Influence of the β‐crystalline phase on the mechanical properties of unfilled and calcium carbonate‐filled polypropylene: Ductile cracking and impact behavior

The β‐crystalline form of isotactic poly(propylene) (PP) has been long recognized to have a greater mechanical absorption capacity than the α‐crystalline form. This is of major importance for improving impact properties and crack resistance of injection‐molding parts. Unfilled PP samples together with calcium carbonate‐filled PP samples having various β/α‐phase ratios, with nearly constant morphological parameters, have been investigated from the standpoint of ductile crack propagation and impact behavior. The presence of the β‐crystalline phase turned out to improve both properties. The β spherulites are notably more prone to craze initiation than α spherulites that display a propensity for cracking. Subsequent crack propagation appears to be faster in the latter ones. The plastic zone ahead from the crack tip broadens, and the specific plastic energy increases with increasing β‐phase content. The lower elastic limit of the β phase is likely to promote the early crazing. However, the suspected higher density of tie molecules in β spherulites provides more numerous and stiffer microfibrils. The impact strength of PP is also improved by the presence of β crystals as a result of greater energy‐absorption capabilities. However, filled samples turned out insensitive to the β phase. A discussion is made about the origins of the β‐phase‐induced improvement of the mechanical properties. The possible role of the β → α transition is also explained. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 40: 31–42, 2002     

uv-理论在一类半无限最小化问题的应用

Lemarechal,Oustry和Sagastizabal(2000)提出的uv分解理论为解决非光滑函数的高阶展开提供了一种新的途径，并将此理论应用于研究具有有限个约束的非线性规划的精确罚函数．本文将这一研究推广到具有无限约束的一类半无限规划的问题上，并给出了与这类最小化问题的精确罚函数的U-Lagrange函数有关的某些结果．     

Intensity factors for subinterface cracks in dissimilar anisotropic piezoelectric media

Summary A subinterface crack paralleling an interface between two dissimilar piezoelectric solids is considered. When the distance between the interface and the crack is small compared to all other in-plane lengths, the problem can be analyzed as an asymptotic problem for a semi-infinite crack lying at some distance away from the interface. An integral equation for the asymptotic subinterface crack is derived, and a solution of the integral equation for small-generalized Dundurs parameters is obtained. Relations between the intensity factors for the subinterface crack and interface intensity factors of the corresponding interface crack are obtained for a conducting crack as well as for an insulating one.This work was supported by the Brain Korea 21 Project in 2000.     

Buckling of stepped composite columns

The stability of elastic columns subjected to axial pressure is studied. An elastic multistepped column with rectangular cross sections are considered assuming that at the re-entrant corners of the column stable cracks are located. The influence of a crack on the loss of stability of the column is described by means of local flexibility and the function of compliance coupled with the stress intensity factor, which is known from the linear elastic fracture mechanics. A column with a single step is studied in more detail. The influence of crack location and length on the buckling load is assessed numerically. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 1, pp. 87–100, January–February, 2006.     

Micromechanical consideration of tensile crack behavior based on virtual internal bond in contrast to cohesive stress

A modified version of the virtual internal bond model (VIB) is presented. This involves the introduction of a R-bond restricting the relative rotation freedom of pairwise mass particle. Such a modification allows the VIB model to consider arbitrary values of the Poisson ratio. A linear elastic cohesive law considering both the R-bond and L-bond are assumed. The constitutive relationship is derived using the Cauchy–Born rules. The derived constitutive associates the bond stiffness with the Young’s modulus and Poisson ratio of materials. This gives the bond stiffness in terms of the Young’s modulus and Poisson ratio of materials.The modified VIB model is then used to analyze the tensile crack behavior. In contrast to the cohesive stress method, the deformation-governed concept will be used. The local materials failure is assumed to coincide with the reduction of the bond density due to the local deformation rather than by the local cohesive stress. A phenomenological relationship between the bond density and the deformation is established. The criterion which is applied to determined crack initiation and propagation is built into the constitutive model. As an example, the method is used to study the crack initiation and propagation behavior under tensile loading.     

The effects of annealing on fatigue crack propagation in polyethylene

Fatigue crack propagation tests on annealed and quenched medium-density polyethylene showed the annealed specimens to have much lower resistance to crack initiation and subsequent propagation. Although the same fracture mechanism, in which the brittle crack gradually becomes more ductile, prevailed in both cases, the voided and fibrillated crack tip root craze in the annealed material was much weaker that the nonfibrillated quenched root craze. Microstructural analyses indicate that the annealed material had separate crystallite populations, whereas the quenched material had a more homogeneous morphology. The highest melting fraction of the annealed material was composed of lamellae that were about 270 Å thick, and the quenched lamellae were estimated to be 160 Å thick. The reduced fatigue crack propagation resistance of the annealed material was suggested to be a result of a lower concentration of tie molecules and its reduced damping capability, compared to the quenched material. © 1995 John Wiley & Sons, Inc.     

Sensitivity analysis in linear semi-infinite programming: Perturbing cost and right-hand-side coefficients

This paper analyzes the effect on the optimal value of a given linear semi-infinite programming problem of the kind of perturbations which more frequently arise in practical applications: those which affect the objective function and the right-hand-side coefficients of the constraints. In particular, we give formulae which express the exact value of a perturbed problem as a linear function of the perturbation.     

An anti-plane propagating crack in a functionally graded piezoelectric strip bonded to a homogeneous piezoelectric strip

Summary A finite crack propagating at constant speed in a functionally graded piezoelectric strip (FGPS) bonded to a homogeneous piezoelectric strip is considered. It is assumed that the electroelastic material properties of the FGPS vary exponentially across the thickness of the strip, and that the bimaterial strip is under combined anti-plane mechanical shear and in-plane electrical loads. The analysis is conducted for the electrically unified crack boundary condition, which includes both the traditional permeable and the impermeable ones. By using the Fourier transform, the problem is reduced to the solution of Fredholm integral equations of the second kind. Numerical results for the stress intensity factor and the crack sliding displacement are presented to show the influences of the crack propagation speed, electric loads, FGPS gradation, crack length, electromechanical coupling coefficient, properties of the bonded homogeneous piezoelectric strip and crack location.     

Stress wave interference effects during fracture of silicon micromachined specimens

We report on unique measurements of multiple microsecond-duration arrest periods during the propagation of high speed (>1 km s⁻¹) cracks in micromachined single-crystal silicon specimens. These events were recorded electronically and in physical features remaining on the fracture plane. Using time-of-flight calculations, we have determined that these arrest patterns are due to the interference of boundary-reflected stress waves with the propagating crack tip. The specimen size, the measurement method, and the low acoustic attenuation in cyrstalline silicon facilitated the observation of these phenomena.