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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenSat, 13 Apr 2024 01:04:00 +0000Aspects of the morphological character and stability of two-phase states in non-elliptic solids
https://resolver.caltech.edu/CaltechETD:etd-01302007-160351
Authors: {'items': [{'email': 'efried@me.wustl.edu', 'id': 'Fried-E', 'name': {'family': 'Fried', 'given': 'Eliot'}, 'show_email': 'NO'}]}
Year: 1991
DOI: 10.7907/WJKM-GB39
Part I. This work focuses on the construction of equilibrated two-phase antiplane shear deformations of a non-elliptic isotropic and incompressible hyperelastic material. It is shown that this material can sustain metastable two-phase equilibria which are neither piecewise homogeneous nor axisymmetric, but, rather, involve non-planar interfaces which completely segregate inhomogeneously deformed material in distinct elliptic phases. These results are obtained by studying a constrained boundary value problem involving an interface across which the deformation gradient jumps. The boundary value problem is recast as an integral equation and conditions on the interface sufficient to guarantee the existence of a solution to this equation are obtained. The contraints, which enforce the segregation of material in the two elliptic phases, are then studied. Sufficient conditions for their satisfaction are also secured. These involve additional restrictions on the interface across which the deformation gradient jumps-which, with all restrictions satisfied, constitutes a phase boundary. An uncountably infinite number of such phase boundaries are shown to exist. It is demonstrated that, for each of these, there exists a solution - unique up to an additive constant - for the constrained boundary value problem. As an illustration, approximate solutions which correspond to a particular class of phase boundaries are then constructed. Finally, the kinetics and stability of an arbitrary element within this class of phase boundaries are analyzed in the context of a quasistatic motion.
Part II. This work investigates the linear stability of an antiplane shear motion which involves a planar phase boundary in an arbitrary element of a wide class of non-elliptic generalized neo-Hookean materials which have two distinct elliptic phases. It is shown, via a normal mode analysis, that, in the absence of inertial effects, such a process is linearly unstable with respect to a large class of disturbances if and only if the kinetic response function - a constitutively supplied entity which gives the normal velocity of a phase boundary in terms of the driving traction which acts on it or vice versa - is locally decreasing as a function of the appropriate argument. An alternate analysis, in which the linear stability problem is recast as a functional equation for the interface position, allows the interface to be tracked subsequent to perturbation. A particular choice of the initial disturbance is used to show that, in the case of an unstable response, the morphological character of the phase boundary evolves to qualitatively resemble the plate-like structures which are found in displacive solid-solid phase transformations. In the presence of inertial effects a combination of normal mode and energy analyses are used to show that the condition which is necessary and sufficient for instability with respect to the relevant class of perturbations in the absence of inertia remains necessary for the entire class of perturbations and sufficient for all but a very special, and physically unrealistic, subclass of these perturbations. The linear stability of the relevant process depends, therefore, entirely upon the transformation kinetics intrinsic to the kinetic response function.
Part III. This investigation is directed toward understanding the role of coupled mechanical and thermal effects in the linear stability of an isothermal antiplane shear motion which involves a single planar phase boundary in a non-elliptic thermoelastic material which has multiple elliptic phases. When the relevant process is static - so that the phase boundary does not move prior to the imposition of the disturbance - it is shown to be linearly stable. However, when the process involves a steadily propagating phase boundary it may be linearly unstable. Various conditions sufficient to guarantee the linear instability of the process are obtained. These conditions depend on the monotonicity of the kinetic response function - a constitutively supplied entity which relates the driving traction acting on a phase boundary to the local absolute temperature and the normal velocity of the phase boundary - and, in certain cases, on the spectrum of wave-numbers associated with the perturbation to which the process is subjected. Inertia is found to play an insignificant role in the qualitative features of the aforementioned sufficient conditions. It is shown, in particular, that instability can arise even when the normal velocity of the phase boundary is an increasing function of the driving traction if the temperature dependence in the kinetic response function is of a suitable nature. Significantly, the instability which is present in this setting occurs only in the long waves of the Fourier decomposition of the moving phase boundary, implying that the interface prefers to be highly wrinkled.https://thesis.library.caltech.edu/id/eprint/410Structural instabilities involving time dependent materials : theory and experiment
https://resolver.caltech.edu/CaltechETD:etd-08082007-100442
Authors: {'items': [{'id': 'Minahen-T-M', 'name': {'family': 'Minahen', 'given': 'Timothy M.'}, 'show_email': 'NO'}]}
Year: 1992
DOI: 10.7907/7h70-2p51
The creep buckling of viscoelastic structures is studied analytically and experimentally to investigate structural stability in the presence of time dependent materials. The theory of linear viscoelasticity is used to model polymeric column specimens subjected to constant compressive end loads. A strength of materials approach (Euler-Bernoulli beam theory) is employed to model the moment-curvature relation for the column. The growth of initial imperfections is calculated using the hereditary integral formulation. Solution techniques are developed for small displacements and then generalized to include the effects of large displacements and rotations. A failure criterion based on maximum deformation allows the column life to be estimated directly from the material relaxation modulus. A discussion generalizing the results to include plates and shells is presented.
Rectangular cross-section polymethylmethacrylate (PMMA) specimens with hinged boundary conditions are used to study viscoelastic buckling experimentally. Constant compressive end loads are applied using a servo-controlled load frame while the specimens are kept in a temperature cabinet at elevated temperatures (accelerating the creep behavior). Specimen shortening and out-of-plane deflections are monitored during the tests. The relaxation modulus of PMMA is approximated by a Prony-Dirichlet series and the model is used to simulate the laboratory experiments. Model and experimental results show good agreement during the "glassy" and slow growth phases of the column response. As the growth rate increases some deviations between theory and experiment are seen. It is shown that the deviations are not a result of geometric nonlinearities, but may, in part, be explained by material nonlinearities not accounted for in the model.
https://thesis.library.caltech.edu/id/eprint/3053Processing and mechanical behavior of ultrafine grain materials
https://resolver.caltech.edu/CaltechETD:etd-10112007-090033
Authors: {'items': [{'id': 'Jain-M-K', 'name': {'family': 'Jain', 'given': 'Mohit Kumar'}, 'show_email': 'NO'}]}
Year: 1995
DOI: 10.7907/8fty-t229
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
The mechanical behavior of ultrafine grain Fe-28A1-2Cr and 304 stainless steel was
examined by conducting conventional mechanical testing and pre- and post-deformation
microstructural characterization on bulk samples.
Shock wave consolidation was used to produce a fully-dense nanophase Fe-28A1-2Cr
(grain size = 80 nm) intermetallic compound. In tension, the nanophase intermetallic
failed in a brittle fashion with failure strength comparable to the coarse grain intermetallic
of similar composition. However, the nanophase intermetallic yielded at 2.1 GPa during
quasi-static compressive deformation and deformed to true strains greater than 1.4 without
work hardening. The elastic-perfectly plastic behavior of nanophase Fe-28A1-2Cr is
significantly different from that of coarse-grained intermetallic of the same composition,
which yielded at 0.25 GPa and works hardened to 1.5 GPa before failure (at true strain
of about 0.37). Microstructural examination before and after compressive deformation
revealed that a significant portion of the microstructure refined to 10 nm grains surrounded
by amorphous material. A similar grain refinement process was observed in 80 urn Fe-
28A1-2Cr produced by ingot metallurgical technique.
A novel thermo-mechanical processing technique was developed for the production of a
ultrafine grain 304 stainless steel (grain size = 200 nm). The key steps to this processing
technique involved (1) formation of ultrafine dislocation cell structure, and (2) the conversion of dislocation cells into grains with medium to high misorientation by initiating
grain boundary sliding in the microstructure. The ultrafine grain steel (grain size = 200
nm) was about six times stronger ([...] = 1700 MPa) than coarse-grained steel of the same
composition. Grain size hardening behavior of 304 stainless steel was also investigated
over a broad range of grain sizes (200 nm to 200[...]).
https://thesis.library.caltech.edu/id/eprint/4037