The exchange of mass and energy density defines the wave velocity to be independent of the physical and geometrical properties of the transport media. This is in contrast to the conventional mechanics models (CMMs) where the material and geometrical properties of the transport media are assumed to be known as an a priori. Elastic waves and Lamb waves pertain, respectively, to medium characterized by elastic constants and to the in-plane and out-of-plane motion of elastic waves. Non-elastic waves are inherently beyond the capability of the CMMs models.

LIGO dedicated Feb. 11, 2016 to the discovery that atoms distanced billion of years away from the Earth have communicated with those on the Earth. No longer valid is the myth that a single particle could be the originator of all others. Equally inapplicable is the mathematical abstraction of the singularity models that render more questions than answers. To answer the unanswerables could be problematic. The multi-atoms (MAs) model predicates communication of the connected atoms as the means of exchanging mass and energy density. Forgetting not the structure of the atoms as referred to have yet to be discovered. The process of naming and renaming will continue.

The Cosmic mirage has no sense of the past, present, and future, while the Cosmic clock keeps tracks of the past, present, and future by the intensities of energization and massimization. The naming and renaming of the changes of the Cosmic mirage reflect the diversified theories and laws that have deceived observers. An energized and massmized version of 1-Ching and Tao Ching invokes the miniscule-DNA of the Cosmo, defined as the virgin state of homogeneity, without time and dimension. In particular, the energy and mass exchange (EME) like relation E = mv(2) shows that the ELPSs are images to be named and renamed. It can also be used to monitor the intensities of energization and massimization of the Cosmic clock. (C) 2017 Elsevier Ltd. All rights reserved.

The falling body velocity is 00000 when mass and energy are interdependent. The overestimated 00000 prevails when mass and energy are separately independent. The falling time is found to be greater by a factor of 00000. A consistent account of the laws of motion from Galileo to Newton is made possible by using E = mv 2 for conservative and dissipative systems. By the same token, the equivalence of energy and mass can be used for the mathematical assessment of gravitational waves at any velocities and not just at the speed of light. The personalized units should be replaced by the “energy density unit” to avoid ambiguities. The key step is the application of the Hookean “force” in conjunction with the work done as energy. The equivalence of mass and energy at any velocity were derived by using Ideomechanics, which is a mathematized verion of I-Ching. Gravitational waves are intimately related to the entanglement of multi-atom space-time.

Purpose – Fatigue crack growth rate data for 2024-T3 aluminum are found using three parameters d*, σ* and μ* for short and long cracks for Regions I-III in conventional fatigue. Asymptotic solution of a line crack with a micro-tip is found to yield a singular stress behavior of order 0.75 in contrast to the 0.50 order known for the macrocrack. The difference is due to the micro-macro interaction effects. The three parameters account for the combined effects of load, material and geometry via the tip region. Data for short and long cracks lie on a straight with a slope of about 3.9-4.8 for R values of 0.286-0.565. The results were based on an initial crack a1 mm where a is the half length for a central crack panel. The paper aims to discuss these issues. Design/methodology/approach – The belief that specimen fatigue data could assist the design of structural components was upended when FAA discovered that the NASGRO FCGD are not valid for short cracks that are tight and may even be closed. The regular ΔK vs da/dN model was limited to long cracks. The issue become critical for short cracks connecting the long ones of a few mm to cm or even m according to da/dN for the same crack history. The danger of short/long fatigue crack growth (SLFCG) prompted FAA to introduce an added test known as Limit of Validity (LOV), a way of setting empirical limits for structural components. The dual scale SLFCG data from ΔK micro/macro provide support for the LOV tests. Findings – Data for short and long cracks lie on a straight with a slope of about 3.9-4.8 for R values of 0.286-0.565. The single dual scale relation on ΔK micro/macro can switch from microscopic to macroscopic or vice and versa. The difference is fundamental. Order other than 0.75 can be obtained for simulating different microstructure effects as well as different materials and test conditions. Originality/value – Scale shifting from short to long fatigue cracks for 2024-T3 aluminum is new. The crack driving force is found to depend on the crack tightness. The sigmoidal curve based on the regular ΔK plot disappeared. The data from ΔK micro/macro for short cracks may supplement the FAA LOV tests for setting more reliable fatigue safe limits.

Multiscaling refers to the segmentation of physical systems of space-time having the same building blocks, a de facto hypothesis that is not likely to be challenged. Physical systems should be relatable to one another by space-time scale shifting. The mathematical proof will rightly so, be disrupted by the overriding force of political and economical expediency of new order of science and technology. Already in practice is that science and technology have globalized and personalized the world according to the priorities of the political and economical expediency. Personalization is definable only when distinction is made between the less from the more personalized. The “unitized function” is therefore invoked such that n number of factor types can be weighed and expressed by an “indicator”, say X 0 * . A similar quantity X j * for the subject, of the mechanical or biological, can then be compared and weighed on the same basis. The subject with the least ΔX 0 * , the difference of X j * and X 0 * , would be ahead in fitness. Physical systems are directed toward the well being of the individual. Multiplicity of scales and factor types in space-time call for partnership of “multiscaling” and “multifactoring”. The unitized function accommodates this combination and the binarism that is intrinsic to scalable data. Monolithic data are not scalable unless they are converted to be dualistic by scale shifting. Simply put, macro data should be converted to macro-micro by a process known as transitionalization. Restoration of the scalable capability in mechanics and physics is also connected with space-time non-symmetry. Non-symmetry refers to a reference (0), while (+) and (—) are directional dependence. This formalism can be degenerated to define a physical fitness ranking index for mechanical and biological systems. Monolithic data have been used in the field of fracture mechanics for decades. Only in recent times that the conversion to dualistic dependent data has restored the consistency required for shifting the space-time scale. The globalization and personalization will be discussed in terms of unitization of personal data at large. The longevity of the human subjects and physical fitness will be used for application, although the method applies to mechanical systems as well. For the human subjects, dualistic ma-mi unitized factor types are defined to avoid the violation of first principle and to show that the indicator X 0 * can be related to the physical fitness indices that are already in use for making health care national policies.

The primary effect of rocks and stones tending to erode towards sphericity symmetry can be identified with the rate change of volume with surface. Marble pebbles of various shapes and sizes are recorded and modeled mathematically as ellipsoids. The rate change of volume with surface dV/dA is computed for flat-shaped pebbles where the thickness dimension is assumed to be unity. Invoked is the hypothesis that the change of shape and size of pebbles can be characterized by a master curve derived from dA/dL, the 2D version of dV/dA. The sphericity symmetry is assumed to be concerned with the preference of roundness to slenderness regardless of the surface roughness, smoothness and the mineralogical composition. The erosiveness and abrasiveness of the surface and time effects can interact with sphericity, which is an issue beyond the scope of this work.

Impact response of adhesive joints has received limited attention compared to quasi-static loading. On the other hand, there are very few studies combining moisture and its effect on the impact strength. Therefore, the present paper aims to study the effect of moisture on the tensile and impact strength of single lap joints with different adherends (high limit elastic steel and a commercial composite). It was possible to conclude that adhesive joints with steel adherends are very sensitive to the environment and exposure time. For adhesive joints with composite adherends, the water showed a marginal effect. A marked hygrothermal effect was observed for all joints. For impact loads the environment effect is similar, but much more severe than that observed in tensile tests. For both tests, adhesive failures occurred for adhesive joints with steel adherends and delaminations for joints involving composite.

The microscopic and macroscopic are mutually supportive for they are parts of the same entity. Their physical properties are intrinsic of the space-time being highly non-symmetry and non-homogeneous. The interchange of energy and mass density (EMD) reflects the space-time non-symmetry (STNS) and non-equilibrium and non-homogeneity (NENH) of the expanding universe. As such, the trade-offs of energy and mass density are scale and time dependent. The proportion of the "light matter" to the so-dubbed "dark matter" reflects only the very early stage of the journey from the big bang to the big crunch, both of which are disputable propositions. The light matter refers to the ordinary matter, while the dark matter differs in ways that are unknown.The exploration of this unknown substance, which may not even be matter in the ordinary sense, involves making hypotheses at the galactic scale of space-time. One of them is the idea of a "cosmological constant" that provokes dubbing dualism to pair with monism, the self-fused supreme (SFS). The SFS is assumed to prevail in another dimension of higher order space-time. Only, SFS possesses the secret of perfect symmetry and homogeneity, in opposition of dualism.The search for the dark matter has prompted the Euclid mission of the European Space Agency (ESA) to study the ways with which the energy density could depend on time or being a constant. To this end, the changeability, inhomogeneity, and mobility (CIM) of the galaxies deserve consideration. An explanation for the illusiveness of the dark matter is offered by Tao Te Ching in connection with the changeable and unchangeable. The dark energy and dark matter are subject to change as they have already been named. The so-dubbed "dark spirit" as the "mysterious one" is the only unchangeable. (C) 2015 Elsevier Ltd. All rights reserved.

Space-time non-symmetry means that physical processes in the (+) direction are not the same as those in the (-) direction. Non-homogeneity and surface-volume interaction (SVI) are two aspects of the same effect that attributes to directional dependency. While the Einstein tensor and stress-energy tensor (SET) of space-time curvature are reminiscence of SVI, non-homogeneity were forsaken such that stress-energy became non-tensorial. The inconsistency definition of body-field energy and surface-traction force can be erased by considering SVI. No less emphasizes can be placed on the interchange of energy, mass and matter. Energy and mass trade-off can occur as a quotient via square of the "velocity" and product via square of the "momentum".SVI was also recognized in the '80s as the missing link to explain crack growth in fatigue and non-equilibrium and non-homogeneous (NENH) problems in mechanics. Space-time non-symmetry (STNS) corresponds, respectively, to dissipated (past) and available (future) energy density. Paradigm-breaking called for higher order mathematical solutions to lock non-homogeneity and non-symmetricity into the experimental data that would otherwise be interpreted with oversimplified assumptions. The trade-offs of energy, mass, matter are made possible for a wide range of the speed of space, larger and smaller than the speed of light. The speed of light is no longer the pillar of particle physics. Corrections to ordinary data can thus be made without knowing the composition of the atomic structures, which may not explain nature in its entity.In the language of fracture mechanics, any available fatigue crack growth data can be corrected to include NENH and STNS for different scale ranges. The "energy density" fits into the space-time non-symmetry (STNS) scheme of non-zero volume/area. Physicists and engineers are no longer next door neighbors, but they live under the same roof. In a nut shell, science has identified the cause of space non-symmetry (SNS) and time non-symmetry (TNS), while technology has recognized the effect of NENH. (C) 2015 Elsevier Ltd. All rights reserved.

At the risk of being presumptuous, the influence of non-equilibrium and non-homogeneity (NENH) is the key to explain the conundrums of today's physics and mechanics on the basis of the NENH Mechanics of Multiscaling (NNMM). Corrective measures have been used to correct errors caused by the neglect of NENH and multiscaling. The separate conservation of mass and energy is a case in point. The inclusion of NENH leads to the simultaneous conservation of mass and energy as a product. The revised conservation law depends on the degree of system inhomogeneity. The aforementioned vouches the credibility for applying NNMM to resolve the impasse of the misinterpreted fatigue crack growth (FCG) data using monoscale concepts. The new paradigm is fundamental to contrast the difference between deterministic and non-deterministic. The phenomena of turbulence and instability in general are determinable when the thresholds are related to the appropriate physical mechanism at the temporal–spatial scale. The correct experiments depend on identifying the role with which NNMM plays in the physical phenomenon. The same applies to FCG. To reiterate, the aim is not to develop new theories but rather to offer corrective measures by including NENH and multiscaling to show that the understanding of FCG is no less challenging than some of the conundrums of physics and mechanics of today.

Aircraft metal components and structures are susceptible to environmental degradation throughout their original design life and in many cases their extended lives. This paper summarizes the results of an experimental program to evaluate the ability of Supersonic Particle Deposition (SPD), also known as cold spray, to extend the limit of validity (LOV) of aircraft structural components and to restore the structural integrity of corroded panels. In this study [LU1]the potential for the SPD to seal the mechanically fastened joints and for this seal to remain intact even in the presence of multi-site damage (MSD) has been evaluated. By sealing the joint the onset of corrosion damage in the joint can be significantly retarded, possibly even eliminated, thereby dramatically extending the LOV of mechanically fastened joints. The study also shows that SPD can dramatically increase the damage tolerance of badly corroded wing skins.

The formalism of the earlier fatigue crack growth models is retained to account for multiscaling of the fatigue process that involves the creation of macrocracks from the accumulation of micro damage. The effects of at least two scales, say micro to macro, must be accounted for. The same data can thus be reinterpreted by the invariancy of the transitional stress intensity factors such that the microcracking and macrocracking data would lie on a straight line. The threshold associated with the sigmoid curve disappears. Scale segmentation is shown to be a necessity for addressing multiscale energy dissipative processes such as fatigue and creep. Path independency and energy release rate are monoscale criteria that can lead to unphysical results, violating the first principles. Application of monoscale failure or fracture criteria to nanomaterials is taking toll at the expense of manufacturing super strength and light materials and structural components. This brief view is offered in the spirit of much needed additional research for the reinforcement of materials by creating nanoscale interfaces with sustainable time in service. The step by step consideraton at the different scales may offer a better understanding of the test data and their limitations with reference to space and time.

The relationship of short and long crack data is analyzed for the fatigue of 2024-T3 aluminum. The micromacro scale range is selected as the reference state of data measurement. Three transitional functions (TRs) contained in Delta S-macro(micro) 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 Delta S-macro(micro). Throughout this work, Delta S is understood to represent the incremental volume energy and not the surface energy. Form-invariance of Delta S-macro(micro), using the transitional functions or variables (mu, sigma, 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 Delta S-micro(nano) and Delta S-large(macro) from Delta S-macro(micro). 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 3-55 mm are used to derive short crack data of lengths 0.040-0.043 mm. Data for very long crack lengths 49-260 mm 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 10(0) for da/dN. The macro-large range involved only two orders from 10(-1) to 10(0). 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". (C) 2014 Elsevier Ltd. All rights reserved.

ABSTRACTPedagogically speaking, crack initiation–growth–termination (IGT) belongs to the process of fracture, the modelling of which entails multiscaling in space and time. This applies to loadings that are increased monotonically or repeated cyclically. Short and long crack data are required to describe IGT for scale ranges from nano to macro, segmented by the SI system of measurement. Unless the data at the nano scale can be connected with the macro, IGT remains disintegrated. The diversity of non‐homogeneity of the physical properties at the different scale ranges results in non‐equilibrium. These effects dubbed as non‐equilibrium and non‐homogeneous are hidden in the test specimens and must be realized. They can be locked into the reference state of measurement at the mi‐ma scale range by application of the transitional functions and transferred to the nano‐micro and macro‐large scale ranges.The aim of this work is to convert the ordinary crack length data to those referred to as short cracks that are not directly measurable. All test data are material, loading and geometry (MLG) specific. The results obtained for the 2024‐T3 aluminium sheets hold only for the MLG tested. The differences are more pronounced for the short cracks. These effects can be revealed by comparing the incremental crack driving force (CDF) for the ma‐mi range the ma‐large range and the na‐mi range The CDF is equivalent to the incremental volume energy density factor (VEDF). The incremental mi‐ma CDF is found to be 10–105 kg mm−1 for cracks 3–55 mm long travelling at an average velocity of 10−5 mm s−1. The crack velocity rises to 10−3 mm s−1 when the incremental CDF is increased to 105–106 kg mm−1, while the crack lengths are 49–260 mm. The crack velocity for the na‐mi range of 0.040–0.043 mm slowed down to 10−8 mm s−1, and the incremental CDF reduces further to 10−8–10−2 kg mm−1. Note that changed several orders of magnitude while the crack advanced from 0.040 to 0.044 mm. Such behaviour is indicative of the highly unstable nature of nanocracks.All results are based on using the transitionalized crack length (TCL). The TCL fatigue crack growth increment Δa is postulated to depend on the incremental CDF ΔS or ΔVEDF. The form invariance of , and is invoked by scale segmentation to reveal the multiscale nature of IGT that is inherent to fatigue crack growth. While the choice of directionality from micro to macro is not the same as that from macro to micro, this difference will not be addressed in this work.

When two contacting solid surfaces are tightly closed and invisible to the naked eye, the discontinuity is said to be microscopic regardless of whether its length is short or long. By this definition, it is not sufficient to distinguish the difference between a micro- and macro-crack by using the length parameter. Microcracks in high strength metal alloys have been known to be several centimeters or longer. Considered in this work is a dual scale fatigue crack growth model where the main crack can be micro or macro but there prevails an inherent microscopic tip region that is damaged depending on the irregularities of the microstructure. This region is referred to as the “micro-tip” and can be simulated by a sharp wedge with different angles in addition to mixed boundary conditions. The combination is sufficient to model microscopic entities in the form of voids, inclusions, precipitations, interfaces, in addition to subgrain imperfections, or cluster of dislocations. This is accomplished by using the method of “singularity representation” such that closed form asymptotic solutions can be obtained for the development of fatigue crack growth rate relations with three parameters. They include: (1) the crack surface tightness σ* represented by σ o/σ ∞ = 0.3–0.5 for short cracks in region I, and 0.1–0.2 for long cracks in region II, (2) the micro/macro material properties reflected by the shear modulus ratio µ* (=µmicro/µmacro varying between 2 and 5) and (3) the most sensitive parameter d* being the micro-tip characteristic length d* (=d/d o) whose magnitude decreases in the direction of region I→II. The existing fatigue crack growth data for 2024-T3 and 7075-T6 aluminum sheets are used to reinterpret the two-parameter da/dN=C(ΔK) n relation where ΔK has now been re-derived for a microcrack with surfaces tightly in contact. The contact force will depend on the mean stress σm or mean stress ratio R as the primary parameter and on the stress amplitude σ a as the secondary parameter.

Mono-scale functions refer to the individual scale range of the SI system of measurement. Coarseness of the segmented scale was dictated by state-of-the-art of technology at that time. By to-day's standard, non-equilibrium and non-homogeneity (NENH) are first order considerations whereby scales must be refined to include micro, nano and pico effects. The conventional technology applies to monoscaling, confined to equilibrium and homogeneity (E&M). Their conversion to multiscaling requires the use of transitional functions. The ultra high strength and light weight structural materials rely on the absorption of energy at more than one scale. For considerations are effects at microscopic, nanoscopic and picoscopic scales.The irony is that NENH are subject to eventual homogenization for otherwise the multiscale effects could not be transferred to improve and modify the monoscale rules in practices. To this end, additional Postulate and Corollary are needed to account for scale directionality of energy transfer, prevalent to NENH. Direction-dependency differentiates the transition of macro -> micro and micro -> macro. Transitional functions are not the same when they traverse up and down the scale. Homogenization averages out NENH effects such that corrections may be applied to monoscaling.Transitional functions can lock-in the load, material and geometry effects of the macro-micro test data to produce the nano-pico data. This is related to the obtainment of small crack data from large crack test data. To this end, the volume energy density factor (VEDF) or the volume energy density (VED) can be used as the transitional functions as a form-invariant criterion such that multiscale effects can be used to correct and modify monoscale results. When NENH effects are highly localized and cannot be averaged out, the time rate of VEDF and VED or the equivalent of the power energy density must be used.The scalar correction for NENH is derived for the macro-micro cracking of a line crack subject to the combined effects of loading, material and geometry. Two correction factors Lambda and Omega are used, one for macro -> micro and another for micro -> macro. The outcome can be checked by results for crack length and/or crack growth rate. (C) 2013 Elsevier Ltd. All rights reserved.