Crystallographic and mechanistic aspects of growth by shear and by diffusional processes

Growth by shear and by diffusional processes, both taking place predominantly by means of ledge mechanisms, are reviewed for the purpose of distinguishing critically between them at the atomic, microscopic, and macroscopic levels. At the atomic level, diffusional growth is described as individual, poorly coordinated, thermally activated jumps occurring in the manner of biased random walk, whereas growth by shear is taken to be tightly coordinated “glide” of atoms to sites in the product phase which are “predestined” to within the radius of a shuffle. Obedience to the invariant plane strain (IPS) surface relief effect and the transformation crystallography prescribed by the phenomenological theory of martensite is shown to be an unsatisfactory means of distinguishing between these two fundamentally different atomic growth mechanisms. In substitutional alloys, continuous differences in compositionand in long-range order (LRO) from the earliest stages of growth onward are concluded to be the most useful phenomenological approach to achieving differentiation. At a more fundamental level, however, the details of interphase boundary structure are the primary determinant of the operative mechanism (when the driving force for growth is sufficient to permit either to occur). In the presence of a stacking sequence change across the boundary, terraces of ledges are immobile irrespective of their structural details during diffusional growth. Kinks on the risers of superledges are probably the primary sites for diffusional transfer of atoms across interphase boundaries. In martensitic transformations, on the other hand, terraces containing edge dislocations in glide orientation or pure screw dislocations are mobile and accomplish the lattice invariant deformation (LID), though probably only after being overrun by a transformation dislocation. Risers associated with transformation dislocations are also mobile and cause the crystal structure change during growth by shear. The successes achieved by the invariant line (IL) component of the phenomenological theory of martensite in predicting precipitate needle growth directions and precipitate plate habit planes (Dahmen and co-workers) are here ascribed to the rate of ledge formation usually being a minimum at an interface containing an IL, primarily because nuclei formed sympathetically at this boundary orientation are likely to have the highest edge energies. Since martensite plate broad faces also contain the IL, the ability of the phenomenological theory to predict the habit plane and the orientation relationships of both precipitate and martensite plates is no longer surprising. The IPS relief effect at a free surface can be generated by precipitate plates when growth ledges are generated predominantly on only one broad face and only one of several crystallographically equivalent Burgers vectors of growth ledges is operative. Both pReferences probably result from larger reductions in transformation strain energy for the particular geometry with which a given plate intercepts the free surface. Precipitate morphology often differs significantly from that of martensite even if precipitates are plate-shaped and can readily differ very greatly. Whereas martensite morphology is determined by the need to minimize shear strain energy, that of precipitates derives from the more flexible base of the interphase boundary orientation-dependence of the reciprocal of the average intergrowth ledge spacing, as modified by both the orientation-dependence of interkink spacing on growth ledge risers and the spacing/ height ratio dependence of diffusion field overlap upon growth kinetics. 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.     

An intergranular creep crack growth model based on grain boundary sliding

An intergranular crack growth model is developed to describe the effect of microstructural features such as grain size, grain boundary precipitates, and serrated grain boundaries on creep crack growth under grain boundary sliding (GBS) conditions. The model considers quantitatively that several deformation mechanisms contribute to the stress redistribution ahead of the crack tip through a stress relaxation process. The crack tip region is divided into three zones: (a) the intragranular-deformation-controlled stress relaxation zone, (b) the GBS-controlled stress relaxation zone, and (c) the elastic region. Intergranular creep crack growth is considered to occur as a result of the GBS-controlled process in all cases. The derived creep crack growth model shows a complex dependence of the creep crack growth rate (CCGR) on fracture mechanics quantities, such as C(t) (the path-independent energy integral with its steady-state value as C*) and K (the stress intensity factor). For creep-brittle materials, the model predicts that the CCGR depends on K to the power of 2 and this is verified experimentally; however, when environmental effects contribute to the crack growth process, the power exponent will increase. A semiempirical factor is introduced to account for the effects of oxidation on CCGR.     

Cavitation damage and creep crack growth

The effect has been investigated of prior damage on the creep crack propagation characteristics of 0.5 pct Cr, 0.5 pct Mo, 0.25 pct V steel at 823 K. On a macroscopic basis, the parametersK ₁ andC ^* both appear to correlate withda/dt although the parameterC ^* is unable to distinguish between virgin and damaged specimens. Rupture lives in the predamaged specimens are reduced by up to 60 pct when compared to virgin samples. Microscopically, it is found that the nature of the cavitation damage suggests that surface and grain boundary diffusion processes may have a minimal part to play, crack growth being controlled by the growth of cavities which is in turn controlled by the deformation of the surrounding matrix. A number of microscopic models are compared with the experimental data and it is suggested that a model which gives the best correlation with results is one proposed on the basis of matrix deformation. Formerly of the Department of Metallurgy, Manchester University Formerly of the Department of Metallurgy, Manchester University     

Effect of microstructure on creep and creep crack growth behaviour of titanium alloy

Creep and creep crack growth behaviour of a near α titanium alloy has been investigated at 600°C which is affected by primary α content. The alloy was heat treated at different temperatures so as to obtain different levels of equiaxed primary α in the range from 5 to 24 %. Constant load creep tests were carried out at 600°C in the stress range 250 to 400 MPa till rupture of the specimens. Creep crack growth tests were carried out at 600°C. Creep data reveals with increase in primary α content leads to creep weakening. On similar lines maximum creep crack growth resistance is associated with the alloy with lowest primary α content. Microstructural and fractographic examination has revealed that creep fracture occurs by nucleation, growth and coalescence of microvoids nucleated at primary β / transformed β (matrix) interfaces. On the other hand, creep crack growth occurs by surface cracks nucleated by fracture of primary α particles as well as by growth and coalescence of microvoids nucleated at primary β / transformed β (matrix) interfaces in the interior of the specimen.     

Diffusion and deformation controlled creep crack growth

A mechanism for creep crack growth is proposed by which the crack grows by formation of grain boundary cavities ahead of the crack tip. Two cases are considered; firstly, when cavity growth is diffusion controlled and secondly, where growth is deformation controlled. The resultant crack growth rates predicted by these theoretical models are compared with experimental data.     

Theory of intergranular creep cavity nucleation,growth and interaction

Creep cavitation is modeled assuming random continuous cavity nucleation, coupled growth by diffusion and plastic deformation, diffusive cavity interactions and cavity interconnection and finally, failure at a critical a real damage fraction. Nucleation is simulated by Monte-Carlo techniques using an empirically-derived nucleation law for copper that depends on the steady-state creep strain. For initially fully-dense materials, cavity nucleation dominates the cavity number density until interconnection and coarsening become important late in rupture life. In this situation, Monkman-Grant behavior is obtained and cavity sizes approach stable log-normal distributions. However, when a small fraction of cavities pre-exist, the cavity density is dominated by cavity interactions and the density remains relatively constant despite continuous nucleation. In this case, cavity growth controls the rupture time and cavity size distributions tend to approach log-normal distribution more slowly. These diffusive interactions diminish for larger but more widely-spaced pre-existing cavities because of limited interactions between the pre-existing and nucleating cavities. The sensitivity of the rupture life on dihederal angle and nucleation rate are also examined, and the statistics of failure are quantified.     

A theory of diffusion controlled intergranular creep crack growth

A theory of intergranular creep crack growth in brittle materials has been developed. The mechanism of crack propagation is removal of atoms from the crack tip by stress induced grain boundary diffusion and their deposition at the grain boundary. The width of the crack is assumed to be constant during crack propagation. Any possible plastic deformation at the crack tip has been neglected. The stress relaxation ahead of the crack tip which arises due to the non-uniform deposition of material onto the grain boundary is calculated and the diffusion process governed by this relaxed stress studied. Thus the theory is analogous to those developed previously for the growth of r-type voids in grain boundaries. Both the steady state and the transient were considered. It was found that the rate of crack growth at any moment was determined by the nominal stress intensity factor K. A minimum stress intensity, K_min' exists below which no crack growth can take place. Conversely there is a maximum limiting rate of crack growth determined by the maximum surface diffusion rate. For K > K_min the steady state is always reached quickly and the length of the transient period t_tr is proportional to K⁻⁶. For K > K_min the rate of crack growth is proportional to K⁴. A comparison with experimental measurements on brittle ½Cr-½Mo-¼V steels show good agreement between the theory and experiment.     

Diffusive intergranular cavity growth in creep in tension and torsion

Creep experiments were performed at 500°C in tension and torsion on high conductivity copper tubes with a uniform initial coverage of implanted water vapor bubbles on all grain boundaries. No significant differences were found in the times to fracture over a wide stress range when the results were correlated according to the maximum principal tensile stress in the two fields. The results indicate that the cavities grow in a crack-like mode but at one tenth the rate predicted from the theoretical model of Pharr and Nix. This difference is attributed partly to load shedding from boundaries normal to the maximum principal tensile stress to slanted boundaries and partly to a lack of knowledge about the surface diffusion constant. The results indicate further, that the contribution to intergranular cavity growth by power-law creep in negligible in comparison to the contribution by diffusional flow. Complementary tension and torsion experiments performed in initially uncavitated samples result in shorter creep lives in torsion than in tension due to more effective cavity nucleation in the former. The times to fracture in both of these cases obey Monkman and Grant's law, indicating the presence of constraints on growth by the lagging deformations by power-law creep in the surroundings of the cavitating isolated grain facets.     

Study of creep crack growth in 2618 and 8009 aluminum alloys

Creep crack growth (CCG) has been investigated in an 8009 (Al-Fe-V-S) P/M alloy at 175 °, 250 °, and 316 ° and in a 2618 ingot alloy at 150 °, 175 °, and 200 °. Under sustained load, subcritical crack growth is observed at stress intensity levels lower thanK _ic ; for 2618, at 200 °, crack growth is observed at stress intensities more than 40 pct lower thanK _ic . Alloys 8009 and 2618 exhibit creep brittle behavior,i.e., very limited creep deformation, during CCG. The CCG rates do not correlate with CCG parameters C* and C but correlate with the stress intensity factor,K, and theJ integral. Generally, crack growth rates increase with increasing temperature. Micromechanisms of CCG have been studied with regard to microstructural deg-radation, environmental attack, and creep damage. Although theoretical estimation indicates that CCG resistance decreases with second-phase coarsening, such coarsening has not been observed at the crack tip. Also, no evidence is found for hydrogen- or oxygen-induced crack growth in comparing test results in moist air and in vacuum. Creep deformation and cavitation ahead of crack tip are responsible for observed time-dependent crack growth. Based on the cavitation damage in the elastic field, a micromechanical model is proposed which semiquantitatively explains the correlations between the creep crack growth rate and stress intensity factor,K.     

Density measurements as an assessment of creep damage and cavity growth

The change in density during creep of several polycrystalline metals may be correlated through the expression —Δρ/ρ =B(∈t/d)(σ/G)^q exp (—Q _gb /RT) where —Δρ is the density change, p is the original density, e is the strain,t is the time,d is the linear intercept grain size,σ is the applied stress,G is the shear modulus,Q _gb is the activation energy for grain boundary diffusion,R is the gas constant,T is the absolute temperature, andB andq are constants withq ≃2 to 3. This expression is consistent with the theory of unconstrained grain boundary diffusion growth of cavities provided there is also concomitant strain-dependent nucleation. The expression does not support the power-law growth of cavities, growth by surface diffusion, or constrained grain boundary diffusion growth. Formerly Research Associate, University of Southern California.     

Investigations on the influence of specimen geometry on stable crack growth

Influence of specimen geometry on the resistance-curve of the steels St 52-3 and 30 CrNiMo 8. Application of the resistance-curve concept to predict instability loads for CT-specimens of various geometries.     

A study of creep crack growth in 2219-T851

Creep crack growth rates were measured in high strength 2219-T851 aluminum alloy with a computerized fully automated test procedure. Crack growth tests were performed on CT specimens with side grooves. The experimental set-up is described. During a test, the specimen is cyclically loaded on a servohydraulic testing machine under computer control, maintained at maximum load for a given hold time at each cycle, unloaded, and then reloaded. Crack lengths are obtained from compliance measurements recorded during each unloading. It is shown that the measured crack growth rates per cycle do represent creep crack growth rates per unit time for hold times longer than 10 seconds. The validity of LEFM concepts for side-grooved specimens is reviewed, and compliance and stress intensity factor calibrations for such specimens are reported. For the range of testing conditions of this study, 2219-T851 is shown to be creep brittle in terms of concepts of fracture mechanics of creeping solids. It is found that, under these testing conditions, a correlation exists between the creep crack growth rates under plane strain conditions and the stress intensity factor (da/dt =A K ^3.8 at 175 °C) for simpleK histories in a regime of steady or quasi-steady state crack growth. The micromechanisms of fracture are determined to be of complex nature. The fracture mode is observed to be mixed inter- and transgranular, the relative amount of intergranular fracture decreasing asK andda/dt increase. Formerly Graduate Student, Massachusetts Institute of Technology, is Ingenieur de l’Armement, ETCA, 94114 Arcueil Cedex, France.     

Influence of cyclic to mean load ratio on creep/fatigue crack growth

Crack growth data under combined creep and fatigue loading conditions are presented on a nickel base superalloy and a brittle and ductile low alloy steel. The main variables that have been examined are minimum to maximum load ratioR and frequency. It is shown that at high frequencies transgranular fatigue failure dominates and at low frequencies time dependent mechanisms govern. Where fatigue processes control, it is demonstrated that crack growth/cycle can be described by the Paris law and that the influence ofR ratio can be accounted for by crack closure caused by fracture surface roughness, oxidation, and creep and plastic strain developed at the crack tip. At the low frequencies where time dependent processes dominate, it is shown that crack growth can be characterized satisfactorily in terms of the creep fracture mechanics parameterC * using a model of crack extension based on ductility exhaustion in a creep damage zone at the crack tip. This model leads to enhanced resistance to creep/fatigue crack growth with increase in material creep ductility. This paper is based on a presentation made in the symposium “Crack Propagation under Creep and Creep-Fatigue” presented at the TMS/AIME fall meeting in Orlando, FL, in October 1986, under the auspices of the ASM Flow and Fracture Committee.     

Unified thermodynamic treatment of cavity nucleation and growth in high temperature creep

Existing models describing the creep nucleation and growth are briefly outlined in orderss to obtain a starting point for a new physical framework which unifies the stochastic treatment of nucleation with the deterministic treatment of growth. For this purpose an original hypothesis was postulated to develop the equations of motion of a thermodynamic system in non-equilibrium state at constant temperature and pressure. It is shown the application of this hypotthesis to a system of creep cavities provides the unified equations describing the evolution of cavities during their nucleation and growth stages. Particular attention is devoted to the role of the elastic relaxation of local normal stress due to deposition of atoms from a cavity its nucleation.     

A numerical study of cavity growth controlled by coupled surface and grain boundary diffusion

The diffusive growth of both two dimensional and axisymmetric cavities initially having equilibrium shapes and located on grain boundaries loaded in tension is studied using finite difference techniques. The shape evolution and growth kinetics of individual cavities as well as the time required for adjacent cavities to grow together is studied as a function of applied stress and the ratio of grain boundary to surface diffusivity. A key feature of this treatment is that the diffusional processes in the grain boundary and on the cavity surface are coupled by boundary conditions at the tip of the cavity. When surface diffusion is much slower than grain boundary diffusion, the cavities become crack-like during growth, and the fracture time varies reciprocally with the third power of the applied stress. When grain boundary diffusion is the slower process, the cavities remain rounded during growth, and the fracture time varies reciprocally with the first power of the stress. The transition between these limiting kinds of behavior is described and the results are compared with previous treatments of these problems.