Creep crack growth models

Creep Crack Growth Models in Monolithic Solids... 

Numerous investigations that support the use of the C, parameter have been carried out by Saxena and co-workers,1,2,42 although there are many fundamental issues to be addressed. The latter essentially are related to the nonexistence of a strain-rate potential for simultaneous elastic and creep deformations. Nevertheless, based upon rigorous mechanics arguments, it is certain that neither C nor / 7 alone can adequately correlate crack growth in SSC. See the next section for more details on crack growth models. 

Crack growth models in monolithic solids have been well document-ed. 1-3,36-45 These have been derived from the crack tip fields by the application of suitable fracture criteria within a creep process zone in advance of the crack tip. Generally, it is assumed that secondary failure in the crack tip process zone is initiated by a creep plastic deformation mechanism and that advance of the primary crack is controlled by such secondary fracture initiation inside the creep plastic zone. An example of such a fracture mechanism is the well-known creep-induced grain boundary void initiation, growth and coalescence inside the creep zone observed both in metals1-3 and ceramics.4-10 Such creep plastic-zone-induced failure can be described by a criterion involving both a critical plastic strain as well as a critical microstructure-dependent distance. The criterion states that advance of the primary creep crack can occur when a critical strain, ec, is exceeded over a critical distance, lc in front of the crack tip. In other words... 

Fig. 10.4 Curve showing the predicted creep crack growth rate versus stress intensity factor based on the model of Hui and Riedel.40...

Modeling of Creep Crack Growth in Ceramic Composites... 

In structural ceramic composites, the principal effect considered was one of crack-face closure tractions, or cohesive forces, brought about, for instance, by bridging fibers. A rigorous evaluation of the crack tip fields where the crack faces are not traction free has not yet been attempted. However, an approximate approach for the small-scale creep case is to assume that the crack tip fields are not functionally altered by crack-face tractions, with the effect of the traction being only to introduce a zone of crack tip shielding. This allows for the development of preliminary models for creep crack growth which is inclusive of the role of crack bridging. These preliminary models predict that,... 

Equation 6.14 provides a formal connection between creep crack growth and the kinetics of creep deformation in that the steady-state crack growth rates can be predicted from the data on uniaxial creep deformation. Such a comparison was made by Yin et al. [3] and is reconstructed here to correct for the previously described discrepancies in the location of the crack-tip coordinates (from dr/2 to dr) with respect to the microstructural features, and in the fracture and crack growth models. Steady-state creep deformation and crack growth rate data on an AlSl 4340 steel (tempered at 477 K), obtained by Landes and Wei [2] at 297, 353, and 413 K, were used. (AU of these temperatures were below the homologous temperature of about 450 K.) The sensitivity of the model to ys, N, and cr is assessed. 

Of the three parameters, a is the most difficult to estimate and is perhaps the least certain to estimate. The estimated influence of hardness a on crack growth rate is shown in Fig. 6.17, and reflects the effect of local strain s ahead of the crack tip. Examination of Fig. 6.17 suggests that a 10% reduction in a from 2010 to about 1800 MPa could conform the creep crack growth rate model to the experimental data. 

The resulting stress rupture data will be used to examir ie the applicability of a generalized fatigue-life (slow crack growth) model. If necessary, model refinements will be implemented to account for both crack blur tlng and creep damage effects. Insights obtained from the characterization studies will be crucial for this modification process. 

Validated models for creep damage assessment are available and these can produce estimates of time to crack initiation. High-temperature crack growth models can then be used to predict both time to failure and the nature of that event. 

Wei, Z., Yang, F., Lin, B., Luo, L., Konson, D. Nikbin, K. 2013. Deterministic and probabilistic creep-fatigue-oxidation crack growth modeling. Probabilistic Engineering Mechanics 33(0) 126-134. 

Presently, efforts are being directed on basic studies of the creep crack growth and failure mechanisms with the objective of developing a model for the application of the LBB criterion to the KALIMER design. 

Figure 2. Relationship between creep crack growth behavior and failure behavior of internally pressurized pipes and corresponding lifetime model.

As mentioned above, for a creep stress exponent, n<3, the crack tip stress field for a continuously growing crack is the applied A -field. For this case, based on the model of Purushothaman and Tien48 the crack growth rate is, for strain-controlled failure,... 

In this equilibrium toughness-controlled (no creep process zone) model, for a a0, the crack growth rate was derived to be31... 

Further development of theoretical models is limited by the lack of availability of information in ceramic composites pertaining to crack shape, crack growth rates, bridging, and process zone sizes associated with growing creep cracks in ceramic composites. 

In a subsequent series of experiments, Landes and Wei [2] demonstrated that the phenomenon is real, and modeled the crack growth response in terms of creep deformation rate within the crack-tip process zone. The effort has been further substantiated by the work of Yin et al. [3]. The results and model development from these studies are briefly summarized, and extension to probabihstic considerations is reviewed. It is hoped that this effort will be extended to understand the behavior of other systems, and affirm a mechanistic basis for understanding and design against creep-dominated failures. The author relies principally on the earher works of Li et aL [1], Landes and Wei [2], Yin et al. [3], Krafft [4] and Krafft and Mulherin [5]. The findings rely principally on the laborious experimental measurements by Landes and Wei [2], and the conceptual modeling framework by Kraftt... 

Krafft [4] and Krafft and Mulherin [5] later extended the TLI model to describe stress corrosion crack growth. Crack growth was viewed in terms of the instability of tensile ligaments where their lateral contraction was augmented by uniform chemical dissolution of the tensile ligaments. For sustained-load crack growth in an inert environment, on the other hand, the reduction in the cross-sectional area of the ligaments would be associated with the creep rate (Landes and Wei [2], Yin et aL... 

Extending on the concepts of Krafft [4,5], and Landes and Wei [2], an analytical model was proposed by Yin et al. [3] to explore the crack growth response over a broader range of K levels. In this model, the phenomenological model of creep proposed by Hart [6] is used. 

The occurrence of creep-controlled crack growth, in an inert environment, has been demonstrated. It can occur even at modest temperatures, and has been linked to localized creep deformation and rupture of ligaments isolated by the growth of inclusion-nucleated voids ahead of the crack tip. Landes and Wei [2] and Yin et al. [3] have made a formal connection between the two processes, and provided a modeling framework and experimental data to link the kinetics of creep to creep-controlled crack growth. Further work is needed to develop, validate, and extend this understanding. In particular, its extension to high-temperature applications needs to be explored. 

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