Fracture of Brittle Microbeams

2004 ◽  
Vol 71 (3) ◽  
pp. 424-427 ◽  
Author(s):  
M. Ostoja-Starzewski
Keyword(s):  
Fracture Criterion ◽  
Dead Load ◽  
Ensemble Averaging ◽  
Critical Crack ◽  
Critical Crack Length ◽  
Crack Driving Force ◽  
Surface Energies ◽  
Crack Stability ◽  
Stored Elastic Energy ◽  
Load Conditions

The random polycrystalline microstructure of microbeams necessitates a reexamination of the crack driving force G stemming from the Griffith fracture criterion. It is found that, in the case of dead-load conditions, G computed by straightforward averaging of the spatially random elastic modulus E is lower than that obtained by correct ensemble averaging of the stored elastic energy. This result holds for both Euler-Bernoulli and Timoshenko models of micro-beams. However, under fixed-grip conditions G is to be computed by a direct ensemble averaging of E. It turns out that these two cases provide bounds on G under mixed loading. Furthermore, crack stability is shown to involve a stochastic competition between potential and surface energies, whose weak randomness leads to a relatively stronger randomness of the critical crack length.

scholarly journals Snow fracture in relation to slab avalanche release: critical state for the onset of crack propagation

2017 ◽  
Vol 11 (1) ◽  
pp. 217-228 ◽  
Author(s):  
Johan Gaume ◽  
Alec van Herwijnen ◽  
Guillaume Chambon ◽  
Nander Wever ◽  
Jürg Schweizer
Keyword(s):  
Crack Propagation ◽  
Slope Angle ◽  
Critical Length ◽  
Snow Layer ◽  
Critical Crack ◽  
Critical Crack Length ◽  
New Model ◽  
Avalanche Forecasting ◽  
Weak Layer ◽  
Recent Developments

Abstract. The failure of a weak snow layer buried below cohesive slab layers is a necessary, but insufficient, condition for the release of a dry-snow slab avalanche. The size of the crack in the weak layer must also exceed a critical length to propagate across a slope. In contrast to pioneering shear-based approaches, recent developments account for weak layer collapse and allow for better explaining typical observations of remote triggering from low-angle terrain. However, these new models predict a critical length for crack propagation that is almost independent of slope angle, a rather surprising and counterintuitive result. Based on discrete element simulations we propose a new analytical expression for the critical crack length. This new model reconciles past approaches by considering for the first time the complex interplay between slab elasticity and the mechanical behavior of the weak layer including its structural collapse. The crack begins to propagate when the stress induced by slab loading and deformation at the crack tip exceeds the limit given by the failure envelope of the weak layer. The model can reproduce crack propagation on low-angle terrain and the decrease in critical length with increasing slope angle as modeled in numerical experiments. The good agreement of our new model with extensive field data and the ease of implementation in the snow cover model SNOWPACK opens a promising prospect for improving avalanche forecasting.

A LIFE PREDICTION MODEL OF THERMAL BARRIER COATINGS

2010 ◽  
Vol 24 (15n16) ◽  
pp. 3161-3166 ◽  
Author(s):  
LIYONG NI ◽  
CHAO LIU ◽  
CHUNGEN ZHOU
Keyword(s):  
Crack Propagation ◽  
Prediction Model ◽  
Thermal Barrier Coatings ◽  
Life Prediction ◽  
Crack Propagation Rate ◽  
Thermal Barrier ◽  
Critical Crack ◽  
Critical Crack Length ◽  
Barrier Coatings ◽  
Life Prediction Model

The durability and reliability of thermal barrier coatings(TBCs) have become a major concern of hot-section components due to lack of a reliable life prediction model. In this paper, it is found that the failure location of TBCs is at the TBC/TGO interface by a sequence of crack propagation and coalescence process. The critical crack length of failure samples is 8.8mm. The crack propagation rate is 3-10µm/cycle at the beginning and increases largely to 40µm/cycle near coating failure. A life prediction model based a simple fracture mechanics approach is proposed.

Fatigue–oxidation–creep damage model under axial-torsional thermo-mechanical loading

2019 ◽  
Vol 29 (5) ◽  
pp. 810-830 ◽  
Author(s):  
Dao-Hang Li ◽  
De-Guang Shang ◽  
Jin Cui ◽  
Luo-Jin Li ◽  
Ling-Wan Wang ◽  
...  
Keyword(s):  
Damage Model ◽  
Creep Damage ◽  
Fatigue Loading ◽  
Damage Mechanism ◽  
Critical Crack ◽  
Critical Crack Length ◽  
Mechanical Fatigue ◽  
Proposed Model ◽  
Oxidation Damage ◽  
Creep Damage Model

A fatigue–oxidation–creep damage model that can take into account the effect of multiaxial cyclic feature on the damage mechanism is proposed under axial-torsional thermo-mechanical fatigue loading. In the proposed model, the effects of non-proportional additional hardening on fatigue, oxidation, and creep damages are considered, and the variation of oxidation damage under different high temperature loading conditions is also described. Moreover, the intergranular creep damage needs to be equivalent to the transgranular damage before accumulating with the fatigue and oxidation damages. The fatigue, oxidation, and creep damages can be expressed as the fractions of fatigue life, critical crack length, and creep rupture time, respectively, which allows the linear accumulation of different types of damages on the basis of life fraction rule. In addition, the proposed model is validated by various fatigue experimental results, including uniaxial thermo-mechanical fatigue, axial-torsional thermo-mechanical fatigue, and isothermal axial-torsional fatigue under proportional and non-proportional loadings. The results showed that the errors are within a factor of 2.

Fracture Mechanics of Bone

1993 ◽  
Vol 115 (4B) ◽  
pp. 549-554 ◽  
Author(s):  
J. W. Melvin
Keyword(s):  
Fracture Mechanics ◽  
Bone Fracture ◽  
Longitudinal Crack ◽  
Compact Bone ◽  
Plastic Zone Size ◽  
Geometric Constraints ◽  
External Loading ◽  
Specimen Thickness ◽  
Critical Crack ◽  
Critical Crack Length

This paper reviews the progress that has been made in applying the principles of fracture mechanics to the topic of fracture of long bones. Prediction of loading conditions which result in the propagation of fractures in bones has been of interest to the field of trauma biomechanics and orthopedics for over one hundred years. Independent verifications, by various investigators, of bone fracture mechanics parameters are reviewed and investigations of the effects of bone density and specimen thickness on the critical fracture mechanics parameters and of other factors such as critical crack length and plastic zone size in bovine femoral bone, and the effects of crack velocity on fracture mechanics parameters in bovine tibial bone are discussed. It took over ten years for the techniques of bone fracture mechanics to be applied to human compact bone, due primarily to geometric constraints from the smaller size of human bones. That work will be reviewed along with other continuing work to define the orientation dependence of the fracture mechanics parameters in bone and to refine the experimental techniques needed to overcome the geometric constraints of specimen size. A discussion is included of work still needed to determine fracture mechanics parameters for transverse and longitudinal crack propagation in human bone and to establish the effects of age on those parameters. Finally, a discussion will be given of how this knowledge needs to be extended to allow prediction of whole bone fracture from external loading to aid in the design of protective systems.

Impact of PWSCC and Current Leak Detection on Leak-Before-Break Acceptance

2005 ◽  
Author(s):  
Gery Wilkowski ◽  
Rick Wolterman ◽  
Dave Rudland
Keyword(s):  
Fatigue Crack ◽  
Crack Length ◽  
Flow Path ◽  
Critical Crack ◽  
Cracking Behavior ◽  
Critical Crack Length ◽  
Crack Morphology ◽  
Actual Flow ◽  
The Difference ◽  
Morphology Parameters

This paper assesses the effect of using primary water stress corrosion cracking (PWSCC) crack morphology parameters (roughness, number of turns, and actual flow path/pipe thickness) in determining the difference in the leakage crack length, and how the difference in the leaking crack lengths changes typical margins from past LBB submittals and published reports. Several past LBB submittal cases were selected; in addition, cases from generic LBB reports published by EPRI were also selected. The results of the analyses showed that the past submittals by nuclear steam system supply (NSSS) companies frequently used the surface roughness comparable to an air-fatigue crack with no turns and the actual flow path equal to the thickness of the pipe. This condition would give the shortest possible leakage flaw length. The roughness, number of turns, and actual flow path to thickness ratio for PWSCC cracks were determined from photomicrographs of service-removed cracks. When using the PWSCC crack morphology parameters that corresponded to the crack growing parallel to the long direction of the dendritic grains (V.C. Summer and Ringhals cases), then the leakage flaw length increased 69 percent over the air-fatigue crack length at the same leak rate. Using the same critical crack length as was used in the initial LBB submittals and the published documents, the margins on the crack length changed from 1.77 to 6.0 for the initial submittals (which we also reproduced) to 0.88 to 2.74 from our calculations for a PWSCC crack. If the crack grew in the buttered region of the bimetallic weld, then based on metallographic sections from service-removed flaws, there would be a more tortuous flow path. For this crack condition, in all but one case, the margins on the normal operating versus N+SSE crack lengths were below the safety factor of two required for LBB approval. The average margin decreased from 3.39 for the air-fatigue crack to 1.55 for the PWSCC crack growing transverse to the long direction of the dendritic grains. This was about an additional 20 percent decrease in the margin from the case of having the PWSCC grow parallel to the long direction of the dendritic grains. These results show that LBB is difficult to satisfy for PWSCC susceptible pipe using the current SRP 3.6.3 LBB approach. This LBB assessment did not consider the possible development of a long circumferential surface crack, which would be more detrimental to LBB behavior. Such cracking behavior would violate the LBB screening criterion.

Probabilistic Leak Before Break

2018 ◽  
Author(s):  
L. Stefanini ◽  
F. J. Blom
Keyword(s):  
Fracture Toughness ◽  
Yield Stress ◽  
Master Curve ◽  
Structural Integrity ◽  
Probabilistic Approach ◽  
Leakage Rate ◽  
Critical Crack ◽  
Critical Crack Length ◽  
Integrity Assessment ◽  
Leak Before Break

In this study a probabilistic Leak-Before-Break (LBB) analysis was carried out based on the R6 FAD Option 1 assessment method. The method uses the material fracture toughness and yield stress in order to determine, deterministically, a Critical Crack Length (CCL) and a Leakage Rate (LR) through a crack. In order to define the fracture toughness of the material, the Master Curve approach was used accordingly to BS7910:2013 Annex J. Initially, deterministic analyses were carried out and the fracture toughness and yield stress were set to 190 MPa√m and 158 MPa, respectively. In order to implement a probabilistic approach, the yield stress and fracture toughness were introduced as stochastic parameter. The Fracture toughness was generated using a Weibull distribution to match the Master Curve. The distribution was built such that 190 MPa√m represents the 5% probability fracture toughness. The Yield stress (0.2% proof strength) was generated using a normal distribution with standard deviation 10.35 MPa such that the average value was 175 MPa and the lower bound (5% of probability of occurrence) was 158 MPa. The choice of building the distribution as above mentioned was justified by the fact that in structural integrity assessment the lower 5% is generally used for material parameters. Thus, once a Detectable Leakage Rate (DLR) was determined, it was possible to assign an implicit probability of failure to the deterministic case. The calculations were then extended by using several LR formulas. The calculations were carried out making use of the probabilistic software RAP++ coupled to MATLAB. The probabilities of failure were calculated with regard to a postulated DLR and a DLRSF corrected with a safety factor of 10. The probabilities of failure for the DLRSF were proved to be 9 to 15 times higher than for the postulated DLR case, which leads to the opportunity of conservatism reduction.

Comparing simulated and manual snow profiles to derive thresholds for modeled snow instability metrics

2020 ◽  
Author(s):  
Stephanie Mayer ◽  
Alec van Herwijnen ◽  
Mathias Bavay ◽  
Bettina Richter ◽  
Jürg Schweizer
Keyword(s):  
Snow Cover ◽  
Input Data ◽  
Climate Models ◽  
Weather Prediction ◽  
Mechanical Instability ◽  
Critical Crack ◽  
Critical Crack Length ◽  
Snow Stratigraphy ◽  
Meteorological Input ◽  
Weather Stations

<p>Numerical snow cover models enable simulating present or future snow stratigraphy based on meteorological input data from automatic weather stations, numerical weather prediction or climate models. To assess avalanche danger for short-term forecasts or with respect to long-term trends induced by a warming climate, the modeled vertical layering of the snowpack has to be interpreted in terms of mechanical instability. In recent years, improvements in our understanding of dry-snow slab avalanche formation have led to the introduction of new metrics describing the fracture processes leading to avalanche release. Even though these instability metrics have been implemented into the detailed snow cover model SNOWPACK, validated threshold values that discriminate rather stable from rather unstable snow conditions are not readily available. To overcome this issue, we compared a comprehensive dataset of almost 600 manual snow profiles with simulations. The manual profiles were observed in the region of Davos over 17 different winters and include stability tests such as the Rutschblock test as well as observations of signs of instability. To simulate snow stratigraphy at the locations of the manual profiles, we obtained meteorological input data by interpolating measurements from a network of automatic weather stations. By matching simulated snow layers with the layers from traditional snow profiles, we established a method to detect potential weak layers in the simulated profiles and determine the degree of instability. To this end, thresholds for failure initiation (skier stability index) and crack propagation criteria (critical crack length) were calibrated using the observed stability test results and signs of instability incorporated in the manual observations. The resulting instability criteria are an important step towards exploiting numerical snow cover models for snow instability assessment.</p>

Fracture of Flat and Curved Aluminum Sheets With Stiffeners Parallel to the Crack

1961 ◽  
Vol 83 (1) ◽  
pp. 32-38 ◽  
Author(s):  
J. Frisch
Keyword(s):  
Crack Propagation ◽  
Crack Length ◽  
Uniaxial Tension ◽  
Radius Of Curvature ◽  
Appreciable Effect ◽  
Critical Crack ◽  
Critical Crack Length ◽  
Crack Location ◽  
Aluminum Sheets ◽  
Curved Panels

The mode of crack propagation and failure in relatively large 2024-T3 aluminum sheets reinforced with stiffeners parallel to the crack direction has been investigated. Curved specimens with a 69-in. radius of curvature as well as flat panels were subjected to uniaxial tension perpendicular to a simulated crack to study the effects of curvature, crack location, and stiffener spacing. Increase in strength due to stiffening particularly in the curved panels was observed although these specimens exhibited considerable lower crack strength than flat ones. For the specimens tested, crack location as well as variations of stiffener spacing from 3 to 12 in. had no appreciable effect on either critical crack length or failure stress.

Numerical Analysis of the Crack Growth in a High Loaded Bolt Connection

2007 ◽  
Vol 348-349 ◽  
pp. 625-628
Author(s):  
Marko Knez ◽  
Srečko Glodež ◽  
Janez Kramberger
Keyword(s):  
Crack Growth ◽  
Crack Size ◽  
Initial Crack ◽  
Structural Elements ◽  
Element Analysis ◽  
Critical Crack ◽  
Critical Crack Length ◽  
Final Failure ◽  
Heavy Loads ◽  
Bolt Connection

The present paper deals with the research on the crack growth in a bolt connection of a lug for crane counter weight bars. Counter weight bars are structural elements that are subjected to very heavy loads and therefore special attention must be paid. The main purpose of this research is to determine the number of the load cycles required for a crack to propagate from initial to critical crack length, when the final failure can be expected to occur. All required material parameters and the experimental results were determined in our previous research. The influence of the initial crack size upon the remaining life of the lug is researched numerically by means of finite element analysis and analytically by use of the corrected analytical model.

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