The risks of non-conservative design and operation resulting from invalidity of linear-elastic fracture mechanics

Abstract

Linear-elastic fracture mechanics (LEFM) is a common approach used to predict the governing conditions (critical stresses, crack lengths, crack growth rates etc) governing material fracture. It has seen widespread application due to its simplicity in comparison with other methodologies. With knowledge of LEFM, it is possible to design components and apply appropriate operating procedures in such a way as to reduce the risk of fracture. However, the use of LEFM is restricted to relatively long cracks, whereas short cracks are more commonly of interest in design. LEFM is not able to give reliable crack growth rates and static failure loads when cracks are short (the cut-off for acceptable crack lengths is defined using a series of validity criteria.). If LEFM cannot validly be used then other more complex and costly methodologies, such as elastic-plastic fracture mechanics (EPFM), must be employed.A number of explanations for the difference between short and long crack behaviour (in terms of static and fatigue failure) have been proposed. Microstructural properties, such as grain boundaries (Lankford, 1982), notch tip plasticity, microplasticity and crack closure (Suresh & Ritchie, 1984) have all been identified as mechanisms for differences in behaviour. A number of models have been proposed to simulate behaviour at different crack lengths but these models are often based on experimental data from one material, which is an issue as microstructure properties can vary greatly between materials (eg polymers vs metals). Additionally, a number of equations put forward by researchers often use conflicting theories to model crack behaviour (Lawson, Chen & Meshii, 1999). A simple numerical approach presented by El Haddad, Smith, & Topper (1979) was implemented to quantify the deviation between valid and invalid cracks for static failure loads and crack growth rates. This approach used an effective crack length ( + 0, a numerical constant) instead of the nominal crack length in LEFM calculations to improve predictions.This approach was tested by collecting static fracture load and fatigue crack growth rate measurements for Compact Tension (CT) acrylic (PMMA) specimens with crack lengths ranging from invalid, borderline invalid/valid to valid cracks. Measured failure loads and crack growth rates were compared to LEFM predicted values and LEFM predicted values using an effective crack length.Using standard LEFM, predicted failure loads were found to be higher than experimental data and predicted crack growth rates were found to be slower than experimental data when LEFM was invalid. It was also found that the further the crack length was from the minimum valid crack length, the more non-conservative the predicted static failure load and crack growth rate would be.This numerical approach yielded much improved LEFM predictions for static failure loads and crack growth rates. For a static loading environment, the effective crack length reduced the predicted failure load significantly for short cracks but not for long cracks. For a cyclic loading environment, the effect crack length introduced an increased ∆ driving force which modelled the faster crack growth rates for short cracks. The numerical approach yielded better correlation with the experimental data at borderline invalidity then for extremely invalid cracks.This numerical approach used is promising due to its simplicity. Further investigation of the 0 concept needs to be considered with respect to different materials, loading and environmental conditions in addition to geometry before it could be used in design.