Journal of Mechanical Science and Technology 26 (8) (2012) 2337~2345 www.springerlink.com/content/1738-494x DOI 10.1007/s12206-012-0617-y Pyramid as test geometry to evaluate formability in incremental forming: Recent results † Ghulam Hussain * , Nasir Hayat and Gao Lin College of Electrical and Mechanical Engineering, Nanjing University of Aeronautics & Astronautics, Nanjing, 210016, China (Manuscript Received June 2, 2011; Revised March 12, 2012; Accepted March 28, 2012) ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Abstract The present work has been undertaken with an objective to fill the gaps of previous studies and to explore guidelines to standardize the test specimen for evaluating formability with a single specimen in single point incremental forming (SPIF). Two candidate geometries for formability testing (i.e. varying wall angle pyramidal frustum and varying wall angle conical frustum) have been compared by vary- ing geometrical parameters and materials. The critical size in horizontal plane (i.e. half-side length/curvature radius) and critical initial forming angle have been identified and compared for the two geometries. The critical size in horizontal plane has been found to be dif- ferent for the two geometries. The critical initial forming angle has been found to be same for the two geometries. For various sheet mate- rials, the difference in the formability of VWACF and VWAPF shows a dependence upon the percent reduction in area at tensile fracture. Keywords: Formability; Geometry; Incremental forming; Parameter; Standardization; Test ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1. Introduction In the last decade, several new manufacturing processes, such as hydro-forming [1-3], laser forming [4], water jet form- ing [5], dimple forming [6], flexible hull forming [7] and in- cremental forming [8], have been introduced. However, owing to high flexibility and low tooling cost, single point incre- mental forming (SPIF) has attained a great attention in indus- trial sector. The SPIF process can perform 3-D shaping with- out dedicated dies. But the process, due to slow forming speed, is feasible for small batch size. The process has found several applications in automotive [9, 10] and biomedical sectors [11]. The process is also useful for waste sheet recycling [12]. Fur- ther, it is capable to process polymers [13] besides sheet metal. In the simplest form of SPIF, the sheet is clamped on a rig and a hemispherical end tool, made of steel rod, incrementally steps down the sheet to form desired contour. The tool motion is controlled through a pre-defined trajectory. For further process details and advances made so far, the reader is re- ferred to Ref. [8]. In SPIF, the deformation imposed by the tool on the sheet is confined to the processing zone only and is combination of stretching and shearing [14]. As a result of this peculiar de- formation mechanism, sheet thinning occurs during SPIF. The final wall thickness (i.e. after thinning) becomes less than that of the original blank sheet and, especially under uni-axial de- formation, can be approximated by the Sine law. Mathemati- cally, the law is expressed as follows: t f = t o Sin (90-θ) (1) where t f is the final wall thickness, t o is the blank thickness and θ is the wall angle. According to the above equation, the wall thinning mainly depends upon the wall angle imposed. Further the sheet fracture will occur somewhere between 0 o and 90 o . Therefore, as agreed upon by the researchers [8], the formabil- ity in SPIF is defined as the maximum value of wall angle (i.e. θ max ) without sheet fracture. Though wall angle is the principal factor affecting wall thinning in SPIF, part curvature and initial forming angle im- posed could also contribute to sheet thinning. Small curvature radii promote biaxial deformation (i.e. ε 2 ≠ 0) [15, 16], and large values of initial forming angle induce thinning band in sheet (thinning band is an excessively thinned, higher than the sine law’s prediction, segment of part located in the flange area) [17]. Both biaxial deformation and thinning band induce undue thinning, higher than the sine law’s prediction, in sheet [15-17]. As a consequence, the sheet achieves its thinning limit at a smaller wall angle and hence the formability (i.e. θ max ) reduces. Cone and pyramid, being simple, are two potential geome- tries for determining formability (i.e. θ max ) in SPIF. Shim and * Corresponding author. Tel.: +86 13675161625, Fax.: +86 25 84896469 E-mail address: gh_ghumman@yahoo.com † Recommended by Associate Editor Youngseog Lee © KSME & Springer 2012