Crack Deflection and Propagation in Layered Silicon Nitride/Boron Nitride Ceramics

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66258/1/j.1151-2916.1998.tb02438.x.pd

Mixed-mode fracture analyses of plastically-deforming adhesive joints

A mode-dependent embedded-process-zone (EPZ) model has been developed and used to simulate the mixed-mode fracture of plastically deforming adhesive joints. Mode-I and mode-II fracture parameters obtained from previous work have been combined with a mixed-mode failure criterion to provide quantitative predictions of the deformation and fracture of mixed-mode geometries. These numerical calculations have been shown to provide excellent quantitative predictions for two geometries that undergo large-scale plastic deformation: asymmetric T-peel specimens and single lap-shear joints. Details of the deformed shapes, loads, displacements and crack propagation have all been captured reasonably well by the calculations.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42756/1/10704_2004_Article_334579.pd

Reply to ‘Comments on “Determining the toughness of plastically deforming joints’”

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43031/1/10855_2004_Article_257152.pd

The Non-Equilibrium Thermodynamics and Kinetics of Focal Adhesion Dynamics

BACKGROUND: We consider a focal adhesion to be made up of molecular complexes, each consisting of a ligand, an integrin molecule, and associated plaque proteins. Free energy changes drive the binding and unbinding of these complexes and thereby controls the focal adhesion's dynamic modes of growth, treadmilling and resorption. PRINCIPAL FINDINGS: We have identified a competition among four thermodynamic driving forces for focal adhesion dynamics: (i) the work done during the addition of a single molecular complex of a certain size, (ii) the chemical free energy change associated with the addition of a molecular complex, (iii) the elastic free energy change associated with deformation of focal adhesions and the cell membrane, and (iv) the work done on a molecular conformational change. We have developed a theoretical treatment of focal adhesion dynamics as a nonlinear rate process governed by a classical kinetic model. We also express the rates as being driven by out-of-equilibrium thermodynamic driving forces, and modulated by kinetics. The mechanisms governed by the above four effects allow focal adhesions to exhibit a rich variety of behavior without the need to introduce special constitutive assumptions for their response. For the reaction-limited case growth, treadmilling and resorption are all predicted by a very simple chemo-mechanical model. Treadmilling requires symmetry breaking between the ends of the focal adhesion, and is achieved by driving force (i) above. In contrast, depending on its numerical value (ii) causes symmetric growth, resorption or is neutral, (iii) causes symmetric resorption, and (iv) causes symmetric growth. These findings hold for a range of conditions: temporally-constant force or stress, and for spatially-uniform and non-uniform stress distribution over the FA. The symmetric growth mode dominates for temporally-constant stress, with a reduced treadmilling regime. SIGNIFICANCE: In addition to explaining focal adhesion dynamics, this treatment can be coupled with models of cytoskeleton dynamics and contribute to the understanding of cell motility

Screening of charged singularities of random fields

Many types of point singularity have a topological index, or 'charge', associated with them. For example the phase of a complex field depending on two variables can either increase or decrease on making a clockwise circuit around a simple zero, enabling the zeros to be assigned charges of plus or minus one. In random fields we can define a correlation function for the charge-weighted density of singularities. In many types of random fields, this correlation function satisfies an identity which shows that the singularities 'screen' each other perfectly: a positive singularity is surrounded by an excess of concentration of negatives which exactly cancel its charge, and vice-versa. This paper gives a simple and widely applicable derivation of this result. A counterexample where screening is incomplete is also exhibited.Comment: 12 pages, no figures. Minor revision of manuscript submitted to J. Phys. A, August 200

Universal Equilibrium Currents in the Quantum Hall Fluid

The equilibrium current distribution in a quantum Hall fluid that is subjected to a slowly varying confining potential is shown to generally consist of strips or channels of current, which alternate in direction, and which have universal integrated strengths. A measurement of these currents would yield direct independent measurements of the proper quasiparticle and quasihole energies in the fractional quantum Hall states.Comment: 4 pages, Revte

Transverse force on a quantized vortex in a superconductor

The total transverse force acting on a quantized vortex in a type-II superconductor determines the Hall response in the mixed state, yet a consensus as to its correct form is still lacking. In this paper we present an essentially exact expression for this force, valid in the superclean limit, which was obtained by generalizing the recent work by Thouless, Ao, and Niu [D. J. Thouless, P. Ao, and Q. Niu, Phys. Rev. Lett. 76, 3758 (1996)] on the Magnus force in a neutral superfluid. We find the transverse force per unit length to be $f = \rho K \times V$, where $\rho = \rho_{n} + \rho_{s}$ is the sum of the mass densities of the normal and superconducting components, $K$ is a vector parallel to the line vortex with a magnitude equal to the quantized circulation, and $V$ is the vortex velocity.Comment: 4 pages, Revtex, 1 figur

Collective excitation spectrum of a disordered Hubbard model

We study the collective excitation spectrum of a d=3 site-disordered Anderson-Hubbard model at half-filling, via a random-phase approximation (RPA) about broken-symmetry, inhomogeneous unrestricted Hartree-Fock (UHF) ground states. We focus in particular on the density and character of low-frequency collective excitations in the transverse spin channel. In the absence of disorder, these are found to be spin-wave-like for all but very weak interaction strengths, extending down to zero frequency and separated from a Stoner-like band, to which there is a gap. With disorder present, a prominent spin-wave-like band is found to persist over a wide region of the disorder-interaction phase plane in which the mean-field ground state is a disordered antiferromagnet, despite the closure of the UHF single-particle gap. Site resolution of the RPA excitations leads to a microscopic rationalization of the evolution of the spectrum with disorder and interaction strength, and enables the observed localization properties to be interpreted in terms of the fraction of strong local moments and their site-differential distribution.Comment: 25 pages (revtex), 9 postscript figure

Development of a process zone in rubber-modified epoxy polymers

The effects of a process zone on toughness and on R-curve behavior were investigated for a model, rubber-modified epoxy polymer. The system studied was one in which the bridging mechanism of toughening does not operate. The characteristic features of R-curve behavior, a rise in toughness with crack extension until an approximate steady-state is reached, were observed using double-cantilever-beam tests. The evolution of the process zone was studied using transmission-optical microscopy. As the crack grew, the process zone appeared to fan out until it reached a steady-state thickness; it then remained a uniform size upon further crack advance. The features of the experimental R-curves were shown to be directly correlated to the evolution of the process zone. Furthermore, the effect of the portion of the process zone in the crack wake was examined by a series of experiments in which the wake was partially removed, and the R-curve re-established by subsequent loading. These experiments demonstrated that removal of the crack wake caused the crack-growth resistance to drop. The toughness then built back up to the steady-state value as the crack wake re-developed. This unambiguously demonstrated a contribution to toughening from the crack wake despite the absence of any observable bridging mechanism. These results support the accepted notion that an extrinsic toughening mechanism is responsible for the increased toughness observed upon adding rubber particles to an epoxy matrixPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42788/1/10704_2004_Article_186417.pd

Determining Mode-I Cohesive Parameters for Nugget Fracture in Ultrasonic Spot Welds

Ultrasonic spot welds have been used as a model system to investigate how to determine the mode-I cohesive parameters associated with interfacial fracture of a spot weld. Numerical analyses indicated that, while multiple combinations of the two cohesive parameters (characteristic strength, , and toughness, Γ I ) could result in virtually indistinguishable behaviors for individual geometries, only a single pair of parameters can provide a unique set of behaviors for different test geometries. This provides the basis for determining the cohesive parameters by comparing numerical predictions to experimental observations. In particular, a direct uniaxial tensile test was found to be particularly useful for measuring the characteristic strength of an ultrasonic weld. With the characteristic strength known, the toughness of the weld was determined by fitting numerical predictions to experimental observations of the load–displacement curves obtained from T-peel specimens bonded with the ultrasonic weld. These two parameters were then used without modification to predict the performance of welded U-peel specimens. The numerical predictions for this third configuration were in excellent agreement with the experimental results, verifying that it may be possible to use cohesive-zone parameters to predict the behavior of different geometries of spot welds formed under nominally similar conditions.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42765/1/10704_2005_Article_6036.pd