Linear Elastic Fracture Mechanics Parameter Research Articles

PROPAGATION BEHAVIOUR OF SHORT FATIGUE CRACKS IN Q2N STEEL

Abstract— The work described in this paper characterizes short fatigue crack growth behaviour of Q2N steel having a complex microstructure and designated for pressure vessel and offshore structure applications. Short and long fatigue crack growth tests for this steel were conducted under three point bend loading conditions. It was found that, in the initial stages of growth, short cracks propagate much faster than those of long cracks when correlated with the linear elastic fracture mechanics (LEFM) parameter ΔK. A period of crack growth retardation was observed at crack lengths of approx 50 μm. The theory of the interaction between short cracks and grain boundaries fails to predict the occurrence of this deceleration minima. A new short crack deceleration mechanism is proposed based on experimental observation. Observation of the characteristic behaviour of short cracks allowed the development of a short crack growth model based on microstructural fracture mechanics analyses.

Crack Growth Rate Behavior of a Titanium-Aluminide Alloy During Isothermal and Nonisothermal Conditions

Observations of isothermal fatigue, isothermal fatigue with superimposed load hold times, and thermomechanical fatigue (TMF) crack growth rate behavior of Ti-24Al-11Nb are presented and compared with results from previous studies on titanium and nickel-base superalloys. Elevated-temperature crack growth mechanisms in this alloy, which involve fatigue, oxidation and creep, and the influence of frequency, temperature, and hold-time are discussed. These mechanisms are used to interpret the observations of TMF crack growth. The limitations of current crack growth rate models based on the linear-elastic fracture mechanics parameter, K, are addressed.

Behavior and Test Method of Subcritical Crack Growth at Elevated Temperatures in Ceramics

Behavior and test method of subcritical crack growth (SCG) at elevated temperatures were investigated on an alumina with 90% purity. The proposed test method enabled to measure SCG at temperatures over 1000°C using the piston displacement of testing machine and fractographic information. In order to evaluate SCG behavior based on the linear elastic fracture mechanics (LEFM), larger specimens are recommended, because a small scale creep (SSC) condition is required in expressing the crack tip singular stress field by LEFM parameter, i.e. stress intensity factor K. Since creep is dependent on both thermal and mechanical factors, requirement of SSC condition, which implies that the creep damage zone is localized at the crack tip region, may be influenced by those factors. Detailed observations of SCG behavior at 900 and 1050°C revealed that a main crack grew by coalescences with microcracks initiated in the creep damage zone at the crack tip. Thus, tortuosity of SCG path increased with increasing size of the creep damage zone. Temperature dependence of SCG characteristics was discussed in terms of the crack growth mechanism and creep deformation scale.

Fatigue fracture behaviour of PEEK: 1. Effects of load level

Results of experimental studies on fatigue fracture behaviour of PEEK are reported. Experiments are conducted on injection moulded single edge notched specimens of 2.68 mm in thickness. At low crack speeds the crack tip is relatively round. At relatively higher crack speeds, the crack tip geometry changes to a triangular shape with an angle of 90° which remains constant until close to unstable fracture. Optical microscopy observations of fracture surfaces and of transverse sections show that at relatively short crack lengths growth occurs in a ‘brittle’ manner. Subsequently necking or lateral contraction of the specimen around the crack tip is observed and is associated with a ‘ductile’ mode of growth. The point of transition from ‘brittle’ to ‘ductile’ fracture is dependent upon the level of the stress. Fatigue striations are observed throughout the fracture surface. Correlation of the striations and the number of cycles indicates a one cycle crack growth mode. The critical crack length is assumed to correspond to the point of minimum thinning which is shortly after the last striation. Hysteretic losses during fatigue crack growth are negligible until a few cycles prior to unstable fracture. Energy release rates evaluated from load displacement curves are practically equal to J 1 = δσ y ( σ y is the yield stress of the material and σ is the crack opening displacement). The ‘brittle’ phase of crack propagation is well described by linear elastic fracture mechanics parameters. For the entire phase of propagation and for the same level of J 1 (= δσ y), the crack speed is practically independent of the stress level.

EFFECT OF NOTCH STRESS FIELD AND CRACK CLOSURE ON SHORT FATIGUE CRACK GROWTH

Abstract— The growth rate of a short fatigue crack that is partly or wholly embedded within the notch plastic zone, is affected by the extent and intensity of the elastic‐plastic notch stress field and closure effect. The notch stress—strain field and plastic zone were analysed by the Finite Element Method (FEM). The growth rate and the closure curve for a short fatigue crack emanating from the notch root were measured. Based on the experimental and numerical analyses, a modified Linear Elastic Fracture Mechanics (LEFM) parameter is proposed for a short through‐thickness crack emanating from a notch root under elastic—plastic loading conditions.

Changes in fatigue strength due to cyclic prestress: II. Fatigue tests of aluminium alloy specimens and evaluation by means of the sequential Wohler curve concept: Pusche, A.C. IfL-Mitt. Mar.–Apr. 1989 28, (2), 43–49 (in German)

The propagation of small cracks in fatigue has received considerable attention over the past decade. Microstructurally and even mechanically small cracks have been shown to consistently exhibit higher crack growth rates than predicted using standard threshold and Paris growth law concepts, based on linear elastic fracture mechanics (LEFM) applied to mechanically long cracks. This has been commonly attributed to several factors, including the influence of microstructure, the breakdown of LEFM parameters for representation of the crack tip field, and the transient development of plasticity-induced closure towards some steady-state value associated with long crack behavior. Other mechanisms related to microstructural effects such as roughness-induced closure and crack face bridging/interference are also potential contributors. Quantitative attempts to explain the fatigue propagation of small cracks in terms of plasticity-induced closure, along with adoption of an additional component of the driving force (e.g. crack tip opening displacement) to reflect the contribution of cyclic plastic strain have met with some success in correlation of the so-called “anomalous” propagation behavior, including crack deceleration and acceleration transients. However, these models rely on the adoption of highly idealized assumptions regarding the self-similarity of crack growth, neglect of local anisotropy and heterogeneity associated with microstructure, etc.; in spite of these compromises, they still involve a considerable degree of complexity. Here, we adopt the viewpoint that multiple, microstructure interactions and closure effects may simultaneously influence the propagation of small cracks; moreover, driving force parameters based on self-similar crack growth arguments of elastic-plastic fracture mechanics (EPFM) for mechanically long cracks, such as the cyclic J-integral or crack tip opening displacement, may apply in principle, but not rigorously, as the driving force for small cracks. As an engineering approach, we consider a recent extension of the multiaxial microcrack propagation model first proposed by McDowell and Berard[1,2] for the growth of microstructurally small and mechanically small fatigue cracks[3] in multiaxial fatigue. Integrated between initial and final crack lengths, the model is fully consistent with standard strain-life laws of fatigue crack initiation mechanics under various states of stress, [1,2] and therefore bridges the mechanics of classical initiation and LEFM/EPFM to some extent. The existence of a fatigue limit (nonpropagating crack limit) is neglected in this particular work. It is shown for uniaxial loading of both 1045 steel and Inconel 718 that the model is able to describe, to first order, the anomalous high propagation rates of small cracks and convergence with long crack d a/ dN - ΔK data as the crack transitions from small to mechanically long scales. The limits of validity of engineering schemes based on decomposition of total fatigue life into “initiation” and propagation phases that rely on strainlife and long crack propagation laws are discussed[4]. Moreover, it is shown that the model essentially reflects a closure transient in the context of a cyclic J-integral approach, similar to the EPFM plasticity-induced closure modeling concepts set forth by Newman[5] and McClung et al. [6] for small cracks in fatigue. However, the present model implicitly reflects multiple forms of crack tip shielding effects, not just plasticity-induced closure. Finally, the model is shown to provide realistic treatment of cumulative damage in two level loading sequences, as reflected by comparison with the damage curve approach of Manson and Halford[7].

Finite element study on size requirement for stress intensity factor characterization under biaxial loading

The size requirement for applying the stress intensity factor K I under biaxial loading in plane strain and plane stress conditions is studied by performing a two-dimensional elastic-plastic finite element analysis. The extent to which K I is validly used is determined by comparing the energy release rate G, a linear elastic fracture mechanics parameter, with the J-integral, an elastic-plastic fracture mechanics parameter. The result shows that the minimum value of the remaining uncracked ligament and the crack length for ensuring K-controlled crack tip characteristics is (0.5∼1.0)(K I/σ ys )2, where σ ys is yield stress depending on the load biaxiality, while ASME suggests 2.5(K I/σ ys )2 for uniaxial loading.

The effects of hold time and frequency on crack growth in alloy 800H at 650 °C

The heat resistant material, Alloy 800H, is presently used in pctrochemical processes and for steam superheater tubing in power generation systems. In service, the alloy may experience steady loading, cyclic loading, or a combination of the two. In this paper, crack growth behavior under fatigue, creep, and hold time loading conditions has been characterized as a temperature of 650 ‡C in laboratory air. Fatigue crack growth rate (per second) was observed to increase with increasing frequency. The linear elastic fracture mechanics (LEFM) parameter, δK, was found to be a useful parameter to correlate crack growth rates for fatigue. In creep and hold time cases, where significant plasticity was observed, the energy rate line integral parameter, C*, is a useful descriptive parameter. In fact, C* is capable of consolidating all creep and hold time data into a single straight line on a logarithmic plot. Both creep and hold time tests show the same characteristic deflection curves. This demonstrates that hold time tests are more creep-like than fatigue-like for the test conditions here. Compared to creep loading, fatigue deflection curves show much less induced plasticity, most of which is gathered during the final stages of the experiments at high-stress intensity values. Microstructural examination revealed that a transgranular crack growth mode is predominant during fatigue, while both creep and hold time tests are cavity-controlled crack growth processes with the exception that striations are observed along cavity edges in the hold time tests.

Macroscopic creep crack growth in type 316 stainless steel.: III. Application of linear and nonlinear elastic fracture mechanics

Creep crack propagation rates have been measured in Type 316 steel at 625°C and correlated in terms of linear and nonlinear elastic fracture mechanics parameters. Two differing specimen geometries from each of two different casts of steel have been used and it appears that crack growth predictions based on a net section stress correlation are preferred to those based on stress intensity factor or the creep energy rate line integral C∗. More importantly an effect of geometrical constraint has been observed, with crack propagation rates decreasing with increasing specimen constraint.

A Procedure for the Assessment of the Structural Integrity of Nuclear Pressure Vessels

This paper presents a simple engineering procedure that the utility industry can use to assess the integrity of typical nuclear-grade pressure vessels. The procedure recognizes both brittle fracture and plastic collapse and is based on a set of proposed failure assessment curves which make up a safety/failure plane. The plane is defined by the stress intensity factor/fracture toughness ratio as the ordinate and the applied stress/reference plastic collapse stress ratio as the abscissa. The failure assessment procedure is based in part on the British Central Electricity Generating Board’s R-6 failure assessment diagram and the deformation plasticity solutions of the General Electric Company. Two parameters, a plastic collapse parameter (Sr′) and linear elastic fracture mechanics parameter (Kr′) are calculated by the user. The point (Sr′, Kr′) is plotted on the appropriate failure assessment diagram. If the point lies inside the respective curve, the structure is safe from failure. Moreover, for a given pressure and a postulated or actual flaw size, the margin of safety of the structure can be simply determined. Consistent with Appendix A of Section XI, (Division 1) of the ASME Boiler and Pressure Vessel Code the procedure presented in this paper is limited to ferritic materials 4 in. (102 mm) and greater in thickness. Details of the derivation of the proposed set of failure assessment curves are provided along with a sample problem illustrating the use of these curves.

Fatigue crack propagation in aluminium alloy NP8 determined from tests on 12.5 mm nominal thickness specimens

Fatigue crack growth tests were carried out on aluminium alloy BS1477 NP8 which has a 0.1% proof stress of 120 MN/m 2. The tests were performed in air at room temperature using centrecrack fracture toughness specimens of 12.5 mm nominal thickness. Crack growth rates were found to depend on the stress ratio σ min/ σ max (the R ratio) and probably on specimen thickness, but not on net section yield. The results were similar to those reported by Frost using high strength aluminium alloys of 3–4 mm thickness, and this has been attributed to the increased thickness of the NP8 specimens. The individual da/dN vs Δ K results formed into bands depending on R; crack growth rates at each R value could be correlated in terms of the linear elastic fracture mechanics parameter ΔK, in the form da/dN=C( ΔK) n suggested by Paris. Crack growth rates were greater than predicted by expressions due to Frost based on thin low strength aluminium specimens and due to Pearson based on 12.7 mm thickness high strength aluminium specimens. A modified Pearson equation has been deduced which is in good agreement with the test results. Used in conjunction with an approximate expression for ΔK, the modified equation leads to conservative estimates of the number of cycles for a crack to reach a given length, which is a safe result of value in engineering practice.

The J-integral as a fracture criterion for fiber reinforced concrete

The J-integral, a one-parameter average measure of the elastic-plastic field near a crack tip was investigated as a fracture criterion for fiber-reinforced concrete. Cement paste, plain concrete and eight different steel and glass fiber concretes in the form of notched beams were tested in bending, and J IC, as well as the linear elastic fracture mechanics parameters K IC and G IC were evaluated. The results suggest that J IC is a promising fracture criterion for all of these, while K IC (or G IC) almost certainly are not, except for cement paste. In evaluating the effect of steel fiber additions, it was found that a fiber addition of less than 0.75% did not improve the strength or fracture behaviour of the concrete, nor did J IC change very much. However, at higher fiber contents, J IC showed significant increases, reflecting the changed character of the material; K IC and G IC did not.

Variability in Fatigue Crack Growth Rate Testing

Abstract To provide the data necessary to develop a recommended practice for fatigue crack growth rate testing, an extensive interlaboratory (round robin) program was conducted and the variability and bias associated with the current state of the art of fatigue crack growth rate testing was determined. Fatigue crack growth rate data (expressed in terms of linear elastic fracture mechanics parameters) were generated for a 190-ksi (1310-MPa) yield strength 10 Ni-8Co-1Mo steel at 15 different laboratories with several test specimen geometries. The results were evaluated statistically and on the basis of a graphical comparison, and the variability and bias associated with both the experimental and analytical aspects of crack growth rate testing were determined. In general, the overall interlaboratory variability was found to be approximately 3 to 1 (on crack growth rate at a given stress intensity range). The intralaboratory variability was typically 2 to 1. No significant geometry or data processing bias was encountered. The results of this study show that the primary source of variability associated with fatigue crack growth rate testing is the experimental procedure used to obtain the raw test data (crack length versus elapsed cycles).

The Dynamic Fracture Toughness of Carbon-Carbon Composites

The dynamic fracture toughness of two types of carbon-carbon com posites (filament wound and felt substrate) and ATJ-S graphite was deter mined from instrumented Charpy impact tests. The resistance to crack initiation from a pre-existing flaw (notch) was examined by investigating the dynamic fracture toughness, KD, a linear elastic fracture mechanics parameter. The resistance to crack initiation and propagation was deter mined using the dynamic work-of-fracture parameter, γ fD. Testing was conducted over a range of impact velocities (4.0-202.8 in/sec), and the parameters KD and γ fD were found to be strongly sensitive to impact velocity for all three materials. As expected, the dynamic fracture tough ness of the highly anisotropic filament wound carbon-carbon composite was dependent on filament orientation.

Fracture Toughness of Carbon-Carbon Composites

The fracture toughnesses of two carbon-carbon composites and ATJ-S graphite were determined from the load-deflection responses of single- edge-notched specimens subjected to three-point bending. The resistance to crack initiation in the presence of a pre-existing flaw (machined notch) was examined using the linear elastic fracture mechanics parameters of critical stress intensity factor Kc, and critical strain energy release rate Gc. The resistance of the materials to both crack initiation and propagation was determined using the work-of-fracture parameter γ F. Both the fracture toughnesses and the failure modes (delamination or crack propagation colinear with the notch) were found to be strongly dependent on material characteristics.

Comparison of fracture toughness test procedures for aluminum alloys

The Dynamic Tear (DT) test permits the measurement of fracture propagation energy across the toughness spectrum for metals which are definable by linear elastic analyses to those requiring gross plastic strains for fracture. The linear elastic fracture mechanics parameter K ic provides a relationship between critical flaw size and stress level at which crack instability will occur. Unlike the DT test, the K ic toughness test cannot be utilized for fracture under conditions of elastic-plastic or gross plastic strain. A correlation has been developed between the DT test and the K IC parameter for ahuminum alloys. The relationship may also be expressed in terms of β ic-DT and ℷ ic-DT. The K ic values were determined with several specimen types and a comparison of the values for different specimens is provided. The correspondence between K ic and DT serves several purposes. It provides a frame of reference for DT values obtained from frangible metals that fracture under linear elastic conditions. Accordingly, it permits utilization of the inexpensive DT test to approximate the flaw size-stress instability conditions which otherwise must be determined by the more expensive K ic test. Furthermore, through extrapolation, it is possible to utilize the DT test to estimate the critical flaw size under an elastic-plastic strain field.