A constitutive theory for creep behavior of initially isotropic materials sustaining unilateral damage

The goal of the present work is to modify structure of the creep constitutive equations existing in the literature, and simultaneously to incorporate both damage induced anisotropy and unilateral damage into the constitutive model. The proposed nonlinear-tensor constitutive equation for creep together with the damage evolution equation take into account the secondary and tertiary creep of the initially isotropic materials. The material parameters of the model are determined using basic experiments. It is shown that the creep model is capable of describing available experimental data for the lateral creep responses under uniaxial compression.     

Biaxial isotropic stochastic visco-elastic creep

This is second part of a paper dealing with the formulation of constitutive equations for statistically isotropic multi-axial visco-elastic stochastic creep in terms of a second moment white noise field model. Herein the biaxial linearized model is studied. After an extensive retrospective introduction recapitulating the basic concepts, the paper presents the solution to the spatial covariance structure of a stress field history which is homogeneous in the mean. Results for the corresponding strain field are also presented. It turns out to be necessary to let the spatial second moment while noise character of the strain tensor field history for given deterministic stress tensor history be approached through a sequence of genuine covariance functions corresponding to isotropic random fields. In the limit the variances of both stress and strain become infinite. Interesting asymptotic results show up in this connection.The appendices give some useful mathematical results concerning Fourier transforms related to the Laplace operator and covariance functions of isotropic random fields.     

《Elaticity of Transversely Isotropic Materials》一书评介

浙江大学土木系丁皓江教授和陈伟球教授及澳大利亚悉尼大学航空、机械与机电工程学院章亮炽教授的专著“Elasticity of Transversely Isotropic Ma- terials”(ISBN：1-4020-4033-4),2006年由Springer公司出版,该书是加拿大著名力学家G．M．L．Gladwell     

Research note on a simple model for pressure-sensitive strain-hardening materials

The true stress-plastic strain curves for pressure-sensitive high strength steels are successfully predicted using a simple constitutive model. Both the strength-differential and plastic compressibility effects are taken into account in the modeling. All material constants appearing in the constitutive relations have been obtained. The procedures outlined can be readily incorporated in standard elastoplastic finite element codes.     

Anisotropy of creep of materials

It has been shown that when ordinary stress-strain (-) diagrams are constructed for 20-mm thick rolled duralumin plate at various temperatures, the alloy behaves like an isotropic material, while a considerable degree of anisotropy is observed in creep testing.Thanks are due to A. F. Nikitenko for his assistance in obtaining and processing the experimental data.     

Vibrational creep of polymer materials

In the mechanics of deformed solids it is usually assumed that superposing small amplitude vibrations on a static load has no effect on the over-all characteristics of a material under strain. This hypothesis is reflected in the fact that the existing equations of state for the case of static loads with superposed small vibrations give deformation characteristics which differ little from the corresponding parameters of deformation processes taking place in the absence of excitations. At the same time, substantial changes in the deformation characteristics of a number of materials are observed under certain conditions after the application of alternating stresses of small amplitude. Reports on studies of creep of metals [1, 2], elastomers [3], and concrete [4] have been published, in which the fatigue curves obtained with small vibrations superposed on static loads lie above curves obtained for static loads corresponding to the maximum pulsating load level. Attempts have been made to explain this effect from the standpoint of the molecular-kinetic [3] and phenomenological [5] theories. Certain theoretical considerations and experimental data, discussed in this article, show that superposing a small dynamic component on a static load leads to an increase in the rate of creep of several polymer materials. This effect, which is due mainly to an increase in the polymer temperature as a result of dissipation of vibrational energy, differs from the vibration effect observed on elastomers by Slonimskii and Alekseev [3], in which the temperature rise due to the heat generated by vibrations plays no substantial part.The authors thank V. A. Volodchenkova, N. I. Gal'china, Yu. S. Levshina, Yu. P. Maksimacheva, and V. V. Tikhomirova who participated in the experimental work.     

Shear modulus of transversely isotropic materials

A new and simple method is presented to determine the inde-pendent shear modulus of transversely isotropic material.Mathematical formulation,derivation and solution are given,and test apparatus and results are presented.The method wastested on one of such materials-Green River Formation oilshale.Comparisons wich other approximate results and acou-stical methods are made.Confirmation of the test methodwith materials having known shear moduli is also presented.     

Two new expanding cavity models for indentation deformations of elastic strain-hardening materials

Two expanding cavity models (ECMs) are developed for describing indentation deformations of elastic power-law hardening and elastic linear-hardening materials. The derivations are based on two elastic–plastic solutions for internally pressurized thick-walled spherical shells of strain-hardening materials. Closed-form formulas are provided for both conical and spherical indentations, which explicitly show that for a given indenter geometry indentation hardness depends on Young’s modulus, yield stress and strain-hardening index of the indented material. The two new models reduce to Johnson’s ECM for elastic-perfectly plastic materials when the strain-hardening effect is not considered. The sample numerical results obtained using the two newly developed models reveal that the indentation hardness increases with the Young’s modulus and strain-hardening level of the indented material. For conical indentations the values of the indentation hardness are found to depend on the sharpness of the indenter: the sharper the indenter, the larger the hardness. For spherical indentations it is shown that the hardness is significantly affected by the strain-hardening level when the indented material is stiff (i.e., with a large ratio of Young’s modulus to yield stress) and/or the indentation depth is large. When the indentation depth is small such that little or no plastic deformation is induced by the spherical indenter, the hardness appears to be independent of the strain-hardening level. These predicted trends for spherical indentations are in fairly good agreement with the recent finite element results of Park and Pharr.     

Subcritical crack growth in strain-hardening materials with allowance for strain anisotropy

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 24, No. 2, pp. 90–94, February, 1988.