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Limit Load Solution for an Edge Cracked Plate under Combined Independent Bi-Axial Membrane and Bending

Limit Load Solution for an Edge Cracked Plate under Combined Independent Bi-Axial Membrane and Bending

A net stress limit load solution for a cracked plate under combined, multiaxial tension and bending, is presented, with the two cases of an edge cracked plate and a semi-elliptical cracked plate highlighted. The solution has been derived specifically for obtaining the secondary reference stress for cases where an out of plane secondary stress is present. Common examples of this may be a bi-axial thermally induced bending stress or weld residual stress fields. Also considered is how the derived solution can be adapted to a cylinder. This is considered an important comparison as current plate solutions (namely the Miller equation) are being used as an approximation to cylinder geometry. The comparisons performed within this report therefore provide guidance to the limits of this assumption. The following conclusions were obtained through the course of the investigation:
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Effect of circular holes on the ratchet limit and crack tip plastic strain range in a centre cracked plate

Effect of circular holes on the ratchet limit and crack tip plastic strain range in a centre cracked plate

The aim of the present paper is to employ a new simplified method for the evaluation of ratchet limit and plastic strain range under the LMM framework for cracked bodies subjected to cyclic load conditions, and to analyse the effect of the circular hole on the ratchet limit and crack tip plastic strain range in a centre cracked plate using the proposed method. In the present paper, a centre cracked plate with symmetric holes subjected to two load conditions, cyclic uniaxial loading and cyclic bending moment with constant tensile loading, is considered by assuming plane strain condition. The effect of circular holes on the ratchet limit and crack tip plastic strain range, which is considered to be a better similitude parameter than the stress intensity range for the fatigue crack growth behaviour [15] in a stable cycle, is presented. Parametric studies involving hole diameter and locations are carried out. The optimum location for reducing the crack tip plastic strain range with the least reduction in ratchet limit is identified considering the fact that reducing the plastic strain range will increase the component’s fatigue life while an unchanged ratchet limit will keep the cyclic loading capacity of the cracked plate. An ABAQUS [11] step-by -step inelastic analysis is also carried out to verify the obtained ratchet limit by the proposed method.
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Prediction of Plastic one Size for Mode II Loading of Bimaterial Cracked Plate under Cyclic Loading

Prediction of Plastic one Size for Mode II Loading of Bimaterial Cracked Plate under Cyclic Loading

plastic deformation occurring in the locality of a fatigue crack tip is sufficient to form a field of residual stress [8] and some recent studies shows that the shape of PZ is not only influence by the fatigue crack propagation rate but also its direction [10,11]. Banks and Garlick (1984) study the effect of Poisson’s ratio and effect of anisotropy on PZ size by carried out work on isotropic materials with Mises criteria and found that size of the PZ under plane strain condition is 1/3 of the plane stress condition and its size increase with decreasing the Poisson ratio [2]. The effect of other parameters like crack sizes, thickness of plate and constant load on PZ sizes was checked by Caputo F. et. al.[6]. Benrahou et al. (2006) found the size of PZ ahead of the crack tip by applying the FEA under mode I, mode II, and mixed mode loading on SENT (single edge notch tension) specimen with the help of Mises and Tresca criteria and found that size of PZ at surface is grater then the mid plane when passing from mode I to mode II [3].
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A Non-Destructive Test Crack Detection Method Using Vibration Acoustic On Aluminium Plate

A Non-Destructive Test Crack Detection Method Using Vibration Acoustic On Aluminium Plate

Vibro-acoustic is a method that will be used for fatigue crack detection based on propagation of high frequency acoustic waves in solid structures with low-frequency excitation [24]. The focus of the test is to determine the relation between fatigue crack sizes with nonlinear wave modulation effects [19, 30]. It is important to analyze the modal parameters of a cracked plate to understand the behavior of movement of crack edges in a plate and plate surface responses to the low-frequency excitation in vibro- acoustic testing [18, 19, 24]
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Cyclic J integral using linear matching method

Cyclic J integral using linear matching method

In this section we will consider first the constitutive relation of a cracked plate with different Ramberg- Osgood material. The ΔJ equation is obtained in section 5, for single edge cracked plate loaded in cyclic tension. The results obtained from the ΔJ equation are compared graphically with Reference Stress Method, with different Ramberg-Osgood parameter n. Fig.18a shows that the variation of ΔJ with Ramberg-Osgood material, against load ratio ΔP/ΔP L , where ΔP L is the limit load range for the cyclic tensile loading, with
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Prediction of crack propagation direction for holes under quasi static loading

Prediction of crack propagation direction for holes under quasi static loading

Figure 6 shows the geometry of the single edge cracked plate with three holes and its final adaptive mesh of the initial crack for cases I and II. The material is polymethylmethacrylate (PMMA). The experiments were conducted by Ingraffea and Grigoriu (1990) from Cornell University. The plate was simply supported near the lower corners and subjected to a concentrated load at the center of the upper edge. The crack trajectory was predicted for two different initial notch configurations which were case I and case II. This configuration was chosen because two different crack growth trajectories had been predicted by the Finite
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Determination of Double-K Fracture Parameters of Concrete Using Split-Tension Cube: A Revised Procedure

Determination of Double-K Fracture Parameters of Concrete Using Split-Tension Cube: A Revised Procedure

A revised formulation for determination of double-K frac- ture parameters using weight function method for split-tension cube test is presented in the paper. In the revised procedure, the weight function of the centrally cracked plate of finite strip with a finite width is used which is an improvement over the previous work of the authors. From the present study con- sidering the specimen sizes (D = 200–500 mm) and dis- tributed-load width (0 B b B 0.15) of split-tension cube test the following conclusions can be drawn.

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Cyclic J-integral using the linear matching method

Cyclic J-integral using the linear matching method

Fig.3 Maximum principal plastic strain for a single edge cracked plate subjected to cyclic tensile loading with a/W = 0.075 (a)ABAQUS result from monotonic case (b)ABAQUS result from step-by-step cyclic loading case (c)LMM result for cyclic loading case From Figs.3b-3c, it is observed that the LMM solution gives better results than the step-by-step cases provided from ABAQUS comparing to the monotonic one. The reason for the poorer results of the step-by- step inelastic analysis may be since while conducting the analysis, the cyclic response values do not reach the steady cyclic state. Past investigations have revealed that the conduction of such solutions requires relatively long analysis times. In order to simplify the calculations, the cyclic solutions (i.e. ΔU e and ΔU p ) from LMM
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Crack   Propagation of Cracked Plates (G427)

Crack Propagation of Cracked Plates (G427)

on Figure 2, the stress intensity factor ratios for cracked plates increase in sinusoid fashion as aspect ratios are increased and increase as crack-length ratios are decreased. According to Figure 3, among the corresponding crack speed ratios the stress intensity factor ratios for cracked plate decrease in sinusoid fashion as crack-length ratios increase.

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Material   Degradation and Fracture in Zirconium Alloys

Material Degradation and Fracture in Zirconium Alloys

In the present study, the model has been used for the simulation of Zircaloy-2 hydrogen embrittlement and initiation of delayed hydride cracking in a cracked plate[r]

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Paradigm for natural frequency of an un cracked cantilever beam and its 
		application to cracked beam

Paradigm for natural frequency of an un cracked cantilever beam and its application to cracked beam

Presence of crack in a beam increases local flexibility; hence dynamics of the structures gets changed to a considerable degree. Crack gets propagated in the material due to fatigue and at the end, it leads to catastrophic failure, hence it needs much attention. Scientific analysis of such phenomena is important because it can be used for crack detection in structures and fault diagnosis. The natural frequency is most important vibration parameter, as it is extensively used as an input for the crack detection by the vibration methods. In the design of the structures or elements, natural frequency plays an important role. In this study, a theoretical method of analysis of the first natural frequency of an un- cracked cantilever beam in a bending mode is presented. The converged natural frequency formula of a paradigm is extended either to a single cracked beam or multiple cracked beam. To get the natural frequency of a cracked beam by a proposed method, vibration parameter such as stiffness is required; therefore in this study; static analysis of a cracked beam is done by using ANSYS software to get the zero frequency deflection. Stiffness of the cracked beam is then calculated by using conventional formula (Load / deflection). This method gives outstanding results for natural frequencies for both single and multiple cracked specimens. Single sided cracks are considered on the beam, as it is very common localized defect and occurred in the beam due to the fatigue load. Modal analysis is done by using ANSYS software to get the natural frequency of intact beam and cracked cantilever beam. The natural frequency obtained by the proposed method for a crack free beam, and beam having either single crack or multiple cracks gives good agreement with the natural frequency obtained by ANSYS. The main attraction of this method is that it gives one more way to the researchers to determine the modal properties of a cracked beam; the only thing is that some additional tools such as simulation software’s or experimental methods are required to evaluate cracked beam stiffness.
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Prevalence and factors associated with cracked nipples in the first month postpartum

Prevalence and factors associated with cracked nipples in the first month postpartum

Two variables related to delivery care were associated with presence of cracked nipples: cesarean section and de- livery at a hospital not accredited by the Baby-Friendly Hospital Initiative. The association between a cesarean section and cracked nipples has been confirmed in some studies [21] and refused in others [10, 19]. It is possible that the pain caused by the surgical incision may affect po- sitioning of the mother-child dyad during breastfeeding. Nevertheless, it has been demonstrated that women who had a cesarean section show better breastfeeding perform- ance when they are assisted in controlling the pain and correcting the child’s position while breastfeeding [22]. The use of anesthetics during the surgical procedure may also interfere with the child’s ability to suck [10].
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Analytic Approach to Free Vibration and Buckling Analysis of Functionally Graded Beams with Edge Cracks using four Engineering Beam Theories

Analytic Approach to Free Vibration and Buckling Analysis of Functionally Graded Beams with Edge Cracks using four Engineering Beam Theories

Sina et al. [21] used an analytical method to investigate the free vibration of FG beams using the first order shear deformation beam theory. Then,Ke et al. [22] studied free vibrations, buckling and post-buckling of FGM Timoshenko beam containing open cracks by assuming an exponential variation of material properties in the thickness direction. Also,Simsek [23] studied free vibrations of FG beams using different higher-order shear deformation theories and derived governing equations using Hamilton’s principle. Recently, Ferezqi et al. [24] presented an analytical approach based on the wave method to study the free vibrations of a FG Timoshenko beam. They investigated transverse vibration characteristics of the cracked FG Timoshenko beam with power law material property distribution. Finally analytical relations between the critical buckling load of a FG Timoshenko beam and that of the corresponding homogeneous Euler–Bernoulli beam subjected to axial compressive load have been studied by Li and Batra [25].
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Theoretical and Experimental Study of Effective Shear Stiffness of Reinforced ECC Columns

Theoretical and Experimental Study of Effective Shear Stiffness of Reinforced ECC Columns

tural members can be divided into two standard regions, known as B-regions and D-regions (Schlaich et al. 1987), respectively. Bernoulli’s hypothesis of plane strain distribu- tion is assumed valid in B-regions, while the strain distribution along a section is disturbed in D-regions. The cracked shear stiffness in B-regions of a RECC column can be calculated by means of CATM, while VATM can be used in D-regions. In general, in a column with a high shear span-depth ratio, D-regions only exist near the concentrated loads and supports, while the other areas can be regarded as B-regions. In this case, a combined truss model (Fig. 1(a)) should be used to analyze the shear behavior of the column. However, the use of a combined truss model is relatively complicated. Pan et al. (2014) concluded that when the length of shear span L s [ d v coth m , the calculated shear stiffness using the CATM is
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The Cracked Tooth: An Engima for the Clinician

The Cracked Tooth: An Engima for the Clinician

Cracked or incompletely fractured teeth can become symptomatic. Patients often present with a protracted history of pain of varying intensity; the origin of which may be difficult to locate. While intermittent pain on biting is the most consistent complaint associated with these teeth, cracks in teeth may result in a wide range of symptoms ranging from occasional discomfort to severe and prolonged pain. Symptoms are often dependent on the depth and direction of the crack and the tissuesinvolved. [3] Cracks in teeth may occur in both horizontal and vertical directions involving the crown and/or root. The etiology is generally a result of occlusal forces and iatrogenic procedures. [4] Crown and crown-root fractures are usually
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Crack Analysis of Composite Cantilever Beam by Using Vibration Analysis Technique

Crack Analysis of Composite Cantilever Beam by Using Vibration Analysis Technique

FEA helps the designer know all the theoretical stresses within the structure by indicating all the problem in detail and thus helping the designer to predict the failure of the structure. It is a cheap method of finding the causes of failure and the way the failures can be avoided. The model of beam with and without crack is originated and used for Finite Element Analysis. The modal analysis of inclined cracked and cracked cantilever beam to determine natural frequency and mode shapes at different location, inclination and depth is

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Consideration of Constraint in Plasticity Enhancement for Combined Primary and Secondary Stresses on Crack Driving Force

Consideration of Constraint in Plasticity Enhancement for Combined Primary and Secondary Stresses on Crack Driving Force

seen to follow the conservative estimates in [4]; that A can be taken as -0.8 and B as 1.25. Of all the cases, only the shallow cracked CCPT specimen fails to comply with this as a value of A of -1.1 is shown. It is also noted that the deeper cracked specimens have a larger value of A (i.e. less negative) indicating that another feature, such as constraint or geometric effects, is also having an effect. It is also noted that the curve fit of the SENB results through modifying A and B is not very good. This may be because the purely tensile secondary stress adopted could be considered as acting more like a primary stress and may require approached adopting estimates of elastic follow-up [2, 3].
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On the ratchet analysis of a cracked welded pipe

On the ratchet analysis of a cracked welded pipe

Abstract: This paper presents the ratchet limit analysis of a pipe with a symmetric crack in a mismatched weld by using the extended Linear Matching Method (LMM). Two loading conditions are considered: i) a cyclic temperature load and a constant internal pressure; and ii) a cyclic temperature load and a constant axial tension. Individual effects of i) the geometry of the Weld Metal (WM), ii) the size of the crack, iii) the location of the crack and iv) the yield stress of WM on the ratchet limits, maximum temperature ranges to avoid ratchetting and limit loads are investigated. Influence functions of the yield stress of WM on the maximum temperature ranges and limit loads are generated. The results confirm the applicability of the extended LMM to the cracked welded pipe.
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Free Vibration of a Cracked and Misaligned Rotor

Free Vibration of a Cracked and Misaligned Rotor

Fatigue cracks are the prompt source of dire failure in shafts. Researchers have been developing a pool proof strategy in identifying the cracks in dynamic machines. These cracks minimize the stiffness of the body. This crack can be modelled in ANSYS or any analyzing software and the natural frequencies can be calculated. This analysis results can be compared with the experimentation or theoretically. In this paper the result obtained from ANSYS can be compared with the cracked theory given by Chondros. [1] This paper has presented the analysis of a cracked beam which is then compared with the numerical integration results which satisfactorily gives the same results. [2] Vibration when integrated with other condition monitoring tools like oil analysis, wear debris analysis gives perfect monitoring program for rotating equipment in process industries and concluded that vibration monitoring technique can reduce the breakdowns of power plants. [3] This paper shows the fault recognition in rotating of Turbine shaft by investigating its vibration data using FFT technique that is well known in checking vibration of any rotating equipment’s and this paper presents an rationalized review of a diversity of vibration feature mining techniques that have demonstrated success when applied to rotating machineries. [4] This appraisal focused on health monitoring of rolling elements like bearings. Bearing Condition Monitoring using signal processing methods, using artificial intelligent diagnostic techniques were discussed. [5] In this paper, smart condition monitoring concept has been outlined. During presentation few case studies presented to support the present smart condition monitoring hypothesis. Some cases of bearing parameter estimation and crack force estimation covered. [6] This paper shows the behavior of turbine shaft under normal as well as
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Random   Vibration of the Simplified Cracked Liners

Random Vibration of the Simplified Cracked Liners

The rational approach for random vibration of an elastic, isotiopic, homogeneous rectangular liner plate with partial-in- depth crack has been proposed with success by means of the[r]

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