Circle grid analysis

Abstract: Incremental forming of hole-flanges in sheet metal parts is an emerging process with a high potential economic payoff for rapid prototyping and for small quantity production. However, as with all new sheet metal forming processes, there is need for examining its deformation mechanics and describing the physics behind the occurrence of failure. How metal fails, how pre-cut holes influence strain and stress in single point incremental forming, and how these subjects can be brought together in order to understand the overall formability of hole-flanging by multi-stage incremental forming are still not well understood. However, they are of great importance for improving the performance and industrial applicability of the process. This paper attempts to provide a new level of understanding for the process by combining circle grid analysis and independent characterization of the mechanical properties and formability limits of the material with the fabrication of conical and cylindrical hole-flanges. Experimental observations, measured strain paths and material formability limits by necking and fracture allow concluding that hole-flanging by incremental forming gives rise to a new mode of deformation, not found in conventional incremental forming of sheet metal blanks without pre-cut holes, and to failure by fracture without previous localized necking.

Abstract: The aim of this paper is to provide an overview into the development and application of single point incremental forming in rapid prototyping and rapid manufacturing of polymer sheet products that will enable the readers to recognize the key influential variables, to identify the process feasibility window, to diagnose possible sources of failure and to understand the routes for selecting the most appropriate materials and operative conditions. The methodology draws from independent determination of mechanical properties and formability limits of polymers to rapid prototyping of truncated conical and pyramidal parts. The investigation is supported by circle grid analysis. Results and observations are explained in the light of theoretical framework based on membrane analysis that is capable of modelling the cold plastic deformation of polymers with pressure-sensitive yield surfaces. The results show that the single point incremental forming of polymer sheets, performed on conventional CNC machining centres, is a cost-effective innovative technology for product development in a manufacturing environment. Applications may span from products with very high depths, taking advantage of the excellent formability of polyethylene terephthalate, to applications in polycarbonate where transparency is kept during cold forming.

Abstract: This paper revisits the formability limits of single point incremental forming (SPIF) in the light of fundamental concepts of plasticity and ductile fracture mechanics. The paper has a twofold objective of investigating the limiting strain pairs at fracture in parts showing and not showing signs of necking before cracking and of demonstrating that failure by fracture occurs by tension in crack opening mode I. The overall methodology is based on the combination of circle grid analysis, measurement of the ‘gauge length’ strains at fracture and determination of fracture toughness from experimental tests performed with truncated conical SPIF parts and double edge notched test specimens loaded in tension. The work is performed in aluminium AA1050-H111 and is a step towards comprehension of the circumstances under which failure will occur in SPIF. It is shown that fracture strain pairs of truncated conical parts, fracture forming limit lines (FFLs) determined from conventional sheet formability tests and fracture toughness in crack opening mode I can be merged to create a new understanding of plastic flow and failure by fracture above the onset of necking.