Nanoindentation has a high load resolution, depth sensing capabilities, and can be used to characterize the local mechanical behavior in material systems with heterogeneous microstructures. Recently nanoindentation has been used to extract useful stress-strain curves, primarily in hard materials such as metals and ceramics. To apply these indentation stress-strain methods to polymer composites, we have to first develop analysis techniques for materials that exhibit viscoelasticity. In a lot of current research the viscoelastic material properties are extracted after the material has been deformed enough to initiate plasticity and in some cases the time dependence of the deformation is ignored. This doesn’t give an accurate representation of the material properties of the undeformed sample or the local deformation behavior of the material. This dissertation develops analysis protocols to extract stress-strain curves and viscoelastic properties from the load-displacement data generated from spherical nanoindentation on materials exhibiting time-dependent response at room temperature. Once these protocols are developed they can then be applied, in the future, to study viscoelastic and viscoplastic properties of various mesoscale constituents of composite material systems. These new protocols were developed and tested on polymethyl methacrylate, polycarbonate, low-density polyethylene, and the bio-polymer chitosan. The properties extracted were consistent under different conditions and we were able to produce stress-strain curves for different loading rates and different indenter tip sizes. This dissertation demonstrates that a set of protocols can be used to reliably investigate the mechanical properties and deformation behavior of time-dependent materials using nanoindentation.

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Several aspects of the stress-strain behaviour of rubber, important for evaluating its properties for finite element analysis and engineering applications, are investigated. Measurements of the deformation behaviour of an elastomer containing a compressible filler are used to assess theoretical equations for the compression modulus of rubber pads bonded to rigid endplates. The volume fraction of filler is estimated from a simple model. The first cycle stress-strain behaviour of filled and unfilled rubbers is characterised from uniaxial tests and by measuring both non-zero principal stresses with a novel pure shear technique. Various theoretical forms for the strain energy density function are assessed. The results support the assumption that the strain energy of filled natural rubber is a function only of the first strain invariant. Finite element modelling of the behaviour of a hyperelastic material in simple shear reveals that the proximity of the free edges in conventional simple shear testpieces strongly influences the stresses and deflections in the thickness direction. These finding are qualitatively supported by experiment. The effect of free edges on the shear modulus is also assessed. Deviations from hyperelastic behaviour are investigated through experimental studies of stress relaxation, cyclic stress softening and the superposition of a torsion on a uniaxial extension. Anisotropic deformations can result in corresponding differences in the amounts of stress relaxation or stress softening in different directions. Isotropic models cannot model these features but may be adequate for most practical applications. The relationship between the modulus and crystallinity of partially crystalline rubber is determined experimentally. The reinforcing effect of the crystals is found to be approximately independent of their morphology and of the modulus of the amorphous rubber. Studies of yielding of partially crystalline rubber show that the yield stress increases with increasing amounts of crystallization whereas the yield strain remains roughly constant.

Thesis (Ph. D.)--West Virginia University, 2005. / Title from document title page. Document formatted into pages; contains x, 104 p. : ill. (some col.). Vita. Includes abstract. Includes bibliographical references (p. 97-100).

Thesis (Ph. D.)--West Virginia University, 2006. / Title from document title page. Document formatted into pages; contains xiii, 105 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 97-98).

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Particulate, discrete and frictional systems such as sand constitute a separate class of materials. In order to derive stress-strain relations for these materials, their key features have to be identified and incorporated into the theoretical formulations. The presence of voids, the ability to undergo continuous and systematic spatial rearrangement of particles, the existence of bounds for the developed ratio of tangent and normal contact forces and the systematic variations of the tangent and normal contact force distributions during general loading, are identified as key features of particulate, discrete and frictional systems. The contact normal and the contact branch length distribution functions describe the spatial arrangement of particles mathematically. The distribution of contact normals exhibit mutually orthogonal principal directions which coincide with the principal stress directions. Most contacts in frictional systems do not develop limiting friction during general loading. Sliding of a few suitably oriented contacts followed by rolling and rigid body rotations and displacements of a large number of particles is the main mechanism causing non-recoverable deformations in frictional systems. As a part of the rearranging process, dominant chains of particles are continuously constructed and destructed, the rates being different at different stages of loading. A change of loading direction is associated with a change of dominant chains of particles resulting in changes in strain magnitudes. Rate insensitive incremental stress-strain relations are derived here using the principle of virtual forces. The key features of frictional systems have been incorporated into the stress-strain relations following the theoretical framework proposed by Rothenburg(1980), for analysing bonded systems of uniform spherical particles. For frictional systems, the load-deformation response at particle contacts is assumed to be non-linear. The deformations resulting from all internal activity are quantified defining equivalent incrementally elastic stiffnesses in the tangent and normal directions at contacts and defining loading and unloading criteria. After each increment of loading, the incremental stiffnesses and contact normal distribution are updated to account for the changes resulting from rearrangement of particles. Laws that describe the spatial rearrangement of particles, changes in the ratio between the tangent and normal contact force distributions and the resistance to deformation resulting from changes in dominant chains of particles are established based on the information from laboratory experiments reported in the literature and numerical experiments of Bathurst(1985). The stress ratio and the state parameter (defined as the ratio of void ratios at the critical-state to the current state, computed for a given mean-normal stress) are identified as key variables that can be used to quantify the extent of particle rearrangements. The proposed formulations are capable of modelling the non-linear stress-strain response which is dependent on the inherent anisotropy, stress induced anisotropy, density of packing, stress level and stress path. To predict the stress-strain response of sand, a total of 24 model parameters have to be evaluated. All the model parameters can be evaluated from five conventional triaxial compression tests. The proposed stress-strain relations have been verified by comparing with laboratory measurements on sand. The data base consists of triaxial tests reported by Negussey(1984), hollow cylinder tests graciously carried out for the author by A. Sayao, and true triaxial and hollow cylinder tests made available for the Cleveland Workshop(1987). / Applied Science, Faculty of / Civil Engineering, Department of / Graduate