{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,30]],"date-time":"2025-12-30T08:58:39Z","timestamp":1767085119936,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2021,10,27]],"date-time":"2021-10-27T00:00:00Z","timestamp":1635292800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Instituto Nacional de Ci\u00eancias e Tecnologia - Estruturas Inteligentes em Engenharia","award":["574001\/2008-5"],"award-info":[{"award-number":["574001\/2008-5"]}]},{"name":"Universal 2016","award":["401128\/2016-4"],"award-info":[{"award-number":["401128\/2016-4"]}]},{"name":"PQ-1C","award":["302740\/2018-0"],"award-info":[{"award-number":["302740\/2018-0"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The mechanical loading frequency affects the functional properties of shape memory alloys (SMA). Thus, it is crucial to study its effect for the successful use of these materials in dynamic applications. Based on the superelastic cyclic behavior, this work presents an experimental methodology for the determination of the critical frequency of the self-heating of a NiTi Belleville conical spring. For this, cyclic compressive tests were carried out using a universal testing machine with loading frequencies ranging from 0.5 Hz to 10 Hz. The temperature variation during the cyclic tests was monitored using a micro thermocouple glued to the NiTi Belleville spring. Numerical simulations of the spring under quasi-static loadings were performed to assist the analysis. From the experimental methodology applied to the Belleville spring, a self-heating frequency of 1.7 Hz was identified. The self-heating is caused by the latent heat accumulation generated by successive cycles of stress-induced phase transformation in the material. At 2.0 Hz, an increase of 1.2 \u00b0C in the average temperature of the SMA device was verified between 1st and 128th superelastic cycles. At 10 Hz, the average temperature increase reached 7.9 \u00b0C and caused a 10% increase in the stiffness and 25% decrease in the viscous damping factor. Finally, predicted results of the force as a function of the loading frequency were obtained.<\/jats:p>","DOI":"10.3390\/s21217140","type":"journal-article","created":{"date-parts":[[2021,10,27]],"date-time":"2021-10-27T23:24:42Z","timestamp":1635377082000},"page":"7140","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Critical Frequency of Self-Heating in a Superelastic Ni-Ti Belleville Spring: Experimental Characterization and Numerical Simulation"],"prefix":"10.3390","volume":"21","author":[{"given":"Emmanuel Ferreira","family":"de Souza","sequence":"first","affiliation":[{"name":"Multidisciplinary Laboratory of Active Materials and Structures (LaMMEA), Department of Mechanical Engineering, Federal University of Campina Grande, Campina Grande 58429-140, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0138-3643","authenticated-orcid":false,"given":"Paulo C\u00e9sar Sales","family":"da Silva","sequence":"additional","affiliation":[{"name":"Multidisciplinary Laboratory of Active Materials and Structures (LaMMEA), Department of Mechanical Engineering, Federal University of Campina Grande, Campina Grande 58429-140, Brazil"}]},{"given":"Estephanie Nobre Dantas","family":"Grassi","sequence":"additional","affiliation":[{"name":"Multidisciplinary Laboratory of Active Materials and Structures (LaMMEA), Department of Mechanical Engineering, Federal University of Campina Grande, Campina Grande 58429-140, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8939-0946","authenticated-orcid":false,"given":"Carlos Jos\u00e9","family":"de Ara\u00fajo","sequence":"additional","affiliation":[{"name":"Multidisciplinary Laboratory of Active Materials and Structures (LaMMEA), Department of Mechanical Engineering, Federal University of Campina Grande, Campina Grande 58429-140, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1691-1872","authenticated-orcid":false,"given":"Antonio Gilson Barbosa","family":"de Lima","sequence":"additional","affiliation":[{"name":"Multidisciplinary Laboratory of Active Materials and Structures (LaMMEA), Department of Mechanical Engineering, Federal University of Campina Grande, Campina Grande 58429-140, Brazil"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,27]]},"reference":[{"key":"ref_1","unstructured":"Lagoudas, D.C. 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