Modeling spring-in of l-shaped structural profiles pultruded at different pulling speeds

Alexander Vedernikov, Alexander Safonov, Fausto Tucci, Pierpaolo Carlone, Iskander Akhatov

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


Cure-induced deformations are inevitable in pultruded composite profiles due to the peculiarities of the pultrusion process and usually require the use of costly shimming operations at the assembly stage for their compensation. Residual stresses formed at the production and assembly stages impair the mechanical performance of pultruded elements. A numerical technique that would allow the prediction and reduction of cure-induced deformations is essential for the optimization of the pultrusion process. This study is aimed at the development of a numerical model that is able to predict spring-in in pultruded L-shaped profiles. The model was developed in the ABAQUS software suite with user subroutines UMAT, FILM, USDFLD, HETVAL, and UEXPAN. The authors used the 2D approach to describe the thermochemical and mechanical behavior via the modified Cure Hardening Instantaneous Linear Elastic (CHILE) model. The developed model was validated in two experiments conducted with a 6-month interval using glass fiber/vinyl ester resin L-shaped profiles manufactured at pulling speeds of 200, 400, and 600 mm/min. Spring-in predictions obtained with the proposed numerical model fall within the experimental data range. The validated model has allowed authors to establish that the increase in spring-in values observed at higher pulling speeds can be attributed to a higher fraction of uncured material in the composite exiting the die block and the subsequent increase in chemical shrinkage that occurs under unconstrained conditions. This study is the first one to isolate and evaluate the contributions of thermal and chemical shrinkage into spring-in evolution in pultruded profiles. Based on this model, the authors demonstrate the possibility of achieving the same level of spring-in at increased pulling speeds from 200 to 900 mm/min, either by using a post-die cooling tool or by reducing the chemical shrinkage of the resin. The study provides insight into the factors significantly affecting the spring-in, and it analyzes the methods of spring-in reduction that can be used by scholars to minimize the spring-in in the pultrusion process.

Original languageEnglish
Article number2748
Issue number16
Publication statusPublished - 2 Aug 2021


  • Cure behavior
  • Finite element analysis (FEA)
  • Process modeling
  • Pultrusion
  • Spring-in


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