Constraint-modified J−R curves and its application to ductile crack growth

The concept of J-controlled crack growth is extended to J–A ₂ controlled crack growth using J as the loading level and A ₂ as the constraint parameter. It is shown that during crack extension, the parameter A ₂ is an appropriate constraint parameter due to its independence of applied loads under fully plastic conditions or large-scale yielding. A wide range of constraint level is considered using five different types of specimen geometry and loading configuration; namely, compact tension (CT), three-point bend (TPB), single edge-notched tension (SENT), double edge-notched tension (DENT) and centre-cracked panel (CCP). The upper shelf initiation toughness J _IC, tearing resistance T _R and J–R curves tested by Joyce and Link (1995) for A533B steels using the first four specimens are analysed. Through finite element analysis at the applied load of J _IC, the values of A ₂ for all specimens are determined. The framework and construction of constraint-modified J–R curves using A ₂ as the constraint parameter are developed and demonstrated. A procedure of transferring the J–R curves determined from standard ASTM procedure to non-standard specimens or practical cracked structures is outlined. Based on the test data, the constraint-modified J–R curves are presented for the test material of A533B steel. Comparison shows the experimental J–R curves can be reproduced or predicted accurately by the constraint-modified J–R curves for all specimens tested. Finally, the variation of J–R curves with the size of test specimens is produced. The results show that larger specimens tend to have lower crack growth resistance curves.     

CARI – a heuristic approach to machine-part cell formation using correlation analysis and relevance index

Machine-part cell formation is the process of identifying part families and the appropriate machine cell for each part family. Grouping efficacy (GE), the widely used measure for assessing the goodness of the machine-part cells depends on identification of correct part families and the appropriate machine cell for each part family. In this paper, a heuristic based on correlation analysis and relevance index is proposed for the formation of machine-part cells. Computational performance of the proposed heuristic on a set of group technology data-set available in the literature is also presented. GE of the solutions produced by the proposed heuristic is equal to the best efficacy reported in the literature for 63% of the test instances and improved the GE for 6% of the total test instances.     

The brittle to ductile transition of single crystal materials—An indentation model

A model for the brittle to ductile transition of brittle single crystal materials under indentation has been investigated. Continuous dislocation pile-ups against the wedge tip are used to explain the plastic deformation. The indentation depth is attributed to the dislocation pile-ups. The critical indentation depth p _cof brittle to ductile transition is proposed. Thus, the single crystal material is in brittle mode during the indentation loading if the indentation depth is greater than p _c. Otherwise, it is ductile. Micrographs support this modeling. Indentation on the surfaces of (100) or (110) in fcc and bcc single crystal materials is compared. The parameter Sis proportional to the number of dislocations and to the reciprocal of wedge angle. The value of Sis smaller for (100) than for (110) in fcc structure, but the trend of bcc structure is opposite. The shape of indenter is similar to that of grinding particles consisting in cutting tools. In order to maintain cutting efficiency in ductile mode, the cutting tool must be replaced if the grinding particles are blunt.     

A dislocation barrier model for fatigue limit – as determined by crack non-initiation and crack non-propagation

Fatigue damage is caused by cyclic slip, and cyclic slip is driven by dislocation glide force. In order to cause fatigue damage, the cyclic glide force has to overcome the resistance of the primary and secondary dislocation barriers. Based on this cyclic damage process, the following diverse fatigue phenomena are synthesized into an integral and self-consistent analysis: Fatigue damage occurs in persistent slip bands (Hempel, 1956; Smith, 1957; Forsyth, 1957, 1961, 1963), and a nucleated fatigue micro crack is a shear crack (Forsyth, 1961). Pre-cracking fatigue damage is confined to the surface layer of a stressed metal (Wood et al., 1963). Fatigue limit is inversely related to grain size as shown in brass (Sinclair and Craig, 1952), in mild steels (Klesnil, Holzmann, Lukáš and P. Ryš 1965; Yoshikawa and Sugeno, 1965; and Taira, Tanaka, and Hoshina, 1979), and in ferritic-martensitic steel, (Kunio, Shimizu, and Yamada, 1969). Forrest and Tate (1964) found fatigue cracks in fine-grained brass at an alternating stress even below the fatigue limit. The cracks were within the boundaries of single grains. But they found no cracks in coarse-grained brass below the fatigue limit. The analysis synthesizes all of these experimental observations. The analysis is based on a realistic physical model. With a better understanding of the model and an improved calculation of the glide force, quantitative evaluations of the resistance of the dislocation barriers would eventually be possible. The needs for additional research are pointed out. A number of means of improving fatigue strength, based on the analysis, are suggested or explained. This revised version was published online in July 2006 with corrections to the Cover Date.     

Modeling ductile to brittle fracture transition in steels—micromechanical and physical challenges

Both scientists and engineers are very much concerned with the study of ductile-to-brittle transition (DBT) in ferritic steels. For historical reasons the Charpy impact test remains widely used in the industry as a quality control tool to determine the DBT temperature. The transition between the two failure modes, i.e. brittle cleavage at low temperature and ductile fracture at the upper shelf occurs also at low loading rate in fracture toughness tests. Recent developments have been made in the understanding of the micromechanisms controlling either cleavage fracture in BCC metals or ductile rupture by cavity nucleation, growth and coalescence. Other developments have also been made in numerical tools such as the finite element (FE) method incorporating sophisticated constitutive equations and damage laws to simulate ductile crack growth (DCG) and cleavage fracture. Both types of development have thus largely contributed to modeling DBT occurring either in impact tests or in fracture toughness tests. This constitutes the basis of a modern methodology to investigate fracture, which is the so-called local approach to fracture. In this study the micromechanisms of brittle cleavage fracture and ductile rupture are firstly shortly reviewed. Then the transition between both modes of failure is investigated. It is shown that the DBT behavior observed in impact tests or in fracture toughness specimens can be reasonably well predicted using modern theories on brittle and ductile fracture in conjunction with FE numerical simulations. The review includes a detailed study of a number of metallurgical parameters contributing to the variation of the DBT temperature. Two main types of steels are considered : (i) quenched and tempered bainitic and martensitic steels used in the fabrication of pressurized water reactors, and (ii) modern high-toughness line-pipe steels obtained by chemical variations and optimized hot-rolling conditions. An attempt is also made to underline the research areas which remain to be explored for improving the strength-toughness compromise in the development of steels.     

J–R curves corrected by load-independent constraint parameter in ductile crack growth

The constraint effect on J–resistance curves of ductile crack growth is considered under the condition of two-parameter J–Q^* controlled crack growth, where Q^* is a modified parameter of Q in the J–Q theory. Both J and Q^* are used to characterize the J–R curves with J as the loading level and Q^* as a constraint parameter. It is shown that Q^* is independent of applied loading under large-scale yielding or fully plastic deformation, and so Q^* is a proper constraint parameter during crack growth. An approach to correct constraint effects on the J–R curve is developed, and a procedure of transferring the J–R curves determined from standard ASTM procedure to nonstandard specimens or real cracked structures is outlined.The test data of fracture toughness, J_IC, and tearing modulus, T_R, by Joyce and Link (Engng. Fract. Mech. 57(4) (1997) 431) for a single-edge notched bend specimen with various depth cracks are employed to demonstrate the efficiency of the present approach. The variation of J_IC and T_R with the constraint parameter Q^* is obtained, and then a constraint-corrected J–R curve is constructed for the test material of HY80 steel. Comparisons show that the predicted J–R curves can match well with the experimental data for both deep and shallow cracked specimens over a reasonably large amount of crack extension.Finally, the present approach is applied to predict the J–R curves of ductile crack growth for five conventional fracture specimens. The results show that the effect of specimen geometry on the J–R curves is generally much larger than the effect of specimen sizes, and larger specimens tend to have lower crack growth resistance curves.     

Fatigue crack propagation work coefficient—a material constant giving degree of resistance to fatigue crack growth

Study on fatigue crack growth in steels was carried out from energetic point of view, i.e. taking account of plastic work around the fatigue crack. Based on the examination of the relation between fatigue crack growth rate (da/dN) and the plastic work around the fatigue crack tip (W_0.02 in SUS304, Fe-3Si and HT 60 steels, a material constant-fatigue crack propagation work coefficient-Q_0.02 is proposed. It is the ratio of W_0.02 to da/dN and means the degree of the resistance to fatigue crack growth. Numerical expression of Q_0.02 by mechanical properties was derived, which is given by

$\text{Q}{}_{0.02}\text{=}\text{9.3x10}{}^1\text{(σ}{}_{\mathrm{y}}\text{+σ}{}_{0.2}\text{)}\text{σ}{}_{\mathrm{y}}{}^{1.3}$

Comparison of Q_0.02 of various steels showed that Q_0.02 of high strength steels is very small compared with that of low strength steels. Graphical representation of the relation between Q_0.02 and da/dN at various values of ΔK/σ_y for steels revealed that da/dN at given value of ΔK/σ_y increase with decreasing Q_0.02. It is shown that fatigue crack growth behaviour of a steel (da/dN-ΔK relation) can be obtained from the Q_0.02-da/dN diagram by knowing the mechanical properties. Discussion on design stress level of the steels is also given.     

Creep crack initiation and growth in AISI 316 (N) weld – FEM and experiments

Abstract

There are two aspects of the creep crack growth behaviour, namely, the crack initiation and the crack propagation. An incubation period is often observed prior to the onset of creep crack growth. In this study, creep crack initiation and propagation in pre-cracked compact tension (CT) specimens of a 316 (N) stainless steel weld at T = 550 and 625°C under static loading is investigated. Both the crack initiation time and the crack growth rate are measured as a function of fracture parameter C*. It is shown that it is possible to correlate the creep crack initiation time with the C* parameter. It is also shown that the creep crack growth rate can be correlated with the C* integral. Additionally, finite element analyses by using the ANSYS software have been performed at one test condition (T=625°C) in order to estimate numerically the crack mouth opening displacement rate history for a propagating crack using the node release technique. When the FEM results are compared with the experimental data, the results show a very satisfactory prediction capability.     

Dynamic emission of dislocations from a crack tip — a computer simulation

The behavior of dynamic emission of dislocations from the tip of a stationary crack under mode II or mode III loading is examined. A critical stress intensity factor, K _D is assumed for dislocation emission. After emission, the dislocation moves with a velocity which varies with the effective shear stress to the third power. The effective shear stress is due to the applied stress , modified by the presence of the crack and all other dislocations minus the lattice friction stress, ^F. The effects of K _D, , and ^F on the rate of emission, the plastic zone strain rate, the plastic zone size, the dislocation distribution, and the dislocation-free zone are reported.

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Résumé On a examiné le comportement d'une émission dynamique de dislocations depuis l'extrémité d'une fissure stationnaire. On suppose que l'émission de dislocations est caractérisée par un facteur critique d'intensité de constrainte K _D. Après son émission, la dislocation se meut avec une vitesse qui varie avec le cube de la constrainte effective de cisaillement. Celle-ci résulte de la constrainte appliquée , modifiée par la présence de la fissure et de toutes les autres dislocations, et sous déduction de la contrainte de friction du réseau, ^F.On étudie les effects de K _D, et ^F sur la vitesse d'émission des dislocations, la vitesse de déformation plastique, la taille de la zone plastique, la distribution des dislocations, et sur la zone qui en est dépourvue.

     

Geometry dependent ductile to brittle transition of 10CrMoNbV ferritic–martensitic steel Manet II in terms of critical crack sizes

Abstract

The 10CrMoNbV Manet II cast has been selected as the reference ferritic–martensitic steel in the framework of the European Fusion Technology Programme. Charpy impact tests have been carried out in the ductile to brittle transition temperature range of this steel, such that a dynamic quasi-equilibrium has been achieved in the process zones of investigated specimens before brittle failure. This type of testing enables the evaluation of dynamic Weibull moduli and, consequently, dynamic Weibull master curves. Thus, Weibull parameters have been calculated for normal size and subsize Charpy impact specimens. The evaluated, geometry dependent dynamic Weibull master curves facilitate computation of the failure probability densities of the investigated steels as functions of scaled critical crack sizes or scaled initial defect sizes.     

Implementation of design of experiments approach for the micronization of a drug with a high brittle–ductile transition particle diameter

Objective: To optimize air-jet milling conditions of ibuprofen (IBU) using design of experiment (DoE) method, and to test the generalizability of the optimized conditions for the processing of another non-steroidal anti-inflammatory drug (NSAID).

Methods: Bulk IBU was micronized using an Aljet mill according to a circumscribed central composite (CCC) design with grinding and pushing nozzle pressures (GrindP, PushP) varying from 20 to 110?psi. Output variables included yield and particle diameters at the 50th and 90th percentile (D₅₀, D₉₀). Following data analysis, the optimized conditions were identified and tested to produce IBU particles with a minimum size and an acceptable yield. Finally, indomethacin (IND) was milled using the optimized conditions as well as the control.

Results: CCC design included eight successful runs for milling IBU from the ten total runs due to powder “blowback” from the feed hopper. DoE analysis allowed the optimization of the GrindP and PushP at 75 and 65?psi. In subsequent validation experiments using the optimized conditions, the experimental D₅₀ and D₉₀ values (1.9 and 3.6?μm) corresponded closely with the DoE modeling predicted values. Additionally, the optimized conditions were superior over the control conditions for the micronization of IND where smaller D₅₀ and D₉₀ values (1.2 and 2.7?μm vs. 1.8 and 4.4?μm) were produced.

Conclusion: The optimization of a single-step air-jet milling of IBU using the DoE approach elucidated the optimal milling conditions, which were used to micronize IND using the optimized milling conditions.     

A cohesive zone model for fatigue and creep–fatigue crack growth in single crystal superalloys

A numerical analysis using cohesive zone model under cyclic loading is proposed to develop a coupled predictive approach of crack growth in single crystal. The process of material damage during fatigue crack growth is described using an irreversible cohesive zone model, which governs the separation of the crack flanks and eventually leads to the formation of free surfaces. The cohesive zone element is modeled to accumulate fatigue damage during loadings and no damage during unloadings. This paper presents the damage model and its application in the study of the crack growth for precracked specimens. The use of cohesive zone approach is validated through a convergence study. Then, a general procedure of parameters calibration is presented in pure fatigue crack growth. In the last section, an extension of the cohesive zone model is presented in the case of creep–fatigue regime at high temperature. The model showed its capability to predict with a good agreement the crack growth in the case of complex loading and complex specimen geometries.     

Fatigue crack growth measurement in a CSM composite using compliance and Moiré techniques

In the present work fatigue crack growth tests under constant load conditions were carried out on centre-notched biaxial specimens in order to measure the effects of load biaxiality in air and also in a dilute acidic environment. Initially a compliance calibration technique was used to determine the effective crack length so as to overcome difficulties connected with visual measurement and to present the fatigue results on a fracture mechanics basis when using conventional stress intensity factors. However, the compliance method becomes unreliable when the biaxiality factor is large or the crack length small, so the Moiré fringe technique was used to provide a method independent of biaxiality and probably of the usual environmental effects. Measurement of the fringe separation allowed the crack length to be determined, while dislocations in the fringe pattern showed the crack opening mode. The merits of the two techniques were compared and assessed using the Paris law relationship, based on conventional fracture mechanics.     

Creep deformation and crack growth rates of a super α2 titanium aluminide alloy

The influences of stress and temperature on creep deformation behavior and the creep crack growth rates of the super α₂ Ti₃Al alloy were investigated with respect to its safe application at high temperatures. In a temperature range of 1033–1093 K at low applied stress levels, the stress exponent was equal to 1.5. At an intermediate stress range (10^?3 < σ/E < 3 × 10^?3), a stress exponent of 3.3 was observed. As the applied stress was increased, the stress exponent changed from 3.3 to 4.4. The high temperature crack growth rate of the Ti₃Al alloy can be correlated with stress intensity factor K rather than C1 at 1033 K due to environmental embrittlement.     

Fatigue striation in a wide range of crack propagation rates up to 70 μm/cycle in a ductile structural steel

The relationship between striation spacing and fatigue crack propagation rate up to 70 m/cycle was investigated for a ductile structural steel, qualified as JIS SM58Q. A modified compact-type specimen 400 mm wide and a centre-cracked specimen 200 mm wide were tested at a stress ratio, R, of 0 and 0.8. The fracture surface of the specimen was examined in detail under a scanning electron microscope. The crack propagation rate was expressed by a power function of the range of stress intensity factor from 0.1 to 70 m/cycle for R=0 and to 0.5 m/cycle for R=0.8. The striation spacing coincided with the fatigue crack propagation rate over the range 0.1 to 70 m/cycle. The profile of striation was found to be a ridge and valley type, and the ridges on one fracture surface coincided with those on the matching surface. It is suggested that the striation is formed by a plastic blunting mechanism.