{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T22:57:28Z","timestamp":1778626648120,"version":"3.51.4"},"reference-count":30,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,1,12]],"date-time":"2023-01-12T00:00:00Z","timestamp":1673481600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Advanced Vehicle and Extreme Environment Electronics (CAVE3)","award":["10.13039\/100007579"],"award-info":[{"award-number":["10.13039\/100007579"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>Solder joints are subjected to varied stress cycle circumstances in the electronic packaging service life but are also influenced by aging. There has been limited investigation into the influence of aging and varying cycles on SnAgCu-Bi (SAC-Bi) solder joint fatigue. Cyclic fatigue tests were performed on solder joints of several alloys, including SnAgCu (SAC305), SnAgCu-Bi (SAC-Q), and SnCu-Bi (SAC-R). Individual solder joints were cycled under varying stress levels, alternating between mild and harsh stress levels. At least seven samples were prepared for each alloy by alternating between 25 mild stress (MS) cycles and three harsh stress (HS) cycles until the solder joint broke off. The impact of aging on Bi-doped solder joints fatigue under varied amplitude stress was examined and predicted for 10 and 1000 h under 125 \u00b0C. Because of the \u201cStep-up\u201d phenomenon of inelastic work, a new fatigue model was developed based on the common damage accumulation (CDA) model. The experimental results revealed that aging reduced the fatigue life of the tested solder alloys, particularly that of SAC305. According to the CDA model, all solder alloys failed earlier than expected after aging. The proposed model uses the amplification factor to assess inelastic work amplification after switching between the MS and HS cycles under varying stress amplitude conditions. The amplification factor for the SAC-Bi solder alloys increased linearly with fracture initiation and substantially followed crack propagation until the final failure. Compared with existing damage accumulation models, the proposed fatigue model provides a more accurate estimation of damage accumulation. For each case, the cut-off positions were examined. The SAC-Q amplification factor increased linearly to 83% of its overall life, which was much higher than that of SAC305 and SAC-R. This study identified three distinct failure modes: ductile, brittle, and near intermetallic compound (IMC) failure. It was also observed that SAC-Q with an organic solderability preservatives (OSP) surface finish was more susceptible to brittle failure owing to the excessive brittleness of the alloy material.<\/jats:p>","DOI":"10.3390\/ma16020750","type":"journal-article","created":{"date-parts":[[2023,1,12]],"date-time":"2023-01-12T03:47:01Z","timestamp":1673495221000},"page":"750","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Analysis and Modeling of Aged SAC-Bi Solder Joints Subjected to Varying Stress Cycling Conditions"],"prefix":"10.3390","volume":"16","author":[{"given":"Minghong","family":"Jian","sequence":"first","affiliation":[{"name":"Department of Industrial and Systems Engineering, Auburn University, Auburn, AL 36849, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0967-6002","authenticated-orcid":false,"given":"Sa\u2019d","family":"Hamasha","sequence":"additional","affiliation":[{"name":"Department of Industrial and Systems Engineering, Auburn University, Auburn, AL 36849, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2994-1504","authenticated-orcid":false,"given":"Ali","family":"Alahmer","sequence":"additional","affiliation":[{"name":"Department of Industrial and Systems Engineering, Auburn University, Auburn, AL 36849, USA"},{"name":"Department of Mechanical Engineering, Faculty of Engineering, Tafila Technical University, Tafila 66110, Jordan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohammad","family":"Hamasha","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering, Faculty of Engineering, The Hashemite University, Zarqa 13133, Jordan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xin","family":"Wei","sequence":"additional","affiliation":[{"name":"Department of Industrial and Systems Engineering, Auburn University, Auburn, AL 36849, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohamed El Amine","family":"Belhadi","sequence":"additional","affiliation":[{"name":"Department of Industrial and Systems Engineering, Auburn University, Auburn, AL 36849, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2338-5700","authenticated-orcid":false,"given":"Khozima","family":"Hamasha","sequence":"additional","affiliation":[{"name":"Department of Basic Scientific Sciences, Al-Huson University College, Al-Balqa Applied University, Al-Salt 19117, Jordan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Akkara, F.J., Hamasha, S., Alahmer, A., Evans, J., Belhadi, M.E.A., and Wei, X. 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