Sheet metal forming is very common in industry for producing various components. The optimal use of light alloys or high strength steels in transportation for energy economy, requires in-depth analysis of their formability. Usually, the formability of sheet metal is controlled by the onset of localized necking. However, under specific loadings (complex strain paths...), fracture characterizes the formability and the forming limit curve at fracture (FLCF) instead of the forming limit curve at necking (FLCN) should be considered. For identifying FLCN and FLCF under linear and non-linear strain paths, conventional methods require different experimental devices and geometrical specifications of specimen to cover a wide range of strain paths. However, using the in-plane biaxial tensile test with just one shape of cruciform is sufficient for that, even changes of strain path without unloading can be made during the test. The first objective of this study is to show that the in-plane biaxial tensile test with a single type of cruciform specimen permits to investigate the FLCN and FLCF of sheet metals under different linear and non-linear strain paths. Firstly, the forming limit strains at fracture of AA5086 sheet (t=4 mm) under linear and non-linear strain paths have been characterized, by testing an existed dedicated cruciform specimen. Thinner sheet metals are often used in industry, so a new shape of cruciform specimen with an original thickness of 2 mm was proposed. This specimen is successfully used to investigate the formability of DP600 sheet under linear and two types of non-linear strain paths. The second objective is to discuss the validity of commonly used ductile fracture criteria to predict the onset of fracture. Some ductile fracture criteria were used to produce numerical FLCFs for AA5086 and DP600 sheet. Finally, for the two tested materials, it is possible to find a criterion to predict the experimental FLCFs for either linear or non-linear strain paths.