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1

Tian, Ni, Xu Jiang, Yaozhong Zhang, Zijie Zeng, Tianshi Wang, Gang Zhao, and Gaowu Qin. "Effect of Precipitates on the Mechanical Performance of 7005 Aluminum Alloy Plates." Materials 15, no. 17 (August 28, 2022): 5951. http://dx.doi.org/10.3390/ma15175951.

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Анотація:
In this study, the strength, elongation, and fatigue properties of 7005 aluminum alloy plates with different configurations of precipitates were investigated by means of tensile tests, fatigue tests, and microstructural observation. We found that the number and size of GP zones in an alloy plate matrix increased and the distribution was more uniform after the aging time was extended from 1 h to 4 h at 120 °C, which led to a rise in both strength and elongation of alloy plates with the extending aging time. The fatigue life of the alloy plates shortened slightly at first, then significantly prolonged, and then shortened again with the aging time extending from 1 h to 192 h and a fatigue stress level of 185 MPa and stress ratio (R) = 0. After aging at 120 °C for 96 h, the precipitates in the alloy plate matrix were almost all metastable η′-phase particles, which had the optimal aging strengthening effect on the alloy matrix, and the degree of mismatch between the α-Al matrix and second-phase particles was the smallest; the fatigue crack initiation and propagation resistances were the largest, leading to the best fatigue performance of alloy plates, and the fatigue life of the aluminum plate was the longest, up to 1.272 × 106 cycles. When the aging time at 120 °C was extended to 192 h, there were a small number of equilibrium η phases in the aluminum plates that were completely incoherent with the matrix and destroyed the continuity of the aluminum matrix, easily causing stress concentration. As a result, the fatigue life of alloy plates was shortened to 9.422 × 105 cycles.
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2

Jian, Hai Gen, Min Xian Du, Feng Jiang, and Zhi Min Yin. "Fatigue Characteristic of Aluminum Alloy Plates with Different Thickness." Applied Mechanics and Materials 477-478 (December 2013): 1284–87. http://dx.doi.org/10.4028/www.scientific.net/amm.477-478.1284.

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The fatigue characteristic of 2124 aluminum alloy in T851 condition was investigated by means of scanning electron microscopy (SEM) and transmission electron microscope (TEM). And the result shows that, the fatigue life is closely related to the thickness of plates, this is because that different thickness of plates results in the variation of grain size, grain boundaries and substructures of alloy, which thus influence the fatigue behavior of 2124-T851 alloy. The number of grain boundaries along the propagation direction of cracks and the amount of substructures after heat treatment increase with the decline of thicknesses of 2124 alloy plates, while the grain size is reverse. However, no obvious size and dispersion changes for the precipitates. Comparatively, the fatigue resistance performance of 30mm thickness plate is better than the 40mm and 55mm thickness plates, which is due to the more profitable grain size, grain boundary and substructure.
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3

You, Xiang, Zhiyu Wang, Xiafang Zhou, Zifeng Liu, Ruijuan Jiang, and Weiming Gai. "Fatigue Life Appraisal and Its Corrected Stress Intensity Factor for Repaired Off-CentrallyCracked Aluminum Plates." Materials 13, no. 18 (September 10, 2020): 4014. http://dx.doi.org/10.3390/ma13184014.

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Анотація:
This paper presents an experimental study on the fatigue life estimation of off-centrally cracked aluminum plates. Typical theoretical equations for off-central, central and edge cracks were reviewed and compared in terms of their sensitive parameters and applicability. A finite element model has been validated in its capacity in modelling the influences of eccentricity and crack size on the boundary correction coefficients. The Forman equation has been employed along with numerical results for the prediction of fatigue lives. Based on the test data, the fatigue life results of aluminum plates with and without patched laminate repair have been compared with codified fatigue classes. It is demonstrated that the repair at the crack tip close to the plate edge is effective in the fatigue life improvement for off-centrally crackedaluminum plates.
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4

Yousefi, Armin, Saman Jolaiy, Reza Hedayati, Ahmad Serjouei, and Mahdi Bodaghi. "Fatigue Life Improvement of Cracked Aluminum 6061-T6 Plates Repaired by Composite Patches." Materials 14, no. 6 (March 15, 2021): 1421. http://dx.doi.org/10.3390/ma14061421.

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Анотація:
Bonded patches are widely used in several industry sectors for repairing damaged plates, cracks in metallic structures, and reinforcement of damaged structures. Composite patches have optimal properties such as high strength-to-weight ratio, easiness in being applied, and high flexibility. Due to recent rapid growth in the aerospace industry, analyses of adhesively bonded patches applicable to repairing cracked structures have become of great significance. In the present study, the fatigue behavior of the aluminum alloy, repaired by a double-sided glass/epoxy composite patch, is studied numerically. More specifically, the effect of applying a double-sided composite patch on the fatigue life improvement of a damaged aluminum 6061-T6 is analyzed. 3D finite element numerical modeling is performed to analyze the fatigue performance of both repaired and unrepaired aluminum plates using the Abaqus package. To determine the fatigue life of the aluminum 6061-T6 plate, first, the hysteresis loop is determined, and afterward, the plastic strain amplitude is calculated. Finally, by using the Coffin-Manson equation, fatigue life is predicted and validated against the available experimental data from the literature. Results reveal that composite patches increase the fatigue life of cracked structures significantly, ranging from 55% to 100% for different applied stresses.
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5

Yang, Xiao Hua, Ding Zhang, and Yong Zhang. "2D FE Modeling of Cracked Aluminum Plates Repaired with Adhesively Bonded Composite Patches." Advanced Materials Research 152-153 (October 2010): 1024–30. http://dx.doi.org/10.4028/www.scientific.net/amr.152-153.1024.

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Анотація:
A 2D FE model of cracked aluminum plates repaired with adhesively bonded composite patches was established in this paper, and then the model was validated by comparing the calculated SIF and fatigue life of repaired structure with existing results. The result shows that the model is accurate enough to be used to analyze the mechanical property of cracked aluminum plates repaired with adhesively bonded composite patches.
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6

Albedah, A., Sohail MA Khan, B. Bachir Bouiadjra, and F. Benyahia. "Fatigue crack propagation in aluminum plates with composite patch including plasticity effect." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 232, no. 11 (June 1, 2017): 2122–31. http://dx.doi.org/10.1177/0954410017710273.

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In this paper, we analyzed experimentally and numerically the behavior of fatigue crack in aluminum plates repaired with bonded composite patch. We studied the behavior of repaired crack in AA 2024 T3 and AA 7075 T6 under two levels of applied fatigue stresses: maximal stresses of 70 and 120 MPa at a load ratio of 0.1. In the experimental part, the fatigue life of unrepaired and repaired notched specimens were determined. In the numerical part, the J integral around repaired and unrepaired crack tips was calculated. The numerical and the experimental results were used to plot the crack velocity (da/dN) as a function of the J integral. The analysis was completed with scanning electron microscopic observations on fracture surfaces of repaired and unrepaired specimens. It was found that patch improves the fatigue life but this improvement is considerably reduced with the increase in the applied fatigue load. The Al 2024 T3 presents better resistance to fatigue crack propagation in both repaired and unrepaired cases.
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7

Wang, Q. Y., and R. M. Pidaparti. "Static characteristics and fatigue behavior of composite-repaired aluminum plates." Composite Structures 56, no. 2 (May 2002): 151–55. http://dx.doi.org/10.1016/s0263-8223(01)00176-3.

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8

Sano, Yuji, Kiyotaka Masaki, and Keiichi Hirota. "Improvement in Fatigue Strength of Friction Stir Welded Aluminum Alloy Plates by Laser Peening." Advanced Materials Research 891-892 (March 2014): 969–73. http://dx.doi.org/10.4028/www.scientific.net/amr.891-892.969.

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Анотація:
Plane bending fatigue testing was performed to study the fatigue properties of friction stir welded (FSW) 3 mm thick AA6061-T6 aluminum alloy plates. Fatigue cracks propagated with bends and curves on the specimens, showing large deviation from a linear line. This might be reflecting the material flow and microstructure in the weld zone. The fatigue strength of the unwelded base material (BM) was 110 MPa at 107 cycles and FSW deteriorated it to 90 MPa. However, laser peening (LP) restored the degraded fatigue strength up to 120 MPa which is higher than that of the BM.
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9

Jia, Yinglian, Zhichao Huang, Yongchao Zhang, and Fan Zhang. "Forming Quality and Fatigue Behavior of Self-Piercing Riveted Joints of DP590 and AA6061 Plates." Advances in Materials Science and Engineering 2021 (October 18, 2021): 1–10. http://dx.doi.org/10.1155/2021/4381544.

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Анотація:
Two kinds of self-piercing riveted (SPR) joints were prepared with DP590 and AA6061 plates. The forming qualities of the joints were studied using the finite element method. The relationships between the fatigue life and failure forms of the joints with different upper plates were discussed. Finally, the failure mechanisms of the joints were analyzed. The results show that the maximum static tension of DA32 joints (with an upper plate of DP590) is significantly greater than that of the other kind, and the fatigue life of DA32 joints is always longer than that of AA40 joints when with a 2.0 mm thick AA6061 aluminum alloy upper plate under the same fatigue load. The failure mode of SPR joints changes obviously due to different upper plates, and the fatigue life of the joints can be effectively improved by reducing the microvibration wear.
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10

Azouaoui, Krimo, and Said Mouhoubi. "Study on Damage Modes of a Sandwich Panel Impacted Repeatedly." Advanced Materials Research 980 (June 2014): 147–51. http://dx.doi.org/10.4028/www.scientific.net/amr.980.147.

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Анотація:
This paper describes an experimental investigation for determining the damage modes under low energy impact-fatigue of sandwich panels consisting of aluminum skins supported by honeycomb core made of aluminum. Square samples of 125mm by 125mm sides and 10mm thickness (skin of 0.6mm and 8.8mm of core) were subjected to impact fatigue loading using a testing machine at four different energy levels (2J, 3J, 5J and 7J). The square plates are clamped in a fixture system over a 100mm diameter hole. Three different diameters of impactor head (15mm, 25mm and 35mm) are used to study their influence on life duration of the sandwich plates. Results showed that damage area at impacted face and propagation of multi-cracks at rear face are greatly affected by energy level and impactor diameter.
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11

Tian, Ni, Zhen Feng, Xu Shi, Wenze Wang, Kun Liu, Gang Zhao, and Gaowu Qin. "Effects of Pre-Tensile Deformation on the Fatigue Fracture Behavior of Annealed 7005 Aluminum Alloy Plate." Materials 15, no. 2 (January 14, 2022): 623. http://dx.doi.org/10.3390/ma15020623.

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Анотація:
In the present study, the fatigue life and fatigue fracture characteristics of annealed 7005 aluminum alloy plates subjected to different pre-tensile deformations were investigated. The results obtained upon increasing the pre-tensile deformation of the alloy plate to 20% revealed that the second-phase particles did not show any obvious changes, and that the thickness of the thin strip grain slightly decreased. The dislocation distribution in the alloy matrix varied significantly among the grains or within each grain as the dislocation density gradually increased with increasing pre-tensile deformation. Moreover, the fatigue performance of the annealed 7005 aluminum alloy plate was significantly improved by the pre-tensile deformation, and the alloy plate subjected to 20% pre-tensile deformation exhibited an optimal fatigue life of ~1.06 × 106 cycles, which was 5.7 times and 5.3 times that of the undeformed and 3% pre-stretched alloy plates, respectively. Two fatigue life plateaus were observed in the pre-tensile deformation ranges of 3–5% and 8–12%, which corresponded to heterogeneous dislocation distribution among various grains and within each grain, respectively. Moreover, two large leaps in the plot of the fatigue-life–pre-tensile-deformation curve were observed, corresponding to the pre-tensile deformation ranges of 5–8% and 16–20%, respectively.
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12

Sarsilmaz, Furkan. "Relationship between micro-structure and mechanical properties of dissimilar aluminum alloy plates by friction stir welding." Thermal Science 22, Suppl. 1 (2018): 55–66. http://dx.doi.org/10.2298/tsci170825271s.

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Анотація:
Friction stir welding can be applied to weld dissimilar aluminum alloys which have different chemical and mechanical properties without causing any weld defects under a wide range of welding conditions. In this study, AA2024-T3 and AA6063-T6 aluminum alloys were selected and successfully welded in butt position together using by friction stir welding. The welding trials were conducted using different rotational speed and traverse speed conditions also investigating their effect on mechanical and micro-structural behavior of friction stir welding joints. The micro-structural evolution of the material was analyzed by optical observations and scanning electron microscopy inspections of the weld cross-sections. Tension and fatigue studies were also employed to the study. On the other hand, the fracture characterizations of samples were examined by scanning electron microscopy. Fatigue tests were performed by using a resonant electro-mechanical fatigue testing machine by axial bending fatigue test procedure. The fatigue strength has been analyzed drawing S-N curves. Experimental results indicate that micro-structural and mechanical properties are significantly affected by changing welding parameters within the chosen range of welding conditions.
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13

Kam, T. Y., Y. C. Tsai, K. H. Chu, and J. H. Wu. "Fatigue Analysis of Cracked Aluminum Plates Repaired with Bonded Composite Patches." AIAA Journal 36, no. 1 (January 1998): 115–18. http://dx.doi.org/10.2514/2.363.

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14

Chung, K. "Mixed mode fatigue crack growth in aluminum plates with composite patches." International Journal of Fatigue 25, no. 4 (April 2003): 325–33. http://dx.doi.org/10.1016/s0142-1123(02)00142-1.

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15

Kam, T. Y., Y. C. Tsai, K. H. Chu, and J. H. Wu. "Fatigue analysis of cracked aluminum plates repaired with bonded composite patches." AIAA Journal 36 (January 1998): 115–18. http://dx.doi.org/10.2514/3.13788.

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16

Chen, Wenjing, Wei Lu, Guoqing Gou, Liwen Dian, Zhongyin Zhu, and Junjun Jin. "The Effect of Fatigue Damage on the Corrosion Fatigue Crack Growth Mechanism in A7N01P-T4 Aluminum Alloy." Metals 13, no. 1 (January 4, 2023): 104. http://dx.doi.org/10.3390/met13010104.

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Анотація:
A7N01P-T4 aluminum alloy plates for high-speed trains will experience a certain amount of fatigue damage under alternating loads. Three groups of samples, P0 (no fatigue damage), P1 (loading stress 30 MPa), and P2 (loading stress 70 MPa), were created, and corrosion fatigue crack growth (CFCG) tests were conducted in 3.5 wt.% NaC1 solution. The crack growth rate was found to increase after fatigue damage as the damage degree increased. In addition, the A7N01P-T4 aluminum alloy base metal exhibited obvious secondary cracks and crack bifurcations after fatigue damage. It is believed that fatigue damage causes stress concentration in the material, while a certain degree of stress corrosion cracking occurs during the CFCG growth process. This is because hydrogen (H) easily accumulates and diffuses along the grain boundary, which reduces the strength of the grain boundary, thereby becoming the preferred orientation for crack growth. This explains why the CFCG rate of the material is accelerated following fatigue damage to a certain extent.
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17

Rahmani Kalestan, M., H. Moayeri Kashani, A. Pourkamali Anaraki, and F. Ashena Ghasemi. "Experimental and numerical investigation of fatigue crack growth in aluminum plates repaired by FML composite patch." International Journal of Structural Integrity 5, no. 4 (November 11, 2014): 242–52. http://dx.doi.org/10.1108/ijsi-08-2013-0019.

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Анотація:
Purpose – The purpose of this paper is to use the fiber metal laminates (FML) composites as a patch for repairing a single notched specimen made of AL1035 aluminum alloy. The FML composite patch was bonded on one side of the cracked specimens by adhesive Araldite 2015. Then the fatigue crack growth tests were conducted on the specimens and the effects of both FML patch lay-up sequence and pre-crack angle on the fatigue life were investigated. Finally, the effect of repairing on the fracture parameters (SIF and crack propagation direction) at the crack front has also been calculated using three-dimensional finite element analysis. Design/methodology/approach – The fatigue crack growth tests were conducted on the specimens and the effects of both FML patch lay-up sequence and pre-crack angle on the fatigue life were investigated. Findings – The results show that the fatigue life of the patched specimens with inclined crack increased approximately 2-6.02 times compared to the un-patched specimens. In addition, the fatigue crack growth rate decreased significantly when the patch was used. Generally, the FML patch with Plate-Fiber-Fiber-AL lay-up has more efficiency than other lay-up sequences. Originality/value – Recently, composite patches are used in the structure repair processes to increase the service life of cracked components. The bonded patch method is one of the efficient methods among repairing methods. Today, the FMLs are used in the aircraft structures as a replacement of high-strength aluminum alloys due to their lightweight and high-strength properties. Many researches have been performed on single and double side repaired panels using composite patches. In this study, the FML composites have been used as a patch for repairing a single notched specimen made of AL1035 aluminum alloy.
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18

Srivatsan, T. S., Satish Vasudevan, Lisa Park, and R. J. Lederich. "The High Cycle Fatigue and Fracture Behavior of Friction Stir Welded Aluminum Alloy 2024." Key Engineering Materials 378-379 (March 2008): 175–206. http://dx.doi.org/10.4028/www.scientific.net/kem.378-379.175.

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In this research paper, the cyclic stress amplitude controlled fatigue response and fracture behavior of an Al-Cu-Mg alloy (Aluminum Association designation 2024) is presented and discussed. The alloy was friction stir welded in the T8 temper to provide two plates one having high tensile ductility and denoted as Plate A and the other having low tensile ductility and denoted as Plate B. Test specimens of the alloy, prepared from the two plates, were cyclically deformed under stress amplitude control at two different load ratios with the primary objective of documenting the conjoint influence of magnitude of cyclic stress, load ratio and intrinsic microstructural effects on cyclic fatigue life and final fracture characteristics. The high cycle fatigue resistance of the alloy is described in terms of maximum stress, R-ratio, and microstructural influences on strength. The final fracture behavior of the friction stir welded alloy is discussed in light of the concurrent and mutually interactive influences of intrinsic microstructural effects, deformation characteristics of the alloy microstructure, magnitude of cyclic stress, and resultant fatigue life.
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19

Ma, Shuyi, Guixian Zhang, Hongfeng Hou, and Lidong Wang. "Mutual Interactions of Lamb Waves in Nonlinear Elastic Plates." Metals 12, no. 12 (December 16, 2022): 2175. http://dx.doi.org/10.3390/met12122175.

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Анотація:
The mutual interactions of Lamb waves in nonlinear elastic plates are studied in this article. Many researchers have investigated the interactions of Lamb wave modes at nonlinear higher harmonics. However, little is known about nonlinearity-driven Lamb modulations from two primary modes with different frequencies. In this study, the existence of symmetric or antisymmetric mode due to Lamb wave mutual interactions is firstly theoretically formulated. Then, an approach is proposed to evaluate the intensity of phase velocity matching for selecting primary modes. Finally, the characteristics of the modulated wave generation are investigated and demonstrated. The generation of modulated waves in an aluminum plate and fatigue crack can be detected by mutual interactions of Lamb waves. The main contribution of this work is the proposed mutual interaction theory of Lamb waves in fatigue plates, which can guide fatigue detection in the metal plate.
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20

Zakharchenko, Kirill, Vladimir Kapustin, Alexey Larichkin, and Yaroslav Lukyanov. "Influence of Technology of Hot Forming of Plates from Aluminum Alloys Al-Cu-Li-Zn and Al-Zn-Mg-Cu on Resistance to Fatigue Fracture." Metal Working and Material Science 22, no. 4 (December 8, 2020): 94–109. http://dx.doi.org/10.17212/1994-6309-2020-22.4-94-109.

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Анотація:
Introduction. One of the primary objectives in the development of promising aircraft products is to reduce the weight of the aircraft structure. This problem can be solved by applying new low density materials such as aluminum alloys alloyed with lithium (for example, Al-Cu-Li-Zn) in the design of parts. The use of these materials in aircraft construction is limited by the processing technology, which must be such as not to damage the material and not reduce its strength properties. Such technologies include processing by pressure with heating, when creep processes are activated and the material passes into a state close to superplasticity. The purpose of the work: assessment of the effect of pressure shaping of aluminum alloys Al-Cu-Li-Zn and Al-Zn-Mg-Cu in creep mode on strength. The paper investigates the influence of the technology of pressure shaping of aluminum alloys Al-Cu-Li-Zn and Al-Zn-Mg-Cu on the resistance to fatigue failure. The work uses a method that allows to determine the ultimate stresses using diagrams of the accumulation of irreversible deformations; method of forming thick plates (40 mm) in the creep mode. The previously selected optimum temperatures for forming the plates are used. A non-contact coordinate measuring system is used to perform surface inspection after shaping. Fractography of the fracture of samples of alloy Al-Cu-Li-Zn and Al-Zn-Mg-Cu after fatigue failure is performed. Mathematical modeling of the deformation process of plates in creep mode is carried out in the MSC.Marc package. As a result, a conservative evaluation of the endurance limit for aluminum alloys Al-Cu-Li-Zn and Al-Zn-Mg-Cu is obtained. The shaping of thick plates in the creep mode is carried out. More than 80% of the board surface is formed with a deviation of less than 1 mm from the target size. Fatigue tests of samples made of molded panels of alloys Al-Cu-Li-Zn and Al-Zn-Mg-Cu are carried out, fatigue curves are plotted. The fractography of the surface of the fatigue fracture showed the presence of oxides in the samples of alloy Al-Cu-Li-Zn, in contrast to alloy Al-Zn-Mg-Cu. The results of fatigue tests are discussed, showing that the characteristics of the technological process of shaping and heat treatment do not deteriorate the fatigue properties of the investigated alloys. Comparative tests show that alloy Al-Cu-Li-Zn has higher fatigue characteristics. Mathematical modeling show that the use of the Boyle-Norton steady-state creep law is not enough to describe the process of plate forming. The necessity of setting the inverse problem of creep age forming is noted, where the coordinates of the punches of the loading device should act as boundary conditions.
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21

Yasniy, P., O. Dyvdyk, O. Semenets, V. Yasnii, and A. Antonov. "Fatigue crack growth in aluminum alloy from cold expanded hole with preexisting crack." Scientific journal of the Ternopil national technical university 99, no. 3 (2020): 5–16. http://dx.doi.org/10.33108/visnyk_tntu2020.03.005.

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Анотація:
The fatigue life of aircraft structure elements with operational damage in the vicinity of the hole was investigated. The plates 60 mm wide and 6 mm thick made of D16chT aluminum alloy with a central hole were taken for the study. Fatigue damage was examined with an corner quarter-elliptical fatigue crack with a length of 1,25 mm, which was initiated from an edge notch of 0,5 x 0,5 mm. The fatigue crack growth rate on the surface of the plate after mandrel hole with cold expansion degree i = 2,7% increases up to15 times and residual lifetime in three times compared to the virgin plate.
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22

Kecsmar, J., and R. A. Shenoi. "Some Notes on the Influence of Manufacturing on the Fatigue Life of Welded Aluminum Marine Structures." Journal of Ship Production 20, no. 03 (August 1, 2004): 164–75. http://dx.doi.org/10.5957/jsp.2004.20.3.164.

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Анотація:
Designers are constantly looking for ways to reduce the structure weight to lower the overall displacement and hence the cost of fast ferries and other high-speed vessels. The easiest option for the designer is to choose a lightweight material. Aluminum has become the adopted choice of material for high-speed vessels owing to its high strength to weight characteristics. Unlike steel, aluminum is more prone to fatigue cracking and has no fatigue limit. In order to minimize weight, the designer will make use of finite element methods to optimize the scantlings and perform fatigue checks against established codes. This can lead to a structure that has the empirical margins of safety reduced owing to the accuracy of mathematical modeling. However, what is often overlooked is the effect the manufacturing process has on the fatigue life of the fabricated structure. This aspect is excluded from the designer's fatigue calculations, which assist in reducing the scantlings. Currently, there is no guidance for fatigue life reduction for the designer that establishes good and bad workshop practice, other than experience, or the implications of basic shipyard fabrication. It is shown that whereas strain-hardened alloys improve mechanical strength, they reduce ductility. This has consequences when forming the hull plate by potentially introducing crack like flaws into the alloy matrix if the plater overrolls the plate. If there is misalignment or there is too much gap between the plates, the weld will create localized stress concentrations. If the welder has poor joint preparation or gas shielding, porosity can be introduced into the weld. Porosity has a significant effect on the fatigue life of the weldment. This paper brings together a collection of data on such issues that the designer needs to be aware of to prevent an unwanted fatigue failure in the fabrication process.
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23

Li, Yanlei, Shanglei Yang, Zeng Peng, Zhentao Wang, and Zihao Gao. "Microstructure, Fatigue Properties and Stress Concentration Analysis of 6005 Aluminum Alloy MIG Welded Lap Joint." Materials 15, no. 21 (November 2, 2022): 7729. http://dx.doi.org/10.3390/ma15217729.

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Анотація:
This paper studies the microstructure and mechanical properties of MIG (Melt Inert Gas) lap welded 6005 aluminum alloy plates. Microstructure analysis (OM) of the joint showed that 15~30 μm small grains were observed at the fusion line. Mechanical analysis shows that the small grains are broken by shielding gas and molten pool flow force. Hardness test shows that there is a softening zone (41~43 HV) in HAZ much lower than BM and WZ. The low cycle fatigue test showed that the performance of lap joint decreased sharply, and the fatigue strength of weld decreased significantly, which was only 27.34% of the base metal. The fatigue fracture (SEM) of the weld observed slip band cracking and a large number of brittle fracture characteristics. Using the stress concentration factor Kt for analysis, it was found that the cause of brittle fracture was mostly stress concentration. Lap joint stress concentration model appears in two ways: firstly, at the weld toe, the weld is subjected to eccentric force, secondly, there is a small gap between the two plates at the weld root, which cracks along the direction of 45° of the maximum shear stress.
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24

Gaur, Vidit, Manabu Enoki, Toshiya Okada, and Syohei Yomogida. "Fatigue life and crack growth behavior of post welded Aluminum 5183 alloy." MATEC Web of Conferences 165 (2018): 21013. http://dx.doi.org/10.1051/matecconf/201816521013.

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Анотація:
In this study we investigated the fatigue life and crack growth behavior of Al-5183 alloy. Microscopic analysis revealed nearly equi-axed grains and no texture in longitudinal or cross-sectional plane of the welded plates. Gas porosities with an average size of 45 μm, comparable to grain size (55 μm), were present and often initiate fatigue failures. Load-controlled cyclic tests at different stress-ratios (R = -1, -0.5, 0.1, 0.5. 0.7 and 0.8) revealed decrease in fatigue lives with increase in R-ratio. At R > 0.7, no fatigue failure could be observed, suggesting a probable mean-stress saturation effect on fatigue. Mean stress also tends to control the crack initiation sites: surface initiated failures at low mean stresses while sub-surface pores induced failures at higher mean stresses. Fatigue-crack growth tests on CT specimens at different R-ratios (0.1, 0.5 and 0.8) revealed reduction in crack growth rates (and in threshold values) with increasing R-ratio. The ΔK applied for pores responsible for fatigue failures were often lower than or near to the threshold values and also, the size of such pores was of order of magnitude of grain size, thus crack initiated from pores are short cracks and further tests are progress.
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25

ADİN, Hamit, Zeyni SAĞLAM, and Mehmet Şükrü ADİN. "Numerical Investigation of Fatigue Behavior of Non-patched and Patched Aluminum/Composite Plates." European Mechanical Science 5, no. 4 (December 20, 2021): 168–76. http://dx.doi.org/10.26701/ems.923798.

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26

Xiao, Xiang, Qi Zhang, Hui-xue Jiang, Cheng Liu, and Ling-fei Cao. "Micro porosity and its effect on fatigue performance of 7050 aluminum thick plates." Journal of Central South University 29, no. 3 (March 2022): 912–23. http://dx.doi.org/10.1007/s11771-022-4961-5.

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27

Lim, Hyung Jin, Young-Joo Lee, and Hoon Sohn. "Continuous fatigue crack length estimation for aluminum 6061-T6 plates with a notch." Mechanical Systems and Signal Processing 120 (April 2019): 356–64. http://dx.doi.org/10.1016/j.ymssp.2018.10.018.

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28

Yasniy, P., S. Glado, and V. Iasnii. "Fatigue crack nucleation and propagation in aluminum alloy plates with cold expanded holes." Procedia Structural Integrity 2 (2016): 3280–87. http://dx.doi.org/10.1016/j.prostr.2016.06.409.

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29

Kim, Yongtak, Hyung Jin Lim, and Hoon Sohn. "Nonlinear ultrasonic modulation based failure warning for aluminum plates subject to fatigue loading." International Journal of Fatigue 114 (September 2018): 130–37. http://dx.doi.org/10.1016/j.ijfatigue.2018.05.014.

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30

Wagle, Sanat, and Hiroshi Kato. "Ultrasonic detection of fretting fatigue damage at bolt joints of aluminum alloy plates." International Journal of Fatigue 31, no. 8-9 (August 2009): 1378–85. http://dx.doi.org/10.1016/j.ijfatigue.2009.03.017.

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31

Peng, Xing Dong, Mei Ling Wang, Sheng Li Li, and Jie Xu. "Development of Hot Rolled Strips for Internal Plates of Automobile." Materials Science Forum 817 (April 2015): 415–20. http://dx.doi.org/10.4028/www.scientific.net/msf.817.415.

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Анотація:
The hot rolled strips for internal plates of automobile was developed by taking the technologies of low-carbon softening steel, including strictly control the chemical composition content during the steel melting and optimization of the rolling processes in the thin slab continuous casting and rolling line. The results showed that when carbon content was 0.04%, adding aluminum content or reducing silicon content and manganese content, reducing the reduction in previous rolling passes and increasing the reduction of the finishing pass at high temperature was beneficial for reducing the yield strength and tensile strength of the hot rolled strips. The precipitate of the samples after annealing showed that the precipitate of aluminum-nitride increased significantly at 850°C. And the texture of the samples after annealing showed that the main texture was {110} <001> and its intensity was 1.7-2.0, annealing with hot rolled strips did not benefit the advantageous texture. Tension-tension fatigue properties of hot rolled strips and cold rolled ones were determined, the results showed that the fatigue properties of hot rolling strips were rather higher than that of cold rolled ones. In the stamping experiments of some automobile parts, there was not any drawback, and the forming properties of hot rolling strips were equal to that of cold rolled ones. It was feasible to replace the cold rolled strips with the hot rolled ones for the internal plates of automobile.
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32

Lipski, Adam, and Zbigniew Lis. "Improving Fatigue Life of Riveted Joints by Rivet Hole Sizing." Key Engineering Materials 598 (January 2014): 141–46. http://dx.doi.org/10.4028/www.scientific.net/kem.598.141.

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The aim of this paper is to assess the impact of the rivet hole sizing process on the fatigue life based on the example of the structural connections characteristic for riveted joints used in aviation industry. Test specimens reflected the structural connection consisting in a riveted lap joint of an airplane plating stiffened with a T-bar. Connected plates and the T-bar are made of D16CzATW aluminum alloy. 3 mm diameter oval head solid rivets for aviation-related purposes were made of PA24 aluminum. During fatigue tests, individual specimens with non-sized holes and with sized holes were subjected to uniaxial, one-sided, fixed-amplitude loading (R = 0). It can be concluded from the fatigue life comparison that introduction of an additional operation in the riveting process, i.e. the hole sizing, results in significant, about two-fold increase of the fatigue life of the riveted structural connection, even at slight sizing degree. The difference of the specimen damage nature was observed between specimens with sized and non-sized holes.
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33

Shelley, T. J., and Chin Kian Liew. "Application of Wavelet Parameters for Impact Damage Detection in Plates." Key Engineering Materials 558 (June 2013): 12–24. http://dx.doi.org/10.4028/www.scientific.net/kem.558.12.

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This study proposes a new nondestructive evaluation methodology named laser lock-in thermography (LLT) for fatigue crack detection. LLT utilizes a high power continuous wave (CW) laser as a heat generation source for lock-in thermography instead of commonly used flash and halogen lamps. The advantages of the proposed LLT method are that (1) the laser heat source can be positioned at an extended distance from a target structure thank to the directionality and low energy loss of the laser source, (2) thermal image degradation due to surrounding temperature disturbances can be minimized because of high temperature gradient generated by the laser source and (3) a large target surface can be inspected using a scanning laser heat source. The developed LLT system is composed of a modulated high power CW laser, galvanometer and infrared camera. Then, a holder exponent-based data processing algorithm is proposed for intuitive damage evaluation. The developed LLT is employed to detect a micro fatigue crack in a metal plate. The test result confirms that 5 μm (or smaller) fatigue crack in a dog-bone shape aluminum plate with a dimension of 400 x 140 x 3 mm3 can be detected.
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34

Bachir Bouiadjra, Bel Abbes, S. M. A. K. Mohammed, Faycal Benyahia, and Abdulmohsen Albedah. "Fatigue Behavior of Al 7075-T6 Plates Repaired with Composite Patch under the Effect of Overload." Metals 11, no. 12 (December 14, 2021): 2025. http://dx.doi.org/10.3390/met11122025.

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Repair of aeronautical structures by composite patch bonding has shown its effectiveness in several studies during the last few decades. This repair technique leads to a retardation in the propagation of repaired cracks via load bridging across the patch throughout the adhesive layer, interfacing it with the repaired structure. The purpose of this study is to analyze the behavior of patch-repaired cracks present in thin plates made of aluminum alloy 7075-T6 and subjected to a single tensile overload. The sequence of application of overload on the fatigue behavior was also studied. Fatigue tests were conducted on Al 7075-T6 notched specimens where crack growth and number of cycles to failure were monitored for different patching/overload scenarios. A detailed fractographic study was performed on failed specimens to analyze the micromechanical behavior of the crack growth related to each scenario. The obtained results showed that the application of the overload before bonding the patch leads to an almost infinite fatigue life of the repaired plates.
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35

Plashchynska, Alla. "On the method of the damage accumulation analysis in front of the fatigue crack in thin plates." Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, no. 3 (2021): 89–92. http://dx.doi.org/10.17721/1812-5409.2021/3.16.

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The problem on modeling the process of damage accumulation along the fracture front at fatigue in a thin isotropic plate is considered. The solution of the problem is based on joined of the concepts of fracture mechanics and mechanics of continuous damage. A numerical solution of the integral equation of crack front motion is proposed. Consideration of this equation as a superposition of a set of recurrent equations for each moment allows us to model the jumping nature of the fatigue crack growth and take into account the history of damage accumulation in the plate material during loading. A numerical solution of the test problem on the fatigue crack propagation in a thin plate made of aluminum alloy 7075-T6 with uniaxial asymmetric cyclic tension-compression is obtained. The constructed dependences of the fatigue crack length on the number of load cycles agree satisfactorily with the experimental data.
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36

Moreira, Pedro Miguel Guimarães Pires, and Paulo Manuel Salgado Tavares de Castro. "Fatigue Crack Growth on FSW AA2024-T3 Aluminum Joints." Key Engineering Materials 498 (January 2012): 126–38. http://dx.doi.org/10.4028/www.scientific.net/kem.498.126.

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Friction stir welding (FSW) is a solid-state joining process which emerged as an alternative technology to join high strength alloys that were difficult to weld with conventional techniques, [1]. Developments of this technique are being driven by aeronautic, aerospace and railway industries. An advantage of this joining technique is its low heat input when compared with arc welding processes. This feature allows the achievement of high mechanical properties, low distortion and low residual stresses, [2]. Also, since it is a solid-state welding process, hydrogen cracking or heat affected zone (HAZ) softening phenomena are limited. This paper presents a study of fatigue crack growth behaviour of friction stir welded butt joints of AA2024-T3, aluminium commonly used in riveted aeronautic fuselage structures. Crack growth studies are often carried out using uniform thickness joints, ASTM E647 [3]. Nevertheless, for some applications there is a need to join components with different thicknesses, which, under certain limits, can be welded using FSW. Crack growth tests on these joints are not standard. The present study concerns butt joints made using two plates with different thicknesses, 3.8mm and 4.0mm. The joints’ mechanical behaviour was studied performing static (tensile) and fatigue tests. The fatigue crack growth rate of cracks growing in different zones of the welded joint (nugget, heat affected zone - HAZ) and in base material was analysed. The microhardness profile was assessed in order to analyse the influence of the welding process in each weld zone. Further to higher static properties, welded joints present lower crack growth rate when compared with its base material.
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37

Kim, Chi-Ok, Hye-Jeong Sohn, and Seon-Jin Kim. "Friction Stir Welding of 7075-T651 Aluminum Plates and Its Fatigue Crack Growth Property." Transactions of the Korean Society of Mechanical Engineers A 35, no. 10 (October 1, 2011): 1347–53. http://dx.doi.org/10.3795/ksme-a.2011.35.10.1347.

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38

Jian-Bin, Hao, Li Xu-Dong, and Mu Zhi-Tao. "Fatigue behavior of thick center cracked aluminum plates repaired by two-sided composite patching." Materials & Design 88 (December 2015): 331–35. http://dx.doi.org/10.1016/j.matdes.2015.09.011.

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39

Maleki, Abdullah, Milad Saeedifar, Mehdi Ahmadi Najafabadi, and Dimitrios Zarouchas. "The fatigue failure study of repaired aluminum plates by composite patches using Acoustic Emission." Engineering Fracture Mechanics 210 (April 2019): 300–311. http://dx.doi.org/10.1016/j.engfracmech.2017.12.034.

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40

Venkatesan, S., G. P. Rajamani, V. Balasubramanian, and G. Padmanaban. "Fatigue Behaviour of Friction Stir Welded AZ31B Magnesium Alloy Joints." Applied Mechanics and Materials 787 (August 2015): 355–60. http://dx.doi.org/10.4028/www.scientific.net/amm.787.355.

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Friction stir welding (FSW) is a relatively better joining technique particularly for magnesium and aluminum alloys that are difficult to weld by fusion welding techniques. Fusion welding of these alloys is not preferable due to hot cracking, formation of porosity, etc. However solid state welding techniques, such as, friction sitr welding are found to offer solution to the above problems. Many research papers available in open literature focusing tensile properties, microstructural characteristics, and corrosion behaviour of friction stir welded AZ31B magnesium alloys but fatigue behaviour of these welds are not yet investigated. Hence, in this investigation, an attempt has been made to evaluate fatigue behaviour of friction stir welded rolled plates of AZ31B magnesium alloys.Fatigue experiment was conducted using servo hydraulic controlled fatigue testing machine. Fatigue strength, fatigue notch factor and notch sensitivity factor were evaluated. It is found that the fatigue strength of AZ31B welded joints is 46 MPa at 2x106cycles which is approximately 34 % lower than that of the base metal fatigue strength.
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41

Zhu, Gong Zhi, Chang Liang Zheng, and Xiao Feng Lu. "The Influence of Loading Rate on the Interfacial Fracture Toughness of Carbon Fiber-Metal Laminates Based on Magnesium Alloy." Advanced Materials Research 328-330 (September 2011): 1373–76. http://dx.doi.org/10.4028/www.scientific.net/amr.328-330.1373.

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Glass fiber reinforced aluminum alloy laminates, such as ARALL, GLARE are used widely for aeronautics and astronautics industry with excellent mechanical properties such as high specific strength, specific Young’s Modulus, high damage tolerance, high resistance to fatigue crack growth and good impact resistance. In order to obtain better mechanical properties, aluminum alloy plates and glass fibers were replaced by magnesium alloy plates and carbon fibers to get carbon fiber-metal laminates based on magnesium alloy. Single cantilever beams were used to examine the influence of loading rate on the interfacial fracture toughness of carbon fiber-metal laminates based on magnesium alloy. The results show that crack propagation is stable at low loading rates whereas unstable at high rates. And loading rates have slight influence on interfacial fracture toughness at low rates range from 1mm/min to 1000mm/min. The fracture toughness at high rates in impact tests is greater than at low rate.
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42

Kurath, P., Z. Khan, and D. F. Socie. "Fatigue Life Estimates for a Notched Member in a Corrosive Environment." Journal of Pressure Vessel Technology 109, no. 1 (February 1, 1987): 135–41. http://dx.doi.org/10.1115/1.3264845.

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It is often assumed that the effects of an aggressive environment can be included in fatigue life estimation procedures by determining the material properties in the environment and at the frequency of interest. An analytical and experimental program was conducted to confirm or refute this assumption. Automotive grade aluminum alloy, 5454-H32, in 3 percent NaCl solution and laboratory environment was selected for this study. A simple model where the total fatigue life is the summation of the portion where fatigue damage is best described by the notch strain field, and the portion where nominal stress and crack length dominate damage assessment, was used to estimate fatigue lives for center notched plates. Smooth cylindrical specimens were employed to determine the material properties for initiation. The environment had a large influence on the initiation resistance of this material at long fatigue lives, whereas at shorter fatigue lives (i.e., <104 cycles) there was little effect. Center cracked plates were used to determine the crack growth rates. Linear elastic fracture mechanics concepts were employed to estimate crack propagation lives. Approximately a factor of three reduction in crack propagation life was attributable to the hostile environment. Center notched plate specimens with Kt = 2.4 and Kt=5.1 were tested in both environments to examine the model. The accuracy of the fatigue life predictions in relation to the experimental data were comparable in 3 percent NaCl solution to the results obtained in laboratory air.
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43

Liu, Hong Tao, Mi Feng Zhao, Fangting Hu, Li Juan Zhu, Zhi Yi Liu, Xiao Feng Bai, and Lei He. "Effect of Pre-Stretching and Under-Aging Treatment on Fatigue Crack Resistance of Al-Cu-Mg Alloy Casing Pipe." Materials Science Forum 1071 (October 18, 2022): 67–73. http://dx.doi.org/10.4028/p-vff7jl.

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The effect of pre-stretching and under-aging treatment on microstructure and fatigue crack resistance of Al-4.1Cu-1.27Mg-0.47Mn-0.02Ti alloy has been investigated in present work. The results showed that the fatigue strength corresponding to 107 stress cycle numbers of the sample pre-stretched 4% and under-aged at for 2 hours reached up to 280MPa, 80MPa higher than that pre-stretched 0% and peak-aged at for 8 hours. Microstructural observations showed that fine and uniformly dispersed S’ plates were present in the sample treated by pre-stretching and under-aging, whereas, a coarse S’ plate was formed in the sample when treated by 0% pre-stretching and peak-aging. It is indicated that the pre-stretching and under-aging treatment promotes the dispersoid formation of strengthening particles, enhancing the fatigue crack resistance and resultant fatigue strength. Keywords: Al-Cu-Mg alloy, fatigue, pre-stretching, aluminum alloy casing pipe
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44

Sano, Yuji, Kiyotaka Masaki, Koichi Akita, Kentaro Kajiwara, and Tomokazu Sano. "Effect of Laser Peening on the Mechanical Properties of Aluminum Alloys Probed by Synchrotron Radiation and X-Ray Free Electron Laser." Metals 10, no. 11 (November 9, 2020): 1490. http://dx.doi.org/10.3390/met10111490.

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Synchrotron radiation (SR) and X-ray free electron laser (XFEL) are indispensable tools not only for the exploration of science but also for the evolution of industry. We used SR and XFEL to elucidate the mechanism and the effects of laser peening without coating (LPwC) which enhances the durability of metallic materials. X-ray diffraction (XRD) employing SR revealed that the residual stress (RS) in the top surface became compressive as the laser pulse irradiation density increased with appropriate overlapping of adjacent laser pulses. SR-based computed tomography (CT) was used to nondestructively reconstruct three-dimensional (3D) images of fatigue cracks in aluminum alloy, revealing that LPwC retarded crack propagation on the surface and inside of the sample. SR-based computed laminography (CL) was applied to friction stir welded (FSWed) aluminum alloy plates to visualize fatigue cracks propagating along the welds. The fatigue crack had complicated shape; however, it became a semi-ellipsoid once projected onto a plane perpendicular to the fatigue loading direction. Ultra-fast XRD using an XFEL was conducted to investigate the dynamic response of aluminum alloy to an impulsive pressure wave simulating the LPwC condition. The diffraction pattern changed from spotty to smooth, implying grain refinement or subgrain formation. Shifts in diffraction angles were also observed, coinciding with the pressure history of laser irradiation. The durations of the dynamic phenomena were less than 1 µs; it may be possible to use high-repetition lasers at frequencies greater than kHz to reduce LPwC processing times.
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45

Wagle, Sanat, and Hiroshi Kato. "Ultrasonic wave intensity reflected from fretting fatigue cracks at bolt joints of aluminum alloy plates." NDT & E International 42, no. 8 (December 2009): 690–95. http://dx.doi.org/10.1016/j.ndteint.2009.06.002.

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46

Myung, Nohjun, Jihye Seo, and Nak-Sam Choi. "Cyclic elastic modulus and low cycle fatigue life of woven-type GFRP coated aluminum plates." Composites Part B: Engineering 174 (October 2019): 107004. http://dx.doi.org/10.1016/j.compositesb.2019.107004.

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47

Zhu, Zongtao, Yuanxing Li, Mingyue Zhang, and Chen Hui. "Effects of stress concentration on the fatigue strength of 7003-T5 aluminum alloy butt joints with weld reinforcement." International Journal of Modern Physics B 29, no. 10n11 (April 23, 2015): 1540023. http://dx.doi.org/10.1142/s0217979215400238.

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Анотація:
7003-T5 Aluminum ( Al ) alloy plates with a thickness of 5 mm are welded by gas metal arc welding (GMAW) method in this work. In order to investigate the influence of stress concentration introduced by weld reinforcement on fatigue strength, the stress concentration factor of the butt joint is calculated. Microscopic and X-ray techniques were utilized to make sure there are no weld defects with large size in butt weld, which can induce extra stress concentration. The cyclic stress – number of cycles to failure (S–N) curves of the joints with and without the welder were obtained by fatigue testing, and the results show that the fatigue strength of 7003-T5 Al alloy butt joints with the weld reinforcement is 50 MPa, which is only 45% of the joints without the weld reinforcement. Fracture surface observation indicated that the fatigue source and propagation are dissimilar for the specimens with and without the welder due to the stress concentration at the weld root. The stress concentration with a factor of 1.7 has great effect on the fatigue strength, but little influence on the tensile strength.
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48

Li, Qi, Qichao Xue, Quansheng Hu, Ting Song, Yonghui Wang, and Siyang Li. "Cold Expansion Strengthening of 7050 Aluminum Alloy Hole: Structure, Residual Stress, and Fatigue Life." International Journal of Aerospace Engineering 2022 (June 9, 2022): 1–17. http://dx.doi.org/10.1155/2022/4057898.

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The 7050 aluminum alloy orifice plate is extruded and strengthened by the cold expansion process of slotted bushing holes. A three-dimensional finite element model was established for cold expansion strengthening of holes, and the residual stress distribution of 7050 aluminum alloy orifice plates is studied after cold expansion. The influence of different relative extrusion amounts and different sample thicknesses on the residual stress around the sample hole was analyzed, and the relationship between the extrusion amounts and the thicknesses of the substrate and the residual stress was obtained by analysis. The research results indicate that the cold expansion process of slotted bushing holes can enhance the residual stress distribution around the hole and form a strong residual stress layer. As the amounts of extrusion increase, the residual stress tends to increase, reaching the maximum when the amounts of extrusion are 4%. The residual stress on the surface of the extrusion inlet increases with the increase in the thickness of the substrate. Within the range of 3%-4% of the extrusion amounts, with the continuous increase of the extrusion amounts, the fatigue life has been substantially enhanced, and the number of fatigue life is more than 3 times that of the empty plate fatigue test.
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49

Moulgada, Abdelmadjid, Djafar Ait kaci, Mohammed El Sallah Zagane, Sahli Abderrahmane, and Rachid Zahi. "Study of mechanical behavior by fatigue of a cracked plate repaired by different composite patches." Frattura ed Integrità Strutturale 15, no. 56 (March 28, 2021): 195–202. http://dx.doi.org/10.3221/igf-esis.56.16.

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Анотація:
This research is based on the study of the fatigue behavior of an aluminum alloy plate with a central crack. The plate is subjected to a tensile loading on its lower and upper parts. Several parameters were highlighted, such as the loading effect with a load ratio R = 0. The effects of the load ratio on both the repaired and not repaired plates, by two composite patches, which are boron/epoxy and graphite/epoxy, were investigated, as well as the effect of the plate material on plate life, comparing different materials
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50

Mei, Hanfei, Mohammad Haider, Roshan Joseph, Asaad Migot, and Victor Giurgiutiu. "Recent Advances in Piezoelectric Wafer Active Sensors for Structural Health Monitoring Applications." Sensors 19, no. 2 (January 18, 2019): 383. http://dx.doi.org/10.3390/s19020383.

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In this paper, some recent piezoelectric wafer active sensors (PWAS) progress achieved in our laboratory for active materials and smart structures (LAMSS) at the University of South Carolina: http: //www.me.sc.edu/research/lamss/ group is presented. First, the characterization of the PWAS materials shows that no significant change in the microstructure after exposure to high temperature and nuclear radiation, and the PWAS transducer can be used in harsh environments for structural health monitoring (SHM) applications. Next, PWAS active sensing of various damage types in aluminum and composite structures are explored. PWAS transducers can successfully detect the simulated crack and corrosion damage in aluminum plates through the wavefield analysis, and the simulated delamination damage in composite plates through the damage imaging method. Finally, the novel use of PWAS transducers as acoustic emission (AE) sensors for in situ AE detection during fatigue crack growth is presented. The time of arrival of AE signals at multiple PWAS transducers confirms that the AE signals are originating from the crack, and that the amplitude decay due to geometric spreading is observed.
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