Fatigue microcrack initiation in polycrystalline alpha-iron with polished and oxidized surfaces

Plastic-strain-controlled fatigue crack initiation experiments were conducted on unoxidized and oxidized, vacuum-melted iron. In the unoxidized, as-polished condition at low plastic strain amplitudes, e.g., 1 or 5 X 10⁻⁴, microcracks initiated along well defined slip bands and in the troughs of surface rumples. Such microcracks tended to stop short of grain boundaries. On increasing the plastic strain amplitude, initiation of fatigue cracks along grain boundaries became important. When the specimens were surface oxidized, intergranular microcrack initiation was the dominant mode even at the plastic strain amplitude of 5 x 10⁻⁴, where transgranular microcracks formed only very infrequently and then only considerably later in the fatigue lifetime. At 1 x 10⁻³ amplitude, transgranular microcracks initiated very early in the cycling compared to the polished condition, but such cracks did not grow or increase in number. Intergranular cracks formed later and led to failure. Surface oxidation led to approximately a 20 pct reduction in lifetime to final failure. Formerly with the Department of Materials Science and Engineering and Materials Research Center, Northwestern University, Evanston, IL     

Diffusion and electrotransport of some transition elements in (b.c.c.) thorium

Diffusion and electrotransport parameters of the transition elements molybdenum, rhenium, tungsten and zirconium in β thorium were measured, for the temperature range 1660–1945 K. For each solute element, except zirconium, the measurement was made at four different temperatures, where as for zirconium, studies were performed for only two temperatures 1770 and 1870K. Our results indicate that all four solute elements migrate to the anode in b.c.c. thorium with mean Z¹ values of −6.6 for Mo, −4.6 for Re, −8.2 for W and about −2.5 for Zr. The results also indicate that molybdenum, rhenium and tungsten diffuse much faster in β thorium than zirconium which suggests a correlation between solute atom electric mobility and diffusivity with the atomic sizes of both the solute and matrix atom. Results of the diffusion studies yield the following equations of diffusion for Molybdenum: D_Mo = 15.1 exp(−51,500/RT) Renium: D_Re = 4.04 × 10⁻³ exp(−20,100/RT) Tungsten: D_W = 0.103 exp(−38,100/RT) Zirconium: D_Zr = 1.70 × 10⁴ exp(−91,700/RT).     

Dislocation structures in fatigued polycrystalline copper

The dislocation structures in fatigued polycrystalline copper with small average grain size were investigated over a plastic strain range from 1.5 x 10⁻⁵ to 10⁻². It was found that the dislocation structures are arranged into three types of configurations, which correspond to the three regions in the cyclic stress-strain curve. Cylidirical loop patch structure are present in region A for low strain amplitudes, similar to those observed previously in coarse grained polycrystals. Moreover, irregular loop patches are also formed in this region for small grains polycrystals rather thanin region B at intermediate strain amplitudes for coarse grained polycrystals. In region B, persistent slip band (PSB) structures are formed but with a low volume content compared with the coarse grained polycrystals. In region C, at high plastic strains, the dislocation structures are dominated by dipolar walls. In addition, labyrinth structures are developed in region C instead of region B for coarse grained polycrystals. All the dislocation structures observed are viewed as forms of dipolized structures. A dipolized dislocation arrangement model is proposed to describe the formation process of dislocation structures. It is shown that all the dislocation configurations formed in cycled polycrystalline copper are low energy structures.     

Cyclic deformation of AISI-310 stainless steel—I. Cyclic stress-strain responses

Cyclic responses of AISI-310 austenitic stainless steel with coarse grains are investigated in the plastic strain amplitude (ε_pl) range 1 × 10⁻⁴–9 × 10⁻³. With respect to the cyclic hardening behaviour, three ranges of ε_pl may be distinguished. ε_pl < 8 × 10⁻⁴: neither cyclic hardening nor cyclic softening is observed; 8 × 10⁻⁴ < ε_pl < 6 × 10⁻³: a cyclic softening follows a cyclic hardening before the saturation is approached; ε_pl > 8 × 10⁻³: a cyclic hardening leads directly to saturation. The cyclic stress-strain (CSS) curve exhibits three regimes of strain dependence of saturation stress (σ_s): in regime I, σ_s increases almost unnoticeably with increasing ε_pl; in regime II, σ_s increases smoothly with increasing ε_pl; in regime III, σ_s increases dramatically with increasing ε_pl. The three regimes of the CSS curve fall into line with the different ranges of ε_pl of different cyclic hardening behaviours.     

Cyclic deformation of pearlitic eutectoid rail steel

Cyclic deformation behavior in pearlitic eutectoid steel strongly depends on the interlamellar spacing with cyclic softening in fine pearlite, cyclic hardening in coarse pearlite, and both cyclic softening and hardening depending on the strain amplitude in medium pearlite. Dislocations in cyclically softened specimens were uniformly distributed, while dislocation cells were observed with cyclic hardening. The cell size decreased with increasing strain amplitude. Using the cell size to interlamellar spacing ratios, conditions for cell formation were quantified. Based on dislocation structure observations, mechanisms for cyclic softening and hardening were proposed. Both monotonic and cyclic yield stresses follow Hall-Petch type relations when plotted against interlamellar spacing. Surface fatigue microcrack initiation usually occurred in the ferrite matrix associated with extrusions and intrusions. Most microcracks were almost parallel to the cementite lamellae and oriented between 30 and 90 deg with respect to the tensile axis. Little influence of MnS inclusions on microcrack initiation was noticed.     

Cyclic strain hardening in polycrystalline copper

Polycrystals of pure copper were cyclically deformed, at room temperature under symmetric tension-compression fatigue at constant total strain amplitude control with an approximate constant plastic strain rate of 10⁻⁴. The relationship between the saturation stress amplitude and strain amplitude over a range of plastic strain from 2 × 10⁻⁷ to 10⁻² reveals three regions of cyclic hardening. A quasi-plateau, where the stresses show a slow constant increase, was observed in the intermediate region extending in the plastic strain range γ_pl, of 1.5 × 10⁻⁵ to 7.5 × 10⁻⁴. In this region, persistent slip bands (PSBs) which consist of “ladder” structures, similar to the case of single crystals, were found in the bulk of the fatigued polycrystals. The fatigue limit was found to be Δσ_s/2 = 73 MPa which corresponds to the plastic strain Δϵ_pl/2 = 1.5 × 10⁻⁵ where PSBs do not form.     

The slip character and low cycle fatigue behaviour: The influence of F.C.C. twinning and strain-induced F.C.C. → H.C.P. martensitic transformation

The influence of slip character on the low cycle fatigue behaviour was investigated in the CoNi system at room temperature. Three alloys of increasing stacking fault energy (SFE) were used: Co31Ni (SFE ∼- 12 mJm⁻²) which deforms by slip and f.c.c. → h.c.p. strain-induced martensitic transformation, Co33Ni (SFE = 15 mJm⁻²) which exhibits slip and twinning and Co45Ni (SFE = 45mJm⁻²) which deforms only by slip with easy cross-slip. Push-pull low cycle fatigue tests were conducted under plastic strain control up to a few 10⁴ cycles. The number of cycles to fracture was found to increase with decreasing SFE which promotes planar deformation mechanisms: the life obtained in Co31 Ni and Co33Ni alloys is respectively about 6 and 3 times higher than that of Co45Ni alloy.Measurements of striation spacings on the fracture surfaces have enabled to show that the influence of twinning on fatigue life is mainly due to a large increase of the initiation period before stage II crack propagation. This behaviour was associated with a difference in crack initiation sites along twin or h.c.p. platelets where there is a strain localization in low SFE alloys or along grain boundaries in the high SFE alloy. The increase of crack initiation period was explained on the basis of a reduced stage I crack propagation rate in the alloys exhibiting planar deformation mechanisms.     

The brittle compressive fracture of ice

The brittle compressive fracture under uniaxial loading of fresh-water, granular ice Ih has been studied. Measurements are reported of the fracture stress at temperatures from −10 to −50°C at strain rates of 10⁻³ and 10⁻¹ s⁻¹ for grain sizes from approximately 1 to 10 mm. Also a summary is reported of measurements by Jones et al. (unpublished) of the kinetic coefficient of friction for ice on ice at temperatures from −10 to −40°C at sliding velocities from 5 × 10⁻⁷ m s⁻¹ to 5 × 10⁻² ms⁻¹. Observations via high speed photography of internal cracking during loading are included. The strength, albeit scattered, increases with decreasing grain size, with decreasing temperature and at −10°C with decreasing strain rate. Similarly, the coefficient of friction increases with decreasing temperature and at −10°C with decreasing sliding velocity. Wing cracks were observed on some inclined cracks nucleated during loading. The results are explained in terms of the frictional crack sliding-wing crack model [as developed by Ashby and Hallam, Acta metall.34, 497 (1986)] of compressive fracture. Finally, a simple model is presented for the transition from ductile to brittle behavior. It is based upon the competition between the building up and the relaxation of internal stresses within the vicinity of the internal cracks, and it leads to a transition strain rate which can be expressed in terms of the fracture toughness, the creep rate, the kinetic coefficient of friction and the microstructural scale of the material.     

Thermomechanical deformation modeling of Al2xxxT4/SiCp composites

A constitutive model for metal matrix composites is developed and its capabilities for predicting cyclic isothermal and cyclic thermomechanical behavior are demonstrated. The silicon carbide particulate reinforced Al2xxxT4 alloy was studied experimentally and theoretically with the model. Cyclic stress-strain behavior of 15 and 20% reinforced silicon carbide particulate reinforced Al2xxx-T4 were successfully predicted at temperatures of 20, 200 and 300°C at strain rates between 3 × 10⁻⁵s⁻¹ and 3 × 10⁻³s⁻¹. The themomechanical stress-strain behaviors (T_min = 100°C, T_max = 200, 300°C) were studied experimentally and the results were closely predicted when temperature-strain phasing was in-phase and out-of-phase. This study clarifies the influence of mechanical property mismatch in the elastic and in the inelastic ranges vs the thermal property mismatch on composite and the matrix behaviors. The transverse and hydrostatic stresses in the matrix, developed during cyclic loading, are reported for both isothermal and thermomechanical loading conditions.     

Mechanical behavior of Al-Li/SiC composites: Part II. Cyclic deformation

The deformation and failure mechanisms under cyclic deformation in an 8090 Al-Li alloy reinforced with 15 vol pct SiC particles were studied and compared to those of the unreinforced alloy. The materials were tested under fully reversed cyclic deformation in the peak-aged and naturally aged conditions to obtain the cyclic response and the cyclic stress-strain curve. The peak-aged materials remained stable or showed slight cyclic softening, and the deformation mechanisms were not modified by the presence of the ceramic reinforcements: dislocations were trapped by the S′ precipitates and the stable response was produced by the mobile dislocations shuttling between the precipitates to accommodate the plastic strain without further hardening. The naturally aged materials exhibited cyclic hardening until failure, which was attributed to the interactions among dislocations. Strain localization and slip-band formation were observed in the naturally aged alloy at high cyclic strain amplitudes, whereas the corresponding composite presented homogeneous deformation. Fracture was initiated by grain-boundary delamination in the unreinforced materials, while progressive reinforcement fracture under cyclic deformation was the main damage mechanism in the composites. The influence of these deformation and damage processes in low-cycle fatigue life is discussed.     

Overview no. 50: Cleavage-limited maximum strength of work-hardened b.c.c. polycrystals

b.c.c. metals and alloys maintain a non-decaying work-hardening rate up to very high plastic strains when deformed monotonically at low temperatures (T < 0.3 T_M), specially by axisymmetric elongation (wire drawing). This fact seems to offer the possibility of production of strong metallic filaments which are tougher than other fibre reinforcing materials. However, b.c.c. metals being prone to cleave, their rising stress-strain curves could be trimmed by brittle failure beyond some point. This paper studies such contingency and shows that two failure modes are possible: a microscopic-type failure, when the flow stress meets the (strain-dependent) tensile cleavage stress, σ_f^T, and, for large strains, a macroscopic-type failure when the critical stress intensity factor (also strain-dependent) is reached for cracks associated to inclusions or for crack-like surface defects. From the rather limited information gathered on the evolution of the brittle failure stress with strain it is deduced that σ_f^T is mainly controlled by the instantaneous—strain-induced—grain size and that it will rarely limit the b.c.c. wire strength directly. On the contrary, macroscopic-type failures can constitute the absolute strength limit for alloys with very high workhardening rate. Guidelines to further improve such strength limit arise from the present overview.     

Influence of f.c.c. rolling textures on biaxial sheet stretching

The behaviour of sheet metals initially having f.c.c. rolling textures is simulated under biaxial stretching conditions. A rate-sensitive crystal plasticity model together with the full-constraint Taylor theory is used. Closed-form analytical solutions for the stress states, slip distributions and lattice spins are obtained for the ideal orientations of f.c.c. rolling textures. The three-dimensional lattice rotation fields at these ideal orientations, and their evolution paths in Euler space, are predicted for various biaxial stretching ratios. Similar simulations are also carried out for polycrystalline textures. It is shown that, for a copper-type initial texture (the β-fibre) and a strain ratio ϱ < 0.5, the corresponding biaxial-stretching texture will not be much different from the initial texture. However, for ϱ > 0.5 the β-fibre deteriorates and the α-fibre increases relatively quickly. If the initial texture is the R-recrystallization texture (cube + S₁), the main component of the simulated biaxial-stretching textures is the fibre near β for ϱ < 0.5, but the α-fibre for ϱ > 0.5. The simulated equibiaxial-stretching texture is an agreement with the published measured textures for aluminum sheets.     

Activation parameters of high-temperature creep in polycrystalline nickel at ambient and high pressures

Polycrystalline specimens of pure nickel were deformed in uniaxial compression at temperatures of 1000–1550 K, strain rates of 1×10⁻⁵-3×10⁻³s⁻¹ and pressures of 0.1–1500 MPa, in order to determine the activation parameters of high temperature creep. Experiments at 0.1 MPa were conducted in an MTS apparatus with the specimen immersed in a molten heat-treating salt to prevent oxidation. The data show a decreasing power-law stress exponent with decreasing normalized steady-state flow stress (σ/G), approaching the “natural law” value of n=3 at normalized stresses <10⁻⁴. In contrast, the activation energy is constant over our range of temperatures (T/T_m = 0.55−0.90), and is indistinguishable from the activation energy of self-diffusion (284 kJ/mol). High pressure experiments were conducted in a modified piston-cylinder apparatus using the same molten heat-treating salt for the confining medium. The small activation volume could not be resolved; however, the trend of the high pressure data parallels that of the 0.1 MPa data with a systematic offset, and is consistent with the measured activation volume of self diffusion. Specimens deformed at 0.1 MPa exhibited significant strain-enhanced grain growth; this effect is greatly reduced under hydrostatic pressure, whereas subgrain size was less affected.     

The development of a flow injection analysis method for the quantification of free cyanide and copper cyanide complexes in gold leaching solutions

The quantification of free cyanide, Cu(CN)₂⁻ and Cu(CN)₃²⁻, is essential in investigating the leaching of copper–gold ores in cyanide solutions. A flow injection analysis (FIA) method has been developed for this purpose which utilizes a flow-through electrochemical cell containing silver and platinum electrodes. The basis of this method is that the measured charge due to either silver oxidation or copper reduction at an applied potential is related to the species concentration. A potential of −150 mV was chosen for free cyanide measurement, at which the measured charge due to silver oxidation is related to the free cyanide concentration. While silver oxidation at 100 mV and copper reduction at −650 mV were used for Cu(CN)₃²⁻ and Cu(CN)₂⁻ analysis, respectively. For the solution containing both free cyanide and Cu(CN)₃²⁻, a two-step analysis technique was developed for the quantification of each of these species. A pretreatment method was also developed to remove the interference of sulfide ions. The versatility of the FIA method developed in this study is demonstrated by measuring the cyanide species formed during the leaching of both Cu₂O and Cu₂S in cyanide solutions.     

Anodic dissolution of copper sulphides in sulphuric acid solution: II. The anodic decomposition of CuS

The anodic decomposition of CuS in sulphuric acid solutions was investigated by means of cyclic voltammetry. The pH of the electrolyte and the scan rate were varied. Our results are interpreted using the experience of semiconductor electrochemistry and of passivation of pure metals. At potentials E < E_np (E_np = potential of pitting nucleation), the current/voltage curves were interpreted by the formation of metastable nonstoichiometric copper oxide or hydroxide. After the dissolution of these layers at the potential E_np, total decomposition of CuS starts. These results were confirmed by rest potential measurements and by scanning electron microscopy.     

Fatigue deformation-induced response in a superduplex stainless steel

The cyclic deformation behavior of SAF 2507 superduplex stainless steel (SDSS) was studied under constant plastic-strain amplitudes. The cyclic hardening/softening curves show initial hardening, followed by softening and, finally, saturation behavior. Two regimes can be differentiated in the cyclic stress-strain curve (CSSC) of SDSS. The transition point at which the cyclic strain-hardening rate changes is identified to be ɛ _p/2=7 × 10⁻³. Transmission electron microscopy (TEM) results on dislocation structures suggested that there is a close relationship between the CSSC, hardening/softening curves, and the dislocation substructure evolution. In the low-plastic-strain-amplitude regime of the CSSC, the dislocation activity in the austenite grains is found to be higher than that in the ferrite grains. At higher plastic strain amplitudes, low-energy dislocation structures are found in the ferrite grains, while clusters and bundles of dislocations can be observed in the austenite grains. Strain localization due to formation of these structures resulted in a decrease in the cyclic strain-hardening rate within the high-plastic-strain-amplitude regime. Dislocation substructure evolution is also used to explain the shape of the hardening/softening curve.     

The brittle compressive failure of fresh-water columnar ice under biaxial loading

The brittle compressive failure of fresh-water, columnar ice was investigated under biaxial loading at a strain rate of ϵ = 10^⇔2s⁻¹ at temperatures of −10 and −40°C. Tests were performed through proportional loading over the range 0 ⩽R<1 where R is the ration of the major to major comprehensive stress, i.e. R = σ₂/σ₁. Two types of confinement were considered, across the long axis of the columnar grains (type-A) and along the columns (type-B). For both types the major stress was orthogonal to the columns. The results reveal two failure regimes under cross-column loading: the failure stress first increases rapidly with increasing R_A in the range 0 ⩽R_A ⩽ R_t, and then decreases as R_A increases further. The transition ratio, R_t, decreases from ∼0.2 at −10°C to ∼0.1 at −40°C. Correspondingly, the failure mode changes from splitting along the columns along the loading direction at zero confinement to shear faulting in the loading plane at 0 < R_A ⩽ R_t to a combined mode of splitting across the columns and shear faulting out of the loading plane at R_A >R_t. The failure envelope at both temperatures resembles a truncated Coulomb envelope. Under along-column confinement (type-B) neither the failure stress nor the failure mode depends upon the confining stress. High-speed photography and thin-section examinations revealed that wing cracking and localized fragmentation are important elements in the failure process. The observations ae explained in terms of two failure mechanisms; viz. frictional crack sliding and contact tensile fractures.     

Dislocation Structures in a Cyclically Deformed Single-Slip-Oriented Fe-35?wt?pct Cr Alloy Single Crystal Containing Fine Cr-Rich Precipitates

The dislocation structures induced by the cyclic deformation of a $ [\bar{1}49] $ single-slip-oriented Fe-35?wt?pct Cr alloy single crystals containing fine Cr-rich precipitates have been studied by transmission electron microscopy (TEM) over the plastic strain amplitude ?? _pl range of 5?×?10^?4 to 5?×?10^?3. Persistent slip bands (PSBs) with different structures, such as ladder-like structure, irregular ladders, elongated cells, etc., were observed to form at plastic strain amplitudes ranging from 5.0?×?10^?4 to 2.5?×?10^?3, and the volume fraction of PSBs increases with increasing ?? _pl. As ?? _pl is as high as 5.0?×?10^?3, dislocation cells dominate the microstructure, even though a small amount of irregular PSB ladder structures still exists and they tend to evolve as labyrinth-like structures. The instability of Cr-rich precipitates during cyclic straining was believed to facilitate the formation of PSBs and thus promote some similarities of cyclic deformation characteristics between the current body-centered cubic (bcc) Fe-Cr single crystals and face-centered cubic (fcc) metal crystals. Whatever the internal structure of PSBs is, they could always carry the majority of the plastic strain in the course of cyclic deformation, thus causing the occurrence of a stress plateau region in the cyclic stress?Cstrain (CSS) curve of Fe-Cr alloy single crystals.     

Fatigue crack initiation and strain-controlled fatigue of some high strength low alloy steels

Initiation and growth of fatigue microcracks were investigated in several Nb and V alloyed high strength low alloy steels, including conventional and dual phase microstructures. Fatigue microcracks initiated along prominent slip bands. Macrocracks formed by linking up of small microcracks. At low applied stress or strain, the number of cycles to crack initiation increased with the cyclic yield stress. Comparing the cyclic stress-strain curves to the monotonie stress-strain curves, cyclic hardening or softening occurred, depending upon strain amplitude. Plateau regions were observed in plots of cyclic stress amplitudevs cyclic plastic strain amplitude obtained by increasing the total strain amplitude in steps after 30 cycles at each step. In polycrystalline 0.03 pct Nb steel, the plateau region was identified with prominent slip band formation, as others have observed in single crystals of copper, C-doped iron, and other metals.     

Investigation of the formation of precipitates of copper cations with sulfhydryl collectors

The formation processes of precipitates of copper cations with diethyldithiocarbamate, xanthates (ethyl and buthyl), and isobutyl dithiophosphate are investigated using potentiometric and optical methods. The minimal value of the potential of the copper electrode (E _Cu) with the formation of precipitates agrees well with the solubility product (SP) and forms the following series: copper diethyldithiocarbamate (E _Cu = −335 mV, SP = 2.8 × 10⁻³⁰) > butyl xanthate (E _Cu = −225 mV, SP ≈ 10⁻²⁶) > ethyl xanthate (E _Cu = −163 mV, SP = 4 × 10⁻²⁴) > isobutyl dithiophosphate (E _Cu = −60 mV, SP ≈ 10⁻¹⁸). The visible agglomerates of precipitate particles are observed for all the studied sulfhydryl collectors (xanthates, dithiocarbamates, dithiophosphates) with the ethyl group of hydrocarbon radical. The butyl xanthate and isobutyl dithiophosphate form colloid precipitates with copper cations.