Crack Growth in Twisted Rubber Disks. Part 3. Effects of Crack Depth and Location

2003 ◽  
Vol 76 (5) ◽  
pp. 1276-1289 ◽  
Author(s):  
A. N. Gent ◽  
O. H. Yeoh
Keyword(s):  
Fracture Energy ◽  
Crack Depth ◽  
Element Analysis ◽  
Crack Location ◽  
Crack Behavior ◽  
Disk Size ◽  
Shallow Crack ◽  
Deep Crack ◽  
Disk Height ◽  
Long Cylinder

Abstract A simple analysis of the fracture energy for a shallow ring crack in a twisted rubber disk is presented and compared to a linear fracture mechanics solution for a similar crack in an infinitely long cylinder. The analysis predicts that the fracture energy increases linearly with crack depth. Since a previous analysis shows that the fracture energy subsequently decreases with crack depth when the crack is deep, it follows that the fracture energy passes through a peak as it transitions from shallow crack to deep crack behavior. The transition occurs when the crack depth becomes comparable to a fraction of the disk height. The analysis is supported by the results of finite element analysis. In addition, the effects of disk size, crack location (in the middle of the cylinder vs. at the bonded ends) and material properties are also considered.

Parametric Evaluation on the Response of Damaged Simple Supported Structure Under Transit Mass

2017 ◽  
Author(s):  
Shakti P. Jena ◽  
Dayal R. Parhi ◽  
B. Subbaratnam
Keyword(s):  
Finite Element Analysis ◽  
Integral Method ◽  
Critical Speed ◽  
Crack Depth ◽  
Element Analysis ◽  
Simply Supported ◽  
Crack Location ◽  
Integral Converge ◽  
Duhamel Integral ◽  
Ansys Workbench

In the present article, the responses of a double cracked simply supported beam have been investigated. The responses of the structure are determined using Duhamel integral method numerically and validated with finite element analysis (FEA) using ANSYS WORKBENCH 2015 along with experimental verifications. The mass is moving on the structure in terms of critical speed of the structure. The normalized deflections of the structure at different damaged configurations are calculated. The influences of speed, mass, crack depth and crack location on the structures response are investigated. It is observed that the results obtained from Duhamel integral converge well with FEA and experimental verifications.

scholarly journals Residual life estimation of structural beam using experimental and numerical modal analysis methods

2020 ◽  
Vol 4 (2) ◽  
pp. 135-146
Author(s):  
Ganda Anand Siva ◽  
Shinigam Ramakrishna
Keyword(s):  
Modal Analysis ◽  
Natural Frequencies ◽  
Residual Life ◽  
Crack Depth ◽  
Common Element ◽  
Cracked Beam ◽  
Element Analysis ◽  
Crack Location ◽  
Parametric Studies ◽  
Ship Propeller

A structural beam is a common element in many mechanical structures such as ship propeller shaft, crane boom, and air craft wings. In the present paper experimental and numerical modal analysis are carried out for estimating the damage detection, geometric location of the damage, severity of damage and residual life of structural beam to prevent unexpected failures of the mechanical structures. Experimental and numerical modal analysis results for healthy and cracked beam are compared for validation of numerical methodology used in the present paper. Experimental modal analysis is performed on both healthy and cracked beam with the help of impact hammer, acceleration sensor and FFT analyzer associated with EDM (Engineering Data Management) software. Modal tests are conducted using impact method on selected locations of the entire healthy and cracked beam to find the first three natural frequencies, which are used to detect the presence of damage and geometric location of the damage. Three parametric studies are carried out to know the effect of crack depth, crack location and crack orientation on the natural frequencies of the cracked beam. Finally,  residual life of a healthy and cracked beam was estimated using Basiquin’s equation and finite element analysis software called ANSYS 18.1.

Crake Effect on the Dynamic Characteristics of Elastically Coupled Beams

2011 ◽  
Vol 110-116 ◽  
pp. 328-336
Author(s):  
Samer A. M. Al-Said
Keyword(s):  
Dynamic Characteristics ◽  
Crack Depth ◽  
Three Dimensional ◽  
Model Verification ◽  
Elastic Coupling ◽  
Element Analysis ◽  
Crack Location ◽  
Dimensional Finite Element ◽  
Coupled Beams ◽  
Three Dimensional Finite Element

Simple mathematical model that describes the lateral vibration of elastically coupled cracked cantilever beams carrying rigid disk at their tips is derived. The derived model is used to study the effect of elastic coupling, crack depth and location on the dynamic characteristics of the system. The cracked beam is presented as two beams connected with torsional spring at the crack location. Model verification is carried out using three dimensional finite element analysis using ANSYS program, the verification results showed good agreement with that obtained from the proposed model. The study reveals that the first system natural frequency is affected by the crack and the elastic coupling.

Torsional Dynamic Response of a Shaft With Longitudinal and Circumferential Cracks

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
H. Abdi ◽  
H. Nayeb-Hashemi ◽  
A. M. S. Hamouda ◽  
A. Vaziri
Keyword(s):  
Dynamic Response ◽  
Resonance Frequency ◽  
Torsional Rigidity ◽  
Crack Depth ◽  
Longitudinal Crack ◽  
Element Analysis ◽  
Crack Location ◽  
Circumferential Crack ◽  
Turbo Generator ◽  
Resonance Frequencies

Turbo generator shafts are often subjected to cyclic torsion resulting in formation of large longitudinal cracks as well as circumferential cracks. The presence of these cracks could greatly impact the shaft resonance frequencies. In this paper, dynamic response of a shaft with longitudinal and circumferential cracks is investigated through a comprehensive analytical study. The longitudinally cracked section of the shaft was modeled as an uncracked shaft with reduced torsional rigidity. Torsional rigidity correction factor (i.e., the ratio of torsional rigidity of the cracked shaft to that of the uncracked shaft) was obtained from finite element analysis and was shown to be only a function of crack depth to the shaft radius. The resonance frequency and frictional energy loss of a shaft with a longitudinal crack were found little affected by the presence of the crack as long as the crack depth was less than 20% of the shaft radius even if the entire shaft is cracked longitudinally. Moreover, we showed that the longitudinal crack location could be more conveniently identified by monitoring the slope of the torsional response along the shaft. The circumferential crack was modeled as a torsional spring with a torsional damping. The torsion spring and damping constants were obtained using fracture mechanics. For a shaft with both a longitudinal crack and a circumferential crack, the resonance frequency was governed by the longitudinal crack when the circumferential crack depth was less than 30% of the shaft radius.

scholarly journals Novel Method for Sizing Metallic Bottom Crack Depth Using Multi-frequency Alternating Current Potential Drop Technique

2015 ◽  
Vol 15 (5) ◽  
pp. 268 ◽  
Author(s):  
Yuting Li ◽  
Fangji Gan ◽  
Zhengjun Wan ◽  
Junbi Liao ◽  
Wenqiang Li
Keyword(s):  
Crack Depth ◽  
Potential Drop ◽  
Alternating Current ◽  
Element Analysis ◽  
Metal Structures ◽  
Voltage Ratio ◽  
Simulation And Experiment ◽  
Novel Method ◽  
Shallow Crack ◽  
Current Potential

Abstract Potential drop techniques are of two types: the direct current potential drop (DCPD) technique and alternating current potential drop (ACPD) technique, and both of them are used in nondestructive testing. ACPD, as a kind of valid method in sizing metal cracks, has been applied to evaluate metal structures. However, our review of most available approaches revealed that some improvements can be done in measuring depth of metal bottom crack by means of ACPD, such as accuracy and sensitivity of shallow crack. This paper studied a novel method which utilized the slope of voltage ratio-frequency curve to solve bottom crack depth by using a simple mathematic equation based on finite element analysis. It is found that voltage ratio varies linearly with frequency in the range of 5-15 Hz; this range is slightly higher than the equivalent frequency and lower than semi-permeable frequency. Simulation and experiment show that the novel method can measure the bottom crack depth accurately.

scholarly journals Fault Diagnosis of Beam-Like Structure Using Modified Fuzzy Technique

2014 ◽  
Vol 2014 ◽  
pp. 1-18 ◽  
Author(s):  
Dhirendranath Thatoi ◽  
Sasanka Choudhury ◽  
Prabir Kumar Jena Jena
Keyword(s):  
Finite Element ◽  
Fuzzy Logic ◽  
Fuzzy Controller ◽  
Crack Depth ◽  
Research Work ◽  
Mode Shapes ◽  
Engineering Structures ◽  
Element Analysis ◽  
Crack Location ◽  
Vibration Signatures

This paper presents a novel hybrid fuzzy logic based artificial intelligence (AI) technique applicable to diagnosis of the crack parameters in a fixed-fixed beam by using the vibration signatures as input. The presence of damage in engineering structures leads to changes in vibration signatures like natural frequency and mode shapes. In the first part of this work, a structure with a failure crack has been analyzed using finite element method (FEM) and retrospective changes in the vibration signatures have been recorded. In the second part of the research work, these deviations in the vibration signatures for the first three mode shapes have been taken as input parameters for a fuzzy logic based controller for calculation of crack location and its severity as output parameters. In the proposed fuzzy controller, hybrid membership functions have been taken. Several fuzzy rules have been identified for prediction of crack depth and location and the results have been compared with finite element analysis. A database of experimental results has also been considered to check the robustness of the fuzzy controller. The results show that predictions for the nondimensional crack location, α, deviate ~2.4% from experimental values and for the nondimensional crack depth, δ, are less than ~−2%.

Response of Cracked Cantilever Beam Subjected to Traversing Mass

2015 ◽  
Author(s):  
Shakti P. Jena ◽  
Dayal R. Parhi ◽  
Devasis Mishra
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Dynamic Response ◽  
Numerical Method ◽  
Cantilever Beam ◽  
Crack Depth ◽  
Numerical Procedure ◽  
Element Analysis ◽  
Crack Location

The present work emphasizes the dynamic response of double cracked cantilever beam subjected to a traversing mass. The cracks are located at different positions of the beam with random crack depths. The response of the damaged structure has been evaluated employing a numerical procedure of Runge-Kuuta method. The effects of crack depth, traversing mass, traversing speed and crack location on the response of the structure are studied. Finite element analysis (FEA) using the commercial ANSYS 15 has been presented to validate the adopted numerical method.

The Effect of Crack Depth (a) and Crack Depth to Width Ratio (a/W) on the Fracture Toughness of A533-B Steel

1994 ◽  
Vol 116 (2) ◽  
pp. 115-121 ◽  
Author(s):  
J. A. Smith ◽  
S. T. Rolfe
Keyword(s):  
Fracture Toughness ◽  
Large Scale ◽  
Crack Depth ◽  
Forthcoming Paper ◽  
Width Ratio ◽  
Element Analysis ◽  
Actual Structure ◽  
Oak Ridge ◽  
Shallow Crack

Constraint, as related to specimen crack depth (a) or crack depth to specimen width ratio (a/W), can have a significant effect on fracture toughness. In laboratory specimens, both crack depth and the a/W ratio can be varied. However, it is not always possible to model the constraint of a structurally relevant geometry in the laboratory. Nonetheless, an understanding of the role of both crack depth and a/W ratio on the toughness behavior of laboratory specimens will help clarify the role of constraint on fracture toughness and better enable engineers to model the effect of constraint on a flaw in an actual structure. An experimental study of the effect of crack depth and a/W ratio on the fracture toughness of an A533-B steel was conducted and results were compared with large-scale specimens tested at Oak Ridge National Labs (ORNL). Smaller size specimens tested at the University of Kansas (KU) were taken from the actual ends of the specimens tested at ORNL. The specimens tested at both KU and ORNL were square single-edge-notched bend (SENB) specimens with widths ranging from 20.3 to 100.0 mm (0.8 to 4.0 in.), crack depths ranging from 2.0 to 50.0 mm (0.08 to 2.0 in.), and a/W ratios ranging from 0.1 to 0.5. The geometries of the specimens tested at KU were chosen such that comparisons of the toughness of specimens with constant crack depth and varying a/W ratio, as well as comparisons of the toughness of specimens with constant a/W ratio and varying crack depths, could be made. A forthcoming paper, containing finite element analysis results, will compare the analytical basis for the behavior of these various size specimens. The results indicate that both crack depth and a/W ratio affect the fracture toughness of the steel. For deep crack geometries (a/W = 0.5), crack depth has limited effect on the fracture toughness. However, for shallow crack geometries (a/W = 0.1), crack depth has a significant effect on the fracture toughness. For constant crack depth, varying the a/W ratio does affect the fracture toughness. Thus, crack depth and a/W ratio are interdependent with respect to fracture toughness. The findings of this study are significant in helping to understand the role of both crack depth and a/W ratio on fracture toughness and serve as a basis for understanding the effect of constraint on the behavior of actual structures with cracks.

Rotordynamic Crack Diagnosis: Distinguishing Crack Depth and Location

2013 ◽  
Author(s):  
Philip Varney ◽  
Itzhak Green
Keyword(s):  
Fatigue Crack ◽  
Condition Monitoring ◽  
Crack Depth ◽  
Forced Response ◽  
System Response ◽  
Contour Plot ◽  
Crack Model ◽  
Finite Width ◽  
Angular Response ◽  
Crack Location

The goal of this work is to establish a condition monitoring regimen capable of diagnosing the depth and location of a transverse fatigue crack in a rotordynamic system. The success of an on-line crack diagnosis regimen hinges on the accuracy of the crack model used. The model should account for the depth of the crack and the localization of the crack along the shaft. Negating the influence of crack location on system response ignores a crucial component of real cracks. Two gaping crack models are presented; the first simulates a finite-width manufactured notch, while the second models an open fatigue crack. An overhung rotordynamic system is modeled, imitating an available rotordynamic test rig. Four degree-of-freedom equations of motion for both crack models are presented and discussed, along with corresponding transfer matrix techniques. Free and forced response analyses are performed, with emphasis placed on results applicable to condition monitoring. It is demonstrated that two identifiers are necessary to diagnose the crack parameters: the 2X resonance frequency and the magnitude of the 2X component of the rotor angular response at resonance. First, a contour plot of the 2X resonant shaft speed versus crack depth and location is generated. The magnitude of the 2X component of the rotor’s angular response along the desired contour is obtained, narrowing the possible pairs of crack location/depth to either one or two possibilities. Practical aspects of the diagnosis procedure are then discussed.

J-Integral Analysis of Surface Cracks in Round Bars under Bending Moments

2011 ◽  
Vol 52-54 ◽  
pp. 43-48 ◽  
Author(s):  
Al Emran Ismail ◽  
Ahmad Kamal Ariffin ◽  
Shahrum Abdullah ◽  
Mariyam Jameelah Ghazali ◽  
Ruslizam Daud
Keyword(s):  
Finite Element ◽  
Crack Depth ◽  
Crack Tip ◽  
Bending Moment ◽  
Limit Load ◽  
Fe Model ◽  
Surface Cracks ◽  
Element Analysis ◽  
Reference Stress ◽  
Proposed Model

This paper presents a non-linear numerical investigation of surface cracks in round bars under bending moment by using ANSYS finite element analysis (FEA). Due to the symmetrical analysis, only quarter finite element (FE) model was constructed and special attention was given at the crack tip of the cracks. The surface cracks were characterized by the dimensionless crack aspect ratio, a/b = 0.6, 0.8, 1.0 and 1.2, while the dimensionless relative crack depth, a/D = 0.1, 0.2 and 0.3. The square-root singularity of stresses and strains was modeled by shifting the mid-point nodes to the quarter-point locations close to the crack tip. The proposed model was validated with the existing model before any further analysis. The elastic-plastic analysis under remotely applied bending moment was assumed to follow the Ramberg-Osgood relation with n = 5 and 10. J values were determined for all positions along the crack front and then, the limit load was predicted using the J values obtained from FEA through the reference stress method.

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