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Polymer composites of particulate smart materials are increasingly relevant due to emerging trends in using additive manufacturing of replacement parts in automotive and aerospace applications. The mechanical properties of the polymer matrix is sufficiently well understood from decades of research and the mechanical properties of the interface between the particulate (smart material) and matrix (polymer) phase is not very well defined. The challenges associated with understanding the interface requires a multidisciplinary approach and expertise and varies dramatically between various material combinations. In this article, we establish a robust approach to experimentally determine the linear interface modulus using cohesive zone model and demonstrate its application for mechanoluminescent elastomeric composite.
The phenomenon of light emission induced by any mechanical action is termed mechanoluminescence and is classified based on the applied load regime as fracto, plastico, and elastico-mechanoluminescence (EML). EML is repeatable as the applied load is within elastic limits and induced strains are recoverable. Repetitiveness paves way for utilization in several applications including, but not limited to, stress sensing, stress visualization, fatigue monitoring, damage detection and failure prevention. Previously published work on EML materials have mostly been exploratory in nature with motivation to fabricate brighter EML materials and characterize/model their mechanism of emission. Through such work, doped zinc sulfide phosphors and doped strontium aluminate phosphors have been reported to emit the brightest emission till date. Characterization studies generally involve testing composites with EML crystals impregnated in a polymeric matrix, or EML thin films grown on various substrates. With both approaches, the focus is generally placed on correlating light output to various applied macroscopic inputs. However, there are no known efforts focusing on interfacial adhesion of EML crystals with the surrounding matrix or the substrate. Preliminary experimental and numerical research work on elastico-mechanoluminescent (EML) composites revealed that the interfacial adhesion between particle and matrix played a significant role in stress transfer and EML emission. Contemporary models for particle-reinforced composites focus on estimating macroscopic composite properties [1, 2 and 3]. No known model focusses on stresses imparted to the functional filler particles at the interface. Since EML emission depends on stress on the filler EML particles and not the macroscopic applied stress, it becomes necessary to develop models for stress transfer between the matrix and the particle at the interface. Estimation of stress transfer at the interface requires knowledge of stress distribution in the elastomer matrix. Hence, the objective of the models to be developed for elastomer composites is to capture variations in macroscopic stress of the matrix due to softening of matrix and degradation of interface with fatigue.
EML-Elastomer Composites
Elastomers are highly non-linear elastic materials which undergo significant softening during first few actuation cycles (Mullins effect) [4]. Mechanical behavior is rate-dependent exhibiting hysteresis during cyclic loading [5], and fatigue analysis of this complex system requires knowledge about loading history, composite composition and filler properties [6]. Debonding of filler-matrix interface is also an important non-linearity that cannot be neglected. While focusing attention on damage and fatigue of filled elastomers, micromechanics based and finite element based approaches have been adopted in combination by researchers to estimate macroscopic mechanical properties of the composite [7, 8]. The micromechanics approach to constitutive modeling of particulate composites generally builds upon the pioneering works of J.D. Eshelby in 1957 and T. Mori and K. Tanaka in 1973 [9, 10]. J.D. Eshelby derived analytical solutions to problems involving ellipsoidal elastic inclusions in infinite elastic bodies which are in general referred to as Eshelby’s solutions. Mori and Tanaka modeled composites with N number of filler particles as ellipsoidal inclusions in perfect adherence with matrix. Extension of the Mori-Tanaka model to elastomeric composites requires consideration of nonlinear hyperelastic and viscoelastic behavior of matrix as well as particle debonding. The non-linearity from hyperelastic behavior of matrix is generally accounted for by finite strain deformations and strain energy based formulations (for example, Ogden’s model), while particle debonding is modeled through non-linear cohesive laws arrived at from experimental data. Cohesive law is the relationship between traction forces and displacements at the interface [11]. Viscoelastic damage and hysteresis have to be accounted for separately, by modifying appropriate energy functions to include viscous dissipation determined from experimental data [12, 13, and 14].
In this article, we establish a robust approach to experimentally determine the linear interface modulus using cohesive zone model and demonstrate its application for mechanoluminescent elastomeric composite. The experimental design uses photoluminescence property of phosphors (Osram Sylvania GG45 - ZnS:Cu) to determine damage propagation and digital image correlation (DIC) to determine stress and strain in the polymer composite at the micron scale.A sample measuring 15mm x 5mm x 1.5mm is prepared using PDMS and GG45 and a notch is introduced to the sample. A microscope is modified to pull the sample apart at a constant speed and the process is observed using a microscope objective and a 4K video camera. The photoluminescence of dispersed GG45 particles is adjusted by mixing black ink to the composite to control halo effect and subsequent processing in image processing. Stress and strain computed from NICORR running in MATLAB is coupled with the opening displacement to obtain a measure of stiffness in Stage-I, II and III stiffness in a sample of varying extents of initial damage. The stiffness measured from linear softening CZM response is used to obtain the interface stiffness that can be subsequently applied in finite element models for modeling the overall property of composite. We demonstrate that an undamaged sample has the highest stiffness. With the formation of micron scale damage in the polymer composite at the interface, the interface stiffness decreases and reduces the maximum load that can be applied to the material in subsequent cycles.
References:
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[9] Eshelby, John D. (1957). "The determination of the elastic field of an ellipsoidal inclusion, and related problems." Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. Vol. 241. No. 1226. The Royal Society.
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[12] Ravichandran, G., & Liu, C. T. (1995). Modeling constitutive behavior of particulate composites undergoing damage. International Journal of Solids and Structures, 32(6-7), 979-990.
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