Photoelasticity method is used to study experimentally the complete Williams series expansion of the stress and displacement fields in the vicinity of the crack tip in isotropic linear elastic plates under Mixed Mode loading. The distribution of the isochromatic fridge patterns is employed for obtaining the stress field near the crack tip by the use of the complete Williams asymptotic expansion for various classes of the experimental specimens (plates with two collinear cracks under tensile loading and under mixed mode loading conditions). The higher order terms of the Williams series expansion are taken into account and the coefficients of the higher order terms are experimentally obtained. The stress field equation of Williams up to fifty terms in each in mode I and mode II has been considered. The comparison of the experimental results and the calculations performed with finite element analysis has shown the importance and significant advantages of photoelastic observations for the multi-parameter description of the stress field in the neighborhood of the crack tip.

In the present work, photoelastic and finite element methods have been employed to study the near crack tip fields in isotropic linear elastic cracked bodies under mixed mode loading. The investigated fracture results have been obtained for a series of cracked specimens by testing plates with two parallel cracks, two inclined parallel cracks, three-point bend specimens, four-point bend specimens, inclined edge crack triangular shape specimens subjected to symmetric three point bend loading. The multi-parameter Williams series expansion is used for the crack tip field characterization. Digital photoelasticity method is utilized for determination of the Williams series expansion’s coefficients. The unknown coefficients in the multi-parameter equation are determined using a linear least squares method in an over-deterministic manner. Together with the experimental determination of the fracture mechanics parameters finite element method is invoked to describe the crack tip stress field. Coefficients of higher order terms are either found numerically by finite element method. A good agreement is found between the numerical and experimental results. The significant advantages using multi-parameter equations in the analysis of the stress field are shown and the errors that a study with a limited number of terms produce is demonstrated. The comparison with finite element analysis highlighted the importance and precision of the photoelastic observation for the evaluation of the fracture mechanics parameters. The experimental SIF, T-stress values and coefficients of higher-order terms estimated using the digital photoelasticity method for the extensive series of cracked specimens are compared with finite element analysis (FEA) results, and are found to be in good agreement.

Elements of structures which work in real conditions are quite often affected by variable temperatures and loadings. Nowadays the growth of interest related to the asymptotic behavior of inelastic structures subjected to cyclic loading leads to development of direct and incremental methods of stabilized state determining. If loadings vary and the body deforms elastically, then its durability is defined by fatigue characteristics of materials; destruction comes after a large number of cycles. If the body experiences elasto-plastic deformation, at loadings below the limit, the achievement of a dangerous state at a rather small number of cycles is possible. Thus it is necessary to distinguish two cases. The first case occurs when destruction comes due to the alternation of plastic deformations with different signs (for example, after plastic stretching there is plastic compression, etc.); it is cyclic plasticity (plastic or low-cyclic fatigue). The second case occurs when plastic deformations do notchange signs, but grow with each cycle (the progressing deformation-ratcheting). It leads to the inadmissible accumulation of plastic deformations. Thestudy results present finite-element (FEM) calculations of the asymptotical behavior of an elastoplastic plate with the central elliptic hole under the biaxial cyclic loading for three different materials. Incremental cyclic loading of the sample with the stress concentrator (the elliptic central hole) is performed in the multifunctional finite-element package SIMULIA Abaqus. The ranges of loads found for the shakedown, cyclic plasticity and ratcheting are presented. The obtained results are generalized and analyzed. Convenient normalization is suggested. At the expense of the chosen normalization all computed results corresponding to separate materials stay within one common curve with a minimum scattering of points. The convenience of the generalized chart consists of a possibility to receive the asymptotical behavior of the inelastic structure for those materials which computer calculations were not made.

In the article the results of finite element calculations for the determination of stress-strain state of elasto-plastic plate with central circular hole which is under the action of cycle loading are presented. Incremental and direct methods of defining asymptotic behaviour of the structure: adaptability, alternating plas- ticility and progressive plastic flow are presented. In the package Simulia Abaqus incremental cyclic loading of samples with stress concentrators is performed.

The review of methods that can be used to define the asymptotic stabilized state of an inelastic structure under cyclic loading is given in the paper. Due to the growth of interest for the knowledge of the asymptotic behaviour of the structure under cyclic loading, incremental (with the use of finite element method) and direct methods (methods of optimal control theory and decomposition of residual stresses in Fourier series) began to develop.