Effect of Three-Dimensional Modeling on the Behavior of Plane Strain or Plane Stress around Crack Tip in Compact-Tension (CT) Specimen

An analysis of the two concepts the failure and crack propagation in various materials has always been of interest to researchers. Thus, it is of necessity to investigate the failure of construction steel as one of the most widely used materials in the industry. Numerical modeling is always a compliment to the analysis of laboratory samples. One important issue, particularly in failure problems, is to study the behavior of laboratory samples according to their dimensions. In the current research, the effect of sample thickness size on crack tip behavior is numerically examined. A standard CT specimen is commonly used to evaluate the failure of ductile materials. The crack tip behavior along the thicknesses of the laboratory samples is a combination of plane stress and plane strain behavior. Accordingly, in the present study, the effect of thickness on the numerical samples was investigated via the numerical result validation. The validated results then were used as a complement to the experimental results. Modeling and analysis of the numerical samples of varying thicknesses indicated that, with progression from the sample thickness center towards the free edges, the behavior shifts from plane strain to plane stress. In the case of the standard CT specimen with 25 mm crack length, the samples with greater than 15 mm thickness have an almost plane strain behavior, and the results are proved to be reliable. Then, with further analysis and taking into account the parameters dependent on sample size, loading value, and stress-strain values perpendicular to the equation plane, an equation was presented which can be used to realize to what extent the behavior in the free edge of the CT specimen operates in the form of plane stress or plane strain.