Issue34

N.R. Gates et alii, Frattura ed Integrità Strutturale, 34 (2015) 27-41; DOI: 10.3221/IGF-ESIS.34.03 37 IC nom q l2 c eff K K 1 e1 4 ,                       (3) where α is the natural/undeformed asperity angle, c is the crack length, l is a material characteristic length, K q,no m is the nominally applied equivalent SIF (not accounting for friction effects), K IC is the material plane-strain fracture toughness, and the parameter, β , describes the influence of loading level on crack face interaction. Although Eq. (3) is phenomenological in nature, it is designed to reflect the complex changes that occur at the crack interface as a crack grows and provides a simple means of quantifying these changes. The undeformed asperity angle, α , is independent of the applied loading and can either be determined through experimental measurements or estimated based on crystallographic structure [10]. Assuming a constant value of average asperity angle, however, would result in a nearly constant frictional effect on effective shear stress. In reality, variations in asperity angle will cause the value of friction stress to change, which will affect the load transfer through the crack interface. This phenomenon is reflected in the current model through a variation in asperity angle with crack length. The idea behind the first bracketed term in Eq. (3) is that initially, when cracks are on the order or a grain size or two, there is not much deviation in their ideal path. This is because there has not been a sufficient amount of growth to encounter slip system misalignment from one grain to the next and/or other microstructural obstacles which lead to crack meandering and the development of crack face asperities. Therefore, the effective asperity angle at zero crack length is reduced to zero by this term and allowed to gradually increase with crack length until it approaches its saturated value at a length equal to that of a few grains. This produces a behavior which agrees with the decreasing crack growth rates observed for short cracks in the constant SIF controlled tests reported in Ref. [11]. The material characteristic length, l , can be considered equal to the average grain size in the direction of crack growth. Similarly, long cracks may also experience a reduction in frictional stresses due to changes in crack face asperities. Unlike short cracks, however, these changes are brought about as a result of asperity destruction due to plasticity and fretting along the crack interface. Additionally, the coefficient of friction is more prone to a reduction in long cracks as well, due to the formation of oxide and/or debris layers between crack faces. Since the effects of these processes generally increase with an increase in local stresses and/or crack length, the second bracketed term in Eq. (3) reflects changes in frictional attenuation by decreasing the effective asperity angle as the ratio of nominal SIF to fracture toughness increases. A linear relationship was chosen based on trends reported in Ref. [25]. The application of this model is fairly straight forward in cases of fully-reversed pure torsion loading, but it can also be applied to cases where nonzero mean and/or mixed-mode loading conditions exist. Because it is based on the stress state at the crack location, it is applicable to any type of loading and the predicted frictional attenuation is sensitive to both the applied shear stress and normal stress components. A simple Mohr’s circle analysis reveals that the model will correctly predict a decrease or increase in crack face interaction due to the presence of an applied tensile or compressive stress, respectively. For situations where loading is not fully reversed, the model can be applied at both the minimum and maximum loadings in a cycle to compute the effective SIF range. However, care should be taken when determining the sign of the stress transformation angle to ensure that the transformed stress, σ x’, is perpendicular to the appropriate crack interface (related to the shear stress direction on crack growth plane) at each loading state considered. C OMPARISONS WITH EXPERIMENTAL RESULTS egardless of how well a model qualitatively agrees with experimental observations, its real value comes from the ability to predict crack growth behavior in a quantitative manner. The following section will evaluate the proposed model’s ability to do so by analyzing the experimental data presented earlier. Correlations will be made concerning both crack branching and crack growth rate. Due to time constraints, however, the analysis presented in this section is only applied to situations involving fully-reversed pure torsion loadings. The effectiveness of the model when applied to situations involving static axial stresses or mixed-mode loadings will be evaluated in a future study. The first step in analyzing the experimental data was to gather the relevant material parameters for the proposed model. The average undeformed crack face asperity angle was measured from the surface crack replicas of several specimens when crack lengths, 2c , were less than 1 mm. Fifteen measured values ranged from 16° to 60° with an average of 36° and standard deviation of 14°. A value for sliding coefficient of friction under ideal conditions could not be found and was instead estimated as being 0.67 times the average reported static values for aluminum on aluminum contact, i.e. 0.67(1.2) R