Analysis on fracture initiation and fracture angle in ductile sheet metal under uniaxial tension by experiments and fini
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The instability and fracture process during uniaxial tension was observed from load-stop tensile tests and finite element simulation. The results indicate that at the end of instability, the direction of the maximum principle stress near the necking groove turns to being perpendicular to the groove. This tensile stress is critical to the growth of fracture. The fracture initiates from the internal of the sheet at the center of volume where the two local necking grooves intersect. Material here is under triaxial tensile stress state and the principle stresses in all three directions are the largest. Once the initial crack occurs, it propagates along the zero-strain-rate necking groove. Moreover, the final fracture angle between the fracture plane and the tensile axis is always larger than theoretical value. An important reason is the ignorance of the triaxial stress state evolution during instability in theoretical calculation.
I. INTRODUCTION
Uniaxial tensile test has been used to describe the mechanical behavior of sheet metal for many years. Tremendous researches have been published to explain the relations between the fundamental mechanical properties of the material and the tensile test observations.1–8 Many of these studies have been regarded as the fundamental theories in material science and also have been wildly accepted in industry. In 1885, Considère firstly suggested that the instability initiates when the strain hardening is at the equivalent level with the geometrical softening.9 In 1952, Swift further developed this idea into plane stress state and proposed the diffuse necking theory.10 Hill also discussed this phenomenon in the same year and established the mathematical model of localized instability for an in-plane deforming rigidplastic sheet.11 Many theories of plasticity such as the yield criterion were established following his initial work.12–16 Thereafter, Keeler and Backofen in 1962 clearly put forward the concept of diffuse and localized instability.17 Tvergaard studied the tensile test of rectangular cross-section bar based on the two necking modes: diffuse necking and localized necking, and concluded the transition between the two modes is a function of crosssection aspect ratio.18 Marciniak and Kuczynski studied the instability propagation of sheet metal in biaxial tensile test.19 In their explanation, a groove is running in
Contributing Editor: Jürgen Eckert a) Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/jmr.2016.412
a direction perpendicular to the larger principle stress during instability process. In this groove, local strains begin to concentrate gradually. Ling proposed a method to predict the true stress–strain curve of sheet metal tensile specimen from engineering stress–strain data after necking occurred. A material function can be defined for finite element analysis (FEA) with a proper selection of a calibrated weight factor.20 However, some details regarding the forming of instability and fracture are not well explained yet. If tension contin
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