Analytical estimate for curing‐induced stress and warpage in coating layers

Abstract

A thermoset coating that is applied to an elastic substrate will develop residual stresses during curing because of polymerization shrinkage of the resin. This shrinkage only partly contributes to the residual stresses because, before gelation, the stresses relax completely. In this study, we developed explicit analytical expressions for the curing efficiency factor, the residual stresses, and the resulting warpage. We did this by assuming that after gelation, the material was in its rubbery state and that viscoelastic effects were absent. A difference between the free and constrained warpages during curing was made. The analytical warpage models were shown to give results comparable to those of the numer-ical calculations with a fully curing-dependent viscoelastic material model. Furthermore, for the first time, accurate analytical expressions for the stress-free temperature and stress-free strain were obtained. With these expressions, the effect of curing shrinkage on the residual stresses could easily be incorporated into existing (numerical) stress analysis without the need for extensive curing-dependent viscoelastic material models.

Mechanical Properties Comparing Composite Fiber Length to Amalgam

“…One of the most characteristic features for free-radical covalent bonding from a resin to solid polymer structure with increased modulus and density properties becomes most apparent in materials that polymerize by covalent chain-growth polymerization as the linear/volumetric cure shrinkage [29, 45, 52–56]. In fact, free radicals are engineered for specific and accurate polymerization application to cross-link molecules with subsequent cure shrinkage and possibly warpage as two of the most distinguished material problems of extensive polymer electron-pair covalent bonding [56]. Because polymerization shrinkage is not necessarily perfect with inhomogeneous material, nonuniform electron-pairing during curing in addition to increasing the modulus or stiffness can also create residual internal stresses to produce warpage of materials which weakens parts [45, 56].…”

“…In fact, free radicals are engineered for specific and accurate polymerization application to cross-link molecules with subsequent cure shrinkage and possibly warpage as two of the most distinguished material problems of extensive polymer electron-pair covalent bonding [56]. Because polymerization shrinkage is not necessarily perfect with inhomogeneous material, nonuniform electron-pairing during curing in addition to increasing the modulus or stiffness can also create residual internal stresses to produce warpage of materials which weakens parts [45, 56]. Subsequent residual cure stresses from polymerization cure shrinkage into the bulk of the material are then prone to opening up a defect at the margins of dental PFCs [29, 52].…”

Closed form expression for residual stresses and warpage during cure of composite laminates

“…If the thermoset used is cured above its glass-transition temperature, dominant effects are from cure shrinkage and modulus increase during cure. Thermoset systems are usually cured above the glass transition temperature since systems that cure at a temperature below their glass transition will vitrify during curing, such that full conversion is never reached [9].…”

“…Therefore, a better prediction model is needed to include both thermal and cure stresses. Jansen et al [9,10] have developed an analytical approach for determining the warpage of electronic packages as well as thermoset coating layers on substrates. They included the cure strain together with the evolution of the epoxy E modulus in the analysis of materials with isotropic layers.…”

Investigation of curing effects on distortion of fibre metal laminates

“…In the research performed by Jansen et Al. in 2012 [37], it has been assumed that the panel consisting a metal layer and an epoxy coating layer has some amount of strain at T cure due to cure shrinkage and therefore T BSF is above T cure . The strain at the cure temperature is defined to be the polymer strain needed to remove the curing-induced warpage.…”