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).

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.

Analysis of Stress Intensity Factor for Cracked Flattened Brazilian Disk: Part I – Analysis Method and Pure Mode I Crack

2012 ◽  
Vol 525-526 ◽  
pp. 85-88 ◽  
Author(s):  
Shi Ming Dong ◽  
Qing Yuan Wang
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Closed Form Expression ◽  
Mode I ◽  
Pure Mode ◽  
Analysis Method ◽  
The Finite Element Method ◽  
Brazilian Disk ◽  
Mode I Loading

In order to solve the problem how to calculate the stress intensity factor for a cracked flattened Brazilian disk under mode I loading, the finite element method was employed to analyze the stress intensity factor for the cracked flattened Brazilian disk under mode I loading, based on the closed-form expression of the stress intensity factor for a cracked Brazilian disk subjected to pressure. The analyzed result shows that within the certain range of the load distribution angle, the formula of the stress intensity factor for the cracked Brazilian disk can be directly used to calculate the stress intensity factor for the cracked flattened Brazilian disk under mode I loading.

scholarly journals Experimental Study on Mixed Mode Fracture Behavior of Sandstone under Water–Rock Interactions

Processes ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 70 ◽  
Author(s):  
Wen Hua ◽  
Jianxiong Li ◽  
Shiming Dong ◽  
Xin Pan
Keyword(s):  
Mechanical Properties ◽  
Fracture Resistance ◽  
Mixed Mode ◽  
Degradation Mechanism ◽  
Mixed Mode Fracture ◽  
Pure Mode ◽  
Brazilian Disk ◽  
Tangential Strain ◽  
Mode Fracture

Water–rock interactions can significantly deteriorate the physical and mechanical properties of rocks, and it has been identified as one of the significant factors influencing the stability and safety of structures in rock–soil engineering. In this study, the fracture mechanical properties of sandstone under periodic water–rock interactions and long-term immersion have been studied with central cracked Brazilian disk specimens. The degradation mechanism of water–rock interactions was also studied using a scanning electron microscope (SEM). Finally, the generalized maximum tangential stress and generalized maximum tangential strain criteria were adopted to evaluate the experimental results. The results show that periodic water–rock interactions can remarkably affect the fracture resistance of sandstone. With the increase in the number of cycles, the pure mode I, pure mode II, and mixed mode fracture toughness decreases greatly, however, the values of KIf/KIC and KIIf/KIC decrease slightly. Furthermore, the fracture resistance of sandstone influenced by cyclic wetting–drying is more significant than long-term immersion. Moreover, the fracture criteria, which considers the effect of T-stress, can reproduce the test results very well.

scholarly journals BER analysis of amplify-and-forward relaying FSO systems using APD receiver over strong atmospheric turbulence channels

2019 ◽  
Vol 9 (5) ◽  
pp. 3678
Author(s):  
Duong Huu Ai ◽  
Van Loi Nguyen
Keyword(s):  
Atmospheric Turbulence ◽  
Closed Form Expression ◽  
Free Space Optical ◽  
Amplify And Forward ◽  
Transmission Distance ◽  
Link Distance ◽  
Optimal Value ◽  
Atmospheric Loss ◽  
The Impact ◽  
Relay Stations

<span lang="EN-US">In this paper, we theoretically analyze the performance of amplify-and-forward (AF) serial relaying free-space optical (FSO) systems using avalanche photodiodes (APD) and subcarrier quadrature amplitude modulation (SC-QAM) over strong atmospheric turbulence channels modelled by gamma-gamma distribution. Closed-form expression for average bit error rate (BER) of system is theoretically derived talking into account APD shot noise, thermal noise as well as the impact of atmospheric loss and turbulence. The numerical results show that using AF relay stations can extend the transmission distance and help to improve performance of FSO system significantly when compared with the direct transmission. Moreover, the selection of APD gain value is indispensable to the system performance. The proposed system could be achieved the best performance by selecting an optimal APD gain value. In addition, the optimal value of APD gain also significantly depends on various conditions, such as link distance, the number of relay stations and APD receiver noise.</span>

Experimental study and numerical simulation of uniaxial compression on artificial rock samples with Z-shaped fractures

2021 ◽  
Author(s):  
Tao Zhou ◽  
Haijun Chen ◽  
Liangxiao Xiong ◽  
Zhongyuan Xu ◽  
Jie Yang ◽  
...  
Keyword(s):  
Elastic Modulus ◽  
Crack Length ◽  
Uniaxial Compression ◽  
Inclination Angle ◽  
Failure Surface ◽  
Peak Strength ◽  
Particle Flow Code ◽  
Compression Tests ◽  
Failure Characteristics ◽  
Change Trend

Abstract To study the influence of the inclination and length of Z-shaped fissures on the mechanical properties and failure characteristics of the rock mass, this study conducts a series of uniaxial compression tests on rock-like materials with prefabricated Z-shaped fractures. In addition, two-dimensional Particle Flow Code software is used to perform uniaxial compression numerical simulations. The results show that when the specified inclination angle γ (γ = 0°, 30° or 45°) of the parallel cracks on both sides remains unchanged, the peak strength and elastic modulus of the sample show an M-shaped change trend with an increase in the inclination angle β of the middle connection crack. When γ = 60° or 90°, however, the peak strength and elastic modulus of the sample show a trend of decreasing, increasing, and then decreasing as β increases. In addition, the peak strength and elastic modulus of the sample decrease with an increase in the crack length. The influence of crack length on the elastic modulus is less than that of compressive strength. Further, the main failure mode of specimens with Z-shaped cracks is determined to be tension–shear mixed failure manifested by crack propagation from the tip of the prefabricated crack to the upper and lower boundaries of the sample. As a result, a through failure surface is formed with the prefabricated crack, which destroys the sample.

Response Properties and Synchronization of Rhythmically Firing Dendritic Neurons

2007 ◽  
Vol 97 (1) ◽  
pp. 208-219 ◽  
Author(s):  
Joshua A. Goldberg ◽  
Chris A. Deister ◽  
Charles J. Wilson
Keyword(s):  
Pyramidal Neurons ◽  
Phase Response Curve ◽  
Qualitative Difference ◽  
Apical Dendrite ◽  
Neuronal Firing ◽  
Closed Form Expression ◽  
Pass Filter ◽  
Cortical Pyramidal Neurons ◽  
The Impact ◽  
High Pass

The responsiveness of rhythmically firing neurons to synaptic inputs is characterized by their phase-response curve (PRC), which relates how weak somatic perturbations affect the timing of the next action potential. The shape of the somatic PRC is an important determinant of collective network dynamics. Here we study theoretically and experimentally the impact of distally located synapses and dendritic nonlinearities on the synchronization properties of rhythmically firing neurons. By combining the theories of quasi-active cables and phase-coupled oscillators we derive an approximation for the dendritic responsiveness, captured by the neuron's dendritic PRC (dPRC). This closed-form expression indicates that the dPRCs are linearly filtered versions of the somatic PRC and that the filter characteristics are determined by the passive and active properties of the dendrite. The passive properties induce leftward shifts in the dPRCs and attenuate them. Our analysis yields a single dimensionless parameter that classifies active dendritic conductances as either regenerative conductances that counter the passive properties by boosting the dPRCs or restorative conductances that high-pass filter the dPRCs. Thus dendritic properties can generate a qualitative difference between the somatic and dendritic PRCs. As a result collective dynamics can be qualitatively different depending on the location of the synapse, the neuronal firing rates, and the dendritic nonlinearities. Finally, we use dual whole cell recordings from the soma and apical dendrite of cortical pyramidal neurons to test these predictions and find that empirical dPRCs are shifted leftward, as predicted, but may also display high-pass characteristics resulting from the restorative dendritic HCN (h) current.

Natural Convection Heat Transfer in a Partially Open Square Cavity With a Thin Fin Attached to the Hot Wall

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
Abdullatif Ben-Nakhi ◽  
M. M. Eftekhari ◽  
D. I. Loveday
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Inclination Angle ◽  
Computational Study ◽  
Vertical Wall ◽  
Temperature Fields ◽  
Arbitrary Length ◽  
Flow Modification ◽  
The Impact

A computational study of steady, laminar, natural convective fluid flow in a partially open square enclosure with a highly conductive thin fin of arbitrary length attached to the hot wall at various levels is considered. The horizontal walls and the partially open vertical wall are adiabatic while the vertical wall facing the partial opening is isothermally hot. The current work investigates the flow modification due to the (a) attachment of a highly conductive thin fin of length equal to 20%, 35%, or 50% of the enclosure width, attached to the hot wall at different heights, and (b) variation of the size and height of the aperture located on the vertical wall facing the hot wall. Furthermore, the study examines the impact of Rayleigh number (104⩽Ra⩽107) and inclination of the enclosure. The problem is put into dimensionless formulation and solved numerically by means of the finite-volume method. The results show that the presence of the fin has counteracting effects on flow and temperature fields. These effects are dependent, in a complex way, on the fin level and length, aperture altitude and size, cavity inclination angle, and Rayleigh number. In general, Nusselt number is directly related to aperture altitude and size. However, after reaching a peak Nusselt number, Nusselt number may decrease slightly if the aperture’s size increases further. The impact of aperture altitude diminishes for large aperture sizes because the geometrical differences decrease. Furthermore, a longer fin causes higher rate of heat transfer to the fluid, although the equivalent finless cavity may have higher heat transfer rate. In general, the volumetric flow rate and the rate of heat loss from the hot surfaces are interrelated and are increasing functions of Rayleigh number. The relationship between Nusselt number and the inclination angle is nonlinear.

OPTIMAL PREVENTIVE-MAINTENANCE WARRANTY POLICIES FOR REPAIRABLE PRODUCTS WITH AGE-DEPENDENT MAINTENANCE COSTS

2005 ◽  
Vol 12 (02) ◽  
pp. 111-125 ◽  
Author(s):  
RUEY HUEI YEH ◽  
MING-YUH CHEN
Keyword(s):  
Optimal Policy ◽  
Preventive Maintenance ◽  
Life Time ◽  
Optimal Number ◽  
Closed Form Expression ◽  
Minimal Repair ◽  
Maintenance Costs ◽  
Special Cases ◽  
Age Dependent ◽  
The Impact

This paper develops a mathematical model to derive the optimal preventive maintenance warranty (PMW) policy for repairable products with age-dependent maintenance costs. Under a PMW, any product failures are rectified by minimal repair, and additional preventive maintenance actions are carried out within the warranty period. When the costs for preventive maintenance and minimal repair are age-dependent, the optimal number of preventive maintenance actions, corresponding maintenance degrees, and the maintenance schedule for designing a PMW policy are derived here such that the expected total warranty cost is minimized. Under some reasonable conditions, we show that there exists a unique optimal PMW policy in which the product is maintained periodically with the same preventive maintenance degree. Using this property, an efficient algorithm is provided to search for the optimal policy. Some related models developed in the literature are discussed and these models are in fact special cases of the model proposed in this paper. Furthermore, when the life-time distribution of a product is Weibull, a closed-form expression of the optimal policy is obtained. Finally, the impact of providing preventive maintenance is evaluated through numerical examples.

scholarly journals Outage Performance of CRNs with Best Relay Selection in Dependent Nonidentical Distributed Nakagami-m Channels

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Zongsheng Zhang ◽  
Jinlong Wang ◽  
Qihui Wu ◽  
Xurong Pi
Keyword(s):  
Closed Form ◽  
Fading Channels ◽  
Relay Selection ◽  
Closed Form Expression ◽  
Form Expression ◽  
Outage Performance ◽  
Interference Temperature ◽  
Primary Users ◽  
Best Relay Selection ◽  
The Impact

The outage performance with best relay selection is proposed for cognitive relay networks with multiple primary users in independent nonidentical distributed Nakagami-m fading channels. Specifically, we take the interference temperature and fading severity into consideration. Exact closed-form expression of outage probability is derived. Based on the exact closed-form expression, we can evaluate the impact of interference temperature, fading severity, number of relays, and number of primary users on the secondary network. Finally, the effects of fading severity, number of relays, number of primary users, and interference temperature on the system performance are examined through some representative numerical plots, and the Monte Carlo results match perfectly with theory results which validates our theory analysis.

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