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<p>This study introduces an enhanced modified Anand model with a single set of parameters for the investigated thermo-mechanical conditions for 95.5Sn–4.0Ag–0.5Cu (SAC405) solder. The goal was to develop a unified parameter set that accurately captures the viscoplastic response of SAC405 solder starting from yielding through the hardening and saturation stages, across diverse thermal and mechanical conditions. Experimental stress–strain data from a wide range of strain rates (ɛ̇ = 0.001&#xa0;s<sup>−1</sup>, 0.0001&#xa0;s<sup>−1</sup>, 0.00001&#xa0;s<sup>−1</sup>) and temperatures (<i>T</i> = 298&#xa0;K to 398&#xa0;K) were used to determine and validate both the original and modified Anand parameters. For the modified Anand model, three critical parameters; initial stress (<i>s</i><sub><i>0</i></sub>), saturation stress (<i>ŝ</i>) and hardening coefficient (<i>h</i><sub><i>0</i></sub>), were expressed as quadratic functions of temperature and strain rate. The modified model and parameters demonstrated improved predictive performance, especially in the low-strain and low-temperature regime, achieving average <i>R</i><sup><i>2</i></sup> values exceeding 98% across all loading conditions. Furthermore, analysis of yield and saturation stress evolution confirms dominant thermal softening, strain-rate strengthening and progressive suppression of hardening capacity at elevated temperatures, demonstrating the mechanistic consistency of the modified formulation. This unified, modified Anand model enables more reliable simulation of SAC405 solder joints within the investigated temperature and strain-rate range.</p>

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High accuracy prediction of yield stress, initial stress and saturation stress in Anand model using quadratic parameterization for wide range of temperature and strain rates for 95.5Sn–4.0Ag–0.5Cu (SAC405) solder

  • 期刊论文

  • 发表日期：

    2026年7月10日

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  • Mohd Syafiq Azfar Rizaman,
  • Ahmad Sufian Abdullah,
  • Aliff Farhan Mohd Yamin,
  • Kamarul-Azhar Kamarudin

摘要

This study introduces an enhanced modified Anand model with a single set of parameters for the investigated thermo-mechanical conditions for 95.5Sn–4.0Ag–0.5Cu (SAC405) solder. The goal was to develop a unified parameter set that accurately captures the viscoplastic response of SAC405 solder starting from yielding through the hardening and saturation stages, across diverse thermal and mechanical conditions. Experimental stress–strain data from a wide range of strain rates (ɛ̇ = 0.001 s−1, 0.0001 s−1, 0.00001 s−1) and temperatures (T = 298 K to 398 K) were used to determine and validate both the original and modified Anand parameters. For the modified Anand model, three critical parameters; initial stress (s0), saturation stress (ŝ) and hardening coefficient (h0), were expressed as quadratic functions of temperature and strain rate. The modified model and parameters demonstrated improved predictive performance, especially in the low-strain and low-temperature regime, achieving average R2 values exceeding 98% across all loading conditions. Furthermore, analysis of yield and saturation stress evolution confirms dominant thermal softening, strain-rate strengthening and progressive suppression of hardening capacity at elevated temperatures, demonstrating the mechanistic consistency of the modified formulation. This unified, modified Anand model enables more reliable simulation of SAC405 solder joints within the investigated temperature and strain-rate range.