ENERGY EMISSIONS FROM FAILURE PHENOMENA: ACOUSTIC, ELECTROMAGNETIC, PIEZONUCLEAR

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1 Symposium on Recent Advances in Mechanics, Dedicated to P.S. Theocaris, Academy of Athens Athens, Greece, 16-19/9/ /9/2009 ENERGY EMISSIONS FROM FAILURE PHENOMENA: ACOUSTIC, ELECTROMAGNETIC, PIEZONUCLEAR Alberto Carpinteri, Giuseppe Lacidogna Department of Structural Engineering and Geotechnics, Politecnico o di Torino, Italy

2 AE signal identified by sensor Signal voltage 10 µs B A Peak amplitude Time AE counting method Signal voltage (a) Threshold level Time Oscillation number counting NT= Oscillations beyond threshold Signal voltage Envelope curve (b) 1 Time Events NT=3 Events counting The event intensity is measured by the oscillation number N T The oscillation number N T increases with the signal amplitude

3 FRACTAL SCALING OF ACOUSTIC EMISSION Recently AE data have been interpreted on the basis of the statistical and fractal theories of fragmentation (I). The following size-scaling scaling law can be considered: W N V D / 3, W: released energy; N: : cumulative number of AE events that the structure provides during damage monitoring; V : specimen volume; D: : fractal exponent, comprised between 2 and 3. (1) (I) Carpinteri, A., Lacidogna, G. and Pugno, N., Structural Damage Diagnosis and Life-Time Assessment by Acoustic Emission Monitoring. Engineering Fracture Mechanics,, 74, (2007).

4 Geometries of the tested specimens 30 mm 60 mm 120 mm

5 Determination of the fractal dimension D 10.5 log Nmax y = x y = x Vol. 2 Vol Vol log V/cm 3 D 2.31

6 AE long-term monitoring on a viaduct built in the 1950s The viaduct and the monitored pilasters P 1 and P 2 P1 P2 AE sensors location points Cracks in pilaster P1 and the applied sensor

7 Pilasters P1 and P2 monitoring data AE counting number Pilaster P AE event rate Time in hours AE counting number Pilaster P AE event rate Time in hours 0

8 N max t N t = N max t max N = current cumulated number of AE events in the structure t = current monitoring time t max = assumed life-time Assessment scheme V N max = N max r Vr max = critical number of AE events in the structure N max r = critical number of AE events in the reference specimen V, V r = volume of structure, reference specimen D = fractal exponent (from lab tests) β D / 3, IN-SITU N, t D N max t max LAB LAB β t Life-time

9 AE FREQUENCY-MAGNITUDE STATISTICS Along the lines of earthquake seismology, the magnitude in terms of AE technique is defined as follows: m = Log10 Amax + f ( r), (2) A max : signal amplitude, measured in microvolt; f(r) : correction taking into account that the amplitude is a decreasing function of the distance r between the source and the sensor.

10 In seismology, earthquakes of larger magnitude occur less frequently than earthquakes of smaller magnitude. This fact can be quantified in terms of a magnitude-frequency relation, proposed by Gutenberg and Richter (1954) in an empirical way: Log 10 N( m) = a bm, or N( m) = 10 a bm, (3) N : cumulative number of earthquakes with magnitude m, in a specified area and over a specified time span; a, b : positive constants varying from region to region.

11 b-value analysis By analogy with earthquakes, the AE damage size-scaling scaling entails the validity of the relationship: (4) N : cumulative number of AE events generated by source defects with h a characteristic linear dimension L; L : linear dimension of the source defects; c : constant of proportionality; D = 2b fractal dimension of the damaged domain.

12 The b-value changes systematically with the different stages of fracture re growth and hence it can be used to estimate the development of fracture process. So that, by determining the b-value it is possible to identify the modalities of energy dissipation in a structural element during the monitoring process. s. The extreme cases are: D = 3.0 b = 1.5, when the energy dissipation takes place through small defects homogeneously distributed throughout the volume; D = 2.0 b = 1.0, when the energy dissipation takes place on a surface. In the former case diffused damage is observed, whereas in the latter l two-dimensional cracks are formed leading to the separation of the structural element ement (II). (II) Carpinteri, A., Lacidogna, G. and Puzzi,, S., From Criticality to Final Collapse: Evolution of the b- Value from 1.5 to 1.0. Chaos, Solitons & Fractals,. 41, (2009).

13 Concrete Specimen in Compression P h/d = 2 AE sensor Steel platen P Load vs. time curve and AE activity b 1.64 b 1.34 b 1.20 b-values during the loading test

14 ACOUSTIC AND ELECTROMAGNETIC EMISSIONS Syracuse Limestone Specimen EME 3 (1.8 µt) 100 EME 2 (1.5 µt) Syracuse Limestone specimen π cm Load (kn) EME 1 (1.4 µt) Piston velocity m s -1 Cumulated AE Load Cumulated AE events Time (s) 0 The dashed line represents the cumulated number of AE The stars on the graph show the moments of EME events with magnetic component comprised between 1.4 and 1.8 µt

15 PIEZONUCLEAR REACTIONS IN COMPRESSED SOLIDS References Cardone, F., Carpinteri, A., Lacidogna, G., Piezonuclear neutrons from fracturing of inert solids, Physics Letters A (in print). Carpinteri, A., Cardone, F., Lacidogna, G., Piezonuclear neutrons from brittle fracture: Early results of mechanical compression tests, Strain, 45, (2009). Fujii,, M. F., et al., Neutron emission from fracture of piezoelectric materials in deuterium atmosphere, Jpn.. J. Appl.. Phys., Pt.1, 41, (2002). Preparata,, G., A A new look at solid-state state fractures, particle emissions and «cold» nuclear fusion, Il Nuovo Cimento,, 104 A, (1991). Derjaguin,, B. V., et al., Titanium fracture yields neutrons?, Nature,, 34, 492 (1989).

16 Neutron emission measurements by means of helium-3 3 neutron detectors were performed on solid test specimens during crushing failure. The materials used were marble and granite,, selected in that they present a different behaviour in compression failure (i.e., a different brittleness index) and a different iron content. All the test specimens were of the same size and shape. Neutron emissions from the granite test specimens were found to be about one order of magnitude larger than the natural background level at the time of failure. These neutron emissions were caused by piezonuclear reactions that occurred in the granite, but did not occur in the marble.

17 Experimental set-up During the experimental analysis four test specimens were used: two made of Carrara marble,, calcite, specimens P1 and P2; two made of Luserna granite,, gneiss, specimens P3 and P4; all of them measuring 6x6x10 cm 3. This choice was prompted by the consideration that, test specimen n dimensions being the same, different brittleness coefficients would cause catastrophic failure in granite, not in marble. P1 P2 P3 P4

18 The same testing machine was used on all the test specimens: a standard servo-hydraulic press Baldwin with a maximum capacity of 500 kn,, equipped with control electronics. The tests were performed in piston travel displacement control by setting, for all the test specimens, a velocity of 10 6 m/s during compression.

19 Neutron emission measurements were made by means of a helium-3 3 detector placed at a distance of 10 cm from the test specimen. The detector was enclosed in a polystyrene case to prevent the results from being altered by acoustical-mechanical stresses.

20 Before the loading tests Neutron emission measurements The neutron background was measured at 600 s time intervals to obtain o sufficient statistical data with the detector in the position shown in the previous figure. The average background count rate was: ± cps. During the loading tests The neutron measurements obtained on the two Carrara marble specimens yielded values comparable with the background, even at the time of test specimen failure. The neutron measurements obtained on the two Luserna granite specimens, instead, exceeded the background value by about one order of magnitude at the test specimen failure.

21 P1 P2 P1 P2 Specimens P1 and P2 in Carrara marble following compression failure. P4 P3 P4 P3 Specimens P3 e P4 in Luserna granite following compression failure.

22 Specimen P1 neutron background cps Load vs. time and cps curve for P1 test specimen in Carrara marble.

23 Specimen P2 neutron background cps neutron background cps Load vs. time and cps curve for P2 test specimen in Carrara marble.

24 Specimen P3 neutron background cps Load vs. time and cps curve for P3 test specimen in Luserna granite.

25 Specimen P4 neutron background cps Load vs. time and cps curve for P4 test specimen in Carrara marble.

26 Factors involved in controlling rock failure Axial Stress, σ ductile brittle Axial Strain, ε catastrophic Ductile, brittle and catastrophic behaviour peak stress A Post-peak regime Axial Stress, σ B C stable Released Energy O unstable D Axial Strain, ε E Energy release and stable vs. unstable stress-strain strain behaviour

27 clεδ= Subsequent stages in the deformation history of a specimen in compression (I) (II) σ c,u (a) (b) (c) δ = ε = σ E c l l; σ l w c c δ = + ; δ w cr. E (I) Carpinteri, A., Cusp catastrophe interpretation of fracture instability, J. of Mechanics and Physics of Solids,, 37, (1989). (II) Carpinteri, A., Corrado,, M., An extended (fractal) overlapping crack model to describe crushing size-scale scale effects in compression, Eng. Failure Analysis,, in print.

28 Stress vs. displacement response of a specimen in compression σ c,u σ c, u σ c, u Normal softening Vertical drop Catastrophic behaviour

29 Elastic strain energy at the peak load, E Test specimen Material E [J] P1 Carrara marble 124 P2 Carrara marble 128 P3 Luserna granite 384 P4 Luserna granite 296 Threshold of energy rate for piezonuclear reactions (III) (IV) : E t ~ W Extension of the energy release zone: t ~ 0.5 ns σ c σ c,u U x = v t ~ 4000m/s 0.5ns ~ 2µm Comparison with the critical value of the interpenetration length: x ~ c w cr? 0 G c F w c cr C ε c,u δ l δ (III) Cardone, F., Mignani, R., Piezonuclear reactions and Lorenz invariance breakdown, Int. J. of Modern Physics E, E Nuclear Physics,, 15 (901), (2006). (IV) Cardone, F., Mignani, R., Deformed Spacetime,, Springer, Dordrecht,, 2007, chaps

30 Evolution of metal abundances in the Earth Crust Based on the appearance after the experiments of aluminium atoms, our conjecture is that the following nucleolysis or piezonuclear fission reaction could have occurred: Fe 2Al neutrons. The present natural abundance of aluminum (7-8% in the Earth crust), which is less favoured than iron from a nuclear point of view, is possibly due to the above piezonuclear fission reaction. This reaction less infrequent than we could think would be activated where the environment conditions (pressure and temperature) are particularly severe, and mechanical phenomena of fracture, crushing, fragmentation, comminution, erosion, friction, etc., may occur.

31 If we consider the evolution of the percentages of the most abundant elements in the Earth crust during the last 3 billion years, we realize that iron and nickel have drastically diminished, whereas aluminum and silicon have as much increased: Ni 2Si + 3 neutrons. It is also interesting to realize that such increases have developed mainly in the tectonic regions, where frictional phenomena between en the continental plates occurred. Many other clues and quantitative data could be presented in favour of the piezonuclear fission reactions, and this will be the t subject of a next publication.

32 30 Si (~28%) Concentration (mass percentage) Si (~24%) Fe (~8%) Al (~4%) Al (~8%) Fe (~4%) Ni (~0.8%) Ni (~0.02%) Billion years ago 0 (1) Favero G. and Jobstraibizer P., The Distribution of Aluminium in the Earth: From Cosmogenesis to Sial Evolution, Coord.Chem. Rev.,, 149, (1996). (2) Kurt O. et al., Oceanic Nickel Depletion and a Methanogen Famine Before the Great Oxidation Event, Nature, 458, (2009). (3) Anbar A. D., Elements and Evolution, Science,, 322, (2008).