The paper presents an outline of a theory of micro-inhomogeneity of stresses and strains resulting from the micro-structural properties of engineering materials. The problem is approached from a statistical point of view and it is experimentally shown that the degree of micro-inhomogeneity can be defined by normal distribution functions.
Using the experimental results a general concept is postulated which takes into account the physical reality as completely as is practicable. It is shown that the suggested approach can be used to take into account the micro-plastic strains which exist while the material is nominally within the elastic limit.
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References
1.
BoasW.HargreavesM. E.‘On the inhomogeneity of plastic deformation in the crystals of an aggregate’, Proc. ray. Soc. (A)1948193, 89.
PaskovP. O.‘Deformation resistance in the plastic flow of crystals’, J. Tech. Physics (U.S.S.R.)194919, 261; 1953, 23, 2013.
4.
VolkovS. D.Statistical strength theory1962 (Gordon and Breach, New York).
5.
AitkenA. C.Statistical mathematics1962 (Oliver and Boyd Ltd, Edinburgh).
6.
CranerH.Mathematical methods of statistics1957 (Princeton University Press).
7.
ChechulinB. E.Fiz. Metallov i Metalloved19551, 246.
8.
HicksonV. M.‘Replica technique for measuring static strains’, J. mech. Engng Sci.19591, 171.
9.
UrieV. M.WainH. L.‘Plastic deformation of coarse grained aluminium’, J. Inst. Mets195281.
10.
BabichV. M.‘Fundamental solutions, of the dynamical equations of elasticity for non-homogeneous media’, Prikl. Mat. Mekh.196125, 38.
11.
MindlinR. D.‘Micro-structure in linear elasticity’, Archs. ration. Mech. Analysis196416, 51.
12.
SobotikaZ.MurzewskiJ.‘Approximate calculations of distribution of a function of random variables and their application to the yield condition’, Bul. Pol. Acad. Sci.19619 (No. 1).
13.
OLSZAK (Editor) ‘Non-homogeneity in elasticity and plasticity’, Proc. Internat. Union Theor. Appl. Mech. Symp. in Warsaw Sept.1958.
14.
WhitemanI. R.‘A mathematical model depicting in the stress-strain diagram and the hysteresis loop’, Trans. Am. Soc. mech. Engrs195926E.
15.
MorrowJ. D.‘Yield by domains’, Discussion sent to (14), Trans. Am. Soc. mech. Engrs195926E.
16.
YokoboriT.Strength, fracture and fatigue of materials1965 (Noordhoff, Groningen).
17.
DornJ. E.MoteJ. D.‘On the plastic behaviour of polycrystalline and aggregates’, Proc. Research Conf. on Structure and Properties of Eng. Materials 19621963 (Plenum Press).
18.
BarrettC. S.Structure of metals1952 (McGraw-Hill Co., New York).
19.
CottrellA. H.Dislocations and plastic flow in crystals1956 (Clarendon Press, Oxford).
20.
KrönerE.‘Zur Plastischen Verformung des Vielkristalls’, Acta Met.19619, 151.
21.
Von MisesR.‘Mechanik der Plastischen Formanderung von Kristallen’, Z. und Math. und Mech.19288, 161.
22.
TaylorG. I.‘Analysis of plastic strain in a cubic crystal’, J. Inst. of Metals1938 62, 307; S. Timoshenko Aniv. Vol.1938, 218 (Macmillan).
23.
BishopJ. F.W.HillP.‘A theory of the plastic dislocation of a polycrystalline aggregate under combined stresses’, Phil. Mag.195142, 414.
24.
BishopJ. F.W.HillP.‘A theoretical derivation of the plastic properties of a polycrystalline face-centred metal, Phil. Mag.195142, 1298.
25.
BishopJ. F.W.‘A theoretical examination of the plastic deformation of crystals by glide’, Phil. Mag.195344, 51.
