Characterization of the Viscoelasticity of Molding Compounds in the Time Domain

Abstract

Although polymer-based materials are widely used in microelectronics packaging and viscoelasticity is an intrinsic characteristic of polymers, viscoelastic properties of polymeric materials are often ignored in package stress analyses due to the difficulty in measuring these properties. However, it is necessary to consider the viscoelastic behavior when an accurate stress model is required. Viscoelastic properties of materials can be characterized in either the time or the frequency domain. In this study, stress relaxation experiments were performed on a molding compound in the time domain. A thermorheologically simple model was assumed to deduce the master curve of relaxation modulus using the time-temperature equivalence assumption. A Prony series expansion was used to express the material's relaxation behavior. Two methods to determine the Prony pairs and shift factors were compared. After they were determined, the master curve at a reference temperature was shifted to every measured temperature for comparison with experimental data.

The effect of barium titanate ceramic loading on the stress relaxation behavior of barium titanate‐silicone elastomer composites

“…For this reason, models incorporating multiple springs and dashpots are needed, a generic example being the generalized Maxwell model. [42] The generalized Maxwell model, composed of a number of springs (representing ideal solids, accounting for the pure hyperelastic or elastic behavior of viscoelastic materials) and dashpots (representing ideal fluids, accounting for the viscous nature of or viscoelastic materials) arranged in a parallel configuration, is the most general form of the linear model that is used to describe the stress relaxation behavior of hyperelastic, [38] viscoelastic [41] or visco-hyper elastic [34,40] materials. Based on the nature of the material chosen, the behavior of the springs is considered either elastic or hyperelastic.…”

“…Based on the nature of the material chosen, the behavior of the springs is considered either elastic or hyperelastic. [34,[38][39][40][41] The simple Maxwell model consisting of a single dashpot in series with a hyperelastic spring has a single relaxation time constant, τ = η/E. Real polymers, however, do not relax with a single relaxation time because the longer molecular segments take more time to relax than the shorter molecular segments.…”

“…[37] Thus, most researchers have used the GMW model or a modified version of the GMW model to study the viscoelastic properties of polymer composites. [18][19][20][21][22][33][34][35][36][37][38][39][40][41] In this study, from the literature and preliminary curve fitting of the experimental stress relaxation data, we found the GMW model (Prony-series) to be the most suitable model to study the influence of BTO loading on the visco-hyperelastic behavior of a BTO-Ecoflex composite material.…”

Controlling uncertain nonlinear structural vibrations of moving continuum system by embedding a vibration monitoring unit to feedback algorithm

“…The flexible mechanism illustrated in Figure 5 is composed of two flexible viscoelastic beams fixed together in the middle with point masses attached at each tip to intensify vibrations in rapid transitions. The viscoelastic behavior of the epoxy resin‐based compound beams including time‐variant elasticity is characterized using 201 terms of the corresponding Prony series and are mentioned in Table 1 36 . The horizontal mechanism is free to move in either vertical or horizontal axis with no rotation and is considered to be mounted using a nonlinear damped oscillator in order to rule out any possible analytic approach toward problem solution.…”

Material Viscoelasticity-Induced Drift of Micro-Accelerometers

“…To measure the viscoelastic characteristics, therefore, is one of most critical steps before evaluating the stability of micro-accelerometers because of the time- and temperature-dependent feature of the adhesive. The common measuring method is through stress relaxation or creep tests [ 24 ]. Hence, a series of stress–relaxation tests were performed using dynamic mechanical analysis (TA instrument DMA Q800, New Castle, DE, USA).…”