Richard D. Sudduth

A Generalized-Model to Predict the Effect of Voids on Modulus in Ceramics

An equation recently developed by the present author to describe the modulus of particulate composites as a function of the volume fraction of particles was modified in this study to describe modulus as a function of porosity. This new equation was applied to available modulus literature for ceramics where voids were the particulate phase. By varying the porosity interaction coefficient, σ, this new generalized void/modulus equation was shown to be able to yield equations previously used to predict modulus as a function of voids for ceramics. Wang theoretically described the mode of porosity interaction during compaction with a constant, α, to calculate the void/modulus relationship for three different compaction conditions. The generalized void/modulus equation developed in this study fit Wangs theoretical data exceptionally well, even though the porosity interaction coefficients, σ, obtained did not agree closely with Wangs values of α. Wang also experimentally measured the porosity and Youngs modulus of manufactured alumina rods prepared with spherical and “egg-shaped” powders. The optimum fit for spherical particles occurred at σ=0.9 and an initial porosity of Pi=0.405 and for “egg-shaped” particles at σ=1.05 and Pi=0.475. The generalized void/modulus the equation for σ=−1 yields an equation that has the same form as Wangs proposed empirical equation that utilized two empirical constants, b and c. Wangs experimental data fitted with his proposed empirical equation gave a positive value for the constant c of 0.982 which corresponded to a negative value of Pi of -0.0743 which was not defined in the theoretical considerations developed in this study. While this value of the initial porosity, Pi, does give a better fit of the data for the interaction constant σ=-1, it still did not fit all the data as well as the results calculated for interaction coefficients nearer 1.0. The results of this study have shown that an excellent fit of most void/modulus data can be obtained using the generalized void/modulus equation developed in this study without making assumptions inconsistent with the theory presented.

Indications that the yield point at constant strain rate and the inception of tertiary creep are manifestations of the same failure criterion using the universal viscoelastic model

In a preceding publication this author introduced a new universal viscoelastic model to describe a definitive relationship between constant strain rate, creep and stress relaxation analysis for viscoelastic polymeric compounds. Since creep failure criterion for this model had not been addressed in detail in previous publications, selected creep failure criterion for this model were addressed in this study.The first manifestation of the yield stress failure criterion as applied to creep was elucidated at the intersection of the yield stress relaxation curve and the creep stress vs time curve. A second way to apply yield point failure criterion to creep failure was through the identification of a specific creep time associated with the limiting strain to yield, ε∞. The creep strain at ε∞ occurs at the very end of the straight line portion of secondary creep and is also the strain at which tertiary creep appears to be initiated, εitc = ε∞.As the strain increases from the inception of tertiary creep, εitc, eventually a strain is reached where a calculation option using this model would require a step back in time to go to the next differential element of strain. Since going back in time is currently impossible, only a huge jump in strain obtained by another calculation option for the next element of time would be realistic. Since this critical creep strain, εCC, is slightly greater than the inception of tertiary creep, if failure did not occur at the inception of tertiary creep then it would almost surely be expected to fail catastrophically at this condition.The near equivalency of the critical creep strain criterion and the yield strain criterion was found to be much more probable the lower the value of efficiency of yield energy dissipation such that 0 < n ≪.4.

Characteristics of the intrinsic modulus as applied to particulate composites with both soft and hard particulates utilizing the generalized viscosity/modulus equation

Recently, four significantly different particulate composite modulus derivations from the literature were found to yield the same theoretical “intrinsic modulus” for a particulate composite. In this article, this new intrinsic modulus was successfully combined with the generalized viscosity/modulus equation to yield a good fit of the shear modulus–particulate concentration data of both Smallwood and Nielsen using a variable intrinsic modulus. Some fillers yielded an intrinsic modulus that was close to the Einstein limiting value ([G] = [η] = 2.5), while other fillers yielded intrinsic moduli that were either somewhat larger or somewhat smaller than this value. The intrinsic modulus for carbon black in rubber was much larger than was Einsteins predicted value. However, intrinsic modulus values for Nielsens data for particulate composites were smaller than were Einsteins prediction at temperatures below the glass transition temperature of the matrix. The explanation for this phenomenon can easily be understood from a review of the properties of the intrinsic modulus. Likewise, the generalized viscosity/modulus equation was also successfully applied to available modulus literature for ceramics where voids were the particulate phase. When applied to Wangs data, the intrinsic modulus was found to be negative when describing the compaction of voids in the hot isostatic pressing of a ceramic. For this application, the modulus of a particulate composite as a function of the volume fraction of particles was modified to describe the modulus as a function of porosity. For the sets of data analyzed, values of the interaction coefficient and the packing fraction were not necessarily unique if the data sets were limited to the lower particulate volume fractions. For applications where a minimum amount of data was found to be available, a new approach was introduced to address a relative measure of the compatibility of the particle and the matrix using a new definition for Kraemers constant.