Derivation of a simplified stress–crack width law for Fiber Reinforced Concrete through a revised round panel test Fausto Minelli ⇑ , Giovanni Plizzari DICATAM – Department of Civil, Environmental, Architectural Engineering and Mathematics, University of Brescia, Italy article info Article history: Received 5 September 2013 Received in revised form 27 December 2014 Accepted 4 January 2015 Available online 7 February 2015 Keywords: Fracture toughness Fiber Reinforced Concrete Round panel Constitutive law Test scatter Kinematic model abstract The Round Determinate Panel (RDP), according to ASTM, was found to be a reliable, consistent and repeatable test method for the measurement of the energy absorption in Fiber Reinforced Concrete (FRC) composites. A smaller panel was proposed and experimentally investigated by the authors in pre- vious scientific contributions. An analytical approach is herein reported toward the definition of a simplified stress–crack width law for FRC, determined from tests on small panels according to the requirements of Model Code 2010 for tension softening materials. To this aim, the measurement of the three crack widths was implemented in the test procedure and, in addition, a kinematic approach was proposed to predict the crack width of panels. Ó 2015 Elsevier Ltd. All rights reserved. 1. Introduction FRC is a structural material nowadays integrated in several international building codes, including the recent Model Code 2010 (referred to as MC2010 in the following) [1,2]. An innovative aspect of the MC2010 concerns the definition of the FRC perfor- mance according to its mechanical properties and not based on the fiber geometry, material and content. The simplest test for the material characterization is the beam test, prescribed by several national and international standards, usually based either on a three [3,4] or four point bending schemes [5]. Early experiences with the low volume fractions of fibers that are nowadays mostly used in practice (V f < 0.3–1.0%), evidence that the characteristic val- ues determined from beam tests are remarkably smaller than the mean values because of the high scatter in beam test results. The latter is not related to the material itself but is mainly due to the small fracture areas (areas of cross sections at notch, ranging from 160 to 190 cm 2 ) linked by a little number of fibers. Such a scatter becomes particularly high when low contents (25–50 kg/m 3 ) of macro steel fibers (length ranging between 30 and 60 mm) are used [6]. The large scatter is a significant drawback both for verifying the material conformity and for the calculation of the design para- meters that, according to MC2010, depend on the residual strengths determined from material characterization tests. As an example, the post-cracking design law that correlates the residual post-cracking strengths to the crack width is given in Fig. 1 [1,2]. MC2010, according to [3], defines the residual strengths f R,j that are effective parameters that any engineer might use for the design of FRC structures. Based on f R,j , MC2010 introduces the following two design parameters: f Fts ¼ 0:45  f R;1 ð1Þ f Ftu ¼ f Fts  w u CMOD 3 f Fts  0:5f R;3 þ 0:2f R;1   P 0 ð2Þ where  CMOD 3 = 2.5 mm;  w u is the maximum crack opening accepted in structural design; its value depends on the ductility and it is basically significant for design purposes; generally w u = CMOD 3 = 2.5 mm, as assumed in the following. It is evident that a higher experimental scatter results in smaller values of f Fts and f Ftu , and this is only due, in the case of beam tests, to a not proper experimental geometry for the material characterization. This is why, as accepted by MC2010, other types of tests might be considered provided that correlation factors are available and proven. As an alternative, a widely available test is the Round Determinate Panel (RDP) test, published by ASTM [7] and standardized for the measurement of energy absorption of Fiber http://dx.doi.org/10.1016/j.cemconcomp.2015.01.005 0958-9465/Ó 2015 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. Cement & Concrete Composites 58 (2015) 95–104 Contents lists available at ScienceDirect Cement & Concrete Composites journal homepage: www.elsevier.com/locate/cemconcomp