scholarly journals The Analysis of a Cracked Material under Combined Unsymmetric Thermal Flux and Symmetric Linear Mechanical Loading

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
B. Wu ◽  
Q. A. Huang ◽  
D. Peng ◽  
X. Y. Yang ◽  
Z. Feng
Keyword(s):  
Mechanical Loading ◽  
Isotropic Material ◽  
Thermal Flux ◽  
Mode Ii ◽  
Crack Model ◽  
Single Crack ◽  
Permeable Crack ◽  
Fracture Parameters ◽  
Thermoelastic Field ◽  
The Fourier Transform

An improved partially permeable crack model is put forward to deal with the problem of a single crack embedded in an orthotropic or isotropic material under combined unsymmetric thermal flux and symmetric linear mechanical loading. With the application of the Fourier transform technique (FTT), the thermoelastic field is given in a closed form. Numerical results show combined unsymmetric linear thermal flux, symmetric linear mechanical loading, and dimensionless thermal conductivity, and the coefficient has influences on fracture parameters. For the improved partially permeable crack, the mode II stress intensity factor and the energy release rate might be zero or positive under combined unsymmetric thermal flux and symmetric linear mechanical loading. Therefore, closure of the crack tip region need not be considered under combined unsymmetric thermal flux and symmetric linear mechanical loading when making use of fracture parameters as a criterion.

Solution for a Semi-Permeable Interface Crack in Elastic Dielectric/Piezoelectric Bimaterials

2008 ◽  
Vol 75 (1) ◽  
Author(s):  
Q. Li ◽  
Y. H. Chen
Keyword(s):  
Electric Field ◽  
Mechanical Loading ◽  
Interface Crack ◽  
Applied Electric Field ◽  
Crack Tip ◽  
Crack Model ◽  
Permeable Crack ◽  
Impermeable Crack ◽  
Silicon Oil ◽  
Elastic Dielectric

A semi-permeable interface crack in infinite elastic dielectric/piezoelectric bimaterials under combined electric and mechanical loading is studied by using the Stroh complex variable theory. Attention is focused on the influence induced from the permittivity of the medium inside the crack gap on the near-tip singularity and on the energy release rate (ERR). Thirty five kinds of such bimaterials are considered, which are constructed by five kinds of elastic dielectrics and seven kinds of piezoelectrics, respectively. Numerical results for the interface crack tip singularities are calculated. We demonstrate that, whatever the dielectric phase is much softer or much harder than the piezoelectric phase, the structure of the singular field near the semi-permeable interface crack tip in such bimaterials always consists of the singularity r−1∕2 and a pair of oscillatory singularities r−1∕2±iε. Calculated values of the oscillatory index ε for the 35 kinds of bimaterials are presented in tables, which are always within the range between 0.046 and 0.088. Energy analyses for five kinds of such bimaterials constructed by PZT-4 and the five kinds of elastic dielectrics are studied in more detail under four different cases: (i) the crack is electrically conducting, (ii) the crack gap is filled with air/vacuum, (iii) the crack gap is filled with silicon oil, and (iv) the crack is electrically impermeable. Detailed comparisons on the variable tendencies of the crack tip ERR against the applied electric field are given under some practical electromechanical loading levels. We conclude that the different values of the permittivity have no influence on the crack tip singularity but have significant influences on the crack tip ERR. We also conclude that the previous investigations under the impermeable crack model are incorrect since the results of the ERR for the impermeable crack show significant discrepancies from those for the semi-permeable crack, whereas the previous investigations under the conducting crack model may be accepted in a tolerant way since the results of the ERR show very small discrepancies from those for the semi-permeable crack, especially when the crack gap is filled with silicon oil. In all cases under consideration the curves of the ERR for silicon oil are more likely tending to those for the conducting crack rather than to those for air or vacuum. Finally, we conclude that the variable tendencies of the ERR against the applied electric field have an interesting load-dependent feature when the applied mechanical loading increases. This feature is due to the nonlinear relation between the normal electric displacement component and the applied electromechanical loadings from a quadratic equation.

scholarly journals Fracture Analysis for a Crack in Orthotropic Material Subjected to Combined 2i-Order Symmetrical Thermal Flux and 2j-Order Symmetrical Mechanical Loading

2021 ◽  
Vol 2 (1) ◽  
pp. 127-146
Author(s):  
Bing Wu ◽  
Daren Peng ◽  
Rhys Jones
Keyword(s):  
Mechanical Loading ◽  
Polynomial Function ◽  
Mechanical Load ◽  
Thermal Flux ◽  
Great Influence ◽  
Fracture Analysis ◽  
Orthotropic Materials ◽  
Crack Model ◽  
Fracture Parameter ◽  
Order Polynomial

The problems of crack formation in orthotropic materials under 2i order polynomial function heat flow and 2j order polynomial function mechanical loading are considered. An extended local insulation crack model is proposed, and fracture analysis is carried out for the above problems. Utilizing Fourier transform technique (FTT) and principle of superposition, the jumps of temperature, elastic displacements on the crack, and so on are obtained. The advantage of this analysis is that the explicit closed form solutions of main parameters in classical fracture mechanics, i.e., the stress intensity factor, the energy release rate, and the energy density have been presented. A simple example is used to demonstrate the method proposed in this paper. The analysis results show that the non-dimensional thermal conductivity and the combined ratio of the heat flux per thickness perpendicular to the crack surface to the mechanical load have a great influence on the calculation of fracture parameters. Only when they meet certain conditions can the correct fracture parameter calculation results be obtained.

Fracture Resistance of AAAS Composites with Ceramic Precursor

2021 ◽  
Vol 322 ◽  
pp. 54-59
Author(s):  
Iva Rozsypalová ◽  
Petr Daněk ◽  
Pavla Rovnaníková ◽  
Zbyněk Keršner
Keyword(s):  
Mouth Opening ◽  
Crack Model ◽  
Arithmetic Means ◽  
Mechanical Fracture ◽  
Three Point Bending ◽  
Static Modulus ◽  
Fracture Parameters ◽  
Ceramic Precursors ◽  
Static Modulus Of Elasticity

The paper deals with selected alkali-activated aluminosilicate (AAAS) composites based on ceramic precursors in terms of their characterization by mechanical fracture parameters. Composites made of brick dust as a precursor and an alkaline activator with a silicate modulus of Ms = 0.8, 1.0, 1.2, 1.4 and 1.6 were investigated. The filler employed with one set of composites was quartz sand, while for the other set it was crushed brick. The test specimens had nominal dimensions of 40 × 40 × 160 mm and were provided with notches at midspan of up to 1/3 of the height of the specimens after 28 days. 6 samples from each composite were tested. The specimens were subjected to three-point bending tests in which force vs. displacement (deflection at midspan) diagrams (F–d diagrams) and force vs. crack mouth opening (F–CMOD) diagrams were recorded. After the correction of these diagrams, static modulus of elasticity, effective fracture toughness, effective toughness and specific fracture energy values were determined using the Effective Crack Model and the Work-of-Fracture method. After the fracture experiments, informative compressive strength values were determined from one of the parts. All of the evaluations included the determination of arithmetic means and standard deviations. The silicate modulus values and type of filler of the AAAS composites significantly influenced their mechanical fracture parameters.

On Global Energy Release Rate of a Permeable Crack in a Piezoelectric Ceramic

2003 ◽  
Vol 70 (2) ◽  
pp. 246-252 ◽  
Author(s):  
S. Li
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Crack Growth ◽  
Release Rate ◽  
Piezoelectric Ceramic ◽  
Piezoelectric Materials ◽  
Dielectric Medium ◽  
Crack Model ◽  
Permeable Crack ◽  
Global Energy

A permeable crack model is proposed to analyze crack growth in a piezoelectric ceramic. In this model, a permeable crack is modeled as a vanishing thin, finite dimension, rectangular slit with dielectric medium inside. A first-order approximation solution is derived in terms of the slit height, h0. The main contribution of this paper is that the newly proposed permeable crack model reveals that there exists a realistic leaky mode for electrical field, which allows applied electric field passing through the dielectric medium inside a crack. By taking into account the leaky mode effect, a correct estimation of electrical and mechanical fields in front of a crack tip in a piezoelectric ceramic is obtained. To demonstrate this new finding, a closed-form solution is obtained for a mode III permeable crack under both mechanical as well electrical loads. Both local and global energy release rates are calculated based on the permeable crack solution obtained. It is found that the global energy release rate derived for a permeable crack is in a broad agreement with some known experimental observations. It may be served as a fracture criterion for piezoelectric materials. This contribution reconciles the outstanding discrepancy between experimental observation and theoretical analysis on crack growth problem in piezoelectric materials.

Modelling of Thermal Fracture of Functionally Graded/Homogeneous Bimaterial Structures under Thermo-Mechanical Loading

2013 ◽  
Vol 592-593 ◽  
pp. 145-148 ◽  
Author(s):  
Vera Petrova ◽  
Siegfried Schmauder
Keyword(s):  
Mechanical Loading ◽  
Thermal Loading ◽  
Thermal Flux ◽  
Integral Equation Method ◽  
Functionally Graded ◽  
Thermal Fracture ◽  
Fracture Characteristics ◽  
Main Fracture ◽  
Graded Material ◽  
Actual Material

Mathematical modeling of thermal fracture of functionally graded/homogeneous bimaterial structures with a system of arbitrarily located cracks is performed and based on the previously suggested theoretical approach [1-which used the integral equation method. It is supposed that the structure is subjected to thermal loading (a thermal flux) and mechanical loading (a tension). The properties of the functionally graded material (FGM) are described by a continuous exponential function. The main fracture characteristics (stress intensity factors and fracture angles) are presented as functions of the geometry of the problem and special inhomogeneity parameters of FGMs. Some typical crack patterns for FGM/homogeneous bimaterial structures resulting from experiments available in literature are studied in detail. Thermal fracture of actual material combinations of FGMs such as: ceramic/ceramic, e.g., TiC/SiC, MoSi2/Al2O3and MoSi2/SiC, and also ceramic/metal FGMs, e.g., zirconia/nickel and zirconia/steel, is investigated.

Fracture Parameters of Alkali-Activated Aluminosilicate Composites with Ceramic Precursor

2020 ◽  
Vol 309 ◽  
pp. 73-79
Author(s):  
Hana Šimonová ◽  
Ivana Kumpová ◽  
Iva Rozsypalová ◽  
Patrik Bayer ◽  
Petr Frantik ◽  
...  
Keyword(s):  
Fracture Process ◽  
Fracture Process Zone ◽  
Process Zone ◽  
Mouth Opening ◽  
Crack Mouth Opening Displacement ◽  
Crack Model ◽  
Mechanical Fracture ◽  
Ceramic Precursor ◽  
Fracture Parameters ◽  
Alkali Activated

This paper deals with selected alkali-activated aluminosilicate composites with a ceramic precursor in terms of their characterization using mechanical fracture parameters. Three composites were studied. They were manufactured using brick powder as a precursor and an alkaline activator with a dimensionless silicate modulus of Ms = 1.0, 1.2 and 1.4. The test specimens were nominally 40 × 40 × 160 mm in size and had a central edge notch with a depth of 1/3 of the specimen’s height. At least 6 specimens made of each composite were tested at the age of 28 days. The specimens were subjected to three-point bending tests, during which diagrams showing force vs. deflection at midspan (F–d diagrams) and force vs. crack mouth opening displacement (F–CMOD diagrams) were recorded. After the processing of these diagrams, values were determined for the static modulus of elasticity, effective fracture toughness (including its initiation component from the analysis of the first part of the F–CMOD diagrams), effective toughness and specific fracture energy using the effective crack model, Work-of-Fracture method, and Double-K fracture model. After the fracture experiments had been performed, compressive strength values were determined for informational purposes from one part of each specimen that remained after testing. In order to obtain visual information about the internal structure of the composites before and after the mechanical testing, the selected specimen was examined via X-ray microtomography. Tomographic measurements and image processing were performed for the qualitative and quantitative evaluation of internal structural changes with an emphasis on the calculation of porosimetry parameters as well as the visualization of the fracture process zone. The fractal dimension of the fracture surface and fracture process zone was determined. The porosity and microstructure images of selected samples taken from specimens were assessed.

Identification of AAAS Composites Mechanical Fracture Parameters

2021 ◽  
Vol 322 ◽  
pp. 66-71
Author(s):  
Martin Lipowczan ◽  
David Lehký ◽  
Iva Rozsypalová ◽  
Petr Daněk ◽  
Pavla Rovnaníková ◽  
...  
Keyword(s):  
Fracture Energy ◽  
Modulus Of Elasticity ◽  
Crack Mouth Opening Displacement ◽  
Crack Model ◽  
Mechanical Fracture ◽  
Specific Fracture Energy ◽  
Static Modulus ◽  
Fracture Parameters ◽  
Static Modulus Of Elasticity ◽  
Specific Fracture

The paper deals with selected alkali-activated aluminosilicate (AAAS) composites based on ceramic precursors in terms of characterization by mechanical fracture parameters. Two composites made of brick dust as a precursor and an alkaline activator with a silicate modulus Ms = 1.0 were investigated. The composites differed in the fineness of grinding of the precursor – in the first set it was 0 to 1 mm, in the second set 0 to 0.3 mm. The filler was crushed brick. The test specimens had nominal dimensions of 40 × 40 × 160 mm and were provided with notches in the middle of the span up to 1/3 of the depth of the specimens after 28 days of hardening. Five to six specimens from each composite set were tested. The specimens were subjected to three-point bending tests, in which force vs. displacement (deflection in the middle of the span) diagrams (F–d diagrams) and force vs. crack mouth opening displacement (F–CMOD) diagrams were recorded. After correction of these diagrams, the values of static modulus of elasticity, effective fracture toughness, effective toughness and specific fracture energy were determined using the Effective Crack Model and the Work-of-Fracture method. After the fracture experiments, the values of informative compressive strength were determined on one of the fractured parts. At the same time, the values of static modulus of elasticity, tensile strength and specific fracture energy were identified using artificial neural networks and F–d diagrams measured and simulated in the ATENA FEM software. All evaluations included the determination of basic statistics of parameters.

scholarly journals Components of the Fracture Response of Alkali-Activated Slag Composites with Steel Microfibers

2019 ◽  
Vol 9 (9) ◽  
pp. 1754 ◽  
Author(s):  
Hana Šimonová ◽  
Petr Frantík ◽  
Zbyněk Keršner ◽  
Pavel Schmid ◽  
Pavel Rovnaník
Keyword(s):  
Mouth Opening ◽  
Crack Mouth Opening Displacement ◽  
Model Parameters ◽  
Crack Model ◽  
Mechanical Fracture ◽  
Alkali Activated Slag ◽  
Fracture Parameters ◽  
Fracture Tests ◽  
Activated Slag ◽  
Alkali Activated

Knowledge of the mechanical and primarily fracture parameters of composites with a brittle matrix is essential for the quantification of their resistance to crack initiation and growth, and also for the specification of material model parameters employed for the simulation of the quasi-brittle behavior of structures made from this type of composite. Therefore, the main target of this paper is to quantify the mechanical fracture parameters of alkali-activated slag composites with steel microfibers and the contribution of the matrix to their fracture response. The first alkali-activated slag composite was a reference version without fibers; the others incorporated steel microfibers amounting to 5, 10, 15 and 20% by weight of the slag. Prism specimens with an initial central edge notch were used to perform the three-point bending fracture tests. Load vs. displacement (deflection at midspan) and load vs. crack mouth opening displacement diagrams were recorded during the fracture tests. The obtained diagrams were employed as inputs for parameter identification, the aim of which was to transfer the fracture test response data to the desired material parameters. Values were also determined for fracture parameters using the effective crack model, work-of-fracture method and double-K fracture model. All investigated mechanical fracture parameters were improved by the addition of steel microfibers to the alkali-activated matrix. Based on the obtained results, the addition of 10 to 15% of microfibers by weight is optimal from the point of view of the enhancement of the fracture parameters of alkali-activated slag composite.

Fracture Parameters on Three-Dimensional Sliding Mode Fracture

2007 ◽  
Vol 340-341 ◽  
pp. 447-452
Author(s):  
Fei Xu ◽  
Yu Long Li ◽  
Wan Lin Guo
Keyword(s):  
Sliding Mode ◽  
Three Dimensional ◽  
Mode Ii ◽  
Stress And Strain ◽  
J Integral ◽  
Mode Fracture ◽  
Fracture Parameters ◽  
T Stress ◽  
Mode Ii Loading ◽  
Different Thickness

In the recent years three-dimensional (3D) elastic-plastic analyses have been conducted extensively for the opening mode (mode I) fracture and the constraint effects are discussed in detail. However less work is focused on other modes as sliding mode (mode II), tearing mode (mode III) or the mixed mode fracture in three-dimensional. In this paper the thickness effect on pure mode II case is discussed by the finite element method (FEM). Modified Boundary Layer (MBL) model is used, which has the ability to take into account the combined effects of the in-plane constraint (T-stress) and the out-of-plane constraint (finite thickness). The result demonstrates the weak thickness dependence on the near tip stress and strain fields under mode II loading. And the size of the 3D zone at mode II loading is determined to range from 1.0 to 1.2 times the thickness. Two fracture parameters of J integral and crack tip sliding displacement (CTSD) are discussed, which are almost same at different thickness planes except those very near the surface. It is interesting to find that the relations between J and CTSD keep linear at different thickness planes. T-stress is symmetry on stress and strain distributions along the crack plane. However its effects indicate weak thickness dependent on the CTSD and J integral fracture parameter.

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