13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Computational Method for Crack Layer Model Haiying Zhang1,*, Alexander Chudnovsky1 1 Department of Civil and Materials Engineering, University of Illinois at Chicago, 60607, USA * Corresponding author: haiyin@uic.edu Abstract Crack layer (CL) model is applied for modeling of brittle fracture of engineering thermoplastics. It specifically used in polyethylene structures, where a process zone (PZ) formed in front of crack is a narrow wage-type layer consisting of drawn fibers and membranes. To model CL requires an evaluation of stress intensity factors (SIF) and crack opening displacements (COD) within the crack and PZ domains. This paper is aimed to construct SIF and COD formulas for three specific geometries: a semi-infinite crack in an infinite solid; a single-edge notched specimen, standard Pennsylvania notch test (PENT, ASTM F 1473) and a new stiff constant-K (SCK) specimen. The approximate SIF and COD formulas are expressed as superposition of two elastic solutions one due to remote load and another associated with closing forces. The paper presents the computational technique in details. The approximate expressions of SIF and COD are used to present the method of computation the shape and the size of PZ, as well as the crack and PZ driving forces. The CL parameters then are used in simulation of CL growth and prediction of the lifetime of engineering structures made of thermoplastics. Keywords Crack layer model, slow crack growth, process zone, Green’s function 1. Introduction In continuum mechanics, a crack is conventionally considered as an ideal cut in an elastic, elasto-plastic or visco-elasto-plastic medium. The concept of surface (fracture) energy associated with crack faces introduced by Griffith [1] was the first important step in thermodynamics of brittle failure. Barenblatt [2, 3] proposed a simple model of cohesive forces acting along the crack surfaces in a vicinity of crack tip. A year later Dugdale [4] independently developed a similar model for plastic deformation along an extension of crack-cut. Mathematically the two models turn to be identical and are commonly referred to as the Dugdale-Barenblatt (D-B) Model (also known as Cohesive Zone Model). The essential assumption of D-B model is that the stress singularity at the crack tip vanishes due to cohesive forces or plastic deformation at the crack front zone. Formally it expressed as zero stress intensity factor (SIF, K), i.e., 0 K . However, the stress singularity results from two basic assumptions of linear elastic fracture mechanics: 1) linear elastic stress-strain relations are maintained in near crack tip region without limitation; 2) the crack is ultimately sharp with zero curvature at the tip. In real engineering materials, however, neither of these two assumptions is correct. Indeed, 1) a damage in form of crazing, micro-cracking, shear-banding, cavitation etc. is formed in response to high stresses and the crack-damage interaction limits the stress level in the damage zone region; 2) large deformation of the crack front region results in the positive crack tip curvature, even when it could be zero before loading. It implies that the crack in engineering materials is commonly surrounded by a damage zone (generally called “process zone”) and the crack-damage interaction plays the major role in formation of stress field as well as in fracture propagation process. This leads to an alternative approach to studies of SCG known as Crack Layer (CL) model [5, 6]. CL model was originally proposed more than 3 decades ago and after that was further developed and applied for modeling various aspects of brittle fracture process [7-13]. In CL model the crack and the process zone, which usually precedes and surrounds the crack during fracture propagation in plastic components, considered as one thermodynamic system, Crack Layer. In HDPE, the process zone (PZ) is a thin wedge shape layer of cold drawn fibers and membranes. The stress and strain fields in CL model can be presented as a superposition of that in the specimen with cut off CL
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