Alan T. Zehnder

On the temperature distribution at the vicinity of dynamically propagating cracks in 4340 steel

Abstract T he heat generated due to plastic deformation at the tip of a dynamically propagating crack in a metal causes a large local temperature increase at the crack tip which is expected to affect the selection of failure modes during dynamic fracture and to thus influence the fracture toughness of the material. The distribution of temperature at the tips of dynamically propagating cracks in two heat treatments of AISI 4340 carbon steel was investigated experimentally using an array of eight high speed indium antimonide, infrared detectors. Experiments were performed on wedge loaded, compact tension specimens with initially blunted cracks, producing crack speeds ranging from 1900 to 730 m/s. The measurements provide the spatial distribution of temperature increase near the crack tip on the specimen surface. Temperature increases were as high as 465° C over ambient and the region of intense heating (greater than 100° C temperature rise) covered approximately one third of the active plastic zone on the specimen surface. The observed temperature increase profiles clearly show the three-dimensional nature of the fracture process near the specimen surface and provide valuable information regarding the dynamic formation of shear lips and their role in the dissipation of energy during dynamic crack growth. Preliminary temperature measurements performed on side-grooved specimens are also reported.

Velocity field for the trishear model

A general method for the derivation of velocity fields consistent with the basic kinematics of the trishear model of fault-propagation folding is given. We show that the fields can be written as explicit functions of position within the deformation zone. To demonstrate the approach, several different linear and non-linear velocity fields are derived and plotted. We show that the trishear zone need not be symmetric and that the trishear model produces 1/r singular strain rates, consistent with results for cracks in elastic–plastic materials. A continuous formulation of heterogeneous trishear is also presented.

Optically pumped parametric amplification for micromechanical oscillators

Micromechanical oscillators in the rf range were fabricated in the form of silicon discs supported by a SiO2 pillar at the disk center. A low-power laser beam, (Plaser∼100 μW), focused at the periphery of the disk, causes a significant change of the effective spring constant producing a frequency shift, Δf(Δf/f∼10−4). The high quality factor, Q, of the disk oscillator (Q∼104) allows us to realize parametric amplification of the disk’s vibrations through a double frequency modulation of the laser power. An amplitude gain of up to 30 was demonstrated, with further increase limited by nonlinear behavior and self-generation. Phase dependence, inherent in degenerate parametric amplification, was also observed. Using this technique, the sensitivity of detection of a small force is greatly enhanced.

Autoparametric optical drive for micromechanical oscillators

Self-generated vibration of a disk-shaped, single-crystal silicon micromechanical oscillator was observed when the power of a continuous wave laser, focused on the periphery of the disk exceeded a threshold of a few hundred μW. With the laser power set to just below the self-generation threshold, the quality factor for driven oscillations increases by an order of magnitude from Q=10 000 to Qenh=110 000. Laser heating-induced thermal stress modulates the effective spring constant via the motion of the disk within the interference pattern of incident and reflected laser beams and provides a mechanism for parametric amplification and self-excitation. Light sources of different wavelengths facilitate both amplification and damping.

A theory for the fracture of thin plates subjected to bending and twisting moments

Stress fields near the tip of a through crack in an elastic plate under bending and twisting moments are reviewed assuming both Kirchhoff and Reissner plate theories. The crack tip displacement and rotation fields based on the Reissner theory are calculated here for the first time. These results are used to calculate the J-integral (energy release rate) for both Kirchhoff and Reissner plate theories. Invoking Simmonds and Duvas [16] result that the value of the J-integral based on either theory is the same for thin plates, a universal relationship between the Kirchhoff theory stress intensity factors and the Reissner theory stress intensity factors is obtained for thin plates. Calculation of Kirchhoff theory stress intensity factors from finite elements based on energy release rate is illustrated. A small scale yielding like model of the crack tip fields is discussed, where the Kirchhoff theory fields are considered to be the far field conditions for the Reissner theory fields. It is proposed that, for thin plates, fracture toughness and crack growth rates be correlated with the Kirchhoff theory stress intensity factors.

Limit cycle oscillations in CW laser-driven NEMS

Limit cycle, or self-oscillations, can occur in a variety of NEMS devices illuminated within an interference field. As the device moves within the field, the quantity of light absorbed and hence the resulting thermal stresses changes, resulting in a feedback loop that can lead to limit cycle oscillations. Examples of devices that exhibit such behavior are discussed as are experimental results demonstrating the onset of limit cycle oscillations as continuous wave (CW) laser power is increased. A model describing the motion and heating of the devices is derived and analyzed. Conditions for the onset of limit cycle oscillations are computed as are conditions for these oscillations to be either hysteretic or nonhysteretic. An example simulation of a particular device is discussed and compared with experimental results.

Frequency entrainment for micromechanical oscillator

We demonstrate synchronization of laser-induced self-sustained vibrations of radio-frequency micromechanical resonators by applying a small pilot signal either as an inertial drive at the natural frequency of the resonator or by modulating the stiffness of the oscillator at double the natural frequency. By sweeping the pilot signal frequency, we demonstrate that the entrainment zone is hysteretic and can be as wide as 4% of the natural frequency of the resonator, 400 times the 1/Q∼10−4 half-width of the resonant peak. Possible applications are discussed based on the wide range of frequency tuning and the power gain provided by the large amplitude of self-oscillations (controlled by a small pilot signal).

Mechanical models of fault propagation folds and comparison to the trishear kinematic model

Abstract Faults propagating through the Earth generate a wave of deformation ahead of their tip lines. We have modeled this process to understand the relationship between fold geometry and fault propagation. Using finite element modeling (FEM), we investigate the response of incompressible frictionless and frictional materials, and a compressible frictional material with associated flow, to vertical and dipping faults whose tip lines propagate at rates 3–3.5 times their slip rates. The fold geometries, finite strain, and velocity fields in models with incompressible materials are very similar to those produced by the trishear kinematic model, even though the latter uses a purely ad hoc linear velocity field. Furthermore, when the trishear grid search is applied to the final geometry of the mechanical folds, the best fit kinematic models have approximately the same propagation-to-slip ratio as was used in the FEM experiments. However, when the compressible frictional material is used, the mechanical models exhibit a main triangular shear band in front of the tip line and a conjugate shear band in the fold backlimb, both migrating with the propagating tip line. The conjugate shear band, antithetic to the fault, produces a gentle anticlinal back limb, even though there is not a bend in the fault.

An experimental study of muonic X-ray transitions in mercury isotopes☆

Abstract Muonic X-ray spectra have been measured for 198–202, 204Hg. These data have been interpreted in terms of a two parameter Fermi distribution for the charge density. We have interred the spectroscopic quadrupole moments (Qs) of some of the 2+ nuclear states. For 199Hg we have determined the spectroscopic quadrupole moments of the first two excited states and the B(E2) connecting these states to the ground state. For 201Hg the ground state quadrupole moment has been obtained as well as several other E2 moments but the interpretation of the data has been hampered by a possible incomplete knowledge of the nuclear scheme of this nucleus. The muonic isotope shifts have been measured and interpreted in terms of σRk and are compared to electronic X-ray and optical isotope shift measurements.

Dynamic full field measurements of crack tip temperatures

This paper presents a detailed investigation of the evolution of temperature field at the tip of a stationary crack subjected to dynamic loading in two different types of steels. A high speed two-dimensional infrared camera was used to image the temperature fields at the crack tips. In a high strength maraging steel, the thermograms reveal the development of plastic zone and the process of crack initiation and propagation. In ductile HY100 steel, the thermograms are used to estimate the evolution of J integral and its critical value at crack initiation. The temperature images are also used to investigate the dominance of HRR field around the crack tip.