Logistic regression analysis for experimental determination of forming limit diagrams

• Published in: International journal of machine tools & manufacture Vol. 46; no. 6; pp. 673 - 682
• Main Authors: Strano, M., Colosimo, B.M.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.05.2006; Elsevier
• Subjects: Applied sciences; Exact sciences and technology; FLD; Forming; Forming limit band; Fracture mechanics (crack, fatigue, damage...); Fundamental areas of phenomenology (including applications); Logistic regression; Mechanical engineering. Machine design; Metals. Metallurgy; Other forming methods; Physics; Press forming of metal foils and wires; Production techniques; Sheet metal forming; Solid mechanics; Structural and continuum mechanics; Logistic regression; Forming limit band; Sheet metal forming; FLD; Data analysis; Costs; Statistical analysis; Probabilistic approach; Linear regression; Empirical method; Rupture; Forming limit curve; Forming; Formability; Regression analysis; Experimental study; Deformation measurement; Sheet metal; Principal stress; Logistics
• ISSN: 0890-6955; 1879-2170
• DOI: 10.1016/j.ijmachtools.2005.07.005

The forming limit diagram (FLD) is probably the most common representation of sheet metal formability and can be defined as the locus of the principal planar strains where failure is most likely to occur. Experimental determination of the FLD consists in performing a set of formability tests on a sheet metal blank, where a regular grid has been previously etched. After each test, the deformation of the grid is measured and the relative strains computed. Strains observed closely at the fracture location are related to as ‘failed’ points, while strains observed on the sound areas of the specimens are labelled as ‘safe’ points. Starting from a set of experimental tests, the FLD should be empirically determined through a statistical analysis of collected data. In fact, statistical approaches (such as linear regression) are required to properly account for the internal randomness of failure occurrence. Linear regression, as well as most of the other empirical approaches in the scientific literature, takes into account only information related to the safe points. This paper proposes a different approach, the logistic regression, for the empirical determination of FLDs. Logistic regression allows to directly derive the probability of an event (e.g. the failure) as a function of different predictor variables (both the principal planar strains). Therefore, by using logistic regression, the process designer can directly associate the failure probability to the scrapping costs, in order to economically evaluate a new sheet metal forming operation. Logistic regression allows the determination of the FLD by including information concerning both safe and failed points.