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Title: A statistical method for determining and representing formability : innovation report
Author: Small, Neil
ISNI:       0000 0004 5923 7838
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2015
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Formability, conventionally characterised by the Forming Limit Curve (FLC), is a critical measure used to define the working limit of sheet metal in a forming operation. The FLC defines the limit strain the material can undergo before failure occurs. The importance of this failure criterion means it is used at various stages in the development of automotive body panels: during material selection; during stamping simulations; and in the purchase of stamping tools before commencing serial production. To mitigate against the risk that the FLC is positioned incorrectly; that mechanical property variation between blanks causes reduced formability; and that conditions imposed by the stamping operation itself cause premature failure, a safety margin is introduced. The size of the safety margin is based on the industrial sponsor’s prior experience and attitude to risk, as opposed to an objective analysis of each of the risks posed to formability. Uncertainty around the position of an FLC arises from the dispersed limit strains that characterise the results of standardised formability tests. The aim of this research was to understand and characterise the uncertainty of the formability test, and develop a more accurate and precise method for determining and representing formability. Initial tests were carried out according to the standard ISO method, and a digital image correlation (DIC) technique was used to measure full-field strains on each specimen throughout the tests. Two observations were made. Firstly, the method of analysis advocated by the ISO standard requires subjective interpretation to define a limit strain. Secondly, the full-field strain measurements showed a “noisy” strain distribution overlaid over the expected strain field. This “noise” was significant compared to the uncertainty of the DIC instrument. A solution was developed by adopting a statistical attitude to model surface strain measurements. Strains from the beginning of deformation up to fracture were characterised by a fundamental analysis. The analysis showed that the forming limit of an individual test is statistical in nature, and that the strains’ statistical character exhibits recognisable trends that evolve from the start of the tests up to necking. A new 'time-dependent' method based on the innovative application of a Gaussian Mixture Model (GMM) was developed to characterise these trends, and quantify the forming limit. The GMM was used to objectively identify the locus of a localised neck; identify the onset of necking; and characterise the neck at the forming limit. Rather than selectively analysing strains in a pre-determined area of a specimen, and at a selected time of the test, the developed technique eliminates the subjectivity that is required by the current ISO-standard method. The new GMM technique describes formability as a probabilistic risk of failure. Strain measurements made on single specimens were turned into a complimentary statistical formability criterion using the logistic regression technique proposed by Strano & Colosimo (2006). Formability Maps (FMs) were constructed to show the probability of failure contours on the Forming Limit Diagram (FLD). FMs derived from the GMM provide the precise representation of formability that is missing from the FLC, and that is required to objectively interpret the risk of failure for an industrial panel. It was postulated that the presence of a surface roughness is responsible for surface strain variation because of the geometry of its asperities. Its evolution is controlled by underlying changes to the microstructure during the course of plastic deformation. A modified M-K model was used to predict the range of strains that arise from surface roughening at the forming limit. Formability predictions correspond well to FLCs drawn from ISO-standard limit strains, but less well to the FMs drawn from the GMM. It was concluded that surface roughening alone does not explain the heterogeneous strain behaviour measured in this research.
Supervisor: Not available Sponsor: Jaguar Land Rover
Qualification Name: Thesis (D.Eng.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: TA Engineering (General). Civil engineering (General)