A new ductile fracture criterion for the formability prediction of steel sheets and its application to finite element analysis

Abstract

Sheet metal forming, one of the most important metal working operations, concerns with the shaping of thin metal sheets (normally less than 6 mm or ¼ in.) by applying force to punches and drawing sheets into dies. There processes are accomplished basically by stretching, bending, deep drawing, embossing, bulging, flanging, rolling, and spinning. There are three important issues in sheet metal forming processes: failure, wrinkling and excessive springback. Failure is the focus of this study. Two failure mechanisms are dominant for metals forming: necking and ductile fracture. Necking failure occurs in tension of conventional carbon steels while ductile fracture is observed for advanced high strength steel sheets not only in tension but also in compression and pure shear such as upsetting tests. Necking is widely accepted as the main failure model from the uniaxial tension to the balanced biaxial tension for sheet metals. Failure due to necking is normally expressed by forming limit diagrams (FLDs). In the last decades, many experiments are carried out to construct FLDs of sheet metal alloys such as steel, aluminum and magnesium. Many theoretical models are proposed to predict FLDs such as the Hill’s localized necking model, the Swift’s diffuse necking model, the popular Marciniak and Kuczynski model (M-K model), the vertex theory and the modified maximum force criterion (MMFC). The analytical models above are mainly applied to predict formability of sheet metals based on necking or thickness reduction. Consequently, failure cannot be estimated by these models in low or negative stress triaxiality where there is no or negligible thickness reduction. Metals and alloys usually fail as ductile fracture induced by nucleation, growth and coalescence of microscopic voids. Therefore, ductile fracture occurs in a wide stress state from compressive upsetting to the balanced biaxial tension. A ductile fracture criterion is proposed to model fracture behavior of sheet meta...