Abstract:
Appropriatecombination of size and time scale can accommodate a crack tocreep a few nano meters in months or to propagate ten kilometersin a couple of seconds. The tip does not have a real mass so tospeak of, but it can pack a high energy state by activating thesurrounding matter. Decrease and increase of activated mass ispresumed to occur before and after scale transition depending onthe direction of arrow of material damage. The segmentationthreshold for each scale range is postulated to depend on theproduct of the squared of the crack tip velocity $\dot {a}^2$ and activated mass density $\cal {M}$. as ${\cal {W}} = {\cal {M}_{\downarrow \uparrow}}{\dot {a}_{ \uparrow \downarrow }^2}$ and ${\cal {D}} = {\cal{M}^{ \downarrow \uparrow}}{\dot {a}_{ \uparrow \downarrow }^2}$.The quantities $\cal {W}$ and $\cal {D}$ are referred to,respectively, as the direct-absorption and self-dissipation energydensity. The activated mass densities $\cal {M}_{ \downarrow\uparrow } $ and $\cal {M}^{ \downarrow \uparrow }$ can increaseor decrease in opposition to the crack tip velocity $\dot {a}$ asindicated by the subscript/superscript notation. The compensatingeffects of $\dot {a}^2$ and $M$. are implicit to the physicalprocess of expansion and/or contraction often used in cosmophysics modeling. The activated mass density has the sameinterpretation when applied to the scale sensitive crack tipbehavior. Multiscaling when segmented may consist of $\cdots$pico, nano, micro and macro $\cdots$. The material damage processcan thus be simulated figuratively speaking by crack growthentailing non-uniform global and local energy transfer. Materialdamage by fatigue crack growth is used to illustrate the size/timearrow of large$\rightarrow$small and slow$\rightarrow$fast asadvocated, respectively, by the thermodynamics ofcold$\rightarrow$hot and order$\rightarrow$disorder. Thisincidentally is opposite to the direction of arrow in cosmicevolution such that the events follow small$\rightarrow$large andfast$\rightarrow$slow while the thermodynamics reverses,respectively, to hot$\rightarrow$cold anddisorder$\rightarrow$order. A new paradigm referred to as Crack Tip Mechanics (CTM) is proposed torepresent inhomogeneity by crack-like defects as the cause ofdamage initiation. The closed ended line is depicted forsimulating the interfacial gap between rows of atoms or a branchcut in a continuum. The range of the size time scale can coverfrom pico to macro or even wider range if necessary. Although thefatigue crack is used for demonstrating the basic principles ofCTM, the scenarios of expansion and contraction associated withthe direct-absorption and self-dissipation energy density in thecontext of cosmo physics can describe the behavior of theactivated or energized mass around the crack tip which can beviewed as an energy sink or source. Singularity is used to capture the character of the energy source or sink, bothphysically as part of an interface or mathematically as part of aline of discontinuity. Energy exchange from one form to another isassumed to depend on the damage time of arrow of energy absorptionor dissipation that involve the combine use of scale segmentationand singularity strength. Time degradation of the materialconstituents are derived according to specified design life suchthat the material response is matched with the time the history ofthe loading rate.A pico/nano/micro/macro fatigue cracking model of a 2024-T3aluminum panel will be used for demonstration where the structurelife portion may be added. Time degradation of thepico/nano/micro/macro/struc system behavior can be described byusing nine scale transitional physical parameters: three for thenano/micro range ($\mu _{na / mi}^\ast ,$ $\sigma _{na / mi}^\ast,d_{na / mi}^\ast )$, three for the micro/macro range ($\mu _{mi/ ma}^\ast ,\sigma _{mi / ma}^\ast ,d_{mi / ma}^\ast )$, and threefor the pico/nano range ($\mu _{pi / na}^\ast ,\sigma _{pi /na}^\ast ,d_{pi / na}^\ast )$. The subscripts pi, na, mi, ma andna/pi na/pi na/pi struc designate, respectively, pico, nano,micro, macro and structure. Only the ratios of two successivescale sensitive parameters need to be known. The time dependentlocal physical parameters at the lower scale completes theformalism of analytical continuation though they need not be madeknown by tests.More specifically, the transitional character of picocracks,nanocracks, micro- cracks and macrocracks are determined from thespecified life expectancy of time arrow according topico$\rightarrow$nano$\rightarrow$micro$\rightarrow$macro with therespective singularity strength of $\lambda$ given by1.25/1.00/0.75/0.50. An additional singularity of strength 0.25may be added for the structural components. Recall that$\lambda$=0.5 corresponds to the inverse square root r$^{-0.5}$in fracture mechanics with r being the distance from themacrocrack tip. The microcrack, nanocrack and picocrack tip areassigned with the singularities r$^{-0.75}$ , r$^{-1.00}$ andr$^{-1.25}$ , respectively. The time of arrow in years will dependon the problem definition. A critical device component may bedesigned to operate at the pico/nano/micro/macro scale with a lifedistribution of 1.5$^{\pm}$ /2.5$^{\pm}$ /3.5$^{\pm}$ /5.5$^{\pm}$and total life of 13$^{\pm}$ years. The superscript ${\pm}$indicates more or less the actual time elapsed. Progressive damageis assumed to occur in the direction ofpico$\rightarrow$nano$\rightarrow$micro$\rightarrow$ macro. Thesame scheme is applied to the fatigue damage of a 2024-T3 panelwith a total life time of 20 years that may be distributed overthe pico, nano, micro, macro and struc scale according to1.5$^{\pm}$ /2.5$^{\pm}$ /3.5$^{\pm}$ /5.5$^{\pm}$ /7.0$^{\pm}$ .Such a specification can only be satisfied by matching the energyused in damaging the internal material structure at each scalerange. Hence, the precise time dependent material propertydegradation process over the total life span can be enforced.
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