Polymer fatigue from the standpoint of the kinetic theory of fracture

A comparison of the static and cyclic lives of various polymers shows that, whatever the loading regime, fracture may be regarded from the standpoint of the thermal-fluctuation theory. Under comparable test conditions the lifetimes in different loading regimes coincide. The experimentally observed cases of a reduced cyclic as compared with static life do not conflict with the kinetic theory of fracture and can be attributed to hysteresis heating effects or to differences in the structural changes that take place in the test material in different loading regimes.From the standpoint of the kinetic theory, fracture is regarded as a certain process that develops in a body under load and not as a critical event that occurs when a critical stress — ultimate strength — is reached.A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 1, pp. 70–96, January–February, 1969.     

Combined primary and secondary log breakdown optimisation

At sawmills logs are converted into boards by a series of cutting operations. Primary cuts reduce logs into slabs of wood, secondary cuts produce boards. Boards incorporating natural defects such as knots (branch sections) are inferior to clear boards. The aim of the sawmill is to cut logs to produce boards of greatest value. However, when logs are pruned, knots are only exposed after primary cutting. This complicates the conversion problem.To effectively convert logs into boards the interrelated effects of the cutting phases must be recognized. In this paper linked dynamic programming formulations are developed. The inner (secondary) formulation determines the optimal sequence for cutting a slab into boards. The result is passed to the master (primary) formulation that determines the optimal sequence for cutting the log into slabs. The objective functions can be modified to maximise either total value of boards (incorporating quality) or total volume. Results from simulations indicate that significant increases in value are possible when quality is considered.     

A problem in machine breakdown

Summary Consider a machine subject to breakdown. The machine, if working, performs a certain kind of task and the probability of completion of a task in time intervalt ist+o (t). The running time, set-up time (that elapses before repair starts) and the repair time are independent random variables, each following exponential distribution. Explicit expressions are derived for quantities of interest, for example (i) the variance of the number of tasks completed in an arbitrary time interval and (ii) the covariance between the number of tasks completed in two successive non-overlapping time intervals. Each result is presented in a slightly more general form obtained by considering that each task may consist of one or more pieces, the number of pieces in each task has a distribution with finite mean and variance.

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Zusammenfassung Betrachtet wird eine Maschine unter Berücksichtigung technischer Störungen. Wenn die Maschine läuft, führt sie gewisse Arbeitsgänge durch. Die Wahrscheinlichkeit, daß ein Arbeitsgang in einem Zeitintervall der Länget beendet wird, beträgtt+o (t). Die Arbeitszeit, Wartezeit (Zeitspanne bis Reparaturbeginn bei Störung) und die Reparaturzeit sind unabhängige, exponentialverteilte Zufallsgrößen. Für gewisse interessierende Größen werden explizite Ausdrücke hergeleitet, z. B. (1) für die Varianz der Anzahl der durchgeführten Arbeitsgänge in einem gegebenen Zeitintervall und (2) für die Kovarianz zwischen den Anzahlen der durchgeführten Arbeitsgänge in zwei aufeinanderfolgenden disjunkten Zeitintervallen. Jedes Ergebnis wird in einer etwas allgemeineren Form dargestellt, die dadurch entsteht, daß angenommen wird, jeder Arbeitsgang bestünde aus mehreren Teilen, deren Anzahl einer Verteilung mit endlichem Mittelwert und endlicher Varianz genügt.

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This research was conducted under Grant received from the University of Alabama Research Committee, Project No. 525, dated May 10, 1966.

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Vorgel. v.:J. Nitsche.     

High breakdown mixture discriminant analysis

Robust S-estimation is proposed for multivariate Gaussian mixture models generalizing the work of Hastie and Tibshirani (J. Roy. Statist. Soc. Ser. B 58 (1996) 155). In the case of Gaussian Mixture models, the unknown location and scale parameters are estimated by the EM algorithm. In the presence of outliers, the maximum likelihood estimators of the unknown parameters are affected, resulting in the misclassification of the observations. The robust S-estimators of the unknown parameters replace the non-robust estimators from M-step of the EM algorithm. The results were compared with the standard mixture discriminant analysis approach using the probability of misclassification criterion. This comparison showed a slight reduction in the average probability of misclassification using robust S-estimators as compared to the standard maximum likelihood estimators.     

Avoiding breakdown and near-breakdown in Lanczos type algorithms

Lanczos type algorithms form a wide and interesting class of iterative methods for solving systems of linear equations. One of their main interest is that they provide the exact answer in at mostn steps wheren is the dimension of the system. However a breakdown can occur in these algorithms due to a division by a zero scalar product. After recalling the so-called method of recursive zoom (MRZ) which allows to jump over such breakdown we propose two new variants. Then the method and its variants are extended to treat the case of a near-breakdown due to a division by a scalar product whose absolute value is small which is the reason for an important propagation of rounding errors in the method. Programming the various algorithms is then analyzed and explained. Numerical results illustrating the processes are discussed. The subroutines corresponding to the algorithms described can be obtained vianetlib.     

Two queues with alternating service and server breakdown

We consider a queueing system with two stations served by a single server in a cyclic manner. We assume that at most one customer can be served at a station when the server arrives at the station. The system is subject to service interuption that arises from server breakdown. When a server breakdown occurs, the server must be repaired before service can resume. We obtain the approximate mean delay of customers in the system.     

Polymer friction

The results of research on the antifriction properties of polymeric materials and expressions for calculating their coefficient of friction are presented. The effect of the mechanical properties of the materials on their antifriction characteristics is discussed.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 421–429, May–June, 1975.     

Polymer fractography and fracture kinetics

On the basis of an analysis of the fractographic data for two polymeric materials (polymethyl-methacrylate and polycaprolactam) it is shown that it is possible to differentiate the effects of local heating and structural changes at the end of the main crack on the reduced lifetime of polymers under cyclic as compared with static loading. A method is proposed for estimating the values of the local temperature and the structure-sensitive coefficient in the cyclic lifetime equation.For communication 2 see [3].Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 5, pp. 869–874, September–October, 1971.     

Polymer fractography and fracture kinetics

A relationship is established between the temperature-time dependence of the radial dimensions of the specular zones on polymer (PMM, PCL) fracture surfaces and the parameters characterizing the kinetics of main-crack growth. This makes it possible to calculate the kinetic crack growth parameters from the data of a fractographic investigation.For the first article on this subject see [1].Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 5, pp. 842–847, September-October, 1970.     

Polymer fractography and fracture kinetics

The fractographic method makes it possible to determine the test temperature and time at which anomalies appear in the temperature-time dependence of the strength of polymethyl methacrylate and polycaprolactam by finding the conditions of disappearance of specular zones from the fracture surfaces of these polymers. For PMMA these values are –40°C and 10^–2 sec, for PCL –120°C and 10^–7 sec, respectively.For communication 1 see [2].Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 2, pp. 232–237, March–April, 1971.     

Match-up scheduling under a machine breakdown

When a machine breakdown forces a modified flow shop (MFS) out of the prescribed state, the proposed strategy reschedules part of the initial schedule to match up with the preschedule at some point. The objective is to create a new schedule that is consistent with the other production planning decisions like material flow, tooling and purchasing by utilizing the time critical decision making concept. We propose a new rescheduling strategy and a match-up point determination procedure through a feedback mechanism to increase both the schedule quality and stability. The proposed approach is compared with alternative reactive scheduling methods under different experimental settings.     

Numerical investigations on supersonic vortex breakdown

Breakdown of a slender vortex caused by a normal shock is studied using a numerical solution of the Navier‐Stokes equations for unsteady, three‐dimensional, supersonic flow at a free stream Mach number of 1.6. The numerical results clearly reveal the time‐dependent flow structure for both the axial and the radial direction. The results compare well with recent experimental findings.     

Avoiding breakdown in the CGS algorithm

The conjugate gradient squared algorithm can suffer of similar breakdowns as Lanczos type methods for the same reason that is the non-existence of some formal orthogonal polynomials. Thus curing such breakdowns is possible by jumping over these non-existing polynomials and using only those of them which exist. The technique used is similar to that employed for avoiding breakdowns in Lanczos type methods. The implementation of these new methods is discussed. Numerical examples are given.     

Vortex breakdown in turbulent pipe flows

In many technical applications turbulent flows with embedded slender vortices exist. Depending on the boundary conditions vortex breakdown can occur. The purpose of this work is to develop and implement a solution scheme for large‐eddy simulations of vortex breakdown in turbulent pipe flows. One of the main problems in this simulation is the formulation of the inflow boundary condition for a fully developed turbulent flow with an embedded vortex. For that purpose a rescaling technique is developed in which a solution at a downstream location is inserted at the inflow boundary after an appropriate rescaling. To determine rescaling laws for pipe flows with an embedded vortex, analytical velocity profiles of swirling flows are first prescribed in a laminar flow. From the spatial development of the vortex a scaling law is deduced. In a next step this procedure is to be transferred to turbulent flows.