Prediction of hole expansion ratio of titanium alloys using R programming

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The hole expansion ratio (HER) is an important material property which defines the extent of edge formability of sheet metals. The stress states observed at the hole edge after the hole expansion test are similar to those seen during traditional uniaxial tensile deformation. This observation has provoked research, directed at ascertaining a correlation between the HER and tensile properties. In order to account for the forming behaviour of complex materials like titanium, a highly robust model that takes into account the material formability in all sheet-processing directions must be considered. The R programming language was used in this research to build a model fitting expression capable of predicting the HER as well as generating a regression model equation for titanium alloys, based on their thickness and Erichsen index number. The proposed regression model equation for predicting HER of titanium alloys exhibited an excellent statistical significance (p= 0.00076), indicating the robustness of the model fitting expression to predict HER values of titanium alloys. An accompanying adjusted R squared value of 0.9987 for the generated regression model equation also shows how well the regression line fits the data for accurate prediction of the HER of titanium alloys. A numerical validation analysis of the strength of the relationship derived between the predicted and the experimental HERs gave a correlation coefficient of 0.9884. This result shows a strong linear relationship between the experimental and predicted HER values of the titanium alloys with an average absolute error of 8.8%.
Original languageEnglish
Pages (from-to)125-137
Number of pages13
JournalJournal of Modeling and Optimization
Issue number2
Early online date25 Oct 2020
Publication statusPublished - 15 Dec 2020


  • titanium alloys
  • R programming
  • hole expansion ratio
  • Erichsen index number
  • abrasive water jet
  • sheet thickness


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