The Dugdale crack model is generalized to the case of plane strain. The governing equations are set up to determine the stresses in the plastic zone. Numerical results from specific problems are analyzed and compared with those for plane stress state and other cases. A relationship between the crack model and K I -T theory is established in the case of small-scale yielding at the crack tip Keywords: Dugdale crack model, generalized model, plane strain, fracture toughness, T-stresses, plastic zone, plane stress state, small-scale yielding Introduction. Classical fracture mechanics, either linear or nonlinear, is based on a one-parameter estimate of the limiting state of a body with a mode I crack. For example, Griffith-Irwin-Orowan theory [31,33,40] considers an asymptotic field of elastic stresses at the crack tip and describes the limiting state by only the stress intensity factor (SIF) K I or energy release rate G I . Nonlinear fracture mechanics based on the Cherepanov-Rice J-integral proceeds from the singularity of the asymptotic stress field in a nonlinearly elastic material [19,32,41].The intensive experimental investigations initiated almost immediately after the above concepts had been put forward revealed that the fracture characteristics depend on specimen geometry and loading conditions, as shown by the dependence of the maximum SIF on the thickness of the specimen, the ratio of the crack length to its width, etc. [16,17]. In this connection, much effort went to the development of standards for determining fracture toughness K IC in the case of plane strain. The weaknesses of the one-parameter approach made themselves evident later, in analyzing the influence of two-axis loading on the limiting state of a cracked body [13,20]: this theoretical approach did not confirmed the experimentally revealed effect of the homogeneous normal stresses along the crack on the maximum SIF.The above-mentioned and other facts are indicative of the limitation of the one-parameter approach to the description of quasibrittle fracture. Two factors influencing the limiting state of cracked bodies attracted the attention of researchers: constrained plastic strains in different stress-strain states (SSSs) at the crack front and regular (according to the elastic solution) terms of the stress field. However small the plastic zone at the crack tip, the stresses at the boundary of the elastic and plastic zones are always finite, and the effect of regular terms may be significant. Obviously, a closed-form elastoplastic solution for a mode I crack would account for these factors. Such analytical solutions are as yet unavailable, however; and researchers have to use crack models to simplify the distribution of stresses and strains and the form of the plastic zone.Recently, the following nonclassical approaches have been developed: -the criteria of plasticity theory and various numerical methods of analyzing the plastic zone at the crack periphery [16,27];-criteria of local buckling near cracks [2, 13]; -more complete description of ...
An efficient method for determining the deformation function of a composite is discussed. The method is based on a fractional exponential representation of the deformation functions of the composite components. The viscoelastic solution is obtained using the Volterra principle. The deformation function is represented as a function of a base operator. Thus, the problem is solved by approximating the deformation function by a continued fraction and applying the method of operator continued fractions. A computational procedure is detailed and illustrated using data on longitudinal relaxation of polymethylmethacrylate. As an example, the deformation of a polymethylmethacrylate-based fibrous composite with viscoelastic properties is analyzed Introduction. Extensive use of polymers and polymer-based composites entails intensive development of the theory of viscoelasticity needed to solve practical deformation problems for composites and boundary-value problems for materials with time-dependent stress-strain state. Typical properties of these materials are relaxation (decreasing stresses at constant strains) and creep (increasing strains at constant stresses). To describe the deformation of viscoelastic materials, Boltzmann proposed a theory of hereditary viscoelasticity based on the superposition principle. According to this theory, the equation relating the strains and stresses in a linear nonaging viscoelastic material under uniaxial loading and isothermal conditions reads
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