Dependence Of Crack Length Research Articles

Relationship between crack length, wedge-shaped cutter geometry, and salt rocks viscosity in a cross-cutting scheme

Introduction. Existing publications lack studies on the relationship between salt rocks physical properties, cutters geometry, cutting force, and intergranular fracture of rock under the cutter. By analyzing the system of cracks formed by the cutters between the cutting lines, it is possible to estimate the effi ciency of fracture and design the nature and conditions of cutting. Research aim is to obtain an analytical dependence that links cracks size, cutter geometry, and salt rocks crack resistance; calculate the cutting force; experimentally determine sylvine, halite and carnallite fracture toughness coeffi cients necessary for the calculation. And fi nally, based on the obtained data, the research aimed to build 3D graphs of crack length dependence on cutter geometry for a cross-cutting scheme. Methodology. Sylvine, halite and carnallite crack resistance coeffi cients were obtained by indentation. The coeffi cient values were used in the formula for calculating the size of cracks between the cutting lines in these rocks. The formula was corrected after D6.22 cutter indentation test in salt rocks. Light microscopy technique was used to study fl uid inclusions in salt rocks. Results. Analytical dependence, values of crack resistance coeffi cients were obtained. 3D graphs for halite, sylvine and carnallite were constructed for the cross-cutting scheme. The type, size and concentration of fl uid inclusions along the grain boundaries are given that accelerate intergranular fracture under the cutter. Conclusions. The resulting formula relates cutter geometry (cutting rim width and cutting angle) to the cutting force and viscosity of rocks. The formula was used to build the 3D graphs for sylvine, halite and carnallite for the cross-cutting scheme. The size of cracks under the cutter is connected with the presence of fl uid inclusions. The obtained analytical dependence allows to model the spatial distribution and size of microfractures in salt rocks under the action of the cutting tool. Excessive branching of cracks, energy intensity, and the number of small fractions decrease, when the trajectory of the cutter partially passes through the “technogenic” cracks of the previous bed. This is implemented in the cross-cutting scheme, where this group of cracks plays the role of “starting” ones. Their length in actual practice is important for justifying the optimal cutting parameters and estimating the cutter’s effi ciency.

반타원 균열을 갖는 유한판의 하한계응력확대계수의 균열길이 의존성

반타원 균열을 갖는 유한판의 하한계응력확대계수의 균열길이 의존성

Ductile-to-brittle transition in tensile failure due to shear-affected zone with a stress-concentration source: a comparative study on punched-plate tensile-failure characteristics of precipitation-hardened and dual-phase steels

The effect of shear-affected zone (SAZ), with a stress-concentration source induced by the punching process, on tensile properties was investigated. Tests using honed specimens (which have the same shapes and stress-concentration without any SAZ) and smooth specimens were conducted to compare the effect with that of the punched specimens. Dual-phase steel, which has a high work-hardening ability and low yield strength, and precipitation-hardened steel, which has a low work-hardening ability and high yield strength, were used in the tests. Materials with two tensile strength grades were prepared from both types of steel. Only the precipitation-hardened steel with higher strength grade punched specimen showed a brittle fracture with extremely short fracture-elongation, whereas the other specimens showed a ductile fracture. The fracture surface analysis revealed that cracks initiated in the maximum shear stress plane of the SAZ under tensile loading at first. We call the crack “shear crack.” The steel which showed brittle fracture used in this study easily exhibited plastic-strain localization compared with the other steels. If the shear crack is sharp, then the transition from ductile to brittle failure tends to occur. Furthermore, the strength characteristics of the punched specimen depend on the crack length dependency of the strength resistance and the failure phenomenon of the original material.

Numerical simulation of two-dimensional problems of creep crack growth with material damage consideration

Approach for numerical simulation of the process of the creep crack growth taking into account the hidden material damage is proposed. The approach is based on the application of finite element creep modeling, accompanied by damage. For calculations, the FEM Creep software package is used. Using the proposed algorithm for rebuilding the grid with the removal of the destroyed elements, the current picture of deformation and fracture is analyzed. This takes into account the growing level of damage during the crack motion in each element. Numerical fracture simulation data are used to determine the constants in the differential creep fracture propagation equation. As an example, the creep fracture of planar specimens with sharp notches in their plane is considered. The material of the specimens is a high-temperature nickel-based alloy EI 867 at a temperature of 950 °C. Calculations are carried out for different values of the load. For different times, finite element grids with remote elements are shown. Graphs of the dependence of crack length on time are built. Comparison of numerical and calculated data obtained with the motion equation of a crack shows their acceptable coincidence. The possibility of using the proposed approach for obtaining constants in the equation of crack motion as an alternative to the existing experimental one is discussed.

Estimation of high cycle fatigue behaviour using a threshold curve concept

Estimation of short crack propagation rates has proven to be a key factor in design and maintenance of metallic components subjected to loading conditions related to high cycle fatigue (HCF). Extrapolation of long crack fracture mechanics approaches fails to correlate short crack behaviour, since crack length dependence of the short crack propagation threshold is not accounted for. In this paper, a fracture mechanics approach for prediction of HCF behaviour involving short cracks is analysed. The method is defined through application of the resistance curve concept and a short crack propagation threshold prediction model. Different threshold estimation methods are reviewed and compared. Application of the proposed model is exemplified and results of predicted crack propagation rates and estimated fatigue lives are presented and discussed.

VGF bulk growth, crystalline perfection and mechanical studies of CdZnTe single crystal: A detector grade materials

Bulk size (∼80 mm long and 20 mm dia.) with high quality single crystal of Cadmium Zinc Telluride (CZT) has been successfully grown by Vertical Gradient Freeze (VGF) method using five zone furnace. The powder X-ray diffraction analysis confirms the phase of CZT crystal and growth direction was found to be (111). The grown crystal was cut and polished into different pieces and crystalline perfection was studied by high-resolution X-ray diffraction (HRXRD) by employing a multicrystal X-ray diffractometer. The HRXRD study shows that the crystalline perfection of the grown crystals is quite good. The mechanical properties were carried out on the (111) face of different portions (2–1, 2-2-, 6–2, 6–4) of CZT single crystal at room temperature in the load ranging from 0.1 to 5.0 N. The load independent hardness values for 2–1, 2-2, 6–2 and 6–4 are found to be 0.62, 0.65, 0.61 and 0.55 GPa, respectively. In addition, the observed crack profile of indentation mark has been recorded and various other parameters such as dependence of crack length, fracture toughness, brittle index number, yield strength were also calculated and discussed.

CF/Epoxy積層板のモードI層間/層内疲労き裂進展抵抗のき裂長さ依存性に関する検討

CF/Epoxy積層板のモードI層間/層内疲労き裂進展抵抗のき裂長さ依存性に関する検討

Effect of the variation of loading frequency on surface failure of bovine articular cartilage

Mechanical loading of synovial joints can damage the articular cartilage surface and may lead to osteoarthritis. It is unknown if, independent of load, frequency alone can cause failure in cartilage. This study investigated the variation of articular cartilage surface damage under frequencies associated with normal, above normal and traumatic loading frequencies. Cartilage on bone, obtained from bovine shoulder joints, was tested. Damage was created on the cartilage surface through an indenter being sinusoidally loaded against it at loading frequencies of 1, 10 and 100 Hz (i.e., relevant to normal, above normal and up to rapid heel-strike rise times, respectively). The frequencies were applied with a maximum load in the range 60-160 N. Surface cracks were marked with India ink, photographed and their length measured using image analysis software. Surface damage increased significantly (P < 0.0001) with frequency throughout all load ranges investigated. The dependence of crack length, c, on frequency, f, could be represented by, c=A(log10(f))2+B(log10(f))+Dc=A(log10(f))2+B(log10(f))+D where A = 0.006 ± 0.23, B = 0.62 ± 0.23 and D = 0.38 ± 0.51 mm (mean ± standard deviation). The increase in crack length with loading frequency indicated that, increased loading frequency can result in cartilage becoming damaged. The results of this study have implications in the early stages of osteoarthritis.

Mechanical examination of crack length dependency and material dependency on threshold stress intensity factor range with Dugdale model

The threshold stress intensity factor range ΔKth was analytically calculated under stress control conditions using the plasticity-induced crack closure analysis with the Dugdale model. Before obtaining ΔKth, the accuracy of the method was verified. The characteristics of the crack closure behavior were discussed by specifying the small-scale yielding (SSY) and large-scale yielding (LSY). The analysis results of ΔKth were discussed systematically by non-dimensionalizing them with the Dugdale model. Under the SSY condition, ΔKth was dependent on Young’s modulus and Poisson’s ratio. Under the LSY condition, ΔKth increased when the initial crack length or yield strain increased.

Conditions for the Transition from Nonlocalized to Localized Damage in Metals and Alloys. Part 3. Determination of the Transition Conditions by the Analysis of Crack Propagation Kinetics

Special features of initiation and growth of short cracks under stresses above the fatigue limit are studied for a wide range of metals and alloys. The authors analyze the growth kinetics of short fatigue cracks, which is assessed by the dependence of crack length or crack growth rate on the number of loading cycles. The transition from the stage of short crack propagation (nonlocalized fatigue damage) to the stage of a main crack propagation (localized fatigue damage) is shown to be characterized by a more intensive increase of the crack growth rate. A procedure for determination of the main crack sizes corresponding to the transition from nonlocalized to localized fatigue damage has been substantiated. It has been found out that the fatigue crack sizes corresponding to this transition at stresses above the fatigue limit decrease with increasing stresses and remain smaller than those at stresses equal to the fatigue limit.

Investigation on mode III interlaminar fracture of glass/epoxy laminates using a modified split cantilever beam test

The mode III interlaminar fracture of composite laminates was investigated with the modified split cantilever beam test. Specimens were made of E-glass/epoxy laminates with 30%, 46% and 55% of fiber volume fraction. The suitability of the current test was validated by virtual crack closure and mixed-mode cohesive zone model techniques. It was observed that more than 94% of total strain energy release rate was allocated to mode-III fracture toughness. It was found that measured GIIIC corresponding to onset of crack propagation and also its crack length dependency, substantially increased with decreasing fiber volume fraction of specimens.

Size and crack length effects on fracture toughness of polycrystalline graphite

In this paper, the effects of specimen size and crack length on the fracture toughness of polycrystalline graphite are studied. The experimental results reported in the previous studies showed that the fracture toughness of graphite increase in bigger specimen. It has been also demonstrated that the fracture toughness of graphite is nearly identical in specimens with crack length ratio less than 0.7 but decreases for grater crack length ratios. To justify the size and crack length dependency of fracture toughness, the modified form of maximum tangential stress (MMTS) criterion, which makes the use of higher order terms in calculating the stress field around the crack tip is employed. It is shown that the MMTS criterion can provide good estimates for the fracture toughness of graphite obtained from specimen with different sizes. It is also indicated that the MMTS criterion can predict very good the reported experimental fracture toughness data for samples with the crack length ratios less than 0.7.

Probability Distribution of the Lengths of Fatigue Cracks in Riveted Joints of an Aircraft

In the case of cyclic loading of aircraft structures, fatigue cracks are initiated and grow in riveted joints, which may lead to a decrease in the residual strength and to the sudden widespread fatigue damage. This phenomenon is induced by multiple-site damage, which is usually described by statistical methods. Since the crack length in multiple-site damage is bounded by the distance between the neighboring holes, it is necessary (for the prediction of the limit state in a row of rivets) to know the size distribution of fatigue cracks, which can be computed according to the distribution of operating times (i.e., the numbers of flight cycles) to fatigue-crack initiation with regard for the dependence of crack length on the number of flight cycles. We deduce a relation for the distribution of crack lengths for a given number of flights of an actual aircraft structure. With the use of the numerical values of the parameters of defect initiation and growth, we show that this distribution can be approximated by a hyperbolic-type power function.

The Influence of Loading Rate on the Mode III Interlaminar Fracture Toughness of Composite/Steel Bi-material Systems

In this article, the Mode III interlaminar fracture properties of a glass/ epoxy-steel bi-material system are investigated as a function of crosshead displacement rates using the edge crack torsion (ECT) test geometry. For purposes of comparison, tests were also undertaken on the plain glass/epoxy composite. For a given crack length, it has been shown that the interlaminar fracture toughness of the bi-material system was inferior to that offered by the plain composite, an effect that is attributed to the reduced toughness of the interface between the two materials. The Mode III fracture toughness of both the plain composite and the bi-material samples exhibited a crack length dependency, with the measured value of GIIIc increasing with crack length. Verification of the trends in the experimental data was achieved by conducting a finite element analysis of the ECT specimen and good agreement was achieved. Furthermore, the interlaminar fracture toughness of the plain composite remained roughly constant over the range of crosshead displacement rates considered here, suggesting that it does not exhibit a rate-sensitive fracture behavior. In contrast, the bi-material samples exhibited very low values of Mode III fracture toughness at impact rates, associated with extensive debonding of the steel from the composite material.

Numerical analysis of the Edge Crack Torsion test for mode III interlaminar fracture of composite laminates

A detailed numerical analysis of the Edge Crack Torsion test was performed to verify its adequacy for the mode III interlaminar fracture characterization of composite laminates. A new data reduction scheme based on specimen compliance was proposed. Three-dimensional finite element analyses including a cohesive damage model were performed in order to evaluate the accuracy of perceived G IIIc values obtained with the proposed method. Despite some degree of crack length dependency of perceived G IIIc, acceptable errors could be achieved within a certain crack length range, which is thus recommended for experimental tests.

The Influence of Loading Rate on the Mode III Fracture Properties of Adhesively Bonded Composites

The Mode III interlaminar fracture properties, GIIIc, of an adhesively-bonded glass/epoxy composite are investigated over a wide range of crosshead displacement rates, using the edge crack torsion (ECT) test geometry. The ECT test fixture has been modified to conduct impact testing on these bonded materials. Tests on all of the samples highlighted a significant crack length dependency with the value of GIIIcincreasing rapidly with increasing crack length. Tests were also undertaken on the plain glass reinforced epoxy over an equally wide range of crosshead displacement rates.For a given crack length, the interlaminar fracture toughness of the adhesively-bonded system was superior to that offered by the plain composite, an effect that is attributed to the presence of significant crack-tip blunting within the adhesive layer. The interlaminar fracture toughness of the composite and the adhesively-bonded system remained roughly constant over the range of crosshead displacement rates considered here, suggesting that these systems do not exhibit any significant rate-sensitive fracture behavior. Finally, the crack tip loading conditions are verified by conducting an FEA analysis of the ECT specimen. Here, it was shown that Mode III loading predominates at the center of the test specimen, whereas regions of Mode II loading were observed close to the test supports.

Thermal shock resistance of ceramic coatings

A methodology is established for the evaluation of the thermal shock resistance of ceramic coatings. The problem is formulated by considering a thin coating to a thick substrate subjected to a sudden cooling on the coating surface. Time-varied thermal stresses and stress intensity factors for various parameters of the problem are obtained. The crack initiation behavior and the thermal shock resistance of the coating are studied. The crack length dependency behavior of the thermal shock resistance of the coating is discussed. Two critical size parameters, which control the applicability of the stress-based criterion and the fracture mechanics-based criterion to the determination of the thermal shock resistance of coatings, are explored.

Influence of the Weld Metal Chemical Composition on the Solidification Cracking Susceptibility of AA6056-T4 Alloy

The present study is one of the first steps towards the clear scientific understanding of the influence of the chemical composition of the weld metal on its susceptibility to the solidification cracking. It focuses on the experimental investigation of the influence of the silicon content in the weld metal by the laser beam welding of the aluminium alloy AA6056-T4. The blind seams have been produced on the so called fan-shape samples of AA6056-T4, varying only the filler wire supply rate. The dependence of centreline crack length on weld composition has been studied. It is shown, that the relatively small additions of the silicon to the weld metal lead to the sufficient increase of the cracking resistance. This positive effect is explained considering the particularities of the solidification cracking mechanism on the microscopic scale.

Crack arrest in Si 3N 4-based layered composites with residual stress

Effect of macroscopic residual stresses on fracture resistance and crack arrest in non-symmetric Si 3N 4/Si 3N 4– xTiN ( x=20, 30 wt%) layered specimens was investigated in this study. One of the aims of the work was also an examination of compliance technique to study R-curve effect as applied to layered specimens. A special attention was paid to the development of an analytical method to calculate fracture resistance – crack length dependence in layered structures having different elastic moduli of layers. The validity of the method and its application were examined by calculating stress intensity coefficients for edge-cracked layered specimens and comparison of the results with mechanical characteristics obtained from bending test.

歯科用低溶陶材の破壊評価線図とグレイジング現象による強度特性(G03-5 実験計測(1),G03 材料力学)

We proposed a failure assessment diagram (FAD) incorporating the process zone size fracture criterion and the probability concept proposed herein and investigated the appropriateness of this diagram as a method for evaluating the safety of dental porcelain. In addition, we investigated the statistical properties of bending strength σ_c and plane strain fracture toughness K_<1c> and the crack length dependence of σ_c and fracture toughness K_c at room temperature under atmospheric conditions, using low fusion dental porcelain, which, despite being a typical brittle material, fractures in a non-linear manner.