Mechanisms and effects of heat generation at the tips of dynamic cracks and notches in metals

Abstract

A high-speed InSb infrared detector array and the method of Coherent Gradient Sensing (CGS) are used in several experimental configurations to explore the mechanisms and effects of heat generation in dynamic fracture and deformation. First, the dependence of the measured dynamic crack tip temperature upon crack tip speed is investigated for cracks propagating dynamically in AISI 4340 carbon steel. Then, the dynamic crack tip temperature in a titanium alloy (Ti-l0V-2Fe-3Al) is measured in order to examine the role of material parameters in determining the crack tip temperature at different crack growth speeds. It is seen that the crack tip temperature increases when crack tip velocities are increased from 600 m/s to 900 m/s in 4340 steel. The extent of the active plastic zone at the surface of the specimen, however, decreases with increasing crack velocity. When the results for temperature measurements in steel are compared with those for titanium, it is seen that the material parameters that are most important are the dynamic yield strength, which determines the amount of plasticity, and the heat capacity of the material. Conductivity has little effect. Next, the nature of hyperbolic heat conduction at the tip of a dynamic crack is investigated. A mathematical model is developed to predict the temperature field around a dynamically propagating crack tip for a material that follows a hyperbolic heat conduction law. A Green's function for the governing partial differential equation is derived. The model is solved for a variety of experimental conditions by numerical integration of the Green's function. Various possible effects of hyperbolic heat conduction around a crack tip are explored. The model is then used to simulate the experimental conditions typically observed in dynamic fracture. Because conduction is minimal around the dynamically propagating crack tip, no effects of hyperbolic heat conduction are observed. It is also observed that the temperature field around the dynamic crack tip is adiabatic. Since adiabatic conditions are observed around a propagating crack tip, an important parameter which governs the distribution and intensity of crack tip heating is the fraction of plastic work rate converted to heat, [beta]. For this investigation [beta] is not treated as a mere parameter, the possibility of the existence of a constitutive relationship between this parameter and strain at high strain-rates is investigated using the Kolsky bar as a loading apparatus. It is found that the conversion of plastic work to heat at high strain-rates is similar to that at low strain rates for aluminum and for steel and that [beta] remains a constant independent of strain at high strains for both these materials. For rate sensitive titanium, [beta] is observed to be a function of strain possibly due to twinning deformation. It is known that heat generation can lead to the formation of shear bands especially in dynamic fracture experiments. The formation of a shear band at the tip of a notch or crack in C-300 steel is examined using the method of CGS. First, the CGS method is used to verify a model of the notch tip stress intensity factor, K[subscript II], as a function of time. Good agreement is found between the experimental measurement of K[subscript II] and the predicted value for PMMA impacted at 5 m/s. Then the method is used to investigate the formation of shear bands at the tip of a notch under the same conditions. A Dugdale crack model is used to interpret the results, and it is seen that the shear stress decreases from 1.6 GPa to 1.3 GPa as the shear band propagates. This result is in good agreement with measurements made using the Kolsky bar.