Crack initiation under thermal fatigue: An overview of CEA experience: Part II (of II): Application of various criteria to biaxial thermal fatigue tests and a first proposal to improve the estimation of the thermal fatigue damage

A Part I accompanying paper clearly showed that for a given level of strain range (Δ?), the number of cycles required to achieve crack initiation is significantly lower in biaxial thermal fatigue than in uniaxial isothermal fatigue.Such discrepancy does not come from a thermal effect, as it is emphasized by a comparison between the uniaxial data, coming either from thermomechanical fatigue tests, or from isothermal low cycle fatigue tests. A detrimental effect of multiaxial loading on fatigue life is noticed in many cases as reported in the literature.In this frame, the goal of this paper is to propose criteria in order to take into account the reduction of fatigue life resulting from the multiaxiality. Among all the examined multiaxial criteria, a criterion based on strain proposed by Zamrik, and a new criterion based on energy proposed by “Ecole Polytechnique” give the best estimations. Furthermore, application of the Zamrik’s criterion using the RCC–MR method is very promising for the design engineer. Indeed, these two criteria exhibit a notable potential, since they are well adapted to all the available thermal fatigue experimental data, despite significant differences between approaches and processes developed by both accessible facilities.However, such investigation must be continued with achievement of additional thermal fatigue tests (for higher number of cycles…), and isothermal biaxial fatigue tests.     

Experimental and analytical studies in crack initiation under fatigue: Part I — Experimental studies

Mechanistic investigations of damage evolution before crack initiation in an amorphous polymer show that damage consists of a core of highly dense crazing and a peripheral less dense zone of crazing. Damage characterization is carried out at consecutive configurations of the damage zone. Analysis of the kinematics of damage at different times involves comparisons of the inertia moments of damage distributions. The results indicate that damage evolution between consecutive configurations can be approximated by a linear transformation of the space variables. Thus, the process of damage growth can be described by translation and deformation of the damage zone. The growth rates of the damage zone movements decrease until crack initiation. In all cases, the average densities exhibit a damping type behavior with the number of cycles. The crack initiates within a core zone immediately ahead of the stress concentrator. The experimental results suggest that damage density within the core zone is independent of the loading conditions considered herein. This value is approximately equal to the damage density around the crack tip during slow crack propagation. The crack length at initiation is found to increase exponentially with the stress level. A simple decaying exponential relationship relates the crack initiation times and the applied stress level. This result is consistent with the fracture models based on absolute reaction theories.     

An experimental investigation into dynamic fracture: I. Crack initiation and arrest

Problems of dynamic crack propagation are examined experimentally in a series of four papers. In this paper, the first of this series, crack initiation and arrest are investigated in thin sheets of Homalite-100. It is found that as the rate of loading increases to as high as 10⁵ MPa/sec, the stress intensity factor required to initiate crack growth increases markedly. Crack arrest resulting from a simulated pressurized semi-infinite crack in an unbounded medium was found to occur abruptly. There was no continuous deceleration and the crack always stopped at a constant value of the stress intensity factor, which value was lower than the stress intensity factor required for quasi-static crack growth initiation.The second paper in this series deals with the occurrence of micro cracks at the front of the running main crack which control the rate of crack growth. The micro cracks are recorded by real time photography. By the same means it is shown that these micro cracks grow and turn away smoothly from the direction of the main crack in the process of branching.The third contribution establishes the hitherto unreported occurrence that cracks can propagate rapidly with constant velocity even though the stress intensity factor varies considerably during this propagation. This velocity is determined by the initial stress wave loading on the crack tip, and is changed, within limits, only by stress pulses of sufficient magnitude and brevity of rise time.The final paper in the series deals with the effect of stress waves on the behavior of running cracks, in particular with the influence of stress waves on the branching phenomenon. Also, crack curving under transient stress waves is examined.These results are believed to apply to materials other than Homalite 100 and the reasons for this belief are discussed in this first contribution.

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Résumé On passe en revue sous l'angle expérimental dans quatre articles les problèmes de propagation dynamique d'une fissure. Dans ce premier mémoire, on étudie l'amorçage et l'arrêt d'une fissure dans des feuillards d'Homalite 100. On trouve que lorsque la vitesse de sollicitation croit jusque 10⁵ MPa/sec, le facteur d'intensité de contrainte nécessaire au démarrage de la propagation de la fissure s'accroît de manière notable. L'arrêt de fissuration caractérisant une fissure semi-infinie supposée soumise à une pression dans un milieu non limité se produit brutalement. On n'observe pas de décélération continue et la fissure s'arrête pour une valeur constante du facteur d'intensité de contraintes, laquelle est inférieure à celle nécessaire à l'amorçage d'une croissance de fissure semi-statique.Le deuxième mémoire de cette série traite de l'apparition de microfissures sur le front de propagation de la fissure principale, et de leur rôle dans la vitesse de croissance d'une fissure. Les microfissures sont enregistrées par photographie en temps réel. On montre par la même méthode comment les microfissures croissent et s'écartent de la direction de propagation principale, dans un processus d'arborescence.La troisième contribution fait état d'un phénomène jusqu'ici non décrit, selon lequel des fissures peuvent se propager rapidement à une vitesse constante, même si le facteur d'intensité de contraintes varie de manière significative au cours de cette propagation.On détermine cette vitesse constante à partir de l'onde de choc initiale associée à la sollicitation de l'extrémité de l'entaille et one montre qu'elle ne peut être modifiée, dans certaines limites, que par des impulsions d'une amplitude et d'une accélération suffisante.Le dernier article de la série est relatif à l'effet des ondes de contraintes sur le comportement de fissures en cours de développement, et, en particulier à leur influence sur le phénomène d'arborescence. On examine également comment des fissures peuvent s'infléchir sous l'effet d'ondes de contraintes.Les auteurs pensent que ces résultats sont applicables à d'autres matériaux que l'Homalite 100. Les raisons de cette assertion sont discutées dans la présente contribution.

     

AlSi10Mg(Cu)铸铝合金的热疲劳裂纹萌生及早期扩展行为

微观观察AlSi10Mg(Cu)铸铝合金在热疲劳裂纹的萌生和早期扩展过程,重点研究共晶硅粒子对热疲劳裂纹行为的影响。结果表明:热疲劳裂纹萌生于脱粘共晶硅粒子与铝基体间的开裂界面,原因是共晶硅粒子与铝基体的热膨胀系数不同,引起热循环过程中两相热应变不协调,从而在两相界面处产生循环应力而引起疲劳破坏。热疲劳裂纹的扩展在长度和宽度上同时进行,具有良好塑性的铝枝晶对疲劳裂纹的扩展起阻碍作用。对热疲劳过程中共晶硅粒子周围应力场的模拟分析进一步解释了实验现象。     

An experimental approach to estimate damage and remaining life of metals under uniaxial fatigue loading

An experimental procedure to estimate damage evolution and remaining fatigue life of metals associated with fatigue loading is presented. Experimental phase involves uniaxial tension–compression fatigue tests performed with solid API 5L X52 and tubular carbon steel 1018 specimens subjected to both constant and variable amplitude loading. A correlation between the so-called damage parameter and the thermal response of a material at different damage levels is proposed. Results demonstrate that the correlation can estimate damage evolution with reasonable accuracy in both constant and variable amplitude fatigue processes. It is shown that under the conditions tested the evolution of damage parameter with respect to the normalized fatigue life is independent of the load amplitude, load ratio, loading sequence, material properties, and specimen geometry. The proposed correlation and the relationship between the damage parameter and the normalized fatigue life are employed to develop a non-destructive method to predict the remaining fatigue life of metallic specimens with prior fatigue damage. The method is applied to both constant and variable amplitude loading and the predicted results are found to be in good agreement with those obtained from the experiments.     

Thermal conductivity of fibre-phenolic resin composites. Part I: Thermal diffusivity measurements

Measurements have been made on the thermal diffusivity of fibre-phenolic resin composites between 20 and 400°C. The matrix material was the phenolic resin SC-1008 manufactured by Monsanto. Two composite systems were considered: a two-directional composite reinforced with carbon fibres woven into an eight-harness satin weave, and a silica fibre composite orthogonally reinforced in three mutually perpendicular directions. One-directional composites were also prepared using the same fibres.To assist mathematical modelling of the thermal conductivity ( Part II of this report ) heat capacity, density, and volume fraction of constitutents were also determined, together with weight and length change during the diffusivity measurement. The problems and uncertainties in obtaining component data are discussed.     

The dynamics of avalanches of granular materials from initiation to runout. Part I: Analysis

Summary This paper describes a model to predict the flow of an initially stationary mass of cohesion-less granular material down rough curved beds. This work is of interest in connection with the motion of rock and ice avalanches and dense flow snow avalanches. The constitutive behaviour of the material making up the pile is assumed to be described by a Mohr-Coulomb criterion while the bed boundary condition is treated by a similar Coulomb-type basal friction law assumption. By depth averaging the incompressible conservation of mass and linear momentum equations that are written in terms of a curvilinear coordinate system aligned with the curved bed, we obtain evolution equations for the depthh and the depth averaged velocity. Three characteristic length scales are defined for use in the non-dimensionalization and scaling of the governing equations. These are a characteristic avalanche lengthL, a characteristic heightH, and a characteristic bed radius of curvatureR. Three independent parameters emerge in the non-dimensionalized equations of motion. One, which is the aspect ratio -H/L, is taken to be small. By choosing different orderings for the other two, the tangent of the bed friction angle and the characteristic non-dimensional curvature =L/R, we can obtain different sets of equations of motion which appropriately display the desired importance of bed friction and bed curvature effects. The equations, correct to order for moderate curvature, are discretized in the form of a Lagrangian-type finite difference representation which proved to be successful in the earlier studies of Savage and Hutter [24] for granular flow down rough plane surfaces. Laboratory experiments were performed with plastic particles flowing down a chute having a bed made up of a straight, inclined portion, a curved part and a horizontal portion. Numerical solutions are presented for conditions corresponding to the laboratory experiments. It is found that the predicted temporal-evolutions of the rear and front of the pile of granular material as well as the shape of the pile agree quite well with the laboratory experiments.     

Crack problems in magnetoelectroelastic solids. Part I: exact solution of a crack

This paper presents an exact treatment on the problem of an elliptic hole or a crack in a magnetoelectroelastic solid subject to the farfield loadings. First, based on the extended version of Eshelby-Stroh’s formulation, the general solution of an elliptical hole is obtained according to exact boundary conditions at the rim of the hole. Then, when the hole degenerates into a crack, explicit solutions are given for the field intensity factors and electric-magnetic fields inside the crack. It is shown that all the singularities of fields are dependent on the applied mechanical loads, not on the applied electric-magnetic loads. Due to its explicitness, the present solution for a crack can also serve as a benchmark to test the validity of various analysis approaches or assumptions to more complicated crack problems in magnetoelectroelastic media.     

Thermomechanical transformation fatigue of TiNiCu SMA actuators under a corrosive environment – Part I: Experimental results

In this two-part paper, the thermomechanical fatigue of TiNiCu shape memory alloy (SMA) wire actuators undergoing thermally induced martensitic phase transformation in a corrosive environment is investigated. The main objective of this work is to evaluate the cyclic response and fatigue behavior of TiNiCu SMA wire under corrosive conditions and to compare it to results obtained for fatigue testing in a corrosion-free environment. Part I focuses on the various experimental aspects of this work, including the presentation of fatigue results as a function of various testing parameters. The variable test parameters are five applied stress levels from about 50 MPa to about 250 MPa, and two different actuation strains, one corresponding to full actuation or complete transformation and the other to partial transformation. The results from fatigue testing in a corrosive environment show a consistent reduction of the fatigue life compared to corrosion-free fatigue results, in both complete and partial transformation conditions. It is also observed that corrosion-assisted fatigue leads to more scattered fatigue data and this spread is mostly attributed to enhanced and accelerated damage mechanisms due to corrosion. From these conclusions, a microstructure evaluation is performed to understand the damage that contributes to lower fatigue limits under corrosion and is presented in Part II of this work. Fracture surfaces, development of fatigue cracks and effect of corrosion are presented and discussed. The conclusion from the microstructure analysis has led to the formulation of a damage accumulation model accounting for a cyclic corrosion mechanism. This modeling approach allows for determining the fatigue life reduction of SMA wire actuators in a corrosive environment. All results of the microstructure analysis and fatigue life modeling are presented in Part II.     

Microstructural aspects of Thermal Stress Resistance of high-strength engineering ceramics. Part I: Data of thermal stress resistance of high-strength engineering ceramics

Based on the criteria for the improvement of thermal shock resistance mainly two microstructural aspects of thermal stress resistance are discussed: First, the influence of microstructure on thermal shock resistance to fracture initiation, and second, the improvement of thermal shock resistance on the basis of microstructural considerations. In this connection, data of thermal stress resistance (thermal shock and thermal cycling) of various engineering ceramic materials are presented. Using laboratory grades with well-defined microstructures the interdependence between various microstructural variables and the mechanical and thermal properties, which control the thermal shock resistance, is discussed and the relation to thermal shock resistance is outlined by the example of the two materials, dense and porous reaction-bonded Si₃N₄. Moreover, the improvement of thermal shock resistance by microstructural optimization is demonstrated. Some examples of the improvement of thermal stress resistance by developing advanced composite materials are given. The paper is divided into three parts: Part I: Data of Thermal Stress Resistance of High-Strength Engineering Ceramics Part II: Influence of Microstructure on Thermal Shock Resistance of High-Strength Engineering Ceramics Part III: Improvement of Thermal Stress Resistance of High-Strength Engineering Ceramics.     

Comparison of performances of displacement and mixing ventilations. Part I: thermal comfort

A numerical simulation using a validated Computational Fluid Dynamics (CFD) model of several types of buildings was used to investigate the difference between mixing and displacement ventilation (DV). The comparison of performances of displacement and mixing ventilations (MV) will be reported in two parts, one on thermal comfort and the other one on indoor air quality. This paper, i.e., Part I, compares the performances of floor-supply DV systems with traditional MV systems for offices, classrooms, retail shops and industrial workshops under a wide range of Hong Kong thermal and flow boundary conditions, such as a very high cooling load. Through proper design, DV can maintain a thermally comfortable environment that has a low air velocity, a small temperature difference between the head and ankle level, and a low percentage of dissatisfied people.     

A computational lifetime prediction of a thermal shock experiment. Part II: discussion on difference fatigue criteria

The SPLASH experiment has been designed in 1985 by the CEA to simulate thermal fatigue due to cooling shocks on steel specimens and is similar to the device reported by Marsh in Ref. [ 1 ]. The purpose of this paper is to discuss the application of different fatigue criteria in this case. The fatigue criteria: dissipated energy, Manson Coffin, Park and Nelson, dissipated energy with a pressure term, are determined for the experiment using results from FEM computations presented in the first part of the paper (Part I) 2 and compared with results from uniaxial and multiaxial experiments from literature. The work emphasizes the evolution of the triaxiality ratio during the loading cycle.     

Some hazards are more attractive than others: Drivers of varying experience respond differently to different types of hazard

The ability to detect hazards in video clips of driving has been inconsistently linked to driving experience and skill. One potential reason for the lack of consistency is the failure to understand the structural differences between those hazards that discriminate between safe and unsafe drivers, and those that do not. The current study used a car simulator to test drivers of differing levels of experience on approach to a series of hazards that were categorized a priori according to their underlying structure. The results showed that learner drivers took longer to fixate hazards, although they were particularly likely to miss hazards that were obscured by the environment (such as a pedestrian emerging from behind a parked truck). While drivers with a moderate amount of experience were as fast as driving instructors to look at hazards, they spent the greatest amount of time looking at them. Only instructors’ ability to detect hazards early in the approach translated into differences in driving speed for certain types of hazard. The results demonstrate that drivers of varying experience respond differently to different hazards, and lay the foundations for a hazard typology.     

Mechanical effects of increases in the load applied in uniaxial and biaxial tensile testing: Part I. Calf pericardium

The authors analyzed the mechanical behavior of the calf pericardium employed in the construction of valve leaflets for cardiac bioprostheses. Forty samples of pericardium were subjected to uniaxial tensile testing, 20 as controls and 20 exposed to loads increasing stepwise until rupture, with a return to zero load between each new increment. Another 20 samples were used similarly in biaxial tensile tests involving loads increasing stepwise until rupture, again returning to zero load between steps. The ultimate stresses in the uniaxial study were very similar and were not influenced by the region of pericardial tissue being tested or the increments in load to which the tissue was exposed. The mean stresses at rupture in the stepwise biaxial assays were significantly greater (p<0.01). Using morphological and mechanical criteria for sample selection, it was possible to obtain mathematical fits for the stress/strain relationship in both types of assays, with excellent coefficients of determination (R ²>0.90). In uniaxial tests in which the selection criteria were not applied, the correlation improved as the load increased, a phenomenon that did not occur in the biaxial studies. The values varied throughout the different cycles, adopting exponential forms when the strain was greatest. These variations, which demonstrate that the increase in the energy consumed is a function of the stress applied and of the strain produced, should be good parameters for assessing the changes in the collagen fiber architecture of pericardial tissue subjected to cyclic stress, and may help to detect early failure.     

A method for determining the heat energy of the fatigue process in metals under uniaxial stress: Part 1. Determination of the amount of heat liberated from a fatigue-tested specimen

A method of determining the amount of heat liberated from a push-pull loaded fatigue specimen is presented. The heat energy was determined by modelling the internal heat sources generated by electrically heating the specimen. It was assumed that under steady-state conditions each value of the intensity of internal heat sources can be ascribed to a single temperature distribution along the specimen length. It was assumed also that the temperature distribution is independent of the nature of heat generation (current flow or internal friction). The method avoids the difficulties involved in an analytical approach to the problem. The validity of the method was proved on fatigue-tested austenitic stainless steel.     

An Overview of Complexity Theory in Discrete Optimizations: Part I. Concepts

Over the past decade, complexity theory has emerged from a branch of computer science almost unknown to the operations research community into a topic of widespread interest and research. The goals of the theory are to broadly classify problems and algorithms according to their convenience for solution by digital computers. Very considerable progress has been achieved, but some of the concepts in the theory are so subtle that their implications are as often misunderstood as grasped correctly. In this and the succeeding paper, we will present an elementary tutorial review of the important concepts and results in complexity theory. Emphasis is placed on constructs and implications for persons interested in discrete optimization—especially scheduling theory. The present Part I develops background concepts and definitions. Part II (in the June 1982 TRANSACTIONS) will cover results and implications.