Theory of adhesion: role of surface roughness

We discuss how surface roughness influence the adhesion between elastic solids. We introduce a Tabor number which depends on the length scale or magnification, and which gives information about the nature of the adhesion at different length scales. We consider two limiting cases relevant for (a) elastically hard solids with weak adhesive interaction (DMT-limit) and (b) elastically soft solids or strong adhesive interaction (JKR-limit). For the former cases we study the nature of the adhesion using different adhesive force laws ($F\sim u^{-n}$, $n=1.5-4$, where $u$ is the wall-wall separation). In general, adhesion may switch from DMT-like at short length scales to JKR-like at large (macroscopic) length scale. We compare the theory predictions to the results of exact numerical simulations and find good agreement between theory and the simulation results

SUMMARY OF EXPERIMENTAL RESULTS 1979 GENERAL PHOSPHOROUS TRIALS

Contiuing trials Stock rate and level of Superhosphate on cyprus medic pasture 66M30 Rates of phosphorus, sulphur and stocking trial - cropping phase 68BR7 Maintenance P x S trials 65N5, 69WH15, 65A1, 65c6 Residual Value of Phosphorus 78M08, 78C4, 78MA2, 75LG26, 78M38 NEW TRIALS Crops N x P Trials 79NA11, 79NA12, 79NA13 Times of P on Lupins 79M030 Lupin and Oat Mixtures 79BA31, 79MT30 Methods Application and Cultivation of P on Wheat 79M1, 79WH1 Methods and Times of P on Wheat Old Land 79N1 Rates of Super on Wheat 79LG Rates of Super on Lupins 79GE PASTURES Rates of P, K and S on Pasture - Dandaragan 79M012, 79M013, 79M015, 79M017 Rates of P, K and S on Pasture – Lancelin 79M011, 79M018 Rates of P on Pasture – Newdegate 79N5, 79N6 Rates of P x Species on Pasture 79N05, 79JE

Gas gun shock experiments with single-pulse x-ray phase contrast imaging and diffraction at the Advanced Photon Source

The highly transient nature of shock loading and pronounced microstructure effects on dynamic materials response call for {\it in situ}, temporally and spatially resolved, x-ray-based diagnostics. Third-generation synchrotron x-ray sources are advantageous for x-ray phase contrast imaging (PCI) and diffraction under dynamic loading, due to their high photon energy, high photon fluxes, high coherency, and high pulse repetition rates. The feasibility of bulk-scale gas gun shock experiments with dynamic x-ray PCI and diffraction measurements was investigated at the beamline 32ID-B of the Advanced Photon Source. The x-ray beam characteristics, experimental setup, x-ray diagnostics, and static and dynamic test results are described. We demonstrate ultrafast, multiframe, single-pulse PCI measurements with unprecedented temporal ($<$100 ps) and spatial ($\sim$2 $\mu$m) resolutions for bulk-scale shock experiments, as well as single-pulse dynamic Laue diffraction. The results not only substantiate the potential of synchrotron-based experiments for addressing a variety of shock physics problems, but also allow us to identify the technical challenges related to image detection, x-ray source, and dynamic loading

General phosphorus and sulphur trials

(A) Long Term Trials/Trial number: Super x Stocking Rate - 66M30. Super Sulphur and Stocking Rate - 68BR7. Maintenance P and S trials - 69E6, 68B1, 65A1, 65N5, 65C5, 69WH15 & 67N05. Continuous Cropping - 75LG26. Cropping Residual Value - 29M/148, 149. (B) Lupin Trials: Rate of P and S - 78A8, 78A9, 78BA9, 78BA10, 78C5, 78C6, 78E8, 78E9, 78WH7, 78WH8 & 78NA25. Current and Residual phosphorus - 75KA4. (C) Cereal Trials: Depth of Placement of P on Wheat - 78M38. Row spacing x P rates on Wheat - 78ME4. Current and Residual Nitrogen on Wheat - 77M033. (D) Pasture Trials: Times of application - 77BA38. Residual value - 77BA21, 78BA7, 77BA22, 77BA24, 78M010. Rates of Phosphorus - 78M011. P and S on irrigated pastures - 77HA10

Phosphorus and sulphur group

Long Term Trials Stocking and superphosphate trials - 66M30, 68BR7. Maintenance Phosphorus x Sulphur trials - 65A1, 65N5, 65C5, 69WH15, 68B1, 69AL3 and 67N05. Low Rainfall Crops and Pastures. Residual phosphorus trials - 76ES8, 75KA4, 75LG26 and 76NA5. Miscellaneous Cropping Trials. Rate of phosphorus on wheat - 77ES2, 77ME5, 77N03. N. P and seed rates on wheat - 77JE1. Row spacing, phosphorus and seed rate on wheat - 77ME6. Phosphorus on nitrogen build up - 77M033. Rate of super on old land lupins - 77A18 & 19, 77BA13 & 14, 77E20. Pasture Trials. Phosphorus and Sulphur on old land pasture - 77BA 17, 18, 19, 20, 21 , 22, 23 and 24. High Rainfall Pasture Trials. Current and residual phosphorus - 75AL5, 75DE5, 75DE7, 75BR13, 76BU13(a), 76KE10 and 76MA2. Phosphorus and Sulphur 1977 Phosphorus Soil Test Series - 77AL5, 77AL6, 77HA10, 77DE6 & 7, 77BR14, 15, 16, 17, 18 & 19, 77BU6 & 7, 77BY3

Towards a modeling of the time dependence of contact area between solid bodies

I present a simple model of the time dependence of the contact area between solid bodies, assuming either a totally uncorrelated surface topography, or a self affine surface roughness. The existence of relaxation effects (that I incorporate using a recently proposed model) produces the time increase of the contact area $A(t)$ towards an asymptotic value that can be much smaller than the nominal contact area. For an uncorrelated surface topography, the time evolution of $A(t)$ is numerically found to be well fitted by expressions of the form [$A(\infty)-A(t)]\sim (t+t_0)^{-q}$, where the exponent $q$ depends on the normal load $F_N$ as $q\sim F_N^{\beta}$, with $\beta$ close to 0.5. In particular, when the contact area is much lower than the nominal area I obtain $A(t)/A(0) \sim 1+C\ln(t/t_0+1)$, i.e., a logarithmic time increase of the contact area, in accordance with experimental observations. The logarithmic increase for low loads is also obtained analytically in this case. For the more realistic case of self affine surfaces, the results are qualitatively similar.Comment: 18 pages, 9 figure

Frictional sliding without geometrical reflection symmetry

The dynamics of frictional interfaces play an important role in many physical systems spanning a broad range of scales. It is well-known that frictional interfaces separating two dissimilar materials couple interfacial slip and normal stress variations, a coupling that has major implications on their stability, failure mechanism and rupture directionality. In contrast, interfaces separating identical materials are traditionally assumed not to feature such a coupling due to symmetry considerations. We show, combining theory and experiments, that interfaces which separate bodies made of macroscopically identical materials, but lack geometrical reflection symmetry, generically feature such a coupling. We discuss two applications of this novel feature. First, we show that it accounts for a distinct, and previously unexplained, experimentally observed weakening effect in frictional cracks. Second, we demonstrate that it can destabilize frictional sliding which is otherwise stable. The emerging framework is expected to find applications in a broad range of systems.Comment: 14 pages, 5 figures + Supplementary Material. Minor change in the title, extended analysis in the second par

Finite-element analysis of contact between elastic self-affine surfaces

Finite element methods are used to study non-adhesive, frictionless contact between elastic solids with self-affine surfaces. We find that the total contact area rises linearly with load at small loads. The mean pressure in the contact regions is independent of load and proportional to the rms slope of the surface. The constant of proportionality is nearly independent of Poisson ratio and roughness exponent and lies between previous analytic predictions. The contact morphology is also analyzed. Connected contact regions have a fractal area and perimeter. The probability of finding a cluster of area $a_c$ drops as $a_c^{-\tau}$ where $\tau$ increases with decreasing roughness exponent. The distribution of pressures shows an exponential tail that is also found in many jammed systems. These results are contrasted to simpler models and experiment.Comment: 13 pages, 15 figures. Replaced after changed in response to referee comments. Final two figures change

1976 Phosphorus and sulphur group

Stocking x Super. rate trials - 66M30, 62MB9, 68BR7. Crossed plot trials - residual value. P x K on Pasture - 74TS4, 74M06, 75GE6. N x P on· Wheat - 75M09. P x Species - 75LG4, 75JE5. Maintenance P x S trials - Wheat Belt Research Station - 65A1; C5, N5, 69WH15. High Rainfall Areas - 68B1, 69E6, 69AL2. Farmers residual value - 66N07, 66ME3,67N011, 66NA3, 66LG1, 68LG1, 66M06, 67M01, 67GE2, 67N05, 67N04, 66N09. Miscellaneous Cropping Trials - Super x Spacing - 76ME26, 76ES8, 9 and 10. Super Study rate and spacing - 76NA7, 76N05, 76JE8. Continuous cropping - 75LG26, 75ES7. Rates, Methods and times of Super - 76KA3, 76JE3. Super on old land lupins - 76BA3 & 4, 76A4 76E3 & 4, 76WH7 & 8. High Rainfall Pasture Trials - 1976 Soil Testing Series - 76BY3,·4, 5, &·6, Skirrow 76BR10, 11, 12, 16 & 17. 76HA2; 3, 4, 5, 6 & 7 76KE5, 6, 7, 8, 9 & 10. 76MA5 & 6. P x S series - 76KE3 & 4, 76MA2 & 4. Cross Plot x Soil test series - 75AL5, 75DE2, 3, 4, 5 & 7. 75Bu8 & 10, 75BY6 & 8 75BR11, 12 & 13, 75AR4, 75HA7