• Title/Summary/Keyword: Paris' law

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XFEM for fatigue and fracture analysis of cracked stiffened panels

  • Kumar, M.R. Nanda;Murthy, A. Ramachandra;Gopinath, Smitha;Iyer, Nagesh R.
    • Structural Engineering and Mechanics
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    • v.57 no.1
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    • pp.65-89
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    • 2016
  • This paper presents the development of methodologies using Extended Finite Element Method (XFEM) for cracked unstiffened and concentric stiffened panels subjected to constant amplitude tensile fatigue loading. XFEM formulations such as level set representation of crack, element stiffness matrix formulation and numerical integration are presented and implemented in MATLAB software. Stiffeners of the stiffened panels are modelled using truss elements such that nodes of the panel and nodes of the stiffener coincide. Stress Intensity Factor (SIF) is computed from the solutions of XFEM using domain form of interaction integral. Paris's crack growth law is used to compute the number of fatigue cycles up to failure. Numerical investigations are carried out to model the crack growth, estimate the remaining life and generate damage tolerant curves. From the studies, it is observed that (i) there is a considerable increase in fatigue life of stiffened panels compared to unstiffened panels and (ii) as the external applied stress is decreasing number of fatigue life cycles taken by the component is increasing.

Crack propagation in flexural fatigue of concrete using rheological-dynamical theory

  • Pancic, Aleksandar;Milasinovic, Dragan D.;Goles, Danica
    • Computers and Concrete
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    • v.27 no.1
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    • pp.55-62
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    • 2021
  • The concrete fatigue analysis can be performed with the use of fracture mechanics. The fracture mechanics defines the fatigue crack propagation as the relationship of crack growth rate and stress intensity factor. In contrast to metal, the application of fracture mechanics to concrete is more complicated and therefore many authors have introduced empirical expressions using Paris law. The topic of this paper is development of a new prediction of fatigue crack propagation for concrete using rheological-dynamical analogy (RDA) and finite element method (FEM) in the frame of linear elastic fracture mechanics (LEFM). The static and cyclic fatigue three-point bending tests on notched beams are considered. Verification of the proposed approach was performed on the test results taken from the literature. The comparison between the theoretical model and experimental results indicates that the model proposed in this paper is valid to predict the crack propagation in flexural fatigue of concrete.

Probabilistic Characteristics of Fatigue Behavior Parameter of Paris-Erdogan Law in Mg-Al-Zn Alloy (Mg-Al-Zn 합금의 Paris-Erdogan 법칙에 따른 피로거동 파라미터의 확률론적 특성)

  • Choi, Seon-Soon
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.35 no.4
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    • pp.375-381
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    • 2011
  • The primary aim of this study is to investigate the probabilistic characteristics of the fatigue parameters that describe the fatigue crack growth behavior in magnesium alloy. Statistical fatigue crack propagation experiments have been performed on rolled AZ31 magnesium alloy CT specimens with different specimen thickness, load ratio, and maximum load at ambient temperature in a laboratory. Using the statistical fatigue data obtained from these experiments, the goodness-of-fit of the probability distribution of the fatigue behavior parameters is evaluated in this study by performing statistical analyses. The crack growth rate coefficient is a fatigue parameter having a very large COV(Coefficient of Variation), but the variation of a crack growth rate exponent is not substantial. It is considered that a crack growth rate exponent can be a material constant. It is also found that the best fit probability distribution of the parameters such as the crack growth rate coefficient and crack growth rate exponent for a magnesium alloy is a three-parameter Weibull distribution, and two-parameter Weibull distribution is a good distribution only for the crack growth rate coefficient.

Effect of Specimen Orientation on Fatigue Crack Growth Behavior in Friction Stir Welded Al7075-T651 Joints (마찰교반용접된 Al7075-T651 용접부의 피로균열전파 거동에 미치는 시험편 채취방향의 영향)

  • Jeong, Yeui Han;Kim, Seon Jin
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.38 no.12
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    • pp.1317-1323
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    • 2014
  • The aim of this paper is to investigate the effects of crack orientation on fatigue crack growth behavior in friction stir welded (FSWed) Al 7075-T651. Fatigue crack growth testing was conducted on compact tension (CT) specimens machined from the friction stir welds and the base metal under constant stress intensity factor range control. Tests were performed with the crack propagating nominally perpendicular to the weld line (termed the TL specimen) and the crack propagating in a parallel direction of the weld line (termed the LT specimen), and with three different constant stress intensity factor ranges. Both these specimen orientations were found to have a considerable effect on the fatigue crack growth behavior. Paris's law was adopted for the analysis of experimental results; the exponent m of the WM-LT specimen was determined to be 3.56, which was the largest value in this experimental conditions.

Evaluation of Corrosion Fatigue Characteristics of 12Cr Steel Using Backward Radiated Ultrasound (후방복사된 초음파를 이용한 12Cr강 부식 피로특성 평가)

  • Kwon, Sung-Duk;Yoon, Seok-Soo;Song, Sung-Jin;Bae, Dong-Ho
    • Journal of the Korean Society for Nondestructive Testing
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    • v.20 no.5
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    • pp.397-401
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    • 2000
  • The corrosion-fatigue characteristics of the 12Cr steel, which is widely used in fossil power plants as a turbine blade material, are evaluated nondestructively by use of the Rayleigh surface wave. In this study, the frequency dependency of the Rayleigh surface wave is investigated indirectly by measuring the angular dependency of the backward radiation of the incident ultrasonic wave in the aged specimens, and then compared to the corrosion-fatigue characteristics. The width of the backward radiation profile decreases as the increase of the aging temperature, which seems to result from the increase of the effective degrading layer thickness. This parameter also shows an inversely proportionality to the exponent, m, in the Paris law which predicts the crack size increasement due to fatigue. The result observed in this study demonstrates high potential of the backward radiated ultrasound as a tool for the nondestructive evaluation of the corrosion-fatigue characteristics of the aged materials.

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The Effect of Specimen Thickness on the Fatigue Crack Propagation Rate (피로크랙전파율에 대한 시험편 두께의 영향)

  • Koh, Sung-Wi;Um, Yoon-Sung
    • Journal of the Korean Society of Fisheries and Ocean Technology
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    • v.24 no.1
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    • pp.44-49
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    • 1988
  • The paper presents the preliminary results of an esperimental study on crack growth under tension-tension fatigue loading. A purpose of the study is to find the effect of the specimen thickness on crack propagation behaviors. The thickness of the low catbon steel specimens the are used in the experiments are 5, 10, 15,20, and 25 mm. the type of specimen considering in the present study is compact tension specimen.Crack growth behaviors are obseved and measured by travelling microscope. From the study, the followings are found; 1. There is a certain specimen thickness that is the shortest farigue life. The fatigue life of 15mm specimen is the shorter then that of any other opecimen 2. The crack initiation of the thick specimen is slower than that of thin specimen. But the crack propagation rate is just the opposite. 3. The range which is the exponent, m of power law(paris) is 1.98-4.59. the thicker the spec-imen is, the higher the value of m is.

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The Legal Status of Military Aircraft in the High Seas

  • Kim, Han Taek
    • The Korean Journal of Air & Space Law and Policy
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    • v.32 no.1
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    • pp.201-224
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    • 2017
  • The main subject of this article focused on the legal status of the military aircraft in the high seas. For this the legal status of the military aircraft, the freedom of overflight, the right of hot pursuit, the right of visit and Air Defense Identification Zone (ADIZ) were dealt. The 1944 Chicago Convention neither explicitly nor implicitly negated the customary norms affecting the legal status of military aircraft as initially codified within the 1919 Paris Convention. So the status of military aircraft was not redefined with the Chicago Convention and remains, as stated in the 1919 Paris Convention, as a norm of customary international law. The analyses on the legal status of the military aircraft in the high seas are found as follows; According to the Article 95 of the 1982 United Nations Convention on the Law of the Sea (UNCLOS) warships on the high seas have complete immunity from the jurisdiction of any State other than the flag State. We can suppose that the military aircraft in the high seas have also complete immunity from the jurisdiction of any State other than the flag State. According to the Article 111 (5) of the UNCLOS the right of hot pursuit may be exercised only by warships or military aircraft, or other ships or aircraft clearly marked and identifiable as being on government service and authorized to that effect. We can conclude that the right of hot pursuit may be exercised by military aircraft. According to the Article 110 of the UNCLOS a warship which encounters on the high seas a foreign ship, is not justified in boarding it unless there is reasonable ground for suspecting that: (a) the ship is engaged in piracy, (b) the ship is engaged in the slave trade, (c) the ship is engaged in an unauthorized broadcasting and the flag State of the warship has jurisdiction under article 109, (d) the ship is without nationality, or (e) though flying a foreign flag or refusing to show its flag, the ship is, in reality, of the same nationality as the warship. These provisions apply mutatis mutandis to military aircraft. As for Air Defence Identification Zone (ADIZ) it is established and declared unilaterally by the air force of a state for the national security. However, there are no articles dealing with it in the 1944 Chicago Convention and there are no international standards to recognize or prohibit the establishment of ADIZs. ADIZ is not interpreted as the expansion of territorial airspace.

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Type 347 stainless steel 피로시험 데이터의 통계처리

  • Min, Gi-Deuk;Kim, Seon-Jin
    • Proceedings of the Materials Research Society of Korea Conference
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    • 2009.11a
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    • pp.35.2-35.2
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    • 2009
  • 최근 전세계적으로 저탄소, 녹색성장으로 인하여 원자력발전이 주목받고 있다. 또한 에너지의 고효율로 인한 발전소의 설비가 대형화가 됨에 따라 발전소의 수명평가와 건전성평가가 중요해지고 있다. 일반적으로 구조물 내에 존재하는 균열의 크기와 형상을 파악하여 피로균열전파속도를 평가함으로써 건전성평가를 확인하고 있다. 그리고 고온, 고압에서의 피로균열전파속도는직류전위차 (Direct Current Potential Drop : DCPD)법을 사용하고 있다. DCPD법은 균열의 정밀한 측정방법으로써 측정시 오차가 발생하기 때문에 ASTM에서 제시된 incremental polynomial 법을 권고하고 있다. 따라서 본 연구에서는 피로균열전파전파속도의통계적처리를 통해서 합리적인 곡선을 구하여 건전성평가에 활용하고자 한다. 실험에 사용된 시편은 두께 5mm, 폭 25.4mm CT시편을 사용하였으며, 1mm의 예비균열을 주었다. 그리고 실험온도는 상온에서 실시 하였으며, 주파수는 10Hz를 주었다. 그리고 DCPD 측정을 위해 5A의 전류를 주었으며, 이때 측정된 전압값을 ASTM에 제시된 관계식에넣어 균열길이로 환산하였으며, 데이터처리는 ASTM에 제시된 incremental polynomial법을 기본적으로 사용하였다. 또한 ASTM에 제시된 2n+1을 이용하여 데이터의 수 n을 1~7 까지 변화를 주어 3~15 point 까지 데이터를 처리하여곡선을 제시하였다. 분석결과 $R^2$값이 1을 기준으로 했을 때 3~7 point 까지는큰 차이를 보이지 않았지만 9-point 이후부터는 $R^2$ 감소함을 알 수 있었다. 또한 적용된 데이터의수에 따라 피로군열전파속도 곡선에서 측정된 Paris law의 n값과 C 값은 큰차이를 보이지 않았다.

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A study on the through crack behavior of aluminum alloy with cantilever beam type under variable load (외팔보 형식의 하중진폭 변화에 대한 Al 합금의 관통균열 거동에 관한 연구)

  • Yoo, Heonil;Kim, Yeob-Rae
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.22 no.4
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    • pp.834-842
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    • 1998
  • This paper examines the crack growth behavior of 7075-T651 and 5052-H32 aluminum alloy under high-low block loading condition. The cantilever beam type specimen with a chevron notch is used in this study. The crack growth and closure ae investigated by compliance method. The applied stress ratios are R=0.15, 0.0, -0.15 and R=-0.15, 0.0, 0.15. The crack growth rate was found to increase as the load amplitude increases. However,${\bigtriangleup}K_eff$ was almost independent on the stress ratio. The experimental constants of 7075-T651 and 5052-H32 in Paris law were c`=1-1.3${\times}{10^-7},m`=3~3.2 and c`=4~6{\times}{10^-9}, m`=4.3-4.8$, respectively. $K_op$ of 7075-T651 and 5052-H32 becomes smaller as the stress ratio decreases. It seems that the crack closure affects $K_op$.

A Study on Fatigue Crack Propagation Behavior in Random Short-Fiber SMC Composites (비규칙 단섬유강화 SMC 복합재료의 피로균열 전파거동에 관한 연구)

  • Kim, Jae-Dong;Koh, Sung-Wi
    • Journal of the Korean Society of Fisheries and Ocean Technology
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    • v.26 no.2
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    • pp.204-212
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    • 1990
  • The SMC composite, now being considered in certain structural applications, is anticipated to experience repeated loading during service. Thus, understanding of the fatigue behavior is essential in proper use of the composite material. In this paper, using the SMC composite composed of E-glass chopped strand and unsaturated polyester resin three point bending fatigue tests are carried out to investigate the fatigue crack propagating behavior under various cyclic stresses and fatigue damage of various microcrack forms. The following results are obtained from this study; 1) Most of the total fatigue life of the SMC composite is consumed at the initial extension or the growth of the macroscopic crack. 2) A Paris' type power-law relationship between the crack propagation rate and stress intensity factor range is obtained, and the value of material constant m is much higher (m=9~11)than that of other metals. 3) In case of high cyclic stress the fatigue damage show high microcrack density and short crack length, but in case of low cyclic stress does it vice versa. 4) Fatigue damage is characterized by microcrack density, crack length and distribution of crack orientation.

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