Interface cracking and particulate size effect in particle-reinforced metal-matrix composites

The mechanical behaviors of the ceramic particle-reinforced metal matrix composites are modeled based on the conventional theory of mechanism-based strain gradient plasticity presented by Huang et al. Two cases of interface features with and without the effects of interface cracking will be analyzed, respectively. Through comparing the result based on the interface cracking model with experimental result, the effectiveness of the present model can be evaluated. Simultaneously, the length parameters included in the strain gradient plasticity theory can be obtained.

能量非局部模型和新的应变梯度理论

提出一种新的基于能量非局部模型的应变梯度理论,并应用此理论对多晶铜以及薄膜基底的微压痕硬度进行理论预测和数值分析.首先,提出了能量非局部模型,并由此模型,得出新应变梯度理论的本构关系;其次,由变分原理,得出相应的有限元公式;再次,给出了微压痕硬度的有限元分析方法;最后,将该理论预测结果与经典理论预测结果以及实验结果进行了对比.结果表明,计算结果与实验结果相符;而经典理论的预测结果远低于实验结果.

Optimal scaling in ductile fracture

This work is concerned with the derivation of optimal scaling laws, in the sense of matching lower and upper bounds on the energy, for a solid undergoing ductile fracture. The specific problem considered concerns a material sample in the form of an infinite slab of finite thickness subjected to prescribed opening displacements on its two surfaces. The solid is assumed to obey deformation-theory of plasticity and, in order to further simplify the analysis, we assume isotropic rigid-plastic deformations with zero plastic spin. When hardening exponents are given values consistent with observation, the energy is found to exhibit sublinear growth. We regularize the energy through the addition of nonlocal energy terms of the strain-gradient plasticity type. This nonlocal regularization has the effect of introducing an intrinsic length scale into the energy. We also put forth a physical argument that identifies the intrinsic length and suggests a linear growth of the nonlocal energy. Under these assumptions, ductile fracture emerges as the net result of two competing effects: whereas the sublinear growth of the local energy promotes localization of deformation to failure planes, the nonlocal regularization stabilizes this process, thus resulting in an orderly progression towards failure and a well-defined specific fracture energy. The optimal scaling laws derived here show that ductile fracture results from localization of deformations to void sheets, and that it requires a well-defined energy per unit fracture area. In particular, fractal modes of fracture are ruled out under the assumptions of the analysis. The optimal scaling laws additionally show that ductile fracture is cohesive in nature, i.e., it obeys a well-defined relation between tractions and opening displacements. Finally, the scaling laws supply a link between micromechanical properties and macroscopic fracture properties. In particular, they reveal the relative roles that surface energy and microplasticity play as contributors to the specific fracture energy of the material. Next, we present an experimental assessment of the optimal scaling laws. We show that when the specific fracture energy is renormalized in a manner suggested by the optimal scaling laws, the data falls within the bounds predicted by the analysis and, moreover, they ostensibly collapse---with allowances made for experimental scatter---on a master curve dependent on the hardening exponent, but otherwise material independent.

Geological evolution of two crustal scale shear zones. Part I. The Rand thrust complex, northwestern Mojave Desert, California. Part II. The Magdalena metamorphic core complex, north central Sonora, Mexico

The geology and structure of two crustal scale shear zones were studied to understand the partitioning of strain within intracontinental orogenic belts. Movement histories and regional tectonic implications are deduced from observational data. The two widely separated study areas bear the imprint of intense Late Mesozoic through Middle Cenozoic tectonic activity. A regional transition from Late Cretaceous-Early Tertiary plutonism, metamorphism, and shortening strain to Middle Tertiary extension and magmatism is preserved in each area, with contrasting environments and mechanisms. Compressional phases of this tectonic history are better displayed in the Rand Mountains, whereas younger extensional structures dominate rock fabrics in the Magdalena area.

In the northwestern Mojave desert, the Rand Thrust Complex reveals a stack of four distinctive tectonic plates offset along the Garlock Fault. The lowermost plate, Rand Schist, is composed of greenschist facies metagraywacke, metachert, and metabasalt. Rand Schist is structurally overlain by Johannesburg Gneiss (= garnet-amphibolite grade orthogneisses, marbles and quartzites), which in turn is overlain by a Late Cretaceous hornblende-biotite granodiorite. Biotite granite forms the fourth and highest plate. Initial assembly of the tectonic stack involved a Late Cretaceous? south or southwest vergent overthrusting event in which Johannesburg Gneiss was imbricated and attenuated between Rand Schist and hornblende-biotite granodiorite. Thrusting postdated metamorphism and deformation of the lower two plates in separate environments. A post-kinematic stock, the Late Cretaceous Randsburg Granodiorite, intrudes deep levels of the complex and contains xenoliths of both Rand Schist and mylonitized Johannesburg? gneiss. Minimum shortening implied by the map patterns is 20 kilometers.

Some low angle faults of the Rand Thrust Complex formed or were reactivated between Late Cretaceous and Early Miocene time. South-southwest directed mylonites derived from Johannesburg Gneiss are commonly overprinted by less penetrative north-northeast vergent structures. Available kinematic information at shallower structural levels indicates that late disturbance(s) culminated in northward transport of the uppermost plate. Persistence of brittle fabrics along certain structural horizons suggests a possible association of late movement(s) with regionally known detachment faults. The four plates were juxtaposed and significant intraplate movements had ceased prior to Early Miocene emplacement of rhyolite porphyry dikes.

In the Magdalena region of north central Sonora, components of a pre-Middle Cretaceous stratigraphy are used as strain markers in tracking the evolution of a long lived orogenic belt. Important elements of the tectonic history include: (1) Compression during the Late Cretaceous and Early Tertiary, accompanied by plutonism, metamorphism, and ductile strain at depth, and thrust driven? syntectonic sedimentation at the surface. (2) Middle Tertiary transition to crustal extension, initially recorded by intrusion of leucogranites, inflation of the previously shortened middle and upper crustal section, and surface volcanism. (3) Gravity induced development of a normal sense ductile shear zone at mid crustal levels, with eventual detachment and southwestward displacement of the upper crustal stratigraphy by Early Miocene time.

Elucidation of the metamorphic core complex evolution just described was facilitated by fortuitous preservation of a unique assemblage of rocks and structures. The "type" stratigraphy utilized for regional correlation and strain analysis includes a Jurassic volcanic arc assemblage overlain by an Upper Jurassic-Lower Cretaceous quartz pebble conglomerate, in turn overlain by marine strata with fossiliferous Aptian-Albian limestones. The Jurassic strata, comprised of (a) rhyolite porphyries interstratified with quartz arenites, (b) rhyolite cobble conglomerate, and (c) intrusive granite porphyries, are known to rest on Precambrian basement north and east of the study area. The quartz pebble conglomerate is correlated with the Glance Conglomerate of southeastern Arizona and northeastern Sonora. The marine sequence represents part of an isolated arm? of the Bisbee Basin.

Crosscutting structural relationships between the pre-Middle Cretaceous supracrustal section, younger plutons, and deformational fabrics allow the tectonic sequence to be determined. Earliest phases of a Late Cretaceous-Early Tertiary orogeny are marked by emplacement of the 78 ± 3 Ma Guacomea Granodiorite (U/Pb zircon, Anderson et al., 1980) as a sill into deep levels of the layered Jurassic series. Subsequent regional metamorphism and ductile strain is recorded by a penetrative schistosity and lineation, and east-west trending folds. These fabrics are intruded by post-kinematic Early Tertiary? two mica granites. At shallower crustal levels, the orogeny is represented by north directed thrust faulting, formation of a large intermontane basin, and development of a pronounced unconformity. A second important phase of ductile strain followed Middle Tertiary? emplacement of leucogranites as sills and northwest trending dikes into intermediate levels of the deformed section (surficial volcanism was also active during this transitional period to regional extension). Gravitational instabilities resulting from crustal swelling via intrusion and thermal expansion led to development of a ductile shear zone within the stratigraphic horizon occupied by a laterally extensive leucogranite sill. With continued extension, upper crustal brittle normal faults (detachment faults) enhanced the uplift and tectonic denudation of this mylonite zone, ultimately resulting in southwestward displacement of the upper crustal stratigraphy.

Strains associated with the two ductile deformation events have been successfully partitioned through a multifaceted analysis. R_f/Ø measurements on various markers from the "type" stratigraphy allow a gradient representing cumulative strain since Middle Cretaceous time to be determined. From this gradient, noncoaxial strains accrued since emplacement of the leucogranites may be removed. Irrotational components of the postleucogranite strain are measured from quartz grain shapes in deformed granites; rotational components (shear strains) are determined from S-C fabrics and from restoration of rotated dike and vein networks. Structural observations and strain data are compatable with a deformation path of: (1) coaxial strain (pure shear?), followed by (2) injection of leucogranites as dikes (perpendicular to the minimum principle stress) and sills (parallel to the minimum principle stress), then (3) southwest directed simple shear. Modeling the late strain gradient as a simple shear zone permits a minimum displacement of 10 kilometers on the Magdalena mylonite zone/detachment fault system. Removal of the Middle Tertiary noncoaxial strains yields a residual (or pre-existing) strain gradient representative of the Late Cretaceous-Early Tertiary deformation. Several partially destrained cross sections, restored to the time of leucogranite emplacement, illustrate the idea that the upper plate of the core complex bas been detached from a region of significant topographic relief. 50% to 100% bulk extension across a 50 kilometer wide corridor is demonstrated.

Late Cenozoic tectonics of the Magdalena region are dominated by Basin and Range style faulting. Northeast and north-northwest trending high angle normal faults have interacted to extend the crust in an east-west direction. Net extension for this period is minor (10% to 15%) in comparison to the Middle Tertiary detachment related extensional episode.

Micromechanical damage and fracture in elastomeric polymers

This thesis aims at a simple one-parameter macroscopic model of distributed damage and fracture of polymers that is amenable to a straightforward and efficient numerical implementation. The failure model is motivated by post-mortem fractographic observations of void nucleation, growth and coalescence in polyurea stretched to failure, and accounts for the specific fracture energy per unit area attendant to rupture of the material.

Furthermore, it is shown that the macroscopic model can be rigorously derived, in the sense of optimal scaling, from a micromechanical model of chain elasticity and failure regularized by means of fractional strain-gradient elasticity. Optimal scaling laws that supply a link between the single parameter of the macroscopic model, namely the critical energy-release rate of the material, and micromechanical parameters pertaining to the elasticity and strength of the polymer chains, and to the strain-gradient elasticity regularization, are derived. Based on optimal scaling laws, it is shown how the critical energy-release rate of specific materials can be determined from test data. In addition, the scope and fidelity of the model is demonstrated by means of an example of application, namely Taylor-impact experiments of polyurea rods. Hereby, optimal transportation meshfree approximation schemes using maximum-entropy interpolation functions are employed.

Finally, a different crazing model using full derivatives of the deformation gradient and a core cut-off is presented, along with a numerical non-local regularization model. The numerical model takes into account higher-order deformation gradients in a finite element framework. It is shown how the introduction of non-locality into the model stabilizes the effect of strain localization to small volumes in materials undergoing softening. From an investigation of craze formation in the limit of large deformations, convergence studies verifying scaling properties of both local- and non-local energy contributions are presented.

Size effects in the conical indentation of an elasto-plastic solid

The size effect in conical indentation of an elasto-plastic solid is predicted via the Fleck and Willis formulation of strain gradient plasticity (Fleck, N.A. and Willis, J.R., 2009, A mathematical basis for strain gradient plasticity theory. Part II: tensorial plastic multiplier, J. Mech. Phys. Solids, 57, 1045-1057). The rate-dependent formulation is implemented numerically and the full-field indentation problem is analyzed via finite element calculations, for both ideally plastic behavior and dissipative hardening. The isotropic strain-gradient theory involves three material length scales, and the relative significance of these length scales upon the degree of size effect is assessed. Indentation maps are generated to summarize the sensitivity of indentation hardness to indent size, indenter geometry and material properties (such as yield strain and strain hardening index). The finite element model is also used to evaluate the pertinence of the Johnson cavity expansion model and of the Nix-Gao model, which have been extensively used to predict size effects in indentation hardness. © 2012 Elsevier Ltd.

Structural ordering and interface morphology in symmetrically strained (GaIn)As/Ga(PAs) superlattices grown on off-oriented GaAs(100)

In this work we investigate the structural properties of symmetrically strained (GaIn)As/GaAs/Ga(PAs)/GaAs superlattices by means of x-ray diffraction, reciprocal-space mapping, and x-ray reflectivity. The multilayers were grown by metalorganic vapor-phase epitaxy on (001) GaAs substrates intentionally off-oriented towards one of the nearest [110] directions. High-resolution triple-crystal reciprocal-space maps recorded for different azimuth angles in the vicinity of the (004) Bragg diffraction clearly show a double periodicity of the x-ray peak intensity that can be ascribed to a lateral and a vertical periodicity occurring parallel and perpendicular to the growth surface. Moreover, from the intensity modulation of the satellite peaks, a lateral-strain gradient within the epilayer unit cell is found, varying from a tensile to a compressive strain. Thus, the substrate off-orientation promotes a lateral modulation of the layer thickness (ordered interface roughness) and of the lattice strain, giving rise to laterally ordered macrosteps. In this respect, contour maps of the specular reflected beam in the vicinity of the (000) reciprocal lattice point were recorded in order to inspect the vertical and lateral interface roughness correlation, A semiquantitative analysis of our results shows that the interface morphology and roughness is greatly influenced by the off-orientation angle and the lateral strain distribution. Two mean spatial wavelengths can be determined, one corresponding exactly to the macrostep periodicity and the other indicating a further interface waviness along the macrosteps. The same spatial periodicities were found on the surface by atomic-force-microscopy images confirming the x-ray results and revealing a strong vertical correlation of the interfaces up to the outer surface.

The effect of flexoelectricity on the dielectric properties of inhomogeneously strained ferroelectric thin films

Recent experimental measurements of large flexoelectric coefficients in ferroelectric ceramics suggest that strain gradients can affect the polarization and permittivity behaviour of inhomogeneously strained ferroelectrics. Here we present a phenomenological model of the effect of flexoelectricity on the dielectric constant, polarization, Curie temperature (T-C), temperature of maximum dielectric constant (T-m) and temperature of the onset of reversible polarization (T-ferro) for ferroelectric thin films subject to substrate-induced epitaxial strains that are allowed to relax with thickness, and the qualitative and quantitative predictions of the model are compared with experimental results for (Ba0.5Sr0.5)TiO3 thin films on SrRuO3 electrodes. It is shown that flexoelectricity can play an important role in decreasing the maximum dielectric constant of ferroelectric thin films under inhomogeneous in-plane strain, regardless of the sign of the strain gradient.

Structural analysis of the Paint Lake Deformation Zone, Northern Ontario /

The Paint Lake Deformation Zone (PLDZ), located within the Superior Province of Canada, demarcates a major structural and lithological break between the Onaman-Tashota Terrane to the north and the Beardmore-Geraldton Belt to the south. The PLDZ is an east-west trending lineament, approximately 50 km in length and up to 1 km in width, comprised of an early ductile component termed the Paint Lake Shear Zone and a late brittle component known as the Paint Lake Fault. Structures associated with PLDZ development including S-, C- and C'-fabrics, stretching lineations, slickensides, C-C' intersection lineations, Z-folds and kinkbands indicate that simple shear deformation dominated during a NW-SE compressional event. Movement along the PLDZ was in a dextral sense consisting of an early differential motion with southside- down and a later strike-slip motion. Although the locus of the PLDZ may in part be lithologically controlled, mylonitization which accompanied shear zone development is not dependent on the lithological type. Conglomerate, intermediate and mafic volcanic units exhibit similar mesoscopic and microscopic structures where transected by the PLDZ. Field mapping, supported by thin section analysis, defines five strain domains increasing in intensity of deformation from shear zone boundary to centre. A change in the dominant microstructural deformation mechanism from dislocation creep to diffusion creep is observed with increasing strain during mylonitization. C'-fabric development is temporally associated with this change. A decrease in the angular relationship between C- and C'-fabrics is observed upon attaining maximum strain intensity. Strain profiling of the PLDZ demonstrates the presence of an outer primary strain gradient which exhibits a simple profile and an inner secondary strain gradient which exhibits a more complex profile. Regionally metamorphosed lithologies of lower greenschist facies outside the PLDZ were subjected to retrograde metamorphism during deformation within the PLDZ.

Reduced relative entropy techniques for a posteriori analysis of multiphase problems in elastodynamics

We give an a posteriori analysis of a semidiscrete discontinuous Galerkin scheme approximating solutions to a model of multiphase elastodynamics, which involves an energy density depending not only on the strain but also the strain gradient. A key component in the analysis is the reduced relative entropy stability framework developed in Giesselmann (2014, SIAM J. Math. Anal., 46, 3518–3539). This framework allows energy-type arguments to be applied to continuous functions. Since we advocate the use of discontinuous Galerkin methods we make use of two families of reconstructions, one set of discrete reconstructions and a set of elliptic reconstructions to apply the reduced relative entropy framework in this setting.

Reduced relative entropy techniques for a priori analysis of multiphase problems in elastodynamics

We give an a priori analysis of a semi-discrete discontinuous Galerkin scheme approximating solutions to a model of multiphase elastodynamics which involves an energy density depending not only on the strain but also the strain gradient. A key component in the analysis is the reduced relative entropy stability framework developed in Giesselmann (SIAM J Math Anal 46(5):3518–3539, 2014). The estimate we derive is optimal in the L∞(0,T;dG) norm for the strain and the L2(0,T;dG) norm for the velocity, where dG is an appropriate mesh dependent H1-like space.

Nanoscale electromechanical properties of CaCu3Ti4O12 ceramics

Piezoresponse Force Microscopy (PFM) is used to characterize the nanoscale electromechanical properties of centrosymmetric CaCu3Ti4O12 ceramics with giant dielectric constant. Clear PFM contrast both in vertical (out-of-plane) and lateral (in-plane) modes is observed on the ceramic surface with varying magnitude and polarization direction depending on the grain crystalline orientation. Lateral signal changes its sign upon 180 degrees rotation of the sample thus ruling out spurious electrostatic contribution and confirming piezoelectric nature of the effect. Piezoresponse could be locally reversed by suitable electrical bias (local poling) and induced polarization was quite stable showing long-time relaxation (similar to 3 hrs). The electromechanical contrast in unpoled ceramics is attributed to the surface flexoelectric effect (strain gradient induced polarization) while piezoresponse hysteresis and ferroelectric-like behavior are discussed in terms of structural instabilities due to Ti off-center displacements and structural defects in this material. (C) 2011 American Institute of Physics. [doi:10.1063/1.3623767]

Local electromethanical properties of the CaCu 3Ti 4O 12 ceramics

Scanning probe microscopy (SPM) was used to probe piezoelectric vibrations and local conductivity in CaCu 3Ti 4O 12 (CCTO) ceramics at room temperature. Piezoelectric contrast was observed on the polished surfaces of CCTO in both vertical (out-of-plane) and lateral (in-plane) modes and depended on the grain orientation varying in sign and amplitude. The piezoelectric contrast is shown to be controlled by the electrical bias (local poling) and displayed a ferroelectric-like reversible hysteresis accompanied with a change of the phase of piezoelectric signal. Flexoelectric effect (strain-gradient-induced polarization) due to surface relaxation was invoked to explain the observed contrast inside the grains. © 2010 Materials Research Society.

Atomically resolved study of the morphology change of InAs/GaAs quantum dot layers induced by rapid thermal annealing

The optoelectronic properties of InAs/GaAs quantum dots can be tuned by rapid thermal annealing. In this study, the morphology change of InAs/GaAs quantum dots layers induced by rapid thermal annealing was investigated at the atomic-scale by cross-sectional scanning tunneling microscopy. Finite elements calculations that model the outward relaxation of the cleaved surface were used to determine the indium composition profile of the wetting layer and the quantum dots prior and post rapid thermal annealing. The results show that the wetting layer is broadened upon annealing. This broadening could be modeled by assuming a random walk of indium atoms. Furthermore, we show that the stronger strain gradient at the location of the quantum dots enhances the intermixing. Photoluminescence measurements show a blueshift and narrowing of the photoluminescence peak. Temperature dependent photoluminescence measurements show a lower activation energy for the annealed sample. These results are in agreement with the observed change in morphology. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4770371]

RF-sputter fabrication of magnetic garnet thin films and simulation modeling for 1-D magnetic photonic crystal waveguide devices

One dimensional magnetic photonic crystals (1D-MPC) are promising structures for integrated optical isolator applications. Rare earth substituted garnet thin films with proper Faraday rotation are required to fabricate planar 1D-MPCs. In this thesis, flat-top response 1D-MPC was proposed and spectral responses and Faraday rotation were modeled. Bismuth substituted iron garnet films were fabricated by RF magnetron sputtering and structures, compositions, birefringence and magnetooptical properties were studied. Double layer structures for single mode propagation were also fabricated by sputtering for the first time. Multilayer stacks with multiple defects (phase shift) composed of Ce-YIG and GGG quarter-wave plates were simulated by the transfer matrix method. The transmission and Faraday rotation characteristics were theoretically studied. It is found that flat-top response, with 100% transmission and near 45o rotation is achievable by adjusting the inter-defect spacing, for film structures as thin as 30 to 35 μm. This is better than 3-fold reduction in length compared to the best Ce-YIG films for comparable rotations, thus allows a considerable reduction in size in manufactured optical isolators. Transmission bands as wide as 7nm were predicted, which is considerable improvement over 2 defects structure. Effect of repetition number and ratio factor on transmission and Faraday rotation ripple factors for the case of 3 and 4 defects structure has been discussed. Diffraction across the structure corresponds to a longer optical path length. Thus the use of guided optics is required to minimize the insertion losses in integrated devices. This part is discussed in chapter 2 in this thesis. Bismuth substituted iron garnet thin films were prepared by RF magnetron sputtering. We investigated or measured the deposition parameters optimization, crystallinity, surface morphologies, composition, magnetic and magnetooptical properties. A very high crystalline quality garnet film with smooth surface has been heteroepitaxially grown on (111) GGG substrate for films less than 1μm. Dual layer structures with two distinct XRD peaks (within a single sputtered film) start to develop when films exceed this thickness. The development of dual layer structure was explained by compositional gradient across film thickness, rather than strain gradient proposed by other authors. Lower DC self bias or higher substrate temperature is found to help to delay the appearance of the 2nd layer. The deposited films show in-plane magnetization, which is advantageous for waveguide devices application. Propagation losses of fabricated waveguides can be decreased by annealing in an oxygen atmosphere from 25dB/cm to 10dB/cm. The Faraday rotation at λ=1.55μm were also measured for the waveguides. FR is small (10° for a 3mm long waveguide), due to the presence of linear birefringence. This part is covered in chapter 4. We also investigated the elimination of linear birefringence by thickness tuning method for our sputtered films. We examined the compressively and tensilely strained films and analyze the photoelastic response of the sputter deposited garnet films. It has been found that the net birefringence can be eliminated under planar compressive strain conditions by sputtering. Bi-layer GGG on garnet thin film yields a reduced birefringence. Temperature control during the sputter deposition of GGG cover layer is critical and strongly influences the magnetization and birefringence level in the waveguide. High temperature deposition lowers the magnetization and increases the linear birefringence in the garnet films. Double layer single mode structures fabricated by sputtering were also studied. The double layer, which shows an in-plane magnetization, has an increased RMS roughness upon upper layer deposition. The single mode characteristic was confirmed by prism coupler measurement. This part is discussed in chapter 5.