On modes and criteria of ABS melt failure in extension

Melt failure of a commercial ABS polymer in uniaxial extension over ranges of elongation rate ([(e)\dot] = 0.01 - 1.0 s ^{- 1}\dot \varepsilon = 0.01 - 1.0\,{\rm s}^{ - 1} ) and temperature (140-200 °C) was investigated. Four methods of experimental and numerical calculation for determination of modes and criteria of melt failure in uniaxial extension were investigated: 1) visual observation of necking; 2) visual observation of non-uniform flow during stress relaxation after cessation of steady elongation; 3) calculation of the Considère criterion from the measured elongational stress-strain curve; 4) numerical calculation of inflection point (‘C²/‘)²=0) from the tensile stress-strain curve. In addition, under higher Deborah number conditions the critical Hencky strains at Considère criterion were calculated using PSM model parameters (! and #) and were compared with those obtained from the measured elongational stress-strain curve. The relationship between these failure modes is discussed in terms of rheological properties of the polymer, putting emphasis on the relationship with the thermoforming process. The Considère criterion appears to be the most effective indicator of the non-uniform deformation of ABS melt in uniaxial extension under conditions where cohesive fracture does not occur. The rheological properties such as elongational viscosity, strain hardening and/or strain softening, and their temperature dependence play an important role in determining the growth and transition of melt failure of ABS polymer in uniaxial extension.     

On Cavitation, Configurational Forces and Implications for Fracture in a Nonlinearly Elastic Material

Experiments on polymers indicate that large tensile stress can induce cavitation, that is, the appearance of voids that were not previously evident in the material. This phenomenon can be viewed as either the growth of pre-existing infinitesimal holes in the material or, alternatively, as the spontaneous creation of new holes in an initially perfect body. In this paper our approach is to adopt both views concurrently within the framework of the variational theory of nonlinear elasticity. We model an elastomer on a macroscale as a void-free material and, on a microscale, as a material containing certain defects that are the only points at which hole formation can occur. Mathematically, this is accomplished by the use of deformations whose point singularities are constrained. One consequence of this viewpoint is that cavitation may then take place at a point that is not energetically optimal. We show that this disparity will generate configurational forces, a type of force identified previously in dislocations in crystals, in phase transitions in solids, in solidification, and in fracture mechanics. As an application of this approach we study the energetically optimal point for a solitary hole to form in a homogeneous and isotropic elastic ball subject to radial boundary displacements. We show, in particular, that the center of the ball is the unique optimal point. Finally, we speculate that the configurational force generated by cavitation at a non-optimal material point may be sufficient to result in the onset of fracture. The analysis utilizes the energy-momentum tensor, the asymptotics of an equilibrium solution with an isolated singularity, and the linear theory of elasticity at the stressed configuration that the body occupies immediately prior to cavitation. This revised version was published online in June 2006 with corrections to the Cover Date.     

Preparation of Bottlebrush Polymers via a One‐Pot Ring‐Opening Polymerization (ROP) and Ring‐Opening Metathesis Polymerization (ROMP) Grafting‐Through Strategy

Bottlebrush polymers are synthesized using a tandem ring‐opening polymerization (ROP) and ring‐opening metathesis polymerization (ROMP) strategy. For the first time, ROP and ROMP are conducted sequentially in the same pot to yield well‐defined bottlebrush polymers with molecular weights in excess of 10⁶ Da. The first step of this process involves the synthesis of a polylactide macromonomer (MM) via ROP of d ,l ‐lactide initiated by an alcohol‐functionalized norbornene. ROMP grafting‐through is then carried out in the same pot to produce the bottlebrush polymer. The applicability of this methodology is evaluated for different MM molecular weights and bottlebrush backbone degrees of polymerization. Size‐exclusion chromatographic and ¹H NMR spectroscopic analyses confirm excellent control over both polymerization steps. In addition, bottlebrush polymers are imaged using atomic force microscopy and stain‐free transmission electron microscopy on graphene oxide.

     

An extension of Reiner's “Deborah Number” concept to a Wide field of rheological investigations

Summary Reiner defined a numeric, which he called theDeborah Number to represent the ratio of a relaxation time to a natural (observation) time. This implies aMaxwell model but is readily extended to complete relaxation spectra. Similar Numbers are proposed for retardation times and also for some conditions of coagulation thixotropy and for data from certain psychophysical experiments.     

The evolution laws of dilatational spherical and cylindrical weak nonlinear shock waves in elastic non-conductors

The theory of singular surfaces yields a set of coupled evolution equations for the shock amplitude and the amplitudes of the higher order discontinuities which accompany the shock. To solve these equations, we use perturbation methods with a perturbation parameter characterising the initial shock amplitude. It is shown that for decaying shock waves, if the accompanying second order discontinuity is of order one, the straightforward perturbation procedure yields uniformly valid solutions, but if the accompanying second order discontinuity is of order , the method of multiple scales is needed in order to render the perturbation solutions uniformly valid with respect to the distance of travel. We also construct shock wave solutions from modulated simple wave solutions which are obtained with the aid ofHunter & Keller's Weakly Nonlinear Geometrical Optics method. The two approaches give exactly the same results within their common range of validity. The explicit evolution laws thus obtained enable us to see clearly how weak nonlinear curved shock waves are attenuated because of the effects of geometry and material nonlinearity, and on what length scale these effects are most pronounced. Communicated by C. C. Wang     

Micro-interferometry for measurement of thermal displacements at fiber/matrix interfaces

A micro-interferometric technique for measuring out-of-plane thermal displacements on a scale commensurate with the dimensions of the fiber/matrix unit cell is described. A scanning micro-interferometer is used to image surface displacements of samples containing a single-pitch-based carbon fiber embedded in an epoxy matrix. The interferometer design gives the necessary resolution to detect small changes in thermal displacements in the fiber/matrix interface region. The samples were heated electrically through the fiber to create radially symmetric temperature and displacement fields. Repeatable displacement measurements were obtained on a radial line across the interface region with an accuracy of ±25 Å. A sharp expansion of the matrix surrounding the fiber was observed with each heating. Overall, the experiments demonstrate the utility of micro-interferometry for measuring submicron displacements.     

Energy Minimising Properties of the Radial Cavitation Solution in Incompressible Nonlinear Elasticity

Consider an incompressible, hyperelastic material occupying the unit ball B⊂ℝ ⁿ in its reference state. Suppose that the deformation u:B→ℝ ⁿ is specified on the boundary by

On the Symmetry of Energy-Minimising Deformations in Nonlinear Elasticity II: Compressible Materials

Consider a homogeneous, isotropic, hyperelastic body occupying the region ${A = \{{\bf x}\in\mathbb{R}^{n}\, : \,a <\,|{\bf x} |\,< b \}}$ in its reference state and subject to radially symmetric displacement, or mixed displacement/traction, boundary conditions. In Part I (Sivaloganathan and Spector in Arch Ration Mech Anal, 2009, in press) the authors restricted their attention to incompressible materials. For a large-class of polyconvex constitutive relations that grow sufficiently rapidly at infinity it was shown that to each nonradial isochoric deformation of A there corresponds a radial isochoric deformation that has strictly less elastic energy than the given deformation. In this paper that analysis is further developed and extended to the compressible case. The key ingredient is a new radial-symmetrisation procedure that is appropriate for problems where the symmetrised mapping must be one-to-one in order to prevent interpenetration of matter. For the pure displacement boundary-value problem, the radial symmetrisation of an orientation-preserving diffeomorphism u : A → A* between spherical shells A and A* is the deformation $${\bf u}^{\rm rad}({\bf x})=\frac{r(R)}{R}{\bf x}, \quad R=|{\bf x}|,\qquad\qquad\qquad\qquad(0.1)$$ that maps each sphere ${S_R\subset\,A}$ , of radius R > 0, centred at the origin into another such sphere ${S_r={\bf u}^{\rm rad}(S_R)\subset\,A^*}$ that encloses the same volume as u(S _R ). Since the volumes enclosed by the surfaces u(S _R ) and u ^rad (S _R ) are equal, the classical isoperimetric inequality implies that ${{{\rm Area}( {\bf u}^{\rm rad} (S_R))\leqq {\rm Area}({\bf u} (S_R))}}$ . The equality of the enclosed volumes together with this reduction in surface area is then shown to give rise to a reduction in total energy for many of the constitutive relations used in nonlinear elasticity. These results are also extended to classes of Sobolev deformations and applied to prove that the radially symmetric solutions to these boundary-value problems are local or global energy minimisers in various classes of (possibly nonsymmetric) deformations of a thick spherical shell.     

Evaluating continuous chirality measure as a 3D descriptor in chemoinformatics applied to asymmetric catalysis

Continuous Chirality Measure (CCM) is a computational metric by which to quantify the chirality of a compound. In enantioselective catalysis, prior work has postulated that CCM is correlated to selectivity and can be used to understand which structural features dictate catalyst efficacy. Herein, the investigation of CCM as a metric capable of guiding catalyst optimization is explored. Conformer-dependent CCM is also explored. Finally, CCM is used with Sterimol parameters to significantly improve the performance of Random Forest models.