Fracture analysis of semi-circular and semi-circular-bend geometries

A fracture mechanics analysis of the semi-circular (SC) and semi-circular-bend (SCB) fracture geometries is presented. The weight function method is implemented to obtain wide ranging stress intensity factor (SIF) and crack opening displacement (COD) expressions. This study has as its basis a finite element analysis of the semi-circular disk (SC) subjected to a reference loading case. The latter is required to determine both the associated reference stress intensity factor and the weight function for the base-edge-cracked semi-circular geometry. With this information, SIF and COD expressions for the full range of crack lengths are obtained. The special cases of the SC subject to a concentrated crack mouth loading and the SCB are analyzed in detail. The weight function for the SCB is fully developed, with an accurate expression for the SIF and and a numerical result for the crack mouth opening displacement (CMOD). The latter wide ranging expressions can, in turn, be applied as a reference solution. From this weight function approach, SIF's and COD's for the SC and SCB subject to any other loading can be obtained.     

A Viscoelastic Fictitious Crack Model for the Fracture of Sea Ice

The fracture of sea ice is modeled using a viscoelastic fictitious crack(cohesive zone) model. The sea ice is modeled as a linear viscoelastic material. The fictitious crack model is implemented via the weight function method. The associated stress-separation curve can be rate dependent. The impact of assuming viscoelastic behavior in the bulk as opposed to elastic behavior is studied. Results from the model are compared to the available exact results for various test cases. The model is applied to a large scale in situ sea ice fracture test. Various implications of such applications are pointed out. This viscoelastic fictitious crack model is found to be a promising tool in investigations pertaining to the fracture of sea ice. This revised version was published online in July 2006 with corrections to the Cover Date.     

LEFM size requirements for the fracture testing of sea ice

The stress-separation curve obtained for the in-situ response of first-year sea ice is used to obtain specimen size requirements for sea ice fracture tests. Issues of notch sensitivity and minimum size requirements for the applicability of linear elastic fracture mechanics are addressed. The role of time dependent deformations in studying sea ice fracture is examined.     

Scale effects on the in-situ tensile strength and fracture of ice. Part II: First-year sea ice at Resolute, N.W.T.

A set of lab- to structural-scale 0.5 < L < 80 m) in-situ full thickness (1.8 m) fracture tests were conducted on first-year sea ice at Resolute, N.W.T. using self-similar (plan view) edge-cracked square plates. With a size range of 1:160, the data is used, via size effect analyses, to evaluate the influence of scale effects on the fracture behavior of sea ice over the range 10-1 m (laboratory) to 100 m and to predict the scale effect on tensile strength up to ≈1000 m. Details of this large-scale sea ice fracture test program are presented in this paper. The experimental results are presented as well as the fracture modeling of the data. The influence of scale on the ice strength and fracture toughness is dramatic. The applicability of various size effect laws are investigated and criteria for LEFM test sizes are presented. For the thick first-year sea ice tested, the size-independent fracture toughness is of order 250 kPa , not the 115 kPa that is commonly used. The number of grains spanned by the associated test piece is 200, much larger than the number 15 typically quoted for regular tension-compression testing. The size-independent fracture energy is 15 J/m2, while the requisite LEFM test size for the edge-cracked square plate geometry (for loading durations of less than 600 s and an average grain size of 1.5 cm), is 3 m square. Size effect analyses of sub-ranges of the data show that unless the specimen sizes tested are themselves sufficiently large, the true nature of the scale effect is not revealed, which was a concern raised by Leicester 25 years ago. In the case of the fracture tests reported in this paper, based on the lab-scale and field-scale strength data measured between 0.1 and 3 m and using Bažant's size effect law, it is possible to accurately predict the tensile strengths for all of the remaining tests, up to and including 80 m. This revised version was published online in July 2006 with corrections to the Cover Date.     

Scale effects on the in-situ tensile strength and fracture of ice Part I: Large grained freshwater ice at Spray Lakes Reservoir, Alberta

At lab-scale, issues such as inhomogeneity and polycrystallinity are especially important to the fracture of S1 freshwater ice. S1 freshwater ice is typically composed of large grains with predominantly vertical c-axes. Because of the very large grain sizes that one can encounter in S1 macrocrystalline ice sheets, it is essential that the effects of sample size on the fracture behavior be determined. In other words, are small scale (lab-scale) results applicable at larger scales (at the scale of ice-structure interactions, for instance)? To answer this question, a set of lab- to structural-scale (0.34>L>28.64m) fracture tests were conducted on S1 freshwater lake ice at Spray Lakes, Alberta, using the base-edge-notched reverse-tapered plate geometry and covering a size range of 1:81. A Ba?ant-type size effect analysis of the measured fracture strengths (which do reveal a significant dependence on scale) is unexpectedly clouded by the fact that the data collected violates the associated scatter requirements, even though the size range tested is large. Moreover, via Hillerborg's fictitious crack model, large fracture energies were back-calculated (of order 20 J/m2), but for miniscule process zone sizes; in addition, not all of the measured deformations for each test could be matched simultaneously. Apparently, these very warm S1 macrocrystalline lake ice experiments were dominated by nonlocal deformation and energy release rate mechanisms, in all likelihood brought about by grain boundary sliding. The reduced effectiveness of both the Ba?ant-type size effect analysis and Hillerborg's fictitious crack model is due mainly to the lack of crack growth stability achieved in the experiments. These unstable fractures truncated the fracture process. Given the irregular and large grain structure, the very warm ice temperatures, and the diffuse grain boundary surface energy, there is a marked dependence on specimen size to grain size ratio and distinctly non-unique pre-failure process zones occurred. Micromechanical simulations are required to resolve these coupled issues.