Abstract
Forming limit curves characterise “mean” failure strains of sheet metals. Safety levels from the curves define the deterministic upper limit of the processing and part design window, which can be small for high strength, low formability materials. Effects of heterogeneity of plastic deformation, widely accepted to occur on the microscale, are neglected. Marciniak tests were carried out on aluminium alloys (AA6111-T4, NG5754-O), dual-phase steel (DP600) and mild steel (MS3). Digital image correlation was used to measure the effect of heterogeneity on failure. Heterogeneity, based on strain variance, was modelled with the 2-component Gaussian mixture model, and a framework was proposed to (1) identify the onset of necking and to (2) re-define formability as a probability to failure. The results were “forming maps” in major-minor strain space of contours of constant probability (from probability, P = 0 to P = 1), which showed how failure risk increased with major strain. The contour bands indicated the unique degree of heterogeneity in each material. NG5754-O had the greatest width (0.07 strain) in plane strain and MS3 the lowest (0.03 strain). This novel characterisation will allow engineers to balance a desired forming window for a component design with the risk to failure of the material.
Highlights
Forming limit curves (FLCs) characterise the failure of metallic sheet materials
FLCs determined with the ISO or time-dependent methods separate the regions of failure and safety in a binary or deterministic manner because they assume that plastic deformation occurs smoothly and homogeneously until failure
Forming limit curves are an important component for the simulation of sheet metal forming processes
Summary
Forming limit curves (FLCs) characterise the failure of metallic sheet materials. They are frequently used for material selection and for the simulation of the sheet metal forming process. Hotz et al [5] monitored thinning rate in a circular area measuring 2 mm across but did not specify the material they tested their materials on They proposed a broken-stick regression to identify the onset of necking. Failure was detected at the threshold of maximum strain rate In their plain strain Marciniak tests, Min et al [6] applied the Martinez-Donnaire et al.’s [9] technique and found that, when compared with the ISO method, the technique measured forming limits that were similar for DP600 and MP980 but was lower for AA6022. Min et al, 2017 compared with ISO: DP600: similar, MP980: similar, AA6022: lower defining the onset of necking more accurately with deformation parameters such as major strain rate has been mixed
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