ISSN 0798 1015

Vol. 38 (Nº 48) Year 2017. Page 38

Management and modeling of the influence of cracks on the temperature distribution in polymers and composites

Gestión y modelización de la influencia de grietas en la distribución de la temperatura en polímeros y compuestos

A.A. VALISHIN 1

Received: 30/09/2017 • Approved: 05/10/2017

Introduction

Fracture of solids, in particular polymers and composites on their basis is a process of accumulation of internal microdamages to a certain critical point (Dimitrienko and Sokolov, 2013; 2012; 2010; Dmitroenko, 1995; 1997). This process is localized predominantly at the weakest points of the structure of the material, where there are pockets of surge in which mechanical stress is much more than away from them. Such foci are, first, micro and macro.

The model and the theory of fracture of polymers and composites on their basis under non-isothermal conditions is the least developed region in the science of strength of solids. There are practically important cases when it is impossible to consider the temperature field of the sample uniform, and to consider non-uniform temperature distribution and, in particular, the perturbation of the temperature field caused by the presence of cracks. You can consider a stationary temperature field, as transient non-stationary processes, as a rule, quickly enough damped.

Experimental data (Finkel, 1977) indicate that in the case of steady heat flow in a sample with a crack is a significant increase in thermal stress caused by a local increase in the magnitude of the temperature gradient in the vicinity of the crack. In this case thermoelastic compressive stresses being imposed on the elastic field of mechanical stresses that can reduce the total stress intensity at the crack tip and thereby can slow down its development.

In turn, the thermoelastic tensile stress can cause crack growth and damage to the specimen even in the absence of mechanical stress. Experiments confirm this conclusion. In the monograph [6] described the experiment, when the plate of a polymeric material with an internal crack, would be destroyed only under the influence of the external temperature field, without mechanical action. Comparison of different experimental results concerning the observations of Cremieu in terms of mechanical or thermal loading of the sample, allowed us to formulate the most important General conclusion: the crack grows under the action of local stresses in the apex. It doesn't matter what factor created by these local stresses: external mechanical stress, inhomogeneous temperature field or maybe even some other factor.

The singular character of thermal stress near the tip of the crack is analyzed in (Si, 1963) where it is shown that the classical conception about the peculiarities of the mechanical stress near the tip of the crack remain in force and thermoelastic stresses. The presence of heat flow in the specimen with a crack does not cause additional singularities, so singulares of thermal stress is the usual form ,  where r is the distance from the top of the crack, and K the ratio of the intensity of thermal stress, which is calculated in each case of thermal loading (Kartashov, 1991). The difference fields of thermoelastic stresses from the mechanical stress is the intensity factor K, which has a different kind in these two cases.

Conclusions

1. When exposed to a steady heat flow in a sample with a crack is a significant increase in thermal stress caused by a local increase of the temperature gradient in the vicinity of the crack.

2. The crack grows under the action of local stresses near its summit. It doesn't matter what factor created by these local stresses.

3. The crack distorts the temperature field characteristic of the sample without cracks. This distortion is localized near the cracks, and distortion is determined by the size of the crack. On the crack in addition to the displacement jump occurs, the jump in temperature proportional to the power of the external heat flux and size of the crack. In the mechanical field, a crack is a hub (local amplifier) voltage, and temperature field, in addition to the hub of the heat flow.

4. The real crack is a crack with asymptotically converging shores. The consequence of this is the existence of a "beak" cracks, i.e., the plot at the end of the crack, where the significant strength of interparticle coupling its shores. These forces provide a smooth closure of the crack faces and limb, stress, as well as a limb component of heat flow near its summit. The beak is Autonomous in relation to the crack, and when movement of the latter moves with it, without changing any size or shape.

5. "Thermal resistance" of the beak cracked more significantly than far from it. As a result, the bill is "overheated" in comparison with the average level. Numerical evaluation for PMMA showed that depending on the initial sizes of cracks overheating of the beak is from a few tenths to a few degrees, and when the cracks, the value of overheating of the beak varies in 2.5 – 3 times.

6. The existence of the mechanical equivalent of heat flux, i.e. the equivalent mechanical stress, which is equivalent to the action of heat flow.

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1. Department of Computational Mathematics and Mathematical Physics. Bauman Moscow State Technical University (BMSTU). Doctor of Physical and Mathematical Sciences, Professor. Contact E-mail:  kseniabadz@gmail.com