Transient analyses of dislocation emission in the three modes of fracture

Exact transient solutions for a micromechanical process of dislocation emission from stationary cracks in each of the three Modes of fracture are assembled. Each process involves a possible slip mechanism for the Mode, and the loading in each case is due to plane wave diffraction.

The solutions are examined in view of an emissions criterion similar to one developed for quasi-static studies on the basis of standard dislocation force concepts. Among the results are formulas for three parameters: emission time, distance traveled by an emitted dislocation prior to arrest, and the time of arrest. The formulas involve material properties such as yield stress and surface energy, as well as a dimensionless variable parameter governing the size of a zone of dislocation attraction at the crack edge.

The parameters themselves exhibit dislocation speed-dependent dynamic effects, but, on the other hand, the Mode I and Mode III cases achieve minimum emission times for the zero-speed limit. The effect of crack blunting serves to raise the emission time required. Order-of-magnitude estimates of the parameters indicate that they are definitely on a micromechanical scale, suggesting that emission may depend only on the region very near the crack edge.  

Two basic wave propagation problems for the non-uniform motion of displacement discontinuities across a bimaterial interface

The splitting of laminated materials is often achieved by, in effect, moving more rigid solids through the material or by causing a shear tearing characterized by the relative slip of adjacent material points. Both processes may take place across the bimaterial interfaces of the laminate. Moreover, both processes involve the motion of displacement discontinuities. This article examines basic wave propagation problems for the non-uniform motion of two arbitrary displacement discontinuities in perfectly-bonded half-planes along paths normal to the interface. The discontinuities impose relative displacements which are, respectively, normal to and along the path. Complete solutions are derived in forms which allow identification of each component of the reflection and transmission-complicated wave pattern. The dependence of these components on specific aspects of the discontinuity behavior can be noted. Finally, two physical examples, the motions of a rigid wedge and an edge dislocation across the interface are studied. It is found that the singularity order and direction of characteristic stresses can be affected by crossing the interface.  

Dynamic analysis of dislocation generation due to sudden indentation

The dynamic analysis of an edge dislocation generated under the edge of a rigid smooth indentor applied suddenly to an elastic half-plane is presented. The physical requirement that the indentor edge cannot induce a corner yields an equation relating the dislocation, indentor and half-plane parameters. Study of the equation allows several general observations on the dislocation motion. In particular, a given dislocation moving at a given speed can move along either of two paths below a certain indentation level.  

Dynamic crack extension along the interface of materials that differ in their thermal properties: with and without thermal relaxation

Summary Moving surface stresses cause crack extension along the interface of perfectly bonded thermoelastic materials at a constant sub-critical speed. The materials differ only in their thermal properties, and are governed by coupled thermoelastic equations that admit as special cases Fourier heat conduction as well as thermal relaxation with one or two relaxation times. A dynamic steady state of plane strain is assumed. The exact transform solution for a propagating displacement and temperature discontinuity is used to find solutions to the interface crack valid away from the crack edge for low extension speeds and solutions valid at the crack edge for high speeds. Results show that Fourier heat conduction dominates the former case, but solution behavior in the latter is dependent upon the particular thermal model. Thermal mismatch is seen to by itself cause a solution behavior similar to that for bonded dissimilar isothermal elastic solids. In particular, the two-relaxation time solution exhibits both oscillatory and non-oscillatory terms, and the interface temperature at the crack edge is finite.  

Debonding of a thermoelastic material from a rigid substrate at any constant speed: thermal relaxation effects

Summary A linear isotropic thermoelastic half-space is debonded from a rigid insulated substrate at constant speed by moving shear and normal line loads. A dynamic steady state is examined, and an exact transform solution for the related problem of an insulated half-space subjected to a moving zone of specified surface displacements is obtained. Asymptotic forms are extracted that are valid near the zone edge and for high speeds, and which highlight thermal relaxation effects. They are used to derive analytical results for debonding at any constant speed. In particular, field variables on the debonded surface and the still-bonded interface are given for the sub-Rayleigh, super-Rayleigh/subsonic, lower and upper transonic, and supersonic speed ranges. The degenerate cases that arise at the three body wave speeds and at twice the rotational wave speed are also given. Calculations for the dynamic fracture energy rate and debonding zone temperature change at sub-Rayleigh speeds in 4340 steel indicate that thermal relaxation enhances energy rate, but mutes thermal response. The latter effect, however, itself decreases as the Rayleigh speed is approached.  

Thermal relaxation effects in rapid sliding contact with friction

Summary. A rigid die slides at constant sub-critical speed on a homogeneous, isotropic linear coupled thermoelastic half-space. Friction exists, and a dynamic steady state of plane strain is considered. An exact integral transform solution for the related problem of moving surface traction is obtained, and asymptotic expressions valid when thermal relaxation is prominent are extracted.These are used to derive an analytic solution for the sliding problem, and formulas for contact zone size and location, and unilateral constraints imposed by non-tensile contact and non-positive frictional work rate. Expressions for three body wave speeds and a Rayleigh wave speed show, save for the rotational wave case, clear dependence on thermoelastic coupling and thermal relaxation.Calculations for 4340 steel show that the problem eigenvalue is similar to its isothermal counterpart for high sliding speeds, but that the average contact zone temperature increase is less pronounced than when classical Fourier heat conduction effects dominate. Calculations for a hypothetical material similar to steel show that increasing the thermal relaxation time can in effect suppress both the Rayleigh wave and second sound body wave.  

An automated noncontact deposition interface for liquid chromatography matrix-assisted laser desorption/ionization mass spectrometry

A new multichannel deposition system was developed for off-line liquid chromatography/matrix-assisted laser desorption/ionization mass spectrometry (LC/MALDI-MS). This system employs a pulsed electric field to transfer the eluents from multiple parallel columns directly onto MALDI targets without the column outlets touching the target surface. The deposition device performs well with a wide variety of solvents that have different viscosities, vapor pressures, polarities, and ionic strengths. Surface-modified targets were used to facilitate concentration and precise positioning of samples, allowing for efficient automation of high-throughput MALDI analysis. The operational properties of this system allow the user to prepare samples using MALDI matrixes whose properties range from hydrophilic to hydrophobic. The latter, exemplified by alpha-cyano-4-hydroxycinnamic acid, were typically processed with a multistep deposition method consisting of precoating of individual spots on the target plate, sample deposition, and sample recrystallization steps. Using this method, 50 amol of angiotensin II was detected reproducibly with high signal-to-noise ratio after LC separation. Experimental results show that there is no significant decrease in chromatographic resolution using this device. To assess the behavior of the apparatus for complex mixtures, 5 microg of a tryptic digest of the cytosolic proteins of yeast was analyzed by LC/MALDI-MS and more than 13,500 unique analytes were detected in a single LC/MS analysis.  

Thermal and slip mechanism effects in rapid indentation by a flat punch

Summary The rapid indentation of a fully-coupled thermoelastic body by a flat, smooth rigid punch is studied in a 2D dynamic analysis. A semi-infinite punch width is assumed to be a valid short-time model, and a zone of slip mechanisms is assumed to form under the punch edge, and to relax the stresses there. The mathematical problem is reduced by superposition and transform methods to a Wiener-Hopf equation which, despite the dependence of poles and branch points on the time transform parameter, can be solved exactly. Imposition of the stress relaxation property of the zone then removes the singularity in punch edge stresses, thereby giving a relation for the contact region temperature change. Because a thermoelastic characteristic length of 0(10^–4)m is the scale factor, this transform can be inverted for so-called long times without invalidating the short-time nature of the model. The inversion shows that, despite the absence of actual plasticity and contact friction, nominal but not negligible temperature increases can occur in the contact region.  

Transient thermal response near dynamically-loaded cracks during dislocation generation

Summary As a step in considering thermal effects prior to dynamic fracture or the development of fully-plastic crack edge zones, a transient 2-D study of edge dislocation generation near cracks in a fully-coupled thermoelastic solid is considered. Dynamic loading is provided either by SV-wave diffraction or tension, and no heat sources are imposed upon the solid. Despite the existence of characteristic lengths in the governing equations, exact solutions to the required mixed boundary/initial value problems are obtained in the multiple transform space, and time transforms extracted by an inversion process similar to the used in classical wave propagation. From them, the temperature changes at the dislocation edges for short times after generation are developed. These show that dislocation motion and dislocation-crack interaction produce constant temperature changes that are small. However, the results for mirror pairs separating at low speeds suggest that, as dislocation arrays form in the process of plastic zone development near the crack edge, the temperature increases could well become important.  

Rapid quasi-brittle tearing of a thermoelastic strip

Summary The displacement-controlled rapid tearing of a thermoelastic strip is modeled as steady-state propagation of a quasi-brittle crack. The strip satisfies the fully-coupled equations of thermoelasticity, and the small-scale plastic effects are represented by a Dugdale inelastic zone which also serves as a heat flux source. An asymptotic analysis gives expressions for the zone length, COD and dynamic fracture toughness. These expressions show, upon comparison with non-thermal results, the importance of fully-coupled thermoelastic effects, and that all the problem characteristic lengths, which range over several orders of magnitude, are prominent features. Zone heat flux values, based on experimental results for near-crack temperature gradients, are then used for calculation purposes. The calculations show that, independent of a particular fracture criterion, thermal effects noticeably increase inelastic zone size and dynamic fracture toughness.