It is well known that the mechanical behavior of polymers shows remarkable time and temperature dependences, that is, viscoelastic properties, as recognized in their creep and relaxation. This might come from their microstructures which have much different characteristics from those of metallic materials. Therefore, analyses of stress and strain in the viscoelastic body should be carried out based on the so-called viscoelasticity, but not on the elasticity. The mechanical behaviors of elastic body are specified by elastic constants like Young's modulus, while those of viscoelastic ones are determined by several coefficients characterized by the function of time and temperature. In this descriptive paper, qualitative explanations of mechanical properties, particularly time and temperature dependent properties, of polymericmaterials are made in relation to their molecular structures, then the fundamental concept on viscoelastic analysis is briefly introduced.

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Recently many kinds of polymeric solid material are used in industrial fields. And it is well known that the mechanical properties of such materials show remarkable dependences on time and temperature. So small number of people, however, seem to be familiar with the viscoelastic and/ or the time and temperature dependent mechanical behaviors of these materials. For students who have just interested in the time dependent characteristics and mechanical behaviors of such kind of polymers, the author would like to explain following items in detail here. ① a fundamental concept on the linearly viscoelastic mechanical behavior under uniaxial stress-strain state, and its mathematical representation in both the differential equation based on the spring-dashpot model and the integral form due to the supereposition principle, ② useful experimental methods for characterization of mechanical properties of solid polymers, and ③ its approximation to numerical functions by the collocation method using a Prony series and the internal transformation of the characteristic functions.

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As industrial use of polymers increases, it becomes more important to take the viscoelastic properties into account, particularly, in structural and mechanical design including such kind of materials. Many engineers and students are, however, not so familiar to treatment of viscoelastic bodies which shows complicated time and temperature dependent behaviors. Thus, the stress and strain analysis of these types of body could easily be misoriented, because of lack in fundamental knowledge on mechanics of viscoelastic body. The author would like to discuss and explain here about the basic concept on a homogeneous, isotropic and linearly viscoelastic body, and its treatment in the two and/or three dimensional analyses. The following items are emphasized here, as 1) basic equations necessary for stress and displacement analysis of a linearly viscoelastic body under isothermal condition, such as the constitutive, the equilibrium and the compatibility equations, are derived for general type of three dimension. 2) In particular, taking usefulness and convenience in usual treatment two dimensional cases, namely, the plane strain and the plane stress problems, are discussed in detail. 3) The correspondence principle and its application to some example problems in pseudo-elastic analysis of linearly visocelastic problem, are also described with the limitations for application. 4) The basic equations for anisothermal cases are also discussed briefly.

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The present paper explains the residual stress and deformation due to thermoviscoelastic behavior of materials and non-uniformity temperature in the cooling process during its molding. The viscoelastic model including an element for thermal expansion is proposed in order to express the viscoelastic behavior of material with temperature change. Using this model, a qualitative prediction of the residual stress and deformation in cooled viscoelastic material is done. Using the linear-viscoelastic theory, fundamental equations for the residual stress and deformation in a viscoelastic beam, where an unsteady and non-uniformity temperature distribution is assumed in the direction of depth, are shown. The theoretical values of residual stress and deformation in beams are calculated under various constraint and temperature conditions for two resins having different viscoelastic characteristics, i. e. epoxy and unsaturated polyester resins. Finally, beams of each resin are actually cooled, and the residual stress and deformation in these beams is measured. The experimental results are compared with the theoretical results and the relations between the residual stress or deformation and thermoviscoelastic behavior are quantitatively explained.

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Although viscoelastic materials are widely used in the recent industrial fields, investigation on criteria for onset and subsequent crack growth in those materials from a viewpoint of continuum mechanics, has not been so active in comparison with those in case of elasto-plastic metallic materials. As one of the reasons for this situation, it is pointed out that difficulties in theoretical and experimental analyses of such kinds of solids and sheets are mainly caused by dependence of viscoelastic mechanical behaviors on loading history in addition to those merely on temperature and loading rate. In this paper, the author would like to explain fundamental treatments of fracture problem in viscoelastic materials based on criterion for onset and subsequent crack growth, which are classified into the following five categories, such as, (1) the global energy balance criterion, (2) the local energy balance criterion, (3) the COD criterion, (4) the displacement field criterion. (5) the criterion based on the conservation law.

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This paper intended to discribe the photoviscoelastic technique to practical use which is known as one of the experimental viscoelastic stress and strain analyses. The fundamental equations for photoviscoelastic analysis are induced by use of two-dimensional linear photoviscoelastic theory. Prior to making a practical photoviscoelastic analysis, mechanical and optical characterizations of the materials are required. In other words, it is necessary to determine the time-and temperature dependent viscoelastic and photoviscoelastic coefficients. In this paper, the procedure for determination of photoviscoelastic coefficients is described in detail using epoxy resin. The practical photoviscoelastic analyses were carried out on three characteristic problems. The first is the analysis of a strip with a circular hole made of polyurethane resin, to which the practical load is subjected at constant temperature. The second is the analysis of a square plate with a central hole made of polyurethane resin, to which the non-proportional load is subjected at constant temperature. In this case, the axes of polarization of light, principal stress and principal strain do not coincide with each other. The third is the analysis of a epoxy strip which is subjected to rapid cooling from both sides. This is so-called a thermoviscoelastic problem, in which there is a large temperature change in the body.

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Microscopic defects such as vacuoles and crazes generated in stressed and/or strained solid material play the important and detrimental roles for strength of thermoplastic. It should be, however, noted that investigations on accumulation and residue of micro-defects under or after stressing and its effect on macroscopic strength characteristics of the material have not been sufficient, because of technical difficulties in detection and trace of behavior of such micro-defects. In this article, the author would like to explain a Small Angle X-ray Scattering (SAXS) method for piriodical trace of micro-vacuoles in a polypropylene sheet. Variations in number as well as size of micro-defects under uniaxial loading were studied by use of Guinier theory. Also, the relationship between cumulative damage due to microdefects and macroscopic mechanical degradation was discussed standing upon the behavior of micro-defect obtained under various types of loading history.

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In recent years, the boundary element methods (BEM) have been used in various fields of computational mechanics. As for the thermoelastic problems the methods have been successfully applied. However, in almost all the boundary element methods developed so far for thermoelasticity, the terms resulting from the temperature change are considered to be the pseudo body force, and the boundary element software for elastostatics are employed for analysis. Therefore, the domain integrals inevitably appear on the boundary integral equations to be analyzed. These integrals are in most cases evaluated numerically by introducing small internal cells, or in extremely simple cases they can be transformed into the equivalent boundary integrals. The present paper is concerned with an alternative boundary integral equation formulation for the thermoelastic problems. In this approach, the governing differential equations of the displacement (or stress) field and the temperature field are transformed into a simultaneous set of the boundary integral equations. The necessary fundamental solutions are derived in a systematic manner after Hormander. The fundamental solutions thus derived and the related expressions are given in detail for some typical problems in thermoelasticity. Finally, the proposed formulation is extended to the so called coupled thermoelastic problems.

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This paper presents an analytical approach for estimating the fiber crossing angle variation and the polar anisotropic elastic moduli of fabric-reinforced-rubber diaphragm by introducing the extension ratio in the forming process as a structural parameter. A good agreement between the theoritical and the experimental results for the fiber crossing angle distribution of the diaphragm was obtained. These results would be useful for further analysis on stroke characteristics, stress distribution and vibration properties of the flexible diaphragm.

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TiO₂, has been widely used as one of functional ceramics, however, it has a fault of decreasing strength in the case when its polycrystalline texture is consisted of large grains. This phenomenon has been considered to be due to its thermal expansion anisotropy, i. e., cracks produced by thermal stress in the quenching process after sintering, propagate in the texture and decrease the strength of TiO₂. The aim of this study is to determine experimentally the statistical character of the effect of grain size on mechanical properties of TiO₂, and clarify its correspondence with microfracture model. The specimens having a grain size range 10-60μm were prepared by various annealing temperatures and times after sintering. Young's modulus and bending strength decreased remarkably when the grain size (abbreviated as d) was larger than approximately 20μm, and indicated almost constant values at d>35μm.Stress intensity factor (K_c') showed a constant value (2.2MNm^-3/2) throughout the all grain sizes tested, when the notch radius in SENB method was taken into consideration.This must imply the plane strain fracture toughness of TiO₂.The relation between bending strength（σ) and grain size (d) was σ=-87.1+829.7d^-1/2 The crack length of fracture origin calculated from bending strength and stress intensity factor was almost constant (1000-1400μm) for low-strength specimens. This resulted in the fact that the bending strength was independent of grain size at d>20μm. The crack length agreed also with the observation results of fracture surface. Critical grain size for crack propagation into grain was calculated from the arrangement of Evans' model in which polycrystals with 2-dimensional hexagonal grains was adopted. The calculated value was 22.2μm and coincided well with the experimental result. Weibull's statistical analysis was used to analize the effect of grain size on fracture diagnostics in the results of bending strength.

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In order to investigate the fatigue strength behavior under fully reversed impact torsional load, two types of the impact fatigue tesing machines were newly developed. By using these testing machines, a series of experiments were carried out on a structural alloy steel JIS. SCM435. The following characteristics of impact torsional fatigue strength behaviors were revealed : (1) the fatigue strength of the plain specimen in impact fatigue is higher than that in non-impact fatigue in the entire range of this experiment ;(2) the fatigue strength of the hole-notched specimen in impact fatigue shows a trend to become lower comparing with the results in non-impact fatigue in high stress cycles region ; (3) the crack growth rate in impact fatigue is lower than in non-impact fatigue.

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The static tensile strength tests were performed for glass-mat reinforced plastics by using three types of rectangular specimens. These specimens involved the straight-sided specimens having the integrally molded tabs (named by Type R-I) and the adhesive tabs with the additional FRP laminates (Type R-F) and aluminum plates (Type R-A). The dumbbell specimen (Type D) was also used to compare the tested results. Failures of every types of tested specimens occurred not only in the gage section, but also near the shoulders between the straight-side and the grip of a specimen. Most of Type R-I specimens failed in the gage section, but about half of the dumbbell specimens failed near the shoulders. As a result of statistical analysis, it was found that the tensile strength distributions were fit to the Weibull distributions with two or three parameters corresponding to the failed location such as the gage-section or the shoulder of each specimen. The dispersions of the tensile strength were maximum for Type-D specimen and minimum for Type R-I specimen.

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