Hot cracks in rubber: origin of the giant toughness of rubberlike materials

We study crack propagation in rubberlike materials and show that the nonuniform temperature distribution which occurs in the vicinity of the crack tip has a profound influence on the crack propagation, and may strongly enhance the crack propagation energy G(v) for high crack velocities v. At very low crack-tip velocities, the heat produced at the crack tip can diffuse away, but already at moderate crack-tip velocities a very large temperature increase occurs close to the crack tip resulting in a "hot-crack" propagation regime. The transition between the low-speed regime and the hot-crack regime is very abrupt and may result in unstable crack motion, e.g., stick-slip motion or catastrophic failure.     

Crack propagation in amorphous polymers and their composites

The fracture energy of a polymer depends strongly on the viscoelastic responses of the material, and therefore is a function of temperature and crack velocity. The toughness of a composite is determined by the way in which the reinforcing filler modifies the energy dissipating mechanisms of the polymeric matrix.

The fracture toughness of a variety of polymeric glasses and their composites with glass beads, glass fibers, and rubber particles was measured. The velocity of rapidly moving cracks and the crack propagation rates under controlled loading conditions were also measured.

It was found that the crack propagation velocities in unfilled and glass bead filled materials were controlled by the longitudinal stress waves in the matrix and that the only effects of the glass beads were to blunt the crack tip and limit the viscous deformation. The effect on fracture toughness was relatively small and either positive or negative, depending on which of the above two factors dominated.

The presence of rubber particles as a second phase lowered terminal crack propagation velocities and greatly increased the fracture toughness, indicating a crack retarding effect of the rubber particles. This is related to the induction of crazes in the matrix by the rubber phase.

Glass fibers had a tendency to bridge the tip of a propagating crack, thereby greatly increasing the fracture toughness. In this case the work of fracture comes from a combination of the elastic strain energy stored in the fibers, the energy dissipated in debonding the fibers from the matrix, and the fracture energy of the matrix itself.     

A convective instability mechanism for quasistatic crack branching in a hydrogel

Experiments on quasistatic crack propagation in gelatin hydrogels reveal a new branching instability triggered by wetting the tip opening with a drop of aqueous solvent less viscous than the bulk one. We show that the emergence of unstable branches results from a balance between the rate of secondary crack growth and the rate of advection away from a non-linear elastic region of size G/E , where G is the fracture energy and E the small strain Young modulus. We build a minimal, predictive model that combines mechanical characteristics of this mesoscopic region and physical features of the process zone. It accounts for the details of the stability diagram and lends support to the idea that non-linear elasticity plays a critical role in crack front instabilities.     

The emission spectrum of HgI

The ultraviolet emission systems of HgI—C → X, D → X, F₃ → X, G → X, and H → X—are photographed and analyzed using tesla-discharge sources containing isotopically pure ²⁰⁰Hg. The previous assignment for F₃ → X is revised, the main change being a decrease by 3 units in the v″ numbering. Results for the other systems corroborate the existing interpretations, except that for C → X there are prominent intensity gaps in the unresolved rotational structure of the bands, not reported previously for “natural” HgI spectra. These gaps are attributed to perturbations of the C state by high levels (v ≈ 90) of the B state. The data for these systems are combined with existing B → X data for ²⁰⁰Hg¹²⁷I and ²⁰⁰Hg¹²⁹I and fitted simultaneously to yield optimal vibrational parameters for all states. In this analysis the X state is fitted to a mixed representation—a polynomial in ( ) for v ≤ 20 and a near-dissociation expansion for v ≥ 20, with G_v and its first derivative constrained to be continuous at v = 20. The revised estimate of _e for X is 2800 ± 40 cm⁻¹. The recommended vibrational parameters (cm⁻¹) for v ≤ 20 are ω_e = 125.41, ω_ex_e = 1.009, ω_ey_e = −0.0159.     

The bubble cloud as an N-degree of freedom harmonic oscillator

The dynamics of a two-dimensional N-bubble static cloud is investigated and shown to be well described by an N-degree of freedom harmonic oscillator model, at least at low enough frequencies. Eigenmodes and eigenfrequencies are calculated and compared with experimental results obtained with an assembly of bubbles caught up under a net in a water tank. Accordance is found to be excellent in the frequency range of validity of the model, the limits of which are discussed. An interpretation of the low-frequency branch of Foldy’s dispersion relation in bubbly liquids is suggested in terms of “bubble waves” in a quasi-incompressible medium.     

Noncommutative Dynamics of Random Operators

We continue our program of unifying general relativity and quantum mechanics in terms of a noncommutative algebra А on a transformation groupoid Γ = E × G where E is the total space of a principal fibre bundle over spacetime, and G a suitable group acting on Γ . We show that every a ∊ А defines a random operator, and we study the dynamics of such operators. In the noncommutative regime, there is no usual time but, on the strength of the Tomita–Takesaki theorem, there exists a one-parameter group of automorphisms of the algebra А which can be used to define a state dependent dynamics; i.e., the pair (А, ϕ), where ϕ is a state on А, is a “dynamic object.” Only if certain additional conditions are satisfied, the Connes–Nikodym–Radon theorem can be applied and the dependence on ϕ disappears. In these cases, the usual unitary quantum mechanical evolution is recovered. We also notice that the same pair (А, ϕ) defines the so-called free probability calculus, as developed by Voiculescu and others, with the state ϕ playing the role of the noncommutative probability measure. This shows that in the noncommutative regime dynamics and probability are unified. This also explains probabilistic properties of the usual quantum mechanics.     

Self-healing slip pulses and the friction of gelatin gels

We present an extensive experimental study and scaling analysis of friction of gelatin gels on glass. At low driving velocities, sliding occurs via propagation of periodic self-healing slip pulses whose velocity is limited by collective diffusion of the gel network. Healing can be attributed to a frictional instability occurring at the slip velocity V = V _c. For V > V _c, sliding is homogeneous and friction is ruled by the shear-thinning rheology of an interfacial layer of thickness of order the (nanometric) mesh size, containing a solution of polymer chain ends hanging from the network. In spite of its high degree of confinement, the rheology of this system does not differ qualitatively from known bulk ones. The observed ageing of the static friction threshold reveals the slow increase of adhesive bonding between chain ends and glass. Such structural ageing is compatible with the existence of a velocity-weakening regime at velocities smaller than V _c, hence with the existence of the healing instability. Received: 7 March 2003 / Accepted: 2 May 2003 / Published online: 11 June 2003 RID="b" ID="b"e-mail: ronsin@gps.jussieu.fr     

Direct observation of standing electron waves in diffusively conducting inas nanowire

We investigate the disturbance of the InAs nanowire resistance by a conductive tip of a scanning probe micro-scope at helium temperature as a function of the tip position in close vicinity to the nanowire. At the tip displacement along the wire the resistance (R _wire ∼ 30 kΩ, what is typical for diffusive regime) demonstrates quasi-periodical oscillations with an amplitude about 3%. The period of the oscillations depends on the number of electrons in the nanowire and is consistent with expected for standing electron waves caused by ballistic electrons in the top subband of the InAs nanowire.     

Temperature dependence of crack propagation in a two-dimensional model quasicrystal

The propagation of cracks in two-dimensional decagonal model quasicrystals is studied under mode I loading by means of molecular dynamics simulations. In particular, we investigate the dependence on temperature, applied load and underlying structure. The samples are endowed with an atomically sharp crack and strained by linear scaling of the displacement field. Three different regimes of propagation and discernible with increasing temperature. For low temperatures the crack velocity increases monotonically with increasing applied load. We observe that the crack follows the path of dislocations nucleated at its tip. For temperatures above 0.3?T _m, where T _m is the melting temperature, the crack does not remain atomically sharp but becomes blunt spontaneously. In the temperature range between 0.7?T _m and 0.8?T _m the quasicrystal fails by nucleation, growth and coalescence of microvoids. This gradual dislocation-free crack extension is caused by plastic deformation which is mediated by localized rearrangements comparable with the so-called shear transformation zones. These are also observed in amorphous solids. Thus, at low temperatures the crack propagates along crystallographic planes just as in periodic crystals, whereas at high temperatures a glass-like behaviour is dominant.     

Fracture and friction: Stick-slip motion

We discuss the stick-slip motion of an elastic block sliding along a rigid substrate. We argue that for a given external shear stress this system shows a discontinuous nonequilibrium transition from a uniform stick state to uniform sliding at some critical stress which is nothing but the Griffith threshold for crack propagation. An inhomogeneous mode of sliding occurs when the driving velocity is prescribed instead of the external stress. A transition to homogeneous sliding occurs at a critical velocity, which is related to the critical stress. We solve the elastic problem for a steady-state motion of a periodic stick-slip pattern and derive equations of motion for the tip and resticking end of the slip pulses. In the slip regions we use the linear friction law and do not assume any intrinsic instabilities even at small sliding velocities. We find that, as in many other pattern forming system, the steady-state analysis itself does not select uniquely all the internal parameters of the pattern, especially the primary wavelength. Using some plausible analogy to first-order phase transitions we discuss a soft selection mechanism. This allows to estimate internal parameters such as crack velocities, primary wavelength and relative fraction of the slip phase as functions of the driving velocity. The relevance of our results to recent experiments is discussed.     

Rashba splitting of kinetically bound states in gated HgCdTe surface quantum wells

The Rashba spin–orbit splitting of 2D electron gas in gated HgCdTe surface quantum wells on n-HgCdTe is studied experimentally (by the magneto-capacitance spectroscopy of Landau level method) and theoretically with emphasis on the peculiarities of spectrum at surface densities N_s corresponding to the onset of 2D subbands occupancy, where the regime of kinetic binding is realized. Although the spin–orbit splitting in kinetic confinement regime is small, the “Rashba polarization” Δn/n can achieve 100% because of strong difference in values of cutoff wave vector k_c for different spin-split sub-subbands.     

Why is nacre strong? II. Remaining mechanical weakness for cracks propagating along the sheets

In our previous paper (Eur. Phys. J. E 4, 121 (2001)) we proposed a coarse-grained elastic energy for nacre, or stratified structure of hard and soft layers found in certain seashells . We then analyzed a crack running perpendicular to the layers and suggested one possible reason for the enhanced toughness of this substance. In the present paper, we consider a crack running parallel to the layers. We propose a new term added to the previous elastic energy, which is associated with the bending of layers. We show that there are two regimes for the parallel-fracture solution of this elastic energy; near the fracture tip the deformation field is governed by a parabolic differential equation while the field away from the tip follows the usual elliptic equation. Analytical results show that the fracture tip is lenticular, as suggested in a paper on a smectic liquid crystal (P.G. de Gennes, Europhys. Lett. 13, 709 (1990)). On the contrary, away from the tip, the stress and deformation distribution recover the usual singular behaviors ( and 1/, respectively, where x is the distance from the tip). This indicates there is no enhancement in toughness in the case of parallel fracture. Received 16 November 2001     

A Numerical Assessment of the Propagation and Coalescence of Delamination Cracks in Thermal Barrier Systems

Interactions have been calculated between cracks induced in thermal barrier coatings (TBCs) upon thermal cycling, motivated by displacement instability in the thermally grown oxide (TGO). The results indicate that the energy release rate G cycles as the temperature changes, with the largest value arising at ambient temperature. It increases on a cycle-by-cycle basis. The trends in G predict two responses. (i) Isolated cracks should be confined to the vicinity of the imperfection, as observed experimentally. (ii) Cracks that converge from neighboring imperfections exhibit a minimum G prior to convergence, providing the possibility that they might coalesce. Equating this minimum to the toughness of the TBC provides a criterion for coalescence and failure. Imposing this criterion allows the change in crack length upon cycling and the number of cycles to failure to be ascertained. The results are consistent with experimental measurements obtained from furnace cycle tests.     

The many levels pairing Hamiltonian for two pairs

We address the problem of two pairs of fermions living on an arbitrary number of single-particle levels of a potential well (mean field) and interacting through a pairing force in the framework of the Richardson equations. The associated solutions are classified in terms of a number v_l, which reduces to the seniority v in the limit of a large pairing strength G and yields the number of pairs not developing a collective behaviour, their energy remaining finite in the G limit. We express analytically, through the moments of the single-particle levels distribution, the collective mode energy and the two critical values G_cr⁺ and G_cr^- of the coupling which can exist on a single-particle level with no pair degeneracy. Notably G_cr⁺ and G_cr^-, when the number of single particle levels goes to infinity, merge into the critical coupling of a one-pair system G_cr (when it exists), which is not envisioned by the Richardson theory. In correspondence of G_cr, the system undergoes a transition from a mean-field- to a pairing-dominated regime. We finally explore the behaviour of the excitation energies, wave functions and pair transfer amplitudes versus G finding out that the former, for G > G_cr^-, come close to the BCS predictions, whereas the latter display a divergence at G_cr, signaling the onset of a long-range off-diagonal order in the system.     

Saturation of nuclear matter and realistic interactions

In this communication we study symmetric nuclear matter for the Brueckner-Hartree-Fock approach, using two realistic nucleon-nucleon interactions (CD-Bonn and Bonn C). The single-particle energy is calculated self-consistently from the real on-shell self-energy. The relation between different expressions for the pressure is studied in cold nuclear matter. For best calculations the self-energy is calculated with the inclusion of hole-hole (hh) propagation. The effects of hh contributions and a self-consistent treatment within the framework of the Green function approach are investigated. Using two different methods, namely, G-matrix and bare potential, the hh term is calculated. We found that using G-matrix brought about non-negligible contribution to the self-energy, but this difference is very small and can be ignored if compared with the large contribution coming from particle-particle term. The contribution of the hh term leads to a repulsive contribution to the Fermi energy which increases with density. For extended Brueckner-Hartree-Fock approach the Fermi energy at the saturation point fulfills the Hugenholtz-Van Hove relation.     

Aging and non-linear glassy dynamics in a mean field model

The mean field approach of glassy dynamics successfully describes systems which are out-of-equilibrium in their low temperature phase. In some cases an aging behaviour is found, with no stationary regime ever reached. In the presence of dissipative forces however, the dynamics is indeed stationary, but still out-of-equilibrium, as inferred by a significant violation of the fluctuation dissipation theorem. The mean field dynamics of a particle in a random but short-range correlated environment, offers the opportunity of observing both the aging and driven stationary regimes. Using a geometrical approach previously introduced by the author, we study here the relation between these two situations, in the pure relaxational limit, i.e. the zero temperature case. In the stationary regime, the velocity (v)-force (F) characteristics is a power law v∼F ⁴, while the characteristic times scale like powers of v, in agreement with an early proposal by Horner. The cross-over between the aging, linear-response regime and the non-linear stationary regime is smooth, and we propose a parametrization of the correlation functions valid in both cases, by means of an “effective time”. We conclude that aging and non-linear response are dual manifestations of a single out-of-equilibrium state, which might be a generic situation. Received 7 May 2000 and Received in final form 22 August 2000     

Orientational dynamics of superfluid He: A “two-fluid” model. II. Orbital dynamics

We present a phenomenological theory of the homogeneous orbital dynamics of the class of “separable” anisotropic superfluid phases which includes the ABM state generally identified with ³He-A. The theory is developed by analogy with the spin dynamics described in the first paper of this series; the basic variables are the orientation of the Cooper-pair wavefunction (in the ABM phase, the l-vector) and a quantity K which we visualize as the “pseudo-angular momentum” of the Cooper pairs but which must be distinguished, in general, from the total orbital angular momentum of the system. In the ABM case l is the analog of d in the spin dynamics and K of the “superfluid spin” S_p. Important points of difference from the spin case which are taken into account include the fact that a rotation of l without a simultaneous rotation of the normal-component distribution strongly increases the energy of the system (“normal locking”), and that the equilibrium value of K is zero even for finite total angular momentum. The theory does not claim to handle correctly effects associated with any intrinsic angular momentum arising from particle-hole asymmetry, but it is shown that the magnitude of this quantity can be estimated directly from experimental data and is extremely small; also, the Landau damping does not emerge automatically from the theory, but can be put in in an ad hoc way. With these provisos the theory should be valid for all frequencies irrespective of the value of ωτ. (Δ = gap parameter, τ = quasi-particle relaxation time.) It disagrees with all existing phenomenological theories of comparable generality, although the disagreement with that of Volovik and Mineev is confined to the “gapless” region very close to T_c.The phenomenological equations of motion, which are similar in general form to those of the spin dynamics with damping, involve an “orbital susceptibility of the Cooper pairs” χ_orb(T). We give a possible microscopic definition of the variable K and use it to calculate χ_orb(T) for a general phase of the “separable” type. The theory is checked by inserting the resulting formula in the phenomenological equations for ωτ 1 and comparing with the results of a fully microscopic calculation based on the collisionless kinetic equation; precise agreement is obtained for both the ABM and the (real) polar phase, showing that the complex nature of the ABM phase and the associated “pair angular momentum” is largely irrelevant to its orbital dynamics. We note also that the phenomenological theory gives a good qualitative picture even when ω Δ(T), e.g., for the flapping mode near T_c. Our theory permits a simple and unified calculation of (1) the Cross-Anderson viscous torque in the overdamped regime, (2) the flapping-mode frequency near zero temperature, (3) orbital effects on the NMR, both at low temperatures and near T_c, (4) the orbit wave spectrum at zero temperature (this requires a generalization to inhomogeneous situations which is possible at T = 0 but probably not elsewhere). We also discuss the possibility of experiments of the Einstein-de Haas type. Generally speaking, our results for any one particular application can be also obtained from some alternative theory, but in the case of orbital and spin relaxation very close to T_c (within the “gapless” region) our predictions, while somewhat tentative and qualitative, appear to disagree with those of all existing theories. We discuss briefly how our approach could be extended to apply to more general phases.     

Kinetics of flow stress in crystals with high intrinsic lattice friction

A relatively simple theoretical model, based on the concept of kink-pair mode of escape of screw dislocations trapped in Peierls valleys, has been developed to account for the observed temperature dependence of the critical resolved shear stress (CRSS), τ, and of the associated activation volume, v, in crystals with high intrinsic lattice friction at rather low temperatures. In this model, the CRSS varies with temperature T as τ^1/2?=?A–BT, and the associated activation volume v depends on temperature T as v ^?1?=?C–DT, where A, B, C and D are positive constants. Moreover, the activation volume v is found to be a function of τ such that vτ^1/2 is constant for a given slip system. Data analysis of the temperature dependence of the CRSS of W, α-Fe, Cr and V metal crystals shows excellent agreement between theory and experiment in both regime III (low temperature or high stress) and regime II (intermediate temperature/stress). However, the predicted temperature and stress dependence of the activation volume are borne out by experiment in regime II, but lack quantitative agreement in regime III. On the other hand, the CRSS of CdTe crystals at low temperatures (T?≤?200?K) is determined by the Peierls mechanism, whereas the weak temperature dependence of the CRSS above 200?K is probably governed by the breakaway of edge dislocation segments from arrays of pinning points due to localized defects in the crystal.     

The second torsional state of acetic acid

We have fitted to within experimental accuracy a data set for acetic acid CH₃COOH consisting of 2103 v_t=0, 1111 v_t=1 and 634 v_t=2 microwave lines, using the so-called “rho axis method” and a model extended to include perturbation terms through eighth order. The previously published 2109 v_t=0 and 409 v_t=1 microwave lines have been extended by new measurements from Kharkov. The final fit requires only 62 parameters to achieve a unitless weighted standard deviation for the whole fit of 0.85 for a total of 3848 lines and includes transitions with J27 (15) and |K_a|13 (8) for the v_t=2 A (E)-species, respectively. This result represents a significant improvement over our previous fit which was dominated by v_t=0 transitions. A calculation of the linestrengths of torsion–rotation transitions is also provided.