Brincker, Rune

Simonsen, John

    Aalborg UniversitetFracture Mechanics of Multiple Fibre Systems in Cement-based MaterialsBrincker, Rune; Simonsen, JohnPublished in:Nordic Concrete ResearchPublication date:1996Document VersionPublisher's PDF, also known as Version of recordLink to publication from Aalborg UniversityCitation for published version (APA):Brincker, R., & Simonsen, J. (1996). Fracture Mechanics of Multiple Fibre Systems in Cement-based Materials.In Nordic Concrete Research: Proceedings Nordic Concrete Research Meeting, Espoo, Finland 1996 (pp. 91-92). Nordic Concrete Federation.General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.            ? Users may download and print one copy of any publication from the public portal for the purpose of private study or research.            ? You may not further distribute the material or use it for any profit-making activity or commercial gain            ? You may freely distribute the URL identifying the publication in the public portal ?Take down policyIf you believe that this document breaches copyright please contact us at vbn@aub.aau.dk providing details, and we will remove access tothe work immediately and investigate your claim.Downloaded from vbn.aau.dk on: April 30, 2017' Fiber 15-16, :rsity of iteborg, metallic iemy of imental ninated 27, No. l l f l· 91 FRACTURE MECHANICS OF MULTIPLE FIBRE SYSTEMS IN CEMENT-BASED MATERIALS Rune Brincker, Ph.D., Associate Professor John Simonsen, M.Sc., Ph.D. Student. Department of Building Technology and Structural Engineering, Aalborg University, Sohngaardsholmsvej 57, 9000 Aalborg, Den-mark ABSTRACT A fracture mechanical model for the fibre bridging in a cement-based material reinforced with straight discontinious fibres is pre-sented. The fibre/matrix interactions are modelled by a 3 para-meter shear-slip relation combining the interfacial debonding and the interfacial friction. From this, the model predicts that the influence of the interfacial debonding on the fibre bridging curve is significant if the fibres are stiff, if the aspect ratio is small or if the fibre length is smal!. Key words: Fibre bridging, Interfacial friction, Interfacial debond-ing, Fracture mechanics. Conventionally, only one fibre type is used in order to ensure a satisfactory mechanical behaviour of a fibre reinforced concrete. However, the geometry and the material parameters of the fibres have a significant influence on the mechanical behaviour. Therefore i t may be expected that a more optimal design can be olitained by adding more than one fibre type into the cement-based material. Therefore, the purpose of the project reported here is to set up models for the mechanical behaviour of multiple fibre systems. In that respect the knowledge of the fibre/matrix interactions and their influence on the fibre bridging for the individual fibre types is essential. T /'" Figure l: Assumed shear·-slip relation for the fibre/matrix interface For straight fibres, the fibre/matrix interactions are believed to be caused mainly by in-terfacial debonding and interfacial friction . The deformations due to inter;facial debonding will be concentrated in thin layers around the fibres. Therefore, it seems natura! to model 92 the interfacial debonding by fracture mechanics. Traditionally, linear elastic fracture me-chanics has been used. However, pull-out tests carried out by Al-shannag [l] have indicated that non-linear fracture mechanics should be used, i.e. the interfacial debonding should be modelled by a shear-slip relation. Therefore, the interfacial debonding and the interfacial frietion eannot easily be distinguished. Al-Shannag [l] proposes that the two components could be combined as shown in figure l. The frietion is modelled by a constant stress Tf and the debonding by a constant stress Tb until the debonding slip ~b is reached, Tb~b defining the debonding energy Gd. · Based on the above shear-slip relation a procedure for calculating the fibre bridging cUI·ve has been set up (A homogeneous fibre distribution is assumed and possible fibre ruptures and snubbing effects are disregarded). By normalizing the fibre bridging stress with CJ* = l/2VJTJLF/di and the crack width with w*= (TJL})/(dJEJ), the fibre bridging curve at small crack widths can approximately be expressed as a function of the two non-dimensional quantities, T* = Tb/TJ and Ed = (d J! L 1 )(G dEJ)/( T} L 1 ). V1 is the fibre valurne fraction, L f is the fibre length, di is the fibre diameter and EJ is the elastic modulus of the fibre. In figu~e 2 normalized fibre bridging curves at small crack widths are shown for the case of pure frietion (Tb = O) and for varying values of T* and Bd. The influence of T* and Ed is shown as the difference from the fibre bridging curve for pure friction. Hereby, it follows that the influence from Tb is significant for large values of Bd. Therefore, in the case of stiff fibres (large EJ), a small aspect ratio (large d f/ L f) o r s m all fibre lengths i t must b e essen t i al to consider the interfacial debonding. Otherwise, it seems reasonable only to consider the interfacial friction. 2.5.---~--~---.-------. 2.5.---~--~---.-------. e .D !+::: l "O Cl) i .~ ! ~0.5 !_ ~ B_d=l B_d=l/2 B_d=l/4 B_d=l/8 -r_b=O %L_ __ ~2--~4---6~-~8 Nonnalized crack width Figure 2: Normalized fibre bridging curves for left : right: Ed = 1/2 and varying values o f T*. REFERENCE 1*=200 1*=10 't*=2 't*=0.5 t*=O.l 't_b=O %L---~2---~4---6~-~8 Nonnalized crack width T* = 2 and varying values of Ed, and [l] Mohammad Jamal Al-Shannag: " Tensile behaviour of fib er reinforced DSP". Ph.D .-dissertation, The University of Michigan, i995. 

Fracture Mechanics of Multiple Fibre Systems in Cement-based Materials

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Fracture Mechanics of Multiple Fibre Systems in Cement-based Materials

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