Short crack data derived from the fatigue data of 2024-T3 Al with long cracks: Material, load and geometry effects locked-in by transitional functions

Abstract

The relationship of short and long crack data is analyzed for the fatigue of 2024-T3 aluminum. The micro–macro scale range is selected as the reference state of data measurement. Three transitional functions (TRs) contained in ΔSmacromicro are used. They correspond to the micro–macro scale portion of the plot of the crack growth rate da/dN vs the volume energy density (VED) factor increment ΔSmacromicro. Throughout this work, ΔS is understood to represent the incremental volume energy and not the surface energy. Form-invariance of ΔSmacromicro using the transitional functions or variables (μ,σ,d) justify scale shifting to obtain the corresponding test data for the nano–micro and macro-large scale segments. A straight line relationship is established for finding ΔSmicronano and ΔSlargemacro from ΔSmacromicro. The effects of load, material and geometry are locked into the macro–micro data and transferred to the nano–micro and macro-large data by using a transitionalized crack length (TCL) of the two parameter model. A scaling law for non-equilibrium and non-homogeneous (NENH) is derived without violating the first principles.The micro–macro test data for crack lengths 3–55mm are used to derive short crack data of lengths 0.040–0.043mm. Data for very long crack lengths 49–260mm are also obtained analytically. The da/dN of the nano–micro range data covered four orders of magnitude from 10−7 to 10−4. The micro–macro range also covered four orders from 10−3 to 100 for da/dN. The macro-large range involved only two orders from 10−1 to 100. In the same way, crack growth in meters for structural applications for time scale measured in years can also be derived from macro–micro test data, which can be regarded as the “Master”.