Doctor of Philosophy / Department of Civil Engineering / Dunja Peric / A low ratio between the compressive strength of concrete and its cost makes concrete one of the most widely used construction materials in civil engineering. Despite of a very good response to compressive stress, concrete exhibits a low tensile strength and limited tensile strain capacity. Adding short discrete fibers to a cementitious matrix can significantly improve its performance under tensile stress, thus ultimately exhibiting a ductile behavior. Nevertheless, in spite of their beneficial properties fiber reinforced cementitious composites remain underutilized in engineering practice. One of the main reasons for this is a lack of an adequate characterization of the tensile behavior as well as a lack of analysis methods that would allow engineers to incorporate fiber reinforced structural concrete elements into their design. Therefore, this dissertation has four key objectives: 1) to computationally model a stress-strain response of high performance fiber reinforced cementitious composites in uniaxial tension and uniaxial compression prior to macro-crack localization, 2) to develop and perform a diagnostic strain localization analysis for high performance fiber reinforced cementitious composites, the results of which can characterize effects of fibers on failure precursors, 3) to devise and perform an experimental program for characterization of ultra-high performance fiber reinforced cementitious composites, and 4) to characterize a full-fledged behavior including stress-strain and stress-crack opening displacement responses of ultra-high performance fiber reinforced cementitious composites in uniaxial tension. To quantify effects of fibers on onset of strain localization in fiber reinforced cementitious composites a combined computational/analytical models have been developed. To this end, linear-elastic multi-directional fibers were embedded into a cementitious matrix. The resulting composite was described by different types of two-invariant non-associated Drucker-Prager plasticity models. In order to investigate effects of a shape of a yield surface and hardening type linear and nonlinear yield surfaces, and linear and nonlinear hardening rules were considered. Diagnostic strain localization analyses were conducted for several plane stress uniaxial tension and uniaxial compression tests on non-reinforced cementitious composites as well as on high performance fiber-reinforced cementitious composites. It was found that presence of fibers delayed the inception of strain localization in all tests on fiber-reinforced composites. Furthermore, presence of fibers exerted a more significant effect on the strain localization direction and mode in uniaxial compression than in uniaxial tension. The main objective of experimental program was to facilitate characterization of the post-cracking tensile behavior of ultra-high performance fiber reinforced cementitious composites. To this end, five different mixes of fiber-reinforced cementitious composites were cast, whereby volumetric fiber content, fiber shape and water to binder ratio were the experimental variables. Two testing methods were adopted, a direct uniaxial tension test and four-point prism bending test. Two different post-cracking behaviors were observed in direct tension tests, softening and strain hardening accompanied with multiple cracking. On the other hand, the response from prism bending tests was less scattered. Several different inverse analyses were carried out to predict stress-strain and stress-crack opening displacement responses in uniaxial tension based on the prism bending tests. The analyses resulted in worthy correlations with the experimental data, thus suggesting that the prism bending test is a viable alternative to a much more challenging to perform direct tension test for ultra-high performance fiber reinforced composites.

Thesis (MScEng)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: Strain Hardening Cement Based Composite (SHCC) is a type of High Performance Fibre Reinforced Cement-based Composite (HPFRCC). SHCC contains randomly distributed short fibres which improve the ductility of the material and can resist the full tensile load at strains up to 5 %. When SHCC is subjected to tensile loading, fine multiple cracking occurs that portrays a pseudo strain hardening effect as a result. The multiple cracking is what sets SHCC aside from conventional Reinforced Concrete (RC). Conventional RC forms one large crack that results in durability problems. The multiple cracks of SHCC typically have an average crack width of less than 80 μm (Adendorff, 2009), resulting in an improved durability compared to conventional RC. The aim of this research project is to quantify the cracking behaviour of SHCC which can be used to quantify the durability of SHCC. The cracking behaviour is described using a statistical distribution model, which represents the crack widths distribution and a mathematical expression that describes the crack pattern. The cracking behaviour was determined by measuring the cracks during quasi-static uni-axial tensile tests. The cracking data was collected with the aid of a non-contact surface strain measuring system, namely the ARAMIS system. An investigation was performed on the crack measuring setup (ARAMIS) to define a crack definition that was used during the determination of the cracking behaviour of SHCC. Several different statistical distributions were considered to describe the distribution of the crack widths of SHCC. A mathematical expression named the Crack Proximity Index (CPI) which represents the distances of the cracks to each other was used to describe the crack pattern of SHCC. The Gamma distribution was found to best represent the crack widths of SHCC. It was observed that different crack patterns can be found at the same tensile strain and that the CPI would differ even though the same crack width distribution was found. A statistical distribution model was therefore found to describe the CPI distribution of SHCC at different tensile strains and it was established that the Log-normal distribution best describes the CPI distribution of SHCC. After the cracking behaviour of SHCC was determined for quasi-static tensile loading, an investigation was performed to compare it to the cracking behaviour under flexural loading. A difference in the crack widths, number of cracks and crack pattern was found between bending and tension. Therefore it was concluded that the cracking behaviour for SHCC is different under flexural loading than in tension. / AFRIKAANSE OPSOMMING: “Strain Hardening Cement-based Composite” (SHCC) is ‘n tipe “High Performance Fibre Reinforced Cement-based Composite” (HPFRCC). SHCC bevat kort vesels wat ewekansig verspreid is, wat die duktiliteit van die material verbeter en dit kan die maksimum trekkrag weerstaan tot en met ‘n vervorming van 5 %. Wanneer SHCC belas word met ‘n trekkrag, vorm verskeie fyn krake wat ‘n sogenaamde vervormingsverharding voorstel. Die verskeie krake onderskei SHCC van normale bewapende beton. Normale bewapende beton vorm een groot kraak met die gevolg dat duursaamheidsprobleme ontstaan. Die gemiddelde kraakwydte van SHCC is minder as 80 μm (Adendorff, 2009) en het dus ‘n beter duursaamheid as normale bewapende beton. Die doel van die navorsingsprojek is om die kraak gedrag van SHCC te kwantifiseer en wat dan gebruik kan word om die duursaamheid van SHCC te kwantifiseer. Die kraak gedrag is beskryf deur ‘n statistiese verspreiding model wat die kraak wydtes se verspreiding voorstel en ‘n wiskundige uitdrukking wat die kraak patroon beskryf. Die kraak gedrag was bepaal deur die krake te meet tydens die semi-statiese een-asige trek toetse. Die kraak data was met behulp van ‘n optiese vervormings toestel, naamlik die ARAMIS, versamel. ‘n Ondersoek is gedoen op die kraak meetings opstelling (ARAMIS), om ‘n kraak definisie te definieer wat gebruik is om die kraak gedrag te bepaal. Daar is gekyk na verskeie statistiese verdelings om die kraak wydtes van SHCC te beskryf. Die kraak patroon van SHCC is beskryf met ‘n wiskundige uitdrukking genoem die “Crack Proximity Index” (CPI) wat die krake se afstande van mekaar voorstel. Dit is bevind dat die Gamma verdeling die kraak wydtes van SHCC die beste beskryf. Daar is waargeneem dat verskillende kraak patrone by dieselfde vervorming verkry kan word en dat die CPI kan verskil al is die kraak wydte verdeling dieselfde. ‘n Statistiese verdelingsmodel is dus gevind om die CPI verdeling van SHCC te beskryf by verskillende vervormings, en daar is vasgestel dat die Log-normaal verdeling die CPI verdeling van SHCC die beste beskryf. Nadat die kraak gedrag van SHCC bepaal is vir semi-statiese trek-belasting, is ‘n ondersoek gedoen waar die trek-kraak gedrag vergelyk is met buig-kraak gedrag. ‘n Verskil in die kraak wydtes, aantal krake en kraak patroon is gevind tussen buiging en trek. Dus is die gevolgtrekking gemaak dat die kraak gedrag van SHCC verskillend is in buiging as in trek.

Thesis (MScEng (Civil Engineering))--University of Stellenbosch, 2009. / ENGLISH ABSTRACT: Strain Hardening Cement-based Composite (SHCC) is part of the High Performance Fibre Reinforced Cement-based Composite (HPFRCC) family and is a relative new concrete composite. This Fibre Reinforced Cement-based Composite (FRCC) contains randomly distributed short fibres and when subjected to a uni-axial tensile load multiple cracking occurs. The multiple cracking generates fine cracks which are normally smaller than 100 μm and achieve a strain capacity of more than 5 %. There are limited publications regarding the research of sustained tensile tests on SHCC and especially the cracking behaviour of SHCC under quasi-static uni-axial as well as sustained tensile loads. The cracking behaviour is described as the average crack width, number of cracks and descriptive statistical properties which could be used to represent the distribution of the multiple fine cracks under uni-axial tension. There are two types of tests that were under consideration to determine the cracking behaviour of SHCC. The first is quasi-static uniaxial tensile tests and the second is sustained tensile tests. The latter was dependant on the uni-axial tensile tests in terms of the sustained load applied. The sustained loads ranged from 40 % to 80 % of the ultimate tensile resistance recorded from the uni-axial tensile tests that correspond with a strain rate of 0.001 /s. Different strain rates were used for the uni-axial tensile tests to determine the effect on the cracking behaviour. The cracking behaviour was determined with the aid of a non-contact optical 3D digital deformation measuring device called ARAMIS. The content of this thesis gives a background study of the cracking behaviour and relevant research performed on SHCC under certain loads as well as some literature about the timedependant effects of a cement-based composite. The functioning of the device called ARAMIS is explained as well as the resulting effects of this device on the preparation of the test specimens. The experimental framework for the uni-axial and sustained tensile tests is discussed. Thereafter, the experimental results of the tests are depicted and discussed. The results shed some light on the basic material properties such as the average ultimate stress and average ultimate strain, Young’s modulus, etc. for the quasi-static tensile tests as well as shrinkage and creep of SHCC. The cracking behaviour such as the average crack width, number of cracks, the variance and skewness of the distribution of the crack widths in the test specimens for the quasi-static uni-axial and sustained tensile tests are depicted and discussed. The cracking behaviour when subjected to uni-axial tensile tests with different strain rates is significantly governed by the formation of new cracks and the average crack width remains small with increase in strain. There is no significant difference for the cracking behaviour found when subjected to different strain rates. However, when SHCC is subjected to a sustained load then the average crack width is dependant on the number of cracks that form over time as well as the load level. The formation of fewer and wider cracks was observed for specimens loaded at average 40 % of the ultimate tensile resistance stress, however at loading percentages of higher than 65 % more cracks developed which resulted in a smaller average crack width. / AFRIKAANSE OPSOMMING: Vervorming Verharding Sement gebaseerde samestelling “Strain Hardening Cement-based Composite” (SHCC) is deel van die familie van “High Performance Fibre Reinforced Cement-based Composite” (HPFRCC) en is ʼn relatiewe nuwe beton samestelling. Hierdie vesel versterkte sement gebaseerde beton bevat willekeurig verspreide kort vesels en veelvoudige klein krake vorm onder monotoniese trekkragte. Hierdie veelvoudige klein krake is minder as 100 μm wyd en lei tot ʼn vervorming van meer as 5 %. Daar is ʼn tekort aan navorsing oor die kruip van SHCC sowel as die kraak gedrag van hierdie sement gebaseerde samestelling onderhewig aan trek. Die kraak gedrag word beskryf as die gemiddelde kraakwydte, aantal krake en ʼn paar beskrywende statistiese parameters. Hierdie kraak gedrag parameters kan gebruik word om ʼn verdeling te kan weergee van die veelvoudige klein krake onder ʼn trek belasting. Twee tipes toetse was uitgevoer om die kraak gedrag te beskryf. Die eerste tipe toets was monotoniese trek toetse en die tweede tipe was kruip toetse. Die tweede toets was afhanklik van die monotoniese trek toetse in terme van die belasting wat gebruik was vir die kruip toetse. Die belasting was gevarieer vanaf 40 % tot 80 % van die breekbelasting wat bepaal is met die monotoniese trektoetse wat ooreenstem met ʼn vervorming tempo van 0.001 /s. Verskillende vervorming tempo’s vir die monotoniese trektoetse was uitgevoer om te bepaal wat die effek is op die kraak gedrag. Die kraak gedrag was bepaal met behulp van ʼn geen-kontak optiese 3D digitale deformasie meet instrument genoem ARAMIS. Die inhoud van die tesis bevat ʼn kort opsoming oor ʼn agtergrond studie van die kraak gedrag en relevante navorsing oor vesel versterkte sement gebaseerde beton, sowel as literatuur oor die tydafhanklike effekte van ʼn sement gebaseerde samestelling. Die beheer en gebruik van die meet instrument ARAMIS word verduidelik, sowel as die effek van hierdie masjien op die voorbereiding vir die eksperimente. Die eksperimentele uiteensetting vir die monotoniese en kruip toetse word beskryf. Daarvolgens is die resultate van die eksperimentele toetse getoon en verduidelik. Die resultate verduidelik die basiese materiaal eienskappe, byvoorbeeld die gemiddelde breekspanning met die ooreenkomstige breekvervorming, Young’s modulus en so voorts vir die monotoniese trektoetse, sowel as eienskappe met betrekking tot krimp en kruip van SHCC. Die kraak gedrag naamlik die gemiddelde kraakwydte, aantal krake per meter, variansie en die skuinsheid van die ontwikkelde krake met die toets proefstukke vir die monotoniese en kruip trek toetse word weergegee en verduidelik. Die kraak gedrag van SHCC wanneer getoets word met verskillende monotoniese trektoets tempo’s word beheer deur die ontwikkeling van nuwe krake en die gemiddelde kraakwydte is beduidend laag met toenemende vervorming. Daar is geen beduidende verskil in die kraak gedrag ten opsigte van die verskillende monotoniese trek tempo’s nie. In teendeel, wanneer SHCC belas word met ʼn konstante las oor tyd word die gemiddelde kraakwydte beheer deur die ontwikkeling van nuwe krake sowel as die belasting wat aangewend is. Onder ʼn belasting van so laag as 40 % van die breekbelasting vorm daar minder krake, maar met ʼn groter gemiddelde kraakwydte. Wanneer belas word met meer as 65 % van die breekbelasting vorm meer krake wat lei tot ʼn kleiner gemiddelde kraakwydte.