Application of Essential Work of Fracture Concept to Toughness Characterization of High-Density Polyethylene H.J. Kwon, P.-Y.B. Jar Department of Mechanical Engineering, University of Alberta, Edmonton, Alberta, Canada T6G 2G8 Deformation and fracture toughness of high-density polyethylene (HDPE) in plane-stress tension was stud- ied using the concept of essential work of fracture (EWF). Strain range for necking was determined from uniaxial tensile test, and was used to explain the defor- mation transition for 2-staged crack growth in double- edge-notched tensile test. Through work-partitioning, EWF values for HDPE were determined for each stage of the crack growth. Appropriateness of these EWF values to represent the material toughness is dis- cussed. The study concludes that the EWF values for ductile polymers like HDPE may not be constant, but vary with the deformation behaviour involved in the crack growth process. POLYM. ENG. SCI., 47:1327–1337, 2007. ª 2007 Society of Plastics Engineers INTRODUCTION The essential work of fracture (EWF) [1–5] is a con- cept for material toughness evaluation. Its value repre- sents the energy consumed within the fracture process zone (FPZ) where new surface is generated. For crack growth subjected to tensile loading, the EWF value is of- ten determined using double-edge-notched tensile (DENT) test [6], for which the specimen is shown in Fig. 1. Under the plane-stress condition, total work consumed in a DENT test consists of two parts: (i) the essential energy for the formation of new fracture surface, and (ii) the energy for plastic deformation around the ligament sec- tion. The EWF concept is a scheme to extract the energy for part (i) from the total fracture energy in the DENT test, and is increasingly popular for evaluation of the toughness for ductile fracture [6]. For materials in ductile fracture, FPZ is known to undergo a necking process that eventually breaks down to form fracture surface. It has been suggested that for neck- ing to be fully developed in the FPZ, specimen dimen- sions have to meet the following constraints [3, 7]. The EWF value so determined is known as the plane-stress specific EWF (w e ). ð3  5Þt 0  L 0  min W 3 or 2r p   (1) where t 0 , L 0 and W are specimen thickness, ligament length and specimen width, respectively, and 2r p is the size of the plastic zone that can be estimated using the following equation: 2r p ¼ 1 p Ew e s 2 y (2) where E is the elastic modulus and s y the tensile yield stress. Value of w e represents energy consumed for the ormation of neck and new fracture surface inside the FPZ. Some work [3, 8–10] has attempted to express the EWF value in terms of the energy consumed before and after the neck formation in FPZ, to take into account the energy for the necking explicitly. There are two types of necking behaviour, based on the stability of the necking process [11]. For many ductile materials, the neck development is an unstable process that leads to final fracture soon after the neck is initiated. This is because increase of strength by the work-harden- ing from the neck formation cannot keep up with the stress increase caused by the cross section reduction. However, for some very ductile materials like high- density polyethylene (HDPE), the work-hardening rate in the neck is fast enough to compensate for the decrease of the cross-sectional area, so that the neck development pro- cess is stabilized, and its size grows at a constant rate [12]. In a plane-stress DENT test of HDPE, neck is initially initiated along the ligament section. As to be shown in this article, after the neck is formed through the whole ligament, it propagates into the neighboring region that has been plastically deformed at the early stage of the test. In the past, studies that evaluated w e of HDPE [3, 8, 13] have largely ignored the neck development process for the energy consumption analysis. Correspondence to: H.J. Kwon; e-mail: hkwon@ualberta.ca Contract grant sponsor: Natural Sciences and Engineering Research Council of Canada (NSERC). DOI 10.1002/pen.20814 Published online in Wiley InterScience (www.interscience.wiley.com). V V C 2007 Society of Plastics Engineers POLYMER ENGINEERING AND SCIENCE—-2007