Influence of mean stress on the fatigue crack growth characreristics of CrlMo steel tube at elevated temperature

The fatigue crack growth characteristics of CrlMo steel have been investigated at 861 K over the R-ratio range 0.1–0.7 utilising a dwell time of 10 min. at maximum load. All tests were conducted under load control in a laboratory air environment. It was established that the R-ratio significantly affected the fatigue crack extension behaviour inasmuch that with increasing R-ratio, the critical ΔK level for the onset of creep fatigue interactive growth, ΔK^IG, decreased from 20 to 7 MPa√m and the threshold stress intensity, ΔK_th, decreased from 9 to about 3 MPa√m. At intermediate ΔK levels, i.e. between ΔK_th and ΔK^IG, the fatigue crack extension rates, for all R-ratio values, resided on or slightly below the CTOD line, which represents the upper bound for contrnuum controlled fatigue crack growth. Creep fatigue interactive growth was typified by crack extension rates that reside above the CTOD line with a ΔK^IG dependence; the attainment of some critical creep condition or crack linkage condition which causes the abrupt change in crack extension behaviour at ΔK^IG; and crack extension occurs almost exclusively in an intergranular manner. The R-ratio and ΔK^IG followed a linear relation. A literature review concerning the effect of temperature on the threshold fatigue crack growth characteristics of low alloy ferritic steels demonstrated powerful effects of temperature; the magnitude of these effects, however, were dependent upon the testing temperature regime and R-ratio level. The effect of R-ratio on ΔK_th was greatest at temperatures >400°C, significant at ambient temperatures and least in the temperature range 90°C to <300°C. The relationship between temperature and ΔK_th, at a given R-ratio, exhibited a through and a minimum ΔK_th value was observed in the temperature range 200–250°C. The magnitude of the temperature effects on ΔK_th decreased with increasing R-ratio. Such effects of temperature and R-ratio on ΔK_th was reasonably explained in terms of crack closure effects. Finally, the present elevated temperature fatigue crack growth data exhibited massive crack extension enhancement values when compared to ambient near-threshold fatigue crack growth data for CrlMo steel. Such large enhancement values were the combined effects of temperature (environment) and frequency.     

Strain strengthening effects in Witwatersrand quartzite

A series of uniaxial compression specimens were tested over a range of applied ram displacement rates of 8.9 × 10⁻⁴ to 8.9 mm/sec to elucidate the effects of loading rate on the uniaxial compressive fracture stress of Witwatersrand quartzite. It was demonstrated that even within standard loading rate ranges, considerable scatter in the fracture strength (under uniaxial compression) existed in this particular quartzite rock. Nevertheless, a definite trend of increasing fracture resistance with increasing monotonic loading rate was evident inasmuch that increasing the loading rate (strain rate) by four orders of magnitude increase the fracture strength by almost 2.8 times. Prior fatigue loading also produced a significant strain strengthening as the uniaxial compressive fracture stress tended to increase in a sigmoidal fashion with increasing number of fatigue cycles prior to testing. Indeed, the fracture strength of quartzite was almost doubled in value after 10⁻ cycles. Plane strain fracture toughness tests utilising three point bend specimens were conducted and an average of K_lc = 1.7 MPa√m was realized. In both the uniaxial compression tests and the fracture toughness tests, failure occurred by crack extension predominantly by a transgranular flat cleavage-like mode through pure quartzite (silica) regions. However, crack extension was also observed to occur in an intergranular “ductile-like” mode through areas associated with inclusions prevalent in the quartzite.     

Effect of intrinsic stress gradient on the effective mode-I fracture toughness of amorphous diamond-like carbon films for MEMS

The influence of intrinsic stress gradient on the mode-I fracture of thin films with various thicknesses fabricated for Microelectromechanical Systems (MEMS) was investigated. The material system employed in this study was hydrogen-free tetrahedral amorphous diamond-like carbon (ta-C). Uniform gauge microscale specimens with thicknesses 0.5, 1, 2.2, and 3 μm, containing mathematically sharp edge pre-cracks were tested under mode-I loading in fixed grip configuration. The effective opening mode fracture toughness, as calculated from boundary force measurements, was 4.25±0.7 MPa√m for 0.5-μm thick specimens, 4.4±0.4 MPa√m for 1-μm specimens, 3.74±0.3 MPa√m for 2.2-μm specimens, and 3.06±0.17 MPa√m for 3-μm specimens. Thus, the apparent fracture toughness decreased with increasing film thickness. Local elastic property measurements showed no substantial change as a function of film thickness, which provided evidence for the stability of the sp²/sp³ carbon binding stoichiometry in films of different thicknesses. Detailed experiments and finite element analysis pointed out that the dependence of the effective fracture toughness on specimen thickness was due to the intrinsic stress gradient developed during fabrication and post-process annealing. This stress gradient is usually unaccounted for in mode-I fracture experiments with thin films. Thicker films, fabricated from multiple thin layers, underwent annealing for extended times, which resulted in a stress gradient across their thickness. This stress gradient caused an out-of-plane curvature upon film release from its substrate and, thus, combined bending and tensile mode-I loading at the crack tip under in-plane forces. Since the bending component cannot be isolated from the applied boundary force measurements, its contribution, becoming important for thick films, remains unaccounted for in the calculation of the critical stress intensity factor, thus resulting in reduced apparent fracture toughness that varies with film thickness and curvature. It was concluded that in the presence of a stress gradient, accounting only for the average intrinsic stresses could lead in an overestimate of the fracture resistance of a brittle film. Under these considerations the material fracture toughness of ta-C, as determined from specimens with negligible curvature, is K_IC=4.4±0.4 MPa√m.     

Enhancement of fracture toughness of steel with defects by warm-prestressing

The technique of warm-prestressing to improve the resistance of structural steel with defects against low temperature fracture has received considerable attention. It is found that warm-prestressing can improve the fracture toughness and change the COD or δ_c, especially the crack tip plastic opening δ_p.The experimental results obtained from three-point bending tests of 42Mn2 steel specimens at −60°C and −20°C are analyzed. Experiments are also made on the bursting of pressure vessels manufactured from #20 steel. The results indicate that warm-prestressing at room temperature increased the bursting pressure at −40°C for d/t = 0.2 to 0.4, where d is the depth of surface crack and t the vessel thickness.     

Fatigue crack growth studies in rail steels and associated weld metal

Fatigue crack growth studies in rail steels and associated weld metal have shown that (a) deformed rail steel exhibited fatigue crack growth rates that are slightly faster than undeformed rail steel and (b) weld metal growth data are appreciably faster than rail steel growth results and exhibit growth rate plateaux that reside above the upper bound reported for rail steel fatigue crack growth.In rail steel microstructures at low ΔK levels fatigue crack extension occurred by a ductile striated growth mechanism. However at K_max values approaching 40 MPa √m transgranular cleavage facets initially formed and their incidence increased with K_max until final fast fracture. The average cleavage facet size agreed well with pearlite nodule dimensions of 60–100 μm.The weld metal microstructure was much coarser than the rail steel and contained highly directional columnar grain growth. At all ΔK levels the dominant fracture mode was transgranular cleavage containing small isolated regions of ductile striated fatigue crack growth. The cleavage facet size varied from 150 to 600 μm; such a large variation was explained by the fact that in general crack extension tended to occur in association with the proeutectoid ferrite phase.     

Failure resistance of intermetallic matrix reinforced by wires

Composite materials with brittle matrices such as ceramics and intermetallic compounds have gained increased importance in application. Ceramics and intermetallic compounds possess unique heat-resistance at high temperatures. They are, however, vulnerable to brittle fracture. This problem can be overcome by reinforcing the intermetallic compounds with wires. NiAl-tungsten composite wire was manufactured by hot diffusion welding of alternate layers of the matrix and wires. These specimens were subjected to a three-point bending in the temperature range from 20° to 1000°C. Temperature dependence of the bending strength exhibited brittle to ductile transition behavior. At room temperature, unstable failure by bending is terminated in a stable fashion. Brittle fracture of the matrix and wire were observed. For text temperatures of 300°, 500° and 700°C, subcritical crack growth occurred where the matrix and wire showed brittle and ductile fracture, respectively. A pronounced necking of the specimen was observed as the temperature is increased. Substantial plastic deformation occurred when the test is performed at 1000°C. The critical stress intensity factor K_1c and specific work of fracture were measured and found to be two to three times larger than the intermetallic compounds without wire reinforcement.     

Effect of T-stress on crack growth under mixed mode I–III loading

For a crack subjected to combined mode I and III loading the influence of a T-stress is analyzed, with focus on crack growth. The solid is a ductile metal modelled as elastic–plastic, and the fracture process is represented in terms of a cohesive zone model. The analyzes are carried out for conditions of small scale yielding, with the elastic solution applied as boundary conditions on the outer edge of the region analyzed. For several combinations of the stress intensity factors K_I and K_III and the T-stress crack growth resistance curves are calculated numerically in order to determine the fracture toughness. In all situations it is found that a negative T-stress adds to the fracture toughness, whereas a positive T-stress has rather little effect. For given values of K_I and T the minimum fracture toughness corresponds to K_III = 0.     

Residual stresses near a rail end

Stress fields near a cut end of a rail containing longitudinal residual stress typical of roller-straightened rail were studied using analysis and a finite element model. For a self-equilibrating residual stress distribution with equal maximum and minimum stresses, the distance to reach 95% of the mid-rail residual stress field is from 0.7 to 1.8 times the rail height, with the finite element model predicting a length of 1.1 times the rail height. This gives a measure of the accuracy of the simpler analytical models. At the rail end, the longitudinal residual stress goes to zero, and the vertical residual stress near mid-web reaches a maximum of approximately 27 ksi (186 MPa) (1.35 times the maximum mid-rail longitudinal residual stress of 20 ksi, or 138 MPa). The maximum shear stresses are 6 ksi (41 MPa) and −8 ksi (−55 MPa) near the head-web and web-base intersections, respectively, approximately 2 in. (51 mm) from the end of a 7.3 in. (185 mm) high rail. The shear stress is zero at the cut end and in mid-rail. The worst possible end-crack is a horizontal web crack in the vertical residual stress field at the rail end. The stress intensity K_I on such a crack is estimated to reach 20 ksi√in. (22 MPa√m) for cracks 0.5 in. (13mm) long. This is already 0.4 to 0.8 times K_I for carbon and alloy rails, and about 0.5 times K_Ic for a long crack.     

Mode II fracture behavior of a Zr-based bulk metallic glass

Shear band formation and fracture are characterized during mode II loading of a Zr-based bulk metallic glass. The measured mode II fracture toughness, K_IIc=75±4 MPa√m, exceeds the reported mode I fracture toughness by ∼4 times, suggesting that normal or mean stresses play a significant role in the deformation process at the crack tip. This effect is explained in light of a mean stress modified free volume model for shear localization in metallic glasses. Thermal imaging of deformation at the mode II crack tip further reveals that shear bands initiate, arrest, and reactivate along the same path, indicating that flow in the shear band leads to permanent changes in the glass structure that retain a memory of the shear band path. The measured temperature increase within the shear band is a fraction of a degree. However, heat dissipation models indicate that the temperature could have exceeded the glass transition temperature for less than 1 ms immediately after the shear band formed. It is shown that this time scale is sufficient for mechanical relaxation slightly above the glass transition temperature.     

Initiation and arrest of cracks on two pipeline steels at low temperature

Dynamic fracture toughness at initiationK _1d and fracture toughness at arrestK _1a were measured on two pipeline steel grades. Dynamic fracture toughness was measured at a very high loading rate with the help of split Hopkinson pressure bars. The values ofK _1d andK _1a are compared. The purpose of this work is to examine the possibilities of using dynamic fracture toughness at crack initiation as a lower bound of crack arrest toughness. This work has practical applications because crack arrest tests are difficult to perform, give scattered results and are costly and time consuming. This procedure shows that it is possible to economize and rationalize using intelligent technology.     

A field model interpretation of crack initiation and growth behavior in ferroelectric ceramics: change of poling direction and boundary condition

Strain energy density expressions are obtained from a field model that can qualitatively exhibit how the electrical and mechanical disturbances would affect the crack growth behavior in ferroelectric ceramics. Simplification is achieved by considering only three material constants to account for elastic, piezoelectric and dielectric effects. Cross interaction of electric field (or displacement) with mechanical stress (or strain) is identified with the piezoelectric effect; it occurs only when the pole is aligned normal to the crack. Switching of the pole axis by 90° and 180° is examined for possible connection with domain switching. Opposing crack growth behavior can be obtained when the specification of mechanical stress σ^∞ and electric field E^∞ or (σ^∞,E^∞) is replaced by strain ε^∞ and electric displacement D^∞ or (ε^∞,D^∞). Mixed conditions (σ^∞,D^∞) and (ε^∞,E^∞) are also considered. In general, crack growth is found to be larger when compared to that without the application of electric disturbances. This includes both the electric field and displacement. For the eight possible boundary conditions, crack growth retardation is identified only with (E_y^∞,σ_y^∞) for negative E_y^∞ and (D_y^∞,ε_y^∞) for positive D_y^∞ while the mechanical conditions σ_y^∞ or ε_y^∞ are not changed. Suitable combinations of the elastic, piezoelectric and dielectric material constants could also be made to suppress crack growth.     

Fracture strength for a high strength steel bridge cable wire with a surface crack

In this paper, the fracture strength of a cracked suspension bridge wire is determined based on linear elastic fracture mechanics (LEFM). The wire is 5 mm in diameter, with an original ultimate strength of 1725 MPa and ultimate elongation that ranges between 5.5% and 6%. The average value of for the wire fracture toughness, K_C, was recently evaluated by the author. The state of practice is to use the ultimate strength of the cracked wire as obtained from tensile tests. This approach may overestimate the strength of the wire due to possible delamination and crack tip plasticity. A case study for a group of in situ wire breaks retrieved from a suspension bridge cable is presented. The failure analysis is performed based on both the fracture toughness criterion and the net section theory. The fracture toughness criterion produced more realistic results for the fracture strength of the wire. The decline in the fracture toughness and the corresponding reduction in the fracture strength of cracked degraded wire are predicted making use of the strain energy density criterion.     

Physical aging and time–temperature behavior concerning fracture performance of polycarbonate

The effects of physical aging on fracture and yielding behavior are polycarbonate are considered. Two groups of Bisphenol A-based polycarbonate, consisted of extruded PC sheets (thickness of 0.25 mm) and injection molded PC bars (thickness of 3.18 mm) are used. These samples were annealed at various temperatures ranging from 60 to 120 °C, for different times varying up to 240 h. For PC sheets the essential work of fracture (EWF) method was used to analyze fracture behavior. The results are compared to the strain energy density with aging time and aging temperature in the ranges investigated. This effect is confirmed by the change in fracture toughness, as measured by three-point bending tests. The concept of fictive temperature (T_f) was used to characterize the degree of aging in the sample. T_f of a glass in an aged state at a time t is defined as the temperature at which the volume would be equal to the equilibrium volume at T_f if the sample were instantaneously removed to that temperature. Differential scanning calorimetry (DSC) was used to determine T_f. The variations of T_f with aging time and aging temperature are in agreement with both the strain energy density measurement and the three-point bending tests. These results contradict the effects of aging on fracture toughness observed by the essential work of fracture approach. The latter showed anomalous regions of increasing fracture toughness with aging, leading to spurious conclusions. The brittle–ductile transition in fracture behavior is analyzed by an activation energy approach. Aging increases the brittle–ductile transition temperature and the effect is more pronounced for the lower molecular-weight sample. Fracture tests also showed a decrease in the entropy with aging, confirming the results observed previously from tension and compression tests.     

A bar impact tester for dynamic fracture testing of ceramics and ceramic composites

A bar impact test was developed to study the dynamic fracture responses of precracked ceramic bars, Al₂O₃ and 15/29-percent volume SiC_w/Al₂O₃. Crack-opening displacement was measured with a laser-interferometric displacement gage and was used to determine the crack velocity and the dynamic stress-intensity factorK _I ^dyn . The crack velocity andK _I ^dyn increased with increasing impact velocity while the dynamic-initiation fracture toughness,K _Id, did not vary consistently with increasing impact velocities.Paper was presented at the 1992 SEM Spring Conference on Experimental Mechanics held in Las Vegas on June 8–11.     

Loading rate spectra for fracture initiation in metals

In the first part of the paper a review of experimental results is presented on the effects of loading rate of the fracture initiation toughness of structural alloys. Recent progress in new experimental techniques enables for measuring the fracture initiation properties over ten orders of magnitude in , where loading rate for plane strain fracture toughness. The range covered in experiments is

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.Experimental results for aluminum and titanium alloys, as well as for some steels are discussed. Those results are shown as loading rate spectra where the fracture toughness K_Ic is plotted versus log at constant temperature. The patterns of the loading rate spectra demonstrate a negative role of the strain rate sensitivity in the process of fracture initiation, at least within a certain ranges of the loading rate .In the second part an attempt is presented to model the observed phenomena. Consequently, a new model has been proposed which combines an semi-empirical correlation between the critical fracture stress σ_F, yield stress σ_y from one side and a simple thermally activated potential of plastic flow from the other. It has been demonstrated that this simple approach can predict properly a fundamental changes in the loading rate spectra for steels.     

End-shaped copper fibers in an epoxy matrix—predicted versus actual fracture toughening

End-shaped copper fibers are placed in a brittle thermoset epoxy matrix at 10 vol% and tested in four-point bending to determine the fracture toughness of the composite. Results from four-point bend tests agree well with the theoretical predictions of the fracture toughness increment ‘ΔG’ of a metal fiber/brittle thermoset matrix composite based on single fiber pullout (SFP) tests. This close agreement demonstrates that SFP testing, along with the theoretical model, can be used as an effective end-shape screening tool for ductile fibers before full scale composite testing. The model predicts that the composite’s fracture toughness will be 46% higher with flat end-impacted fibers and 4% lower with rippled fibers compared to straight fibers at a 0° orientation. Four-point bend results show the actual composite’s fracture toughness is 49% higher with flat end-impacted fibers and 5% lower with rippled fibers compared to straight fibers. Further, four-point bend results show that end-shaped copper fibers improve both the flexural strength and modulus of the composite, demonstrating that end-shaped ductile fibers provide a good stress transfer to the fibers by anchoring the fibers into the matrix. Lastly, experimental validation of the model also indicates that at low fiber volume fractions, fiber–fiber interaction has only a minor influence on the fracture toughness for the tested ductile fiber/brittle matrix composite.     

Fatigue behavior of E-glass fiber reinforced phenolic composites: effect of temperature, mean stress and fiber surface treatment

Phenolic matrix is reinforced by unidirectional E-glass fibers with volume fractions of 0.30 and 0.45. Three different surface treatments are applied to the E-glass fibers. The composite specimens are tested at ambient condition and temperatures of 100°C 150° and 200°C with stress levels of R(σ_min/σ_max) equal to 0 and 0.4 for load frequencies of 1.5, 10 and 25 Hz. Data are presented in terms of S/N curves and assessed by degradation of modulus based on compliance. For a particular fiber glass surface treatment and volume fraction, the composite specimen is notched and tested at room temperature and 200°C. A fatigue strength reduction factor K_f is defined and obtained such that the results could be compared with those of the unnotched specimens. Notch effect is small if the hole diameter is equal to the specimen thickness; it would be important for larger hole sizes. Fractured surfaces are examined by the scanning electron microscope.     

R-similarity criterion of plastic deformation instability and its use for KIC determination for steels

The paper reports an investigation of the application of the similarity theory, strain energy density concept and fracture mechanics to the fracture toughness (K_IC) determination. The method K_IC determination is described using R-similarity criterion of plastic deformation instability. It allows to determine the true K_IC value for ductile steels using specimens not satisfying linear fracture mechanics requirements.     

Quasi-static behavior of Mg-alloys with and without short-fiber reinforcement

Magnesium alloys AE42 and AZ91 reinforced with 23 vol.% carbon short fibers (D_f ≈ 7 μm, L_f ≈ 100 μm) were tested under quasi-static loading. The carbon fibers were quasi-isotropically distributed in the horizontal plane (reinforced plane) of the casting. Compression and tensile tests were carried out on both the matrix alloys and the composites at temperatures between 20 °C and 300 °C. Specimens were machined to be loaded either parallel or normal to the reinforced plane. Due to the reinforcement, the compression yield stress of the composite AE42-C increased to a value approximately three-fold greater than the yield strength of the matrix; for composite AZ91-C this parameter was approximately 2.5-fold greater than that of the AZ91 matrix. The improvement in tensile strength was less than that in compression, which could be related to early tensile fracture through decohesion at the matrix–fiber interface, as detected by SEM investigations conducted on failed tensile specimens. Flow curves for the matrix alloys at different temperatures were described by a modified Kocks–Mecking material law. An idealization of a 2-D mesomodel was used for finite-element simulation of the mechanical behavior of the composites. The fibers were first considered as elastic bodies and the behavior of the matrix material was set according to the material law determined from the flow curves for the matrix alloys. Other calculations were carried out by considering elasto-plastic behavior of the fibers for application of a failure initiation technique to simulate the behavior of the composite materials beyond the ultimate stress.