scholarly journals Complete Williams asymptotic expansion of the stress field near the crack tip: Analytical solutions, interference-optic methods and numerical experiments

2016 ◽  
Author(s):  
Larisa Stepanova ◽  
Pavel Roslyakov
Keyword(s):  
Asymptotic Expansion ◽  
Stress Field ◽  
Analytical Solutions ◽  
Numerical Experiments ◽  
Crack Tip

scholarly journals EXPERIMENTAL DETERMINATION OF COEFFICIENTS OF A MULTIPARAMETER DECOMPOSITION OF FIELD OF CRACK TIP STRESSES: PHOTOELASTICITY METHOD

2017 ◽  
Vol 23 (1) ◽  
pp. 59-68 ◽  
Author(s):  
L. V. Stepanova ◽  
V. S. Dolgikh
Keyword(s):  
Asymptotic Expansion ◽  
Analytical Solution ◽  
Stress Field ◽  
Infinite Plate ◽  
Crack Tip ◽  
Digital Processing ◽  
Optical Methods ◽  
Collinear Cracks ◽  
Deformable Solid ◽  
Complete Asymptotic Expansion

The purpose of this study is multiparameter asymptotic analysis of the stress field in the immediate vicinity of the crack tip in a linearly elastic material and construction of complete asymptotic expansion of M. Williams stress field in the vicinity of the crack tip. Multiparametric analysis of the stress field is based on the polarization-optical methods of mechanics of a deformable solid (the method of photoelasticity). Digital processing of the results of optoelectronic measurements performed on a series of samples with cracks and notches is carried out. Different classes of samples from optically sensitive materials, in particular a sample with two collinear cracks under conditions of normal detachment, were considered. A set of programs has been prepared that makes it possible to determine the scale (amplitude) multipliers of complete asymptotic expansion of M.Villiams for the stress field at the crack tip. Using the basic law of photoelasticity, first five coefficients of complete asymptotic expansion of M. Williams are calculated. The results of the experiments are compared with the available analytical solution. It is shown that the results of processing optoelectronic measurements are in good agreement with the analytical solution obtained for an infinite plate with two collinear cracks.

scholarly journals Analytical Investigation of Viscoelastic Stagnation-Point Flows with Regard to Their Singularity

2021 ◽  
Vol 11 (15) ◽  
pp. 6931
Author(s):  
Jie Liu ◽  
Martin Oberlack ◽  
Yongqi Wang
Keyword(s):  
Stress Distribution ◽  
Stress Field ◽  
Stagnation Point ◽  
Analytical Solutions ◽  
Wide Spectrum ◽  
Momentum Conservation ◽  
Stagnation Point Flow ◽  
Model Parameters ◽  
Viscoelastic Models ◽  
Special Cases

Singularities in the stress field of the stagnation-point flow of a viscoelastic fluid have been studied for various viscoelastic constitutive models. Analyzing the analytical solutions of these models is the most effective way to study this problem. In this paper, exact analytical solutions of two-dimensional steady wall-free stagnation-point flows for the generic Oldroyd 8-constant model are obtained for the stress field using different material parameter relations. For all solutions, compatibility with the conservation of momentum is considered in our analysis. The resulting solutions usually contain arbitrary functions, whose choice has a crucial effect on the stress distribution. The corresponding singularities are discussed in detail according to the choices of the arbitrary functions. The results can be used to analyze the stress distribution and singularity behavior of a wide spectrum of viscoelastic models derived from the Oldroyd 8-constant model. Many previous results obtained for simple viscoelastic models are reproduced as special cases. Some previous conclusions are amended and new conclusions are drawn. In particular, we find that all models have singularities near the stagnation point and most of them can be avoided by appropriately choosing the model parameters and free functions. In addition, the analytical solution for the stress tensor of a near-wall stagnation-point flow for the Oldroyd-B model is also obtained. Its compatibility with the momentum conservation is discussed and the parameters are identified, which allow for a non-singular solution.

scholarly journals Analytical corrections for double-cantilever beam tests

2021 ◽  
Author(s):  
T. Chen ◽  
C. M. Harvey ◽  
S. Wang ◽  
V. V. Silberschmidt
Keyword(s):  
Elastic Foundation ◽  
Analytical Solutions ◽  
Data Reduction ◽  
Crack Tip ◽  
Beam Theory ◽  
Dynamic Loads ◽  
Structural Vibration ◽  
Mode I ◽  
Mode I Fracture ◽  
Reduction Methods

AbstractDouble-cantilever beams (DCBs) are widely used to study mode-I fracture behavior and to measure mode-I fracture toughness under quasi-static loads. Recently, the authors have developed analytical solutions for DCBs under dynamic loads with consideration of structural vibration and wave propagation. There are two methods of beam-theory-based data reduction to determine the energy release rate: (i) using an effective built-in boundary condition at the crack tip, and (ii) employing an elastic foundation to model the uncracked interface of the DCB. In this letter, analytical corrections for a crack-tip rotation of DCBs under quasi-static and dynamic loads are presented, afforded by combining both these data-reduction methods and the authors’ recent analytical solutions for each. Convenient and easy-to-use analytical corrections for DCB tests are obtained, which avoid the complexity and difficulty of the elastic foundation approach, and the need for multiple experimental measurements of DCB compliance and crack length. The corrections are, to the best of the authors’ knowledge, completely new. Verification cases based on numerical simulation are presented to demonstrate the utility of the corrections.

The Analysis of the Stress Field and Crack of Rock under the Blast Loading

2010 ◽  
Vol 168-170 ◽  
pp. 1252-1255
Author(s):  
Zhong Guo Zhang ◽  
Ya Dong Bian ◽  
Bin Gao
Keyword(s):  
Stress Field ◽  
Crack Initiation ◽  
Crack Extension ◽  
Crack Tip ◽  
Blast Loading ◽  
Crack Arrest ◽  
The Stability ◽  
Crack Tip Stress

The crack tip stress field of rock is analyzed under blast loading, and the crack arrest criterion, the conditions of rock crack initiation and crack extension are presented in this paper. The study will help the design of maintaining the stability of stope drift active workings.

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