Materials Science and Technology

The mechanisms by which failure is initiated in small-scale yielding and full plasticity are discussed with particular reference to micro void nucleation, growth, and coalescence in the multiaxial states of stress ahead of cracks in plane-strain conditions.

Crack initiation and extension in polymers is generally accompanied by localized viscoelastic and plastic energy dissipative processes occurnng in the vicinity of the crack tip. Two such micromechanisms of major importance are crazing and shear yielding and these are discussed with particular emphasis on the morphology, criteria, and kinetics involved and the influence of the polymer's chemical and physical structure.

The micromechanisms of cleavage fracture in ferritic steels are reviewed. Mechanisms of crack nucleation by dislocation interaction are compared with those involving the formation of stable microcracks. It is concluded that cleavage in steels containing discrete carbide particles is nucleated by microcracks formed in the carbide particles when fracture obeys a critical tensile stress criterion. The cleavage fracture stress in these steels is seen to depend largely upon the size of the cracked carbide particle. No micromechanisms have been established for cleavage in martensitic or low-carbon bainitic steels but the packet size seems to control cleavage fracture in these materials.

Two models of the relationship between the micromechanism of cleavage and fracture toughness are discussed in some detail. The statistical competition between different sized crack nuclei at a loaded crack tip can be represented by the requirement that the fracture stress be exceeded over a microstructurally determined characteristic distance. This simply expressed fracture criterion can be combined with fracture mechanics analyses to explain many features of the fracture behaviour of ferritic steels.

The majority of theories of ductile fracture consider the values of the imposed strains needed to initiate and grow voids. However, in describing the microstructural damage resulting from the production and growth of voids, it is important to consider the spatial distribution of the damage in relation to the microstructure. It is shown that the process of void initiation is dominated by the location and size of second-phase particles rather than the average imposed strain level. In the growth stage the use of recovery anneal cycles indicates that the accumulation of microstructural damage depends not only on the local level of the flow stress and the imposed strain rate, but on the work-hardening rate of the matrix. If the work-hardening capacity can be restored it is possible to coax the material to much larger strains prior to failure.

The concept of representing K _c as a critical stress at a critical distance is described. Fractures stemming from crazes are then considered and the stresses and distances associated with this type of failure are given. The determination of critical distances, and hence stresses, using blunt notches is described and it is found that in some cases crazes are formed, but in others they are not. In these fractures, the stresses are approximately 500 MN m⁻². A model of fatigue cracking which incorporates a stress and distance concept is used to show that at high K _c values craze-type failures result from initially much higher stresses, again about 500 MN m⁻². At low K values, damage appears to occur for stresses around 2000 MN m⁻². It is suggested that primary bond rupture may be involved for the very high values and that the 500 MN m⁻² stress may represent the breaking of van der Waals’ forces to form crazes.

Typical engineering composites consist of brittle fibres, such as glass or carbon, in a weak, brittle, plastic matrix such as epoxy or polyester resin. An important characteristic of these composites, however, is that they are surprisingly tough, largely as a result of their heterogeneous nature and the manner of their construction. During deformation, microstructural damage is widespread throughout the composite, but much damage can be sustained before load-bearing ability is impaired. Beyond some critical level of damage, failure may occur by the propagation of a crack which usually has a much more complex character than cracks in homogeneous materials. Crack growth is inhibited by the presence of interfaces both at the microstructural level between fibres and matrix and at the macroscopic level as planes of weakness between separate laminations in a multiple laminate. The fracturing of a composite therefore involves not only the breaking of the load-bearing fibres and the weak matrix, but a complex combination of excursions along these weak interfaces. A variety of mechanisms has been suggested to explain the overall level of toughness in a composite material. These are discussed in the light of experimental results on a range of composite types and in relation to the common materials and environmental variables which affect their mechanical properties.

The micromechanisms of crack extension at room temperature in ceramic single crystals are compared with those in bicrystals and in polycrystals. The toughness of polycrystals is found to depend upon their macroscopic ductility, their single crystal cleavage strength, and their intergranular cohesion. For some cubic materials plastic deformation may contribute to the measured toughness, whereas for brittle anisotropic ceramics over a wide range of grain sizes, the intergranular cohesion determines the toughness. The roles of thermal expansion anisotropy, of grain size and shape, and of porosity are considered in some detail, particularly with regard to their effect on lowering the intergranular cohesion. Porosity is of primary importance in determining toughness since the crack seeks the path of minimum solid area, but it can also toughen since it lowers the elastic modulus and increases the compliance. In the same way microcracking lowers the elastic modulus and at the same time increases the absorption of energy by increasing the total area of fracture surface. A process zone of microcracking enables slow crack growth to be stabilized and this is believed to be responsible for the increased toughness found in Al₂O₃ and Si₃N₄ to which critical volume fractions of ZrO₂ have been added. A further mechanism of toughening occurs in certain partially stabilized zirconias, in which metastable coherent precipitates of tetragonal ZrO₂ transform in the stress field of the crack, absorbing energy as they do and giving rise to compressive stress fields which further inhibit the crack. So far it has proved possible to increase the fracture surface energy of carefully prepared and treated alloys by a factor of about five.

A method for determining the local tensile stress σ* required to initiate brittle fracture at a grain boundary as a function of the concentration of segregated impurity on that boundary is presented. This method has been applied to Ni-Cr steels doped with Sb, Sn, or P, and the embrittling effects have been compared. In order to determine the relationship between the measured changes in σ* and the changes in the cohesive energy γ, a fracture theory has been developed which is the analogue of the Griffith theory for a deformable crystalline solid. In this theory the processes of bond breaking and dislocation emission at the crack tip are treated as concomitant so that a relationship between the local plastic work at fracture and γ is established. This gives criteria for unstable micro crack extension in terms of the relevant plastic properties of the crystal and of the cohesive energy γ. The relationship of the foregoing to the fracture toughness K _1C is discussed. The physical basis of embrittlement is further discussed using inputs from other fields of solid state research. The hypothesis developed here treats embrittlement in terms of volumetric and chemical, or bonding, effects. The embrittling behaviour of hydrogen fits into this framework in a natural way.

A model in which cracks propagate by nucleation, growth, and coalescence with cavities in front of the crack tip is analysed in detail. The applied stress field is assumed to be elastic or elastic–plastic, and the relaxation of stresses from the growth of cavitation damage is included in the analysis. The spacing of the cavities, the threshold stress for the nucleation of cavities, and the self-diffusion coefficients are the important material parameters. The model results in a threshold stress intensity and a K _I ⁿ dependence of steady-state crack propagation rate when K _I > K _th. The stress distribution in front of the crack during the transient and the steady states is calculated. The size of the ‘damage zone’ varies from about 10 to 100 cavity spacings. Since the typical cavity spacing in engineering materials is about 1 μm, the damage zone is expected to be a few grain diameters in length.

Approximate methods are used to calculate the growth of grain-boundary cavities by power-law creep, under multi axial stress states. The time to fracture at constant stress is given by

t _f =t _n+ɑ/n+1)ε_ss1n(1/(n+1)f _i )

where t _n is the nucleation time (the time at which the voids first appear), ε_ss is the steady-state creep rate, n is the creep exponent and f _i is the original area fraction of cavities. The quantity α is defined by:

ɑ=1/sinh-{2(n-½)/(n½)P/σ_e}

where p is the hydrostatic pressure and σ_e the von Mises equivalent stress. Differential equations are given which allow the times and the strains to failure under variable loading histories to be calculated.

The diffusional growth of an isolated intergranular cavity is studied in a uniformly loaded body and also ahead of a crack. The corresponding rates of cavity growth as functions of the applied stress and stress intensity factor, respectively, are found. In the former case, a cavity which possesses an equilibrium shape with constant curvature can, for physically reasonable applied stresses, grow independently of other cavities only if the average separation of the cavities is in excess of 10³ times the cavity size. The reason is that the transition towards the Hull and Rimmer type steady state takes place for smaller cavity spacing due to the large extent of the region of material deposition onto the boundary. On the other hand, crack-like cavities may grow independently even if the average cavity separation is small, provided their width is about two orders of magnitude smaller than their length which may be the case when the surface diffusion is appreciably slower than the grain boundary diffusion. However, ahead of a crack both the equilibrium and crack-like cavities can grow independently since the extent of the region of the material deposition is comparable with the size of the cavities for physically reasonable values of the crack stress intensity factor. Since there are factors which may prevent the development of the Hull and Rimmer type diffusional mechanism in regions which are large compared with the cavity size, it is suggested that cavity growth controlled purely by grain boundary diffusion is more likely to be observed in creep crack growth experiments than in creep experiments on uncracked uniformly loaded specimens.

The micromechanisms of fatigue crack growth in metals in Stage II and Stage III are examined in detail. The link between crack advance and crack tip opening is emphasized. Empirical crack growth laws are reviewed in the light of the micromechanisms involved.

Results from investigations of the fatigue crack growth behaviour and ∆K threshold levels in α-titanium, α-brass, and low-carbon ferritic steels are presented. The observations show that microstructure has a substantial influence on the mechanisms and modes of fatigue crack growth. The role played by transgranular and intergranular modes of failure in the intermediate and low ∆K regions are considered. The development of irregular fracture faces due to out-of-plane crack trajectories with the associated ‘non-closure‘ of the fatigue cracks is suggested as a substantial contributor to the factors determining ∆K threshold levels.

This paper considers the crack growth process for a carbon steel and a sensitized stainless steel in elevated-temperature oxygenated water. The results are interpreted from the viewpoint of a proposed design procedure based on a crack growth criterion. Cyclic growth to a critical size is allowed as determined by the sustained stress on the component and the K _ISCC for the material/environment combination. Predictions for the cyclic crack growth margin based on a linear superposition model are compared with experimental results. It is found that environmentally sensitive cyclic growth can be predicted on this basis only when the cyclic period approaches several hours; for shorter periods the predicted crack growth rates are too low and the design lives so derived are considerably lower than those derived from linear superposition assumptions.

The nucleation and propagation of cracks in aligned continuous glass fibre reinforced polyester composites in the presence of hydrochloric acid have been studied using ring specimens subjected to parallel plate compression. The appearance of the fracture surfaces depends on the initial strain but is characterized by planar cracks normal to the fibre direction with little fibre pull-out. The planar cracks are separated by interlaminar cracks. A model is presented for the nucleation and growth of cracks in stress and strain corrosion conditions.

At normal temperatures and pressures water is known to have a strong influence on the strength of ceramics and glasses. Behaving as a stress corrosion agent, water causes these materials to fail prematurely as a consequence of subcritical crack growth. A basic premise of this paper is that stress corrosion cracking of ceramics is a chemical process which involves a stress-enhanced chemical reaction between the water and the highly stressed ceramic near the crack tip. Plastic deformation is believed to play no role in this fracture process. After a brief survey of chemical reaction rate theory, the basic rate equation from this theory is modified to reflect physical and chemical processes which occur at crack tips. Modification of the rate equation is based on the assumption thatl the crack tip can be modelled as an elastic continuum, an assumption that is supported by a simple atomistic model of crack growth. When tested against experimental data collected on glass the theory was found to be consistent with measurements of the crack growth dependence on temperature, applied stress intensity factor, and concentration of reactive species in the environment.

A review of understanding of the statistical variations in strength in terms of microstructural features shows that the situation is highly complex. Models will require a considerable increase in sophistication before reliable predictions of strength variations can be made.