S. Shyam Sunder

Crack nucleation due to elastic anisotropy in polycrystalline ice

Abstract This paper presents a theoretical analysis of crack nucleation in isotropic polycrystalline ice due to the elastic anisotropy of the constituent crystals. The singularity of the associated stress concentrations near a grain-boundary facet junction provides the mechanism for inducing microcrack precursors, if similar nuclei do not already exist. The first-order microstructural stress field created by the elastic anisotropy mechanism is linearly superposed on the applied stress field. This total stress field causes the precursors to nucleate into microcracks. The analysis of the nucleation stress is based on a solution to the general problem of an extending precursor in a combined stress field including the effects of Coulombic frictional resistance. The local material resistance is characterized in terms of a critical value for the maximum principal tensile stress which can be determined from the surface free energy of either the grain boundary or the solid-vapor interface. Model predictions show that: (a) the stress required to nucleate cracks in compression is about 2.5 times that in tension, unlike other microstructural models which predict them to be equal; (b) elastic anisotropy rather than dislocation pile-up as proposed by others may govern crack nucleation in tension over a wide range of strain rates; (c) the stress required to nucleate a crack in compression is strongly dependent on crystal orientation and, as a consequence of the random orientation of crystals in isotropic polycrystalline ice, there can be a distinct beginning and end to the microcrack nucleation phase when stress is increased and if failure does not occur prematurely; (d) the grain size effect due to the elastic anisotropy mechanism is similar to that due to the dislocation pile-up mechanism over the typical range of grain sizes encountered in nature; and (e) a generalization of the limiting tensile strain criterion ∗ which accounts for the anisotropy of the constituent crystals is an excellent phenomenological approximation of the nucleation surface under multiaxial states of stress.

A differential flow model for polycrystalline ice

Abstract A differential model is proposed for the pure flow of polycrystalline ice. The theory is based on the concept of state variables and accounts for two deformation-rate mechanisms: (i) transient flow, associated with generally reversible isotropic and kinematic hardening, and (ii) steady-state flow, associated with irreversible viscous deformation. Dimensional requirements for creep as well as constant deformation-rate stress-strain response are satisfied. Correspondence is established between constant-stress creep and constant strain-rate tests. The uniaxial model contains a total of six parameters and follows experimental data on the creep of fresh-water polycrystalline ice obtained by Jacka (1984), Sinha (1978), and Brill and Camp (reproduced in Sinha, 1979).

On the constitutive modeling of transient creep in polycrystalline ice

Abstract The theoretical generality of constitutive models for the transient creep of polycrystalline ice and the ability of such models to represent knowledge derived from experimentation in a physically consistent manner are examined in this paper. The focus is on physically based but phenomenological models that employ evolving internal state variables to characterize the deformation resistance offered by the material. These include the models of Le Gac and Duval (1980) and Shyam Sunder and Wu (1989a, b). The widely used model of Sinha (1978), though not based on the theory of internal state variables, is also discussed briefly. A set of nine criteria are identified that should be used in evaluating transient-creep models for polycrystalline ice. These include the well-known correspondence between the creep and constant strain-rate responses observed experimentally by Mellor and Cole (1982, 1983) and the ability to reduce creep and constant strain-rate responses into non-dimensional forms that are independent of the loading parameters, viz., temperature and stress or strain rate, as proposed by Ashby and Duval (1985). The kinematic consistency between the response variables during transient creep, i.e., strain, strain rate and time, also emerges as an important consideration in constitutive modeling and the subsequent use of such models in a finite element framework. To satisfy this requirement, the model must accurately predict the experimentally observed relationship between all three pairs of kinematic variables (strain versus time, strain rate versus time, and strain rate versus strain) keeping the material parameters fixed. This paper finds that the formulations of Le Gac and Duval (1980) and Sinha (1978) are unable to satisfy the requirement of kinematic consistency. On the basis of the nine evaluation criteria, the formulation proposed by Shyam Sunder and Wu (1989a) emerges as the more complete creep model for polycrystalline ice. In conclusion, the paper identifies difficult problems that will benefit from future research.

A multiaxial differential model of flow in orthotropic polycrystalline ice

Abstract A multiaxial differential model is proposed for pure flow in orthotropic polycrystalline ice. The derivation of the constitutive equations is based on thermodynamics with internal-state variables. The model equations consist of the equations-of-state and evolution equations for the internal variables and a nonelastic deformation variable. The internal state of the material is described in terms of a scalar and a second-rank tensor, which represent isotropic and kinematic hardening in the material, respectively. The nonelastic deformation-rate tensor is additively decomposed into transient and steady-state components. The orthotropic texture of ice during incompressible flow is characterized by five material parameters which define appropriate measures of the thermodynamic forces and deformations. Conventionally-used mechanical tests under constant-stress creep and constant strain-rate loading are sufficient to determine these parameters.

Anisotropic elasticity of polycrystalline ice Ih

Abstract A theory to determine the complete tensor of elastic moduli of generally anisotropic polycrystalline ice and its temperature dependence from the elastic properties of single ice crystals is presented in this paper. The model, expressed in closed-form, predicts the upper and lower bound limits of the elastic moduli for such polycrystals by generalizing the methods of Voigt (1910) and Reuss (1929), respectively, that were developed for isotropic aggregates. This involves obtaining the spatial average of the elastic moduli and compliances of individual crystals of ice by weighting them with the relative frequency of their orientations in the anisotropic fabric. Single ice crystals possess an open hexagonal structure and are transversely isotropic in their elastic properties. The theory is then applied to predict the elastic constants of transversely isotropic S1 and S2 ice, and orthotropic S3 ice. The predicted upper and lower bound limits are in excellent agreement with available experimental data.

Crack nucleation due to elastic anisotropy in porous ice

Abstract This paper presents a theoretical analysis of crack nucleation in isotropic but porous ice due to the elastic anisotropy of the constituent crystals. Samples of freshwater polycrystalline ice made in the laboratory and those found in nature are in general porous materials. Even relatively dense samples of laboratory ice contain bubbles with average diameters in the range of 0.06–0.12 mm and average bubble densities of 350−6500 bubbles-cm −3 . Concentrated stress fields are produced both due to geometrical discontinuities such as grain-boundary-facet junctions and the presence of the pores which are often located in the vicinity of grain boundaries. The singularity of the microstructural stress field produced by crystal anisotropy provides the mechanism for inducing microcrack precursors on the surface of the pores, if similar nuclei do not already exist. Formation of the precursor relieves the stress singularity and a first-order approximation is adequate to characterize the remaining microstructural field. The precursors can nucleate into microcracks through the local intensification of the concentrated stress field around the pore produced by the applied stresses and the first-order microstructural stresses. The analysis of the nucleation stress is based on a solution to the general problem of an extending precursor in a combined stress field including the effects of Coulombic frictional resistance. The local material resistance is characterized in terms of a critical value for the maximum principal tensile stress which can be determined from the surface free energies of either the grain boundary or the solid-vapor interface. The stress gradients acting along the plane of the precursor due to the presence of the pore are taken into account in modeling frictional effects and computing the stress-intensity factors. Model predictions for relatively dense polycrystalline ice show that: (i) the presence of the pore influences the nucleation stresses at smaller grain sizes, i.e., less than about 5 mm, where the precursor and pore become comparable in size; (ii) the stress required to nucleate cracks in compression varies between 2.25–3.60 times that in tension, the larger values occur as the grain size decreases below 5 mm; (iii) the nucleation stress in tension closely follows the well-known linear Hall-Petch relationship with the inverse square root of grain size exhibited by experimental data; (iv) the stress required to nucleate a crack in compression is strongly dependent on crystal orientation and, as a consequence of the random orientation of crystals in isotropic polycrystalline ice, there can be a distinct beginning and end to the microcrack-nucleation phase when stress is increased and if failure does not occur prematurely; (v) the pore serves to change the nature of first crack nucleation from a shearing or mixed-mode phenomenon to a tension-dominated phenomenon as the grain size decreases below 5 mm, and this tends to align the microcracks perpendicular to the loading axis in tension and parallel to it in compression; (vi) a generalization of the limiting tensile-strain criterion proposed by Shyam Sunder and Ting (1985) which accounts for the anisotropy of the constituent crystals is an adequate phenomenological approximation of the nucleation surface under multiaxial states of stress.

Ice/Solid Adhesion Analysis Using Low-Temperature Raman Microprobe Shear Apparatus

In order to understand the molecular mechanics involved in the adhesion of a bimaterial interface bond, a Raman microprobe shear apparatus has been designed and fabricated. The apparatus is fabricated to perform a pure shear experiment on a bimaterial interface produced by the vapor deposition of a thin film of ice on a cold metallic substrate under a controlled temperature, humidity, and vapor-flow rate environment. The textures of four metal surfaces (titanium, copper, aluminum, stainless steel) and one polymer surface have been investigated with the use of the scanning electron micrograph. The shear experiment is optically coupled to a Raman microprobe at the 180° and 135° scattering geometry. The Raman spectra provide in situ information regarding the molecular structure and vibrational modes at the bimaterial interface before and after the shearing event. The results indicate that the adhesive bonds are formed primarily by the interaction of oxygen atoms in the ice lattice with the atoms of the solid surface. A solid, which displays good lattice matching with ice, shows good adhesive strength. The adhesive strength is found to be proportional to the extent of mechanical interlocking and inversely proportional to the contact angle of the water droplet. An activation energy analysis of the adhesive strength shows that the failure of the ice/metal bond is rate sensitive while the ice/polymer bond is relatively insensitive to the strain rate. The failure of the ice/metal bond is cohesive while the failure of the ice/polymer bond is interfacial. The structure of the ice layers on metals is polycrystalline, which is marginally influenced by the crystalline structure of the substrate and shows increased ordering in vibrational modes. The sheared ice has a larger number of defects as reflected by the increase in the half-power bandwidth of the Raman peaks.

Elastic anisotropy and micro-damage processes in polycrystalline ice

This paper discusses numerical predictions of a microstructural damage model for polycrystalline ice which is presented in a companion paper [1]. The results are relevant for ice deforming at the high end of the quasi-static domain of loading. First, the fracture mechanics-based model of damage is investigated by comparing model predictions of the stresses to form (nucleate) the first microcracks with test data. This is followed by a detailed simulation of loading under uniaxial compression using the damage model and an internal variable creep model, also summarized in the companion paper [1]. This simulation allows the prediction of the evolving damaged elastic properties, and delineates the relative contribution of creep and microcracking to the total deformation.The importance of load history on the deformation response is then illustrated by studying the influence of load path in biaxial loading. In these simulations, the competition between the mechanisms of failure by shear faulting and axial splitting is discussed in terms of the development of compliance anisotropy in the damaged body. Finally, the critical crack density is used as a macroscopic failure criterion to predict compressive strengths in the ductile-to-brittle transitional domain of strain rates, and its validity in more general states of stress involving different failure modes is questioned.

Elastic anisotropy and micro-damage processes in polycrystalline ice Part I: Theoretical formulation

A microstructural damage model is developed for polycrystalline ice deforming at the high end of the quasi-static domain of loading. The formation (nucleation) of microcracks is attributed to the extension of grain boundary precursors under the influence of the applied stresses and microstructural stresses resulting from the elastic anisotropy mechanism. In a compressive stress field, a growing population of stable cracks leads to progressive damage in the material. Nucleation, and hence damage accumulation, is influenced by three random variables-the precursor orientation, the basal plane orientation of the grains adjoining the precursor of interest, and the grain size. Model predictions consist of the following steps: (a) computation of microstructural stresses using a first-order approximation of the Eshelby procedure, (b) analysis of nucleation using a mixed-mode fracture criterion, and (c) computation of the elastic compliance using the self-consistent method. When coupled to a creep model, the relative contribution of microcracking and creep to the total deformation can be delineated.

Flexibility monitoring of offshore platforms

Abstract Flexibility monitoring has been proposed as an ambient vibration monitoring technique for detecting the occurrence and location of damage on steel jacket offshore platforms. The technique is based on the heuristic observation that the fundamental mode shapes of platforms closely resemble the deflections of a shear beam caused by a concentrated load at its free end in the associated direction. This paper presents a theoretical framework for evaluating the flexibility monitoring concept. Detailed studies are performed with the following three objectives: 1. 1. To investigate the nature of the relationship between the flexibility ratios used in damage detection that are obtained from mode shape measurements and the true flexibility ratios for a structure derived from its stiffness properties. 2. 2. To assess the effects of both random and bias errors arising from inaccuracies in the data measurement systems and parameter estimation algorithms on the reliability of damage detection. 3. 3. To assess through a modal sensitivity analysis: (i) the influence of the structural framing system on the damage detection ability, (ii) the damage detection capability under multiple member failures, and (iii) the ability to discriminate between structural damage and changes in foundation stiffness and structural mass. The paper also includes a brief introductory review of the history of vibration monitoring research in order to provide the necessary perspective within which to view the present development.