Abstract
The aim of the present paper is to investigate the scaling behaviour of the experimental tensile softening (or catastrophic) curves and it concludes a series of papers from the same research group published inMaterials and Structures [1–4]. Experimentally, it is evident how these curves become steeper by increasing the size of the specimens (ductile-to-brittle transition). To study this phenomenon, a completely new testing apparatus, made up of three orthogonally placed actuators, was bult at the Politecnico di Torino by the authors [1, 5–7]. This set-up makes it possible to apply a purely tensile force, so that the secondary flexural stresses, if kept under control, constitute a degree of error comparable to the values allowed for normal testing apparatus. The method enables a stress vs. strain curve to be plotted with the descending (softening) branch up to the point where the cross section of the tensile specimen breaks away. The results of a new experimental investigation, performed over a very large scale-range of unnotched concrete specimens (16∶1), will be presented. Particular attention will be paid to the scale effects both on nominal tensile strength and on fracture energy. The renormalized experimental curves will be presented in a load vs. displacement plane characterized by anomalous physical dimensions. The renormalization of experimental curves enables obtaining the same response for all specimen dimensions, and then defining the universal (scale-independent) behaviour of the material.
Résumé
Cet article étudie les effets d’échelle sur le comportement des courbes expérimentales de radoucissement à la traction (ou catastrophiques); il conclut une série d’articles publiés dansMatériaux et Constructions par la même équipe de recherche [1–4]. Les expériences démontrent de façon évidente que ces courbes deviennent plus raides en fonction de l’augmentation de la taille des éprouvettes, montrant la transition de la ductilité à la fragilité. Afin d’étudier ce phénomène, un appareil d’essai innovant, composé de trois dispositifs de commande placés orthogonalement, a été construit par les auteurs à la Politecnico di Torino [1, 5–7]. Cet appareil permet d’appliquer une force de traction pure, afin que les contraintes de flexion secondaires, à condition d’être sous contrôle, constituent un degré d’erreur comparable aux valeurs permises pour un appareil d’essai classique. Cette méthode permet de déterminer une courbe contrainte/déformation ayant une branche déroissante (radoucissement) jusqu’au point ou les parties de l’éprouvette en traction se séparent. On présente les résultats d’une nouvelle étude expérimentale, menée sur une gamme d’éprouvettes de béton non-entaillé de dimensions variées (16∶1). Une attention particulière est accordée aux effets d’échelle sur la résistance à la traction nominale et à l’énergie de rupture. Les courbes expérimentales normalisées sont présentées sur un plan charge/déplacement caractérisé par des dimensions physiques anormales. La normalisation des courbes expérimentales permet d’obtenir la même réponse pour toutes les dimensions des éprouvettes, et de définir ensuite le comportement universel (indépendant de l’échelle) du matériau.
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Editorial Note: Prof. Alberto Carpinteri is a RILEM Senior Member. He is a member of the Editorial Group of RILEM Technical Committee 090-FMA (Fracture Mechanics of Concrete) and is involved in the work of TCs 147-FMB (Fracture Mechanics Applications to Anchorage and Bond), 148-SSC (Test Methods for the Strain Softening Response in Concrete) and QFS (Size Effect and Scaling of Quasibrittle Fracture). Prof. Carpinteri was awarded the Robert l’Hermite Medal in 1982.
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Carpinteri, A., Ferro, G. Scaling behaviour and dual renormalization of experimental tensile softening responses. Mat. Struct. 31, 303–309 (1998). https://doi.org/10.1007/BF02480671
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DOI: https://doi.org/10.1007/BF02480671