 . 161 . 161 . 161 . 162 . 164 . 167 . 171 . 171 . 171 . 171 . 177 . 183
A A.3 Pub Ack Cur Pro Stel A A.2.3.1. D A.2.3.2. A.2.4. Conc . Reference blications in knowledgem rriculum V opositions .. llingen ... Apparatus st Data acquisi clusions ... es ... n Journals ments ... Vitae ... ... ... tructure and ition and ins ... ... ... ... ... ... ... d key parts .. strumentatio ... ... ... ... ... ... ... ... on ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... . 183 . 188 . 193 . 194 . 195 . 197 . 199 . 201 . 203
1.1. Exp been are eng hou mat [4,5 Mat imp safe prop volu man requ Mat mee syst app Mec that at h as c prov ener requ stra dyn con can for d The the Imp the . Backgro ploring the n a topic o enablers for ineering s usehold appl terials and t 5]. terials can b pact-resistan ety and secu perties. Mo ume of stru ny cases, th uirements is terial techn et these req tems with h lication. chanical pro t can be exp high strain r crash situat vide the str rgy and so uire an unde in rates. D namic loadin stitutive ma be of great defence, saf e study of d most activ portant issue crack tip du ound potential of f great inte r virtually th tructures t liances. Dis the abilities be tailored n nt structures urity require ost material uctures and hese increas s towards w nologies, hy quirements. high special operties det pected from rates is requ tions, explo ress-strain r on at the co erstanding o amage eval ng also nee aterial mode t help for m fety and sec dynamic de ve research es are crack uring crack
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f advanced erest for dec he entire lis to automob scoveries of s to process nowadays f s and equipm ements. The s currently d equipmenses are unac weight redu ybrid and h They prov l strength (s termine the m the materia uired by the osions, blas elation, giv orrespondin of the dynam luation and ed the data el [6,7]. So, more efficie curity. formation a h fields in k initiation, k evolution.
Introduc
materials f cades [1-5] st of engine biles, prot f new mater s, mold and for their eng ment have r ey require d available l nt to meet t acceptable. F uction and heterogeneo vide the po strength-to-range of us al. The cha e service const and balli ving the info ng strain rat mic mechan d safety ass on the dyn , characteriz ent engineer and fracture both mec crack prop These even
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for serving . Materials ering achiev tective equ rials or new d join them gineering ap received co dedicated de lead to an the impact-For this rea strength inc ous material otential to -weight rati sefulness an racterizatio nditions in istic impac formation on te [1-3]. Rel nical respon sessment of namic mater zing the dyn ring applica e behaviour chanics and pagation an nts are know Chapter in extreme and materi vements ran uipment, e w application are keys to pplication. nsiderable a esign concep increase in -resistant re ason, the tr crease at re l concepts design adv io) for the i nd the servi n of mecha impact rela t. Mechani n strength, liable struct nse of a mat f structural rial respons namic mech ations and m r has recent d material d crack arre wn to be de r 1 Introduc e conditions ial technolo nging from electronics ns of traditi o breakthrou In recent ye attention du pts and mat n weight an equirements rend in mat easonable c are enabler vanced mat impact-resis ice qualifica anical prope ated events ical testing ductility, st ture design terial at rele integrity u se and dyna hanical resp material des tly been on sciences [ est occurrin ependent on ction s has ogies civil and ional ughs ears, ue to terial nd/or s. In terial osts. rs to terial stant ation erties such can train will evant under amic onse signs ne of 8,9]. ng at n theloading rate. Catastrophic failure is likely to occur under dynamic loading due to abrupt crack initiation and propagation. In order to analyze the dynamic mechanical response of a structure and to prevent dynamic catastrophic failure through design, it is of paramount importance to quantify the dynamic mechanical properties of materials in terms of mechanical response and fracture behaviour. The dynamic deformation behaviour and fracture mechanisms of materials studied in both science and engineering have become prevalent and increasingly relevant to many technological applications.
The knowledge about the change of material mechanical properties with strain rate is warranted to design the structures that would not fail prematurely and unexpectedly at high loading rate [10,11]. Determination of dynamic mechanical properties of material would also enable a sound design of a new composite impact-resistant structure. The above argument reinforces the need for dynamic mechanical response characterization of material at various strain rates. Afterwards, the analysis on the strain rate dependency of mechanical properties is of interest to explore the intrinsic physical reasons to understand the material dynamic response mechanisms. So, when rate dependency and dynamic failure can be controlled, emerging into new concepts for impact-resistant material design becomes possible.
Therefore, in the current project, we study the dynamic response of a polyurethane elastomeric polymer material and polymer composite systems with a potential for impact resistant applications. The experimental procedure is as follows. An advanced polymer material and polymer composite systems will be carefully prepared. A Split Hopkinson bar apparatus has been built for the characterization of the dynamic mechanical response. Deformation and fracture behaviour under dynamic loading are analyzed with a special interest towards the inherent physical origin of the mechanical response as well as the rate dependency. This experimentally oriented research was also defined to provide the basic input data and knowledge to the development of an impact resistant particle(s)-polymer system which is relevant for propellants consisting of a polymer binder and solid energetic particles, and of a multi-scale computational model for a hybrid particles-filled composite material system for transient dynamic load conditions.
1.2. Research motivations and objectives
When structures and equipment are required for the protection to impact and impulsive loading, this generally leads to an increase in weight and volume, which has a drawback regarding the overall design. Solution from the material point of view is exploiting new impact-resistant materials with new features that meet the requirements of reduced weight and volume. Furthermore, a hybrid composite concept of this new material should be developed. Besides, experimental techniques should be available to characterize the high-strain-rate mechanical properties of the
Chapter 1 Introduction
new material at relevant strain rates. In the broader STW-project where this project is part of also multi-physics and multi-scale analysis, spatial and temporal discretisation techniques as well as diagnostic techniques are needed together in order to gain the qualitative and quantitative insight in the dominant deformation and failure mechanisms. In line with the above research procedure, the experimental results of the dynamic mechanical responses of the target material will provide the basic data for the computational modeling, and conversely the computational modelling will be used to optimize the new protective material design. The main features of these protective materials predominantly are that they can resist extreme dynamic loading and absorb energy in a controlled way.
Recently, a promising transparent impact-resistant material concept has been developed by the Netherlands Organisation for Applied Scientific Research (TNO). In this concept, a polymer is used as one of the main constituents playing a dominant role in the dynamic response [12]. It is a transparent polyurethane elastomeric material and has a branched structure of molecular chains with a random distribution. This polymer has been selected for the current study because it offers a sufficiently wide range of relevant scales to study multi-physics phenomena at high rate loading. Because of transparency, the polymer also offers the potential to apply non-destructive, optical diagnostic techniques to experimentally study wave phenomena and damage development. The mechanical resistance to dynamic loading in the impact resistant concept of TNO is mainly governed at meso-scale (10-2-10-3 m). To gain experimental data on the response at meso-level during the dynamic loading, the heterogeneous material is designed consisting of a skeleton of particles embedded in a polymer matrix. To enable the application of optical diagnostic techniques during an impact event, glass is selected for the particle, while the matrix consists of the transparent polymer. The target materials investigated in this thesis concern the monolithic polymer material and a polymer matrix with an embedded single glass particle and with multiple PMMA particles (25wt.% and 50wt.%).
Since the dominant scale of material response decreases with increasing stress gradients, the loading rate should be varied. The Split Hopkinson Bar (SHB) technology is selected as the dynamic experimental method. The reasons are that (i) it is a highly relevant dynamic loading case; (ii) the amplitude and impulse of dynamic loading can be tuned; (iii) it is reproducible and (iv) the required knowledge on impact experiments is available from previous research. The compressive and tensile versions of SHB setups will be developed at the proper scale. The multiple dynamic experiments are conducted at different strain rate levels for inducing the varied stress gradients in the materials. They provide the possibility of investigating rate dependency of yield strength, maximum strength and strain energy.
Under high-rate loading, a complex set of interacting stress waves causes a material response with temporal and spatial stress gradients, which may result in the simultaneous initiation of dynamic cracks at different scales. Meanwhile, damage
development and redistribution of stresses occur at multiple scales at the same time and most probably not sequentially. Determining and quantifying these multi-scale, interacting processes is the main scientific objective of the overall experimental and computational research project. Thus, coupled to the optical diagnostic technique at
meso scale, a post-test analysis is conducted at micro scale (about 10-6 m). The
response and damage development in the cohesive zone (monolithic polymer material) and the interface with the embedded particle (polymer matrix with an embedded single glass particle and with multiple PMMA particles) will be analyzed in this study. In additions, in impact events, accompanying high frequency stress waves, significant temperature gradients might be induced, which significantly affect the material response. Dependent on the intensity of the impact and the type of material, a multi-physics approach is necessary. Application of diagnostics for the transient temperature fields is also one of the project objectives. The temperature fields should be coupled to the stress state being a function of time.
1.3. Research approach
Based on the project motivation and objectives, it is proposed to design and build a small scale Split Hopkinson Bar (SHB) device dedicated to study polymer matrix material and more in particular the properties and behaviour of the bonding zone between polymer and glass particle under dynamic compressive and tensile loading. The device should also support the application of diagnostics for dynamic heating effects.
The properties of the transparent polymer material and individual components under dynamic loading as well as a full scale post experimental analysis will function as a reference for the numerical research and multi-physics, multi-scale modeling development in a parallel project. The study of dynamic mechanical response and damage of the monolithic and hybrid polymer is reported in this thesis. The various steps in the study are as follows:
1. Specimen preparation of monolithic polymer material and a polymer matrix with an embedded single glass particle and with multiple PMMA particles; 2. Development of high rate loading devices, Split Hopkinson Pressure Bar
(SHPB) and Split Hopkinson Tension Bar (SHTB) for dynamic compression and tension experiments;
3. Evaluation applicability of non-destructive, optical diagnostic techniques (high-speed camera) for damage observation at meso-scale coupled to time scale;
4. Evaluation application of diagnostic techniques (infrared radiation camera) for high-rate heating effects;
Chapter 1 Introduction
5. Material research of dynamic response to produce data for theoretical and numerical models:
a. Mechanical behaviour under static and dynamic loading, b. Rate-dependent behaviour of mechanical properties, c. Effect of impact-induced temperature gradients;
6. Post-test analysis of damage at micro scale (scanning electron microscope); 7. Study to a full understanding of the deformation, damage and fracture
characteristics.
The techniques developed in this thesis will also serve to determine and understand the ultimate impact resistance of existing materials. The experimental knowledge on the internal damage mechanisms may also have a spin-off towards the development of smart- and self-healing materials as well as computational spatial-temporal modelling techniques.
1.4. Thesis outline
Following the research steps, this thesis consists of #8 Chapters. A summary of the content of each chapter is given below and is schematically shown in Figure 1.1.
Chapter 1 gives a brief introduction of this thesis, including the research background
of the impact-resistant material and the motivation of the current research as well as the objectives of the ongoing project.
Chapter 2 gives a literature review on the development of material science for
impact-resistant application and the advancement of experimental techniques for the dynamic mechanical experiment at high strain rate.
Chapter 3 gives the high-strain-rate tension testing results of the monolithic polymer
material, including the dynamic deformation behaviour, loading speed effect on the mechanical properties, and dynamic fracture origin and characteristics. Herein, the craze evolution, crack formation and toughening mechanism are highlighted.
Chapter 4 gives the high-strain-rate tension testing results of the polymer matrix with
an embedded single glass particle, including the dynamic deformation behaviour, loading speed effect on the mechanical properties, and dynamic fracture origin and characteristics. Herein, the glass interface effects on dynamic tensile response of the polymer are characterized.
Chapter 5 gives the high-strain-rate compression testing results of the monolithic
polymer material, including the dynamic deformation behaviour, loading speed effect on the mechanical properties, loading speed effect on the temperature rise, and dynamic fracture origin and characteristics. Herein, the impact-resistant performances of this transparent polymer material are systematically revealed.
Chapter 6 gives the high-strain-rate compression testing results of the polymer
matrix with an embedded single glass particle, including the dynamic deformation behaviour, loading speed effect on the mechanical properties, and dynamic fracture origin and characteristics. Herein, in the glass-polymer system, the contributions of glass particle to the improvement of static stiffness and the influences on dynamic compressive response are investigated.
Chapter 7 gives the high-strain-rate compression testing results of the polymer
matrix with the embedded 25wt.% and 50wt.% PMMA particles, including the dynamic deformation behaviour, loading speed effect on the mechanical properties, and dynamic fracture origin and characteristics. Herein, in the particles-polymer system, the contributions of multiple PMMA particles to the improvement of static stiffness and the influences on dynamic compressive response are studied.
Chapter 8 gives the conclusions and recommendations from the experimental
research.
Figure 1.1 Outline of this thesis.
1.5. References
[1] Mulliken A, Boyce MC. Mechanics of the rate-dependent elastic-plastic deformation of glassy polymers from low to high strain rates. Int J Solids Struct 2006;43(5):1331-56.
[2] Richeton J, Ahzi S, Vecchio KS, Jiang FC, Adharapurapu RR. Influence of temperature and strain rate on the mechanical behavior of three amorphous polymers: Characterization and modeling of the compressive yield stress. Int J Solids Struct 2006;43(7-8):2318-35.
[3] Roland CM, Twigg JN, Vu Y, Mott PH. High strain rate mechanical behavior of polyuria. Polymer 2007;48(2):574-8.
Chapter 1 Introduction
[4] Naik NK, Pandya KS, Kavala VR, Zhang W, Koratkar NA. High-strain rate compressive behavior of multi-walled carbon nanotube dispersed thermoset epoxy resin. J Compos Mater 2015;49(8):903-10.
[5] Deshpande VS, Fleck NA. High strain rate compressive behaviour of aluminium alloy foams. Int J Impact Eng 2000;24(3):277-98.
[6] Chuban VD, Ivanteyev VI, Chudayev BJ, Avdeyev EP, Shvilkin VA. Numerical simulation of flutter validated by flight-test data for TU-204 aircraft. Comput Struct 2002;80(32):2551-63.
[7] Ghoshal A, Harrison J, Sundaresan MJ, Hughes D, Schulz MJ. Damage detection testing on a helicopter flexbeam. J Intell Mater Syst Struct 2001;12(5):315-30.
[8] Yang J, Han CR, Zhang XM, Xu F, Sun RG. Cellulose nanocrystals mechanical reinforcement in composite hydrogels with multiple cross-links: Correlations between dissipation properties and deformation mechanisms. Macromolecules 2014;47(12):4077-86.
[9] Meyers MA, Nesterenko VF, LaSalvia JC, Xue Q. Shear localization in dynamic deformation of materials: Microstructural evolution and self-organization. Mater Sci Eng A 2001;317(1-2):204-25.
[10] Gensler R, Plummer CJG, Grein C, Kausch HH. Influence of the loading rate on the fracture resistance of isotactic polypropylene and impact modified isotactic polypropylene. Polymer 2000;41(10):3809-19.
[11] Shokrieh MM, Mosalmani R, Omidi MJ. A strain-rate dependent micromechanical constitutive model for glass/epoxy composites. Compos Struct 2015;121:37-45.
[12] van Ekeren PJ, Carton EP. Polyurethanes for potential use in transparent armour. J Therm Anal Calorim 2011;105:591-98.
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2.2.1. Concrete materials for impact-resistant application
Concrete is one of the oldest building materials and is still in wide use. Concrete is an extremely complex composite material where various physical and mechanical processes at multiple scales take place, ranging from initial curing to final deterioration. One of the research topics is the investigation of the strain rate effect on the mechanical properties. Concrete is a strain-rate-dependent material that exhibits a strengthening effect with increasing loading rate [17-29]. The rate-dependent strength is often applied as a ratio of the dynamic to static strength, which is described as dynamic increase factor (DIF). The DIF is used to describe the relative strength enhancement under dynamic loading [30, 31].
A general review was made by Bischoff and Perry in 1991 [32] to show the increasing compressive strength of concrete materials with the increase of strain rate, as shown in Figure 2.2. It represents a compilation of the research results from many programmes. During impact loading (at a strain rate of about 10/s), the compression strength of concrete material has been found to be as much as 85% to 100% higher than the static strength.
Chapter 2 Literature review
Figure 2.2 A variety of data sources about the rate-dependent DIF indicating the
improved compressive strength of concrete materials with increasing strain rate [33].
Figure 2.3 Strain rate dependency of dynamic increase factor, DIF of concrete
It is well known that concrete materials have a low tension strength compared to the compression strength. Since concrete is inherently weak in tension, it is necessary to investigate the tensile mechanical properties. In real engineering applications, even though quasi-static tensile loading on concrete can be avoided, it is difficult to prevent concrete structures being exposed to dynamic tensile stresses. The dynamic tensile stress in concrete structure can be generated by explosions, projectile impact, earthquakes and so on [35, 36]. The rate-dependent tensile strength of concrete was also extensively investigated [37]. The rate dependency of the tensile strength is much more pronounced than for compressive loading. The dynamic response mechanisms and data are presented and discussed in reference [34]. The strain rate effect on dynamic tension strength, reported as a dynamic increase factor, DIF versus strain rate, is shown in Figure 2.3.
The data on rate dependency are based on the results of different testing programmes that used various testing techniques to load the specimen and different methods to analyze and interpret the results. The testing programmes were conducted by different researchers where there are differences in mix designs, type of measurement, specimen size and shape (cube, cylinder or prism) as well as aspect ratio. Besides, in the studies on rate dependence in concrete material, material microstructure, specimen size, etc, are also reported to influence the dynamic tensile strength [38]. Herein, the experimental data represent the measurements on the specimens of different sizes and shapes, different concrete qualities and different contents of water. Therefore, it is not surprising that there is a relative large scatter of the dynamic experimental data with respect to the measured strain rate. However, the band of experimental results for measured strength confirms the strain rate dependency of concrete.
Physical mechanisms have been reported about the strength increase of concrete induced by strain rate. Rossi and Van Mier [39] considered that the free water contained in concrete can cause the increase of strength at high strain rate. According to the experimental and analytical works, Rossi and Toutlemonde [40] came to the following conclusions: (1) at a strain rate smaller than approximately 1.0/s, the main physical mechanism is a viscous mechanism [41] which retards the development and propagation of cracks; (2) at strain rates greater than approximately 10/s, the inertia stress becomes predominant. Yan and Lin, founded upon an experimental observation, proposed that cracks are forced to propagate through regions of greater resistance at rapid loading and thus an improved stress level is needed to fracture the material [21]. In reference [34], Weerheijm et al. gave a summary on the aspects to be taken into account for analysing the dynamic mechanical properties of concrete. These aspects are: (i) the overall structural response, (ii) the specimen geometry, size and the structural inertia, (iii) the pore structure and moisture content, (iv) inertia effects around the (micro) cracks affecting crack initiation and propagation (i.e. denoted as micro inertia effects) and (v) (structural) inertia effect of the softening zone.
Chapter 2 Literature review
2.2.2. Metal materials for impact-resistant application
For metal materials, mechanical properties are also found to be sensitive to the strain rate in many cases [42-52]. Of particular interest for materials subjected to impact loading are their mechanical properties at high strain rate, resistance to dynamic crack initiation and propagation and the corresponding dynamic damage mechanisms. Herein, some metal materials are reviewed to illustrate the typical rate-dependent mechanical properties of metal materials as well as the corresponding damage mechanisms.
Figure 2.4 Flow stress dependency on strain rate of copper reported [42-44].
An important upturn in the stress dependency on strain rate of copper has been reported by Follansbee et al. [43], which was revealed by using the SHPB technology, as shown in Figure 2.4. With the increase of strain rate, an increasing flow stress was determined, which indicates the strain rate dependency of flow stress of copper material. A dislocation drag mechanism is supposed to analyze the inherent physical mechanism [45]. In particular, an increase in material ductility has been pointed out at high strain rates [44, 45]. Further research conducted by Zerilli and Armstrong [44-46] showed that the control of strain rate was being taken over by a new mechanism of dislocation generation. Support for the dislocation generation mechanism has been provided by the connection of measurements with shock-induced plasticity [42]. Dislocation nucleation, generation and multiplication at a propagating shock front induced by the high shock pressure have been extensively investigated [47-50]. In any case, the shock front is imagined to be a narrow zone at nanoscale experiencing an adiabatic shear stress near to the theoretical limit of dislocation generation.
The upturn of the nanoscale dislocation generation mechanism is proposed, which establishes the connection with pioneering dynamic experimental results of copper and iron materials [52]. Figure 2.5(a) shows the adaptation on the same stress with the log strain rate scale of copper [43], which combines the dynamic experimental results and the shock measurement results. Herein, the flow stress was determined over a wide range of strain rates in an isochronous increasing relation, which indicates the transition in mechanism from constitutive behaviour controlled by dislocation mobility to that controlled by shock-induced dislocation generation. The same phenomenon is also observed in polycrystalline Armco iron material (see Fig. 2.5(b)), which indicates the transition in mechanism. In any case, the rate-dependent mechanical properties of polycrystalline copper and iron have been investigated. The controlling factors in the mechanism are at nano scale.
Figure 2.5 Flow stress determined over a wide range of strain rates indicating the
transition from constitutive behaviour controlled by dislocation mobility to that of (a) shock control by dislocation generation in polycrystalline copper and of (b) shock control by deformation twin generation in polycrystalline Armco iron material, as
reported by Armstrong et al. [51].
2.2.3. Polymer materials for impact-resistant application
Polymer has been used extensively as structural material of engineering components that are designed to resist impact, ranging from bus windows and eyeglasses to helmets and body armors. The choice of polymer material for these applications has been made appealing by the relative low density and the transparency that is the characteristic of amorphous homopolymers. One of the studies on polymer materials focuses on the capability of absorbing dynamic energy and strain rate dependency [53-64]. Strain rate dependency of the stress-strain behaviour of polymer materials has been well documented, where, in particular, the yield stress is found to increase with increasing strain rate. This feature of mechanical behaviour is highly relevant to engineering applications, when designing a polymer component required to resist impact loading.
Chapter 2 Literature review
The thermoplastic elastomer polyurethane and the elastomeric thermoset polyure are found to have new applications by increasing the survivability of structures under impact loading, including these encountered in blast and ballistic events. Yi et al. [65] studied the large deformation and rate-dependent stress-strain behaviour of polyure and polyurethanes in dynamic compressive tests. A set of data were presented to quantify the rate-dependent behaviour of these materials from low strain rate (<1/s) to high strain rates (>1000/s), as shown in Figure 2.6.
Figure 2.6 Flow stress vs strain rate relations of polyure and three polyurethanes
determined at the deformation strain of (a) 0.15 and (b) 0.30 [65].
Figure 2.7 Stress (taken at true strain of 0.4 and 0.9) as a function of true strain rate
(from low to high strain rates), where the value of true strain rate used for each point is also taken at its respective true strain value of 0.4 or 0.9) plotted for polyure [66].
The polyure displayed a transition from rubber-like behaviour at low strain rates to leathery behaviour at high strain rates, whereas, one of these three polyurethanes displayed a transition from rubber-like behaviour at low strain rates to glassy-like behaviour at high strain rates. Figure 2.6 presents the rate-dependent behaviour by means of the stress vs logarithm strain rate, taking the stress evaluated at a strain level of 0.15 and 0.30 for (a) and (b), respectively. For both strain levels, the flow stress obviously demonstrated a close-to-linear dependency on the logarithm strain rate in both the high strain rate (>∼103 /s) and low strain rate (<∼100 /s) regions. So, the mechanical behaviour, as illustrated by the yield stress of thermoplastic-elastomeric polyurethanes and elastomeric-thermoset polyures is strongly dependent on strain rate. In addition, continuous investigation was conducted on the characterization of mechanical properties at very high strain rates under both dynamic compression and tension loading [66]. The experimental results are shown in Figure 2.7.
The uniaxial compression and tension data for polyure are found to be consistent over the strain rate range from 0.001 /s to 10000 /s, both of which increase with the increase of strain rate. Therefore, a strong dependency of flow stress on strain rate is clarified in the material of thermoplastic-elastomeric polyurethane and elastomeric-thermoset polyure, which is of particular interest when they play a role as a protective coating to enhance survivability of structures in high rate loading events.
In addition, Song et al. [67] used a pulse-shaped SHPB setup to study the high- and low strain-rate compression experiments of epoxidized soybean oil (ESO)/clay nanocomposites with nanoclay of 0%, 5% and 8% in weight. Figure 2.8 shows the strain-rate effects on the dynamic compressive properties of nanocomposites with different nanoclay weights. It clearly displays that the stress at a certain strain level increases with increasing strain rate. A phenomenological rate-dependent material model was developed to describe the stress-strain response, which agrees well with the experimental data at both low and high strain rates.
Figure 2.8 Stress at the strain of 10% for the epoxidized soybean oil/clay
anocomposites at various strain rates: strain rate of lower than 0.1/s; (b) strain rate of higher than 1/s [67].
Chapter 2 Literature review
Figure 2.9 True yield stress of PMMA material as a function of true strain rate
(logarithmic scale)-low to high strain rates [64].
Moreover, another specific example is PMMA material [64]. A combined experimental and analytical method has been performed to investigate the mechanical behaviour of PMMA material at strain rates ranging from 10-4/s to 104/s. The relation of yield stress and strain rate is documented in Figure 2.9. The yield stress was found to increase as a non-linear function with the logarithmic strain rate, displaying the strain rate sensitivity. The mechanisms of the rate-dependent elastic-plastic deformation of PMMA material from low to high strain rates were also studied. A computational model was developed based on the concepts of both the Ree-Eyring yield theory and the viscoelastic theory, which indicates that intermolecular resistance to deformation may be decomposed into the contributions of different molecular processes, each with their own unique rate and temperature dependency. This model is probably suitable for two-component polymer materials.
Therefore, rate-dependent behaviour of polymer materials was revealed and mechanisms for impact resistance were also explored using the combined experimental and computational methods. A concerted effort has been made to investigate and develop new polymer materials with improved characteristics for impact resistance and damage tolerance. Concerns regarding rate dependency and impact resistance of polymer materials are basis for extensive research.
Recently, at the Netherlands Organisation for Applied Scientific Research (TNO), it was found that the material, Clear Flex 75 (CF 75 in short) is very promising to be used in transparent armour concepts. It is an amorphous polyurethane elastomeric material and has a branched structure of molecular chains with a random distribution.
CF 75 is a transparent, flexible and UV resistant polymer with a glass transition temperature of 2 ºC [68]. The CF 75 polymer material is selected to be studied in this thesis. The dynamic mechanical response is studied of CF 75 as a monolithic material as well as in hybrid form as matrix with a single embedded particle. The research aims to fill gaps in data and knowledge on the dynamic response of this type of soft polymer (see Chapter 1).
2.3. Review on the experimental technology development for characterizing dynamic material response
High loading rate testing is necessary for engineering structural applications, where components must be designed to function for impact resistance. One of the defining features of impact is that most of these deformations occur at high strain rates [69]. The high-rate testing method should be qualified to characterize the intrinsic mechanical behaviour of materials and to reveal the corresponding mechanical properties. A number of experimental techniques have been developed to measure the mechanical properties of materials at a wide range of strain rates. A classification of loading techniques and mechanical states is shown in Figure 2.10.
Figure 2.10 Classification of loading techniques and mechanical states of materials
over a wide range of strain rates: intermediate strain rate (ISR); high strain rate (HSR); very high strain rate (VHSR) [69].
Chapter 2 Literature review
It presents a schematic diagram of the strain rate range from creep (over periods of several years) to plate impact techniques (nanoseconds). Conventional commercial mechanical testing machines can cover the low strain rate range up to around 10/s. Drop-weight machines have been developed for a standard test in the intermediate strain rate (ISR) range of 10-100/s. The most successful loading techniques for obtaining material data at high strain rate (HSR) have been reported to be the split Hopkinson bars (SHB). The plate impact techniques have been employed for mechanical tests at very high strain rate (VHSR). A fundamental difference between quasi-static and dynamic loading is that inertia and wave propagation effects become pronounced at higher strain rate. From low to high strain rate loading, a transition exists in the tested material from nominally isothermal conditions to quasi-isothermal/adiabatic conditions. In low strain rate experiments, all maintain one-dimensional (1D) stress states in the material, while the high speed loading techniques produce a 1D strain state [69].
In this Section, we focus on reviewing experimental techniques to obtain dynamic mechanical properties of materials at a strain rate range from intermediate to very high. The techniques are the drop-weight machine, the Taylor impact technology and the split Hopkinson bar.
2.3.1. Drop weight test technology
The drop weight machine, as a cost effective facility to provide experimental data, is designed to perform impact tests at intermediate strain rate [70]. The sketch of a typical drop weight machine is shown in Figure 2.11.
In the drop weight machine, a mass impactor is guided by rails in a free fall motion from a given height, . Sensors can detect the velocity at the time of impact. The impact energy, and velocity, are calculated from the following equations:
(2.1) 2 (2.2) in which is the mass of the drop weight impactor and is the acceleration ratio of
gravity. The impact energy, is converted into kinetic energy during impact
loading onto the tested specimen. Herein, friction in the machine is supposed to be zero due to the free fall motion of the impactor.
The standard analyzing method for the output of a drop weight impact test assumes that the impactor behaves as a rigid body and hence Newton’s laws of motion can be applied. Thus, for determining the calibration factor, of a drop weight force
transducer dynamically, one can replace by ∆ . So,
/ ∆ / (2.3)
in which, is the integral of the output voltage signal of strain gage bridge and
∆ is the change of the velocity of impactor produced by impact on the force transducer. It is noted that the velocity is a vector so that the magnitudes of impact and rebound speeds can be added.
In a drop weight test, the output voltage signal often shows oscillations comparable in size to a signal produced by the mechanical resistance of specimen. This is particularly true if the drop weight machine itself is instrumented with accelerometers [71]. Elastic waves reverberate around inside until the momenta of the constituent parts of weight have been reversed. Then, the rebound occurs and the specimen is unloaded. Recent work has demonstrated that it is possible to obtain high-quality data from such machines either by the use of a momentum trap in weight [72] or by a careful design of the separate force transducers placed below the specimen [73]. Besides, a drop weight machine is also widely used for explosives safety qualification [74]. A modification to the drop weight apparatus is to machine a light path through the weight, which has proved useful in the elucidation of explosives ignition mechanism. Another modification is to perform the deformation between the transparent glass anvils [75-78], which allows a high-speed camera to record the impact event.
Ozbek et al. [7] developed a high-speed photography to record a typical drop weight impact test performed on a porous concrete material. It has a laser velocity measurement system and alternatively a high-speed photography. Crack propagation and coalescence to form small particles due to the stress wave can be progressively seen, as shown in Figure 2.12. Thus, the fracture patterns observed during the test and the fragments examined after failure demonstrate that cracks are not only located in
Chapter 2 Literature review
the cement paste which is a weak bridge to bond the coarse aggregates, but are also sometimes forced to propagate through the coarse aggregates.
The drop weight machine for impact testing has been successfully developed. The machine can produce an impact loading to a tested specimen. Impact tests can produce the validated experimental data of the impact speed and the time history of crushing force. By using a displacement sensor, which can measure the displacement of the impactor during the impact test, the force versus displacement curves can be generated by combining the time history of force and displacement data. The modification with a light path through the weight and the development of a high-speed camera can improve the usefulness of the drop weight machine.
Figure 2.12 High-speed photographs for demonstrating the fracture patterns of porous
concrete material subjected to a drop weight impact test [7].
2.3.2. Taylor impact technology
The Taylor impact test was developed by Taylor during 1930s [79-81] as a method of measuring the dynamic strength of ductile materials in compression. It is a flexible, repeatable and efficient dynamic testing system. The experiment involves the launch (at normal incidence) of a rod triggered by a high-pressure air gas gun onto a plate (assumed to be nearly rigid), where the velocity can be measured just before impact. Substantial dynamic deformation starts at the impact site of the rod, leading to local expansion followed by the development of a final shape, which depends on the impact velocity and the rod material properties. The Taylor impact test can characterize material behaviour at very high strain rate (>10000/s).
The advantage of the Taylor impact technology is that it is extremely simple to perform. Only a high-pressure air gas gun is needed for launching the rod at a desired velocity, together with the ability to measure the deformed shape of the rod. However, the disadvantage of this technology is an inverse problem: material properties on the
basis of the macroscopic measurement of an inhomogeneous deformation should be determined. High-speed photography can record the deformation process. The technique for measuring the internal hardness variation within the deformed material is developed to improve the Taylor impact experiment.
For a plastic material, the deformation process during the Taylor impact experiment is seen as a sequence of elastic and plastic wave propagation into the cylinder specimen. Figure 2.13 shows the sequence of material deformation in the Taylor impact
experiment [82]. A cylindrical specimen of length, 0 impacts on the plate at a
velocity, . At this moment, the elastic wave is faster than the plastic wave and moves at a velocity, . This elastic compressive wave travels until it reaches the back end surface of the cylindrical specimen, reflects there and then returns as a release wave. When this elastic compressive wave returns toward the plastic wave, they interact with each other. This marks the end of the deformation process, because the stress is reduced to zero. The stress within the region that has plastically deformed is assumed to be constant and equal to the yield stress, of the material at that strain rate, which is the dynamic yield strength.
Figure 2.13 Sequence of material deformation during a Taylor impact test of
cylindrical specimen against a rigid wall [82].
From the conservation of mass and momentum, the following expression is derived [82]:
/ / 1 (2.4) Where, is the initial density of material, and is the strain, which can be calculated as:
/ 1 / (2.5) Wherein, and are the area of the local cross-section and the length of the
deformed specimen, respectively; and are the same quantities before
