Energy absorption and dissipation associated with mass activation and deactivation for open systems

Energy dissipation at the macroscopic scale, applied to large bodies, relies on using the average bulk or global properties. The normal procedure is to load/unload a uniaxial tensile specimen, and account for the difference of the area under the stress and strain curve, even though unloading does not occur in reality. The same procedure, however, is not feasible for treating the energy dissipation at the microscopic scale, applied to small bodies, where the space/time dependency of the local material properties plays a role. That is the transient character of the energy transfer between the specimen surface and surrounding can no longer be neglected. Moreover, there is no way to simulate microscopic unloading. Besides, the coupon test scheme of load/unload, an artifact, that has been used because of no other choice.Energy lost is an intrinsic process that defies empirical determination in the true sense. Incomplete homogeneous loading and/or unloading rate at all locations of the material gives rise to dissipation. This effect has been described by using the transitional function   that entails multiscaling and segmentation for the simulation of material damage at the different scales. Segmented damage initiation/termination thresholds are invoked that may consist of, say pico- to nano-cracking and nano- to micro-cracking followed by micro- to macro-cracking and so on. The idealized “crack tip” is used to model the sink and source that can absorb and dissipate energy, respectively. The mass surrounding the crack tip is said to be activated by direct-absorption of energy and deactivated by self-dissipation of energy. The threshold for each scale range is assumed to depend on the square of the crack tip velocity a˙2 and mass densities M↓↑M↓↑ and M↓↑M↓↑ such that W=M↓↑a↑↓2 and D=M↓↑a↑↓2. The quantities WW and DD are referred to, respectively, as the direct-absorption and self-dissipation energy density. They fluctuate in time and determine whether the surrounding crack tip field of inhomogeneity is expanding or contracting. Singularity representation is used to capture the character of the crack tip field strength while scaling is reflected by the characteristic length.Demonstrated will be a pico/nano/micro/macro fatigue cracking model of a 2024-T3 aluminum panel. Only the undamaged material properties are employed. Time degradation of the pico/nano/micro/macro material structure behavior is derived by using nine scale transitional physical parameters: three for the pico/nano range (μpi/na∗,σpi/na∗,dpi/na∗), three for the nano/micro range (μna/mi∗,σna/mi∗,dna/mi∗) and three for the micro/macro range (μmi/ma∗,σmi/ma∗,dmi/ma∗). The subscripts pi, na, mi, and ma designate, respectively, pico, nano, micro, and macro. Only the ratios of two successive scale sensitive parameters need to be known. The time dependent physical parameters at the lower scale are implicit and needed only for analytical continuation.More specifically, the transitional character of picocracks, nanocracks, microcracks, and macrocracks are determined from the specified life expectancy of time arrow according to pico → nano → micro → macro with the respective singularity strength of λ given by 1.25/1.00/0.75/0.50. Recall that λ = 0.5 corresponds to the inverse square root r−0.5 in fracture mechanics with r being the distance from the macrocrack tip. The microcrack, nanocrack, and picocrack tips are assigned with the singularities r−0.75 and r−1.00and r−1.25, respectively. The time of arrow in years will depend on the problem definition. Progressive damage is assumed to occur in the direction of pico → nano → micro → macro. The same scheme is applied to the fatigue damage of a 2024-T3 panel with a total life time of 18.5+ to 20 years that may be distributed over the pico, nano, micro, macro, and structure scale according to 1.5+/2.5+/3.5+/5.5+/7.0+. Such a specification can only be satisfied by matching the energy dissipated in damaging the internal material structure at each scale range. Hence, the precise time dependent material property degradation process over the total life span can be enforced. Material inhomogeneities at the different scales are thus compensated by the inhomogeneous reinforcements at the same different scales such that energy release rate at each scale would be relatively homogeneous and controlled.