Experimental Investigation of T-Stress Effects on Photoelastic Fringes in Brazilian Disk under Mode II Conditions

2007 ◽  
Vol 348-349 ◽  
pp. 969-972
Author(s):  
Mario Guagliano ◽  
Majid R. Ayatollahi ◽  
Mahnaz Zakeri ◽  
Chiara Colombo
Keyword(s):  
Mode Ii ◽  
Pure Mode ◽  
Brazilian Disk ◽  
Stress Effects ◽  
Stress Changes ◽  
Isochromatic Fringes ◽  
Theoretical Predictions ◽  
T Stress ◽  
Fringe Patterns ◽  
Definition Of

According to classical definition of crack deformation modes, the constant stress term (Tstress) exists only in presence of mode I. However, some studies show that this term can exist in mode II problems as well; and significantly affect the elastic stress field around the crack tip. Based on the previous analytical results, T-stress changes the photoelastic fringe patterns from symmetric closed shapes to asymmetric and discontinuous loops. In this research, the effects of T-stress on the fringe patterns in mode II cracks is investigated experimentally. Test specimens are Brazilian disks made of polycarbonate, and thermal treatment is performed to remove the residual stresses after generation of the cracks. Observed isochromatic fringes are in good agreement with theoretical predictions. Also, experimental results indicate that this specimen contains a negative T-stress in pure mode II condition.

T-Stress Effects on Isochromatic Fringe Patterns in Mode II

2007 ◽  
Vol 143 (2) ◽  
pp. 189-194 ◽  
Author(s):  
M. R. Ayatollahi ◽  
Mahnaz Zakeri
Keyword(s):  
Mode Ii ◽  
Isochromatic Fringe ◽  
Stress Effects ◽  
T Stress ◽  
Fringe Patterns

Theoretical Error Analysis of the T-Stress for a Central Cracked Brazilian Disk Specimen

2020 ◽  
Vol 12 (05) ◽  
pp. 2050058 ◽  
Author(s):  
Wen Hua ◽  
Jianxiong Li ◽  
Jiuzhou Huang ◽  
Shiming Dong
Keyword(s):  
Error Analysis ◽  
Crack Length ◽  
Inclination Angle ◽  
Length Ratio ◽  
Closed Form Expression ◽  
Pure Mode ◽  
Brazilian Disk ◽  
T Stress ◽  
The Impact ◽  
Stress Error

The central cracked Brazilian disk (CCBD) specimen is one of the most favored samples to measure the combined mode fracture resistance of brittle materials. The T-stress in this sample has a great influence on the experimental results, which are extensively used in fracture criteria for evaluating the fracture behavior of CCBD specimens for different materials. Due to the errors in geometric dimension and crack inclination angle for CCBD specimens, it becomes essential to conduct error analysis of T-stress. In this work, a closed-form expression of T-stress for a CCBD specimen under radial concentrated force was presented with weight function method. Based on this expression, two error transfer functions were also derived to study the T-stress error caused by the errors of crack length ratio and crack inclination angle. The theoretical analysis indicated that the relative error of T-stress increases with the increase of crack length ratio and crack inclination angle under the combined modes I and II. It was also found that the crack length ratio has a very little impact on the T-stress error for pure mode I loading. Furthermore, T-stress is more sensitive to the impact of crack length ratio than pure mode II stress intensity factor (SIF).

Effect of Confining Pressure on Stress Intensity Factors for Cracked Brazilian Disk

2015 ◽  
Vol 07 (03) ◽  
pp. 1550051 ◽  
Author(s):  
Wen Hua ◽  
Jigang Xu ◽  
Shiming Dong ◽  
Jizhou Song ◽  
Qingyuan Wang
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Stress Intensity Factors ◽  
Confining Pressure ◽  
Mode Ii ◽  
Pure Mode ◽  
Intensity Factors ◽  
Brazilian Disk ◽  
Mode Ii Crack

An analytical model, verified by the finite element method, is developed to study the effect of confining pressure on stress intensity factors for the cracked Brazilian disk. The closed-form expressions for stress intensity factors under both confining pressure and diametric forces are obtained based on the weight function method. The results show that the confining pressure has no effect on the mode II stress intensity factor; however, the mode I stress intensity factor decreases with the increase of confining pressure and the change may be above 100% for a large confining pressure. In addition, the effect of confining pressure on the loading condition of pure mode II crack is also investigated. It is shown that the critical loading angle for pure mode II crack decreases as the confining pressure increases. Depending on the magnitude of confining pressure, the failure problem of a disk may be no longer a pure fracture problem. These results have established the theoretical foundation to measure the fracture toughness of materials under confining pressure.

Finite Element Analysis of an Improved Center Crack Specimen

2007 ◽  
Vol 347 ◽  
pp. 441-446
Author(s):  
Majid R. Ayatollahi ◽  
M.R.M. Aliha ◽  
S. Rahmanian
Keyword(s):  
Finite Element ◽  
Stress Component ◽  
Full Range ◽  
Mode Ii ◽  
Pure Mode ◽  
The Finite Element Method ◽  
Singular Stress ◽  
Element Analysis ◽  
Center Crack ◽  
T Stress

A new crack specimen called the diagonally loaded square plate (DLSP) containing an angled central crack is analyzed using the finite element method. The stress intensity factors and the T-stress are calculated for the new specimen in the full range from pure mode I to pure mode II. Unlike the conventional center cracked specimen under uniaxial loading, the improved specimen is able to provide pure mode II. It is shown that the effect of non-singular stress component T in the DLSP specimen is not ignorable relative to the singular stress terms, particularly for mode II dominated loading conditions.

Mode I and Mode II Fracture Toughness Testing for a Coarse Grain Marble

2006 ◽  
Vol 5-6 ◽  
pp. 181-188 ◽  
Author(s):  
M.R.M. Aliha ◽  
R. Ashtari ◽  
Majid R. Ayatollahi
Keyword(s):  
Fracture Toughness ◽  
Coarse Grain ◽  
Mode I ◽  
Mode Ii ◽  
Pure Mode ◽  
Mode I Fracture ◽  
Mode Ii Fracture ◽  
Mode I Fracture Toughness ◽  
Mode Ii Fracture Toughness ◽  
T Stress

A series of fracture toughness tests have been conducted on a type of coarse grain marble. The tests were carried out either in pure mode I or in pure mode II conditions by using the cracked chevron notched Brazilian disc (CCNBD) specimen. A total number of 44 CCNBD specimens were tested, half in pure mode I and the rest in pure mode II, to obtain reliable values for mode I and mode II fracture toughness (KIc and KIIc) of the tested marble. The average value of KIc for this marble was approximately about 1.12 MPa m showing a good agreement with those reported for similar coarse grain marbles. The mode II fracture toughness was found to be 2.25 MPa m in average which is approximately twice the mode I fracture toughness. However, the conventional fracture criteria suggest that the mode I fracture toughness should be higher than the mode II fracture toughness, (KIc>KIIc). According to these criteria, the ratio of KIIc / KIc is a figure typically between 0.63 and 0.96. It is shown in this paper that enhanced mode II fracture toughness of CCNBD specimen could be due to the effects of highly negative T-stress when the specimen is subjected to mode II. It is also shown that an improved prediction for the ratio KIIc / KIc can be achieved when the effect of T-stress is taken into account.

scholarly journals Mixed-Mode Interlaminar Fracture Toughness of Glass and Carbon Fibre Powder Epoxy Composites—For Design of Wind and Tidal Turbine Blades

Materials ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2103
Author(s):  
Christophe Floreani ◽  
Colin Robert ◽  
Parvez Alam ◽  
Peter Davies ◽  
Conchúr M. Ó. Brádaigh
Keyword(s):  
Fracture Toughness ◽  
Carbon Fibre ◽  
Composite Structures ◽  
Mixed Mode ◽  
Epoxy Composites ◽  
Mode I ◽  
Mode Ii ◽  
Pure Mode ◽  
Interlaminar Fracture Toughness ◽  
Interlaminar Fracture

Powder epoxy composites have several advantages for the processing of large composite structures, including low exotherm, viscosity and material cost, as well as the ability to carry out separate melting and curing operations. This work studies the mode I and mixed-mode toughness, as well as the in-plane mechanical properties of unidirectional stitched glass and carbon fibre reinforced powder epoxy composites. The interlaminar fracture toughness is studied in pure mode I by performing Double Cantilever Beam tests and at 25% mode II, 50% mode II and 75% mode II by performing Mixed Mode Bending testing according to the ASTM D5528-13 test standard. The tensile and compressive properties are comparable to that of standard epoxy composites but both the mode I and mixed-mode toughness are shown to be significantly higher than that of other epoxy composites, even when comparing to toughened epoxies. The mixed-mode critical strain energy release rate as a function of the delamination mode ratio is also provided. This paper highlights the potential for powder epoxy composites in the manufacturing of structures where there is a risk of delamination.

scholarly journals Asymptotic analysis for personalized Web search

2010 ◽  
Vol 42 (02) ◽  
pp. 577-604 ◽  
Author(s):  
Yana Volkovich ◽  
Nelly Litvak
Keyword(s):  
Web Search ◽  
Power Laws ◽  
User Preference ◽  
Importance Measure ◽  
Web Documents ◽  
Original Definition ◽  
Theoretical Predictions ◽  
Heavy Tailed ◽  
Definition Of ◽  
Good Agreement

PageRank with personalization is used in Web search as an importance measure for Web documents. The goal of this paper is to characterize the tail behavior of the PageRank distribution in the Web and other complex networks characterized by power laws. To this end, we model the PageRank as a solution of a stochastic equationwhere theRis are distributed asR. This equation is inspired by the original definition of the PageRank. In particular,Nmodels the number of incoming links to a page, andBstays for the user preference. Assuming thatNorBare heavy tailed, we employ the theory of regular variation to obtain the asymptotic behavior ofRunder quite general assumptions on the involved random variables. Our theoretical predictions show good agreement with experimental data.

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