Break to build: fracture as a unifying morphogenetic strategy.

The linear amplitude sweep (LAS) test has been widely accepted for estimating the fatigue resistance of asphalt binders in the last 10 years. This paper proposes a fracture mechanics–based analytical approach for crack initiation and propagation characterization in the LAS test, aiming to more precisely explore the binder crack growth and failure mechanism. Seven unmodified neat asphalt binders and one styrene-butadiene-styrene (SBS) polymer-modified binder are selected in this study. The crack length (a), rate of cracking (da/dN), stress intensity factor (K), and energy release rate (G) are the fundamental parameters for the data interpretation approach proposed in this paper. Experimental and analysis results demonstrate that the energy-based failure definition (either from continuum damage mechanics or fracture mechanics) should be utilized to detect the material-dependent failure occurrence in LAS test. The fracture behavior of asphalt binder in the LAS test follows the two-phase crack growth (TPCG) model in terms of the crack initiation and crack propagation. The crack propagation phase further consists of stable crack growth and unstable crack growth. It is found that the fatigue performance of asphalt binder is intrinsically governed and dominated by its resistance to the crack propagation. The SBS binder in this study clearly displays slower crack propagation behavior than other neat binders. Additionally, the traditional fatigue life can also be divided into the crack initiation life and crack propagation life, which is promising to clarify the specific modification contribution to binder fatigue resistance. The two critical crack lengths of initiated crack and propagated crack for a given asphalt binder are found to be correlated to each other, indicating the potential links between the binder crack initiation and propagation behaviors.

The overall stable crack initiation and propagation behaviour of fracture mechanics specimens cut from plastic pipes that were composed of different polyolefin materials were investigated using concepts of elastic–plastic fracture mechanics including the crack propagation kinetics. The effect of specimen shape, orientation, welding and lading rate on the crack resistance (R) behaviour of these materials has been thereby assessed. It was found in principle that specimen shape, orientation and welding have an influence indeed but only an unexpected small one on crack initiation behaviour and, particularly, on crack propagation behaviour. The crack initiation toughness is not sensitive to the orientation in most cases. In contrast, the crack propagation toughness is significantly affected by the orientation where the values for crack propagation in extrusion direction are larger than ones for crack propagation crosswise to that. This confirms that the morphology affects the stable crack propagation behaviour more than the stable crack initiation behaviour. In agreement with results of the microindentation test, fracture mechanics investigations also show that a lower welding pressure and a larger welding temperature, respectively, have no or a positive effect on the mechanical and fracture mechanics properties, whereas a larger pressure and a lower temperature, respectively, result in deterioration of the performance of the welded joint. Furthermore, the R-curve behaviour was investigated using specimens cut from bilayer pipe segments. It has been shown that an additional layer has a clear impact on the R-curve behaviour compared to the crack propagation in single-layer pipes, which can be explained thereby that the plastic constraint was affected by this additional layer. For clarification of the toughness-in- or -decreasing effect of an additional layer (with differing mechanical characteristics) on the layer where the crack was growing, R-curve ratios were introduced, that showed that the asymmetric mechanical properties of different layers were directly reflected in an asymmetric impact on the stable crack initiation and propagation behaviour.

Many power generation facilities equipped with turbomachinery are designed to provide electric energy on an as-needed basis and, as a consequence, impart a mixture of fatigue and creep damage to high-value components at elevated temperatures. Cracks are often initiated on free surfaces of these parts near stress-raising features and propagate under thermal-mechanical cycling until the component is removed from service. Whether the emphasis is on creep or fatigue failure, most conventional structural life prediction approaches decouple crack initiation from crack propagation. Turbine designers are in need of approaches that span the full life cycle of components in which both initiation and propagation are the consequences of a variety of mechanical failure modes. Although recent fracture mechanics methods have been developed to account for fatigue- and creep-crack growth, a tacit assumption is that a precrack exists. Another main limitation of these approaches is the small scale yielding assumption, associated with linear elastic fracture mechanics, in which extensive plasticity invalidates such analyses. In this study, utilizing a blunt notch compact tensile specimen, experimental routines involving crack initiation and propagation within a single specimen at elevated temperatures with plastic-inducing loads and hold periods were conducted. Founded on existing elastic and elastic-plastic fracture mechanics (EPFM), a coupled crack initiation and propagation model is presented. Through the use of the EPFM parameter J, the proposed models are observed to accurately predict crack initiation and replicate crack propagation rates based on the imposed experimental conditions. The model is demonstrated on an austenitic stainless steel, type 304, subjected to moderate temperatures in air. Mechanical testing, metallurgical analysis, and analytical modeling allow for a simplified phenomenological life prediction model capable of predicting crack initiation and propagation at elevated temperatures. Consequently, structural analysis of critical locations of components can span the gamut of crack initiation, crack growth, and instability (i.e., total life assessment).

Experimental investigation on fatigue crack initiation and propagation mechanism of friction stir lap welded dissimilar joints of magnesium and aluminum alloys

Foreword. Preface. Symbols and Abbreviations. 1 Introduction. 2 Basic Concepts of Metal Fatigue and Fracture in the Engineering Design Process. 2.1 Historical Overview. 2.2 Metal Fatigue, Crack Propagation and Service-Life Prediction: A Brief Introduction. 2.2.1 Fundamental Terms in Fatigue of Materials. 2.2.2 Fatigue-Life Prediction: Total-Life and Safe-Life Approach. 2.2.3 Fatigue-Life Prediction: Damage-Tolerant Approach. 2.2.4 Methods of Fatigue-Life Prediction at a Glance. 2.3 Basic Concepts of Technical Fracture Mechanics. 2.3.1 The K Concept of LEFM. 2.3.2 Crack-Tip Plasticity: Concepts of Plastic-Zone Size. 2.3.3 Crack-Tip Plasticity: The J Integral. 3 Experimental Approaches to Crack Propagation. 3.1 Mechanical Testing. 3.1.1 Testing Systems. 3.1.2 Specimen Geometries. 3.1.3 Local Strain Measurement: The ISDG Technique. 3.2 Crack-Propagation Measurements. 3.2.1 Potential-Drop Concepts and Fracture Mechanics Experiments. 3.2.2 In Situ Observation of the Crack Length. 3.3 Methods of Microstructural Analysis and Quantitative Characterization of Grain and Phase Boundaries. 3.3.1 Analytical SEM: Topography Contrast to Study Fracture Surfaces. 3.3.2 SEM Imaging by Backscattered Electrons and EBSD. 3.3.3 Evaluation of Kikuchi Patterns: Automated EBSD. 3.3.4 Orientation Analysis Using TEM and X-Ray Diffraction. 3.3.5 Mathematical and Graphical Description of Crystallographic Orientation Relationships. 3.3.6 Microstructure Characterization by TEM. 3.3.7 Further Methods to Characterize Mechanical Damage Mechanisms in Materials. 3.4 Reproducibility of Experimentally Studying the Mechanical Behavior of Materials. 4 Physical Metallurgy of the Deformation Behavior of Metals and Alloys. 4.1 Elastic Deformation. 4.2 Plastic Deformation by Dislocation Motion. 4.3 Activation of Slip Planes in Single- and Polycrystalline Materials. 4.4 Special Features of the Cyclic Deformation of Metallic Materials. 5 Initiation of Microcracks. 5.1 Crack Initiation: Definition and Significance. 5.1.1 Influence of Notches, Surface Treatment and Residual Stresses. 5.2 Influence of Microstructual Factors on the Initiation of Fatigue Cracks. 5.2.1 Crack Initiation at the Surface: General Remarks. 5.2.2 Crack Initiation at Inclusions and Pores. 5.2.3 Crack Initiation at Persistent Slip Bands. 5.3 Crack Initiation by Elastic Anisotropy. 5.3.1 Definition and Significance of Elastic Anisotropy. 5.3.2 Determination of Elastic Constants and Estimation of the Elastic Anisotropy. 5.3.3 FE Calculations of Elastic Anisotropy Stresses to Predict Crack Initiation Sites. 5.3.4 Analytical Calculation of Elastic Anisotropy Stresses. 5.4 Intercrystalline and Transcrystalline Crack Initiation. 5.4.1 Influence Parameters for Intercrystalline Crack Initiation. 5.4.2 Crack Initiation at Elevated Temperature and Environmental Effects. 5.4.3 Transgranular Crack Initiation. 5.5 Microstructurally Short Cracks and the Fatigue Limit. 5.6 Crack Initiation in Inhomogeneous Materials: Cellular Metals. 6 Crack Propagation: Microstructural Aspects. 6.1 Special Features of the Propagation of Microstructurally Short Fatigue Cracks. 6.1.1 Definition of Short and Long Cracks. 6.2 Transgranular Crack Propagation. 6.2.1 Crystallographic Crack Propagation: Interactions with Grain Boundaries. 6.2.2 Mode I Crack Propagation Governed by Cyclic Crack-Tip Blunting. 6.2.3 Influence of Grain Size, Second Phases and Precipitates on the Propagation Behavior of Microstructurally Short Fatigue Cracks. 6.3 Significance of Crack-Closure Effects and Overloads. 6.3.1 General Idea of Crack Closure During Fatigue-Crack Propagation. 6.3.2 Plasticity-Induced Crack Closure. 6.3.3 Influence of Overloads in Plasticity-Induced Crack Closure. 6.3.4 Roughness-Induced Crack Closure. 6.3.5 Oxide- and Transformation-Induced Crack Closure. 6.3.6 &delta K/K max Thresholds: An Alternative to the Crack-Closure Concept. 6.3.7 Development of Crack Closure in the Short Crack Regime. 6.4 Short and Long Fatigue Cracks: The Transition from Mode II to Mode I Crack Propagation. 6.4.1 Development of the Crack Aspect Ratio a/c. 6.4.2 Coalescence of Short Cracks. 6.5 Intercrystalline Crack Propagation at Elevated Temperatures: The Mechanism of Dynamic Embrittlement. 6.5.1 Environmentally Assisted Intercrystalline Crack Propagation in Nickel-Based Superalloys: Possible Mechanisms. 6.5.2 Mechanism of Dynamic Embrittlement as a Generic Phenomenon: Examples. 6.5.3 Oxygen-Induced Intercrystalline Crack Propagation: Dynamic Embrittlement of Alloy 718. 6.5.4 Increasing the Resistance to Intercrystalline Crack Propagation by Dynamic Embrittlement: Grain-Boundary Engineering. 7 Modeling Crack Propagation Accounting for Microstructural Features. 7.1 General Strategies of Fatigue Life Assessment. 7.2 Modeling of Short-Crack Propagation. 7.2.1 Short-Crack Models: An Overview. 7.2.2 Model of Navarro and de los Rios. 7.3 Numerical Modeling of Short-Crack Propagation by Means of a Boundary Element Approach. 7.3.1 Basic Modeling Concept. 7.3.2 Slip Transmission in Polycrystalline Microstructures. 7.3.3 Simulation of Microcrack Propagation in Synthetic Polycrystalline Microstructures. 7.3.4 Transition from Mode II to Mode I Crack Propagation. 7.3.5 Future Aspects of Applying the Boundary Element Method to Short-Fatigue-Crack Propagation. 7.4 Modeling Dwell-Time Cracking: A Grain-Boundary Diffusion Approach. 8 Concluding Remarks. References. Subject Index.

The consequence of this result on the fracture behavior of graphene, including the crack initiation, crack propagation, blunting, fracture strength and energy release rate is the main topic of this paper. We proposed three mechanisms by which crack growth can occur in such blunted regions and also performed simulations on three different specimens of graphene sheets to demonstrate elastic blunting. For the study of fracture strength of graphene with different crack tip radius, different crack initiation behaviors are revealed, and it is demonstrated that the blunting effect of tip edges plays an important role in the fracture crack initiation and propagation of graphene. The characterized crack tip radius from 1.642 to 2.843 A is observed, which can be used to estimate the fracture strength due to blunting at crack tip. The results of this work are deemed to be of importance from the perspective of modeling the fracture behavior of graphene sheet and in predicting its ultimate failure, post-blunting in fracture mechanism.

Interfacial fatigue fracture of elastomer bilayers under cyclic large deformation

Observations of fatigue crack initiation and propagation in an epoxy adhesive

—A model for a description of a shear crack (fault) propagation is proposed on the basis of the unification of continuum damage and fracture mechanics with ideas of fracture models for random media. Energy release linked with local failures of elements as a result of evolution of fracture processes at lower scale levels (stimulated by the stress concentration in the vicinity of the fault) is treated as a seismicity source. 2d simulations are performed for analysis of the effect of the size of pre-existing fault on characteristic features of rupture evolution. Scaling (including multifractal) character of crack propagation and of respective energy release is shown.

Crack propagation tests were conducted on a composite modified double-base (CMDB) propellant with the use of center-cracke d strip biaxial specimens. Constant strain rate tests were conducted at several temperatures (40-105°F) and crosshead rates (0.02-200 in./min) to define the crack initiation and propagation characteristics for monotonically increasing strain history. The tests were conducted at ambient, 250, and 500 psig pressure to evaluate the effect of pressure on initiation and crack velocity. A second series of tests was conducted to evaluate the effect of a prestrain damage history on crack propagation. In the second series, the samples (without precut cracks) were initially prestrained to 15-25% and held for a period of time to induce material damage. After load release and sufficient recovery time, cracks were inserted in the specimens and they were then pulled to failure at a constant strain rate. Similar tests were conducted on round, notched tensile samples to define the critical stress intensity factor (Klc) and to provide a comparison between uniaxial and biaxial fracture initiation. Schapery's viscoelastic fracture theory was used to evaluate the crack velocity data under constant strain rate conditions. One important result of the study was the finding that the crack velocity depended rather strongly on imposed strain level. I. Introduction C RACK initiation and propagation in polymeric materials has been given considerable attention during the last 15 years, stimulated primarily by their unique viscoelastic behavior and also by the use of polymerics as solid propellant rocket fuels. Filled polymers are used extensively as solidpropellant grains which must undergo a variety of environmental loading conditions, during motor storage and handling and during actual operational firing conditions, which impose pressure loads at high rates and for relatively long times. The consequence of a crack can be the failure of the rocket motor as a result of overpressuriz ation, case burnthrough, erratic pressure-time response, or a variety of events related to structural or ballistic performance failure. The primary work over the last decade has been aimed at defining the laws which govern crack initiation, propagation, and trajectory under motorlike operational conditions to arrive at an assessment of overall crack criticality for a given rocket motor system. A number of investigators have studied viscoelastic crack propagation in polymers and solid propellants. l~l°

Crack propagation tests were conducted on a composite modified double-base (CMDB) propellant with the use of center-cracke d strip biaxial specimens. Constant strain rate tests were conducted at several temperatures (40-105°F) and crosshead rates (0.02-200 in./min) to define the crack initiation and propagation characteristics for monotonically increasing strain history. The tests were conducted at ambient, 250, and 500 psig pressure to evaluate the effect of pressure on initiation and crack velocity. A second series of tests was conducted to evaluate the effect of a prestrain damage history on crack propagation. In the second series, the samples (without precut cracks) were initially prestrained to 15-25% and held for a period of time to induce material damage. After load release and sufficient recovery time, cracks were inserted in the specimens and they were then pulled to failure at a constant strain rate. Similar tests were conducted on round, notched tensile samples to define the critical stress intensity factor (Klc) and to provide a comparison between uniaxial and biaxial fracture initiation. Schapery's viscoelastic fracture theory was used to evaluate the crack velocity data under constant strain rate conditions. One important result of the study was the finding that the crack velocity depended rather strongly on imposed strain level. I. Introduction C RACK initiation and propagation in polymeric materials has been given considerable attention during the last 15 years, stimulated primarily by their unique viscoelastic behavior and also by the use of polymerics as solid propellant rocket fuels. Filled polymers are used extensively as solidpropellant grains which must undergo a variety of environmental loading conditions, during motor storage and handling and during actual operational firing conditions, which impose pressure loads at high rates and for relatively long times. The consequence of a crack can be the failure of the rocket motor as a result of overpressuriz ation, case burnthrough, erratic pressure-time response, or a variety of events related to structural or ballistic performance failure. The primary work over the last decade has been aimed at defining the laws which govern crack initiation, propagation, and trajectory under motorlike operational conditions to arrive at an assessment of overall crack criticality for a given rocket motor system. A number of investigators have studied viscoelastic crack propagation in polymers and solid propellants. l~l°

Effect of the Size of the Apical Enlargement with Rotary Instruments, Single-cone Filling, Post Space Preparation with Drills, Fiber Post Removal, and Root Canal Filling Removal on Apical Crack Initiation and Propagation

Being good structural replacement for other conventional material, the pultruded glass fiber reinforced polymer (GFRP) profiles are being increasingly used in civil engineering structures. The connection between components is considered the most suspect area for failure initiation. The adhesive bonding is preferred for FRP composite structures, rather than the mechanical fastening, due to the brittle failure nature of composite materials. During past decades, many efforts have been made by researchers to better understand the mechanism of adhesive bonding, to analyze the stress distributions and to improve the strength of composite structural joints. However there is still no commonly accepted design code/standard existing for adhesively-bonded joints in civil engineering infrastructures since several important knowledge gaps are to be filled. Besides the joint strength at failure, the characterization and modeling of the progressive failure process, in particular involving the so-called crack initiation and propagation phases, is also an important concern. By employing the strain energy release rate (SERR) as the fracture parameter, the linear-elastic fracture mechanics (LEFM) approach is considered an efficient method to model the fracture behavior of structural joints. However, due to the uncontrollable crack initiation and the complex geometric configurations, the crack measurement techniques and the calculation method for the SERR are to be validated. In fracture mechanics, the fracture of a material or component can be described by a single mode or the combinations of the following three basic modes: opening mode (Mode I), shearing mode (Mode II), and tearing mode (Mode III). During the fracture of a structural joint, crack initiation and propagation are driven by combined through-thickness tensile (peeling), and shear stresses, thus resulting in a mixed mode fracture. In order to use the fracture results of structural joints to form the mixed fracture criterion for a specific composite material, a feasible analytical or numerical method are to be developed to determine the Mode I and II components of the SERR during fracture. Although many efforts have been made to better understand the short-term behavior of structural joint under quasi-static loading, the long-term performance under fatigue loading and different environmental conditions is a more demanding task when adhesively-bonded joints are applied in a real structure. Most of structural failures occur due to mechanisms that are driven by fatigue loading and for composite structures, the fatigue produced by the repeated application of live load is more critical due to its lighter self-weight, in other words the lower dead load. Besides the fatigue loading, a structure in practice may also experience the combined environmental effects of two basic factors: temperature and humidity. These environmental conditions may directly affect properties of structural joints, including the failure mechanism, the stiffness and strength, the crack initiation and propagation and etc.. Thus, the missing knowledge and confidences in the long-term behavior under cyclic loading and the durability under different environmental conditions are the main obstacles to the further development of FRP composites in civil engineering infrastructures. In this research, the mechanical and fracture behavior of adhesively-bonded double-lap and stepped-lap joints (DLJs and SLJs) composed of pultruded GFRP laminates and an epoxy adhesive were experimentally and numerically investigated under both quasi-static and fatigue loadings. The crack measurement techniques and the calculation methods for the SERR were validated for DLJs and SLJs. The LEFM approach was successfully applied to characterize and model the progressive failure process of structural joints. The Mode I and II components of the SERR of DLJs and SLJs were determined using the Virtual Crack Closure Technique in finite element analysis. Combining with the results of pure Mode I and II experiments, a mixed mode fracture criterion for pultruded GFRP composite was formed. Under fatigue loading, the fatigue behavior of structural joints was successfully modeled by using the stiffness-based and fracture mechanics approaches, besides the F-N curves. Based on the stiffness degradation, a linear and a sigmoid non-linear model were established and the fatigue live corresponding to the failure and allowable stiffness degradation can be predicted. Concerning fracture mechanics approach, the Fatigue Crack Growth (FCG) curves were formed for DLJs and SLJs and the corresponding fracture parameters were obtained. Similarly to stiffness-based approach, fatigue lives corresponding to the failure and allowable crack length can be predicted. The environmental effects on both short- and long-term performances of structural joints were experimentally evaluated and numerically modeled based on experimental results. The temperature-dependent joint stiffness can be predicted using the finite element analysis based on the thermomechanical properties of constituent materials. A relationship between the equivalent quasi-static joint strength under different environmental conditions and the cyclic stresses and the fatigue life was established.

This study discusses the effect of additive elements on crack initiation and propagation behavior for Sn-Bi solders at high temperatures. Sn-Bi solders are lower melting point temperature materials, so that it is useful for low temperature soldering. Cyclic push-pull fatigue test with center through holed specimen were conducted at 313K and 353K in order to investigate the crack initiation and propagation behavior from stress concentration part of three kinds of Sn-Bi solders. Crack initiated at the early stage and almost of the life period were crack propagation process for the three kinds of Sn-Bi solders. Crack propagation direction at 353K was the maximum shear direction although the maximum principal direction at 313K. The reason for the crack propagation direction difference might be change of slip system at high temperature. There were additive elements Ag, Cu, Ni and Ge effect on the crack propagation rate although there was no effect on the crack initiation cycle. The crack propagation of Ag, Cu, Ni and Ge added solder seems to have a slower rate than that of Sn-58Bi solder. We also investigated the adaptation of J-integral range parameter which is usual used for crack propagation rate evaluation for conventional steel. The J-integral range parameter evaluates the crack propagation rate independent of the additive elements at high temperatures.

Double notched specimens of nickel base superalloy N18 have been subjected to creep fatigue loading at 650°C. Finite element analysis using the elastoviscoplastic constitutive equation of N18, exhibited a strong stress relaxation at the notch root. By introducing the computed viscoplastic stress gradient into the calculation of the stress intensity factor (SIF), crack growth rates measured on notched specimens are much closer to those measured on smooth specimens. INTRODUCTION With the need of improvement of aircraft gas turbine performances, security components, such as turbine and compressor discs, should be subjected to increasing stresses and temperatures. They now tend to be fabricated with powder metallurgy superalloys which have excellent mechanical properties under these conditions. However the presence of inclusions introduced in the melt process (Denda et al (1)) can considerably affect their fatigue life. Therefore disc failure due to crack initiation on inclusions at firtree fixtures of turbine blades is a key problem for engine designers (McClung (2)). Short crack propagation is studied, in double notched specimens of N18, subjected to a specific loading schedule corresponding to service conditions. EXPERIMENTAL PROCEDURE Material The alloy tested, N18 is an advanced Nickel base y strengthened disc alloy. It was developped by SNECMA as a PM alloy for service up to 700°C. Transactions on Engineering Sciences vol 6, © 1994 WIT Press, www.witpress.com, ISSN 1743-3533 438 Localized Damage Currently N18 is being used for compressors and turbine discs of the M88 engine for the new Rafale fighter. The chemical analysis of the material tested is reported in table 1. Further informations about this alloy can be found in the work of Guedou et al (3) and Wlodek et al (4). TABLE 1Chemical composition ofNIS (At %) C Co Ni Cr Mo Al Ti B Hf Zr 0,015 15,7 base 11,5 5,5 4,35 4,35 0,015 0,45 0,03 Creep fatigue testing. Double edge notched specimens (see figure 1) were machined into a turbine disc and were subjected to trapezoidal cycles (10-300-10): 10 s loading, 300s dwell time, 10 s unloading with Ra=0 at 650°C in air corresponding to service conditions. Cracks initiate on artificial U-shape defects which are nearly 100 p,m deep. The crack length is obtained through the potential technique. The potential is measured around each notch during the whole crack propagation, the uncracked side being used as a reference to detect crack initiation earlier. The calibrating curve was obtained by marking the fracture surface, using a change in crack path with temperature and cycling mode. Under usual testing conditions the crack path is intergranular while in marking conditions (400°C, pure fatigue IHz) the crack path becomes transgranular (see figure 2). Crack initiation can be detected as soon as cracks are 120|imdeep. EXPERIMENTAL RESULTS Experiments have been conducted with nominal loads of 700, 800 and 900MPa. Crack growth rates were plotted as a function of the SIF, using a general expression of the SIF for semi-elliptical cracks growing from a notch given by Kujawski (5). If we compare these results with those obtained by G.Hochstetter (6) on the same material under the same testing conditions applied on CT specimens, crack growth rates in notched specimens are much higher than those in CT specimens. FINITE ELEMENT ANALYSIS Finite element computations, using the elastoviscoplastic constitutive equations of N18, have been conducted on Zebulon, the Finite Elements software developped by Ecole des Mines de Paris. The meshed structure has been subjected up to 300 cycles (10-300-10). Transactions on Engineering Sciences vol 6, © 1994 WIT Press, www.witpress.com, ISSN 1743-3533 Localized Damage 439 The notch root is highly plastified at the first loading, and within a few cycles the tensile stresses and strains become steady and the stress-strain curve hysteresis loop is insignificant (7) As a matter of fact the center of the sample remaining elastic, the plastic deformation of the notch root is limited, thus creep deformation during dwell time becomes quickly negligible. Looking at the local peak tensile stresses, figure 4, for a nominal load of 500MPa, almost no stress redistribution occurs, the stress profile could have been calculated in elasticity. However for higher loads, the stresses near the surface are much lower than in elasticity while at the center of the specimen they are sligthly higher. Then when the structure is unloaded, see figure 5, the notch root go through compression. The stress ratio can be very negative behind the surface (-0.7 for a nominal load of lOOOMPa) but quickly becomes positive inside the structure. The viscoplastic steady stress profiles, Aa=amax, at peak nominal stress for each nominal load were calculated and fitted by five degree polynomials, that were used in the calculation of the SIF (7) derived from the solution of RJ.Hand (8). The experimental results are then in better agreement with those obtained on CT specimens, (see figure 6) though for short cracks, i.e. cracks under the influence of the notch, crack growth rates are still higher than for long cracks in CT specimens DISCUSSION As the stress relaxation is very strong at the notch root (see figure 4), the SIF predicted in viscoplasticity for short cracks are lower than those predicted in elasticity. For long cracks, SIF are higher, the stresses being sligthly higher near the center of the sample than in elasticity. Then for short cracks the da/dN versus AK curve is shifted to the left whereas for longer cracks it is shifted to the right (see figure 3). So the slope of the curve being lower in viscoplasticity than in elasticity, the results are in better agreement with those obtained on CT specimens (see figure 3). Nevertheless short crack growth rates are still higher than for long cracks in CT specimens. This can be explained by a change in the opening threshold. In the SIF calculation proposed in (7) the crack was supposed to open as soon as the local stress became positive throughout the whole crack propagation. But this opening threshold changes with the loading conditions and the crack length. As the stress ratio is highly negative at the notch root and slightly positive at the center of the sample (see figure 5), stress profiles Aa=Aaeff should be used instead of Aa=amax in the calculation of the SIF, to be able to predict crack propagation rate in a notched sample from crack propagation law obtained on CT specimens.. Transactions on Engineering Sciences vol 6, © 1994 WIT Press, www.witpress.com, ISSN 1743-3533 440 Localized Damage CONCLUSIONS (1) Creep fatigue tests were performed at 650°C, with a dwell time of 300 sec, on the Nickel base superalloy N18, for nominal loads of 700, 800 and 900 MPa. (2) The Finite Element analysis, conducted using the elastoviscoplastic constitutive equations of N18, exhibit a strong stress redistribution at the notch root (3) Using solution for KI which takes into account the cyclic stress redistribution at the notch root the results are in better agreement with those obtained by G.Hochstetter on CT specimens. (4) Opening thresholds should be taken into account in the determination of the crack propagation law. ACKNOWLEDGEMENTS SNECMA is gratefully acknowledged for fruitful discussions and financial support. REFERENCES 1. Denda, T., Bretz, P.L. and Tine, J.K., ' Inclusion size effect on the fatigue Crack propagation mechanism and fracture Mechanics of a Superalloy', Met Trans A, Vol 23A, Feb 1992, pp. 519-526. 2. McClung, R.C., ' a Simple Model for Fatigue Crack Growth near Stress Concentrators', Trans of ASME, Vol 113, Nov 1991, pp. 542-548. 3. Guedou, JY., Lautridou, JC. and Honnorat, Y., ' N18, PM Superalloy for Discs : development and applications', in Superalloy 92 (Ed S.D. Antolovitch, R.W. Stusrud, R.A. macKay, D.L. Anton, T. Khan, R.D. Kissinger, D.L. Klarstrom), pp. 267 to 216proceedings of the Minerals & Materials Society., Cincinnati, 1992. 4. Wlodek, ST., Kelly, M. and Alden, D. ,' The Structure of N18', in Superalloy 92 (Ed S.D. Antolovitch, R.W. Stusrud, R.A. macKay, D.L. Anton, T. Khan, R.D. Kissinger, D.L. Klarstrom), pp. 267 to 276, Proceedings of the Minerals & Materials Society., Cincinnati, 1992. 5. Kujawski, D. , ' Estimations of Stress Intensity Factors for Small Cracks at Notches', Fatigue Fract. Engng Mater. Struct., Vol. 14, No. 10, pp. 953-965, 1991 6. Hochstetter, G., ' Propagation des Fissures a haute temperature dans le superalliage pour disque de turbomachine N18, interaction entre la nature des solicitations mecaniques et les effets d'oxydation.' Thesis of Ecole Nationale Superieure des Mines de Paris, 14 January 1994. 7. Pommier, S., Rongvaux, J.M., Prioul, C., Frangois, D., ' Stress intensity factor for creep fatigue cracks growing from a notch', in Structural Integrity Tenth Conference on Fracture (Ed ESIS) Berlin, FRG, 20-23 Sept. 1994, to be published. 8. Hand, R.J., ' Stress Intensity Factors for penny and half penny shaped Cracks subjected to a stress Gradient', Int. J. of Fract., Vol 57, 1992, pp. 237-247. Transactions on Engineering Sciences vol 6, © 1994 WIT Press, www.witpress.com, ISSN 1743-3533