A general method for estimation of fracture surface roughness: Part I. Theoretical aspects

An assumption-free general method is developed for quantitative estimation of fracture surface roughness from the measurements performed on the fracture profiles generated by sectioning planes which are normal to the average topographic plane of the fracture surface. The input data are the profile roughness parameter,R _L, and angular orientation distribution of line elements on the fracture profile,f(α). It is shown that

Wetting of the (0001) <Emphasis Type="Italic">α</Emphasis>-Al<Subscript>2</Subscript>O<Subscript>3</Subscript> Sapphire Surface by Molten Aluminum: Effect of Surface Roughness

The wetting of molten aluminum on the “c”-plane (0001) of single-crystal α-Al₂O₃ (sapphire) was studied by the sessile drop technique from 800 °C (1073 K) to 1200 °C (1473 K). Systematically increasing the (0001) surface roughness by SiC abrasion increased the wetting contact angle, resulting in reduced wetting. The surface roughness factor R originally defined by Wenzel, was determined as a function of the abrasion, temperature, and time. The wetting decreases as the surface roughness increases. Rough surfaces also create time and temperature effects on wetting, changing those for a smoothly polished surface. The existence of a high-temperature surface structural transition for (0001) of α-Al₂O₃, which has been previously suggested, was confirmed. Increased roughness R accents the effect of the surface structural transition, increasing the wetting contact angle changes during the transition.     

The fracture energy of bimaterial interfaces

This article describes a framework applicable to the measurement and interpretation of the fracture energy of bimaterial interfaces. A major conclusion of this study is that the fracture energy, Γ_i, is not unique and usually exhibits values substantially larger than the thermodynamic “work of adhesion. ” The lack of uniqueness is related to mode mixity (shear/opening) effects experienced by interface cracks, as characterized by the phase angle of loading, ψ: typically, Γ_i, is found to increase as ψ increases. These trends are attributed to crack shielding caused by roughness of the interface fracture surface, to material nonlinearity,etc. The phase angle is, in turn, influenced by the choice of test specimen, resulting in values of Γ_i that differ between specimens in a manner attributed to the locus of Γ_i with ψ. Preliminary models that relate Γ_i to roughness, plasticity, segregation,etc., are described, leading to insights concerning microstructural aspects of “weaklrd and “strong” interfaces. This paper is based on a presentation made in the symposium “Interface Science and Engineering” presented during the 1988 World Materials Congress and the TMS Fall Meeting, Chicago, IL, September 26–29, 1988, under the auspices of the ASM-MSD Surfaces and Interfaces Committee and the TMS Electronic Device Materials Committee.     

Fracture toughness and the extents of primary void growth

It is generally believed that, for an otherwise constant microstructure, the crack tip opening displacement at fracture(δ, _IC) will scale with the primary particle spacing,X _o. However, fracture toughness is also influenced by the microstructure as well as by particle spacing and volume fraction. It has been proposed that the extents of primary void growth could be used as a measure of the influence of microstructure on toughness. Two approaches to using the extents of primary void growth have been suggested. In one, it was proposed that δ,_IC would scale asX _o(R_v/R_I), whereR _v is the radius of the void as viewed normal to the fracture surface andR, is the radius of the particle nucleating the void. In the second, it has been proposed that a measure of the true local strain would be Inh/2R ₁), whereh is the depth of the void, and that δ_IC would scale asL Inh/2R ₁), whereL is some microstructural distance, taken here to beX _o. These two approaches have been tested for materials for which δ_IC ranges from about 7 to over 150 μm. The results suggest that the two proposed scalings hold only for high-strength microstructures of low constrained ductility containing primary particles of small spacings and which blunt smoothly and not to vertices. Formerly Graduate Student, Carnegie Mellon University Formerly Graduate Student, Carnegie Mellon University     

The interrelationship of fracture toughness and microstructure in a Ti-5.25Al-5.5V-0.9Fe-0.5Cu alloy

Fracture toughness of anα-Β titanium alloy heat treated to a constant yield strength has been found to depend upon the morphology of α produced or remaining after the initial solution treatment. In equiaxed α structures, fracture toughness depends linearly upon the grain boundary area per unit volume,S _v, and is independent of equiaxed α particle size or spacing. In a grain boundary α structure fracture toughness depends both onS _v and, within limits, linearly on the thickness of the α. Explanations are offered for the observed propagation of cracks at α-@#@ Β interfaces and for the observation that high fracture toughness can accompany low tensile ductility. This paper is based on a thesis to be submitted by M. A. Greenfield in partial fulfillment of the requirements for the Ph.D. degree in metallurgy at New York University.     

Martensitic phases in splat quenchedβ Ag Mg alloys

Retainedβ-phase as well as martensitic phases have been obtained by splat quenching Ag-46.6 at. pct Mg and Ag-43.1 at. pct Mg alloys. The retainedβ-phase exhibitsB ₂ orDO ₃ type ordering. Two martensitic phases have been identified in these alloys. These phases are3R and2H stacking modulations derived by stacking (110) type planes of the (β-phases. A close examination of electron diffraction patterns of the retained (β-phase reveals extra intensity maxima. These extra maxima are explained in terms of fine particles of2H and3R type surface martensites in retainedβ-phase.     

Creep-rupture in powder metallurgical nickel-base superalloys at intermediate temperatures

To gain insight into the factors which control the creep-rupture properties of powder metallurgical nickel-base superalloys at intermediate temperatures (650 to 775°C), a comparative study was conducted on the alloys AF115, modified MAR-M432 (B6) and modified IN100 (MERL76). Creep-rupture properties in these alloys were characterized in terms of the stress and temperature dependence of the secondary creep rate, ε^S, andrupture time,t _R . Within the limited stress ranges used, the stress dependence of both ε^S andt _R at 704°C can be represented by power laws ε^S andC ⁿ andt _R =Mσ ^-p ; whereC,M, n, andp are constants. The stress exponentsn andp are approximately equal for both AF115 and B6 with values of 16 and 7, respectively. In the case of MERL76,n andp are different, with values of 15 and 5, respectively. The apparent activation energies,Q, are 700, 370 and 520 KJ mol^-1 for AF115, B6 and MERL76, respectively. For these alloys, long creep-rupture lives are associated with large values ofn andQ. The sig-nificant differences inn andQ values between AF115 and B6 were related to creep re-covery processes for which the lattice misfit between the gamma and the gamma prime was identified to be an important parameter. However, the unequaln andp values in MERL76 compared with those in AF115 and B6, were traced to differences in fracture mode. Failures in AF115 and B6 were initiated at carbide particles at grain boundaries. In contrast, fracture in MERL76 was initiated at grain boundary triple junctions. The rupture lives of AF115 and B6 can be modeled reasonably well by the growth of cavities during secondary creep and propagation of a surface-nucleated crack during the tertiary creep.     

The effect of matrix strength on void nucleation and growth in an alpha-beta titanium alloy,CORONA-5

This work was undertaken to examine the effect of increasing matrix strength at constant equiaxed microstructure on void nucleation and growth in the titanium alloy, CORONA-5, Ti-4.5Al-5Mo-1.5Cr. A martensite and a beta matrix were used in the as-quenched and the heat treated conditions. For each matrix, fine and coarse alpha sizes were produced and a third size of alpha was used for the as-quenched condition of the martensite series. The processing procedures produced an aligned alpha structure which was most pronounced in the fine structure. Void nucleation occurred in an aligned fashion and took place predominantly atα /martensite orα/β interfaces. An explanation is offered for the aligned nucleation in terms of nonuniform deformation of the banded structure which appeared most prominently after heat treatment to produce the coarser microstructure. An incubation strain was found for both types of matrices. The incubation strain increased for the interface in the following order: martensite/martensite,α /martensite, andα/ β. The incubation strain for martensite/martensite interfaces was relatively independent of the matrix strength. Void growth as a function of true strain was generally found to occur in two stages, a slow stage I and a more rapid stage II. Stage II growth occurred as a result of coalescence of voids growing toward one another from nearby particles. Stage II growth was more rapid for the martensite matrix than for theβ matrix. For the martensite matrix void growth rates could not be accounted for either on the basis of strength or strain hardening rates. However, the longest void growth rate was found to increase as the function λ ^N /d _α ^L increased. λ^N is the interparticle spacing normal to the tensile axis and _α ^L is the alpha particle size parallel to the tensile axis. For the beta matrix void growth rates increased with increasing yield s trength and decreased with increasing strain hardening. It was not possible to relate fracture strength to an extrapolated longest void at fracture as was done in earlier studies. This is explained in terms of the nonuniformity of fracture paths observed in the alloy.     

A unified microscale-parameter approach to solidification-transport phenomena-based macrosegregation modeling for dendritic solidification: Part I. Mixture average-based analysis

Based on the scale-length comparisons of the microscale heat or solutal-mass transfers with dendrite structures, a general form for the time-differential mixture-averaged composition (TDMAC) term for a macroscale metallic dendrite solidification model with any finite solid backdiffusion (SBD) was shown to be necessary and valid. Starting from such an integral term-included TDMAC expression with a general dendrite geometric modeling, Fick’s second diffusion law and the species massconservation principle were applied to confirm the equivalency of a unified Φ-parameter-involved all-differential TDMAC form to the original TDMAC term. Through the modeling, the unified microscale parameter Φ was found to be a function of the Fourier diffusion number with dendrite geometrical modifications (ϕ) and of another nondimensional parameter, θ, representing the sensibility of the interdendritic-liquid-concentration variation in response to the SBD inside the growing dendrites. In the solved ϕ-parameter function of ϕ= (D _S(T)/R _f)ζ·A _2N , the scalar vector product defines the geometric modification accounting for a general growing dendrite morphology with five basic units of spherical, cylindrical, platelike, inward cylindrical, and inward spherical shapes. Through an approximate solution to the integral equation with respect to the solutal-mass solid/liquid (S/L) interface flux, (Eq. [19]), the unified Φ parameter was proposed to take a function form of Φ=θ·ϕ/(1+θ · ϕ), where θ=(1+β) · k · f _S/f _L ² . The result discussions and ϕ-f _S, and θ-f _S, and Φ-f _S curve sample calculations on an Al-4.5 pct Cu alloy with different constant alloy properties, solidifying phase morphologies, and solidification parameters were carried out to investigate the behaviors of various influential factors on the extent of SBD in a dendrite solidification process.     

Mixing models for gas stirred metallurgical reactors

The mixing of liquids in ladles, (0.5 ≦L/D ≦ 2.0), agitated by a centrally rising bubble plume, has been analyzed both theoretically and experimentally. An exhaustive review of previous metallurgical literature on mixing in ladles and furnaces demonstrates that the majority of previous investigators in the field consider mixing to be brought about primarily by turbulent diffusion phenomena. The present study clearly shows that mixing is a combination of both convection and eddy diffusion processes, neither of which can be disregarded for gas stirred systems. For predicting mixing times during such gas injection procedures, a simple empirical equation is proposed for axisymmetric systems:τ _mαε_m ^−1/3L⁻¹R^5/3. Hereτ _m is the 95 pct mixing time,ε _m is the specific energy input rate,R is the vessel radius, andL is the depth of liquid. On the basis of physical and mathematical modeling, the rate of liquid mixing in conventional gas injection ladle metallurgy operations is compared with those observed in C.A.S. (composition adjustment by sealed argon bubbling) systems. It was found that mixing in C.A.S. operations is relatively slow and highly insensitive to gas flowrates(i.e., specific energy input rates).     

Structure and properties of a β solution treated,quenched, and aged si-bearing near-α titanium alloy

The microstructure, tensile properties, and fractographic features of a near-α titanium alloy, IMI 829(Ti-6.1 wt pct Al-3.2 wt pct Zr-3.3 wt pct Sn-1 wt pct Nb-05 wt pct Mo-0.32 wt pct Si) have been studied after aging over a temperature range of 550°C to 950°C for 24 hours following solution treatment in the β phase field at 1050°C and water quenching. Transmission electron microscopy studies revealed that aging at 625°C and above produced discrete silicides at α′ interplatelet boundaries. However, aging at 900°C and above has also resulted in the precipitation of β phase along the lath boundaries of martensite. The silicides have been found to have a hexagonal structure withc=0.36 nm anda=0.70 nm (designated as S₂ by earlier workers). There is a significant improvement in yield and ultimate tensile strength after aging at 625°C, but there is less improvement at higher aging temperatures. The tensile ductility is found to be drastically reduced. While the fracture surface of the unaged specimen shows elongated dimples, the aged samples show a mixed mode of fracture, consisting of facets, featureless parallel bands, and extremely fine dimples.     

Effect of surface roughness on low-cycle fatigue behavior of type 304 stainless steel

The effects of surface roughness on the low-cycle fatigue life of Type 304 stainless steel at 593°C in air have been investigated. It is observed that, at a strain rate of 4 × 10⁻³ s⁻¹ and a total strain range of 1 pct, the fatigue life (N _f cycles) decreases with an increase in surface roughness. Information on crack growthvs strain cycles has been generated, as a function of surface roughness, by the measurement of striation spacing on fractured surfaces of specimens tested to failure. Crack propagation follows the Ina ∞N (wherea is the crack length afterN strain cycles) relation for longer specimen fatigue lives (N_f > 2700 cycles) and departs from Ina ∞N for shorter fatigue lives. A quantitative estimate is made of the number of cycles N_o(r) to generate a crack length equal to 0.1 mm (≈ 1 grain diam). The initial surface roughness significantly affects only the initiation component of specimen life time. The effect of roughness on crack initiation is described byN ₀ (R) = 1012R^−0.21, whereR is the surface roughness (root-mean-square value) in microns.     

Elevated temperature fracture of RS/PM alloy 8009: part i. fracture mechanics behavior

Increasing temperature and decreasing loading rate degrade the plane strain initiation (K _ICifrom theJ integral) and growth (tearing modulus,T _R) fracture toughnesses of RS/PM 8009 (Al-8.5Fe-1.3V-1.7Si, wt pct).K _ICidecreases with increasing temperature from 25 ‡C to 175 ‡C (33 to 15 MPa√m for an extrusion and 28 to 11 MPa√m for hot cross-rolled plate) and further declines to 10 MPaVm at 316 ‡C without a minimum.T _Ris greater than zero at all temperatures and is minimized at 200 ‡C. A four order-of-magnitude decrease in loading rate, at 175 ‡C, results in a 2.5-fold decrease inK _ICiand a 5-fold reduction inT _R.K _ICiandT _Rare anisotropic for extruded 8009 but are isotropic for cross-rolled plate. Cross rolling does not improve the magnitude or adverse temperature dependence of toughness. Delamination occurs along oxide-decorated particle boundaries for extruded but not cross-rolled 8009. Delamination toughening plays no role in the temperature dependence ofK _ICi, however,T _Ris increased by this mechanism. Macroscopic work softening and flow localization do not occur for notch-root deformation; such uniaxial tensile phenomena may not be directly relevant to crack-tip fracture. Micromechanical modeling, employing temperature-dependent flow strength, modulus, and constrained fracture strain, reasonably predicts the temperature dependencies ofK _ICiandT _Rfor 8009. While E and σ_ys decrease with increasing temperature for all aluminum alloys, the strain to nucleate crack-tip damage dominates the fracture toughness of 8009 and decreases with increasing temperature for a range of constraint. Damage mechanisms for this novel behavior are evaluated in Part II. Formerly Graduate Student Department of Materials Science and Engineering, University of Virginia     

Effects of cold work on precipitation in Al-Cu-Mg-(Ag) and Al-Cu-Li-(Mg-Ag) alloys

A study has been made of the effects of cold work prior to aging on precipitation hardening in selected Al-Cu-Mg-(Ag) and Al-Cu-Li-(Mg-Ag) alloys. General aging characteristics have been determined by differential scanning calorimetry, and response to hardening has been correlated with microstructure using transmission electron microscopy (TEM), selected area electron dif-fraction (SAED), and quantitative stereology. Particular attention has been given to the phases Ω andT ₁ that form on the {111 }_α planes, although information on the precipitates θ′,S′ (orS), and δ′ is also reported. Although Ω andT ₁, have similar morphologies and habit planes, their response to cold work prior to aging is different. Deformation promotesT ₁ formation at the expense of the δ′ phase in Al-Cu-Li alloys and at the expense of δ′, θ′, andS′ in Al-Cu-Li-Mg-Ag alloys. On the other hand, in Al-Cu-Mg-Ag alloys, deformation assists precipitation of θ′ at the expense of Ω phase, and some decrease is recorded in the hardening response. Prior cold work is also found to reduce the response during natural aging in most alloys. These results are discussed in terms of the role of particular alloying additions. Formerly Research Fellow, Department of Materials Engineering, Monash University     

Microstructural characterisation of near-α titanium alloy Ti-6Al-4Sn-4Zr-0.70Nb-0.50Mo-0.40Si

Microstructural stability in the near-α titanium alloy (alloy 834) containing Ti-6Al-4Sn-4Zr-0.70Nb-0.50Mo-0.40Si (in weight percent), in the β and(α + β) solution-treated and quenched conditions, has been investigated. The β transus for this alloy is approximately 1333 K. Solution treatment in the β phase field at 1353 K followed by quenching in water at room temperature resulted in the formation of α′ martensite platelets with high dislocation density and stacking faults. Thin films of β are found to be sandwiched between interface phases, which, in turn, are sandwiched at the interplatelet boundaries of lath martensite. The interface phase is a subject of much controversy in the literature. Solution treatment at 1303 K in the(α + β) phase field followed by quenching in water at room temperature resulted in the near-equiaxed primary α and transformed β. Both the β and(α + β) solution-treated specimens were aged in the temperature range of 873 to 973 K. While aging the —treated specimen at 973 K,(α + β)-treated specimen, even at a lower temperature of 873 K for 24 hours, caused precipitation of suicides predominantly at the interplatelet boundaries of martensite laths. Electron diffraction analysis confirmed them to be hexagonal suicide S₂ witha = 0.70₂ nm andc = 0.36₈ nm. The above difference in the precipitation could be attributed to the partitioning of a higher amount of β- stabilizing elements as well as silicide-forming elements to the transformed β in the(α + β) solution-treated condition. However, ordering of theα′ phase was observed under all of the aging conditions studied. The ordered domains were due to the longer aging times, which cause local increases in the level of theα-stabilizing elements. Formerly Research Associate, Department of Metallurgical Engineering, Baranas Hindu University.     

The effect of oxygen on the structure and mechanical behavior of Aged Ti-8 Wt pct Al

It is shown that for a Ti-8 wt pct Al alloy aged at a temperature high in the two-phase region (695°C) to precipitate the ordered α₂ phase, an increase in oxygen content from 600 ppm to 1200 ppm decreases the fracture strain from 20 to 1 pct elongation at room temperature and slightly increases the yield strength. The fracture mode is changed from dimpled rupture to predominantly cleavage. Further increase in oxygen content to 3000 ppm does not produce significant additional changes in ductility or yield strength. It is demonstrated that oxygen additions alter the position of the α/α + α₂ coherent solvus, resulting in formation of coherent α₂ in specimens containing ⪞ 1000 ppm oxygen aged at 968 K (695°C). For a given aging time the volume fraction of α₂ increases with increasing oxygen up to 1300 wt ppm and then levels off. The changes in mechanical behavior are attributed to the presence of α₂. The experimental evidence suggests that oxygen partitions preferentially into α₂. Formerly a Graduate Student in the Department of Metallurgy and Materials Science, University of Pennsylvania     

The influence of stress trlaxiality on the damage mechanisms in an equiaxedα/β Ti-6AI-4V alloy

The influence of the stress triaxiality on void formation, void growth, and fracture was investigated for an equiaxed Ti-6A1-4V alloy. Void nucleation in theα phase was found to occur for a critical value of macroscopic plastic strain, whereas void nucleation at theα/β interface also depends on triaxiality. Under low triaxiality and important plastic strain, voids appear and grow in the area where the microshear bands develop, with an angle close to 45 deg to the stress axis in theα particles. In contrast, with high triaxiality, voids nucleate preferably at theα/β interfaces and grow perpendicular to the stress axis by a cleavage mechanism. In a middle range of triaxiality and plastic strain, voids nucleate inα because of the sufficient plastic strain and also at theαβ interfaces because of the sufficient triaxiality(X). Void growth occurs with an angle of 60 deg to the stress axis, sinceX is not high enough to create cleavage andε _p is high enough to provide a ductile growth. Two types of fracture were identified and reported on a fracture map: under low triaxiality, failure appears by plastic instability, whereas for high triaxiality, the instability is induced by a void-growth process discussed with the help of Rice and Tracey’s approach.     

Fracture and toughening mechanisms in an α2 titanium aluminide alloy

The deformation and fracture behaviors of the Ti-24Al-11Nb alloy with an equiaxed α₂ + β microstructure have been characterized as a function of temperature by performing uniaxial tension andJ _IC fracture toughness tests. The micromechanisms of crack initiation and growth have been studied bypost mortem fractographic and metallographic examinations of fractured specimens, as well as byin situ observation of the fracture events in a scanning electron microscope (SEM) equipped with a high-temperature loading stage. The results indicate that quasistatic crack growth in the Ti-24Al-11Nb alloy occurs by nucleation and linkage of the microcracks with the main crack, with the latter frequently bridged by ductile β ligaments. Three microcrack initiation mechanisms have been identified: (1) decohesion of planar slipbands in the α₂ matrix, (2) formation of voids and microcracks in β, and (3) cracking at or near the α₂ + β interface due to strain incompatibility resulting from impinging planar slip originated in α₂. The sources of fracture toughness in the 25 °C to 450 °C range have been attributed to crack tip blunting, crack deflection, and a bridging mechanism provided by the ductile β phase. At 600 °C, a change of toughening mechanisms leads to a lowering of the initiation toughness (theK _IC value) but a drastic increase in the crack growth toughness and the tearing modulus.     

Microstructural investigation on the precipitation of α″ nitrides and α″ → γ′ nitride transformation in ion-nitrided pure iron

The precipitated characteristics of α″-Fe₁₆N₂ nitrides in the diffusion layer of ion-nitrided pure iron were investigated with transmission electron microscopy (TEM) and high-resolution electron microscopy (HREM). Three sets of α″ nitrides, whose habit planes are (100)_α,(010)_α,(001)_α, respectively, do not precipitate simultaneously from the diffusion layer, which is different from the normal homogeneous precipitation in Fe-N alloys. Unlike the typical disc-shaped morphology reported widely, the α″ nitrides in the diffusion layer appear as ribbonlike slices. They grow on {001}_α matrix planes with a parallel orientation relationship, and the direction of their length is parallel to the <110>_α direction. The interface between the α″ nitride and α matrix and a 7 deg [111]/(112) low-angle-tilt grain boundary in the α″ nitride were examined with HREM. The distributions of dislocations at the interface and the grain boundary were investigated. During microstructural examination, it was observed that a γ′-Fe₄N nitride could grow on an α″ nitride directly. The orientation relationship during the α″ → γ′ nitride transformation was determined as to be (001)_γ//(110)_α,[110]_γ//[111]_α.