Accurate Critical Stress Intensity Factor Griffith Crack Theory Measurements by Numerical Techniques

Critical stress intensity factor (K_Ic) has been an approximation for fracture toughness using only load-cell measurements. However, artificial man-made cracks several orders of magnitude longer and wider than natural flaws have required a correction factor term (Y) that can be up to about 3 times the recorded experimental value [1-3]. In fact, over 30 years ago a National Academy of Sciences advisory board stated that empirical K_Ic testing was of serious concern and further requested that an accurate bulk fracture toughness method be found [4]. Now that fracture toughness can be calculated accurately by numerical integration from the load/deflection curve as resilience, work of fracture (WOF) and strain energy release (S_Ic) [5, 6], K_Ic appears to be unnecessary. However, the large body of previous K_Ic experimental test results found in the literature offer the opportunity for continued meta analysis with other more practical and accurate fracture toughness results using energy methods and numerical integration. Therefore, K_Ic is derived from the classical Griffith Crack Theory [6] to include S_Ic as a more accurate term for strain energy release rate (𝒢_Ic), along with crack surface energy (γ), crack length (a), modulus (E), applied stress (σ), Y, crack-tip plastic zone defect region (r_p) and yield strength (σ_ys) that can all be determined from load and deflection data. Polymer matrix discontinuous quartz fiber-reinforced composites to accentuate toughness differences were prepared for flexural mechanical testing comprising of 3 mm fibers at different volume percentages from 0-54.0 vol% and at 28.2 vol% with different fiber lengths from 0.0-6.0 mm. Results provided a new correction factor and regression analyses between several numerical integration fracture toughness test methods to support K_Ic results. Further, bulk K_Ic accurate experimental values are compared with empirical test results found in literature. Also, several fracture toughness mechanisms are discussed especially for fiber-reinforced composites.