scholarly journals A Macro–Micro Damage Model for Rock under Compression Loading

2021 ◽  
Vol 11 (24) ◽  
pp. 12154
Author(s):  
Zhixiong Peng ◽  
Yawu Zeng ◽  
Xi Chen ◽  
Shufan Cheng

Rock damage caused by its microcrack growth has a great influence on the deformation and strength properties of rock under compressive loading. Considering the interaction of wing cracks and the additional stress caused by rock bridge damage, a new calculation model for the mode-I stress intensity factor at wing crack tip was proposed in this study. The proposed calculation model for the stress intensity factor can not only accurately predict the cracking angle of wing crack, but can also simulate the whole range of variation of wing crack length from being extremely short to very long. Based on the modified stress intensity factor, a macro–micro damage model for rock materials was also established by combining the relationship between microcrack growth and macroscopic strain. The proposed damage model was verified with the results from the conventional triaxial compression test of sandstone sample. The results show that the proposed damage model can not only continuously simulate the stress-strain curves under different confining pressures, but also can better predict the peak strength. Furthermore, the sensitivities of initial crack size, crack friction coefficient, fracture toughness, initial damage and parameter m on the stress-strain relationship are discussed. The results can provide a theoretical reference for understanding the effect of microcrack growth on the progressive failure of rock under the compressive loading.

2012 ◽  
Vol 166-169 ◽  
pp. 2929-2932
Author(s):  
Ya Zhen Sun ◽  
Xiao Xing Zhai ◽  
Jie Min Liu

This paper analyzed the failure mode for crack in uniaxial compression according to the stress intensity factor, and obtain that the failure mode for crack in uniaxial compression is compression-shear. The wing crack was deformed, after the crack tip initiate. By analyzing the dimensionless stress intensity factor, we obtain that the failure mode for wing crack in uniaxial compression is tension-shear, and we obtain that the dimensionless stress intensity factor for wing crack decreased with inclined angle increased. The inclined crack propagation in uniaxial compression was numerically studied using rock failure process analysis code (rfpa), and obtain that one inclined crack in uniaxial compression formed mode I offset crack parallel to load direction in the end. The numerical results of failure mode are accordance with stress intensity factor.


1987 ◽  
Vol 54 (1) ◽  
pp. 54-58 ◽  
Author(s):  
M. Ortiz

A phenomenological constitutive model is proposed which aims at describing the overall effect of microfracture in ceramics. Based on this model, the asymptotic stress, strain, and displacement fields at the tip of a stationary macroscopic crack are determined in closed form. The near-tip stress-intensity factor is computed and observed to be significantly smaller than the applied stress-intensity factor even for moderate amounts of damage.


2019 ◽  
Vol 24 (10) ◽  
pp. 3216-3230 ◽  
Author(s):  
S Kozinov ◽  
A Sheveleva ◽  
V Loboda

A closed-form solution is constructed for a bi-material consisting of two piezoelectric (or piezoelectric and dielectric) half-planes, which are periodically bonded along the interface and can partially contact along the initially unbonded parts. Under compressive loading, the size of the frictionless contact zone is usually quite large; in some cases the interface is completely closed. Such a situation is frequently observed in industrial applications. Since the periodic bonding of two different materials is extremely widespread, it is very important to study the influence of the mutual material properties of the composite and the applied loading on the size and shape of the opened regions, as well as the stress intensity factor at the bonding points. To formulate the problem, the electromechanical factors are presented through piecewise analytic functions, so that the problem in question is reduced to the combined periodic Dirichlet–Riemann problem, which is solved exactly. The obtained solution provides explicit formulas for the mechanical stresses and displacements along the interface and allows one to find the dependence of the contact zones and the stress intensity factor on the ratio of the bonded parts of the interface to the period for the different values of applied loading and materials.


2017 ◽  
Vol 2 (87) ◽  
pp. 56-65 ◽  
Author(s):  
T.M. Lenkovskiy ◽  
V.V. Kulyk ◽  
Z.A. Duriagina ◽  
R.A. Kovalchuk ◽  
V.G. Topilnytskyy ◽  
...  

Purpose: To create an effective in engineering strength calculation three-dimensional submodel of the near crack tip region in solids for hi-fidelity analysis of their stress-strain state by the finite element method. Design/methodology/approach: To create a volume near the crack tip, regular threedimensional 20-node prismatic isoparametric elements and 15-node special elements with edge length of 12.5 μm with shifted nodes in order to simulate the singularity of stress at the crack tip were used. Using these two types of elements, a cylindrical fragment of diameter of 100 μm was built. In its base is a 16-vertex polygon, and its axis is the crack front line. In the radial direction the size of the elements was smoothly enlarged by creating of 5 circular layers of elements, and in the axial direction 8 layers were created. For convenience of the sub-model usage, the cylindrical fragment was completed by regular elements to a cubic form with edge size 400 μm. For the sub-model approbation, the full-scale three-dimensional models of standard specimens with cracks were built. The stress intensity factor K at normal tension was calculated assuming small scale yielding conditions in a plane between 4th and 5th layers of special elements on the basis of analysis of displacement fields near the crack tip. Findings: An effective three-dimensional sub-model of the near crack tip region is proposed. The sub-model was used to obtain the dependence of the stress intensity factor on the relative crack length at normal tension for four types of standard specimens. The obtained dependences show excellent correlation with known analytical solutions. Research limitations/implications: The concept of finite element meshing at threedimensional modelling of the near crack tip region for high-fidelity stress-strain state analysis was generalized. A sub-model of the near crack tip region was created and used to determine the stress intensity factor at normal tension of four types of standard specimens. It is shown that the proposed methodology is effective for precise analysis of the stressstrain state of solids with cracks within the framework of linear fracture mechanics. Practical implications: By applying the generalized approach and the proposed threedimensional sub-model of the near crack tip region, one can determine the stress-strain state of structure elements and machine parts when analysing their workability by the finite element method. Originality/value: An effective finite-element sub-model for the stress-strain state analysis in the vicinity of the crack tip within the framework of the linear fracture mechanics is proposed.


Author(s):  
D. E. Tulin ◽  

The study of the elastic and elastoplastic stress-strain state of a plate with a semi-elliptical crack when changing its geometry has been carried out. The process of transition of a semi-elliptical crack into a through one was considered. Options of the stress-strain state were determined by means of the FEA method. An approximating dependence of the stress intensity factor on geometry of the plate is suggested. Keywords: strength, semi-elliptical crack, K-calibration, stress intensity factor, elastoplastic deformation, stress state intensity.


Author(s):  
T.M. Lenkovskiy ◽  
V.V. Kulyk ◽  
Z.A. Duriagina ◽  
L.V. Dzyubyk ◽  
V.V. Vira ◽  
...  

Purpose: Carefully investigate the stress-strain state of the side grooved I-beam specimen with edge crack and determine the effect of crack length and crack faces friction on stress intensity factor at transverse shear. Design/methodology/approach: The finite element method was used to estimate the stress-strain state of I-beam specimen at transverse shear. For this purpose, a fullscale, three-dimensional model of the specimen was created, which precisely reproduces its geometry and fatigue crack faces contact. For the correct reproduction of the stress singularity at the crack tip, a special sub-model was used, which has been tested earlier in solving similar problems of fracture mechanics. In order to improve the accuracy of the calculations, for crack plane and cross-section of the specimen on the crack extension modeling, an algorithm for changing the crack length without changing the total number of elements in the model was developed and applied. Young's modulus and Poisson's ratio of structural steels were specified for the model material. The static loading of the model was realized assuming small scale yielding condition. The stress intensity factor was found through the displacement of nodes in the prismatic elements adjacent to the plane and the front of the crack. Findings: Mathematical dependences, which show an increase of stress intensity factor in the I-beam specimen with an increase in the crack length, and its decrease with an increase of crack faces friction factor at transverse shear, were established. The results are compared with the partial cases known from the literature and their good convergence was shown. Research limitations/implications: By analyzing the obtained graphical dependences, it is established that for relative crack lengths less than 0.4 there is a significant influence of the initial notch on the stress-strain state of the specimen, and for the lengths greater than 0.9 an influence of constrained gripping part took place. For this reason, all subsequent calculations were carried out in the range of relative crack length from 0.4 to 0.9, which represents the applicability range of the final calculation formula. Increasing of the crack faces friction factor from 0 to 1 monotonically reduces the stress at the crack tip. For a short crack, this effect is 1.5 times greater than for a long one, which is reflected by the calculation formula. Practical implications: Using the proposed calculation formula, one can calculate the stress intensity factor in the I-beam specimen, and to determine the crack growth resistance characteristics of structural steels at transverse shear. Originality/value: A new, easy-to-use in engineering calculations formula is proposed for stress intensity factor determination in the I-beam specimen at transverse shear. The formula takes into account crack faces friction for various crack lengths.


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